The peer-reviewed International Journal of Engineering Inventions (IJEI) is started with a mission to encourage contribution to research in Science and Technology. Encourage and motivate researchers in challenging areas of Sciences and Technology.
Dyadics algebra.
Please send comments and suggestions to solo.hermelin@gmail.com. Thanks.
For more presentations on different subjects visit my website at http://www.solohermelin.com.
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 kind of quantum gates, higher braiding gates, as matrix solutions of the polyadic braid equations (different from the generalized Yang–Baxter equations) is introduced. Such gates lead to another special multiqubit entanglement that can speed up key distribution and accelerate algorithms. Ternary braiding gates acting on three qubit states are studied in detail. We also consider exotic non-invertible gates, which can be related with qubit loss, and define partial identities (which can be orthogonal), partial unitarity, and partially bounded operators (which can be non-invertible). We define two classes of matrices, star and circle ones, such that the magic matrices (connected with the Cartan decomposition) belong to the star class. The general algebraic structure of the introduced classes is described in terms of semigroups, ternary and 5-ary groups and modules. The higher braid group and its representation by the higher braid operators are given. Finally, we show, that for each multiqubit state, there exist higher braiding gates that are not entangling, and the concrete conditions to be non-entangling are given for the obtained binary and ternary gates.
Dyadics algebra.
Please send comments and suggestions to solo.hermelin@gmail.com. Thanks.
For more presentations on different subjects visit my website at http://www.solohermelin.com.
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 kind of quantum gates, higher braiding gates, as matrix solutions of the polyadic braid equations (different from the generalized Yang–Baxter equations) is introduced. Such gates lead to another special multiqubit entanglement that can speed up key distribution and accelerate algorithms. Ternary braiding gates acting on three qubit states are studied in detail. We also consider exotic non-invertible gates, which can be related with qubit loss, and define partial identities (which can be orthogonal), partial unitarity, and partially bounded operators (which can be non-invertible). We define two classes of matrices, star and circle ones, such that the magic matrices (connected with the Cartan decomposition) belong to the star class. The general algebraic structure of the introduced classes is described in terms of semigroups, ternary and 5-ary groups and modules. The higher braid group and its representation by the higher braid operators are given. Finally, we show, that for each multiqubit state, there exist higher braiding gates that are not entangling, and the concrete conditions to be non-entangling are given for the obtained binary and ternary gates.
Higher braiding gates, a new kind of quantum gate, are introduced. These are matrix solutions of the polyadic braid equations (which differ from the generalized Yang-Baxter equations). Such gates support a special kind of multi-qubit entanglement which can speed up key distribution and accelerate the execution of algorithms. Ternary braiding gates acting on three qubit states are studied in detail. We also consider exotic non-invertible gates which can be related to qubit loss, and define partial identities (which can be orthogonal), partial unitarity, and partially bounded operators (which can be non-invertible). We define two classes of matrices, the star and circle types, and find that the magic matrices (connected with the Cartan decomposition) belong to the star class. The general algebraic structure of the classes introduced here is described in terms of semigroups, ternary and 5-ary groups and modules. The higher braid group and its representation by higher braid operators are given. Finally, we show that for each multi-qubit state there exist higher braiding gates which are not entangling, and the concrete conditions to be non-entangling are given for the binary and ternary gates discussed.
International Journal of Research in Engineering and Science is an open access peer-reviewed international forum for scientists involved in research to publish quality and refereed papers. Papers reporting original research or experimentally proved review work are welcome. Papers for publication are selected through peer review to ensure originality, relevance, and readability.
Second Part of Inner Products including Cauchy Schwarz inequality, Pythagorean theorem, Orthogonal complement, Projection theorem with geometrical interpretation, Least Square Solution
The Analytical Nature of the Greens Function in the Vicinity of a Simple Poleijtsrd
It is known that the Green function of a boundary value problem is a meromorphic function of a spectral parameter. When the boundary conditions contain integro differential terms, then the meromorphism of the Greens function of such a problem can also be proved. In this case, it is possible to write out the structure of the residue at the singular points of the Greens function of the boundary value problem with integro differential perturbations. An analysis of the structure of the residue allows us to state that the corresponding functions of the original operator are sufficiently smooth functions. Surprisingly, the adjoint operator can have non smooth eigenfunctions. The degree of non smoothness of the eigenfunction of the adjoint operator to an operator with integro differential boundary conditions is clarified. It is indicated that even those conjugations to multipoint boundary value problems have non smooth eigenfunctions. Ghulam Hazrat Aimal Rasa "The Analytical Nature of the Green's Function in the Vicinity of a Simple Pole" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-4 | Issue-6 , October 2020, URL: https://www.ijtsrd.com/papers/ijtsrd33696.pdf Paper Url: https://www.ijtsrd.com/mathemetics/applied-mathamatics/33696/the-analytical-nature-of-the-greens-function-in-the-vicinity-of-a-simple-pole/ghulam-hazrat-aimal-rasa
FITTED OPERATOR FINITE DIFFERENCE METHOD FOR SINGULARLY PERTURBED PARABOLIC C...ieijjournal
In this paper, we study the numerical solution of singularly perturbed parabolic convection-diffusion type
with boundary layers at the right side. To solve this problem, the backward-Euler with Richardson
extrapolation method is applied on the time direction and the fitted operator finite difference method on the
spatial direction is used, on the uniform grids. The stability and consistency of the method were established
very well to guarantee the convergence of the method. Numerical experimentation is carried out on model
examples, and the results are presented both in tables and graphs. Further, the present method gives a more
accurate solution than some existing methods reported in the literature.
Weighted Analogue of Inverse Maxwell Distribution with ApplicationsPremier Publishers
In the present study, we established a new statistical model named as weighted inverse Maxwell distribution (WIMD). Its several statistical properties including moments, moment generating function, characteristics function, order statistics, shanon entropy has been discussed. The expression for reliability, mode, harmonic mean, hazard rate function has been derived. In addition, it also contains some special cases that are well known. Moreover, the behavior of probability density function (p.d.f) has been shown through graphs by choosing different values of parameters. Finally, the performance of the proposed model is explained through two data sets. By which we conclude that the established distribution provides better fit.
INFLUENCE OF OVERLAYERS ON DEPTH OF IMPLANTED-HETEROJUNCTION RECTIFIERSZac Darcy
In this paper we compare distributions of concentrations of dopants in an implanted-junction rectifiers in a
heterostructures with an overlayer and without the overlayer. Conditions for decreasing of depth of the
considered p-n-junction have been formulated.
A Common Fixed Point Theorem on Fuzzy Metric Space Using Weakly Compatible an...inventionjournals
The aim of this paper is to prove a fixed point theorem in a complete fuzzy metric space using six self maps. We prove our theorem with the concept of weakly compatible mappings and semi-compatible mappings in complete fuzzy metric space.
Solutions of Maxwell Equation for a Lattice System with Meissner EffectQiang LI
We show that Maxwell equation of a lattice system may have Meissner effect solutions when all carriers are surface state electrons. Some limitations on the wave function distributions of electrons in the system are identified.
In this paper, we study the cartesian product of intuitionistic fuzzy soft normal subgroup structure over snorm. By using s-norm of S, we characterize some basic results of intuitionistic S-fuzzy soft subgroup of normal subgroup. Also, we define the relationship between intuitionistic S-fuzzy soft subgroup and intuitionistic S-fuzzy soft normal subgroup. Finally we prove some basic properties
PROBABILISTIC INTERPRETATION OF COMPLEX FUZZY SETIJCSEIT Journal
The innovative concept of Complex Fuzzy Set is introduced. The objective of the this paper to investigate
the concept of Complex Fuzzy set in constraint to a traditional Fuzzy set , where the membership function
ranges from [0, 1], but in the Complex fuzzy set extended to a unit circle in a complex plane, where the
member ship function in the form of complex number. The Compressive study of mathematical operation of
Complex Fuzzy set is presented. The basic operation like addition, subtraction, multiplication and division
are described here. The Novel idea of this paper to measure the similarity between two fuzzy relations by
evaluating δ -equality. Here also we introduce the probabilistic interpretation of the complex fuzzy set
where we attempted to clarify the distinction between Fuzzy logic and probability.
Location of Regions Containing all or Some Zeros of a Polynomialijceronline
In this paper we locate the regions which contain all or some of the zeros of a polynomial when the coefficients of the polynomial are restricted to certain conditions. Mathematics Subject Classification: 30C10, 30C15.
In this paper, restricting the coefficients of a polynomial to certain conditions, we locate a region containing all of its zeros. Our results generalize many known results in addition to some interesting results which can be obtained by choosing certain values of the parameters. Mathematics Subject Classification: 30C10, 30C15
Higher braiding gates, a new kind of quantum gate, are introduced. These are matrix solutions of the polyadic braid equations (which differ from the generalized Yang-Baxter equations). Such gates support a special kind of multi-qubit entanglement which can speed up key distribution and accelerate the execution of algorithms. Ternary braiding gates acting on three qubit states are studied in detail. We also consider exotic non-invertible gates which can be related to qubit loss, and define partial identities (which can be orthogonal), partial unitarity, and partially bounded operators (which can be non-invertible). We define two classes of matrices, the star and circle types, and find that the magic matrices (connected with the Cartan decomposition) belong to the star class. The general algebraic structure of the classes introduced here is described in terms of semigroups, ternary and 5-ary groups and modules. The higher braid group and its representation by higher braid operators are given. Finally, we show that for each multi-qubit state there exist higher braiding gates which are not entangling, and the concrete conditions to be non-entangling are given for the binary and ternary gates discussed.
International Journal of Research in Engineering and Science is an open access peer-reviewed international forum for scientists involved in research to publish quality and refereed papers. Papers reporting original research or experimentally proved review work are welcome. Papers for publication are selected through peer review to ensure originality, relevance, and readability.
Second Part of Inner Products including Cauchy Schwarz inequality, Pythagorean theorem, Orthogonal complement, Projection theorem with geometrical interpretation, Least Square Solution
The Analytical Nature of the Greens Function in the Vicinity of a Simple Poleijtsrd
It is known that the Green function of a boundary value problem is a meromorphic function of a spectral parameter. When the boundary conditions contain integro differential terms, then the meromorphism of the Greens function of such a problem can also be proved. In this case, it is possible to write out the structure of the residue at the singular points of the Greens function of the boundary value problem with integro differential perturbations. An analysis of the structure of the residue allows us to state that the corresponding functions of the original operator are sufficiently smooth functions. Surprisingly, the adjoint operator can have non smooth eigenfunctions. The degree of non smoothness of the eigenfunction of the adjoint operator to an operator with integro differential boundary conditions is clarified. It is indicated that even those conjugations to multipoint boundary value problems have non smooth eigenfunctions. Ghulam Hazrat Aimal Rasa "The Analytical Nature of the Green's Function in the Vicinity of a Simple Pole" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-4 | Issue-6 , October 2020, URL: https://www.ijtsrd.com/papers/ijtsrd33696.pdf Paper Url: https://www.ijtsrd.com/mathemetics/applied-mathamatics/33696/the-analytical-nature-of-the-greens-function-in-the-vicinity-of-a-simple-pole/ghulam-hazrat-aimal-rasa
FITTED OPERATOR FINITE DIFFERENCE METHOD FOR SINGULARLY PERTURBED PARABOLIC C...ieijjournal
In this paper, we study the numerical solution of singularly perturbed parabolic convection-diffusion type
with boundary layers at the right side. To solve this problem, the backward-Euler with Richardson
extrapolation method is applied on the time direction and the fitted operator finite difference method on the
spatial direction is used, on the uniform grids. The stability and consistency of the method were established
very well to guarantee the convergence of the method. Numerical experimentation is carried out on model
examples, and the results are presented both in tables and graphs. Further, the present method gives a more
accurate solution than some existing methods reported in the literature.
Weighted Analogue of Inverse Maxwell Distribution with ApplicationsPremier Publishers
In the present study, we established a new statistical model named as weighted inverse Maxwell distribution (WIMD). Its several statistical properties including moments, moment generating function, characteristics function, order statistics, shanon entropy has been discussed. The expression for reliability, mode, harmonic mean, hazard rate function has been derived. In addition, it also contains some special cases that are well known. Moreover, the behavior of probability density function (p.d.f) has been shown through graphs by choosing different values of parameters. Finally, the performance of the proposed model is explained through two data sets. By which we conclude that the established distribution provides better fit.
INFLUENCE OF OVERLAYERS ON DEPTH OF IMPLANTED-HETEROJUNCTION RECTIFIERSZac Darcy
In this paper we compare distributions of concentrations of dopants in an implanted-junction rectifiers in a
heterostructures with an overlayer and without the overlayer. Conditions for decreasing of depth of the
considered p-n-junction have been formulated.
A Common Fixed Point Theorem on Fuzzy Metric Space Using Weakly Compatible an...inventionjournals
The aim of this paper is to prove a fixed point theorem in a complete fuzzy metric space using six self maps. We prove our theorem with the concept of weakly compatible mappings and semi-compatible mappings in complete fuzzy metric space.
Solutions of Maxwell Equation for a Lattice System with Meissner EffectQiang LI
We show that Maxwell equation of a lattice system may have Meissner effect solutions when all carriers are surface state electrons. Some limitations on the wave function distributions of electrons in the system are identified.
In this paper, we study the cartesian product of intuitionistic fuzzy soft normal subgroup structure over snorm. By using s-norm of S, we characterize some basic results of intuitionistic S-fuzzy soft subgroup of normal subgroup. Also, we define the relationship between intuitionistic S-fuzzy soft subgroup and intuitionistic S-fuzzy soft normal subgroup. Finally we prove some basic properties
PROBABILISTIC INTERPRETATION OF COMPLEX FUZZY SETIJCSEIT Journal
The innovative concept of Complex Fuzzy Set is introduced. The objective of the this paper to investigate
the concept of Complex Fuzzy set in constraint to a traditional Fuzzy set , where the membership function
ranges from [0, 1], but in the Complex fuzzy set extended to a unit circle in a complex plane, where the
member ship function in the form of complex number. The Compressive study of mathematical operation of
Complex Fuzzy set is presented. The basic operation like addition, subtraction, multiplication and division
are described here. The Novel idea of this paper to measure the similarity between two fuzzy relations by
evaluating δ -equality. Here also we introduce the probabilistic interpretation of the complex fuzzy set
where we attempted to clarify the distinction between Fuzzy logic and probability.
Location of Regions Containing all or Some Zeros of a Polynomialijceronline
In this paper we locate the regions which contain all or some of the zeros of a polynomial when the coefficients of the polynomial are restricted to certain conditions. Mathematics Subject Classification: 30C10, 30C15.
In this paper, restricting the coefficients of a polynomial to certain conditions, we locate a region containing all of its zeros. Our results generalize many known results in addition to some interesting results which can be obtained by choosing certain values of the parameters. Mathematics Subject Classification: 30C10, 30C15
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
FITTED OPERATOR FINITE DIFFERENCE METHOD FOR SINGULARLY PERTURBED PARABOLIC C...ieijjournal
In this paper, we study the numerical solution of singularly perturbed parabolic convection-diffusion type
with boundary layers at the right side. To solve this problem, the backward-Euler with Richardson
extrapolation method is applied on the time direction and the fitted operator finite difference method on the
spatial direction is used, on the uniform grids. The stability and consistency of the method were established
very well to guarantee the convergence of the method. Numerical experimentation is carried out on model
examples, and the results are presented both in tables and graphs. Further, the present method gives a more
accurate solution than some existing methods reported in the literature.
Exact Solutions of the Klein-Gordon Equation for the Q-Deformed Morse Potenti...ijrap
In this work, we solve the Klein-Gordon (KG) equation for the general deformed Morse potential with
equal scalar and vector potentials by using the Nikiforov-Uvarov (NU) method, which is based on the
solutions of general second-order linear differential equation with special functions. The energy
eigenvalues and corresponding normalized eigenfunctions are obtained. It is found that the eigenfunctions
can be expressed by the Laguerre polynomials. Our solutions have a good agreement with earlier study.
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.
International Journal of Engineering Research and Development (IJERD)IJERD Editor
journal publishing, how to publish research paper, Call For research paper, international journal, publishing a paper, IJERD, journal of science and technology, how to get a research paper published, publishing a paper, publishing of journal, publishing of research paper, reserach and review articles, IJERD Journal, How to publish your research paper, publish research paper, open access engineering journal, Engineering journal, Mathemetics journal, Physics journal, Chemistry journal, Computer Engineering, Computer Science journal, how to submit your paper, peer reviw journal, indexed journal, reserach and review articles, engineering journal, www.ijerd.com, research journals,
yahoo journals, bing journals, International Journal of Engineering Research and Development, google journals, hard copy of journal
International Journal of Engineering Inventions (IJEI) provides a multidisciplinary passage for researchers, managers, professionals, practitioners and students around the globe to publish high quality, peer-reviewed articles on all theoretical and empirical aspects of Engineering and Science.
International Journal of Engineering Research and DevelopmentIJERD Editor
Electrical, Electronics and Computer Engineering,
Information Engineering and Technology,
Mechanical, Industrial and Manufacturing Engineering,
Automation and Mechatronics Engineering,
Material and Chemical Engineering,
Civil and Architecture Engineering,
Biotechnology and Bio Engineering,
Environmental Engineering,
Petroleum and Mining Engineering,
Marine and Agriculture engineering,
Aerospace Engineering.
-type and -type four dimensional plane wave solutions of Einstein's field eq...inventy
In the present paper, we have studied - type and -type plane wave solutions of Einstein's field equations in general theory of relativity in the case where the zero mass scalar field coupled with gravitational field and zero mass scalar field coupled with gravitational & electromagnetic field and established the existence of these two types of plane wave solutions in . Furthermore we have considered the case of massive scalar field and shown that the non-existence of these two types of plane wave solutions in GR theory.
MODELING OF REDISTRIBUTION OF INFUSED DOPANT IN A MULTILAYER STRUCTURE DOPANT...mathsjournal
In this paper we used an analytical approach to model nonlinear diffusion of dopant in a multilayer structure with account nonstationary annealing of the dopant. The approach do without crosslinking solutions at
the interface between layers of the multilayer structure. In this paper we analyzed influence of pressure of
vapor of infusing dopant during doping of multilayer structure on values of optimal parameters of technological process to manufacture p-n-junctions. It has been shown, that doping of multilayer structures by
diffusion and optimization of annealing of dopant gives us possibility to increase sharpness of p-n-junctions
(single p-n-junctions and p-n-junctions within transistors) and to increase homogeneity of dopant distribution in doped area.
MODELING OF REDISTRIBUTION OF INFUSED DOPANT IN A MULTILAYER STRUCTURE DOPANT...mathsjournal
In this paper we used an analytical approach to model nonlinear diffusion of dopant in a multilayer structure with account nonstationary annealing of the dopant. The approach do without crosslinking solutions at
the interface between layers of the multilayer structure. In this paper we analyzed influence of pressure of
vapor of infusing dopant during doping of multilayer structure on values of optimal parameters of technological process to manufacture p-n-junctions. It has been shown, that doping of multilayer structures by
diffusion and optimization of annealing of dopant gives us possibility to increase sharpness of p-n-junctions
(single p-n-junctions and p-n-junctions within transistors) and to increase homogeneity of dopant distribution in doped area.
Analytic Solutions of an Iterative Functional Differential Equation with Dela...inventionjournals
ABSTRACT : This This paper is concerned with an iterative functional differential equation with the form
z C
x z
b
x az
x z
,
)
( )
(
1
( ) .By constructing a convergent power series solution of an auxiliary equation
b [ag(z) g( z)] [g( z) ag( z)][ g( z) ag(z)] g(z), zC 2 2 2
the analytic solutions for the original equation are obtained. We not only discuss the constant given in Schröder
transformation at resonance( i.e., at a root of the unity), but also discuss those near resonance (i.e., near a
root of the unity) under Brjuno condition.
On the Zeros of A Polynomial Inside the Unit DiscIJERDJOURNAL
ABSTRACT: In this paper we find the number of zeros of a polynomial inside the unit disc under certain conditions on the coefficients of the polynomial. Mathematics Subject Classification: 30C10, 30C15.
Analytical Solution Of Schrodinger Equation With Mie-Type Potential Using Fac...ijrap
we have obtained the analytical solution of Schrödinger wave equation with Mie – type potential
using factorization method. We have also obtained energy eigenvalues of our potential and the
corresponding wave function using an ansatz and then compare the result to standard Laguerre’s
differential equation. Under special cases our potential model reduces two well known potentials such as
Coulomb and the Kratzer Feus potentials.
Similar to On the Zeros of Complex Polynomials (20)
Neuro-symbolic is not enough, we need neuro-*semantic*Frank van Harmelen
Neuro-symbolic (NeSy) AI is on the rise. However, simply machine learning on just any symbolic structure is not sufficient to really harvest the gains of NeSy. These will only be gained when the symbolic structures have an actual semantics. I give an operational definition of semantics as “predictable inference”.
All of this illustrated with link prediction over knowledge graphs, but the argument is general.
Epistemic Interaction - tuning interfaces to provide information for AI supportAlan Dix
Paper presented at SYNERGY workshop at AVI 2024, Genoa, Italy. 3rd June 2024
https://alandix.com/academic/papers/synergy2024-epistemic/
As machine learning integrates deeper into human-computer interactions, the concept of epistemic interaction emerges, aiming to refine these interactions to enhance system adaptability. This approach encourages minor, intentional adjustments in user behaviour to enrich the data available for system learning. This paper introduces epistemic interaction within the context of human-system communication, illustrating how deliberate interaction design can improve system understanding and adaptation. Through concrete examples, we demonstrate the potential of epistemic interaction to significantly advance human-computer interaction by leveraging intuitive human communication strategies to inform system design and functionality, offering a novel pathway for enriching user-system engagements.
Connector Corner: Automate dynamic content and events by pushing a buttonDianaGray10
Here is something new! In our next Connector Corner webinar, we will demonstrate how you can use a single workflow to:
Create a campaign using Mailchimp with merge tags/fields
Send an interactive Slack channel message (using buttons)
Have the message received by managers and peers along with a test email for review
But there’s more:
In a second workflow supporting the same use case, you’ll see:
Your campaign sent to target colleagues for approval
If the “Approve” button is clicked, a Jira/Zendesk ticket is created for the marketing design team
But—if the “Reject” button is pushed, colleagues will be alerted via Slack message
Join us to learn more about this new, human-in-the-loop capability, brought to you by Integration Service connectors.
And...
Speakers:
Akshay Agnihotri, Product Manager
Charlie Greenberg, Host
Key Trends Shaping the Future of Infrastructure.pdfCheryl Hung
Keynote at DIGIT West Expo, Glasgow on 29 May 2024.
Cheryl Hung, ochery.com
Sr Director, Infrastructure Ecosystem, Arm.
The key trends across hardware, cloud and open-source; exploring how these areas are likely to mature and develop over the short and long-term, and then considering how organisations can position themselves to adapt and thrive.
State of ICS and IoT Cyber Threat Landscape Report 2024 previewPrayukth K V
The IoT and OT threat landscape report has been prepared by the Threat Research Team at Sectrio using data from Sectrio, cyber threat intelligence farming facilities spread across over 85 cities around the world. In addition, Sectrio also runs AI-based advanced threat and payload engagement facilities that serve as sinks to attract and engage sophisticated threat actors, and newer malware including new variants and latent threats that are at an earlier stage of development.
The latest edition of the OT/ICS and IoT security Threat Landscape Report 2024 also covers:
State of global ICS asset and network exposure
Sectoral targets and attacks as well as the cost of ransom
Global APT activity, AI usage, actor and tactic profiles, and implications
Rise in volumes of AI-powered cyberattacks
Major cyber events in 2024
Malware and malicious payload trends
Cyberattack types and targets
Vulnerability exploit attempts on CVEs
Attacks on counties – USA
Expansion of bot farms – how, where, and why
In-depth analysis of the cyber threat landscape across North America, South America, Europe, APAC, and the Middle East
Why are attacks on smart factories rising?
Cyber risk predictions
Axis of attacks – Europe
Systemic attacks in the Middle East
Download the full report from here:
https://sectrio.com/resources/ot-threat-landscape-reports/sectrio-releases-ot-ics-and-iot-security-threat-landscape-report-2024/
Essentials of Automations: Optimizing FME Workflows with ParametersSafe Software
Are you looking to streamline your workflows and boost your projects’ efficiency? Do you find yourself searching for ways to add flexibility and control over your FME workflows? If so, you’re in the right place.
Join us for an insightful dive into the world of FME parameters, a critical element in optimizing workflow efficiency. This webinar marks the beginning of our three-part “Essentials of Automation” series. This first webinar is designed to equip you with the knowledge and skills to utilize parameters effectively: enhancing the flexibility, maintainability, and user control of your FME projects.
Here’s what you’ll gain:
- Essentials of FME Parameters: Understand the pivotal role of parameters, including Reader/Writer, Transformer, User, and FME Flow categories. Discover how they are the key to unlocking automation and optimization within your workflows.
- Practical Applications in FME Form: Delve into key user parameter types including choice, connections, and file URLs. Allow users to control how a workflow runs, making your workflows more reusable. Learn to import values and deliver the best user experience for your workflows while enhancing accuracy.
- Optimization Strategies in FME Flow: Explore the creation and strategic deployment of parameters in FME Flow, including the use of deployment and geometry parameters, to maximize workflow efficiency.
- Pro Tips for Success: Gain insights on parameterizing connections and leveraging new features like Conditional Visibility for clarity and simplicity.
We’ll wrap up with a glimpse into future webinars, followed by a Q&A session to address your specific questions surrounding this topic.
Don’t miss this opportunity to elevate your FME expertise and drive your projects to new heights of efficiency.
Generating a custom Ruby SDK for your web service or Rails API using Smithyg2nightmarescribd
Have you ever wanted a Ruby client API to communicate with your web service? Smithy is a protocol-agnostic language for defining services and SDKs. Smithy Ruby is an implementation of Smithy that generates a Ruby SDK using a Smithy model. In this talk, we will explore Smithy and Smithy Ruby to learn how to generate custom feature-rich SDKs that can communicate with any web service, such as a Rails JSON API.
Accelerate your Kubernetes clusters with Varnish CachingThijs Feryn
A presentation about the usage and availability of Varnish on Kubernetes. This talk explores the capabilities of Varnish caching and shows how to use the Varnish Helm chart to deploy it to Kubernetes.
This presentation was delivered at K8SUG Singapore. See https://feryn.eu/presentations/accelerate-your-kubernetes-clusters-with-varnish-caching-k8sug-singapore-28-2024 for more details.
GraphRAG is All You need? LLM & Knowledge GraphGuy Korland
Guy Korland, CEO and Co-founder of FalkorDB, will review two articles on the integration of language models with knowledge graphs.
1. Unifying Large Language Models and Knowledge Graphs: A Roadmap.
https://arxiv.org/abs/2306.08302
2. Microsoft Research's GraphRAG paper and a review paper on various uses of knowledge graphs:
https://www.microsoft.com/en-us/research/blog/graphrag-unlocking-llm-discovery-on-narrative-private-data/
Dev Dives: Train smarter, not harder – active learning and UiPath LLMs for do...UiPathCommunity
💥 Speed, accuracy, and scaling – discover the superpowers of GenAI in action with UiPath Document Understanding and Communications Mining™:
See how to accelerate model training and optimize model performance with active learning
Learn about the latest enhancements to out-of-the-box document processing – with little to no training required
Get an exclusive demo of the new family of UiPath LLMs – GenAI models specialized for processing different types of documents and messages
This is a hands-on session specifically designed for automation developers and AI enthusiasts seeking to enhance their knowledge in leveraging the latest intelligent document processing capabilities offered by UiPath.
Speakers:
👨🏫 Andras Palfi, Senior Product Manager, UiPath
👩🏫 Lenka Dulovicova, Product Program Manager, UiPath
UiPath Test Automation using UiPath Test Suite series, part 3DianaGray10
Welcome to UiPath Test Automation using UiPath Test Suite series part 3. In this session, we will cover desktop automation along with UI automation.
Topics covered:
UI automation Introduction,
UI automation Sample
Desktop automation flow
Pradeep Chinnala, Senior Consultant Automation Developer @WonderBotz and UiPath MVP
Deepak Rai, Automation Practice Lead, Boundaryless Group and UiPath MVP
Securing your Kubernetes cluster_ a step-by-step guide to success !KatiaHIMEUR1
Today, after several years of existence, an extremely active community and an ultra-dynamic ecosystem, Kubernetes has established itself as the de facto standard in container orchestration. Thanks to a wide range of managed services, it has never been so easy to set up a ready-to-use Kubernetes cluster.
However, this ease of use means that the subject of security in Kubernetes is often left for later, or even neglected. This exposes companies to significant risks.
In this talk, I'll show you step-by-step how to secure your Kubernetes cluster for greater peace of mind and reliability.
Securing your Kubernetes cluster_ a step-by-step guide to success !
On the Zeros of Complex Polynomials
1. International Journal of Engineering Inventions
e-ISSN: 2278-7461, p-ISSN: 2319-6491
Volume 2, Issue 11 (July 2013) PP: 54-59
www.ijeijournal.com Page | 54
On the Zeros of Complex Polynomials
M. H. Gulzar
Department of Mathematics, University of Kashmir, Srinagar
Abstract: In the framework of the Enestrom-Kakeya Theorem various results have been proved on the
location of zeros of complex polynomials. In this paper we give some new results on the zeros of complex
polynomials by restricting the real and imaginary parts of their coefficients to certain conitions.
Mathematics Subject Classification: 30C10, 30C15
Key-words and Phrases: Coefficients, Polynomials, Zeros
I. Introduction and Statement of Results
The following result known as the Enestrom-Kakeya Theorem [10] is well-known in the theory of
distribution of zeros of polynomials:
Theorem A: Let
n
j
j
j zazP
0
)( be a polynomial of degree n such that its coefficients satisfy
0... 011 aaaa nn .
Then all the zeros of P(z) lie in the closed unit disk 1z .
In the literature [1-9, 12] there exist several generalisations and extensions of this result .
Recently Y. Choo [3] proved the following results:
Theorem B: Let
n
j
j
j zazP
0
)( be a polynomial of degree n with
njaa jjjj ,....,2,1,0,)Im(,)Re( , such that for some and , and for some 1k , 2k ,
011111 ...... nnk
011112 ...... nnk .
Then P(z) has all its zeros in 21 RzR where
1
0
1
M
a
R and
na
M
R 2
2
with
)(2)1()1( 211 nnn kkaM )()( 001 nnk
and
)(2)1()1( 212 nn kkM 00021 )()( akk nn .
M. H. Gulzar [8] made an improvement on the above result by proving the following result:
Theorem C: Let
n
j
j
j zazP
0
)( be a polynomial of degree n with
njaa jjjj ,....,2,1,0,)Im(,)Re( , such that for some and , and for some 1k , 2k , 21, ,
011111 ...... nnk
021112 ...... nnk .
Then P(z) has all its zeros in 43 RzR where
3
0
3
M
a
R and
na
M
R 4
4
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with
)()(2)1()1( 21213 nnnnn kkkkaM
02020101 )1()1(
and
)()(2)1()1( 21214 nnnn kkkkM
002020101 )1()1( a .
The aim of this paper is to find a ring-shaped region between two concentric circles with centre not necessarily
on the origin. More precisely, we prove the following results:
Theorem 1: Let
n
j
j
j zazP
0
)( be a polynomial of degree n with
njaa jjjj ,....,2,1,0,)Im(,)Re( , such that for some and , and for some 1k , 2k , 21, ,
011111 ...... nnk
021112 ...... nnk .
Then P(z) has all its zeros in 615 RzR where
n
n
a
k
)1( 1
1
,
n
n
a
k
M
a
R
)1( 1
5
0
5
and
na
M
R 6
6
with
)()(2)1()1( 21215 nnnnn kkkkaM
02020101 )1()1(
and
nnn kkkM )1()()(2 2216
002020101 )1()1( a .
Theorem 2: Let
n
j
j
j zazP
0
)( be a polynomial of degree n with
njaa jjjj ,....,2,1,0,)Im(,)Re( , such that for some and , and for some 1k , 2k , 21, ,
011111 ...... nnk
021112 ...... nnk .
Then P(z) has all its zeros in 827 RzR where
n
n
a
ki
)1( 2
2
,
n
n
a
k
M
a
R
)1( 2
7
0
7
and
na
M
R 8
8
with
)()(2)1()1( 21217 nnnnn kkkkaM
02020101 )1()1(
and
nnn kkkM )1()()(2 1218
002020101 )1()1( a .
Remark 1: The bounds for the zeros of P(z) in both Theorem 1 and Theorem 2 are easily seen to be sharper
than those of Theorems B and C. For different values of the parameters 2121 ,,, kk , we get many other
interesting results. For example for
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11 k , 12 , in Theorem 2 ,we get a result due to B. L. Raina et al [11].
For 1,1 21 , Theorem 1 reduces to Theorem B.
For 11 k , 12 k ,, in Theorem 1, we get the following result:
Corollary 1: Let
n
j
j
j zazP
0
)( be a polynomial of degree n with
njaa jjjj ,....,2,1,0,)Im(,)Re( , such that for some and , and for some 21, ,
01111 ...... nn
02111 ...... nn .
Then P(z) has all its zeros in 109 RzR where
9
0
9
M
a
R and
na
M
R 10
10
with
)()(29 nnnaM 02020101 )1()1(
and
)()(210 nnM 002020101 )1()1( a .
II. Proofs of Theorems
Proof of Theorem 1: Consider the polynomial
)()1()( zPzzF
......)()(
)......)(1(
1
211
1
01
1
1
n
nn
n
nn
n
n
n
n
n
n
zaazaaza
azazazaz
001
2
12 )()( azaazaa
......)()1()( 1
21111
1
n
nn
n
n
n
nn
n
n zzkzkza
})1()(......)(
)1(){()1()(
02021
1
21
212001011
zzz
zkzkiazz
n
nn
n
n
n
nn
......){(})1([{ 21
111
z
kkzaz nn
nnnn
n
}]
)1(
......
)1(
){(}
)1(
02
1
02121
2
12
0
1
01
1
011
nn
nn
n
nnnnn
zzz
z
k
ki
z
a
zz
For 1z , we have nj
z
jn
,......,1,0,1
1
and, therefore ,
....{)1([)(
21
111
z
kkzazzF
nn
nnnn
n
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}]
)1(
......
)1()1(
02
1
02121
2
12
0
1
01
1
011
nn
nn
n
nnnnn
zzz
z
k
k
z
a
zz
01121111 ......{)1([ nnnnnn
n
kkzaz
21212001 )1()1( nnnnn kka
}])1( 02021
)(......)(){()1([ 112111 nnnnnn
n
kkzaz
}])1()(
......)()(......)()1(
)()1()(......)(
02021
11122
210010111
nnn
nn
k
ka
nnnnn
n
kkkkzaz )1()()(2{)1([ 2211
}])1()1( 002010201 a
0
if
nnnnn kkkkza )1()()(2{)1( 2211
})1()1( 002010201 a
or
nnn
nn
n
kkk
aa
k
z
)1()()(2[{
1)1(
221
1
This shows that those zeros of F(z) and hence P(z) whose modulus is greater than 1 lie in
nnn
nn
n
kkk
aa
k
z
)1()()(2[{
1)1(
221
1
}])1()1( 02010201 .
Since the zeros of P(z) of modulus less than or equal to 1 already satisfy the above inequality, it follows that all
the zeros of P(z) lie in
61 Rz .
To prove the other half of the theorem, we have
......)()1()()( 1
21111
1
n
nn
n
n
n
nn
n
n zzkzkzazF
002021
1
21
21201011
})1()(......)(
)1(){()1()(
azzz
zkzkizz
n
nn
n
n
n
nn
0)( azQ ,
where
......)()1()()( 1
21111
1
n
nn
n
n
n
nn
n
n zzkzkzazQ
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})1()(......)(
)1(){()1()(
02021
1
21
21201011
zzz
zkzkizz
n
nn
n
n
n
nn
For 1z ,
)-()-(......)()k-()1()( 1112n11-n1 nnnn kzazQ
0202111
1221201011
)1()(......)-()-(......
)()()1()1()(......
nnnnn kk
nnnnn kkkkza )1()()(2)1( 2211
02010201 )1()1( .
Rkza nn )1( 1
51 )1( MRka nn ,
where
nnn kkkR )1()()(2 221
02020101 )1()1(
Since Q(z) is analytic and Q(0)=0, it follows by Rouche’s theorem that
zMzQ 5)( for 1z .
Therefore , for 1z ,
)()( 0 zQazF
)(0 zQa
zMa 50
0
if
5
0
M
a
z .
This shows that F(z) does not vanish in
5
0
M
a
z .It is easy to see that 05 aM . In other words, it follows
that F(z) and hence P(z) has all its zeros in z
M
a
5
0
.
Since
1111 zzz ,
we have
11
5
0
zz
M
a
.
Therefore
11
5
0
z
M
a
i.e.
6. On the Zeros of Complex Polynomials
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1
1
5
0 )1(
z
a
k
M
a
n
n
.
Hence, it follows that P(z) has all its zeros in
1
1
5
0 )1(
z
a
k
M
a
n
n
.
That completes the proof of Theorem 1.
Proof of Theorem 2: Similar to that of Theorem 2.
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