Search results for: chaotic differential evolution (CDDE)

Authors: Hamdi Belgacem, Fradi Aymen

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In this paper we present a low power, low cost differential logic unit (LU). The proposed LU receives dual-rail inputs and generates dual-rail outputs. The proposed circuit can be used in Arithmetic and Logic Units (ALU) of processor. It can be also dedicated for self-checking applications based on dual duplication code. Four logic functions as well as their inverses are implemented within a single Logic Unit. The hardware overhead for the implementation of the proposed LU is lower than the hardware overhead required for standard LU implemented with standard CMOS logic style. This new implementation is attractive as fewer transistors are required to implement important logic functions. The proposed differential logic unit can perform 8 Boolean logical operations by using only 16 transistors. Spice simulations using a 32 nm technology was utilized to evaluate the performance of the proposed circuit and to prove its acceptable electrical behaviour.

Keywords: differential logic unit, double pass transistor logic, low power CMOS design, low cost CMOS design

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Authors: Mohamed Sadok Bensalem, Soulef Amamria, Khaled Lazzez, Mohamed Ghanmi

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The southern-central Tunisian Atlas presents a typical example of an external zone. It occupies a particular position in the North African chains: firstly, it is the eastern limit of atlassic structures; secondly, it is the edges between the belts structures to the north and the stable Saharan platform in the south. The evolution of deformation study is based on several methods, such as classical or numerical methods. The principals parameters controlling the genesis of folds in the southern central Tunisian Atlas are; the reactivation of pre-existing faults during the later compressive phase, the evolution of decollement level, and the relation between thin and thick-skinned. One of the more principal characters of the southern-central Tunisian Atlas is the variation of belts structures directions determined by: NE-SW direction, named the attlassic direction in Tunisia, the NW-SE direction carried along the Gafsa fault (the oriental limit of southern atlassic accident), and the E-W direction defined in the southern Tunisian Atlas. This variation of direction is the result of important variation of deformation during different tectonics phases. A classical modelling of the Jebel ElKebar anticline, based on faults throw of the pre-existing faults and its reactivation during compressive phases, shows the importance of extensional deformation, particular during Aptian-Albian period, comparing with that of later compression (Alpine phases). A numerical modelling, based on the software Rampe E.M. 1.5.0, applied on the anticline of Jebel Orbata confirms the interpretation of “fault related fold” with decollement level within the Triassic successions. The other important parameter of evolution of deformation is the vertical migration of decollement level; indeed, more than the decollement level is in the recent series, most that the deformation is accentuated. The evolution of deformation is marked the development of duplex structure in Jebel At Taghli (eastern limit of Jebel Orbata). Consequently, the evolution of deformation is proportional to the depth of the decollement level, the most important deformation is in the higher successions; thus, is associated to the thin-skinned deformation; the decollement level permit the passive transfer of deformation in the cover.

Keywords: evolution of deformation, pre-existing faults, decollement level, thin-skinned

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Authors: Gebreegziabher Hailu

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This paper presents the development of residual power series methods aimed at efficiently solving stiff differential equations, which pose significant challenges in numerical analysis due to their rapid changes in solution behavior. The RPSM is a numerical approach that generates polynomial-based approximate solutions without the need for linearization, discretization, or perturbation techniques, making it straightforward to implement and less prone to computational errors. We introduce an approach that utilizes power series expansions combined with residual minimization techniques to enhance convergence and stability. By analyzing the theoretical foundations of stiffness, we delve into the formulation of the residual power series method, detailing how it effectively captures the dynamics of stiff systems while maintaining computational efficiency. Numerical experiments demonstrate the method's superiority in terms of accuracy and computational cost when compared to traditional methods like implicit Runge-Kutta or multistep techniques. We also explore adaptive strategies within our framework to automatically adjust parameters based on the stiffness characteristics of the problem at hand. Ultimately, our findings contribute to the broader toolkit for tackling stiff differential equations, offering a robust alternative that promises to streamline computational workflows in various applied mathematics and engineering contexts.

Keywords: residual power series methods, stiff differential equoations, numerical approach, Runge Kutta methods

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Authors: Malik Imtiaz Ahmad

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The development of In Vitro Fertilization (IVF) has revolutionized the field of reproductive medicine, offering hope to myriad individuals and couples facing infertility issues. IVF, a process involving the fertilization of eggs with sperm outside the body, has evolved over decades from an experimental procedure to a mainstream medical practice. The study sought to understand the evolution of IVF from its early stages to its present status as a groundbreaking fertility treatment. It also aimed to analyze the legal complexities surrounding IVF, including issues like embryo ownership, surrogacy agreements, and custody disputes. This research focused on the multidisciplinary approach involving both medical and legal fields. It aimed to explore the historical evolution of IVF, its techniques, and legal challenges concerning family law, health law, and privacy policies it has given rise to in modern times. This research aimed to provide insights into the intersection of medical technology and the law, offering valuable knowledge for policymakers, legal experts, and individuals involved in IVF. The study utilized various methods, including a thorough literature review, a historical analysis of IVF’s evolution, an examination of legal cases, and a review of emerging regulations. These approaches aimed to provide a comprehensive understanding of IVF and its modern legal issues, facilitating a holistic exploration of the subject matter.

Keywords: in vitro fertilization development, IVF techniques evolution, legal issues in IVF, IVF legal frameworks, ethical dilemmas in IVF

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Authors: Ebraheem Al-Jouri, Youssef Abu-Ahmad, Ramasamy Srinivasan

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The parasitoid, Diadegma semiclausum (Hymenoptera: Ichneumonidae) is one of the most effective exotic parasitoids of diamondback moth (DBM), Plutella xylostella in the lowland areas of Homs, Syria. Molecular evolution studies are useful tools to shed light on the molecular bases of insect geographical spread and adaptation to new hosts and environment and for designing better control strategies. In this study, molecular evolution analysis was performed based on the 42 nuclear internal transcribed spacer-2 (ITS2) sequences representing the D. semiclausum and eight other Diadegma spp. from Syria and worldwide. Possible recombination events were identified by RDP4 program. Four potential recombinants of the American D. insulare and D. fenestrale (Jeju) were detected. After detecting and removing recombinant sequences, the ratio of non-synonymous (dN) to synonymous (dS) substitutions per site (dN/dS=ɷ) has been used to identify codon positions involved in adaptive processes. Bayesian techniques were applied to detect selective pressures at a codon level by using five different approaches including: fixed effects likelihood (FEL), internal fixed effects likelihood (IFEL), random effects method (REL), mixed effects model of evolution (MEME) and Program analysis of maximum liklehood (PAML). Among the 40 positively selected amino acids (aa) that differed significantly between clades of Diadegma species, three aa under positive selection were only identified in D. semiclausum. Additionally, all D. semiclausum branches tree were highly found under episodic diversifying selection (EDS) at p≤0.05. Our study provide evidence that both recombination and positive selection have contributed to the molecular diversity of Diadegma spp. and highlights the significant contribution of D. semiclausum in adaptive evolution and influence the fitness in the DBM parasitoid.

Keywords: diadegma sp, DBM, ITS2, phylogeny, recombination, dN/dS, evolution, positive selection

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Authors: Sergio Haram Sarmiento, Arcady Ponosov

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Based on appropriate multivariate statistical methodology, we suggest a generic framework for efficient parameter estimation for ordinary differential equations and the corresponding nonlinear models. In this framework classical linear regression strategies is refined into a nonlinear regression by a locally linear modelling technique (known as metamodelling). The approach identifies those latent variables of the given model that accumulate most information about it among all approximations of the same dimension. The method is applied to several benchmark problems, in particular, to the so-called ”power-law systems”, being non-linear differential equations typically used in Biochemical System Theory.

Keywords: principal component analysis, generalized law of mass action, parameter estimation, metamodels

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Authors: Shih-Hao Chen, Chi-Wai Chow

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Visible light communication combined with spread spectrum modulation is demonstrated in this study. Differential signaling method also ensures the proposed system that can support high immunity to ambient light interference. Experiment result shows the proposed system has 6 dB gain comparing with the original On-Off Keying modulation scheme.

Keywords: Visible Light Communication (VLC), Spread Spectrum Modulation (SSM), On-Off Keying, visible light communication

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Authors: S. Srednyak

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We study a class of functional partial differential equations(FPDEs). This class is suggested by Quantum Field Theory. We derive general properties of solutions to such equations. In particular, we demonstrate that they lead to systems of coupled integral equations with singular kernels. We show that solutions to such hierarchies can be sought among functions with regular singularities at a countable set of subvarieties of the physical space. We also develop a formal analogy of basic constructions of differential geometry on functional manifolds, as this is necessary for in depth study of FPDEs. We also consider the case of linear overdetermined systems of functional differential equations and show that it can be completely solved in terms of formal solutions of a functional equation that is a functional analogy of a system of determined algebraic equations. This development leads us to formally define the functional analogy of algebraic geometry, which we call functional algebraic geometry. We study basic properties of functional algebraic varieties. In particular, we investigate the case of a formally discrete set of solutions. We also define and study functional analogy of discriminants. In the case of fully determined systems such that the defining functionals have regular singularities, we demonstrate that formal solutions can be sought in the class of functions with regular singularities. This case provides a practical way to apply our results to physics problems.

Keywords: functional equations, quantum field theory, holomorphic functions, Yang Mills mass gap problem, quantum chaos

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Authors: Arcady Ponosov., Ramazan Kadiev

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The work studies the global moment stability of solutions of systems of nonlinear differential Itô equations with delays. A modified regularization method (W-method) for the analysis of various types of stability of such systems, based on the choice of the auxiliaryequations and applications of the theory of positive invertible matrices, is proposed and justified. Development of this method for deterministic functional differential equations is due to N.V. Azbelev and his students. Sufficient conditions for the moment stability of solutions in terms of the coefficients for sufficiently general as well as specific classes of Itô equations are given.

Keywords: asymptotic stability, delay equations, operator methods, stochastic noise

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Authors: Reni M. Sagayaraj, Anand Gnana S. Selvam, Reynald R. Susainathan

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In this paper, we consider stochastic queueing models for Steady-state behavior of a multi-phase M/M/1 queue in random evolution subject to catastrophe failure. The arrival flow of customers is described by a marked Markovian arrival process. The service times of different type customers have a phase-type distribution with different parameters. To facilitate the investigation of the system we use a generalized phase-type service time distribution. This model contains a repair state, when a catastrophe occurs the system is transferred to the failure state. The paper focuses on the steady-state equation, and observes that, the steady-state behavior of the underlying queueing model along with the average queue size is analyzed.

Keywords: M/G/1 queuing system, multi-phase, random evolution, steady-state equation, catastrophe failure

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Authors: Aisha Iddrisu

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The proliferation of cyberviolence in the wave of increased social media consumption calls for immediate attention both at the local and global levels. With over 4.70 billion social media users worldwide and 8.8 social media users in Ghana, various forms of violence have become the order of the day in most countries and communities. Cyber violence is defined as producing, retrieving, and sharing of hurtful or dangerous online content to cause emotional, psychological, or physical harm. The urgency and severity of cyber violence have led to the enactment of laws in various countries though lots still need to be done, especially in Ghana. In Ghana, studies on cyber violence have not been extensively dealt with. Existing studies concentrate only on one form or the other form of cyber violence, thus cybercrime and cyber bullying. Also, most studies in Africa have not explored cyber violence forms using empirical theories and the few that existed were qualitatively researched, whereas others examine the effect of cyber violence rather than examining why those who involve in it behave the way they behave. It is against this backdrop that this study aims to examine various cyber violence behaviour among social media users in Ghana by applying the theory of Self-control and Social control theory. This study is important for the following reasons. The outcome of this research will help at both national and international level of policymaking by adding to the knowledge of understanding cyberviolence and why people engage in various forms of cyberviolence. It will also help expose other ways by which such behaviours are enforced thereby serving as a guide in the enactment of the rightful rules and laws to curb such behaviours. It will add to literature on consequences of new media. This study seeks to confirm or reject to the following research hypotheses. H1 Social media usage has direct significant effect of cyberviolence behaviours. H2 Ineffective parental management has direct significant positive relation to Low self-control. H3 Low self-control has direct significant positive effect on cyber violence behaviours among social, H4 Differential association has significant positive effect on cyberviolence behaviour among social media users in Ghana. H5 Definitions have a significant positive effect on cyberviolence behaviour among social media users in Ghana. H6 Imitation has a significant positive effect on cyberviolence behaviour among social media users in Ghana. H7 Differential reinforcement has a significant positive effect on cyberviolence behaviour among social media users in Ghana. H8 Differential association has a significant positive effect on definitions. H9 Differential association has a significant positive effect on imitation. H10 Differential association has a significant positive effect on differential reinforcement. H11 Differential association has significant indirect positive effects on cyberviolence through the learning process.

Keywords: cyberviolence, social media users, self-control theory, social learning theory

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Authors: Ahmed Machmoum, Malika El Kyal

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We consider iterative parallel multi-splitting method for differential algebraic equations. The main feature of the proposed idea is to use the asynchronous form. We prove that the multi-splitting technique can effectively accelerate the convergent performance of the iterative process. The main characteristic of an asynchronous mode is that the local algorithm not have to wait at predetermined messages to become available. We allow some processors to communicate more frequently than others, and we allow the communication delays tobe substantial and unpredictable. Note that synchronous algorithms in the computer science sense are particular cases of our formulation of asynchronous one.

Keywords: computer, multi-splitting methods, asynchronous mode, differential algebraic systems

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Authors: Arcady Ponosov

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A novel mathematical approach is suggested, which facilitates a compressed representation and efficient validation of parameter-rich ordinary differential equation models describing the dynamics of complex, especially biology-related, systems and which is based on identification of the system's latent variables. In particular, an efficient parameter estimation method for the compressed non-linear dynamical systems is developed. The method is applied to the so-called 'power-law systems' being non-linear differential equations typically used in Biochemical System Theory.

Keywords: generalized law of mass action, metamodels, principal components, synergetic systems

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Authors: Bhaskar Chakravorti, Christopher Tunnard, Ravi Shankar Chaturvedi

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This report introduces the Digital Evolution Index (DEI) as a way to gauge the transformation of economies in the advanced and developing world from traditional brick-and-mortar to digitally enabled. The DEI measures the digital trajectories of 50 countries to provide actionable, data-informed insights for businesses, investors and policymakers. Created by The Fletcher School, in collaboration with MasterCard Worldwide and DataCash, the DEI analyzes the key underlying drivers and barriers that govern a country’s evolution into a digital economy: Demand, Supply, Institutional Environment and Innovation. A longitudinal analysis of these four drivers during the years 2008 to 2013 reveals both the current state of a country’s digital economy, as well as changes over time. Combining these two measures allows us to assign each country to one of four Trajectory Zones: • Stand Out countries have shown high levels of digital development in the past and continue to remain on an upward trajectory. • Stall Out countries have achieved a high level of evolution in the past but are losing momentum and risk falling behind. • Break Out countries have the potential to develop strong digital economies. Though their overall score is still low, they are moving upward and are poised to become Stand Out countries in the future. • Watch Out countries face significant opportunities and challenges, with low scores on both current level and upward motion of their DEI. Some may be able to overcome limitations with clever innovations and stopgap measures, while others seem to be stuck.

Keywords: e-commerce, digital evolution, digital commerce ecosystems, e-consumer

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Authors: Luke Ukpebor, C. E. Abhulimen

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Stiff initial value problems in ordinary differential equations are problems for which a typical solution is rapidly decaying exponentially, and their numerical investigations are very tedious. Conventional numerical integration solvers cannot cope effectively with stiff problems as they lack adequate stability characteristics. In this article, we developed a new family of four-step second derivative exponentially fitted method of order six for the numerical integration of stiff initial value problem of general first order differential equations. In deriving our method, we employed the idea of breaking down the general multi-derivative multistep method into predator and corrector schemes which possess free parameters that allow for automatic fitting into exponential functions. The stability analysis of the method was discussed and the method was implemented with numerical examples. The result shows that the method is A-stable and competes favorably with existing methods in terms of efficiency and accuracy.

Keywords: A-stable, exponentially fitted, four step, predator-corrector, second derivative, stiff initial value problems

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Authors: Noor Hayati Binti Ismail, Mastor Bin Surat, Raja Nafida Binti Raja Shahminan, Shahrul Kamil Bin Yunus

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This study is to look the changes, development and evolution taking place in the Minangkabau house. Minangkabau traditional house is a part of the assets of Indonesia's culture and history. In addition to custom house, traditional Minangkabau building also serves as a place to live within the context of human habitats but has slowly through the changes. Luhak Nan Tigo of Luhak Tanah Datar, Agam And Luhak 50 Kota are holding the Minangkabau. ‘Induk’ house is the sole home, Main house or an older home for a gathering place doing activities together. The 'Genius Loci' refers to the unique aspects of the history, the value of a place, culturally and socially. Main house has the aspect of Minangkabau is a house occupied by custom rules that practice matrilineal kinship system and tendency to move out from the community. The study involves several villages and traditional houses at Padang, Bukit Tinggi, Kampar Kiri in Indonesia and Rembau, kuala Pilah, tampin in Negeri Sembilan has been selected to serve as a research field. These factors were the occurrence of evolution Minangkabau house from the ‘induk’, kampar and Negeri Sembilan. In this regard, the identity and uniqueness of the house increasingly difficult to sustain as well as lack of clarity can be understood by the people of the present generation.

Keywords: evolution, Genius loci, ‘Induk’ house, matrilineal kinship

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Authors: Yuan Yan Tang, Lina Yang, Hong Li

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Harmonic model is a very important approximation for the image transform. The harmanic model converts an image into arbitrary shape; however, this mode cannot be described by any fixed functions in mathematics. In fact, it is represented by partial differential equation (PDE) with boundary conditions. Therefore, to develop an efficient method to solve such a PDE is extremely significant in the image transform. In this paper, a novel Integral Equation-Wavelet based method is presented, which consists of three steps: (1) The partial differential equation is converted into boundary integral equation and representation by an indirect method. (2) The boundary integral equation and representation are changed to plane integral equation and representation by boundary measure formula. (3) The plane integral equation and representation are then solved by a method we call wavelet collocation. Our approach has two main advantages, the shape of an image is arbitrary and the program code is independent of the boundary. The performance of our method is evaluated by numerical experiments.

Keywords: harmonic model, partial differential equation (PDE), integral equation, integral representation, boundary measure formula, wavelet collocation

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Authors: Dave Kenneth Tayao Cayado, Carlo P. Magno

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The most common source of bias detected are those of gender and socioeconomic status. The present study investigated the Differential Item Functioning (DIF) or item bias between public and private school students in a vocabulary test. Studies on DIF were expanded by using the type of school as a source of bias. There were 200 participants in this study. 100 came from a public secondary school and 100 came from a private secondary school. The vocabulary skills of students were measured using a standardized vocabulary test for grade 7 students. Using DIF, specifically the Rasch-Welch approach, it was found that out of 24 items, 12 were biased for a specific group. The vocabulary skills on the use of slang, idiomatic expression, personification, collocations, and partitive relations were biased for private schools while the use of slang and homonymous words were biased for public school students. The analysis debunked the trend that private school students are outperforming public school students in terms of academic achievement. It was revealed that there are some competencies that private school students are having difficulty and vice versa.

Keywords: differential item functioning, item bias, public school students, private school students, vocabulary

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Authors: Renu Gupta, Ashim K. Pramanik

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We report the evolution of structure and magnetic properties in perovskite ruthenates Sr1-xPrxRuO3 (x = 0.0 and 0.1). Our main expectations, to induce the structural modification and change the Ru charge state by Pr doping at Sr site. By the Pr doping on Sr site retains orthorhombic structure while we find a minor change in structural parameters. The SrRuO3 have itinerant type of ferromagnetism with ordering temperature ~160 K. By Pr doping, the magnetic moment decrease and ZFC show three distinct peaks (three transition temperature; TM1, TM2 and TM3). Further analysis of magnetization of both samples, at high temperature follow modified CWL and Pr doping gives Curie temperature ~ 129 K which is close to TM2. Above TM2 to TM3, the inverse susceptibility shows upward deviation from CW behavior, indicating the existence AFM like clustered in this regime. The low-temperature isothermal magnetization M (H) shows moment decreases by Pr doping. The Arrott plot gives spontaneous magnetization (Ms) which also decreases by Pr doping. The evolution of Rhodes-Wohlfarth ratio increases which suggests the FM in this system evolves toward the itinerant type by Pr doping.

Keywords: itinerant ferromagnet, Perovskite structure, Ruthenates, Rhodes-Wohlfarth ratio

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Authors: Zoran Spasovski

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The paper shortly discusses the significance and the benefits of the historical approach in the research of languages by presenting examples of it in the fields of phonetics and phonology, lexicology, morphology, syntax, and even in the onomastics (toponomy and anthroponomy). The examples from the field of phonetics/phonology include insights into animal speech and its evolution into human speech, the evolution of the sounds of human speech from vocals to glides and consonants and from velar consonants to palatal, etc., on well-known examples of former researchers. Those from the field of lexicology show shortly the formation of the lexemes and their evolution; the morphology and syntax are explained by examples of the development of grammar and syntax forms, and the importance of the historical approach in the research of place-names and personal names is briefly outlined through examples of place-names and personal names and surnames, and the conclusions that come from it, in different languages.

Keywords: animal speech, glotogenesis, grammar forms, lexicology, place-names, personal names, surnames, syntax categories

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Authors: Elio El Kahi, Michel Khouri, Olivier Deck, Pierre Rahme, Rasool Mehdizadeh

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Recent developments in civil engineering create multiple interaction problems between the soil and the structure. One of the major problems is the impact of ground movements on buildings. Consequently, managing risks associated with these movements, requires a determination of the different influencing factors and a specific knowledge of their variability/uncertainty. The main purpose of this research is to study the behavior of structures submitted to differential settlement, in order to assess their vulnerability, taking into consideration the different sources of uncertainties. Analytical approach is applied to investigate on one hand the influence of these uncertainties that are related to the soil, and on the other hand the structure stiffness variation with the presence of openings and the movement transmitted between them as related to the origin and shape of the free-field movement. Results reveal the effect of taking these uncertainties into consideration, and specify the dominant and most significant parameters that control the ground movement associated with the Soil-Structure Interaction (SSI) phenomenon.

Keywords: analytical approach, building, damage, differential settlement, soil-structure interaction, uncertainties

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Authors: Elmongi Elbellili, Ben Lauwens, Daan Huybrechs

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The increasing complexity of modern engineering systems presents a challenge to the digital simulation of these systems which usually can be represented by differential equations. The Linearly Implicit Quantized State System (LIQSS) offers an alternative approach to traditional numerical integration techniques for solving Ordinary Differential Equations (ODEs). This method proved effective for handling discontinuous and large stiff systems. However, the inherent discrete nature of LIQSS may introduce oscillations that result in unnecessary computational steps. The current oscillation detection mechanism relies on a condition that checks the significance of the derivatives, but it could be further improved. This paper describes a different cycle detection mechanism and presents the outcomes using LIQSS order one in simulating the Advection Diffusion problem. The efficiency of this new cycle detection mechanism is verified by comparing the performance of the current solver against the new version as well as a reference solution using a Runge-Kutta method of order14.

Keywords: numerical integration, quantized state systems, ordinary differential equations, stiffness, cycle detection, simulation

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Authors: Tran Le Luu, Jeyong Yoon

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RuO2-TiO2 electrode now becomes popular in the chlor-alkali industry because of high electrocatalytic and stability with chlorine and oxygen evolutions. Using alternative green method for preparation RuO2-TiO2 electrode is necessary to reduce the cost, time. In addition, it is needed to increase the electrocatalyst performance, stability, and environmental compatibility. In this study, the Ti/RuO2-TiO2 electrodes were synthesized using sol-gel method under microwave irradiation and investigated for the anodic chlorine and oxygen evolutions. This method produced small size and uniform distribution of RuO2-TiO2 nanoparticles with mean diameter of 8-10 nm on the big crack size surface which contributes for the increasing of the outer active surface area. The chlorine, oxygen evolution efficiency and stability comparisons show considerably higher for microwave-assisted coated electrodes than for those obtained by the conventional heating method. The microwave-assisted sol-gel route has been identified as a novel and powerful method for quick synthesis of RuO2–TiO2 electrodes with excellent chlorine and oxygen evolution performances.

Keywords: RuO2, electro-catalyst, sol-gel, microwave, chlorine, oxygen evolution

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Authors: Kushakov Kholmurodjon, Muhammadjonov Akbarshox

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This present paper is devoted to a system of second-order nonlinear differential equations with a special right-hand side, exactly, the linear part and a third-order polynomial of a special form. It is shown that for some relations between the parameters, there is a second-order curve in which trajectories leaving the points of this curve remain in the same place. Thus, the curve is invariant with respect to the given system. Moreover, this system is invariant under a non-degenerate linear transformation of variables. The form of this curve, depending on the relations between the parameters and the eigenvalues of the matrix, is proved. All solutions of this system of differential equations are shown analytically.

Keywords: dynamic system, ellipse, hyperbola, Hess system, polar coordinate system

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Authors: J. A. Gbadeyan, R. A. Kareem

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In this paper, we investigated the effects of unsteady internal heat generation of a two-step exothermic reactive hydromagnetic fluid flow under different chemical kinetics namely: Sensitized, Arrhenius and Bimolecular kinetics through an isothermal wall temperature channel. The resultant modeled nonlinear partial differential equations were simplified and solved using a combined Laplace-Differential Transform Method (LDTM). The solutions obtained were discussed and presented graphically to show the salient features of the fluid flow and heat transfer characteristics.

Keywords: unsteady, reactive, hydromagnetic, couette ow, exothermi creactio

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Authors: Francys Souza, Alberto Ohashi, Dorival Leao

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We present a general solution for finding the ε-optimal controls for non-Markovian stochastic systems as stochastic differential equations driven by Brownian motion, which is a problem recognized as a difficult solution. The contribution appears in the development of mathematical tools to deal with modeling and control of non-Markovian systems, whose applicability in different areas is well known. The methodology used consists to discretize the problem through a random discretization. In this way, we transform an infinite dimensional problem in a finite dimensional, thereafter we use measurable selection arguments, to find a control on an explicit form for the discretized problem. Then, we prove the control found for the discretized problem is a ε-optimal control for the original problem. Our theory provides a concrete description of a rather general class, among the principals, we can highlight financial problems such as portfolio control, hedging, super-hedging, pairs-trading and others. Therefore, our main contribution is the development of a tool to explicitly the ε-optimal control for non-Markovian stochastic systems. The pathwise analysis was made through a random discretization jointly with measurable selection arguments, has provided us with a structure to transform an infinite dimensional problem into a finite dimensional. The theory is applied to stochastic control problems based on path-dependent stochastic differential equations, where both drift and diffusion components are controlled. We are able to explicitly show optimal control with our method.

Keywords: dynamic programming equation, optimal control, stochastic control, stochastic differential equation

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Authors: Hamid Hamli Benzahar

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The main goal of this research is to study the deflection of a composite beam CB taking into account the effect of shear deformation. The structure is made up of two beams of different sections, joined together by thin adhesive, subjected to end moments and a distributed load. The fundamental differential equation of CB can be obtained from the total energy equation while considering the shear deformation. The differential equation found will be compared with those found in CB, where the shear deformation is zero. The CB system is numerically modeled by the finite element method, where the numerical results of deflection will be compared with those found theoretically.

Keywords: composite beam, shear deformation, moments, finites elements

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Authors: Faroudja Meziani, Amar Kahil

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In order to study the variation in settlement of soil under a dyke dam, the modelisation in our study consists of applying an imposed displacement at the base of the mass of soil (consisting of a saturated sand). The imposed displacement follows the evolution of acceleration of the earthquake of Boumerdes 2003 in Algeria. Moreover, the gravity load is taken into consideration by taking account the specific weight of the materials constituting the dyke. The results obtained show that the gravity loads have a direct influence on the evolution of settlement, especially at the center of the dyke where these loads are higher.

Keywords: settlement, dynamic analysis, rockfill dam, effect of earthquake, soil dynamics

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Authors: Ayaz Ahmad

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In this work, we present the effect of noise on the solution of a partial differential equation (PDE) in three different setting. We shall first consider random initial condition for two nonlinear dispersive PDE the non linear Schrodinger equation and the Kortteweg –de vries equation and analyse their effect on some special solution , the soliton solutions.The second case considered a linear partial differential equation , the wave equation with random initial conditions allow to substantially decrease the computational and data storage costs of an algorithm to solve the inverse problem based on the boundary measurements of the solution of this equation. Finally, the third example considered is that of the linear transport equation with a singular drift term, when we shall show that the addition of a multiplicative noise term forbids the blow up of solutions under a very weak hypothesis for which we have finite time blow up of a solution in the deterministic case. Here we consider the problem of wave propagation, which is modelled by a nonlinear dispersive equation with noisy initial condition .As observed noise can also be introduced directly in the equations.

Keywords: drift term, finite time blow up, inverse problem, soliton solution

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Authors: Johnson Oladele Fatokun, I. P. Akpan

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In this paper, the one-dimensional time dependent Schrödinger equation is discretized by the method of lines using a second order finite difference approximation to replace the second order spatial derivative. The evolving system of stiff ordinary differential equation (ODE) in time is solved numerically by an L-stable trapezoidal-like integrator. Results show accuracy of relative maximum error of order 10-4 in the interval of consideration. The performance of the method as compared to an existing scheme is considered favorable.

Keywords: Schrodinger’s equation, partial differential equations, method of lines (MOL), stiff ODE, trapezoidal-like integrator

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