Search results for: fifth-order evolution equations

Authors: Fatemeh Nemati, Lucinda Leonard, Gwyn Lintern, Richard Thomson

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In this study, we will use modern numerical modeling approaches to estimate tsunami risks to the southern coast of British Columbia from landslides. Wave generation is to be simulated using the NHWAVE model, which solves the Navier-Stokes equations due to the more complex behavior of flow near the landslide source; far-field wave propagation will be simulated using the simpler model FUNWAVE_TVD with high-order Boussinesq-type wave equations, with a focus on the accurate simulation of wave propagation and regional- or coastal-scale inundation predictions.

Keywords: FUNWAVE-TVD, landslide-generated tsunami, NHWAVE, tsunami risk

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Authors: John Hardy

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The expansion of special operations forces (SOF) in the twenty-first century is often discussed in terms of the size and disposition of SOF units. Research regarding the number SOF personnel, the equipment SOF units procure, and the variety of roles and mission that SOF fulfill in contemporary conflicts paints a fascinating picture of changing expectations for the use of force. A strong indicator of the changing nature of SOF in contemporary conflicts is the fusion of strike and intelligence functions in the SOF in many countries. What were once more distinct roles on the kind of battlefield generally associated with the concept of conventional warfare have become intermingled in the era of persistent conflict which SOF face. This study presents a historical analysis of the co-evolution of the intelligence and direct action functions carried out by SOF in counterterrorism, counterinsurgency, and training and mentoring missions between 2004 and 2016. The study focuses primarily on innovation in the US military and the diffusion of key concepts to US allies first, and then more broadly afterward. The findings show that there were three key phases of evolution throughout the period of study, each coinciding with a process of innovation and doctrinal adaptation. The first phase was characterized by the fusion of intelligence at the tactical and operational levels. The second phase was characterized by the industrial counterterrorism campaigns used by US SOF against irregular enemies in Iraq and Afghanistan. The third phase was characterized by increasing forward collection of actionable intelligence by SOF force elements in the course of direct action raids. The evolution of strike and intelligence functions in SOF operations between 2004 and 2016 was significantly influenced by reciprocity. Intelligence fusion led to more effective targeting, which then increased intelligence collection. Strike and intelligence functions were then enhanced by greater emphasis on intelligence exploitation during operations, which further increased the effectiveness of both strike and intelligence operations.

Keywords: counterinsurgency, counterterrorism, intelligence, irregular warfare, military operations, special operations forces

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Authors: Chahid K. Ghaddar

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The spreadsheet engine is exploited via a non-conventional mechanism to enable novel worksheet solver functions for computational calculus. The solver functions bypass inherent restrictions on built-in math and user defined functions by taking variable formulas as a new type of argument while retaining purity and recursion properties. The enabling mechanism permits integration of numerical algorithms into worksheet functions for solving virtually any computational problem that can be modelled by formulas and variables. Several examples are presented for computing integrals, derivatives, and systems of deferential-algebraic equations. Incorporation of the worksheet solver functions with the ubiquitous spreadsheet extend the utility of the latter as a powerful tool for computational mathematics.

Keywords: calculus, differential algebraic equations, solvers, spreadsheet

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Authors: Mostefa Bendouba, Djebli Abdelkader, Abdelkrim Aid, Mohamed Benguediab

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The damage evolution mechanism is one of the important focuses of fatigue behaviour investigation of composite materials and also is the foundation to predict fatigue life of composite structures for engineering application. This paper is dedicated to a damage investigation under two block loading cycle fatigue conditions submitted to composite material. The loading sequence effect and the influence of the cycle ratio of the first stage on the cumulative fatigue life were studied herein. Two loading sequences, i.e., high-to-low and low-to-high cases are considered in this paper. The proposed damage indicator is connected cycle by cycle to the S-N curve and the experimental results are in agreement with model expectations. Some experimental researches are used to validate this proposition.

Keywords: fatigue, damage acumulation, composite, evolution

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Authors: Alireza Rafie Boldaji, Ahmad Saboonchi

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Chokes are commonly used in oil and gas production systems. A choke is a restriction basically designed to control flow rates of oil and gas wells, to prevent the downstream disturbances from propagating upstream (critical flow), and to protect the surface equipment facilities against slugging at high flowing pressures. There are different methods to calculate the multiphase flow rate, one of the multiphase flow measurement methods is the separation and measurement by on¬e-phaseFlow meter, another common method is the use of movable separator, their operations are very labor-intensive and costly. The current method used is based on the flow differential pressure on both sides of choke. Three groups of correlations describing two-phase flow through wellhead chokes were examined. The first group involved simple empirical equations similar to those of Gilbert, the second group comprised derived equations of two-phase flow incorporating PVT properties, and third group is computational method. In the article we calculate the flow of oil and gas through choke with simulation of this two phase flow bye computational fluid dynamic method, we use Ansys- fluent for this simulation and finally compared results of computational simulation whit empirical equations, the results show good agreement between experimental and numerical results.

Keywords: CFD, two-phase, choke, critical

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Authors: Hassan Youssef Mohamed

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In this paper, we show new wave equations, and by using the equations, we concluded that the strong force and the weak force are not fundamental, but they are quantum effects for electromagnetism. This result is different from the current scientific understanding about strong and weak interactions at all. So, we introduce three evidences for our theory. First, we prove the asymptotic freedom phenomenon in the strong force by using our model. Second, we derive the nuclear shell model as an approximation of our model. Third, we prove that the leptons do not participate in the strong interactions, and we prove the short ranges of weak and strong interactions. So, our model is consistent with the current understanding of physics. Finally, we introduce the electron-positron model as the basic ingredients for protons, neutrons, and all matters, so we can study all particles interactions and nuclear interaction as many-body problems of electrons and positrons. Also, we prove the violation of parity conservation in weak interaction as evidence of our theory in the weak interaction. Also, we calculate the average of the binding energy per nucleon.

Keywords: new wave equations, the strong force, the grand unification theory, hydrogen atom, weak force, the nuclear shell model, the asymptotic freedom, electron-positron model, the violation of parity conservation, the binding energy

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Authors: M. Srilatha, R. Hemalatha, T. Sri Aditya

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Communication of today world is dominated by wireless technology. This is mainly due to the revolutionary development of new wireless communication system generations. The evolving new generations of wireless systems are accommodating the demand through better resource management including improved transmission technologies with optimized communication devices. To keep up with the evolution of technologies, the communication systems must be designed to optimize transparent insertion of newly evolved technologies virtually at all stages of their life cycle. After the insertion of new technologies, the upgraded devices should continue the communication without squalor in quality. The concern of improving spectrum access and spectrum efficiency combined with both the introduction of Software Defined Radios (SDR) and the possibility of the software application to radios has led to an evolution of wireless radio research. The software defined radio term was coined in the 1970s to overcome the problems in the application of software to wireless radios which eliminates the requirement of hardware changes. SDR has become the prime theme of research since it eliminates the drawbacks associated with conventional wireless communication systems implementation. This paper identifies and discusses key enabling technologies and possibility of research and development in SDRs. In addition transmitter and receiver architectures of SDR are also discussed along with their feasibility for reconfigurable radio application.

Keywords: software defined radios, wireless communication, reconfigurable, reconfigurable transmitter, reconfigurable receivers, FPGA, DSP

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Authors: David Gottlieb, Jason Yoder

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The feeling of loneliness is not uncommon in modern society, and yet, there is a fundamental lack of understanding in its origins and purpose in nature. One interpretation of loneliness is that it is a subjective experience that punishes a lack of social behavior, and thus its emergence in human evolution is seemingly tied to the survival of early human tribes. Still, a common counterintuitive response to loneliness is a state of hypervigilance, resulting in social withdrawal, which may appear maladaptive to modern society. So far, no computational model of loneliness’ effect during evolution yet exists; however, agent-based models (ABM) can be used to investigate social behavior, and applying evolution to agents’ behaviors can demonstrate selective advantages for particular behaviors. We propose an ABM where each agent contains four social behaviors, and one goal-seeking behavior, letting evolution select the best behavioral patterns for resource allocation. In our paper, we use an algorithm similar to the boid model to guide the behavior of agents, but expand the set of rules that govern their behavior. While we use cohesion, separation, and alignment for simple social movement, our expanded model adds goal-oriented behavior, which is inspired by particle swarm optimization, such that agents move relative to their personal best position. Since agents are given the ability to form connections by interacting with each other, our final behavior guides agent movement toward its social connections. Finally, we introduce a mechanism to represent a state of loneliness, which engages when an agent's perceived social involvement does not meet its expected social involvement. This enables us to investigate a minimal model of loneliness, and using evolution we attempt to elucidate its value in human survival. Agents are placed in an environment in which they must acquire resources, as their fitness is based on the total resource collected. With these rules in place, we are able to run evolution under various conditions, including resource-rich environments, and when disease is present. Our simulations indicate that there is strong selection pressure for social behavior under circumstances where there is a clear discrepancy between initial resource locations, and against social behavior when disease is present, mirroring hypervigilance. This not only provides an explanation for the emergence of loneliness, but also reflects the diversity of response to loneliness in the real world. In addition, there is evidence of a richness of social behavior when loneliness was present. By introducing just two resource locations, we observed a divergence in social motivation after agents became lonely, where one agent learned to move to the other, who was in a better resource position. The results and ongoing work from this project show that it is possible to glean insight into the evolutionary advantages of even simple mechanisms of loneliness. The model we developed has produced unexpected results and has led to more questions, such as the impact loneliness would have at a larger scale, or the effect of creating a set of rules governing interaction beyond adjacency.

Keywords: agent-based, behavior, evolution, loneliness, social

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Authors: Agostinho Antunes

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The completion of the human genome sequencing in 2003 opened a new perspective into the importance of whole genome sequencing projects, and currently multiple species are having their genomes completed sequenced, from simple organisms, such as bacteria, to more complex taxa, such as mammals. This voluminous sequencing data generated across multiple organisms provides also the framework to better understand the genetic makeup of such species and related ones, allowing to explore the genetic changes underlining the evolution of diverse phenotypic traits. Here, recent results from our group retrieved from comparative evolutionary genomic analyses of selected marine animal species will be considered to exemplify how gene novelty and gene enhancement by positive selection might have been determinant in the success of adaptive radiations into diverse habitats and lifestyles.

Keywords: comparative genomics, adaptive evolution, bioinformatics, phylogenetics, genome mining

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Authors: Tala Toonsi, Marah Alagha, Lina Alnowaiser, Hala Rajab

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This report is about the Photomath app, which is an AI application that uses image recognition technology, specifically optical character recognition (OCR) algorithms. The (OCR) algorithm translates the images into a mathematical equation, and the app automatically provides a step-by-step solution. The application supports decimals, basic arithmetic, fractions, linear equations, and multiple functions such as logarithms. Testing was conducted to examine the usage of this app, and results were collected by surveying ten participants. Later, the results were analyzed. This paper seeks to answer the question: To what level the artificial intelligence features are accurate and the speed of process in this app. It is hoped this study will inform about the efficiency of AI in Photomath to the users.

Keywords: photomath, image recognition, app, OCR, artificial intelligence, mathematical equations.

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Authors: Saeed Otarod

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In a different simple and straight forward analysis a closed-form integral solution is found for nonhomogeneous second order linear ordinary differential equations, in terms of a particular solution of their corresponding homogeneous part. To find the particular solution of the homogeneous part, the equation is transformed into a simple Riccati equation from which the general solution of non-homogeneouecond order differential equation, in the form of a closed integral equation is inferred. The method works well in manyimportant cases, such as Schrödinger equation for hydrogen-like atoms. A non-homogenous second order linear differential equation has been solved as an extra example

Keywords: explicit, linear, differential, closed form

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Authors: M. R. Martinez-Torres, S. L. Toral, M. Olmedilla

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Typically, virtual communities exhibit the well-known phenomenon of participation inequality, which means that only a small percentage of users is responsible of the majority of contributions. However, the sustainability of the community requires that the group of active users must be continuously nurtured with new users that gain expertise through a participation process. This paper analyzes the time evolution of Open Source Software (OSS) communities, considering users that join/abandon the community over time and several topological properties of the network when modeled as a social network. More specifically, the paper analyzes the role of those users rejoining the community and their influence in the global characteristics of the network.

Keywords: open source communities, social network Analysis, time series, virtual communities

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Authors: Mohammad Besharatloo

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Intrusion detection is an important research topic in network security because of increasing growth in the use of computer network services. Intrusion detection is done with the aim of detecting the unauthorized use or abuse in the networks and systems by the intruders. Therefore, the intrusion detection system is an efficient tool to control the user's access through some predefined regulations. Since, the data used in intrusion detection system has high dimension, a proper representation is required to show the basis structure of this data. Therefore, it is necessary to eliminate the redundant features to create the best representation subset. In the proposed method, a hybrid model of differential evolution and firefly algorithms was employed to choose the best subset of properties. In addition, decision tree and support vector machine (SVM) are adopted to determine the quality of the selected properties. In the first, the sorted population is divided into two sub-populations. These optimization algorithms were implemented on these sub-populations, respectively. Then, these sub-populations are merged to create next repetition population. The performance evaluation of the proposed method is done based on KDD Cup99. The simulation results show that the proposed method has better performance than the other methods in this context.

Keywords: intrusion detection system, differential evolution, firefly algorithm, support vector machine, decision tree

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Authors: H. N. Agiza, M. A. Sohaly, M. A. Elfouly

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Parkinson's disease (PD) is a heterogeneous disorder with common age of onset, symptoms, and progression levels. In this paper we will solve analytically the PD model as a non-linear delay differential equation using the steps method. The step method transforms a system of delay differential equations (DDEs) into systems of ordinary differential equations (ODEs). On some numerical examples, the analytical solution will be difficult. So we will approximate the analytical solution using Picard method and Taylor method to ODEs.

Keywords: Parkinson's disease, step method, delay differential equation, two delays

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Authors: Tahseen Saad, Halim Ceylan, Jonathan Weaver, Osman Nuri Çelik, Onur Gungor Sahin

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A new concept of uniform delay offset dependent mathematical optimization problem is derived as the main objective for this study using a differential evolution algorithm. To control the coordination problem, which depends on offset selection and to estimate uniform delay based on the offset choice in a traffic signal network. The assumption is the periodic sinusoidal function for arrival and departure patterns. The cycle time is optimized at the entry links and the optimized value is used in the non-entry links as a common cycle time. The offset optimization algorithm is used to calculate the uniform delay at each link. The results are illustrated by using a case study and are compared with the canonical uniform delay model derived by Webster and the highway capacity manual’s model. The findings show new model minimizes the total uniform delay to almost half compared to conventional models. The mathematical objective function is robust. The algorithm convergence time is fast.

Keywords: area traffic control, traffic flow, differential evolution, sinusoidal periodic function, uniform delay, offset variable

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Authors: Chengwei Wang, Shuqing Xu, Philipp M. Schlüter

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The genus Ophrys is remarkable for its mimicry, flower-lip closely resembling pollinator females in a species-specific manner. Therefore, floral traits associated with pollinator attraction, especially scent, are suitable models for investigating the molecular basis of adaption, speciation, and evolution. Within the two Ophrys species groups: O. sphegodes (S) and O. fusca (F), pollinator shifts among the same insect species have taken place. Preliminary data suggest that they involve a comparable hydrocarbon profile in their scent, which is mainly composed of alkanes and alkenes. Genes encoding stearoyl-acyl carrier protein desaturases (SAD) involved in alkene biosynthesis have been identified in the S group. This study aims to investigate the control and parallel evolution of ecologically significant alkene production in Ophrys. Owing to the central role those SAD genes play in determining positioning of the alkene double-bonds, a detailed understanding of their functional mechanism and of regulatory aspects is of utmost importance. We have identified 5 transcription factors potentially related to SAD expression in O. sphegodes which belong to the MYB, GTE, WRKY, and MADS families. Ultimately, our results will contribute to understanding genes important in the regulatory control of floral scent synthesis.

Keywords: floral traits, transcription factors, biosynthesis, parallel evolution

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Authors: Gilbert Makanda, Roelf Sypkens

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A mathematical model for knowledge acquisition in teaching and learning is proposed. In this study we adopt the mathematical model that is normally used for disease modelling into teaching and learning. We derive mathematical conditions which facilitate knowledge acquisition. This study compares the effects of dropping out of the course at early stages with later stages of learning. The study also investigates effect of individual interaction and learning from other sources to facilitate learning. The study fits actual data to a general mathematical model using Matlab ODE45 and lsqnonlin to obtain a unique mathematical model that can be used to predict knowledge acquisition. The data used in this study was obtained from the tutorial test results for mathematics 2 students from the Central University of Technology, Free State, South Africa in the department of Mathematical and Physical Sciences. The study confirms already known results that increasing dropout rates and forgetting taught concepts reduce the population of knowledgeable students. Increasing teaching contacts and access to other learning materials facilitate knowledge acquisition. The effect of increasing dropout rates is more enhanced in the later stages of learning than earlier stages. The study opens up a new direction in further investigations in teaching and learning using differential equations.

Keywords: differential equations, knowledge acquisition, least squares nonlinear, dynamical systems

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Authors: Mr. Liju Elias, A. Chitharanjan Hegde

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Ni-W alloy coatings have been developed galvanostatically on copper substrate from tri-sodium citrate bath, using glycerol as the additive. The deposition conditions for production of Ni-W coatings have been optimized for peak performance of their electrocatalytic activity, namely hydrogen evolution reaction (HER) and oxygen evolution reaction (OER). The corrosion behavior of the coatings were tested under working conditions of electrocatalysis (1M KOH). Electrocatalytic behaviours were tested by cyclic voltammetry and chrono-potentiometry techniques. Experimental results demonstrated that Ni-W coatings at low and high current densities (c. d.) showing superior performance for OER and HER respectively. The increased electrocatalytic activity for HER with increase of deposition c. d. was attributed to the phase structure, surface morphology and chemical composition of the coatings, confirmed by XRD, SEM and EDX analysis, respectively. The dependency of hardness and thickness of the coatings on HER and OER were examined, and results were discussed.

Keywords: electrocatalytic behavior, HER, Ni-W alloy, OER

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Authors: Cletus Abhulimen, L. A. Ukpebor

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In this paper, we construct a class of four-step third derivative exponential fitting integrator of order six for the numerical integration of stiff initial-value problems of the type: y’= f(x,y); y(x₀) =y₀. The implicit method has free parameters which allow it to be fitted automatically to exponential functions. For the purpose of effective implementation of the proposed method, we adopted the techniques of splitting the method into predictor and corrector schemes. The numerical analysis of the stability of the new method was discussed; the results show that the method is A-stable. Finally, numerical examples are presented, to show the efficiency and accuracy of the new method.

Keywords: third derivative four-step, exponentially fitted, a-stable, stiff differential equations

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Authors: Manana Chumburidze

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We have considered a non-classical model of dynamical problems for a conjugated system of differential equations arising in thermo-piezoelectricity, which was formulated by Toupin – Mindlin. The basic concepts and the general theory of solvability for isotropic homogeneous elastic media is considered. They are worked by using the methods the Laplace integral transform, potential method and singular integral equations. Approximate solutions of mixed boundary value problems for finite domain, bounded by the some closed surface are constructed. They are solved in explicitly by using the generalized Fourier's series method.

Keywords: thermo-piezoelectricity, boundary value problems, Fourier's series, isotropic homogeneous elastic media

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Authors: Hamidreza Fazlollahi

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The Re ́nyi entropy comprises a group of data estimates that sums up the well-known Shannon entropy, acquiring a considerable lot of its properties. It appears as unqualified and restrictive entropy, relative entropy, or common data, and has found numerous applications in information theory. In the Re ́nyi’s argument, the area law of the black hole entropy plays a significant role. However, the total entropy can be modified by some quantum effects, motivated by the randomness of a system. In this note, by employing this modified entropy relation, we have derived corrections to Friedmann equations. Taking this entropy associated with the apparent horizon of the Friedmann-Robertson-Walker Universe and assuming the first law of thermodynamics, dE=T_A (dS)_A+WdV, satisfies the apparent horizon, we have reconsidered expanding Universe. Also, the second thermodynamics law has been examined.

Keywords: Friedmann equations, dark energy, first law of thermodynamics, Reyni entropy

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Authors: Mohammed Sabri Ali Akresh

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The modern technologies and developments in computer and Global Positioning System (GPS) as well as Geographic Information System (GIS) and total station TS. This paper presents a new proposal for coordinates system by a harmonic equations “United projections”, which have five projections (Mercator, Lambert, Russell, Lagrange, and compound of projection) in one zone coordinate system width 14 degrees, also it has one degree for overlap between zones, as well as two standards parallels for zone from 10 S to 45 S. Also this paper presents two cases; first case is to compare distances between a new coordinate system and UTM, second case creating local coordinate system for the city of Sydney to measure the distances directly from rectangular coordinates using projection of Mercator, Lambert and UTM.

Keywords: harmonic equations, coordinate system, projections, algorithms, parallels

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Authors: Elena M. Kopteva, Pavlina Jaluvkova, Zdenek Stuchlik

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The question of constructing a consistent model of the cosmological black hole remains to be unsolved and still attracts the interest of cosmologists as far as it is important in a wide set of research problems including the problem of the black hole horizon dynamics, the problem of interplay between cosmological expansion and local gravity, the problem of structure formation in the early universe etc. In this work, the model of the cosmological black hole is built on the basis of the exact solution of the Einstein equations for the spherically symmetric inhomogeneous dust distribution in the approach of the mass function use. Possible trajectories for massive particles and photons near the black hole immersed in the nonstatic dust cosmological background are investigated in frame of the obtained model. The reference system of distant galaxy comoving to cosmological expansion combined with curvature coordinates is used, so that the resulting metric becomes nondiagonal and involves both proper ‘cosmological’ time and curvature spatial coordinates. For this metric the geodesic equations are analyzed for the test particles and photons, and the respective trajectories are built.

Keywords: exact solutions for Einstein equations, Lemaitre-Tolman-Bondi solution, cosmological black holes, particle and photon trajectories

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Authors: Olteanu Constanta, Olteanu Lucian

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Researchers note that algebraic reasoning and sense making is essential for building conceptual knowledge in school mathematics. Consequently, pre-service teachers’ own reasoning and sense making are useful in fostering and developing students’ algebraic reasoning and sense making. This article explores the forms of reasoning and sense making that pre-service mathematics teachers exhibit and use in the process of analysing problem-posing tasks with a focus on first-degree equations. Our research question concerns the characteristics of the problem-posing tasks used for reasoning and sense making of first-degree equations as well as the characteristics of pre-service teachers’ reasoning and sense making in problem-posing tasks. The analyses are grounded in a post-structuralist philosophical perspective and variation theory. Sixty-six pre-service primary teachers participated in the study. The results show that the characteristics of reasoning in problem-posing tasks and of pre-service teachers are selecting, exploring, reconfiguring, encoding, abstracting and connecting. The characteristics of sense making in problem-posing tasks and of pre-service teachers are recognition, relationships, profiling, comparing, laddering and verifying. Beside this, the connection between reasoning and sense making is rich in line of flight in problem-posing tasks, while the connection is rich in line of rupture for pre-service teachers.

Keywords: first-degree equations, problem posing, reasoning, rhizomatic assemblage, sense-making, variation theory

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Authors: Petre Stan, Marinica Stan

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In this paper, a new way to define the vortex plane cyclic motion is exposed, starting from the physical cause of reacting the vortex. The Navier-Stokes equations are used in cylindrical coordinates for viscous fluids in laminar motion, and are integrated in case of a infinite long revolving cylinder which rotates around a pintle in a viscous fluid that occupies the entire space up to infinite. In this way, a revolving field of velocities in fluid is obtained, having the shape of a vortex in which the intensity is obtained objectively, being given by the physical phenomenon that generates this vortex.

Keywords: cylindrical coordinates, Navier-Stokes equations, viscous fluid, vortex plane

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Authors: S. Nagheli, N. Samani, D. A. Barry

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In this paper, the velocity potential and stream function of capture zone for a well field in an aquifer bounded by two parallel streams with or without a uniform regional flow of any directions are presented. The well field includes any number of extraction or injection wells or a combination of both types with any pumping rates. To delineate the capture envelope, the potential and streamlines equations are derived by conformal mapping method. This method can help us to release constrains of other methods. The equations can be applied as useful tools to design in-situ groundwater remediation systems, to evaluate the surface–subsurface water interaction and to manage the water resources.

Keywords: complex potential, conformal mapping, image well theory, Laplace’s equation, superposition principle

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Authors: J. Shamash

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The high-school curriculum in algebra deals mainly with the solution of different types of equations. However, modern algebra has a completely different viewpoint and is concerned with algebraic structures and operations. A question then arises: What might be the relevance and contribution of an abstract algebra course for developing expertise and mathematical perspective in secondary school mathematics instruction? This is the focus of this paper. The course Algebra: From Equations to Structures is a carefully designed abstract algebra course for Israeli secondary school mathematics teachers. The course provides an introduction to algebraic structures and modern abstract algebra, and links abstract algebra to the high-school curriculum in algebra. It follows the historical attempts of mathematicians to solve polynomial equations of higher degrees, attempts which resulted in the development of group theory and field theory by Galois and Abel. In other words, algebraic structures grew out of a need to solve certain problems, and proved to be a much more fruitful way of viewing them. This theorems in both group theory and field theory. Along the historical ‘journey’, many other major results in algebra in the past 150 years are introduced, and recent directions that current research in algebra is taking are highlighted. This course is part of a unique master’s program – the Rothschild-Weizmann Program – offered by the Weizmann Institute of Science, especially designed for practicing Israeli secondary school teachers. A major component of the program comprises mathematical studies tailored for the students at the program. The rationale and structure of the course Algebra: From Equations to Structures are described, and its relevance to teaching school algebra is examined by analyzing three kinds of data sources. The first are position papers written by the participating teachers regarding the relevance of advanced mathematics studies to expertise in classroom instruction. The second data source are didactic materials designed by the participating teachers in which they connected the mathematics learned in the mathematics courses to the school curriculum and teaching. The third date source are final projects carried out by the teachers based on material learned in the course.

Keywords: abstract algebra , linking abstract algebra and school mathematics, school algebra, secondary school mathematics, teacher professional development

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Authors: Abdelaziz Rabhi, Mohamed Amrani, Abderrazek Ziane, Nabil Belkadi, Abdelraouf Hocini

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In this paper, a bedimensional simulation program of the electric characteristics of reverse biased lateral polysilicon PIN diode is presented. In this case we have numerically solved the system of partial differential equations formed by Poisson's equation and both continuity equations that take into account the effect of impact ionization. Therefore we will obtain the current-voltage characteristics (I-V) of the reverse-biased structure which may include the effect of breakdown.The geometrical model assumes that the polysilicon layer is composed by a succession of defined mean grain size crystallites, separated by lateral grain boundaries which are parallel to the metallurgic junction.

Keywords: breakdown, polycrystalline silicon, PIN, grain, impact ionization

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Authors: Mehtap Lafcı

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In recent years, oscillation, periodicity and convergence of solutions of linear differential equations with piecewise constant arguments have been significantly considered but there are only a few papers for impulsive differential equations with piecewise constant arguments. In this paper, a first order nonlinear impulsive differential equation with piecewise constant arguments is studied and the existence of solutions and periodic solutions of this equation are investigated by using Carvalho’s method. Finally, an example is given to illustrate these results.

Keywords: Carvalho's method, impulsive differential equation, periodic solution, piecewise constant arguments

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Authors: Anuar Ishak

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The mixed convection stagnation point flow toward a vertical plate is investigated. The external flow impinges normal to the heated plate and the surface temperature is assumed to vary linearly with the distance from the stagnation point. The governing partial differential equations are transformed into a set of ordinary differential equations, which are then solved numerically using MATLAB routine boundary value problem solver bvp4c. Numerical results show that dual solutions are possible for a certain range of the mixed convection parameter. A stability analysis is performed to determine which solution is linearly stable and physically realizable.

Keywords: dual solutions, heat transfer, mixed convection, stability analysis

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