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The second edition of the symposium on Mathematical Problems in Engineering focuses on new results of engineering researches carried out by using mathematical techniques. The aim of the Session is to collect relevant papers dealing with important approaches of applied mathematics, which have relevance to the engineering in the field of Computer Engineering, Engineering Applications of Aerospace and Intelligent Transportation Systems in order to create new collaborations between mathematicians and engineers. Papers are characterized by innovative models, methods and approaches that can found practical application to the engineering field or by new useful application of existing models to solve engineering problems. [ABSTRACT FROM AUTHOR]

Normally in engineering, conceptual models provide formal model of the system. Mathematical modeling gives the systematic representation in terms of properties. Modeling process is performed by using design space analysis and mathematical equations and this can be performed with different design alternatives. Conceptual analysis of natural convection is described. In this paper the modeling of heat and mass transfer is performed with the concepts of heat and mass transfer and properties of objects in the design space. Numerical solution has been conducted for energy equation with different boundary conditions. The present work analyses the heat and mass transfer modeling process with mathematical equations. [ABSTRACT FROM AUTHOR]

This paper deals with Protter problems for Keldysh type equations in R4: Originally such type problems are formulated by M. Protter for equations of Tricomi type. Now it is well known that Protter problems for mixed type equations of the first kind are ill-posed and for smooth right-hand side functions they have singular generalized solutions. In the present paper Protter problem for equations of second kind (Keldysh type) is formulated and it is shown that in the frame of classical solvability this problem is not well posed. Further, a notion for a generalized solution in suitable functional space is given. Results for existence and uniqueness of generalized solution of the considered problem are obtained. Some a priori estimates are stated. [ABSTRACT FROM AUTHOR]

In this paper, we search the efficiency of the reproducing kernel method (RKM) in solving the strongly nonlinear equation. An example is presented to prove the power of the technique. The results attained from the technique are compared with the other techniques. Results prove that the presented technique is very effective. [ABSTRACT FROM AUTHOR]

We study the existence of infinitely many solutions for anisotropic variable exponent problem of the type {– Σi=1 N ∂xiai(x, ∂xiu) + Σi=1 N ai(x,u) = λ|u|q(x)-2u in Ω, ∂u/∂v = 0 on ∂Ω. (1) Where Ω ⊂ RN(x) ≥ 2,∀x ∈ Ω and i ∈ {1,2,...,N}. The main result of this paper establishes the existence of two positive constants λi,q are continuous functions on Ω̅ such that pi(x) ≥ 2,∀x ∈ Ω and i ∈ {1,2,...,N}. The main result of this paper establishes the existence of two positive constants λ0 and λ1 with λ0 ≤ λ1 such that every λ ∈ (λ1, ∞) is an eigenvalue, while no λ ∈ (0, λ0) can be an eigenvalue of the above problem. [ABSTRACT FROM AUTHOR]

The paper is a continuation of research undertaken in paper [22]. The considered problem consists in presenting some condition sufficient for approximation of the selective points in normed spaces by subseries of the given series. [ABSTRACT FROM AUTHOR]

This paper is a continuation of the paper [8] and presents more applications of Fitzpatrick functions for solving optimization problems. The main purpose of the present work is to introduce some new properties of Fitzpatrick functions useful for solving optimization problems, using also their already presented specific properties, as the maximal monotonicity, proper, convex and lower semi-continuity. [ABSTRACT FROM AUTHOR]

In this work a new nonlocal boundary value problem for an equation of the mixed type is formulated. This equation is parabolic-hyperbolic and belongs to the first kind because the line of type change is not a characteristic of the equation. Nonlocal condition binds points on boundaries of the parabolic and hyperbolic parts of the domain with each other. This problem is generalization of the well-known problems of Frankl type. A boundary value problem for the heat equation with conditions of the Samarskii-Ionlin type arises in solving this problem. Unlike the existing publications of the other authors related to the theme it is necessary to note that in this papers the nonlocal problems were considered in rectangular domains. But in our formulation of the problem the hyperbolic part of the domain coincides with a characteristic triangle. Unique strong solvability of the formulated problem is proved. [ABSTRACT FROM AUTHOR]

Many planning problems for robots are of considerable interest. In this paper, we consider the discrete minimum constraint removal motion planning problem that can be used for a motion planning formulation with explanations for failure. We consider an efficient approach to solve the problem. In particular, we consider an explicit reduction from the decision version of the problem to the satisfiability problem. We present the results of computational experiments for different satisfiability algorithms. [ABSTRACT FROM AUTHOR]

In the paper Neumann type boundary value problems for inhomogeneous biharmonic equation are studied. Necessary and sufficient conditions on solvability of the considered problems are established. [ABSTRACT FROM AUTHOR]

In this paper, we are interested in solving systems of nonlinear equations with inexact data, denoted by perturbed nonlinear system of equations, using interval Newton-like methods. The main scope of this research is to develop an interval Newton-like method to solve those perturbed nonlinear systems. The existence of the solution of these systems, obtained using the proposed method, is proved. A two-stage interval Newton-like method is proposed which further improves convergence and computational time. The effectiveness of interval methods over the traditional solvers is illustrated through an example. The results obtained show an improvement in the performance of the proposed method over other interval Newton-like methods, an exhaustive search method and the Monte-Carlo simulation method. [ABSTRACT FROM AUTHOR]

Firefly Algorithm is a recent swarm intelligence method, inspired by the social behavior of fireflies, based on their flashing and attraction characteristics [1, 2]. In this paper, we analyze the implementation of a dynamic penalty approach combined with the Firefly algorithm for solving constrained global optimization problems. In order to assess the applicability and performance of the proposed method, some benchmark problems from engineering design optimization are considered. [ABSTRACT FROM AUTHOR]

Problems of swarm robotics are extensively studied in contemporary robotics. In this paper, we consider the problem of robot swarms control with only global signals. We propose an efficient approach to solve the problem. In particular, we consider an explicit reduction from the decision version of the problem to the satisfiability problem. For different satisfiability algorithms, we present the results of computational experiments. [ABSTRACT FROM AUTHOR]

In this paper, an efficient new optimized implicit two-step hybrid block method is presented for the integration of general second-order initial value problems. Numerical experiments reveal the superiority of the new method for solving this kind of problems, in comparison with methods of similar characteristics in the literature. [ABSTRACT FROM AUTHOR]

To improve space utilization, the method for handling spaces plays an important role in the container loading problem. This paper deals with loading a set of cuboid items into a single container to maximize the utilization of the space. Six space partitions are presented and a set of rules for merging spaces is proposed. Through experimentation, using a benchmark data set, the influence of partitioning and merging are analyzed. The experimental results show that partitioning and merging in which all loaded boxes have one hundred percent support from below can produce good space utilization. [ABSTRACT FROM AUTHOR]

Technical initial problems are defined as initial problems where the right-hand side functions of the system are those occurring in the technical practice, that is functions generated by adding, multiplying and superposing elementary functions. Such systems can be expanded into systems with only rationals operations on the right-hand sides of the equations. In such a case the Taylor series terms can easily be calculated [1]. Test examples are presented in the paper. Stiffness in technical initial problems can be eliminated by the TKSL software and solved by the direct use of the explicit and implicit Taylor series methods. [ABSTRACT FROM AUTHOR]

We study a control problem governed by a semilinear elliptic partial differential equation. Bound constraints are imposed on the control, as well as finitely many pointwise constraints are imposed on the state. Both equality and inequality constraints are considered. Theoretical results published in [1] are quoted and a complete numerical analysis of the problem is developed. Detailed proofs will be provided in a forthcoming paper. [ABSTRACT FROM AUTHOR]

The paper concerns the classification problem of a subclass of nilpotent Leibniz algebras. This subclass arises from naturally graded non Lie filiform Leibniz algebras. An invariant-theoretic approach to the classification problem of this subclass has been suggested by Rakhimov and Bekbaev. This approach provides to solve the problems with minimum difficulty. Implementing this approach, it is given complete list of isomorphism classes for a subclass of filiform Leibniz algebras and appropriate invariants in dimension nine. [ABSTRACT FROM AUTHOR]

The starting point of the paper is the system of differential equations proposed by D. M. Dubois to express conjugate retardation and anticipation variables. The research proposes to find the relation between time shift, the constant parameters of the equations and the solutions of these equations. The 2nd and 3rd parts of the paper present mathematical calculus to solve the case when the current state of the slave system is an exponential function, then this state is presumed to be a linear function. There are demonstrated four theorems, especially by means of classical methods to solve ordinary differential equations. Conclusions are presented about each hypothesis which was considered. It is also studied the case when the time shift for the anticipation is different from the time shift of the retardation. The 4th part deals with the problem of systems which have an oscillating movement. The last part of the paper introduces man and his environment as advanced—retarded conjugate systems and makes links with the results of the mathematical calculus. [ABSTRACT FROM AUTHOR]

This paper presents a gradient-related algorithm for solving large scale, spatially explicit, welfare models with transportation. It introduces the theory, describes the different components of the algorithm, and reports on experience gained in applying it. [ABSTRACT FROM AUTHOR]

We consider solving large-scale systems of linear equations Ax = b that are inconsistent due to corruptions in the measurement vector b, possibly of arbitrarily large size. We develop an approach for this setting that allows detection of the corrupted entries and thus convergence to the "true" solution of the original system. We provide analytical justification for our approaches as well as experimental evidence on synthetic systems. [ABSTRACT FROM AUTHOR]

The purpose of this action research was to increase the mastery level of Form Five Social Science students in Tawau II National Secondary School in the operations of addition, subtraction and multiplication of matrices in Mathematics. A total of 30 students were involved. Preliminary findings through the analysis of pre-test results and questionnaire had identified the main problem faced in which the students felt confused with the application of principles of the operations of matrices when performing these operations. Therefore, an action research was conducted using an intervention programme called "G.P.S Matrices" to overcome the problem. This programme was divided into three phases. 'Gift of Matrices' phase aimed at forming matrix teaching aids. The second and third phases were 'Positioning the Elements of Matrices' and 'Strenghtening the Concept of Matrices'. These two phases were aimed at increasing the level of understanding and memory of the students towards the principles of matrix operations. Besides, this third phase was also aimed at creating an interesting learning environment. A comparison between the results of pre-test and post-test had shown a remarkable improvement in students' performances after implementing the programme. In addition, the analysis of interview findings also indicated a positive feedback on the changes in students' attitude, particularly in the aspect of students' understanding level. Moreover, the level of students' memory also increased following the use of the concrete matrix teaching aids created in phase one. Besides, teachers felt encouraging when conducive learning environment was created through students' presentation activity held in third phase. Furthermore, students were voluntarily involved in these student-centred activities. In conclusion, this research findings showed an increase in the mastery level of students in these three matrix operations and thus the objective of the research had been achieved. [ABSTRACT FROM AUTHOR]

For any given two graphs G and H, we use the notation F→(G,H) to mean that in any red-blue coloring of the edges of F, the following must hold: F contains either a red subgraph G or a blue subgraph H. A graph F is a Ramsey (G,H)-minimal graph if F→(G,H) but F*↛(G,H) for any proper subgraph F* of F. Let R(G,H) be the class of all Ramsey (G,H)-minimal graphs. In this paper, we derive the properties of graphs belonging to R(3K2,P3). By using these properties we determine all graphs belonging to this class. [ABSTRACT FROM AUTHOR]

Let G be a group. The intersection of normal subgroups N of G in which G/N is soluble is called soluble residual of G. Soluble residuals are important tools since they are perfect and contains all perfect subgroups. We will give soluble residuals of some maximal subgroups of Sp(6,r). [ABSTRACT FROM AUTHOR]

The future cost in many industrial problem is obviously uncertain. Then a mathematical analysis for a problem with uncertain cost is needed. In this article, we deals with the fuzzy expected value analysis to solve an integrated supplier selection and supplier selection problem with uncertain cost where the costs uncertainty is approached by a fuzzy variable. We formulate the mathematical model of the problems fuzzy expected value based quadratic optimization with total cost objective function and solve it by using expected value based fuzzy programming. From the numerical examples result performed by the authors, the supplier selection problem was solved i.e. the optimal supplier was selected for each time period where the optimal product volume of all product that should be purchased from each supplier for each time period was determined and the product stock level was controlled as decided by the authors i.e. it was followed the given reference level. [ABSTRACT FROM AUTHOR]

One of the little-known techniques for ordinary integro-differential equations in literature is Green's functional method, the origin of which dates back to Azerbaijani scientist Seyidali S. Akhiev. According to this method, Green's functional concepts for some simple forms of such equations have been introduced in the several studies. In this study, we extend Green's functional concept to a higher order ordinary integro-differential equation involving generally nonlocal conditions. A novel kind of adjoint problem and Green's functional are constructed for completely nonhomogeneous problem. By means of the obtained Green's functional, the solution to the problem is identified. [ABSTRACT FROM AUTHOR]

When dealing with unconstrained non-linear optimization problems using quasi-Newton methods, updating the approximation to the inverse Hessian is a computationally expensive operation and, therefore, in this paper we investigate the possibility of skipping updates on every second step. The experimental results show that the new methods (i.e. with skipping) give better performance in general than existing multi-step methods, particularly as the dimension of the test problem increases. [ABSTRACT FROM AUTHOR]

We present a theoretical basis which proposes a solution to the problem that very large possibilities of exam timetables can be minimalised the possible ones satisfying all restrictions and nearly all of requests, via the concept of descriptive neighborhoods which is one of important concepts in descriptive proximity spaces. [ABSTRACT FROM AUTHOR]

The simultaneous diagonalization problem of various size matrices is considered. We propose an algorithm for the problem that always finds a solution if one exists. The algorithm uses an algorithm for the simultaneous diagonalization of square matrices as a subroutine. [ABSTRACT FROM AUTHOR]

A nonlinear stochastic control system is considered. We discuss a problem of the synthesis of stochastic attractors and suggest a constructive approach based on the design of the stochastic sensitivity and corresponding confidence domains. Details of this approach are demonstrated for the problem of the control of confidence ellipses near the equilibrium. An example of the control for stochastic Van der Pol equation is presented. [ABSTRACT FROM AUTHOR]

The cutting and pasting processes that occur in DNA molecules have led to the formulation of splicing system. Since then, there are few models used to model the splicing system. The splicing language, which is the product of splicing system, can be categorized into two, namely the adult and limit language. In this research, limit language is extended to the second order limit language. Few problems are approached which lead to the formation of second order limit language which is then analyzed using various types of splicing system [ABSTRACT FROM AUTHOR]

Utilizing the integral expression of Coulomb's Law to determine the electric potential from a continuous charge distribution is a canonical exercise in Electricity and Magnetism (E&M). In this study, we use both think-aloud interviews and responses to traditional exam questions to investigate student difficulties with this topic at the upper-division level. Leveraging a theoretical framework for the use of mathematics in physics, we discuss how students activate, construct, execute and reflect on the integral form of Coulomb's Law when solving problems with continuous charge distributions. We present evidence that junior-level E&M students have difficulty mapping physical systems onto the mathematical expression for the Coulomb potential. Common challenges include difficulty expressing the difference vector in appropriate coordinates as well as determining expressions for the differential charge element and limits of integration for a specific charge distribution. We discuss possible implications of these findings for future research directions and instructional strategies. [ABSTRACT FROM AUTHOR]

Several new integral inequalities similar to Čebyšev and Ostrowski's inequalities are presented [ABSTRACT FROM AUTHOR]

Probability calculus is understood, and uniquely defined as the only rational tool for consistent inference. Yet two problems remain. One is a matter of principle: how do we assign the prior distribution that expresses the question we wish to ask? The other is a matter of practice: how do we navigate the parameter space in order to compute the posterior inference? Probability distributions have a natural geometry, which can be used to help in both these. But, like any other professional tool, geometry should be used with intelligence and care. [ABSTRACT FROM AUTHOR]

This research investigated students’ transfer of learning from calculus courses to an introductory physics course. We used semi-structured think aloud interviews to assess the extent to which students transfer their calculus knowledge when solving problems in a physics course. Results indicate that students needed prompting and scaffolding to connect the calculus knowledge with the physics problem. © 2006 American Institute of Physics [ABSTRACT FROM AUTHOR]

In this study, we give an identity for known special number sequences then prove it using Laplace expansion formula. [ABSTRACT FROM AUTHOR]

The article highlights the use of perturbation approach in assessing the bifurcation behavior for brake squeal problems in the U.S. It states that modulation equations for amplitude and phase can be calculated using modal data of the unperturbed system. Moreover, the approach yields accurate results, if both eigenmotions develop on different time scales.