Table of contents

The 4th International Conference on the Advancement of Science and Technology 2012 (iCAST 2012), with theme 'Contemporary Mathematics, Mathematical Physics and their Applications', took place in Kuantan, Malaysia, from Wednesday 7 to Friday 9 November 2012. The conference was attended by more than 100 participants, and hosted about 160 oral and poster papers by more than 140 pre-registered authors. The key topics of the 4th iCAST 2012 include Pure Mathematics, Applied Mathematics, Theoretical/Mathematical Physics, Dynamical Systems, Statistics and Financial Mathematics. The scientific program was rather full since after the Keynote and Invited Talks in the morning, four parallel sessions ran every day. However, according to all attendees, the program was excellent with a high level of talks and the scientific environment was fruitful; thus all attendees had a creative time.

The conference aimed to promote the knowledge and development of high-quality research in mathematical fields concerned with the application of other scientific fields as well as modern technological trends in physics, chemistry, biology, medicine, economics, sociology and environmental sciences.

We would like to thank the Keynote and the Invited Speakers for their significant contributions to 4th iCAST 2012. We would also like to thank the members of the International Scientific Committee and the members of the Organizing Committee. We cannot end without expressing our many thanks to International Islamic University Malaysia and our sponsors for their financial support .

This volume presents selected papers which have been peer-reviewed. The editors hope that it may be useful and fruitful for scholars, researchers, and advanced technical members of the industrial laboratory facilities for developing new tools and products.

Guest EditorsNasir Ganikhodjaev, Farrukh Mukhamedov and Pah Chin Hee

The PDF contains the committee lists, board list and biographies of the plenary speakers.

All papers published in this volume of Journal of Physics: Conference Series have been peer reviewed through processes administered by the proceedings Editors. Reviews were conducted by expert referees to the professional and scientific standards expected of a proceedings journal published by IOP Publishing.

Let A be the class of functions which are analytic in the open unit disc . We denote by S the subclass of A consisting of all functions in A which are also univalent in D. In this paper, the subclasses of S denoted by C_s(g) and K*_s(g) are introduced. We obtain coefficient bounds for f ∊ C_s(g) and f ∊ K*_s(g). These results generalize many known results.

In this paper we study certain properties of Dobrushin's ergodicity coefficient for stochastic operators defined on non-associative L¹-spaces associated with semi-finite JBW-algebras. Such results extends the well-known classical ones to a non-associative setting. This allows us to investigate the weak ergodicity of nonhomogeneous discrete Markov processes (NDMP) by means of the ergodicity coefficient. We provide a necessary and sufficient conditions for such processes to satisfy the weak ergodicity.

A quadratic stochastic operator (in short QSO) is usually used to present the time evolution of differing species in biology. Some QSO has been studied by Lotka and Volterra. The general problem in the nonlinear operator theory is to study the behavior of operators. This problem was not fully finished even for the quadratic stochastic operators. To study this problem it was investigated several classes of such QSO. In this paper we study ξ^(s)-QSO class of operators. We study such kind of operators on 2D simplex. We first classify these ξ^(s)-QSO into 20 classes. Further, we investigate the dynamics of one class of such operators.

Let (Ω, Σ, λ) be a measurable space with a finite complete measure λ and L₀ = L₀(Ω) be an algebra of equivalence classes of complex measurable functions on Ω. In the present paper we define C* -algebras over ideals of L₀. It is proved that any C* -algebra over ideal can be represented as measurable bundle of C*-algebras.

In this paper we consider a set of all extremal Volterra quadratic stochastic operators on three dimensional simplex S³, show that this set is parted into four equivalence classes with respect to group of transformations generated by permutations and describe the behaviour of trajectories extremal Volterra quadratic stochastic operators for each class. It is proved that the operators in some classes are non-ergodic transformation.

In this paper, we obtain some proximity points of two mappings in metric space (X, d) by using (ψ, ϕ) contractive condition, where ψ and ϕ are altering distance mappings. Our results generalized several well-known results in the literature. Also, we apply our results to get an application of common fixed point theorem of integral types.

Let F stand for the field of real or complex numbers, φ : Fⁿ → Fⁿ be any given polynomial map of the form ψ(x) = x + "higher order terms". We attach to it the following operator D : F[x] → F[x] defined by D(f) = f − f o ψ, where F[x] = F[x₁,x₂, ..., x_n]-the F-algebra of polynomials in variables x₁,x₂, ..., x_n, f ∊ F[x] and o stands for the composition(superposition) operation. It is shown that trajectory of any f ∊ F[x] tends to zero, with respect to a metric, and stabilization of all trajectories is equivalent to the stabilization of trajectories of x₁, x₂, ..., x_n.

In this paper, a new notion of the fuzzy generalized closed sets called fuzzy θ-semi-generalized closed sets in fuzzy topological spaces is introduced and studied their properties. Furthermore, we study these new sets in relation to some other types of already known fuzzy sets.

In this note, cubature formulas are constructed to evaluate the double integrals on the rectangle with algebraic singularity by replacing the density function f(x,y) with the S_Δ(P) modified spline function interpolation of type (0,2). Rate of convergence are obtained in the classes of function f(x,y) ∊ C^2,α(D).

We study sufficient conditions for uniform convergence of eigenfunction expansions associated with Schrodinger's operator.

Let f be piecewise smooth circle homeomorphisms with break points and the rotation number ρ is irrational. We provide a necessary condition for the absolute continuity of f-invariant measure with respect to Lebesgue measure.

Applications of p-adic numbers mathematical physics, quantum mechanics stimulated increasing interest in the study of p-adic dynamical system. One of the interesting investigations is p-adic logistics map. In this paper, we consider a new generalization, namely we study a dynamical system of the form f_a(x) = ax(1−x²). The paper is devoted to the investigation of a trajectory of the given system. We investigate the generalized logistic dynamical system with respect to parameter a and we restrict ourselves for the investigation of the case |a|_p < 1. We study the existence of the fixed points and their behavior. Moreover, we describe their size of attractors and Siegel discs since the structure of the orbits of the system is related to the geometry of the p-adic Siegel discs.

It is known that the theory of Markov process is a rapidly developing field with numerous applications to many branches of mathematics and physics, biology and so on. But there are some physical models which cannot be described by such processes. One of such models is related to population genetics. These processes are called quadratic stochastic processes (q.s.p.). In this theory it is important to construct nontrivial examples of such processes. In the present paper we are going to provide a construction of q.s.p. by means of two given processes. We should stress that such a construction allows us to produce lots of nontrivial examples of q.s.o. We also associate to given q.s.p. two kind of processes. Note that one of such processes is Markov. It is proved that such kind of processes uniquely define q.s.p. Moreover, we also derive some differential equations for q.s.p.

In this work uniformly convergent problems of the eigenfunction expansions of the Schrödinger operator −Δ+q(y₁, y₂) with singular potential from W¹₂(Ω) are investigated. Using the estimation of the spectral function of the Schrödinger operator on closed domain and mean value formula for the eigenfunction the uniformly convergent of the eigenfunction expansions of the functions continuous on the closed domain is proved.

The aim of this work is to investigate the problems of localization of spectral expansions of the distributions on closed domain, related to biharmonic operator. Using the mean value formula for the eigenfunctions of the biharmonic operator the Riesz means of the spectral function is estimated. Moreover, isomorphism of the generalized Holder spaces is applied.

In this work we investigate the localization principle of the Fourier-Laplace series of the distribution. Here we prove the sufficient conditions of the localization of the Riesz means of the spectral expansions of the Laplace-Beltrami operator on the unit sphere.

We investigate a pursuit-evasion differential game of countably many pursuers and one evader. Integral constraints are imposed on control functions of the players. Duration of the game is fixed and the payoff of the game is infimum of the distances between the evader and pursuers when the game is completed. Purpose of the pursuers is to minimize the payoff and that of the evader is to maximize it. Optimal strategies of the players are constructed, and the value of the game is found. It should be noted that energy resource of any pursuer may be less than that of the evader.

In this paper we describe bistochastic Kadison-Schawrz operators acting on M₂(). Such a description allows us to find positive, but not Kadison-Schwarz operators. Moreover, by means of that characterization we are able to construct Kadison-Schawrz operators, which are not completely positive.

In this paper we have established some coupled coincidence and coupled common fixed point theorems on (ψ, ϕ)-weakly contractive condition for mapping having the g-mixed monotone property in partially ordered generalized metric spaces which generalize some recent fixed point theorems given in the literature.

We study the Klein-Gordon equation in a non-commutative space-time as applied to the Hydrogen atom to extract the energy levels, by considering the second-order corrections in the non-commutativity parameter. By comparing to the 2S – 1S transition energies we obtain an upper bound on the non-commutativity parameter. Phenomenologically we show that non-commutativity is the source of lamb shift corrections and spin of the electron.

In this paper we consider a spin 1/2 particle interacting with a damped rotating magnetic field using path integral formalism. The propagator is first of all written in the standard form by replacing the spin by two fermionic oscillators via the Schwinger's model; then it is determined exactly thanks to the introduction of a particular rotations in coherent state space which has eliminated the rotation angle of the magnetic field and has simplified the Hamiltonian of the considered system. Thus, the Rabi formula are deduced.

In this paper, compact planar microstrip antennas comprising of broad slots for enhancing various antenna parameters are discussed and presented. The proposed microstrip slot antennas achieved a compactness of maximum 58 % with a peak gain of 7.58 dB. These antennas can be operated for S band applications such as WiMax, operating in the frequency range of 3.3 – 3.6 GHz, RADAR, WLAN, fixed satellite services and maritime mobile services etc. covering 2 – 6 GHz frequency range. The antennas can be used as a compact antenna system where limited size is a foremost requirement. Results also show the satisfactory performance with the dual band frequency characteristics. Details of the antenna design structure, results of return loss (RL), impedance bandwidth and radiation pattern with co-cross polarization are also given

Wave wall type solutions for waves on the surface of an ocean with slowly varying depth are constructed. It is a generalization of the solution of quasi-photon type. Wave wall is a packet of short waves concentrated near the moving line which forms the wave front. The approach is based on the representation of the solution in the form of asymptotic space-time rays (STR) series each term of which is a formal power series. The appropriate form of the ansatz is suggested. Chains of equations for coefficients of formal power series for phase and amplitude terms are derived. These equations are investigated and the solvability of the problem at each step is proved. As a result, asymptotic space-time series for the wave wall moving with group velocity on the surface of a heavy liquid is obtained.

Dynamics of the width and center-of-mass position of a matter wave soliton subject to interaction with arbitrary external potential is analyzed using the collective coordinates approach. It is shown that approximation of the trial function and external potential only in the interaction region of the spatial domain is sufficient for adequate description of the soliton scattering process. The validity of the developed approach is illustrated for the Gaussian and Pöschl-Teller potentials.

The spin coherent state path integral describing the dynamics of a two-level system interacting with electromagnetic wave of circular polarization is considered. The propagator is first written in the standard form by replacing the spin by a unit vector aligned along the polar and azimuthal directions. Then it is determined exactly using perturbation methods. Thus, the exact energy spectra with corresponding wave functions are deduced.

We use homoclinic orbits to find solutions of a dynamical system of the dipolar Bose Einstein Condensate (BEC) in a deep optical lattice. The equation of motion is transformed to a two-dimensional map and its homoclinic orbits are computed numerically. Each homoclinic orbit leads to a different solution. These different solutions lead to different types of solitons. We also analyse the stability of the solutions.

A black hole can emit radiation called Hawking radiation. Such radiation seen by an observer outside the black hole differs from the original radiation near the horizon of the black hole by the so-called "greybody factor". In this paper, the bounds of the greybody factors for the Reissner-Nordström black holes are obtained. These bounds can be derived by using the 2 × 2 transfer matrices. It is found that the charges of black holes act as good barriers.

This article deals with a mathematical technique for the study of functionality of semiconductor laser, by its rate equations, to be used in the simulation of high speed optical systems. We describe the development of numerical simulation model of a p-ZnO laser emitting in UV optical wavelength. A powerful dynamic algorithmical model is used to study the p-ZnO active region waveguide laser. It is based on time dependant rate equations of a quasi two levels system for the population density and time dependant for the pump and optical signal power. The model is sufficient to account for many of the observed dynamics in a single mode semiconductor laser in response to a dynamic drive current, such as relaxation oscillations and frequency chirping.

The effect of uniform distribution of internal heat generation on the linear stability analysis of the Benard-Marangoni convection in an Eringen's micropolar fluids with feedback control is investigated theoretically. The upper free surface is assumed to be non-deformable and the lower boundary is taken to be rigid and isothermal with fixed temperature and span-vanishing boundaries. The eigenvalue is solved numerically using the Galerkin method. The influence of the internal heat generation; Q and feedback control; K in micropolar fluids with various parameters on the onset of stationary convection has been analysed.

In this work, non – adiabatic effects manifested in the magnetic properties of low-lying states of even-even deformed nuclei are studied. A simple phenomenological model which takes into account the Coriolis mixing of states of the ground and K^π = 2⁺_n and K^π = 1⁺_v bands are proposed.

The Calculations for isotopes ¹⁶⁰Dy and ^170,172,174Yb, are carried out. The calculated g_R–factor for the states of ground band which are compared with experimental data. Decreases of g_R–factor with increasing angular momentum I have been discussed. The probability of M1–transition from 1+_v and coefficients of multipole mixture δ(E2/M1) from 0⁺₂, 0⁺₃, 2⁺₁, and 2⁺₂ bands are calculated and compared with the experimental data. Decreases of g_R–factor with increasing angular momentum I have been discussed.

That these is an obvious inverse relation between g_R – factor and angular momentum I of the ground band states. This has been explained by a mixing ground and K^π = 1⁺ bands which have a strong B(M1) to ground state.

We consider the Vannimenus model on a Cayley tree of arbitrary order k with competing nearest-neighbour interactions J₁ and next-nearest-neighbour interactions J₂ and J₃ in the presence of an external magnetic field h. In this paper we study the phase diagram of the model using an iterative scheme for a renormalized effective nearest-neighbour coupling K_r and effective field per site X_r for spins on the rth level; it recovers, as particular cases, previous works by Vannimenus, Inawashiro et al, Mariz et al and Ganikhodjaev and Uǧuz. Each phase is characterized by a particular attractor and the phase diagram is obtained by following the evolution and detecting the qualitative changements of these attractors. These changements can be either continuous or abrupt, respectively characterizing second- or first- order phase transitions. We present a few typical attractors and at finite temperatures, several interesting features (evolution of reentrances, separation of the modulated region into few disconnected pieces, etc) are exhibited for typical values of parameters.

We investigate an Ising model with two restricted competing interactions (nearest neighbors, and one-level neighbors) on the Cayley tree of order four. We derive a recurrent equation for the Cayley tree of order k. We found an analytic solution for the given interactions in the case of order 4. Our result of the critical curve shows the existence of the phase transition occurs in this model. We also give the calculation of the free energy from the description of Gibbs measure of the given Hamiltonian on Cayley tree of order four.

On a Cayley tree of arbitrary order k we consider two different Potts models with competing nearest-neighbour interactions J₁ and next-nearest-neighbour interactions J_p and J_o, where coupling J_p corresponds to interaction of spins belonging to the same branch of the tree (prolonged) and coupling J_o corresponds to interaction of spins belonging to the same shell of the tree (one-level) and find for each model in addition to the expected paramagnetic, ferromagnetic and antiferromagnetic phases, an intermediate range of coupling values where the local magnetization has chaotic oscillatory glass-like behaviour. We also show that the ranges corresponding two models are different.

In this work we are using initial conditions in the form of two separated bright pulses with the rectangular shape to analyse the interaction of pulses in a defocusing Nonlinear Scrödinger Equation (NLSE). By exact solution of the direct scattering problem associated with the defocusing NLSE, we have obtained the expressions for long time behavior of the solution. Obtained results interpreted as a nonlinear interference of two pulses.

We consider a Potts model on a Bethe lattice with competing nearest-neighbour J and next-nearest-neighbour interactions J_p. The phase diagram of this model was studied by Ganikhodjaev et al. In this paper we investigate the problem of phase transition for the considered model and show that for some parameter values of the model there is phase transition.

We consider a model describing a truncated operator H (truncated with respect to the number of particles) acting in the direct sum of zero-, one-, and two-particle subspaces of a fermionic Fock space _a(L²(³)) over L²(³). We admit a general form for the "kinetic" part of the hamiltonian H, which contains a parameter γ to distinguish the two identical particles from the third one.

In this note:

(i) We find a critical value γ* for the parameter γ that allows or forbids the Efimov effect (infinite number of bound states if the associated generalized Friedrichs model has a threshold resonance) and we prove that only for γ < γ* the Efimov effect is absent, while this effect exists for any γ > γ*.

(ii) In the case γ > γ* we also establish the following asymptotics for the number N(z) of eigenvalues z below E_min, the lower limit of the essential spectrum of H:

A common method of handling the problem of missing variances in meta-analysis of continuous response is through imputation. However, the performance of imputation techniques may be influenced by the type of model utilised. In this article, we examine through a simulation study the effects of the techniques of imputation of the missing SDs and type of models used on the overall meta-analysis estimates. The results suggest that imputation should be adopted to estimate the overall effect size, irrespective of the model used. However, the accuracy of the estimates of the corresponding standard error (SE) is influenced by the imputation techniques. For estimates based on the fixed effects model, mean imputation provides better estimates than multiple imputations, while those based on the random effects model responds more robustly to the type of imputation techniques. The results showed that although imputation is good in reducing the bias in point estimates, it is more likely to produce coverage probability which is higher than the nominal value.

Extrapolation parameters in Refinement of Jacobi over Relation method in solving fuzzy linear systems were hypothesized to influence the rate of convergence. This paper aims to investigate the relationship between extrapolation parameters and approximate solutions of fuzzy linear systems when solved using Refinement of Jacobi over Relaxation method. The Algorithms of Refinement of Jacobi over Relaxation method are proposed based on the Jacobi method that specifically used in solving the system. A five by five fuzzy linear system is given to investigate the convergence to exact solution with three different values of extrapolation parameters. The numerical results show that there is a positive correlation between extrapolation parameter and convergence to exact solution. The three extrapolation parameters suggest that convergence to exact solution can be increased in line with the increase in the values of extrapolation parameters.

An upper bound for the ratio of wealths of the best constant -rebalanced portfolio to that of the multinomial universal portfolio is derived. The finite- order multinomial universal portfolios can reduce the implementation time and computer-memory requirements for computation. The improved performance of the finite-order portfolios on some selected local stock-price data sets is observed.

A multi-product fish production planning produces simultaneously multi fish products from several classes of raw resources. The goal in sustainable production planning is to meet customer demand over a fixed time horizon divided into planning periods by optimizing the tradeoff between economic objectives such as production cost, waste processed cost, and customer satisfaction level. The major decisions are production and inventory levels for each product and the number of workforce in each planning period. In this paper we consider the management of small scale traditional business at North Sumatera Province which performs processing fish into several local seafood products. The inherent uncertainty of data (e.g. demand, fish availability), together with the sequential evolution of data over time leads the sustainable production planning problem to a nonlinear mixed-integer stochastic programming model. We use scenario generation based approach and feasible neighborhood search for solving the model.

Most statistical tests such as t-tests, linear regression analysis and Analysis of Variance (ANOVA) require the normality assumptions. When the normality assumption is violated, interpretation and inferences may not be reliable. Therefore it is important to assess such assumption before using any appropriate statistical test. One of the commonly used procedures in determining whether a random sample of size n comes from a normal population are the goodness-of-fit tests for normality. Several studies have already been conducted on the comparison of the different goodness-of-fit(see, for example [2]) but it is generally limited to the sample size or to the number of GOF tests being compared(see, for example [2] [5] [6] [7] [8]). This paper compares the power of six formal tests of normality: Kolmogorov-Smirnov test (see [3]), Anderson-Darling test, Shapiro-Wilk test, Lilliefors test, Chi-Square test (see [1]) and D'Agostino-Pearson test. Small, moderate and large sample sizes and various contamination levels were used to obtain the power of each test via Monte Carlo simulation. Ten thousand samples of each sample size and contamination level at a fixed type I error rate α were generated from the given alternative distribution. The power of each test was then obtained by comparing the normality test statistics with the respective critical values. Results show that the power of all six tests is low for small sample size(see, for example [2]). But for n = 20, the Shapiro-Wilk test and Anderson – Darling test have achieved high power. For n = 60, Shapiro-Wilk test and Liliefors test are most powerful. For large sample size, Shapiro-Wilk test is most powerful (see, for example [5]). However, the test that achieves the highest power under all conditions for large sample size is D'Agostino-Pearson test (see, for example [9]).

In this work, we present a computational method for solving double and triple integrals with variable limits of integrations which is based on Haar wavelets. This approach is the generalization and improvement of the methods [3]. The advantage of this new methods is its more efficient and simple applicability than the previous methods. Error analysis for the case of two dimension are considered. Finally, we also give some numerical examples to compared with existing methods.

The discrete-time approach to real option valuation has typically been implemented in the finance literature using a binomial tree framework. Instead we develop a new model by randomizing the environment and call such model a random binomial tree. Whereas the usual model has only one environment (u, d) where the price of underlying asset can move by u times up and d times down, and pair (u, d) is constant over the life of the underlying asset, in our new model the underlying security is moving in two environments namely (u₁, d₁) and (u₂, d₂). Thus we obtain two volatilities σ₁ and σ₂. This new approach enables calculations reflecting the real market since it consider the two states of market normal and extra ordinal. In this paper we define and study Futures options for such models.

In this paper, we present a new algorithm to find exact and approximate analytical solutions of singular two-point boundary-value problems (BVPs) based on Bernstein operational matrix of differentiation. Different from other numerical techniques, Bernstein polynomials and their properties are employed for deriving a general procedure for forming this matrix. The proposed method can be applied to linear and nonlinear problems. The scheme is tested for some examples and the obtained results demonstrate efficiency of the proposed method.