Work is devoted to the study of nonlinear algebraic systems with three unknowns and is a
continuation of the author's research in this area. Previously, for nonlinear algebraic of system of equations
was built analog determinant of Kramer and it is given a necessary and sufficient condition for the existence of
solutions of nonlinear algebraic systems with a complex dependence on the variables. For two-parameter
systems in the abstract case, it is obtained the results to determine the conditions for finding the number of
solutions.
In this paper describes the method of determining the conditions on the coefficients of algebraic systems to
establish the number of solutions of the algebraic system of equations, when an unknowns part in the system as
polynomials in any finite degree. This method can be applied to other algebraic systems with more than
three unknown variables.
I am Anthony F. I am a Digital Signal Processing Assignment Expert at matlabassignmentexperts.com. I hold a Ph.D. in Matlab, University of Cambridge, UK. I have been helping students with their homework for the past 8 years. I solve assignments related to Digital Signal Processing.
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The Cramer-Rao Inequality provides us with a lower bound on the variance of an unbiased estimator for a parameter.
The Cramer-Rao Inequality Let X = (X1,X2,. . ., Xn) be a random sample from a distribution with d.f. f(x|θ), where θ is a scalar parameter. Under certain regularity conditions on f(x|θ), for any unbiased estimator φˆ (X) of φ (θ)
I am Anthony F. I am a Digital Signal Processing Assignment Expert at matlabassignmentexperts.com. I hold a Ph.D. in Matlab, University of Cambridge, UK. I have been helping students with their homework for the past 8 years. I solve assignments related to Digital Signal Processing.
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I am Keziah D. I am a Mechanical Engineering Assignment Expert at matlabassignmentexperts.com. I hold a Ph.D. Matlab, University of North Carolina, USA. I have been helping students with their homework for the past 8 years. I solve assignments related to Mechanical Engineering.
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You can also call on +1 678 648 4277 for any assistance with Mechanical Engineering Assignments.
The Cramer-Rao Inequality provides us with a lower bound on the variance of an unbiased estimator for a parameter.
The Cramer-Rao Inequality Let X = (X1,X2,. . ., Xn) be a random sample from a distribution with d.f. f(x|θ), where θ is a scalar parameter. Under certain regularity conditions on f(x|θ), for any unbiased estimator φˆ (X) of φ (θ)
I am Leonard K. I am a Stochastic Processes Assignment Expert at statisticsassignmenthelp.com. I hold a Masters in Statistics from, University of Arkansas, USA.
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International Journal of Computational Engineering Research(IJCER)ijceronline
International Journal of Computational Engineering Research(IJCER) is an intentional online Journal in English monthly publishing journal. This Journal publish original research work that contributes significantly to further the scientific knowledge in engineering and Technology.
Whenever we have variables which contain exponents and have equal bases, we can do certain mathematical operations to them. Those operations are called the “Laws of Exponents”
On a Deterministic Property of the Category of k-almost Primes: A Determinist...Ramin (A.) Zahedi
In this paper based on a sort of linear function, a deterministic and simple algorithm with an algebraic structure is presented for calculating all (and only) k-almost primes (where ∃n∊ℕ, 1 ≤ k ≤ n) in certain intervals. A theorem has been proven showing a new deterministic property of the category of k-almost primes. Through a linear function that we obtain, an equivalent redefinition of the k-almost primes with an algebraic characteristic is identified. Moreover, as an outcome of our function’s property some equalities which contain new information about the k-almost primes (including primes) are presented.
Comments: Accepted and presented article in the 11th ANTS , Korea, 2014. The 11th ANTS is one of international satellite conferences of ICM 2014:The 27th International Congress of Mathematicians, Korea. (Expanded version)
Copyright: CC Attribution-NonCommercial-NoDerivs 4.0 International
License URL: https://creativecommons.org/licenses/by-nc-nd/4.0/
Novel analysis of transition probabilities in randomized k sat algorithmijfcstjournal
In this paper, we propose a new analysis for randomized 2-SAT and 3-SAT algorithms, and show that we could determine more precise boundaries for transition probability of Markov chain using Karnaugh map. In our analysis we will show the probability that the selected literal has been flipped correctly is so close to 32 and74, respectively for 2-SAT and 3-SAT with large number of variables. Then we will extend our result to k-SAT and show that both transition probability of Markov chain in randomized algorithm for k-SAT approaches to 0.5. Finally we use this result to determine the probability and complexity of finding the satisfying assignment for randomized k-SAT algorithm. It will be shown that the probability of finding satisfying assignment and its complexity respectively are within a polynomial factor of)9272.0(nand)0785.1(nfor satisfiable 3-SAT withnvariables (forn).
I am Lawrence B. I am a Signal Processing Assignment Expert at matlabassignmentexperts.com. I hold a Masters's in Matlab from, Durham University, UK. I have been helping students with their assignments for the past 5 years. I solve assignments related to Signal Processing.
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The research of technology for automatically cutting Patterns' edge with edge...IJRES Journal
With the designed optical systems, machine vision systems, laser cutting machine body constitute automatic boundary cutting machine vision systems with the clothing patterns. The use of digital image processing technologies, such as filtering, edge detecting and edge tracking algorithms ,has effectively extracted continuous contour of patterns which will significantly distinguish the foreground from background as cutting information of the target edge called cutting vectors, and thus cutting vectors control the laser cutting equipment SPIN1006 to precisely cut the target pattern. This technology can achieve the automatic boundary cutting of the full version of alien costumes’ pattern.
Application and development of numerical simulation technology in CastingIJRES Journal
The basic theory of the numerical simulation of casting and casting process, also the development and application of numerical calculations in the foundry engineering. Outlined the main feature of the softwares of numerical simulation of casting both here and abroad , analyzes the softwares played a significant role in actual casting and research, meanwhile pointed out the problems and development direction of the casting simulation softwares. Description reasonable use of simulation software can improve the quality of castings, Optimize the casting process, shorten the duration of the casting design and reduce costs.
I am Leonard K. I am a Stochastic Processes Assignment Expert at statisticsassignmenthelp.com. I hold a Masters in Statistics from, University of Arkansas, USA.
I have been helping students with their homework for the past 6 years. I solve assignments related to Stochastic Processes.
Visit statisticsassignmenthelp.com or email info@statisticsassignmenthelp.com.
You can also call on +1 678 648 4277 for any assistance with Stochastic Processes Assignments.
I am John G. I am a Stochastic Processes Assignment Expert at statisticsassignmenthelp.com. I hold a Masters in Statistics, from London, UK. I have been helping students with their homework for the past 5 years. I solve assignments related to Stochastic Processes.
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You can also call on +1 678 648 4277 for any assistance with Stochastic Processes Assignments.
I am Stacy W. I am a Statistical Physics Assignment Expert at statisticsassignmenthelp.com. I hold a Masters in Statistics from, University of McGill, Canada
I have been helping students with their homework for the past 7years. I solve assignments related to Statistical.
Visit statisticsassignmenthelp.com or email info@statisticsassignmenthelp.com.
You can also call on +1 678 648 4277 for any assistance with Statistical Physics Assignments.
International Journal of Computational Engineering Research(IJCER)ijceronline
International Journal of Computational Engineering Research(IJCER) is an intentional online Journal in English monthly publishing journal. This Journal publish original research work that contributes significantly to further the scientific knowledge in engineering and Technology.
Whenever we have variables which contain exponents and have equal bases, we can do certain mathematical operations to them. Those operations are called the “Laws of Exponents”
On a Deterministic Property of the Category of k-almost Primes: A Determinist...Ramin (A.) Zahedi
In this paper based on a sort of linear function, a deterministic and simple algorithm with an algebraic structure is presented for calculating all (and only) k-almost primes (where ∃n∊ℕ, 1 ≤ k ≤ n) in certain intervals. A theorem has been proven showing a new deterministic property of the category of k-almost primes. Through a linear function that we obtain, an equivalent redefinition of the k-almost primes with an algebraic characteristic is identified. Moreover, as an outcome of our function’s property some equalities which contain new information about the k-almost primes (including primes) are presented.
Comments: Accepted and presented article in the 11th ANTS , Korea, 2014. The 11th ANTS is one of international satellite conferences of ICM 2014:The 27th International Congress of Mathematicians, Korea. (Expanded version)
Copyright: CC Attribution-NonCommercial-NoDerivs 4.0 International
License URL: https://creativecommons.org/licenses/by-nc-nd/4.0/
Novel analysis of transition probabilities in randomized k sat algorithmijfcstjournal
In this paper, we propose a new analysis for randomized 2-SAT and 3-SAT algorithms, and show that we could determine more precise boundaries for transition probability of Markov chain using Karnaugh map. In our analysis we will show the probability that the selected literal has been flipped correctly is so close to 32 and74, respectively for 2-SAT and 3-SAT with large number of variables. Then we will extend our result to k-SAT and show that both transition probability of Markov chain in randomized algorithm for k-SAT approaches to 0.5. Finally we use this result to determine the probability and complexity of finding the satisfying assignment for randomized k-SAT algorithm. It will be shown that the probability of finding satisfying assignment and its complexity respectively are within a polynomial factor of)9272.0(nand)0785.1(nfor satisfiable 3-SAT withnvariables (forn).
I am Lawrence B. I am a Signal Processing Assignment Expert at matlabassignmentexperts.com. I hold a Masters's in Matlab from, Durham University, UK. I have been helping students with their assignments for the past 5 years. I solve assignments related to Signal Processing.
Visit matlabassignmentexperts.com or email info@matlabassignmentexperts.com. You can also call on +1 678 648 4277 for any assistance with Signal Processing Assignments.
I am Irene M. I am a Diffusion Assignment Expert at statisticsassignmenthelp.com. I hold a Masters in Statistics from California, USA.
I have been helping students with their homework for the past 8 years. I solve assignments related to Diffusion. Visit statisticsassignmenthelp.com or email info@statisticsassignmenthelp.com.
You can also call on +1 678 648 4277 for any assistance with Diffusion Assignments.
The research of technology for automatically cutting Patterns' edge with edge...IJRES Journal
With the designed optical systems, machine vision systems, laser cutting machine body constitute automatic boundary cutting machine vision systems with the clothing patterns. The use of digital image processing technologies, such as filtering, edge detecting and edge tracking algorithms ,has effectively extracted continuous contour of patterns which will significantly distinguish the foreground from background as cutting information of the target edge called cutting vectors, and thus cutting vectors control the laser cutting equipment SPIN1006 to precisely cut the target pattern. This technology can achieve the automatic boundary cutting of the full version of alien costumes’ pattern.
Application and development of numerical simulation technology in CastingIJRES Journal
The basic theory of the numerical simulation of casting and casting process, also the development and application of numerical calculations in the foundry engineering. Outlined the main feature of the softwares of numerical simulation of casting both here and abroad , analyzes the softwares played a significant role in actual casting and research, meanwhile pointed out the problems and development direction of the casting simulation softwares. Description reasonable use of simulation software can improve the quality of castings, Optimize the casting process, shorten the duration of the casting design and reduce costs.
Alumina-Based Composites Reinforced With Ductile ParticlesIJRES Journal
Al2O3/Metal composite ceramics were fabricated by the use of mechanical milling and pressureless sintering. Al2O3 + 10 vol.% of La, Mn, Si or Y were mixed and milled during 12 h at 300 rpm in a horizontal mill, then with the powder mixture it was conformed cylindrical samples by uniaxial pressing using 300 MPa. Pressed samples were sintered during 2 h in an electrical furnace at 1500°C. During sintered it was used an argon atmosphere inside the furnace in order to inhibit metal oxidation. XRD results indicate that alumina and metals retain its crystalline structure. Reached density by samples is small and less than 90%. Scanning electron microscopy observations show alumina’s microstructure with very fine and homogeneous distributions of metal particles. Both the Mn and Si are not suitable metals to improve the mechanical properties of alumina, in particular the fracture toughness. Considered rare earth metals such as yttrium and lanthanum, have yielded favorable results in improving the fracture toughness of the alumina. However, it should be made more dense materials with them to better explore this potential.
Energy Demand Analysis of Telecom Towers of Nepal with Strategic Scenario Dev...IJRES Journal
Telecom towers, technically known as BTS (Base Transceiver Stations) are the most energy intensive part of cellular network architecture and contribute up to 60 to 80% of total cellular power consumption and varies in response to the real traffic demand throughout the day and night. But, thelack of grid availability highlightsa potential barrier to telecom industry growth in Nepal. Nepal has approximately 5,222 telecom towers of which about 22% do operate on diesel generators (DGs) while the remaining by grid electricity with some shares of renewable energy technologies (RETs: solar and/or wind). Despite the large carbon imprint, the uncertainty in power availability has compelled telecom operators to use DGs to ensure continuous supply of power for the better network availability, which translates huge operating costs along with adverse environmental impact. So, it becomes an imperative solution for telecom operators to evaluate all alternatives in order to increase network reliability with reduced energy cost. This study report intentionally focus on current energy consumptionof such telecom towers and forecast thefuture energydemand with reference to growing subscriber trend up to 2025 using LEAP (Long Range Energy Alternative Planning System)withBusiness As Usual (BAU) scenario. A clean energy technology (CET) scenario with possible RET options is also developed and compared with base case scenario through some policy mechanics on behalf of environmental benefits and sustainable cellular communication. Furthermore, this study concludes a potential energy cum cost saving with RET adoption with basic cost economics analysis.
Design of the floating-type memristor emulator and its circuit implementationIJRES Journal
Memristor is a kind of nonlinear resistance with memory ability. The resistance of the memristor
changes depending on the charge quantity or the magnetic flux passing through it. As a basic two-terminal
device, the memristor should be connected with other electronic devices in any form and not limited to the
grounding-type. In this paper, a new memristor emulator is proposed based on HP memristor model and then a
floating-type memristor emulator is designed. Finally, the corroding physical circuits are built to verify the
correctness of the design.
Synergistic Effect of Halide Ions on the Corrosion Inhibition of Mild Steel i...IJRES Journal
The inhibition effect of alkyl substituted piperdin-4-one with thiosemicarbazones on mild steel
corrosion in 1N sulphuric acid solution was studied by weight loss method and electrochemical techniques. The
influence of halides viz., KCl, KBr and KI on the corrosion inhibition of thiosemicarbazones were also
investigated. Results show that alkyl substituted piperidin-4-one with thiosemicarbazones alone provided
satisfactory inhibition on the corrosion of mild steel and it was also found that the inhibition efficiency increased
synergistically in the presence of halide ions. The synergistic effect of halide ions was found to follow the order:
KI > KBr > KCl. The inhibitor reduced the corrosion rate through adsorption.
An Enhanced P2P Architecture for Dispersed Service DiscoveryIJRES Journal
Service discovery is a critical issue in Service Oriented Computing (SOC).Service discovery protocols used to detect and discover services offered by the nodes in the network. It must be scalable, reliable and robust service discovery mechanism. In traditional discovery mechanism uses decentralized service discovery approach named as chord4s.This method suffer from some problems such as scalability, node failure and efficient query routing. This paper addresses additional functionalities of chord4s protocol. In this paper data availability in chord4s protocol is improved by distributing functionally equivalent services to different successor nodes. If one node fails service consumer gets equivalent services from the other successor nodes. In this paper efficient query routing can be improved by getting multiple services with single query. Quality of service also improved by qos aware service discovery methods. Semantic information of services is integrated in order to increase flexibility, accuracy of service discovery.
Study and evaluation for different types of Sudanese crude oil propertiesIJRES Journal
Sudanese crude oil is regarded as one of the sweet types of crude in the world, Sulphur containing
compounds are un desirable in petroleum because they de activate the catalyst during the refining processes and
are the main source of acid rains and environmental pollution.(Mark Cullen 2001),Since it contains considerable
amount of salts and acids, it negatively impact the production facilities and transportation lines with corrosive
materials. However it suffers other problems in flow properties represented by the high viscosity and high
percentage of wax. Samples were collected after the initial and final treatment at CPF, and tested for
physical and chemical properties.wax content is in the range 23-31 weight % while asphalting content is about
0.1 weight% . Resin content is 13-7 weight % and deposits are 0.01 weight%. The carbon number distribution in
the crude is in the range 7-35 carbon atoms. The pour point vary between 39°C-42°C and the boiling point is in
the range 70 °C - 533 °C.
The implementation of BPJS health program At public health center martapura i...IJRES Journal
Improving the quality of health services at the primary level is very important to reduce the burden of services which will be covered hospital when the BPJS program applied. The aimed of this study is to describe the implementation of the program of BPJS in Public Health Center (PHC) Martapura. This study was a qualitative research with case study design. The informants are the head of PHC and manager program were taken by purposive sampling. Data were collected through interviews using in-depth interview guide. Result of this study was since the enactment BPJS January 1, 2014, Banjar Regency Health Office only once to disseminate ie in March 2014. This makes the health center to get the barriers in the field of the sustainability of the information obtained from the health department with the information captured on the official website BPJS. Another barriers was the disbursement claims that have not been implemented which should have been right to health centers for services provided. Support from the health department and BPJS needed to inform about the national health insurance program regularly to health centers so that health centers do not confusion in implementing the program.
Criterion of functional fullness in many-valued logicIJRES Journal
Using Slupecki’s criterion of functional fullness we give very simple proof of Jablonskij’s criterion. Then using
Jablonskij’s criterion we get criterion of minimal closed sets: a subset of functions of Pk ( k2 ) is full in k P , if
it contains a non-fictitious two-ary function taking all values and functions of minimal closed sets of some type.
The criterion is very useful. In particular, Slupecki’s criterion uses 27 functions, Jablonskij’s criterion uses 21
functions, the criterion of minimal closed sets uses 3 functions in 3-valued logic. The criteria use 255, 231, 6
functions in 4-valued logic respectively and 3125, 3005, 10 functions in 5-valued logic.
Interpreting Health Status Of Indian Population Using Phase Angle As Health P...IJRES Journal
Bio Electrical Impedance Analyser is a simple Non-Invasive tool that is used for the Human body composition Analysis. It has been found that the basic principle of Human Body composition Analysis is the measurement of fat vs lean muscle tissue. And it is well known fact that biological tissues the path of least resistance. While Analysing the body composition through Bio Electrical Impedance Analyser body resistance and body reactance are taken into account. Phase Angle is directly calculated from resistance and reactance and Phase Angle is an important indicator of cellular health and integrity. This paper aims at discussing the significance of Phase Angle in Analysis of Human Body Composition and developing and validating prediction equation of Phase Angle at different frequencies.
Comparison of the Performances of Two Commercial Membranes in Demineralizatio...IJRES Journal
In this work, comparison of the performances of two commercial membranes in demineralization of drinking water of M’rirt city (conductivity 2140 μS/cm) by nanofiltration in continuous mode was carried out. The pilot used (supplied by the French Company TIA, Techniques Industrilles Appliquées) is an industrial nanofiltration pilot plant having two modules equipped with various spiral commercial membranes with an area of 7.6 m2. Two configurations were tested: simple pass and supplied batch configuration. The water parameters were followed as a function of the running conditions (time, pressure) in order to follow the behaviour of the membranes tested.
PID Compensator Control Scheme of Synchronous Buck DC-DC Converter with ZVS L...IJRES Journal
This paper deals with PID compensator control of Synchronous Rectifier (SR) Buck Converter to improve its conversion efficiency under different load conditions with the help of a Zero Voltage Switching(ZVS)Logic Circuit. Since the freewheeling diode is replaced by a high frequency switch MOSFET in this buck configuration, the SR control technique itself will be sufficient under heavy load condition to attain better normal mode performance. However, this technique does not hold well in light load condition, due to increased switching losses. A newPID compensator control techniqueis introduced in the paper will enable synchronous buck converter to realize ZVS, while feeding light load. This is also cost effective and highly efficient simple control method without use of extra auxiliary switches and RLC components. This control technique also proved to be efficient under input voltage variations. Simulation is done for proving stabilization provided by the PID compensator with the help of ZVS logic circuit for synchronous rectifier (SR) buck converter in MATLAB Simulink.
A Case Study on Academic Services Application Using Agile Methodology for Mob...IJRES Journal
Recently, Mobile Cloud Computing reveals many modern development areas in the Information
Technology industry. Several software engineering frameworks and methodologies have been developed to
provide solutions for deploying cloud computing resources on mobile application development. Agile
methodology is one of the most commonly used methodologies in the field. This paper presents the MCCAS a
Web and Mobile application that provide feature for the Palestinian higher education/academic institutions. An
Agile methodology was used in the development of the MCCAS but in parallel with emphasis on Cloud
computing resources deployment. Also many related issues is discussed such as how software engineering
modern methodologies (advances) influenced the development process.
Status of Heavy metal pollution in Mithi river: Then and NowIJRES Journal
The Mithi River runs through the heart of suburban Mumbai. Its path of flow has been severely
damaged due to industrialization and urbanization. The quality of water has been deteriorating ever since. The
Municipal and industrial effluents are discharged in unchecked amounts. The municipal discharge comprises
untreated domestic and sewage wastes whereas the industries are majorly discharge chemicals and other toxic
effluents which are responsible in increasing the metal load of the river. In the current study, the water is
analysed for heavy metals- Copper, Cadmium, Chromium, Lead and Nickel. It also includes a brief
understanding on the fluctuations that have occurred in the heavy metal pollution, through the compilation of
studies carried out in the area previously.
Distillery Wastewater Decontamination by the Fenton Advanced Oxidation MethodIJRES Journal
This study evaluated the effect of Fenton advanced oxidation process on the treatment of an industrial wastewater (distillery). The comparison of the effects of Fe2+ loadings, H2O2 dosages (2%(v/v)and 4%(v/v)), reaction temperature and reaction time, established optimum efficiency in terms of BOD and COD reductions. The best operating conditions for the treatment of the distillery wastewater containing 43.85 mg/L BOD concentration and 274.28 mg/L COD concentration in the raw effluent was 2% H2O2 dosage at constant loadings of Fe2+ (1.5 g), 80 oC pretreatment temperature, and 1 h reaction time. At this optimized condition, the BOD content reduced to about 35 mg/L (about 21% removal) and COD content reduced to about 53 mg/L (about 81% removal). There was a complete removal of the initial colour present in the wastewater after the treatment process. The process proved the ability to effectively reduce the COD content which when high in industrial wastewaters can lead to serious impacts to the environment.
Automated airfield controller system for avoiding air crashes in runwayIJRES Journal
This work is an attempt to develop an advanced technology in airport control systems. As the existing system is manually operated, it is difficult to find solutions for some unexpected problems, for example: fire accident, ice, rain, fog and snow which may occur on the runway during the landing of the flight, which leads to air crashes in the runway . To take protective measures, introducing an automatic system to detect whether the runway is safe before landing the flight and this system also takes protective measures until the flight completely stops in the Airport. GPS (Global Positioning System) is used for inform the user to about exact location of the landing zone in the runway. Stepper motor is used as barrier system to control entry for vehicles and human. Zigbee transceiver is used as wireless communication protocol between aircraft and airfield controller system.
The Drill Geometry Influence on PCB Drilling PerformanceIJRES Journal
To adapt to the rapid development of PCBs, a high-property drill is desired. An applicable way is demonstrated by a design method based on analysis of drill structure, cutting force experiment , cutter wear observation to improve the drilling performance.Finally the drill wear is well improved by web thinning and chip dividing groove grinding.
Optimizing Shock Models In The Study Of Deteriorating SystemsIJRES Journal
This research is to make a detailed study of deteriorating systems using the shock model approach. Cumulative damage models in which the damages due to various shocks accumulate and the system failure is viewed as the first passage problem of the cumulative damage process past a threshold are analyzed. We consider the cumulative damage models in a totally different perspective by considering the optimal stopping in an accumulative damage model. The stopping rule is that the cumulative damage may surpass a prescribed threshold level only with a small probability but should approach the threshold as precise as possible. Finally we analyze shock models for which the system failure is based on the frequency of shocks rather than the cumulative damage caused by them. Numerical examples and discussions are provided to illustrate the results.
A numerical solution for Sine-Gordon type system was done by the use of two finite difference schemes, the first is the explicit scheme and the second is the Crank-Nicholson scheme. A comparison between the two schemes showed that the explicit scheme is easier and has faster convergence than the Crank-Nicholson scheme which is more accurate. The MATLAB environment was used for the numerical computations.
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An Improved Iterative Method for Solving General System of Equations via Gene...Zac Darcy
Various algorithms are known for solving linear system of equations. Iteration methods for solving the
large sparse linear systems are recommended. But in the case of general n× m matrices the classic
iterative algorithms are not applicable except for a few cases. The algorithm presented here is based on the
minimization of residual of solution and has some genetic characteristics which require using Genetic
Algorithms. Therefore, this algorithm is best applicable for construction of parallel algorithms. In this
paper, we describe a sequential version of proposed algorithm and present its theoretical analysis.
Moreover we show some numerical results of the sequential algorithm and supply an improved algorithm
and compare the two algorithms.
An Improved Iterative Method for Solving General System of Equations via Gene...Zac Darcy
Various algorithms are known for solving linear system of equations. Iteration methods for solving the
large sparse linear systems are recommended. But in the case of general n× m matrices the classic
iterative algorithms are not applicable except for a few cases. The algorithm presented here is based on the
minimization of residual of solution and has some genetic characteristics which require using Genetic
Algorithms. Therefore, this algorithm is best applicable for construction of parallel algorithms. In this
paper, we describe a sequential version of proposed algorithm and present its theoretical analysis.
Moreover we show some numerical results of the sequential algorithm and supply an improved algorithm
and compare the two algorithms.
Comparative Study of the Effect of Different Collocation Points on Legendre-C...IOSR Journals
We seek to explore the effects of three basic types of Collocation points namely points at zeros of Legendre polynomials, equally-spaced points with boundary points inclusive and equally-spaced points with boundary point non-inclusive. Established in literature is the fact that type of collocation point influences to a large extent the results produced via collocation method (using orthogonal polynomials as basis function). We
analyse the effect of these points on the accuracy of collocation method of solving second order BVP. For equally-spaced points we further consider the effect of including the boundary points as collocation points. Numerical results are presented to depict the effect of these points and the nature of problem that is best handled by each.
Third-kind Chebyshev Polynomials Vr(x) in Collocation Methods of Solving Boun...IOSR Journals
This paper proposed the use of third-kind Chebyshev polynomials as trial functions in solving boundary value problems via collocation method. In applying this method, two different collocation points are considered, which are points at zeros of third-kind Chebyshev polynomials and equally-spaced points. These points yielded different results on each considered problem, thus possessing different level of accuracy. The
method is computational very simple and attractive. Applications are equally demonstrated through numerical examples to illustrate the efficiency and simplicity of the approach
AN IMPROVED ITERATIVE METHOD FOR SOLVING GENERAL SYSTEM OF EQUATIONS VIA GENE...Zac Darcy
Various algorithms are known for solving linear system of equations. Iteration methods for solving the
large sparse linear systems are recommended. But in the case of general n× m matrices the classic
iterative algorithms are not applicable except for a few cases. The algorithm presented here is based on the
minimization of residual of solution and has some genetic characteristics which require using Genetic
Algorithms. Therefore, this algorithm is best applicable for construction of parallel algorithms. In this
paper, we describe a sequential version of proposed algorithm and present its theoretical analysis.
Moreover we show some numerical results of the sequential algorithm and supply an improved algorithm
and compare the two algorithms.
IOSR Journal of Electronics and Communication Engineering(IOSR-JECE) is an open access international journal that provides rapid publication (within a month) of articles in all areas of electronics and communication engineering and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications in electronics and communication engineering. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
Numerical Solutions of Second Order Boundary Value Problems by Galerkin Resid...iosrjce
IOSR Journal of Mathematics(IOSR-JM) is a double blind peer reviewed International Journal that provides rapid publication (within a month) of articles in all areas of mathemetics and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications in mathematics. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
International Journal of Engineering Research and Development (IJERD)IJERD Editor
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Numerical solution of oscillatory reaction–diffusion system of $\lambda-omega$ type was done by using two finite difference schemes . The first one is the explicit scheme and the second one is the implicit Crank– Nicholson scheme with averaging of f(u,v) and without averaging of f(u,v). The comparison showed that Crank–Nicholson scheme is better than explicit scheme and Crank–Nicholson scheme with averaging of f(u,v) is more accurate but it needs more time and double storage and double time steps than Crank–Nicholson scheme without averaging of f(u,v).
Illustration Clamor Echelon Evaluation via Prime Piece PsychotherapyIJMER
International Journal of Modern Engineering Research (IJMER) is Peer reviewed, online Journal. It serves as an international archival forum of scholarly research related to engineering and science education.
International Journal of Modern Engineering Research (IJMER) covers all the fields of engineering and science: Electrical Engineering, Mechanical Engineering, Civil Engineering, Chemical Engineering, Computer Engineering, Agricultural Engineering, Aerospace Engineering, Thermodynamics, Structural Engineering, Control Engineering, Robotics, Mechatronics, Fluid Mechanics, Nanotechnology, Simulators, Web-based Learning, Remote Laboratories, Engineering Design Methods, Education Research, Students' Satisfaction and Motivation, Global Projects, and Assessment…. And many more.
Similar to Nonlinear Algebraic Systems with Three Unknown Variables (20)
Exploratory study on the use of crushed cockle shell as partial sand replacem...IJRES Journal
The increasing demand for natural river sand supply for the use in construction industry along
with the issue of environmental problem posed by the dumping of cockle shell, a by-product from cockle
business have initiated research towards producing a more environmental friendly concrete. This research
explores the potential use of cockle shell as partial sand replacement in concrete production. Cockle shell used
in this experimental work were crushed to smaller size almost similar to sand before mixed in concrete. A total
of six concrete mixtures were prepared with varying the percentages of cockle shell viz. 0%, 5%, 10%, 15%,
20% and 25%. All the specimens were subjected to continuous water curing. The compressive strength test was
conducted at 28 days in accordance to BS EN 12390. Finding shows that integration of suitable content of
crushed cockle shell of 10% as partial sand replacement able to enhance the compressive strength of concrete.
Adopting crushed cockle shell as partial sand replacement in concrete would reduce natural river sand
consumption as well as reducing the amount of cockle shell disposed as waste.
Congenital Malaria: Correlation of Umbilical Cord Plasmodium falciparum Paras...IJRES Journal
The vertical (trans-placental) transmission of the parasite Plasmodium falciparum from
pregnant mother to fetus during gestational period was investigated in a clinical research involving 43 full term
pregnant women in selected Hospitals in Jimeta Yola, Adamawa State Nigeria. During the observational study,
parasitemia was determined by light microscopic examination of umbilical and maternal peripheral blood film
for the presence of the trophozoites of Plasmodium falciparum. Correlational analysis was then carried on the
result obtained at p<0.05.><0.05) was established between maternal peripheral blood and umbilical cord
blood parasitemia with Pearson’s correlation coefficient of 0.762. Thus, in a malaria endemic area like Yola,
Adamawa State, Nigeria, with a stable transmission of parasite, there is a high probability of vertical
transmission of Plasmodium falciparum parasite from mother to fetus during gestation that can be followed by
the presentation of the symptoms of malaria by the newborn and other malaria related complications. Families
are advised to consistently sleep under appropriately treated insecticide mosquito net to avoid mosquito bite and
subsequent infestation.
Review: Nonlinear Techniques for Analysis of Heart Rate VariabilityIJRES Journal
Heart rate variability (HRV) is a measure of the balance between sympathetic mediators of heart
rate that is the effect of epinephrine and norepinephrine released from sympathetic nerve fibres acting on the
sino-atrial and atrio-ventricular nodes which increase the rate of cardiac contraction and facilitate conduction at
the atrio-ventricular node and parasympathetic mediators of heart rate that is the influence of acetylcholine
released by the parasympathetic nerve fibres acting on the sino-atrial and atrio-ventricular nodes leading to a
decrease in the heart rate and a slowing of conduction at the atrio-ventricular node. Sympathetic mediators
appear to exert their influence over longer time periods and are reflected in the low frequency power(LFP) of
the HRV spectrum (between 0.04Hz and 0.15 Hz).Vagal mediators exert their influence more quickly on the
heart and principally affect the high frequency power (HFP) of the HRV spectrum (between 0.15Hz and 0.4
Hz). Thus at any point in time the LFP:HFP ratio is a proxy for the sympatho- vagal balance. Thus HRV is a
valuable tool to investigate the sympathetic and parasympathetic function of the autonomic nervous system.
Study of HRV enhance our understanding of physiological phenomenon, the actions of medications and disease
mechanisms but large scale prospective studies are needed to determine the sensitivity, specificity and predictive
values of heart rate variability regarding death or morbidity in cardiac and non-cardiac patients. This paper
presents the linear and nonlinear to analysis the HRV.
Dynamic Modeling for Gas Phase Propylene Copolymerization in a Fluidized Bed ...IJRES Journal
A two-phase model is proposed for describing the dynamics of a fluidized bed reactor used for
polypropylene production. In the proposed model, the fluidized bed is divided into an emulsion and bubble
phase where the flow of gas is considered to be plug flow through the bubbles and perfectly mixed through the
emulsion phase. Similar previous models, consider the reaction in the emulsion phase only. In this work the
contribution of reaction in the bubble phase is considered and its effect on the overall polypropylene production
is investigated the kinetic model is combined with hydrodynamic model in order to develop a comprehensive
model for gas-phase propylene copolymerization reactor. Simulation profiles of the proposed model were
compared with those of well mixed model for the emulsion phase temperature. The simulated temperature
profile showed a lower rate of change compared to the previously reported models due to lower polymerization
rate. Model simulation showed that about 13% of the produced polymer comes from the bubble phase and this
considerable amount of polymerization in the bubbles should not be neglected in any modeling attempt.
A Short Report on Different Wavelets and Their StructuresIJRES Journal
This article consists of basics of wavelet analysis required for understanding of and use of wavelet
theory. In this article we briefly discuss about HAAR wavelet transform their space and structures.
Wear Analysis on Cylindrical Cam with Flexible RodIJRES Journal
Firstly, the kinetic equation of spatial cylindrical cam with flexible rod has been established. Then, an
accurate cylindrical cam mechanism model has been established based on the spatial modeling software
Solidworks. The dynamic effect of flexible rod on mechanical system was studied in detail based on the
mechanical system dynamics analytical software Adams, and Archard wear model is used to predict the wear of
the cam. We used Ansys to create finite element model of the cam link, extracted the first five order mode to
export into Adams. The simulation results show that the dynamic characteristics of spatial cylindrical cam
mechanical system with flexible rod is closed to ideal mechanism. During the cam rotate one cycle, the collision
in the linkage with a clearance occurs in some special location, others still keep a continuous contact, and the
prediction of wear loss is smaller than rigid body.
DDOS Attacks-A Stealthy Way of Implementation and DetectionIJRES Journal
Cloud Computing is a new paradigm provides various host service [paas, saas, Iaas over the internet.
According to a self-service,on-demand and pay as you use business model,the customers will obtain the cloud
resources and services.It is a virtual shared service.Cloud Computing has three basic abstraction layers System
layer(Virtual Machine abstraction of a server),Platform layer(A virtualized operating system, database and
webserver of a server and Application layer(It includes Web Applications).Denial of Service attack is an attempt
to make a machine or network resource unavailable to the intended user. In DOS a user or organization is
deprived of the services of a resource they would normally expect to have.A Successful DOS attack is a highly
noticeable event impacting the entire online user base.DOS attack is found by First Mathematical Metrical
Method (Rate Controlling,Timing Window,Worst Case and Pattern Matching)DOS attack not only affect the
Quality of the service and also affect the performance of the server. DDOS attacks are launched from Botnet-A
large Cluster of Connected device(cellphone,pc or router) infected with malware that allow remote control by an
attacker. Intruder using SIPDAS in DDOS to perform attack.SIPDAS attack strategies are detected using Heap
Space Monitoring Algorithm.
An improved fading Kalman filter in the application of BDS dynamic positioningIJRES Journal
Aiming at the poor dynamic performance and low navigation precision of traditional fading
Kalman filter in BDS dynamic positioning, an improved fading Kalman filter based on fading factor vector is
proposed. The fading factor is extended to a fading factor vector, and each element of the vector corresponds to
each state component. Based on the difference between the actual observed quantity and the predicted one, the
value of the vector is changed automatically. The memory length of different channel is changed in real time
according to the dynamic property of the corresponding state component. The actual observation data of BDS is
used to test the algorithm. The experimental results show that compared with the traditional fading Kalman filter
and the method of the third references, the positioning precision of the algorithm is improved by 46.3% and
23.6% respectively.
Positioning Error Analysis and Compensation of Differential Precision WorkbenchIJRES Journal
Positioning error is a widely problem exists in mechanism, the important factors affecting machining
precision. In order to reduce the error caused by positioning problem processing, based on the differential
workbench as the research object, using the method of theoretical analysis and experimental verification, the
analysis of positioning error mechanism and source of complete differential precision workbench error
compensation, improve the accuracy of the device, provides a method for the application of modern machine
tools. table.
The Low-Temperature Radiant Floor Heating System Design and Experimental Stud...IJRES Journal
In order to analyze the temperature distribution of the low-temperature radiant floor heating system
that uses the condensing wall-hung boiler as the heat source, the heating system is designed according to a typical
house facing south in Shanghai. The experiments are carried out to study the effects of the supply water
temperature on the thermal comfort of the system. Eventually, the supply water temperature that makes people in
the room feel more comfortable is obtained. The result shows that in the condition of that the outside temperature
is 8~15℃ and the relative humidity is 30~70%RH, the temperature distribution in the room is from high to low
when the height is from bottom to top. The floor surface temperature is highest, but its uniformity is very poor.
When the heating system reaches the steady state, the air temperature of the room is uniform. When the supply
water temperature is 63℃ The room is relatively comfortable at the above experimental condition.
Experimental study on critical closing pressure of mudstone fractured reservoirsIJRES Journal
In the process of oil and gas exploitation of mudstone-fractured reservoir in Daqing oilfield, the
permeability of fracture is easily affected by the influence of stress change, which is shown by the sensitivity of
the permeability to the stress. With the extension of time mining in the fractured mudstone reservoir, fracture
stress sensitivity is obvious in vast decline of production and great influence on reduced yields. In order to
reasonably determine the way of developing method, working system and the exploitation rate of the reservoir,
correspondingly protecting reservoir productivity, improve ultimate recovery. On the basis of the previous
research on the stress sensitivity of fractured mudstone, this essay studied the critical closing pressure of the
simulated underground fractured mudstone under the laboratory condition.
Correlation Analysis of Tool Wear and Cutting Sound SignalIJRES Journal
With the classic signal analysis and processing method, the cutting of the audio signal in time
domain and frequency domain analysis. We reached the following conclusions: in the time domain analysis,
cutting audio signals mean and the variance associated with tool wear state change occurred did not change
significantly, and tool wear is not high degree of correlation, and the mean-square value of the audio signal
changes in the size and tool wear the state has a good relationship.
Reduce Resources for Privacy in Mobile Cloud Computing Using Blowfish and DSA...IJRES Journal
Mobile cloud computing in light of the increasing popularity among users of mobile smart
technology which is the next indispensable that enables users to take advantage of the storage cloud computing
services. However, mobile cloud computing, the migration of information on the cloud is reliable their privacy
and security issues. Moreover, mobile cloud computing has limitations in resources such as power energy,
processor, Memory and storage. In this paper, we propose a solution to the problem of privacy with saving and
reducing resources power energy, processor and Memory. This is done through data encryption in the mobile
cloud computing by symmetric algorithm and sent to the private cloud and then the data is encrypted again and
sent to the public cloud through Asymmetric algorithm. The experimental results showed after a comparison
between encryption algorithms less time and less time to decryption are as follows: Blowfish algorithm for
symmetric and the DSA algorithm for Asymmetric. The analysis results showed a significant improvement in
reducing the resources in the period of time and power energy consumption and processor.
Resistance of Dryland Rice to Stem Borer (Scirpophaga incertulas Wlk.) Using ...IJRES Journal
Rice stem borer is one of the important pests that attack plants so as to reduce production. One way
to control pests is to use organic fertilizers that make the plant stronger and healthier. This study was conducted
to determine the effects of organic fertilizers with various doses without the use of pesticides in controlling stem
borer, Scirpophaga incertulas. Methods using split-split plot design which consists of two levels of the whole
plot factor (solid and liquid organic fertilizers), two levels of the subplot factor (conventional and industry,
Tiens and Mitraflora), and four levels of the sub-subplot factor of conventional and industry (5, 10, 15, 20
tonnes/ha), and one level of the sub-subplot factor of Tiens and Mitraflora (each 2 ml/l). Based on the results
Statistical analysis there were no significant differences among treatments and this shows that the use of organic
fertilizers that only a dose of 5 tonnes/ha is sufficient available nutrients that make plants more robust and
resistant to control stem borer, besides that can reduce production costs and friendly to the environment when
compared with using inorganic fertilizers.
A novel high-precision curvature-compensated CMOS bandgap reference without u...IJRES Journal
A novel high-precision curvature-compensated bandgap reference (BGR) without using op-amp
is presented in this paper. It is based on second-order curvature correction principle, which is a weighted sum of
two voltage curves which have opposite curvature characteristic. One voltage curve is achieved by first-order
curvature-compensated bandgap reference (FCBGR) without using op-amp and the other found by using W
function is achieved by utilizing a positive temperature coefficient (TC) exponential current and a linear
negative TC current to flow a linear resistor. The exponential current is gained by using anegative TC voltage to
control a MOSFET in sub-threshold region. In the temperature ranging from -40℃ to 125℃, experimental
results implemented with SMIC 0.18μm CMOS process demonstrate that the presented BGR can achieve a TC
as low as 2.2 ppm/℃ and power-supply rejection ratio(PSRR)is -69 dB without any filtering capacitor at 2.0 V.
While the range of the supply voltage is from 1.7 to 3.0 V, the output voltage line regulation is about1 mV/ V
and the maximum TC is 3.4 ppm/℃.
Structural aspect on carbon dioxide capture in nanotubesIJRES Journal
In this work we reported the carbon dioxide adsorption (CO2) in six different nanostructures in order
to investigate the capturing capacity of the materials at nanoscale. Here we have considered the three different
nanotubes including zinc oxide nanotube (ZnONT), silicon carbide nanotube (SiCNT) and single walled carbon
nanotube (SWCNT). Three different chiralities such as zigzag (9,0), armchair (5,5) and chiral (6,4) having
approximately same diameter are analyzed. The adsorption binding energy values under various cases are
estimated with density functional theory (DFT). We observed CO2 molecule chemisorbed on ZnONT and
SiCNT’s whereas the physisorption is predominant in CNT. To investigate the structural aspect, the tubes with
defects are studied and compared with defect free tubes. We have also analyzed the electrical properties of tubes
from HOMO, LUMO energies. Our results reveal the defected structure enhance the CO2 capture and is
predicted to be a potential candidate for environmental applications.
Thesummaryabout fuzzy control parameters selected based on brake driver inten...IJRES Journal
In this paper, the brake driving intention identification parameters based on the fuzzy control are
summarized and analyzed, the necessary parameters based on the fuzzy control of the brake driving intention
recognition are found out, and I pointed out the commonly corrupt parameters, and through the relevant
parameters , I establish the corresponding driving intention model.
An understanding of the electronic bipolar resistance switching behavior in C...IJRES Journal
In this study, TiO2 films and devices were prepared by sol-gel method. The bipolar resistive switching
phenomena was observed in the Cu/TiO2/ITO device. The conduction mechanism of devices were analyzed. It was
found that the conduction mechanism is dominated by space charge limited current in high resistance state, and
Schottky emission in low resistance state.
A fast and effective impulse noise filterIJRES Journal
In order to eliminate the high density salt and pepper noise effectively in the image, this paper
proposes a new algorithm that can eliminate the noise .Other similar algorithms need to adjust the filtering
window in the image which is polluted by different concentration of noise constantly. The proposed algorithm
use the fixed small scale of filtering window only, at the same time of filter, it can reserve the detail of the image
features well. The proposed algorithm extracted the noise points from the contaminated image firstly, according
to the relationship between the gray value of signal points and noise points, then determine which is the real
noise. The experimental results show us that the proposed algorithm achieved satisfactory result in filter out
noise, especially in the treatment of the images that have high levels of noise pollution, and it is better than
other algorithm.
Immunizing Image Classifiers Against Localized Adversary Attacksgerogepatton
This paper addresses the vulnerability of deep learning models, particularly convolutional neural networks
(CNN)s, to adversarial attacks and presents a proactive training technique designed to counter them. We
introduce a novel volumization algorithm, which transforms 2D images into 3D volumetric representations.
When combined with 3D convolution and deep curriculum learning optimization (CLO), itsignificantly improves
the immunity of models against localized universal attacks by up to 40%. We evaluate our proposed approach
using contemporary CNN architectures and the modified Canadian Institute for Advanced Research (CIFAR-10
and CIFAR-100) and ImageNet Large Scale Visual Recognition Challenge (ILSVRC12) datasets, showcasing
accuracy improvements over previous techniques. The results indicate that the combination of the volumetric
input and curriculum learning holds significant promise for mitigating adversarial attacks without necessitating
adversary training.
Automobile Management System Project Report.pdfKamal Acharya
The proposed project is developed to manage the automobile in the automobile dealer company. The main module in this project is login, automobile management, customer management, sales, complaints and reports. The first module is the login. The automobile showroom owner should login to the project for usage. The username and password are verified and if it is correct, next form opens. If the username and password are not correct, it shows the error message.
When a customer search for a automobile, if the automobile is available, they will be taken to a page that shows the details of the automobile including automobile name, automobile ID, quantity, price etc. “Automobile Management System” is useful for maintaining automobiles, customers effectively and hence helps for establishing good relation between customer and automobile organization. It contains various customized modules for effectively maintaining automobiles and stock information accurately and safely.
When the automobile is sold to the customer, stock will be reduced automatically. When a new purchase is made, stock will be increased automatically. While selecting automobiles for sale, the proposed software will automatically check for total number of available stock of that particular item, if the total stock of that particular item is less than 5, software will notify the user to purchase the particular item.
Also when the user tries to sale items which are not in stock, the system will prompt the user that the stock is not enough. Customers of this system can search for a automobile; can purchase a automobile easily by selecting fast. On the other hand the stock of automobiles can be maintained perfectly by the automobile shop manager overcoming the drawbacks of existing system.
Explore the innovative world of trenchless pipe repair with our comprehensive guide, "The Benefits and Techniques of Trenchless Pipe Repair." This document delves into the modern methods of repairing underground pipes without the need for extensive excavation, highlighting the numerous advantages and the latest techniques used in the industry.
Learn about the cost savings, reduced environmental impact, and minimal disruption associated with trenchless technology. Discover detailed explanations of popular techniques such as pipe bursting, cured-in-place pipe (CIPP) lining, and directional drilling. Understand how these methods can be applied to various types of infrastructure, from residential plumbing to large-scale municipal systems.
Ideal for homeowners, contractors, engineers, and anyone interested in modern plumbing solutions, this guide provides valuable insights into why trenchless pipe repair is becoming the preferred choice for pipe rehabilitation. Stay informed about the latest advancements and best practices in the field.
Industrial Training at Shahjalal Fertilizer Company Limited (SFCL)MdTanvirMahtab2
This presentation is about the working procedure of Shahjalal Fertilizer Company Limited (SFCL). A Govt. owned Company of Bangladesh Chemical Industries Corporation under Ministry of Industries.
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.
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.
Welcome to WIPAC Monthly the magazine brought to you by the LinkedIn Group Water Industry Process Automation & Control.
In this month's edition, along with this month's industry news to celebrate the 13 years since the group was created we have articles including
A case study of the used of Advanced Process Control at the Wastewater Treatment works at Lleida in Spain
A look back on an article on smart wastewater networks in order to see how the industry has measured up in the interim around the adoption of Digital Transformation in the Water Industry.
Quality defects in TMT Bars, Possible causes and Potential Solutions.PrashantGoswami42
Maintaining high-quality standards in the production of TMT bars is crucial for ensuring structural integrity in construction. Addressing common defects through careful monitoring, standardized processes, and advanced technology can significantly improve the quality of TMT bars. Continuous training and adherence to quality control measures will also play a pivotal role in minimizing these defects.
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Overview of the fundamental roles in Hydropower generation and the components involved in wider Electrical Engineering.
This paper presents the design and construction of hydroelectric dams from the hydrologist’s survey of the valley before construction, all aspects and involved disciplines, fluid dynamics, structural engineering, generation and mains frequency regulation to the very transmission of power through the network in the United Kingdom.
Author: Robbie Edward Sayers
Collaborators and co editors: Charlie Sims and Connor Healey.
(C) 2024 Robbie E. Sayers
Forklift Classes Overview by Intella PartsIntella Parts
Discover the different forklift classes and their specific applications. Learn how to choose the right forklift for your needs to ensure safety, efficiency, and compliance in your operations.
For more technical information, visit our website https://intellaparts.com
Nonlinear Algebraic Systems with Three Unknown Variables
1. International Journal of Research in Engineering and Science (IJRES)
ISSN (Online): 2320-9364, ISSN (Print): 2320-9356
www.ijres.org Volume 2 Issue 6 ǁ June. 2014 ǁ PP.54-59
www.ijres.org 54 | Page
Nonlinear Algebraic Systems with Three Unknown Variables
R. M. Dzhabarzadeh
Institute Mathematics and Mechanics of NAN Azerbaijan
ABSTRACT: Work is devoted to the study of nonlinear algebraic systems with three unknowns and is a
continuation of the author's research in this area. Previously, for nonlinear algebraic of system of equations
was built analog determinant of Kramer and it is given a necessary and sufficient condition for the existence of
solutions of nonlinear algebraic systems with a complex dependence on the variables. For two-parameter
systems in the abstract case, it is obtained the results to determine the conditions for finding the number of
solutions.
In this paper describes the method of determining the conditions on the coefficients of algebraic systems to
establish the number of solutions of the algebraic system of equations, when an unknowns part in the system as
polynomials in any finite degree. This method can be applied to other algebraic systems with more than
three unknown variables.
Keywords: eigen and associated vectors, finite dimensional space, multiparameter system of operators,
nonlinear algebraic system of equations, Resultant-operator for two pencils
I. Introduction
The technique, developed by the author allowed constructing the spectral theory of non-selfadjoint
multiparameter system of operators, linear and nonlinear depending on parameter in Hilbert spaces. Considered
in this paper the nonlinear algebraic system of equations is a special case multiparameter system when operators
are numbers in Hilbert space .R Naturally, that in case of the algebraic systems the got results can be deeper,
and methodology less difficult. The proof uses the notion of resultant of two polynomial pencils
Let be the nonlinear algebraic system with three unknown variables.
0......),,( 11
1
111
1
1 ,10 zayayaxaxaazyxa nm
n
nmm
m
m
i
0.........),,( 2
22222
2
222
2
2 1110
r
rnmnm
n
nmm
m
m zbzbybybxbxbbzyxb i
(1)
0.........),,( 3
33333
3
333
3
3 1110
r
rnmnm
n
nmm
m
m zczcycycxcxcczyxc
In [1,2] for nonlinear algebraic systems with any finite number of unknown variables is given way of
constructing an analogue of the determinant of Cramer, in particular, proved: if the continuant of this Cramer
i
s
determinant is not equal to zero, then the algebraic system has a solution.
In addition [3,4,5], for systems of nonlinear algebraic equations with polynomial dependence on two variables
under certain conditions it is defined the number of solutions.
Give some of well-known definitions and concepts necessary for understanding the subsequent presentation.
For two polynomials is introduced the concept of Resultant as follows. Let
1
1 0
1
1 0
( ), ( ); ( ) ... , 0;
( ) ... , 0;
n n
n n n
m m
m m m
f x g x f x a x a x a a
g x b x b x b b
be two polynomials. Resultant of these polynomials is the operator acting in the space
n m
R
or
n m
C
(probably, in some expansion of a field).
2. Nonlinear algebraic systems with three unknown variables
www.ijres.org 55 | Page
Re ( , )s f g
1 1 0
2 1 0
1 0
1 3 2 1 0
4 3 2 1 0
1 1 0
... 0 ... ... 0 0
0 ... ... ... 0 0
. . ... . . . ... ... . .
. . ... . . . ... ... . .
0 0 ... 0 0 ... ...
... ... 0 0
0 ... ... 0 0
. ... . . . . ... . .
. ... . . . . ... . .
0 0 0 0 ...
n n
n
n
m m
m
m m
a a a a
a a a a
a a a
b b b b b b
b b b b b b
b b b b
In a matrix ),(Re gfs the number of lines with coefficients ia to equally leading degree of unknown x of
a polynomial )(xg , that is m, the number of lines of a matrices with numbers ib coincides with the leading
degree of unknown x of a polynomial )(xf , that is n. Continuant of this Resultant is a polynomial from
coefficients and equal to zero then and only then when polynomials also have a common roots (probably, in
some expansion of a field).
The continuant of Resultant can be discovered as a continuant of Sylvester Matrix. Sylvester matrix,
allowing calculating continuant of Resultant of two polynomials, is opened by English mathematician James
Sylvester.
For a separable polynomial (in particular, for fields of performance zero) this continuant is equal to product of
values of one of polynomials on radicals of another (as before, product undertakes in view of a multiplicity of
radicals):
The study of such nonlinear algebraic system (1) of equations is spent with help following result from [3]:
let the n bundles depending on the same parameter
niBBBB ik
k
iii i
i
,...,2,1,...)( ,,1,0
)(i
B - operational bundles acting in a finite dimensional Hilbert space i
H correspondingly. Suppose that
n
kkk ...21
. In the space
21 kk
H
(the direct sum of 21
kk tensor product
n
HHH ...1
of spaces n
HHH ,...,, 21
) are introduced the operators
)1,...,1( niRi
with the help of operational matrices (3.12)
Let )(i
B be the operational bundles acting in a finite dimensional Hilbert space i
H , correspondingly.
Without loss ofcopies with
ikii
ikii
ikii
k
kk
k
i
i
i
i
BBB
BBB
BBB
BBB
BBBB
BBB
R
,,1,0
,,1,0
,,1,0
1,1,11,0
1,1.11,11,0
1,1,11,0
1
00
00
0.0
00
00
0
1
11
1
, .,...,2 ni
3. Nonlinear algebraic systems with three unknown variables
www.ijres.org 56 | Page
The number of lines with operators 11 ,...,1,0, ksBs in the matrix 1iR is equal to 2k and the number of
lines with operators isi ksB ,...,1,0, is equal to .1k We designate )( ip
B the set of eigen values
of an operator )(i
B .From [3] we have the result:
Theorem 1.
))((
1
ip
n
i
B then and only then when }).{(, 1
1
1
ki
n
i
KerBKerR
In particular, in [5] the two-parameter system operators
0)......(),( 11`
1
11
1
110
xAAAAAxA nm
n
mm
m
0)......(),( 22`
2
22
2
110
yBBBBByB nm
n
mm
m
(2)
is studied in tensor product 21
HH of finite-dimensional spaces 1
H and 2
H .
Dimension of space H is the product of dimensions of spaces 1
H and 2
H . In (2) linear operators
),...,1,0( 11
nmiAi
act in finite-dimensional space 1
H ; and linear operators
),...,1,0( 22
nmiBi
act in finite-dimensional space 2
H .
If 2121
HHff and 2121
HHgg then inner product of these elements in space
21
HH is defined by means of the formulae
2121
),(,],[ 21112121 HHHH
gggfggff
This definition is spread to other elements of tensor product spaces on linearity.
Let's reduce a series of known positions concerning the spectral theory of multiparameter system.
Definition1. [7]
2
),( C is an eigen value of the system (2) if there are nonzero elements
1 2,x H y H such that (2) is fulfilled. A tensor yxz is named an eigenvector of system (2).
Definition2. [7]. An operator 2
EAA kk
(accordingly, kk
BEB
1
) where 1
E (accordingly,
2
E ) is identical operators in 1
H (accordingly, 2
H ), names operator, induced in 21
HHH by
operators k
A (accordingly, k
B ).
Definition3.[8] A tensor
21 ,mm
z name 21
,mm - the associated vector to an eigenvector yxz 0,0
if following conditions are satisfied
21
21
),(
!!
1
0
21
rr
rr
kr
A
rrii
02211 ,
rkrk
z
21
21
),(
!!
1
,0
21
rr
rr
kr
A
rri
02211 ,
rkrk
z
.2,1;2,1; simk ss
21
,kk is arrangement from set of the whole nonnegative numbers on 2 with possible recurring and zero.
By means of the approach stated in [5,6], we can establish completeness, multiple completeness of
system of eigen and associated vectors, a possibility of multiple expansions on system of eigen and associated
vectors of multiparameter system (2).
4. Nonlinear algebraic systems with three unknown variables
www.ijres.org 57 | Page
Theorem2. Let operators ),...,1,0( 11
nmiAi
also ),...,1,0( 22
nmiBi
act in finite-
dimensional spaces 1
H and 2
H , accordingly, and one of three following conditions is fulfilled:
a) 211221
),max( nmnmnm , 221
, nmm
KerBKerA ;
221
, nmm
BA
are self -
conjugate operators everyone in their space
b) 121221
),max( nmnmnm , 112
, nmm
KerAKerB
111
, mnm BA - self-conjugate operators, acting in their spaces
c) 1221
nmnm , ))1(( 1
2
2
11
211
11
2
1
n
m
n
nm
nnn
nm
n
m BABAKer ,
221121
,,, nmnmmm
BABA
are
the self-conjugate operators, acting everyone in finite-dimensional space, correspondingly.
Then the ),max( 1221
nmnm -fold base on system of eigen and associated vectors of (2) takes place.
At the study of the system (1) we will be used essentially the results from [5,6].:
In (1) we fix variables yx, . Let 00 , yyxx be. Then the system (1) contains three polynomials
depending on one variable .z Using the result of the theorem2, we build operators 1R и 2R .They are the
Resultant- operators of polynomials ),,( 00 zyxa and ),,( 00 zyxb , and also polynomials
),,( 00 zyxa and ),,( 00 zyxc , correspondingly.
Introduce the notations:
1
111
1
1
......),(~
,10
n
nmm
m
m yayaxaxaayxa i
2
222
2
2
......),(
~
110
n
nmm
m
m ybybxbxbbyxb i
(3)
3
333
3
3
......),(~
110
n
nmm
m
m ycycxcxccyxc
For the polynomials ),,( 00 zyxa and ),,( 00 zyxb Resultant 1R has a form
2222222
11
11
11
...),(
~
),(~......
.......
0...),(~0
.....),(~
)},,(),,,({
2100
100
100
100
00001
rnmnmnm
nm
nm
nm
bbbyxb
ayxa
ayxa
ayxa
zyxbzyxaRR
(4)
In the matrices of the operator 1R the number of lines with 100 11
),,(~
nmayxa equal to 2r and the
number of lines with 22222
,...,),,(
~
100 rnmnm bbyxb is equal to1.
By analogy operator 2R in the space
13 r
R is determined with the help of matrices
3333333
11
11
11
...),(~
),(~......
.......
0...),(~0
.....),(~
)},,(),,,({
2100
1000
1000
1000
00002
rnmnmnm
nm
nm
nm
cccyxc
ayxa
ayxa
ayxa
zyxczyxaRR (5)
5. Nonlinear algebraic systems with three unknown variables
www.ijres.org 58 | Page
Continuants of Resultants 1R and 2R are equal to zero if and only if matrices of operators 1R and 2R have
nonzero kernels.
So at the expansion of continuants of Resultants 1R and 2R we obtain very bulky forms, in obtained equationswe
will operate with the leading degrees of variables in 1R and 2R . Further we will work only with the members
having the leading degrees. We can write the expansions of continuants of Resultants 1R and 2R in the forms:
2
22
2
11
2
2
2
11
21
222
2
11
21
222
2
010100 ............ r
nm
r
nm
m
m
r
nm
rn
rnm
r
nm
rm
rnm
r
m ybaxbaybaxba (6)
3
33
3
11
3
3
3
11
31
333
3
11
31
333
3
010100 ............ r
nm
r
nm
m
m
r
nm
rn
rnm
r
nm
rm
rnm
r
m ycaxcaycaxca (7)
(6) is the expansion of the continuant of the Resultant of the polynomials ),,( 00 zyxa and
),,( 00 zyxb from (1),when 0xx and 0yy .
Expression (7) is the expansion of the continuant of the Resultant –operator of polynomials ),,( 00 zyxa
and ).,,( 00 zyxc
If the couple of numbles( 1x , 1y ) turns expression (6) to zero, then from the definition of Resultant follows that
at these meanings of variables 1xx and 1yy 0),,( 1 zyxa and 0),,( 1 zyxb .Thus the
first and second equations from (1) have the common decision ).,( 111 yxz
If the couple ( 2x , 2y ) turns (7) to zero, then from the definition of Resultant follows that at these meanings of
variables 2xx and 2yy we have 0),,( 2 zyxa and 0),,( 2 zyxc .Thus the first and
third equations from (1) have the common decision ).,( 221 yxz
Now we consider the system
: 0............ 2
22
2
11
2
2
2
11
21
222
2
11
21
222
2
11
n
nm
r
nm
m
m
r
nm
rn
rnm
r
nm
rm
rnm
r
m ybaxbaybaxba
0............ 3
33
3
11
3
3
3
11
31
333
3
11
31
333
3
11
n
nm
r
nm
m
m
r
nm
rn
rnm
r
nm
rm
rnm
r
m ycaxcaycaxca , (8)
For any solution ),( yx of the system (8) the common solution of 0),,( 1 zyxa и
0),,( 1 zyxb denote ),(1 yxz and the common solution of 0),,( 2 zyxa and
0),,( 2 zyxc denote ),(2 yxz . So variable z enter the equation 0),,( zyxa linearly we
have ),(1 yxz = ),(2 yxz = ),( yxz . Consequently, any solution ),( yx of (8) corresponds to only one
solution ),,( zyx of the system (1), i.e. the number of solutions of (1) equals the number of solutions of a
nonlinear algebraic system (8) with two unknowns.
System (8) is a special case of (2), studied by the author in [5]. In (8) the real numbers
),...,2,1;,...,2,1;1,...,2,1(,, 33322211 rnmkrnmjnmicba kji are operators in
the space R , variables yx, act as parameters, the eigenvectors of the system (8) is constant
Let 331221331;221 ,,, nrnnrnmrmmrm be then the system (8) is written in the form
0...... 21
222
2
11
21
222
2
1
rn
rnm
r
nm
rm
rnm
r
m ybaxba
0...... 31
333
3
11
31
333
3
1
rn
rnm
r
nm
rm
rnm
r
m ycaxca (9)
Theorem3. Suppose the following conditions satisfy:
6. Nonlinear algebraic systems with three unknown variables
www.ijres.org 59 | Page
1) 331221331;221 ,,, nrnnrnmrmmrm (10)
2) 0)()()1()()( 31
333
3
1
31
222
2
11
21
2
121
33311
331
222
3
1
rn
rnm
r
m
rn
rnm
r
nm
rrnrn
rnmnm
rrn
rnm
r
m cabacaba
Then the system (1) has 2111 rrnm solutions.
Using this approach, we can consider different cases ( for example: ,, 331;221 mrmmrm
331221 , nrnnrn and so on)
II. Conclusion
This paper presents a method of determining the number of solutions of nonlinear algebraic equations.
Partiсularly, it is considered the nonlinear algebraic system of equations with three unknowns.
Since the proof of Theorem 3 we are faced with an unwieldy calculations we restrict ourselves to a
single nonlinear algebraic system.
. If necessary, this method will allow to reader to determine the number of solutions of the interested algebraic
system.
References
Theses:
[1] Dzhabarzadeh R.M. Materials of International conferences:”The theory of functions and problems of a Fourier analysis”,
devoted to 100 years anniversary of acad. I.I.Ibragimov, pp.92-94, Baku-2012. Not linear algebraic systems and analogs of
continuants of Cramer.
Chapters in Books:
[2] Dzhabarzadeh R.M. Multiparameter spectral theory. Lambert Academic Publishing, 2012, p. 184 (on Russian) ,pp.78-81
Theses:
[3] Dzhabarzadeh R.M. Baku International Topology conference, 3-9 оct., 1987, Теz. 2, Baku, 1987, p.93 On existence of
common eigen value of some operator-bundles, that depends polynomial on parameter.
Proceedings Papers:
[4] Dzhabarzadeh R.M. , Salmanova G.H. American Journal of Mathematics and Mathematical Sciences.-2012, vol.1, №1, pp.32-
37, 2013 Multiparameter system of operators, not linearly depending on parameters.
Proceedings Papers:
[5] Dzhabarzadeh R.M. Pure and Applied Mathematics Journal, vol. 2, No. 1, pp. 32-37, 2013 About solutions of nonlinear algebraic
system with two variables.
Chapters in Books:
[6] Dzhabarzadeh R.M. Nonlinear algebraic system of equations. Lambert Academic Publishing, 2013, p. 101 (on Russian), pp.80-
92.
Proceedings Papers:
[7]. Atkinson F.V. Bull.A mer.Math.Soc.1968, 74, 1-271. Multiparameter spectral theory.
Proceedings Papers:
[8] Dzhabarzadeh R.M. Transactions of NAS Azerbaijan, v. 3-4 1998, p.12-18 Spectral theory of two parameter system in finite-
dimensional spa’ce.