This document presents two new Boolean combination methods called "orthogonalizing difference-building" and "orthogonal OR-ing". These methods calculate the difference and complement of functions, as well as the EXOR and EXNOR of minterms or functions, resulting in orthogonal forms. Orthogonal forms have advantages for further calculations. The methods are based on set theory and treat minterms and functions as ternary-vector lists. Equations are provided to define the difference and disjunction of minterms or functions in terms of their ternary-vector list representations.
Financial Time Series Analysis Based On Normalized Mutual Information FunctionsIJCI JOURNAL
A method of predictability analysis of future values of financial time series is described. The method is based on normalized mutual information functions. In the analysis, the use of these functions allowed to refuse any restrictions on the distributions of the parameters and on the correlations between parameters. A comparative analysis of the predictability of financial time series of Tel Aviv 25 stock exchange has been carried out.
INDUCTIVE LEARNING OF COMPLEX FUZZY RELATIONijcseit
The objective of this paper to investigate the notion of complex fuzzy set in general view. In constraint to a
traditional fuzzy set, the membership function of the complex fuzzy set, the range from [0.1] extended to a
unit circle in the complex plane. In this article the comprehensive mathematical operations on the complex
fuzzy set are presented. The basic operation of complex fuzzy set such as union, intersection, complement
of complex fuzzy set and complex fuzzy relation are studied. Also vector aggregation and fuzzy relation
over the complex fuzzy set are discussed. Two novel operations of complement and projection for complex
fuzzy relation are introduced.
The numerical solution of Huxley equation by the use of two finite difference methods is done. The first one is the explicit scheme and the second one is the Crank-Nicholson scheme. The comparison between the two methods showed that the explicit scheme is easier and has faster convergence while the Crank-Nicholson scheme is more accurate. In addition, the stability analysis using Fourier (von Neumann) method of two schemes is investigated. The resulting analysis showed that the first scheme
is conditionally stable if, r ≤ 2 − aβ∆t , ∆t ≤ 2(∆x)2 and the second
scheme is unconditionally stable.
A hybrid bacterial foraging and modified particle swarm optimization for mode...IJECEIAES
This paper study the model reduction procedures used for the reduction of large-scale dynamic models into a smaller one through some sort of differential and algebraic equations. A confirmed relevance between these two models exists, and it shows same characteristics under study. These reduction procedures are generally utilized for mitigating computational complexity, facilitating system analysis, and thence reducing time and costs. This paper comes out with a study showing the impact of the consolidation between the Bacterial-Foraging (BF) and Modified particle swarm optimization (MPSO) for the reduced order model (ROM). The proposed hybrid algorithm (BF-MPSO) is comprehensively compared with the BF and MPSO algorithms; a comparison is also made with selected existing techniques.
In this paper we introduce an approach to increase vertical integration of elements of transistor-transistor logic with function AND-NOT. Framework the approach we consider a heterostructure with special configuration. Several specific areas of the heterostructure should be doped by diffusion or ion implantation. Annealing of dopant and/or radiation defects should be optimized.
Financial Time Series Analysis Based On Normalized Mutual Information FunctionsIJCI JOURNAL
A method of predictability analysis of future values of financial time series is described. The method is based on normalized mutual information functions. In the analysis, the use of these functions allowed to refuse any restrictions on the distributions of the parameters and on the correlations between parameters. A comparative analysis of the predictability of financial time series of Tel Aviv 25 stock exchange has been carried out.
INDUCTIVE LEARNING OF COMPLEX FUZZY RELATIONijcseit
The objective of this paper to investigate the notion of complex fuzzy set in general view. In constraint to a
traditional fuzzy set, the membership function of the complex fuzzy set, the range from [0.1] extended to a
unit circle in the complex plane. In this article the comprehensive mathematical operations on the complex
fuzzy set are presented. The basic operation of complex fuzzy set such as union, intersection, complement
of complex fuzzy set and complex fuzzy relation are studied. Also vector aggregation and fuzzy relation
over the complex fuzzy set are discussed. Two novel operations of complement and projection for complex
fuzzy relation are introduced.
The numerical solution of Huxley equation by the use of two finite difference methods is done. The first one is the explicit scheme and the second one is the Crank-Nicholson scheme. The comparison between the two methods showed that the explicit scheme is easier and has faster convergence while the Crank-Nicholson scheme is more accurate. In addition, the stability analysis using Fourier (von Neumann) method of two schemes is investigated. The resulting analysis showed that the first scheme
is conditionally stable if, r ≤ 2 − aβ∆t , ∆t ≤ 2(∆x)2 and the second
scheme is unconditionally stable.
A hybrid bacterial foraging and modified particle swarm optimization for mode...IJECEIAES
This paper study the model reduction procedures used for the reduction of large-scale dynamic models into a smaller one through some sort of differential and algebraic equations. A confirmed relevance between these two models exists, and it shows same characteristics under study. These reduction procedures are generally utilized for mitigating computational complexity, facilitating system analysis, and thence reducing time and costs. This paper comes out with a study showing the impact of the consolidation between the Bacterial-Foraging (BF) and Modified particle swarm optimization (MPSO) for the reduced order model (ROM). The proposed hybrid algorithm (BF-MPSO) is comprehensively compared with the BF and MPSO algorithms; a comparison is also made with selected existing techniques.
In this paper we introduce an approach to increase vertical integration of elements of transistor-transistor logic with function AND-NOT. Framework the approach we consider a heterostructure with special configuration. Several specific areas of the heterostructure should be doped by diffusion or ion implantation. Annealing of dopant and/or radiation defects should be optimized.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
THE LEFT AND RIGHT BLOCK POLE PLACEMENT COMPARISON STUDY: APPLICATION TO FLIG...ieijjournal
It is known that if a linear-time-invariant MIMO system described by a state space equation has a number of states divisible by the number of inputs and it can be transformed to block controller form, we can design a state feedback controller using block pole placement technique by assigning a set of desired Block poles. These may be left or right block poles. The idea is to compare both in terms of system’s response.
Model reduction of unstable systems based on balanced truncation algorithm IJECEIAES
Model reduction of a system is an approximation of a higher-order system to a lower-order system while the dynamic behavior of the system is almost unchanged. In this paper, we will discuss model order reduction (MOR) strategies for unstable systems, in which the method based on the balanced truncation algorithm will be focused on. Since each MOR algorithm has its strengths and weakness, practical applications should be suitable for each specific requirement. Simulation results will demonstrate the correctness of the algorithms.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
BINARY TREE SORT IS MORE ROBUST THAN QUICK SORT IN AVERAGE CASEIJCSEA Journal
Average case complexity, in order to be a useful and reliable measure, has to be robust. The probability distribution, generally uniform, over which expectation is taken should be realistic over the problem domain. But algorithm books do not certify that the uniform inputs are always realistic. Do the results hold even for non uniform inputs? In this context we observe that Binary Tree sort is more robust than the fastand popular Quick sort in the average case.
LOGNORMAL ORDINARY KRIGING METAMODEL IN SIMULATION OPTIMIZATIONorajjournal
This paper presents a lognormal ordinary kriging (LOK) metamodel algorithm and its application to
optimize a stochastic simulation problem. Kriging models have been developed as an interpolation method
in geology. They have been successfully used for the deterministic simulation optimization (SO) problem. In
recent years, kriging metamodeling has attracted a growing interest with stochastic problems. SO
researchers have begun using ordinary kriging through global optimization in stochastic systems. The
goals of this study are to present LOK metamodel algorithm and to analyze the result of the application
step-by-step. The results show that LOK is a powerful alternative metamodel in simulation optimization
when the data are too skewed.
INVERSIONOF MAGNETIC ANOMALIES DUE TO 2-D CYLINDRICAL STRUCTURES –BY AN ARTIF...ijsc
Application of Artificial Neural Network Committee Machine (ANNCM) for the inversion of magnetic
anomalies caused by a long-2D horizontal circular cylinder is presented. Although, the subsurface targets
are of arbitrary shape, they are assumed to be regular geometrical shape for convenience of mathematical
analysis. ANNCM inversion extract the parameters of the causative subsurface targets include depth to the
centre of the cylinder (Z), the inclination of magnetic vector(Ɵ)and the constant term (A)comprising the
radius(R)and the intensity of the magnetic field(I). The method of inversion is demonstrated over a
theoretical model with and without random noise in order to study the effect of noise on the technique and
then extended to real field data. It is noted that the method under discussion ensures fairly accurate results
even in the presence of noise. ANNCM analysis of vertical magnetic anomaly near Karimnagar, Telangana,
India, has shown satisfactory results in comparison with other inversion techniques that are in vogue.The
statistics of the predicted parameters relative to the measured data, show lower sum error (<9.58%) and
higher correlation coefficient (R>91%) indicating that good matching and correlation is achieved between
the measured and predicted parameters.
Two-Layer Crystal Square for Transistors on a Single Chipcsandit
The number of transistors on a chip plays the main
role in increasing the speed and performance of a
microprocessor; more transistors, more speed. Incre
asing the number of transistors will be limited due
to
the design complexity and density of transistors. T
his article aims to introduce a new approach to
increasing the number of transistors on a chip. The
basic idea is to construct two-layer crystal squar
e for
transistors; this allows to increase the number of
transistors two additional times (four times as man
y) if
the number of transistors incorporated in a one lay
er of crystal square will approximately double ever
y 24
months according to Moore’s Law without changing ra
pidly the design complexity and density in a crysta
l
square and without changing the size of a chip (len
gth and width), in this case the height of a chip m
ust be
changed for the two layers.
An Android Application for Volunteer Blood Donorscsandit
There is an expectation that the blood will always
be there when it is really needed. Blood
donor volunteers constitute the main supply source
in an effective blood supply chain
management. They feed blood stocks through their do
nation. In an emergency situation, if the
stocks are insufficient, the only source of blood s
upply will be the people who come to the health
center and donate the blood on a voluntary basis. I
t is certain that time is a very important
component in such situation. For this reason, the h
ealth care center should call the nearest
available donor in order to ensure to get the servi
ce as quickly as possible. A smart phone
application is developed to facilitate the identifi
cation of the nearest available blood donor
volunteer and the communication with him/her in the
emergency situations where the blood
can’t be supplied through the blood banks’ stocks.
In this paper this application will be
presented.
Bandwidth-Performance Tradeoffs for a Transmission with Concurrent Signalscsandit
We consider a bandwidth-efficient transmission sche
me, where two signals are sent
concurrently. The BER and the achievable minimum di
stances for the signals’ constellations at
the receivers are derived as functions of the signa
ls’ energies and their input probability
distributions. Finally, trade-offs between bandwidt
h, signals’ energies and achievable
performances are discussed.
Use of eigenvalues and eigenvectors to analyze bipartivity of network graphscsandit
This paper presents the applications of Eigenvalues and Eigenvectors (as part of spectral
decomposition) to analyze the bipartivity index of graphs as well as to predict the set of vertices
that will constitute the two partitions of graphs that are truly bipartite and those that are close
to being bipartite. Though the largest eigenvalue and the corresponding eigenvector (called the
principal eigenvalue and principal eigenvector) are typically used in the spectral analysis of
network graphs, we show that the smallest eigenvalue and the smallest eigenvector (called the
bipartite eigenvalue and the bipartite eigenvector) could be used to predict the bipartite
partitions of network graphs. For each of the predictions, we hypothesize an expected partition
for the input graph and compare that with the predicted partitions. We also analyze the impact
of the number of frustrated edges (edges connecting the vertices within a partition) and their
location across the two partitions on the bipartivity index. We observe that for a given number
of frustrated edges, if the frustrated edges are located in the larger of the two partitions of the
bipartite graph (rather than the smaller of the two partitions or equally distributed across the
two partitions), the bipartivity index is likely to be relatively larger.
The recent advances in computer technology and data networking have made videoconferencing
system a popular medium for users to interact with one another from remote locations. This
system offers communication between more than two users, who are able to interact through
their webcams, microphone and other components. The use of this system has been increased
recently due to many reasons, for one thing, progress in Internet access in different networks
like companies, universities and houses, with the increase of available bandwidth whereas the
decrease of delay in sending and receiving packets . On the other hand, the coming of Rich
Internet Applications (RIA) means that a large part of web application started to be
implemented on the web browsers. This paper discusses the conception of multiparty
videoconferencing systems using technologies of Web 2.0. For our conceptual
Videoconferencing Platform, we have developed many feature : live audio video, text
chat, video recording, user and room management and quality control. Videoconferencing
modules have been carried out using open source technologies Flex and J2EE.
The screening of chemical libraries is an important step in the drug discovery process. The
existing chemical libraries contain up to millions of compounds. As the screening at such scale
is expensive, the virtual screening is often utilized. There exist several variants of virtual
screening and ligand-based virtual screening is one of them. It utilizes the similarity of screened
chemical compounds to known compounds. Besides the employed similarity measure, another
aspect greatly influencing the performance of ligand-based virtual screening is the chosen
chemical compound representation. In this paper, we introduce a fragment-based
representation of chemical compounds. Our representation utilizes fragments to represent a
compound where each fragment is represented by its physico-chemical descriptors. The
representation is highly parametrizable, especially in the area of physico-chemical descriptors
selection and application. In order to test the performance of our method, we utilized an existing
framework for virtual screening benchmarking. The results show that our method is comparable
to the best existing approaches and on some data sets it outperforms them.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
THE LEFT AND RIGHT BLOCK POLE PLACEMENT COMPARISON STUDY: APPLICATION TO FLIG...ieijjournal
It is known that if a linear-time-invariant MIMO system described by a state space equation has a number of states divisible by the number of inputs and it can be transformed to block controller form, we can design a state feedback controller using block pole placement technique by assigning a set of desired Block poles. These may be left or right block poles. The idea is to compare both in terms of system’s response.
Model reduction of unstable systems based on balanced truncation algorithm IJECEIAES
Model reduction of a system is an approximation of a higher-order system to a lower-order system while the dynamic behavior of the system is almost unchanged. In this paper, we will discuss model order reduction (MOR) strategies for unstable systems, in which the method based on the balanced truncation algorithm will be focused on. Since each MOR algorithm has its strengths and weakness, practical applications should be suitable for each specific requirement. Simulation results will demonstrate the correctness of the algorithms.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
BINARY TREE SORT IS MORE ROBUST THAN QUICK SORT IN AVERAGE CASEIJCSEA Journal
Average case complexity, in order to be a useful and reliable measure, has to be robust. The probability distribution, generally uniform, over which expectation is taken should be realistic over the problem domain. But algorithm books do not certify that the uniform inputs are always realistic. Do the results hold even for non uniform inputs? In this context we observe that Binary Tree sort is more robust than the fastand popular Quick sort in the average case.
LOGNORMAL ORDINARY KRIGING METAMODEL IN SIMULATION OPTIMIZATIONorajjournal
This paper presents a lognormal ordinary kriging (LOK) metamodel algorithm and its application to
optimize a stochastic simulation problem. Kriging models have been developed as an interpolation method
in geology. They have been successfully used for the deterministic simulation optimization (SO) problem. In
recent years, kriging metamodeling has attracted a growing interest with stochastic problems. SO
researchers have begun using ordinary kriging through global optimization in stochastic systems. The
goals of this study are to present LOK metamodel algorithm and to analyze the result of the application
step-by-step. The results show that LOK is a powerful alternative metamodel in simulation optimization
when the data are too skewed.
INVERSIONOF MAGNETIC ANOMALIES DUE TO 2-D CYLINDRICAL STRUCTURES –BY AN ARTIF...ijsc
Application of Artificial Neural Network Committee Machine (ANNCM) for the inversion of magnetic
anomalies caused by a long-2D horizontal circular cylinder is presented. Although, the subsurface targets
are of arbitrary shape, they are assumed to be regular geometrical shape for convenience of mathematical
analysis. ANNCM inversion extract the parameters of the causative subsurface targets include depth to the
centre of the cylinder (Z), the inclination of magnetic vector(Ɵ)and the constant term (A)comprising the
radius(R)and the intensity of the magnetic field(I). The method of inversion is demonstrated over a
theoretical model with and without random noise in order to study the effect of noise on the technique and
then extended to real field data. It is noted that the method under discussion ensures fairly accurate results
even in the presence of noise. ANNCM analysis of vertical magnetic anomaly near Karimnagar, Telangana,
India, has shown satisfactory results in comparison with other inversion techniques that are in vogue.The
statistics of the predicted parameters relative to the measured data, show lower sum error (<9.58%) and
higher correlation coefficient (R>91%) indicating that good matching and correlation is achieved between
the measured and predicted parameters.
Two-Layer Crystal Square for Transistors on a Single Chipcsandit
The number of transistors on a chip plays the main
role in increasing the speed and performance of a
microprocessor; more transistors, more speed. Incre
asing the number of transistors will be limited due
to
the design complexity and density of transistors. T
his article aims to introduce a new approach to
increasing the number of transistors on a chip. The
basic idea is to construct two-layer crystal squar
e for
transistors; this allows to increase the number of
transistors two additional times (four times as man
y) if
the number of transistors incorporated in a one lay
er of crystal square will approximately double ever
y 24
months according to Moore’s Law without changing ra
pidly the design complexity and density in a crysta
l
square and without changing the size of a chip (len
gth and width), in this case the height of a chip m
ust be
changed for the two layers.
An Android Application for Volunteer Blood Donorscsandit
There is an expectation that the blood will always
be there when it is really needed. Blood
donor volunteers constitute the main supply source
in an effective blood supply chain
management. They feed blood stocks through their do
nation. In an emergency situation, if the
stocks are insufficient, the only source of blood s
upply will be the people who come to the health
center and donate the blood on a voluntary basis. I
t is certain that time is a very important
component in such situation. For this reason, the h
ealth care center should call the nearest
available donor in order to ensure to get the servi
ce as quickly as possible. A smart phone
application is developed to facilitate the identifi
cation of the nearest available blood donor
volunteer and the communication with him/her in the
emergency situations where the blood
can’t be supplied through the blood banks’ stocks.
In this paper this application will be
presented.
Bandwidth-Performance Tradeoffs for a Transmission with Concurrent Signalscsandit
We consider a bandwidth-efficient transmission sche
me, where two signals are sent
concurrently. The BER and the achievable minimum di
stances for the signals’ constellations at
the receivers are derived as functions of the signa
ls’ energies and their input probability
distributions. Finally, trade-offs between bandwidt
h, signals’ energies and achievable
performances are discussed.
Use of eigenvalues and eigenvectors to analyze bipartivity of network graphscsandit
This paper presents the applications of Eigenvalues and Eigenvectors (as part of spectral
decomposition) to analyze the bipartivity index of graphs as well as to predict the set of vertices
that will constitute the two partitions of graphs that are truly bipartite and those that are close
to being bipartite. Though the largest eigenvalue and the corresponding eigenvector (called the
principal eigenvalue and principal eigenvector) are typically used in the spectral analysis of
network graphs, we show that the smallest eigenvalue and the smallest eigenvector (called the
bipartite eigenvalue and the bipartite eigenvector) could be used to predict the bipartite
partitions of network graphs. For each of the predictions, we hypothesize an expected partition
for the input graph and compare that with the predicted partitions. We also analyze the impact
of the number of frustrated edges (edges connecting the vertices within a partition) and their
location across the two partitions on the bipartivity index. We observe that for a given number
of frustrated edges, if the frustrated edges are located in the larger of the two partitions of the
bipartite graph (rather than the smaller of the two partitions or equally distributed across the
two partitions), the bipartivity index is likely to be relatively larger.
The recent advances in computer technology and data networking have made videoconferencing
system a popular medium for users to interact with one another from remote locations. This
system offers communication between more than two users, who are able to interact through
their webcams, microphone and other components. The use of this system has been increased
recently due to many reasons, for one thing, progress in Internet access in different networks
like companies, universities and houses, with the increase of available bandwidth whereas the
decrease of delay in sending and receiving packets . On the other hand, the coming of Rich
Internet Applications (RIA) means that a large part of web application started to be
implemented on the web browsers. This paper discusses the conception of multiparty
videoconferencing systems using technologies of Web 2.0. For our conceptual
Videoconferencing Platform, we have developed many feature : live audio video, text
chat, video recording, user and room management and quality control. Videoconferencing
modules have been carried out using open source technologies Flex and J2EE.
The screening of chemical libraries is an important step in the drug discovery process. The
existing chemical libraries contain up to millions of compounds. As the screening at such scale
is expensive, the virtual screening is often utilized. There exist several variants of virtual
screening and ligand-based virtual screening is one of them. It utilizes the similarity of screened
chemical compounds to known compounds. Besides the employed similarity measure, another
aspect greatly influencing the performance of ligand-based virtual screening is the chosen
chemical compound representation. In this paper, we introduce a fragment-based
representation of chemical compounds. Our representation utilizes fragments to represent a
compound where each fragment is represented by its physico-chemical descriptors. The
representation is highly parametrizable, especially in the area of physico-chemical descriptors
selection and application. In order to test the performance of our method, we utilized an existing
framework for virtual screening benchmarking. The results show that our method is comparable
to the best existing approaches and on some data sets it outperforms them.
Data characterization towards modeling frequent pattern mining algorithmscsandit
Big data quickly comes under the spotlight in recent years. As big data is supposed to handle
extremely huge amount of data, it is quite natural that the demand for the computational
environment to accelerates, and scales out big data applications increases. The important thing
is, however, the behavior of big data applications is not clearly defined yet. Among big data
applications, this paper specifically focuses on stream mining applications. The behavior of
stream mining applications varies according to the characteristics of the input data. The
parameters for data characterization are, however, not clearly defined yet, and there is no study
investigating explicit relationships between the input data, and stream mining applications,
either. Therefore, this paper picks up frequent pattern mining as one of the representative
stream mining applications, and interprets the relationships between the characteristics of the
input data, and behaviors of signature algorithms for frequent pattern mining.
An important role performed by Zero Padding (ZP) in multi-band OFDM (MB-OFDM) System.
This role show for low-complexity in résistance against multipath interference by reducing
inter-carrier interference (ICI) and eliminating the inter-symbol interference (ISI) Also, zeropadded
suffix can be used to eliminate ripples in the power spectral density in order to conform
to FCC requirements.
At the receiver of MB-OFDM system needs to use of a technique called as overlap-and-add
(OLA). Which maintain the circular convolution property and take the multipath energy of the
channel.
In this paper, we proposed a method of performing overlap-and-add length for zero padded
suffixes. Then, we studied the effect of this method, dynamic optimization of overlap-and-add
(OLA) equalization, on the performance of MBOFDM system on Bit Error Rate (BER) with
AWGN channel and Saleh-Valenzuela (S-V) Multipath channel Model.
In the dynamic optimization OLA, the Length of ZP depends on length of channel impulse
response (CIR). These measures, based on SNR, insert the ZP according to the measurement.
Dynamic optimization of length of ZP improves the Performance of MBOFDM system. In fact
we developed a technique to select the length of ZP as function of SNR and CIR
estimate(repetition). In our simulation this technique improve to 3 dB at BER=10-2 with a
multipath channels CM4.
How to detect middleboxes guidelines on a methodologycsandit
Internet middleboxes such as VPNs, firewalls, and proxies can significantly change handling of
traffic streams. They play an increasingly important role in various types of IP networks. If end
hosts can detect them, these hosts can make beneficial, and in some cases, crucial improvements
in security and performance But because middleboxes have widely varying behavior and effects
on the traffic they handle, no single technique has been discovered that can detect all of them.
Devising a detection mechanism to detect any particular type of middlebox interference involves
many design decisions and has numerous dimensions. One approach to assist with the
complexity of this process is to provide a set of systematic guidelines. This paper is the first
attempt to introduce a set of general guidelines (as well as the rationale behind them) to assist
researchers with devising methodologies for end-hosts to detect middleboxes by the end-hosts.
The guidelines presented here take some inspiration from the previous work of other
researchers using various and often ad hoc approaches. These guidelines, however, are mainly
based on our own experience with research on the detection of middleboxes. To assist
researchers in using these guidelines, we also provide an example of how to bring them into
play for detection of network compression
The proposal of giving two receipts for voters to increase the security of el...csandit
Holding an election with aim of selecting only one person or approval / rejection of a state law,
is a special kind of election which every few years in the different countries going to happen.
Given the pervasiveness of this election, we must take special measures to provide high security
for the referendum. Using two receipts for each voter which one is named barcode receipt, a
secret indicator of vote and another is named key receipt that is a key to acknowledged the
voters information box, including: voter’s National Code, the candidate code which is voted by
this voter, code of election station and barcode information. In this paper is proposed to enable
people and social networks using data on bar code’s receipts without Intrusion into the privacy
of other voters, so they will put together their personal information from monitoring the election
process on a social network which can help to prevent any violation in election. The security of
the proposed scheme is based on the turnout in recount of votes
Framework for developed simple architecture enterprise fdsaecsandit
In This article presents a framework for develop de Architecture enterprise based on the
articulation of emerging paradigms for architecture development of information enterprise [1].
The first one comes from the agile methods and it is inspired on the Scrum model which aim to
simplify the complex task of developing a quality software, the second the processes models
whose are oriented the development of Architectures Enterprise as Zachman and TOGAF in a
paradigm of the Model Driven and principles de reference de architecture de Software form the
paradigms Generation (MDG), these approaches are integrated eventually leading to the
formulation and presentation of an framework for developed simple architecture enterprise –
FDSAE- The goal is to present a simple, portable, understandable terms enabling, modeling
and design business information architecture in any organizational environment, in addition to
this, there are important aspects related to the unified Modeling Language UML 2.5 and the
Business Process Modeling BPMn that become tools to obtain the products in the FDSAE
Framework, This framework is an improved version of Framework MADAIKE [2] developed by
the same authors.
Min-based qualitative possibilistic networks are one of the effective tools for a compact representation of decision problems under uncertainty. The exact approaches for computing decision based on possibilistic networks are limited by the size of the possibility distributions.
Generally, these approaches are based on possibilistic propagation algorithms. An important step in the computation of the decision is the transformation of the DAG into a secondary structure, known as the junction trees. This transformation is known to be costly and represents a difficult problem. We propose in this paper a new approximate approach for the computation
of decision under uncertainty within possibilistic networks. The computing of the optimal optimistic decision no longer goes through the junction tree construction step. Instead, it is performed by calculating the degree of normalization in the moral graph resulting from the merging of the possibilistic network codifying knowledge of the agent and that codifying its preferences.
In the area of network security, the fundamental security principles and security practice skills are both required for students’ understanding. Instructors have to emphasize both; the theoretical part and practices of security. However, this is a challenging task for instructors’
teaching and students’ learning. For this reason, researchers are eager to support the lecture
lessons by using interactive visualization tools. The learning tool CrypTool 2 is one of these tools that mostly cover all of the above. In fact, the evaluations of the effectiveness of the tools in teaching and learning are limited. Therefore, this paper provides an overview of an empirical evaluation for assessing CrypTool 2 tool. The effectiveness of this tool was tested using an empirical evaluation method. The results show that this visualization tool was effective in
meeting its learning objectives.
Cryptography is a security technique that must be applied in both communication sides to protect
the data during its transmission through the network from all kinds of attack. On the sender
side, the original data will be changed into different symbols or shapes by using a known key;
this is called encryption. On the other communication side, the decryption process will be done
and the data will be returned to its former shape by using the agreed key. The importance of
cryptography is to fulfil the communication security requirements. Real time applications (RTA)
are vulnerable for the moment because of their big size. However, some of the current algorithms
are not really appropriate for use with these kinds of information. In this paper, a novel
symmetric block cipher cryptography algorithm has been illustrated and discussed. The system
uses an 8x8x8 cube, and each cell contains a pair of binary inputs. The cube can provide a huge
number of combinations that can produce a very strong algorithm and a long key size. Due to
the lightweight and fast technique used in this idea, it is expected to be extremely rapid compared
to the majority of current algorithms, such as DES and AES.
The recruitment of new personnel is one of the most essential business processes which affect the quality of human capital within any company. It is highly essential for the companies to ensure the recruitment of right talent to maintain a competitive edge over the others in the
market. However IT companies often face a problem while recruiting new people for their ongoing projects due to lack of a proper framework that defines a criteria for the selection process. In this paper we aim to develop a framework that would allow any project manager to
take the right decision for selecting new talent by correlating performance parameters with the
other domain-specific attributes of the candidates. Also, another important motivation behind this project is to check the validity of the selection procedure often followed by various big companies in both public and private sectors which focus only on academic scores, GPA/grades
of students from colleges and otheracademic backgrounds. We test if such a decision will produce optimal results in the industry or is there a need for change that offers a more holistic approach to recruitment of new talent in the software companies. The scope of this work extends beyond the IT domain and a similar procedure can be adopted to develop a recruitment
framework in other fields as well. Data-mining techniques provide useful information from the historical projects depending on which the hiring-manager can make decisions for recruiting high-quality workforce. This study aims to bridge this hiatus by developing a data-mining
framework based on an ensemble-learning technique to refocus on the criteria for personnel selection. The results from this research clearly demonstrated that there is a need to refocus on the selection-criteria for quality objectives.
A considerable interest has been given to Multiword Expression (MWEs) identification and treatment. The identification of MWEs affects the quality of results of different tasks heavily used in natural language processing (NLP) such as parsing and generation. Different
approaches for MWEs identification have been applied such as statistical methods which employed as an inexpensive and language independent way of finding co-occurrence patterns.Another approach relays on linguistic methods for identification, which employ information such as part of speech (POS) filters and lexical alignment between languages is also used and
produced more targeted candidate lists. This paper presents a framework for extracting Arabic
MWEs (nominal or verbal MWEs) for bi-gram using hybrid approach. The proposed approach starts with applying statistical method and then utilizes linguistic rules in order to enhance the results by extracting only patterns that match relevant language rule. The proposed hybrid
approach outperforms other traditional approaches.
This paper deals with the optimization of the capacity of a terminal railway station using the Ant Colony Optimization algorithm. The capacity of the terminal station is defined as the
number of trains that depart from the station in unit interval of time. The railway capacity
optimization problem is framed as a typical symmetrical Travelling Salesman Problem (TSP),
with the TSP nodes representing the train arrival /departure events and the TSP total cost
representing the total time-interval of the schedule. The application problem is then optimized
using the ACO algorithm. The simulation experiments validate the formulation of the railway
capacity problem as a TSP and the ACO algorithm produces optimal solutions superior to those
produced by the domain experts.
Nowadays we can observe the change of the structure of energy resources, which leads to the
increasing fraction of a renewable energy sources. Traditional underground coal mining loses
its significance in a total but there are countries, including Poland, which economy is still coal
based. A decreasing coal resources imply an exploitation a becoming harder accessible coal
beds what is connected with the increase of the safety of the operation. One of the most
important technical factor of the safety of underground coal mining is the diagnostic state o a
longwall powered roof support. It consists of dozen (or hundreds) of units working in a row. The
diagnostic state of a powered roof supports depends on the diagnostic state of all units. This
paper describes the possibility of unit diagnostic state analysis based on the biclustering
methods.
Liver segmentation from ct images using a modified distance regularized level...csandit
Organ segmentation from medical images is still an open problem and liver segmentation is a
much more challenging task among other organ segmentations. This paper presents a liver
segmentation method from a sequence of computer to mography images.We propose a novel
balloon force that controls the direction of the evolution process and slows down the evolving
contour in regions with weak or without edges and discourages the evolving contour from going
far away from the liver boundary or from leaking at a region that has a weak edge, or does not
have an edge. The model is implemented using a modified Distance Regularized Level Set
(DRLS) model. The experimental results show that the method can achieve a satisfactory result.
Comparing with the original DRLS model, our model is more effective in dealing with over
segmentation problems.
A simple multi-stable chaotic jerk system with two saddle-foci equilibrium po...IJECEIAES
This paper announces a new three-dimensional chaotic jerk system with two saddle-focus equilibrium points and gives a dynamic analysis of the properties of the jerk system such as Lyapunov exponents, phase portraits, Kaplan-Yorke dimension and equilibrium points. By modifying the GenesioTesi jerk dynamics (1992), a new jerk system is derived in this research study. The new jerk model is equipped with multistability and dissipative chaos with two saddle-foci equilibrium points. By invoking backstepping technique, new results for synchronizing chaos between the proposed jerk models are successfully yielded. MultiSim software is used to implement a circuit model for the new jerk dynamics. A good qualitative agreement has been shown between the MATLAB simulations of the theoretical chaotic jerk model and the MultiSIM results.
ANALYSIS OF ELEMENTARY CELLULAR AUTOMATA BOUNDARY CONDITIONSijcsit
We present the findings of analysis of elementary cellular automata (ECA) boundary conditions. Fixed and variable boundaries are attempted. The outputs of linear feedback shift registers (LFSRs) act as continuous inputs to the two boundaries of a one-dimensional (1-D) Elementary Cellular Automata (ECA) are analyzed and compared. The results show superior randomness features and the output string has passed the Diehard statistical battery of tests. The design has strong correlation immunity and it is inherently amenable for VLSI implementation. Therefore it can be considered to be a good and viable candidate for parallel pseudo random number generation
Modeling of the damped oscillations of the viscous beams structures with swiv...eSAT Journals
Abstract
Mechanic studies realized on the two dimensional beams structures with swivel joints show that in statics, the vertical displacement is
continuous, but the rotation is discontinuous at the node where there is a swivel joint. Moreover, in dynamics, many authors do not
usually take into account the friction effect, modeling of these structures. We propose in this paper, a modeling of the beams structures
with swivel joints which integrates viscosity effects in dynamics. Hence this work we will present the formulation of motion equations
of such structures and the modal analysis method which is used to solve these equations.
Keywords: Beams, Swivel joint, Viscosity, Vibration, Modal Method.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
A NEW SURVEY ON BICLUSTERING OF MICROARRAY DATAcscpconf
There are subsets of genes that have similar behavior under subsets of conditions, so we say
that they coexpress, but behave independently under other subsets of conditions. Discovering
such coexpressions can be helpful to uncover genomic knowledge such as gene networks or
gene interactions. That is why, it is of utmost importance to make a simultaneous clustering of
genes and conditions to identify clusters of genes that are coexpressed under clusters of
conditions. This type of clustering is called biclustering.
Biclustering is an NP-hard problem. Consequently, heuristic algorithms are typically used to
approximate this problem by finding suboptimal solutions. In this paper, we make a new survey
on biclustering of gene expression data, also called microarray data.
There are subsets of genes that have similar behavior under subsets of conditions, so we say
that they coexpress, but behave independently under other subsets of conditions. Discovering
such coexpressions can be helpful to uncover genomic knowledge such as gene networks or
gene interactions. That is why, it is of utmost importance to make a simultaneous clustering of
genes and conditions to identify clusters of genes that are coexpressed under clusters of
conditions. This type of clustering is called biclustering.
Biclustering is an NP-hard problem. Consequently, heuristic algorithms are typically used to
approximate this problem by finding suboptimal solutions. In this paper, we make a new survey
on biclustering of gene expression data, also called microarray data.
MODIFIED LLL ALGORITHM WITH SHIFTED START COLUMN FOR COMPLEXITY REDUCTIONijwmn
Multiple-input multiple-output (MIMO) systems are playing an important role in the recent wireless
communication. The complexity of the different systems models challenge different researches to get a good
complexity to performance balance. Lattices Reduction Techniques and Lenstra-Lenstra-Lovàsz (LLL)
algorithm bring more resources to investigate and can contribute to the complexity reduction purposes.
In this paper, we are looking to modify the LLL algorithm to reduce the computation operations by
exploiting the structure of the upper triangular matrix without “big” performance degradation. Basically,
the first columns of the upper triangular matrix contain many zeroes, so the algorithm will perform several
operations with very limited income. We are presenting a performance and complexity study and our
proposal show that we can gain in term of complexity while the performance results remains almost the
same.
Reconstruction of electrical impedance tomography images based on the expecta...ISA Interchange
Electrical impedance tomography (EIT) calculates the internal conductivity distribution within a body using electrical contact measurements. The image reconstruction for EIT is an inverse problem, which is both non-linear and ill-posed. The traditional regularization method cannot avoid introducing negative values in the solution. The negativity of the solution produces artifacts in reconstructed images in presence of noise. A statistical method, namely, the expectation maximization (EM) method, is used to solve the inverse problem for EIT in this paper. The mathematical model of EIT is transformed to the non-negatively constrained likelihood minimization problem. The solution is obtained by the gradient projection-reduced Newton (GPRN) iteration method. This paper also discusses the strategies of choosing parameters. Simulation and experimental results indicate that the reconstructed images with higher quality can be obtained by the EM method, compared with the traditional Tikhonov and conjugate gradient (CG) methods, even with non-negative processing.
VIBRATION ANALYSIS OF AIRFOIL MODEL WITH NONLINEAR HEREDITARY DEFORMABLE SUSP...ijmech
In the present work, the vibratory behavior of an airfoil is discussed. The airfoil is considered as twodegree-of-freedom structure with hereditary deformable suspensions. The weak singular integrodifferential equation is numerically solved using numerical integration method. Finally, numerical results for the creep response and resonance behavior of the viscoelastic materials were analyzed. These results are obtained for the perfect elastic and viscoelastic suspensions with the nonlinearity feature. As demonstrated in the airfoil model, the equation of motion with hereditary and nonlinear terms successfully illustrate realistic vibratory characteristics of two-dimensional viscoelastic problems.
A modular abstraction is presented to implement model predictive control (MPC) on a three phase two level voltage source inverter to control its output current. Traditional ways of coded implementation do not provide insights into the complex nature of MPC; hence a more intuitive, logical and flexible approach for hardware implementation is conceptualized in the form of signal flow graphs (SFGs) for estimation, prediction and optimization. Simulation results show good performance of the approach and easier code generation for real time implementation. RL load is assumed for the inverter and the importance of choosing load inductance and sampling time ratio is emphasized for better control performance.
Similar to Boolean Orthogonalizing Combination Methods (20)
Sachpazis:Terzaghi Bearing Capacity Estimation in simple terms with Calculati...Dr.Costas Sachpazis
Terzaghi's soil bearing capacity theory, developed by Karl Terzaghi, is a fundamental principle in geotechnical engineering used to determine the bearing capacity of shallow foundations. This theory provides a method to calculate the ultimate bearing capacity of soil, which is the maximum load per unit area that the soil can support without undergoing shear failure. The Calculation HTML Code included.
Water scarcity is the lack of fresh water resources to meet the standard water demand. There are two type of water scarcity. One is physical. The other is economic water scarcity.
Hybrid optimization of pumped hydro system and solar- Engr. Abdul-Azeez.pdffxintegritypublishin
Advancements in technology unveil a myriad of electrical and electronic breakthroughs geared towards efficiently harnessing limited resources to meet human energy demands. The optimization of hybrid solar PV panels and pumped hydro energy supply systems plays a pivotal role in utilizing natural resources effectively. This initiative not only benefits humanity but also fosters environmental sustainability. The study investigated the design optimization of these hybrid systems, focusing on understanding solar radiation patterns, identifying geographical influences on solar radiation, formulating a mathematical model for system optimization, and determining the optimal configuration of PV panels and pumped hydro storage. Through a comparative analysis approach and eight weeks of data collection, the study addressed key research questions related to solar radiation patterns and optimal system design. The findings highlighted regions with heightened solar radiation levels, showcasing substantial potential for power generation and emphasizing the system's efficiency. Optimizing system design significantly boosted power generation, promoted renewable energy utilization, and enhanced energy storage capacity. The study underscored the benefits of optimizing hybrid solar PV panels and pumped hydro energy supply systems for sustainable energy usage. Optimizing the design of solar PV panels and pumped hydro energy supply systems as examined across diverse climatic conditions in a developing country, not only enhances power generation but also improves the integration of renewable energy sources and boosts energy storage capacities, particularly beneficial for less economically prosperous regions. Additionally, the study provides valuable insights for advancing energy research in economically viable areas. Recommendations included conducting site-specific assessments, utilizing advanced modeling tools, implementing regular maintenance protocols, and enhancing communication among system components.
Cosmetic shop management system project report.pdfKamal Acharya
Buying new cosmetic products is difficult. It can even be scary for those who have sensitive skin and are prone to skin trouble. The information needed to alleviate this problem is on the back of each product, but it's thought to interpret those ingredient lists unless you have a background in chemistry.
Instead of buying and hoping for the best, we can use data science to help us predict which products may be good fits for us. It includes various function programs to do the above mentioned tasks.
Data file handling has been effectively used in the program.
The automated cosmetic shop management system should deal with the automation of general workflow and administration process of the shop. The main processes of the system focus on customer's request where the system is able to search the most appropriate products and deliver it to the customers. It should help the employees to quickly identify the list of cosmetic product that have reached the minimum quantity and also keep a track of expired date for each cosmetic product. It should help the employees to find the rack number in which the product is placed.It is also Faster and more efficient way.
2. 10 Computer Science & Information Technology (CS & IT)
2. THEORETICAL FOUNDATIONS
2.1. Isomorphism: Set Theory as Basis for Switching Algebra
In Figure1a), the set difference from the set theory is shown. If the set difference is called,ܵܯ
the remaining set of these two sets is the set of all elements belonging to set ,ܯ but not to set ܵ
(ܯwithout ܵ). In Figure1b), the union of set ܵଵ and ܵଶ, that isܵଵ ∪ ܵଶ, is illustrated [2][3].
Figure 1: a) Set Difference ;ܵܯ b) Set Union ܵଵ ∪ ܵଶ
Due to the isomorphism the set difference and the set union out of the set theory are expressed in
the propositional logic as follows:
ܥଵ ൌ ܵܯ ൌ ܯ ∩ ܵ̅ ↣ ܯ ∧ ܵ̅ (1)
ܥଶ ൌ ܵଵ ∪ ܵଶ ↣ ܵଵ ∨ ܵଶ (2)
Thus, an Equation (3) to build the difference of two minterms in the switching algebra is defined
out of (1). The minuend minterm is indentified with݉ெ ≔ ⋀ ݔି
ିଵ
ୀ , the subtrahend minterm
is indentified with ݉ௌ ≔ ⋀ ݔି௦
ିଵ
௦ୀ and with ݊ ∈ ℕfollows:
݉ெ݉ௌ ൌ ൭ሥ ݔି
ିଵ
ୀ
൱ ൭ሥ ݔି௦
ିଵ
௦ୀ
൱ ≔ ൭ሥ ݔି
ିଵ
ୀ
൱ ∧ ൭ሥ ݔି௦
ିଵ
௦ୀ
൱
തതതതതതതതതതതതതതത
ൌ
ൌ ൭ሥ ݔି
ିଵ
ୀ
൱ ∧ ൭ሧ ̅ݔି
ିଵ
௦ୀ
൱ ൌ ሺݔ ⋅ ݔିଵ ⋅. .⋅ ݔଵሻெ ∧ ሺݔ ⋅ ݔିଵ ⋅. .⋅ ݔଵሻௌ (3)
An Equation (4) building the disjunction of two minterms where the first summand minterm is
identified with ݉ௌభ
≔ ⋀ ݔି௦భ
ିଵ
௦భୀ and the second summand minterm is identified with ݉ௌమ
≔
⋀ ݔି௦మ
ିଵ
௦మୀ is defined out of (2). And with ݊ ∈ ℕ follows:
݉ௌభ
∨ ݉ௌమ
ൌ ቌሥ ݔି
ିଵ
௦భୀ
ቍ ∨ ቌሥ ݔି௦
ିଵ
௦మୀ
ቍ ൌ ሺݔ ⋅ ݔିଵ ⋅. .⋅ ݔଵሻௌభ
∨ ሺݔ ⋅ ݔିଵ ⋅. .⋅ ݔଵሻௌమ
(4)
Equation (3) and (4) only indicate the value of the variable at the corresponding position in terms
of its index. That means ̅ݔis the complement value of variable at thei-th place, whereasݔ hows
the value of the variable at the i-th place. The general validity is proved by the method of
mathematical induction.
3. Computer Science & Information Technology (CS & IT) 11
2.2. Ternary-Vector-List (TVL)
Ternary-Vector-Lists are representations of Boolean functions which can take one of three
possible values for each point. A non-negated variable is characterized by ‘1’, a negated by ‘0’
and not included by ‘-‘. Boolean equations represented by TVL can be treated computationally
easier [5][10]. A TVL consists of m-rows (number of conjunctions or disjunctions contained in
the function) and n-columns (number of independent variables) and is characterized with݊ ∈
ℕand ݐ ∈ {0, 1, −}. Any form of a function, that means disjunctive form (DF), conjunctiveform
(KF), equivalent form (EF) and antivalence form (AF), can be represented as a TVL. As no
operators (∨, ∧, ⨀, ⨁ ) in the TVL presentation are given, the designations of the matrix by D(f),
K(f), E(f) and A(f) show the type of the TVL [5][10][12].
ݔ … ݔଶݔଵ
ܸܶܮ ൌ ൦
ܸܶଵ
ܸܶଶ
∶
ܸܶ
൪ ≔
1. ݓݎ
2. ݓݎ
∶
݉. ݓݎ
൦
ݐଵ
ݐଶ
∶
ݐ
…
…
∶
…
ݐଵଶ
ݐଶଶ
∶
ݐଶ
ݐଵଵ
ݐଵଶ
∶
ݐଵ
൪ ൌ [ݐ]
(5)
The rule for AND-ing (∧) of two TVs (ܸܶ,) which represent an average TV (ܸܶ), is defined by
Table 1:
Table 1. Rule for AND-ing of two TVs
∧ 0 1 -
0 0 × 0
1 × 1 1
- 0 1 -
if × ≥ 1
else
×: empty set
ܸܶ ൌ×
ܸܶ ൌ ܸܶ ∧ ܸܶ
The rule for OR-ing (∨) of two TVs (ܸܶ,), which represent the union of both TVs, is defined as
follows:
ܸܶ ∨ ܸܶ ൌ
ܸܶ
ܸܶ
൨
(6)
The difference-building of two TVs with ܸܶெ ൌ [ݐ, ݐିଵ, . . , ݐଵ]ெ and ܸܶௌ ൌ [ݐ, ݐିଵ, . . , ݐଵ]ௌ is
distinguished out of Equation (3):
ܸܶெ ܸܶௌ ൌ [ݐ, ݐିଵ, . . , ݐଵ]ெ [ݐ, ݐିଵ, . . , ݐଵ]ௌ ≔ [ݐ, ݐିଵ, . . , ݐଵ]ெ ∧ [ݐ, ݐିଵ, . . , ݐଵ]ௌ
തതതതതതതതതതതതതതതതതതതത ൌ
ൌ [ݐ, ݐିଵ, . . , ݐଵ]ெ ∧ ൦
ݐ̅ −
− ݐିଵതതതതതത
⋮
−
⋮
−
… −
… −
⋮
…
⋮
ݐ̅ଵ
൪
ௌ
(7)
2.3. Orthogonality
A function or TVL is orthogonal if its minterms respectively its TVs are disjoint to one another in
pairs at least in one column. Consequently, these minterms (݉,) or these TVs (ܸܶ,) then have
no common covering after their logical conjunction. An orthogonal function has no redundant
minterm. Thus, the following Equations in (8) can be formulated for the proof of orthogonality
[17]:
4. 12 Computer Science & Information Technology (CS & IT)
3. ORTHOGONALIZING D
3.1. Method
The method of orthogonalizing difference
corresponds to the removal of the intersection which is formed between the minuend
subtrahend ݉ௌ, from the minuend
several disjoint minterms, which cover all of the remaining 1s an
other. For this purpose, an example is shown in a K
group of 2 (subtrahend: ݔଷݔଶݔଵ) is subtracted from group of 8 (minuend:
of several blocks (1st
Block, 2nd
Block, 3
ݔସณ
୧୬୳ୣ୬ୢ
⊝ ݔଷᇣ
ୗ୳ୠ୲୰ୟ୦ୣ୬ୢ
• The first literal of the subtrahend, here
minterm of the minuend, here
• Then the second literal, here
minuend and to the first literal
ݔସݔଷݔଶതതത.
• Following the next literal, hier
the minuend and to the first literal
third block of the difference is
• This process is continued until all literals of the subtrahend are singly complemented and
linked by AND-ing to the minuend in a separate minterm.
The Equation (9) is applied to calculate the orthogonalizing difference
In this case, the formula does not show the value of the individual literals, but it shows whether
the associated literal exists complement or not. The indices declare only the order of literals
which have to be calculated. In thi
formed from [18] is applied to describe the orthogonalizing difference
mathematically easier way:
Computer Science & Information Technology (CS & IT)
DIFFERENCE-BUILDING ⊝
The method of orthogonalizing difference-building ⊝ illustrated in the Karnaugh map (Fig
corresponds to the removal of the intersection which is formed between the minuend
from the minuend ݉ெ, which means ݉ெ ሺ݉ெ ∧ ݉ௌሻ. The result consists of
several disjoint minterms, which cover all of the remaining 1s and are pairwise orthogonal to each
other. For this purpose, an example is shown in a K-map with 4 variables (Fig. 2
) is subtracted from group of 8 (minuend: ݔସ). The resu
Block, 3rd
Block) which are pairwise orthogonal to each other.
Figure 2: Example of ⊝ in a K-map
ݔଷݔଶݔଵᇣᇧᇤᇧᇥ
ୗ୳ୠ୲୰ୟ୦ୣ୬ୢ
ൌ ݔସݔଷതതതถ
ଵ౩౪୪୭ୡ୩
∨ ݔସݔଷݔଶതതതᇣᇧᇤᇧᇥ
ଶౚ୪୭ୡ୩
∨ ݔସݔଷݔଶݔଵതതതᇣᇧᇧᇤᇧᇧᇥ
ଷ౨ౚ୪୭ୡ୩ᇣᇧᇧᇧᇧᇧᇧᇧᇧᇧᇤᇧᇧᇧᇧᇧᇧᇧᇧᇧᇥ
ୈ୧ୣ୰ୣ୬ୡୣ
The first literal of the subtrahend, here ݔଷ, is taken complement and AND
minterm of the minuend, here ݔସ. Consequently, the first block of the difference is
Then the second literal, hereݔଶ, is taken complement and AND-ing to the minterm of the
minuend and to the first literal ݔଷ of the subtrahend. Therefore, the second block is
Following the next literal, hier ݔଵ, is taken complement and AND-ing to the minterm of
the minuend and to the first literal ݔଷ and second literal ݔଶ of the subtrahend. Thus, the
of the difference is ݔସݔଷݔଶݔଵതതത.
This process is continued until all literals of the subtrahend are singly complemented and
ing to the minuend in a separate minterm.
is applied to calculate the orthogonalizing difference-building of two minterms.
In this case, the formula does not show the value of the individual literals, but it shows whether
the associated literal exists complement or not. The indices declare only the order of literals
which have to be calculated. In this case, the formula ሺ⋁ ݔపഥ
ೕ
ୀଵ
ൌ ݔଵതതത ∨ ݔଵݔଶതതത ∨. .∨
formed from [18] is applied to describe the orthogonalizing difference-building in a
illustrated in the Karnaugh map (Fig. 2)
corresponds to the removal of the intersection which is formed between the minuend ݉ெand the
The result consists of
d are pairwise orthogonal to each
. 2),in which a
). The result consists
Block) which are pairwise orthogonal to each other.
, is taken complement and AND-ing to the
. Consequently, the first block of the difference is ݔସݔଷതതത.
ing to the minterm of the
of the subtrahend. Therefore, the second block is
ing to the minterm of
of the subtrahend. Thus, the
This process is continued until all literals of the subtrahend are singly complemented and
building of two minterms.
In this case, the formula does not show the value of the individual literals, but it shows whether
the associated literal exists complement or not. The indices declare only the order of literals
ത ∨ ݔଵݔଶ ⋅. .⋅ ݔതതതሻ
building in a
5. Computer Science & Information Technology (CS & IT) 13
݉ெ ⊝ ݉ௌ ൌ ൭ሥ ݔି
ିଵ
ୀ
൱ ⊝ ൭ሥ ݔି௦
ିଵ
௦ୀ
൱ ≔ ൭ሥ ݔି
ିଵ
ୀ
൱ ∧ ቌ ሧ ̅ݔି௦
ೕିଵ
௦ୀ
ቍ ൌ
ൌ ሺݔ ⋅ ݔିଵ ⋅. .⋅ ݔଵሻெ ∧ ሺ̅ݔ ∨ ݔ̅ݔିଵ ∨. .∨ ݔ ⋅ ݔିଵ ⋅. .⋅ ݔଵሻௌ (9)
The result may differ depending on the starting literal. There are many equivalent options. They
only differ in the form of coverage. The minterms of the difference are pairwise disjoint to each
other, so that the result is already availabe in an orthogonal form. The the result corresponds to
the minuend if the subtrahend is already orthogonal to the minuend (݉ெ ⊥ ݉ௌ):
ܑ: ݉ௌ ⊈ ݉ெ:ܖ܍ܐܜ ݉ெ ⊝ ݉ௌ ൌ ݉ெ (10)
The number of the minterms (blocks) in the result called ݊ corresponds to the number of the
variables presented in the subtrahend and are not presented in the minuend at the same time. The
number of the possible results can be defined by ݊! for ݊ > 0. The orthogonalizing difference-
building of two TVs (ܸܶெ, ܸܶௌ), is defined by a corresponding Equation (11):
ܸܶெ ⊝ ܸܶௌ ൌ [ݐ, ݐିଵ, . . , ݐଵ]ெ ⊝ [ݐ, ݐିଵ, . . , ݐଵ]ௌ ≔
ൌ [ݐ, ݐିଵ, . . , ݐଵ]ெ ∧ ൦
ݐ̅ −
ݐ ݐିଵതതതതതത
⋮
ݐ
⋮
ݐ݊
… −
… −
⋮
…
⋮
ݐ̅ଵ
൪
ௌ
(11)
By the use of this new method, two calculation procedures - building the difference and the
subsequent orthogonalization - can be performed in one step. That means that the orthogonalizing
difference-building ⊝represents the composition of the difference-building and the subsequent
orthogonalization Orth [6].
3.2. Analysis
3.2.1. Mathematical
The general validity is proved by mathematical induction:
Basis: n = 1
൭ሥ ݔଵି
ଵିଵ
ୀ
൱ ∧ ൭ሧ ̅ݔଵି௦
ଵିଵ
௦ୀ
൱ ൌ ሺݔଵሻெ ∧ ሺ̅ݔଵሻௌ
ሺݔଵሻெ ∧ ሺ̅ݔଵሻௌ ൌ ሺݔଵሻெ ∧ ሺ̅ݔଵሻௌ
Statement is true:
Inductive step: n = n + 1
൭ሥ ݔሺାଵሻି
ୀ
൱ ∧ ቌሧ ̅ݔሺାଵሻି௦
ೕ
௦ୀ
ቍ ൌ ൫ݔሺାଵሻݔݔିଵ. . ݔଵ൯
ெ
∧ ቀ̅ݔሺାଵሻ ∨ ݔሺାଵሻሺ̅ݔ ∨ ݔ̅ݔିଵ ∨. .∨ ݔ ⋅. .⋅ ݔଵሻቁ
ௌ
൭ݔሺାଵሻ ሥ ݔି
ିଵ
ୀ
൱ ∧ ቌ̅ݔሺାଵሻ ∨ ݔሺାଵሻ ሧ ̅ݔି௦
ೕିଵ
௦ୀ
ቍ ൌ ൭ݔሺାଵሻ ሥ ݔି
ିଵ
ୀ
൱ ∧ ቌ̅ݔሺାଵሻ ∨ ݔሺାଵሻ ሧ ̅ݔି௦
ೕିଵ
௦ୀ
ቍ
The new Equation (3) is equated with the usual Equation (9) to show the equivalence. Since the
term of the minuend (⋀ ݔି
ିଵ
ୀ ) is equal on both sides, it can be neglected:
6. 14 Computer Science & Information Technology (CS & IT)
൭ሧ
ି
௦ୀ
̅ݔ ∨ ̅ݔିଵ
Due to the axiom of absorption with
confirmed. They only differ in their form of coverage. The right side is the orthogonal form of the
left side. This proves that the orthogonalizing difference
the difference-building derived out of the set theory.
3.2.2. Computing Time
A study between usual and new method in computing time depe
(dimension݀݅݉[݅]) of the minuend and subtrahend indicates almost identical co
The new method (orth_Diff) has a slightly longer computing time with increasing dimension than
the method of difference-building (
shows a maximum difference of just 1.2
complexity. The supplementation instruction per loop iteration results in a multiplicative
constant which explains the minimal difference. Against it, the results are orthogonal. The
comparison in Figure 3 illustrates that the method
increasing dimension ݀݅݉[݅] as the composition of method
orthogonalizing Orth [19].
Figure 3: Comparison of computing time of
In Diagram (Fig. 4) the explanation for the higher computing time of the composition is provided.
With increasing dimension the computing
Diff decreases with respect to the composition. In dimension
same percentage value of the whole computing time. Thereafter, the percentage value of
low and at the same time the percentage value of
Computer Science & Information Technology (CS & IT)
൭ሧ ̅ݔି௦
ିଵ
ୀ
൱ ൌ ቌ ሧ ̅ݔି௦
ೕିଵ
௦ୀ
ቍ
ଵ ∨. .∨ ̅ݔଵ ൌ ̅ݔ ∨ ݔ̅ݔିଵ ∨. .∨ ݔݔିଵ ⋅. .⋅ ݔଶ̅ݔଵ
Due to the axiom of absorption with ݔపഥ ∨ ݔݔఫഥ ൌ ݔపഥ ∨ ݔఫഥ, the equivalence between two methods is
confirmed. They only differ in their form of coverage. The right side is the orthogonal form of the
proves that the orthogonalizing difference-building supplies equivalent results as
building derived out of the set theory.
A study between usual and new method in computing time depending on the length
of the minuend and subtrahend indicates almost identical computing times.
has a slightly longer computing time with increasing dimension than
building (Diff). The comparison of the average values of both methods
shows a maximum difference of just 1.2µs, which can be explained by the consideration
The supplementation instruction per loop iteration results in a multiplicative
the minimal difference. Against it, the results are orthogonal. The
illustrates that the method orth_Diff has faster computing
] as the composition of method Diff and the subsequent method of
Figure 3: Comparison of computing time of orth_Diff⊝ and composition of Diff and
) the explanation for the higher computing time of the composition is provided.
With increasing dimension the computing time of the method Orth increases, whereas the method
decreases with respect to the composition. In dimension ݀݅݉[14] both functions have the
same percentage value of the whole computing time. Thereafter, the percentage value of
the same time the percentage value of Orthincreases.
, the equivalence between two methods is
confirmed. They only differ in their form of coverage. The right side is the orthogonal form of the
building supplies equivalent results as
nding on the length
mputing times.
has a slightly longer computing time with increasing dimension than
The comparison of the average values of both methods
, which can be explained by the consideration
The supplementation instruction per loop iteration results in a multiplicative
the minimal difference. Against it, the results are orthogonal. The
has faster computing time with
uent method of
and Orth
) the explanation for the higher computing time of the composition is provided.
increases, whereas the method
both functions have the
same percentage value of the whole computing time. Thereafter, the percentage value of Diffruns
7. Computer Science & Information Technology (CS & IT)
Figure 4: Percentage value of whole computing of
At the dimension݀݅݉[50]the share of computing time of
percentage value of Diffis 6.7 %. Finally,
the new method orth_Diff brings a significant advantage due to the orthogonal results [19].
3.2.3. Complexity
The complexity of both methods is analyzed by the evaluation of their implemented functions.
The dimension of the inserted minterms respectively ternary
size ݆. Figure 5 shows the pseudocode of
according to the rules of the
accordingly comparisons and two inte
complexity is ܱሺ݆ଶ
ሻ [19]. The complexity of the function
not required and may be replaced by three linear operations with the complexity of
Figure 5
However, the additive and multiplicative constants have no influence on the
omitted for this reason. Although the total complexity of the usual method is minor but it
increases in total by an additional code for orthogonalization.
Computer Science & Information Technology (CS & IT)
Percentage value of whole computing of Diff and Orth
the share of computing time of Orth is already 93.7
%. Finally, the measurement of computing time demonstrates that
brings a significant advantage due to the orthogonal results [19].
The complexity of both methods is analyzed by the evaluation of their implemented functions.
The dimension of the inserted minterms respectively ternary-vectors is determined as the input
shows the pseudocode of orth_Diff. For the function orth_Diff
according to the rules of the ܱ-calculus many complexities of ܱሺ1ሻ for instructions and
accordingly comparisons and two interleaved nested complexities ofܱሺ1ሻ. As the result, the total
[19]. The complexity of the function Diff is ܱሺ݆ሻ because the inner loops are
not required and may be replaced by three linear operations with the complexity of ܱ
5: Pseudocode of orth_Diff with complexity
However, the additive and multiplicative constants have no influence on the complexity and are
omitted for this reason. Although the total complexity of the usual method is minor but it
increases in total by an additional code for orthogonalization.
15
is already 93.7 % and the
the measurement of computing time demonstrates that
brings a significant advantage due to the orthogonal results [19].
The complexity of both methods is analyzed by the evaluation of their implemented functions.
s determined as the input
orth_Diff is obtained
for instructions and
esult, the total
because the inner loops are
ܱሺ1ሻ (Fig. 6).
complexity and are
omitted for this reason. Although the total complexity of the usual method is minor but it
8. 16 Computer Science & Information Technology (CS & IT)
Figure 6: Pseudocode of Diff with complexity
3.2.4. Data Memory Request
First, the memory request of the data structures TV and TVL is determined for this comparison
[19]. A TV consists of an array of ݉ ⋅ byte elements. Each byte represents an element of the
ternary variables. This means that the memory request of the data structures depends on the
dimension of the ternary variables. In C# the data type Byte consists of 8Bits. For a 64 bit system
a minimum memory request ்ܾܵሺ݉ሻfor the data structure of TV with an addressing pointer is
calculated by:
்ܾܵሺ݉ሻ ൌ ݉ ⋅ 8 ݏݐ݅ܤᇣᇧᇧᇤᇧᇧᇥ
⋅௬௧ିா௧௦
+ 32 ݏݐ݅ܤᇣᇧᇤᇧᇥ
௧ ௧ ்
(12)
Since a TVL consists of a list of TVs. The memory request of a TVL depends on the number of
ternary variables and also the number of the consisting TVs called ݇. The easiest way to
implement a list is the use of a linked list. Each entry in the list has a pointer at its follower. Thus,
a minimal memory request ்ܾܵሺ݇, ݉ሻis calculated by:
்ܾܵሺ݇, ݉ሻ ൌ ݇ ⋅ ்ܾܵሺ݉ሻ + 32 ݏݐ݅ܤᇣᇧᇤᇧᇥ
௧ ௧ ்
(13)
For this reason, the minimal total memory requestܾܵ௧௧ for the operation of two TVs, the
difference-building and orthogonalizing difference-building in this case is:
ܾܵ௧௧ ൌ 2 ⋅ ்ܾܵሺ݉ሻᇣᇧᇧᇧᇤᇧᇧᇧᇥ
்ಾ&்ೄ
+ ்ܾܵሺ݇, ݉ሻᇣᇧᇧᇧᇤᇧᇧᇧᇥ
ோ௦௨௧ି்
(14)
The theoretical memory request has to be calculated equally for both function. Because of that,
they have the same minimal memory request. Addional memory request for a function for
orthogonalization is not needed, because an orthogonal TVL of the orthogonalizing difference is
already provided. That shows that the new method, which is the composition of two functions has
the advantage of reducing the memory request in addition to faster computing time. The minimal
theoretical memory request depending on the dimension ݀݅݉[݅]and the number of n which
primarily affects the memory usage is illustrated in Figure 7. Thereby, ݀݅݉[݅] is varied at a
constant n and afterwards in the reverse case and analyzed on memory request. For
constant݀݅݉[݅]and changing ݊the memory usage is higher than in the reverse case. It
applies∆ܾܵ௧௧ሺ݊ሻ ൌ ∆ܾܵ௧௧ሺ݀݅݉[݅]ሻ.
9. Computer Science & Information Technology (CS & IT)
Figure 7: Minimal theoretical memory request
3.3. Applications of Orthogonalizing Difference
3.3.1. Orthogonalizing Difference
By Equation (14) (presented in TVL
it is possible to calculate an orthogonal difference of two functions respectively two TVLs. One
of them is the minuend function
subtrahend function ݂ௌ. The minuend is subducted the common set of subtrahend and minuend;
the result is represented in an orthogonal form. The associated minterms (TVs) have the
corresponding index-notation, which means
subtrahend:
ܦ൫݂ெ
௧
൯ ⊝ ܦሺ݂ௌሻ ൌ ൦
ܸܶଵெ
ܸܶଶெ
∶
ܸܶெ
ൌ ൦
ሺܸܶଵ
ሺܸܶଶ
ሺܸܶெ
In this case it is important to stress that any outcome of each individual
considered. That means, if the combination of
complete the appropriate row to 0
building has already been proved in general validity, there is no need proof for generel validity in
this case, because all the single links are generally valid. Therefore, out of logical conclusion,
Equation (14) is generally valid. If two functions are disjoint to each other (
difference cannot be formed and it follows:
ܑ
Computer Science & Information Technology (CS & IT)
Figure 7: Minimal theoretical memory request
Applications of Orthogonalizing Difference-Building
Difference-Building of two Functions
(presented in TVL-arithmetic) based on the orthogonalizing difference
it is possible to calculate an orthogonal difference of two functions respectively two TVLs. One
ion ݂ெ
௧
which has to be orthogonal and the other one is the
. The minuend is subducted the common set of subtrahend and minuend;
the result is represented in an orthogonal form. The associated minterms (TVs) have the
notation, which means ܯ stands for the minuend and ܵ stands for the
ெ
ெ
ெ
൪ ⊝ ൦
ܸܶଵௌ
ܸܶଶௌ
∶
ܸܶௌ
൪ : ൌ
ሺ ଵெ ⊝ ܸܶଵௌሻ ∧ ሺܸܶଵெ ⊝ ܸܶଶௌሻ ∧. .∧ ሺܸܶଵெ ⊝ ܸܶௌ
ሺ ଶெ ⊝ ܸܶଵௌሻ ∧ ሺܸܶଶெ ⊝ ܸܶଶௌሻ ∧. .∧ ሺܸܶଶெ ⊝ ܸܶௌ
∶
ሺ ெ ⊝ ܸܶଵௌሻ ∧ ሺܸܶெ ⊝ ܸܶଶௌሻ ∧. .∧ ሺܸܶெ ⊝ ܸܶௌ
In this case it is important to stress that any outcome of each individual ⊝-linkings has to be
considered. That means, if the combination of ሺܸܶଵெ ⊝ ܸܶଵௌሻ ൌ 0 arises for example, this will
omplete the appropriate row to 0 because of: ݔ ∧ 0 ൌ 0. Since the orthogonalizing difference
building has already been proved in general validity, there is no need proof for generel validity in
ingle links are generally valid. Therefore, out of logical conclusion,
is generally valid. If two functions are disjoint to each other (݂ெ
difference cannot be formed and it follows:
ܑ: ݂ௌ ⊈ ݂ெ:ܖ܍ܐܜ ݂ெ ⊝ ݂ௌ ൌ ݂ெ
17
arithmetic) based on the orthogonalizing difference-building
it is possible to calculate an orthogonal difference of two functions respectively two TVLs. One
which has to be orthogonal and the other one is the
. The minuend is subducted the common set of subtrahend and minuend;
the result is represented in an orthogonal form. The associated minterms (TVs) have the
stands for the
ሻ
ሻ
ௌሻ
൪
(14)
linkings has to be
arises for example, this will
Since the orthogonalizing difference-
building has already been proved in general validity, there is no need proof for generel validity in
ingle links are generally valid. Therefore, out of logical conclusion,
⊥ ݂ௌ) then a
(15)
10. 18 Computer Science & Information Technology (CS & IT)
3.3.2. Orthogonal Complement of a Function
A further application is the building of an orthogonal complement of a function of the disjunctive
normal form. In the set theory the set difference of universal set ܩand a set ܣcorresponds to set
ܣ̅which is the complement of the given set ܣ:
ܩ ܣ ൌ ܣ̅ → ܩ ∩ ܣ̅ ൌ ܣ̅ (16)
Transferred to the switching (Boolean) algebra the complement of a function ݂̅ሺݔሻ can be
determined from the difference of a unit function ݂൫ݔ൯ ൌ 1 and the function ݂ሺݔሻ:
݂ሺ1ሻ ݂ሺݔሻ ൌ ݂̅ሺݔሻ → ݂ሺ1ሻ ∧ ݂̅ሺݔሻ ൌ ݂̅ሺݔሻ (17)
As both methods are equivalent, Equation (17) can be formulated with ⊝ to find out an
orthogonal complement:
݂ሺ1ሻ ⊝ ݂ሺݔሻ ൌ ݂̅൫ݔ൯
௧
or ܦሺ1ሻ ⊝ ܦሺ݂ሻ ൌ ܦሺ݂̅௧
ሻ (18)
3.3.3. Orthogonal EXOR of two Functions
The EXOR-operation of two minterms ݉,and also of two functions ݂,can be calculated as:
݂ ⊕ ݂ ൌ ݂݂̅ ∨ ݂݂̅ ൌ
ൌ ሺ݂ ∨ ݂ሻ ∧ ሺ݂̅ ∨ ݂̅ሻ ൌ
ൌ ሺ݂ ∨ ݂ሻ ∧ ሺ݂ప ∧ ݂ఫሻതതതതതതതതതത ൌ
ൌ ሺ݂ ∨ ݂ሻሺ݂ ∧ ݂ሻ ൌ (19)
It may be formulated with ⊝ due to the equivalence to get orthogonal result:
݂ ⊕ ݂ ൌ ሺ݂ ∨ ݂ሻ ⊝ ሺ݂ ∧ ݂ሻ (20)
By AND-ing and OR-ing of the functions ݂,an inherent relation between these two functions is
constructed.Thus, the minuend function does not need to be orthogonal. The advantage is the
orthogonal result again. By using ⊝ the difficulties which arise with the building of the
complement of a function are circumvented. The form of the function changes by building the
complement and the transformation back to its original form requires a more sophisticated
calculation.
3.3.4. Orthogonal EXNOR of two Functions
The EXNOR-operation of two minterms ݉,or two function݂,is basically the complement of the
EXOR-operation of the same minterms or functions. The EXNOR can be expressed by the
complement of EXOR, which also can be formulated by using ⊝. Accordingly, the result is
orthogonal:
݂ ⊙ ݂ ൌ ݂ప ⊕ ݂ఫ
തതതതതതതതത ൌ ݂ሺ1ሻ ⊝ ൫݂ ⊕ ݂൯ ൌ ݂ሺ1ሻ ⊝ [ሺ݂ ∨ ݂ሻ ⊝ ሺ݂ ∧ ݂ሻ] (21)
11. Computer Science & Information Technology (CS & IT) 19
v
3.3.5. Orthogonalizing OR-ing
Another method, the orthogonalizing OR-ing, which is based on the orthogonalizing difference-
building, is formed in the following. The orthogonalizing OR-ing is a variant of building the
disjunction of two summand-minterms (ܵଵ, ܵଶ) whereby the result is orthogonal. Orthogonalizing
OR-ing is going to be explained by an example in a K-map with 4 variables (Fig. 8). Two
summand-minterms (a group of 8 and a group of 4) are orthogonalizing OR-ed and a result
consisting of several blocks appears; the several blocks are pairwise orthogonal to each other.
Figure 8: Orthogonalizing OR-ing in K-map
The idea out of the K-map is noted as propositional logic which a Boolean form is going to be
derived. By the use of orthogonalizing OR-ing, the intersection set of first and second summand-
minterm (ܵଵ, ܵଶ) is removed from the first summand-minterm ܵଵand the second summand-
minterm ܵଶ is linked by a disjunction to that subtraction:
The Boolean form of orthogonalizing OR-ing of two minterms ݉ௌభ
ൌ ⋀ ݔିௌభ
ିଵ
ௌభୀ and ݉ௌభ
ൌ
⋀ ݔିௌమ
ିଵ
ௌమୀ is defined by Equation (24), which does not give the value of separate literals, but it
shows whether the value of the variable is complement or not. The indices only indicate the order
of the variables to be calculated:
12. 20 Computer Science & Information Technology (CS & IT)
v
By swapping the two summands in their position, the result changes. Both solutions, however, are
equivalent because the same set is covered. They only differ in the form of coverage which also
be seen in Figure 8, in which both possible solutions are presented. But in order to represent the
orthogonal result with a minimum of minterms to work in the TVL-representation with low
memory request, the summand-minterm with more literals has to be accepted as the first
summand-minterm,because the commutativity applies for and also for ⊝. The following
Equation (25) is used for the orthogonalizing OR-ing of two ternary vectors
ܸܶௌభ
ൌ [ݐ, ݐିଵ, . . , ݐଵ]ௌభ
and ܸܶௌమ
ൌ [ݐ, ݐିଵ, . . , ݐଵ]ௌమ
:
The number of the minterms in the result called ݊ corresponds to the number of the variables
presented in the second summand ݉ௌమ
and are not presented in the first summand ݉ௌభ
at the same
time; plus1 for the second summand ݉ௌమ
as the last linked minterm. The number of the possible
results can be charged by ݊!for ݊ > 0. Depending on the starting literal the result may differ.
There are many equivalent options which only differ only in the form of coverage. If both
minterms are disjoint (orthogonal) to each other, the result corresponds to the disjunction of both
minterms:
By the use of orthogonalizing OR-ing , two calculation procedures - OR-ing and subsequent
orthogonalizing - can be performed in one step. That means that the orthogonalizing OR-ing
is the composition of OR-ing (∨) and the subsequent orthogonalization Orth.
It is not necessary to prove this method for general validity because it includes the already general
method of orthogonalization difference-building. The Equations (23) and (2) are equalized to
indicate the equivalence of orthogonalization OR-ing and usual OR-ing:
ܵଵܵଶ
തതത ∨ ܵଶ ൌ ܵଵ ∨ ܵଶ (27)
Due to the axiom of the absorption the equivalence is verified. The right side is the orthogonal
form of the left side which means they only differ in the form of coverage. So, the results of both
sides are equal.
13. Computer Science & Information Technology (CS & IT) 21
4. CONCLUSION
This work shows that the method of the orthogonalizing difference-building is generally valid and
is also equivalent to the usual method of difference-building. In contrast to the composition,
orthogonalizing difference-building has faster computing time with increasing dimension. In
addition, the method does not require additional memory request for an additional function for
orthogonalization because this method already provides orthogonal results. The orthogonalizing
difference-building is used to calculate the orthogonal difference of two minterms respectively
two TVs, two functions or two TVLs. It is also employed to determine the complement of a
function as well as the EXOR and EXNOR of two functions to achieve an orthogonal result.
Another method, the orthogonalizing OR-ing of two minterms or TVs, is developed out of the
orthogonalizing difference-building. The application of ternary-vector-list is amplified by these
new methods to implement simple and quick elementary functions. Due to the inner
orthogonalization further processing steps in the TVL arithmetic are considerably simplified
because the orthogonal form of disjunctive normal form has the advantage to consider it as
antivalence normal form. Thus, additional calculation such as the differential calculus are
remarkably facilitated.
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[19] Kassim,H.; Can, Y.; Sattler, M.S.:Untersuchung eines neuen Algorithmus zur Berechnung
orthogonalisierter Differenz. Bachelor-Thesis, Lehrstuhl für Zuverlässige Schaltungen und Systeme,
Friedrich-Alexander-Universität Erlangen Nürnberg, Germany, 2014.
[20] Can, Y.; Fischer, G.: Orthogonalizing Boolean Subtraction of Minterms or Ternary Vektors.
International Conference on Computational and Experimental Science and Engineering
(ICCESEN2014), 24-29 October, 2014, Antalya-Turkey.
AUTHORS
Yavuz Canwas born in Erlangen, Germany, in 1979. He received his Diploma (Dipl.-Ing.)
degree in me-chatronics from Friedrich-Alexander-University Erlan-gen-Nürnberg,
Germany, in 2010. He is currently a Research Assistant of Prof. Georg Fischer working
toward his Ph.D. degree in the Institute for Electronics Engineering at Friedrich-Alexander
University in Erlangen. His research interest include orthogonality of Boolean functions and
Ternary-Vector-List.
Georg Fischer was born in Lower Rhine region, Germany, in 1965. He received the
Diploma degree in electrical engineering with focus on communications, micro-wave and
electro-dynamics from RWTH Aachen University, Aachen, Germany, in 1992, and the Dr.-
Ing. degree in electrical engineering from the University of Paderborn, Paderborn,
Germany, in 1997. From 1993 to 1996, he was a Research Assistant with the University of
Paderborn, where he was involved with adaptive antenna array systems for mobile satellite
communications. From 1996 to 2008, he performed research with Bell Laboratories,
Lucent (later Alcatel-Lucent), where he focused on the RF and digital architecture of mobile
communication basestations for global system for mobile communications (GSM), Universal Mobile
Telecommunications System (UMTS), and features for network coverage and capacity enhancements. In
2000, he became a Bell Labs Distinguished Member of Technical Staff (DMTS), and in 2001, a Bell Labs
Consulting Member of Technical Staff (CMTS). He was also a Chairman with the European Telecom-
munications Standards Institute (ETSI) during the physical layer standardization of the GSM-EDGE
system. From 2001 to 2007, he was a Part-Time Lecturer with the University of Erlangen–Nuremberg,
Erlangen, Germany, during which time he lectured on basestation RF and digital technology. Since April
2008, he has been a Professor of electronics engineering with the University of Erlangen–Nuremberg. He
holds over 50 patents concerning microwave and communications technology. His research interests are in
transceiver design, analog/digital partitioning, digital signal processing, con-verters, enhanced amplifier
architectures, duplex filters, metamaterial structures, GaN transistor technology and circuit design, and RF
microelectromechanical systems (MEMS) with specific emphasis on frequency agile, tunable, and
reconfigurable RF systems for software-define radio (SDR) and cognitive radio (CR) applications. His new
research interests concentrate on medical electronics like using microwaves for detection of vital
parameters. Georg Fischer is a Senior Member of the IEEE Microwave Theory and Techniques Society
(MTT-S)/Antennas and Propagation Society (AP-S)/Communications Society (COMSOC)/ Vehicular
Technology Society (VTC) and Engineering in Medicine and Biology Society (EMBS). He is a member of
VDE-ITG and the European Microwave Association (EUMA). He was the co-chair of the European
Conference on Wireless Technology (ECWT) of European Microwave Week Conference (EUMW 2007).
For EUMW 2013, Nuremberg, Germany and GeMiC 2015, Nuremberg, Germany he has served as the
General Technical Program Committee (TPC) chairman.