Search results for: algebraic reasoning

Authors: Fola John Adeyeye

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In this paper, we propose a cryptosystem private and public key base on symmetric group Pn and validates its theoretical formulation. This proposed system benefits from the algebraic properties of Pn such as noncommutative high logical, computational speed and high flexibility in selecting key which makes the discrete permutation multiplier logic (DPML) resist to attack by any algorithm such as Pohlig-Hellman. One of the advantages of this scheme is that it explore all the possible triangular symmetries. Against these properties, the only disadvantage is that the law of permutation multiplicity only allow an operation from left to right. Many other cryptosystems can be transformed into their symmetric group.

Keywords: cryptosystem, private and public key, DPML, symmetric group Pn

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Authors: Rohtash

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Academically, the concept of Justice in the literature is vast, and theories are voluminous and definitions are numerous but it is very difficult to define. Through the ages, justice has been evolving and developing reasoning that how individuals and communities do the right thing that is just and fair to all in that society. Justice is a relative and dynamic concept, not absolute one. It is different in different societies based on their morality and ethics. The idea of justice cannot arise from a single morality but interaction of competing moralities and contending perspectives. Justice is the conditional and circumstantial term. Therefore, justice takes different meanings in different contexts. Justice is the application of the Laws. It is a values-based concept in order to protect the rights and liberties of the people. It is a socially created concept that has no physical reality. It exists in society on the basis of the spirit of sharing by the communities and members of society. The conception of justice in society or among communities and individuals is based on their social coordination. It can be effective only when people’s judgments are based on collective reasoning. Their behavior is shaped by social values, norms and laws. People must accept, share and respect the set of principles for delivering justice. Thus justice can be a reasonable solution to conflicts and to coordinate behavior in society. The subject matter of distributive justice is the Public Good and societal resources that should be evenly distributed among the different sections of society on the principles developed and established by the State through legislation, public policy and Executive orders. The Socioeconomic transformation of the society is adopted by the constitution within the limit of its morality and gives a new dimension to transformative justice. Therefore, both Procedural and Transformative justice is part of Distributive justice. Distributive justice is purely an economic phenomenon. It concerns the allocation of resources among the communities and individuals. The subject matter of distributive justice is the distribution of rights, responsibilities, burdens and benefits in society on the basis of the capacity and capability of individuals.

Keywords: distributive justice, constitutionalism, institutionalism, constitutional morality

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Authors: Puttaswamy, Anwar Alwardi, Nayaka S. R.

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One of the algebraic representation of a graph is the graph polynomial. In this article, we introduce the paired-domination polynomial of a graph G. The paired-domination polynomial of a graph G of order n is the polynomial Dp(G, x) with the coefficients dp(G, i) where dp(G, i) denotes the number of paired dominating sets of G of cardinality i and γpd(G) denotes the paired-domination number of G. We obtain some properties of Dp(G, x) and its coefficients. Further, we compute this polynomial for some families of standard graphs. Further, we obtain some characterization for some specific graphs.

Keywords: domination polynomial, paired dominating set, paired domination number, paired domination polynomial

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Authors: Vadim Vagin, Marina Fomina, Oleg Morosin

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This paper contains the description of argumentation approach for the problem of inductive concept formation. It is proposed to use argumentation, based on defeasible reasoning with justification degrees, to improve the quality of classification models, obtained by generalization algorithms. The experiment’s results on both clear and noisy data are also presented.

Keywords: argumentation, justification degrees, inductive concept formation, noise, generalization

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Authors: N. Senu, I. A. Kasim, F. Ismail, N. Bachok

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In this paper zero-dissipative explicit Runge-Kutta method is derived for solving second-order ordinary differential equations with periodical solutions. The phase-lag and dissipation properties for Runge-Kutta (RK) method are also discussed. The new method has algebraic order three with dissipation of order infinity. The numerical results for the new method are compared with existing method when solving the second-order differential equations with periodic solutions using constant step size.

Keywords: dissipation, oscillatory solutions, phase-lag, Runge-Kutta methods

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Authors: Amber Lim, Ted Ruffman

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A vast amount of research evidence indicates that children develop social attitudes that are similar to those of their parents. When using general measures of social attitudes, such as social dominance orientation (SDO), right-wing authoritarianism (RWA), and prejudice, studies show that parents' and children’s attitudes were correlated. However, the mechanisms behind the intergenerational transmission of attitudes remain largely unexplained. Since it was speculated that the origins of RWA could be traced back to one’s relationship with their parents, the aim of this study was to assess how parents’ social attitudes and parenting behavior are related to children’s social development. One line of research suggests that the different ways in which authoritarian and authoritative parents reason with their children may impact Theory of Mind (ToM) development. That is, inductive discipline (e.g., emphasising how the child’s actions affect others) facilitates empathy and ToM development. Conversely, past evidence shows that children have poorer ToM development when parents enforce rules without explanation. Thus, this study addresses the question of how parent behavior plays a role in the gradual acquisition of a ToM and social attitudes. Seventy parents reported their social attitudes, parenting behavior, and their child’s mental state and non-mental state vocabulary. Their children were given ToM and perspective-taking tasks, along with a friend choice task to measure racial bias and anti-fat bias. As hypothesised, parents’ use of inductive reasoning correlated with children’s performance on Theory of Mind tasks. Mothers’ inductive reasoning facilitated children’s acquisition of mental state vocabulary. Parents’ autonomy granting was associated with improved mental state vocabulary. Authoritarian parenting traits such as verbal hostility were linked to children’s racial bias. These findings highlight the importance of parent-child discussion in shaping children’s social understanding.

Keywords: parenting style, prejudice, social attitudes, social understanding, theory of mind

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Authors: Alexandra Andrade Brandão Soares, Paulo Batista Gonçalves

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Using a modal expansion that satisfies the boundary and continuity conditions and expresses the modal couplings characteristic of cylindrical shells in the nonlinear regime, the equations of motion are discretized using the Galerkin method. The resulting algebraic equations are solved by the Newton-Raphson method, thus obtaining the nonlinear frequency-amplitude relation. Finally, a parametric analysis is conducted to study the influence of the geometry of the shell, the gradient of the functional material and vibration modes on the degree and type of nonlinearity of the cylindrical shell, which is the main contribution of this research work.

Keywords: cylindrical shells, dynamics, functionally graded material, nonlinear vibrations

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Authors: M. Khoshab, M. J. Sedigh

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Dynamic systems, which in mathematical point of view are those governed by differential equations, are much more difficult to study and to predict their behavior in comparison with static systems which are governed by algebraic equations. Economical systems such as market are among complicated dynamic systems. This paper tries to adopt a very simple mathematical model for market and to study effect of supply and demand function on behavior of the market while the supply side experiences a lag due to production restrictions.

Keywords: dynamic system, lag on supply demand, market stability, supply demand model

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Authors: Ladznar S. Laja, Rosalio G. Artes, Jr.

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This paper introduced a graph polynomial relating convexity concepts. A graph polynomial is a polynomial representing a graph given some parameters. On the other hand, a subgraph H of a graph G is said to be convex in G if for every pair of vertices in H, every shortest path with these end-vertices lies entirely in H. We define the convex subgraph polynomial of a graph G to be the generating function of the sequence of the numbers of convex subgraphs of G of cardinalities ranging from zero to the order of G. This graph polynomial is monic since G itself is convex. The convex index which counts the number of convex subgraphs of G of all orders is just the evaluation of this polynomial at 1. Relationships relating algebraic properties of convex subgraphs polynomial with graph theoretic concepts are established.

Keywords: convex subgraph, convex index, generating function, polynomial ring

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Authors: Francesca Marsili

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The reliability assessment of existing structures with probabilistic methods is becoming an increasingly important and frequent engineering task. However probabilistic reliability methods are based on an exhaustive knowledge of the stochastic modeling of the variables involved in the assessment; at the moment standards for the modeling of variables are absent, representing an obstacle to the dissemination of probabilistic methods. The framework according to probability distribution functions (PDFs) are established is represented by the Bayesian statistics, which uses Bayes Theorem: a prior PDF for the considered parameter is established based on information derived from the design stage and qualitative judgments based on the engineer past experience; then, the prior model is updated with the results of investigation carried out on the considered structure, such as material testing, determination of action and structural properties. The application of Bayesian statistics arises two different kind of problems: 1. The results of the updating depend on the engineer previous experience; 2. The updating of the prior PDF can be performed only if the structure has been tested, and quantitative data that can be statistically manipulated have been collected; performing tests is always an expensive and time consuming operation; furthermore, if the considered structure is an ancient building, destructive tests could compromise its cultural value and therefore should be avoided. In order to solve those problems, an interesting research path is represented by investigating Artificial Intelligence (AI) techniques that can be useful for the automation of the modeling of variables and for the updating of material parameters without performing destructive tests. Among the others, one that raises particular attention in relation to the object of this study is constituted by Case-Based Reasoning (CBR). In this application, cases will be represented by existing buildings where material tests have already been carried out and an updated PDFs for the material mechanical parameters has been computed through a Bayesian analysis. Then each case will be composed by a qualitative description of the material under assessment and the posterior PDFs that describe its material properties. The problem that will be solved is the definition of PDFs for material parameters involved in the reliability assessment of the considered structure. A CBR system represent a good candi¬date in automating the modelling of variables because: 1. Engineers already draw an estimation of the material properties based on the experience collected during the assessment of similar structures, or based on similar cases collected in literature or in data-bases; 2. Material tests carried out on structure can be easily collected from laboratory database or from literature; 3. The system will provide the user of a reliable probabilistic description of the variables involved in the assessment that will also serve as a tool in support of the engineer’s qualitative judgments. Automated modeling of variables can help in spreading probabilistic reliability assessment of existing buildings in the common engineering practice, and target at the best intervention and further tests on the structure; CBR represents a technique which may help to achieve this.

Keywords: reliability assessment of existing buildings, Bayesian analysis, case-based reasoning, historical structures

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Authors: Somveer Singh, Vineet Kumar Singh

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This work contributes a numerical method based on Legendre wavelet approximation for the treatment of partial integro-differential equation (PIDE). Operational matrices of Legendre wavelets reduce the solution of PIDE into the system of algebraic equations. Some useful results concerning the computational order of convergence and error estimates associated to the suggested scheme are presented. Illustrative examples are provided to show the effectiveness and accuracy of proposed numerical method.

Keywords: legendre wavelets, operational matrices, partial integro-differential equation, viscoelasticity

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Authors: Sartaj Singh, Amar Singh, Ashok Sharma, Sandeep Kaur

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With upcoming threats in a digital world, we need to work continuously in the area of security in all aspects, from hardware to software as well as data modelling. The rise in social media activities and hunger for data by various entities leads to cybercrime and more attack on the privacy and security of persons. Cryptography has always been employed to avoid access to important data by using many processes. Symmetric key and asymmetric key cryptography have been used for keeping data secrets at rest as well in transmission mode. Various cryptosystems have evolved from time to time to make the data more secure. In this research article, we are studying various cryptosystems in asymmetric cryptography and their application with usefulness, and much emphasis is given to Elliptic curve cryptography involving algebraic mathematics.

Keywords: cryptography, symmetric key cryptography, asymmetric key cryptography

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Authors: Sana Ansari, Sirus Mohammadi

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In distribution systems, shunt capacitors are used to reduce power losses, to improve voltage profile, and to increase the maximum flow through cables and transformers. This paper presents a new method to determine the optimal locations and economical sizing of fixed and/or switched shunt capacitors with a view to power losses reduction and voltage stability enhancement. General Algebraic Modeling System (GAMS) has been used to solve the maximization modules using the MINOS optimization software with Linear Programming (LP). The proposed method is tested on 33 node distribution system and the results show that the algorithm suitable for practical implementation on real systems with any size.

Keywords: power losses, voltage stability, radial distribution systems, capacitor

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Authors: F. Maass, P. Martin, J. Olivares

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The aim of this work is the application of the program GeoGebra in teaching the study of nonhomogeneous linear second order differential equations with constant coefficients. Different kind of functions or forces will be considered in the right hand side of the differential equations, in particular, the emphasis will be placed in the case of trigonometrical functions producing the resonance phenomena. In order to obtain this, the frequencies of the trigonometrical functions will be changed. Once the resonances appear, these have to be correlationated with the roots of the second order algebraic equation determined by the coefficients of the differential equation. In this way, the physics and engineering students will understand resonance effects and its consequences in the simplest way. A large variety of examples will be shown, using different kind of functions for the nonhomogeneous part of the differential equations.

Keywords: education, geogebra, ordinary differential equations, resonance

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Authors: Ke Ma

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Through the long course of history, Buddhism has captivated generations of brilliant minds with its enlightening but elusive discernment. Far from religious dogmas, Buddhism not only represents spiritual revelation, but also logical reasoning.Among all of Buddhism’s concepts, emptiness is the most famous, and abstruse one. This word resulted from an inaccurate translation confuses both Buddhists and religious scholars who understand Heart Sutra based on its English version. In this essay, the idea of “emptiness” will be reinterpreted as “information,” leading not only to a clarification of the ideology of Buddhism, but also to greater correspondence between Buddhism concepts and cognitive science.

Keywords: religion, cognitive science, psychology, Buddhism

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Authors: Paria Tajabor, Azin Azarbani

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The purpose of this research study is exploring two kind of semantic repositories with regards to various factors to find the best approaches that an artificial manager can use to produce ontology in a system based on their interaction, association and research. To this end, as the best way to evaluate each system and comparing with others is analysis, several benchmarking over these two repositories were examined. These two semantic repositories: OWLIM and AllegroGraph will be the main core of this study. The general objective of this study is to be able to create an efficient and cost-effective manner reports which is required to support decision making in any large enterprise.

Keywords: OWLIM, allegrograph, RDF, reasoning, semantic repository, semantic-web, SPARQL, ontology, query

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Authors: Mamyrbek A. Beisenbi, Nurgul M. Kissikova, Saltanat E. Beisembina, Salamat T. Suleimenova, Samal A. Kaliyeva

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The paper proposes a method for constructing a self-organizing control system for unstable and deterministic chaotic processes in the class of catastrophe “hyperbolic umbilic” for objects with m-inputs and n-outputs. The self-organizing control system is investigated by the universal gradient-velocity method of Lyapunov vector functions. The conditions for self-organization of the control system in the class of catastrophes “hyperbolic umbilic” are shown in the form of a system of algebraic inequalities that characterize the aperiodic robust stability in the stationary states of the system.

Keywords: gradient-velocity method of Lyapunov vector-functions, hyperbolic umbilic, self-organizing control system, stability

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Authors: Abdelkarim Boua, Abdelhakim Chillali

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The study of non-associative structures in algebraic structures has become a separate entity; for, in the case of groups, their corresponding non-associative structure i.e. loops is dealt with separately. Similarly there is vast amount of research on the nonassociative structures of semigroups i.e. groupoids and that of rings i.e. nonassociative rings. However it is unfortunate that we do not have a parallel notions or study of non-associative near-rings. In this work we shall attempt to generalize a few known results and study the commutativity of Jordan ideal in 3-prime near-rings satisfying certain identities involving the Jordan ideal. We study the derivations satisfying certain differential identities on Jordan ideals of 3-prime near-rings. Moreover, we provide examples to show that hypothesis of our results are necessary. We give some new results and examples concerning the existence of Jordan ideal and derivations in near-rings. These near-rings can be used to build a new codes.

Keywords: 3-prime near-rings, near-rings, Jordan ideal, derivations

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Authors: Galal Elkobrosy, Amr M. Abdelrazek, Bassuny M. Elsouhily, Mohamed E. Khidr

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Crank shaft length, connecting rod length, crank angle, engine rpm, cylinder bore, mass of piston and compression ratio are the inputs that can control the performance of the slider crank mechanism and then its efficiency. Several combinations of these seven inputs are used and compared. The throughput engine torque predicted by the simulation is analyzed through two different regression models, with and without interaction terms, developed according to multi-linear regression using LU decomposition to solve system of algebraic equations. These models are validated. A regression model in seven inputs including their interaction terms lowered the polynomial degree from 3^rd degree to 1^st degree and suggested valid predictions and stable explanations.

Keywords: design of experiments, regression analysis, SI engine, statistical modeling

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Authors: Nicole Merkle, Stefan Zander

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Ambient Assisted Living (AAL) describes a technological and methodological stack of (e.g. formal model-theoretic semantics, rule-based reasoning and machine learning), different aspects regarding the behavior, activities and characteristics of humans. Hence, a semantic representation of the user environment and its relevant elements are required in order to allow assistive agents to recognize situations and deduce appropriate actions. Furthermore, the user and his/her characteristics (e.g. physical, cognitive, preferences) need to be represented with a high degree of expressiveness in order to allow software agents a precise evaluation of the users’ context models. The correct interpretation of these context models highly depends on temporal, spatial circumstances as well as individual user preferences. In most AAL approaches, model representations of real world situations represent the current state of a universe of discourse at a given point in time by neglecting transitions between a set of states. However, the AAL domain currently lacks sufficient approaches that contemplate on the dynamic adaptions of context-related representations. Semantic representations of relevant real-world excerpts (e.g. user activities) help cognitive, rule-based agents to reason and make decisions in order to help users in appropriate tasks and situations. Furthermore, rules and reasoning on semantic models are not sufficient for handling uncertainty and fuzzy situations. A certain situation can require different (re-)actions in order to achieve the best results with respect to the user and his/her needs. But what is the best result? To answer this question, we need to consider that every smart agent requires to achieve an objective, but this objective is mostly defined by domain experts who can also fail in their estimation of what is desired by the user and what not. Hence, a smart agent has to be able to learn from context history data and estimate or predict what is most likely in certain contexts. Furthermore, different agents with contrary objectives can cause collisions as their actions influence the user’s context and constituting conditions in unintended or uncontrolled ways. We present an approach for dynamically updating a semantic model with respect to the current user context that allows flexibility of the software agents and enhances their conformance in order to improve the user experience. The presented approach adapts rules by learning sensor evidence and user actions using probabilistic reasoning approaches, based on given expert knowledge. The semantic domain model consists basically of device-, service- and user profile representations. In this paper, we present how this semantic domain model can be used in order to compute the probability of matching rules and actions. We apply this probability estimation to compare the current domain model representation with the computed one in order to adapt the formal semantic representation. Our approach aims at minimizing the likelihood of unintended interferences in order to eliminate conflicts and unpredictable side-effects by updating pre-defined expert knowledge according to the most probable context representation. This enables agents to adapt to dynamic changes in the environment which enhances the provision of adequate assistance and affects positively the user satisfaction.

Keywords: ambient intelligence, machine learning, semantic web, software agents

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Authors: N. Ould Cherchali, A. Tlemçani, M. S. Boucherit, A. Morsli

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Nature-inspired metaheuristic algorithms, particularly those founded on swarm intelligence, have attracted much attention over the past decade. Firefly algorithm has appeared in approximately seven years ago, its literature has enlarged considerably with different applications. It is inspired by the behavior of fireflies. The aim of this paper is the application of firefly algorithm for solving a nonlinear algebraic system. This resolution is needed to study the Selective Harmonic Eliminated Pulse Width Modulation strategy (SHEPWM) to eliminate the low order harmonics; results have been applied on multilevel inverters. The final results from simulations indicate the elimination of the low order harmonics as desired. Finally, experimental results are presented to confirm the simulation results and validate the efficaciousness of the proposed approach.

Keywords: firefly algorithm, metaheuristic algorithm, multilevel inverter, SHEPWM

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Authors: Khosrow Maleknejad, Yaser Rostami

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In this paper, semi-orthogonal B-spline scaling functions and wavelets and their dual functions are presented to approximate the solutions of integro-differential equations.The B-spline scaling functions and wavelets, their properties and the operational matrices of derivative for this function are presented to reduce the solution of integro-differential equations to the solution of algebraic equations. Here we compute B-spline scaling functions of degree 4 and their dual, then we will show that by using them we have better approximation results for the solution of integro-differential equations in comparison with less degrees of scaling functions.

Keywords: ıntegro-differential equations, quartic B-spline wavelet, operational matrices, dual functions

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Authors: Brogan Guest, Amy Donaldson-Perrott

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The Master’s of Physician Associate Studies (MPAS) programme at St George’s, University of London (SGUL), is an intensive two-year course that trains students to become physician associates (PAs). PAs are generalized healthcare providers who work in primary and secondary care across the UK. PA programmes face the difficult task of preparing students to become safe medical providers in two short years. Our goal is to teach students to develop clinical reasoning early on in their studies and historically, this has been done predominantly though problem-based learning (PBL). We have had an increase concern about student engagement in PBL and difficulty recruiting facilitators to maintain the low student to facilitator ratio required in PBL. To address this issue, we created ‘Clinical Application of Anatomy and Physiology (CAAP)’. These peer-led, interactive, problem-based, small group sessions were designed to facilitate students’ clinical reasoning skills. The sessions were designed using the concept of Team-Based Learning (TBL). Students were divided into small groups and each completed a pre-session quiz consisting of difficult questions devised to assess students’ application of medical knowledge. The quiz was completed in small groups and they were not permitted access of external resources. After the quiz, students worked through a series of openended, clinical tasks using all available resources. They worked at their own pace and the session was peer-led, rather than facilitator-driven. For a group of 35 students, there were two facilitators who observed the sessions. The sessions utilised an infinite space whiteboard software. Each group member was encouraged to actively participate and work together to complete the 15-20 tasks. The session ran for 2 hours and concluded with a post-session quiz, identical to the pre-session quiz. We obtained subjective feedback from students on their experience with CAAP and evaluated the objective benefit of the sessions through the quiz results. Qualitative feedback from students was generally positive with students feeling the sessions increased engagement, clinical understanding, and confidence. They found the small group aspect beneficial and the technology easy to use and intuitive. They also liked the benefit of building a resource for their future revision, something unique to CAAP compared to PBL, which out students participate in weekly. Preliminary quiz results showed improvement from pre- and post- session; however, further statistical analysis will occur once all sessions are complete (final session to run December 2022) to determine significance. As a post-graduate healthcare professional programme, we have a strong focus on self-directed learning. Whilst PBL has been a mainstay in our curriculum since its inception, there are limitations and concerns about its future in view of student engagement and facilitator availability. Whilst CAAP is not TBL, it draws on the benefits of peer-led, small group work with pre- and post- team-based quizzes. The pilot of these sessions has shown that students are engaged by CAAP, and they can make significant progress in clinical reasoning in a short amount of time. This can be achieved with a high student to facilitator ratio.

Keywords: problem based learning, team based learning, active learning, peer-to-peer teaching, engagement

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Authors: Amal Ezzidani, Abdelghani Ben Tahar, Mohamed Hanini

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A sequence of finite tandem queue is considered for this study. Each one has a single server, which operates under the egalitarian processor sharing discipline. External customers arrive at each queue according to a renewal input process and having a general service times distribution. Upon completing service, customers leave the current queue and enter to the next. Under mild assumptions, including critical data, we prove the existence and the uniqueness of the fluid solution. For asymptotic behavior, we provide necessary and sufficient conditions for the invariant state and the convergence to this invariant state. In the end, we establish the convergence of a correctly normalized state process to a fluid limit characterized by a system of algebraic and integral equations.

Keywords: fluid limit, fluid model, measure valued process, processor sharing, tandem queue

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Authors: Ömer Aktaş, Olga A. Suvorova, Oleg Tretyakov

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The boundary value problem on non-canonical and arbitrary shaped contour is solved with a numerically effective method called Analytical Regularization Method (ARM) to calculate propagation parameters. As a result of regularization, the equation of first kind is reduced to the infinite system of the linear algebraic equations of the second kind in the space of L2. This equation can be solved numerically for desired accuracy by using truncation method. The parameters as cut-off wavenumber and cut-off frequency are used in waveguide evolutionary equations of electromagnetic theory in time-domain to illustrate the real-valued TM fields with lossy and lossless media.

Keywords: analytical regularization method, electromagnetic theory evolutionary equations of time-domain, TM Field

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Authors: Abdi Ammar, Ouazir Youcef, Laissaoui Abdelmalek

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In this work, an approach based on transmission lines theory is presented. It is exploited for the calculation of overvoltage created by direct impacts of lightning waves on a guard cable of an overhead high-voltage line. First, we show the theoretical developments leading to the propagation equation, its discretization by finite difference time domain method (FDTD), and the resulting linear algebraic equations, followed by the calculation of the linear parameters of the line. The second step consists of solving the transmission lines system of equations by the FDTD method. This enabled us to determine the spatio-temporal evolution of the induced overvoltage.

Keywords: lightning surge, transient overvoltage, eddy current, FDTD, electromagnetic compatibility, ground wire

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Authors: Wiem Gadri

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This study delves into the intriguing properties of Pisot and Salem numbers within the framework of formal Laurent series over finite fields, a domain where these numbers’ spectral charac-teristics, Λm(β) and lm(β), have yet to be fully explored. Utilizing a methodological approach that combines algebraic number theory with the analysis of power series, we extend the foundational work of Erdos, Joo, and Komornik to this new setting. Our research uncovers bounds for lm(β), revealing how these depend on the degree of the minimal polynomial of β and thus offering a novel characterization of Pisot and Salem formal power series. The findings significantly contribute to our understanding of these numbers, highlighting their distribution and properties in the context of formal power series. This investigation not only bridges number theory with formal power series analysis but also sets the stage for further interdisciplinary research in these areas.

Keywords: Pisot numbers, Salem numbers, formal power series, over a finite field

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Authors: Sachin Kumar

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Fuzzy fractional diffusion equation is widely useful to depict different physical processes arising in physics, biology, and hydrology. The motive of this article is to deal with the fuzzy fractional diffusion equation. We study a mathematical model of fuzzy space-time fractional diffusion equation in which unknown function, coefficients, and initial-boundary conditions are fuzzy numbers. First, we find out a fuzzy operational matrix of Legendre polynomial of Caputo type fuzzy fractional derivative having a non-singular Mittag-Leffler kernel. The main advantages of this method are that it reduces the fuzzy fractional partial differential equation (FFPDE) to a system of fuzzy algebraic equations from which we can find the solution of the problem. The feasibility of our approach is shown by some numerical examples. Hence, our method is suitable to deal with FFPDE and has good accuracy.

Keywords: fractional PDE, fuzzy valued function, diffusion equation, Legendre polynomial, spectral method

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Authors: Mrigakshi Das

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The ethics of a business is currently a high profile issue owing to sensational corporate scandals that had taken place in many countries causing extensive damages to the economy and society. These corporate scandals question the morality of businessmen in general and accountants in particular. It is argued that the accountants have been the main contributors to the decline in ethical standards of a business. This researcher has reviewed the need and impact of ethics education in accounting profession. Despite of ethical interventions, the rate of accounting scandals are increasing and have left the public questioning that has the profession become really less ethical?

Keywords: accounting, ethics education and intervention in accounting, accounting education, accounting profession, moral reasoning and development, ethics education

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Authors: Farshad Badie

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The central focus of this article is on the fact that knowledge is constructed from an interaction between humans’ experiences and over their conceptions of constructed concepts. Logical characterisation of ‘human inductive learning over human’s constructed concepts’ within terminological systems and providing a logical background for theorising over the Human Concept Learning Problem (HCLP) in terminological systems are the main contributions of this research. This research connects with the topics ‘human learning’, ‘epistemology’, ‘cognitive modelling’, ‘knowledge representation’ and ‘ontological reasoning’.

Keywords: human concept learning, concept construction, knowledge construction, terminological systems

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