In this paper we present a pair of operators (t-norm, t-conorm) dual with a strong negation with n-threshold $a_1,\;{\ldots}, a_n\;{\in}(0,1),\;a_1\;<\;a_2\;<\;{\ldots}\;<\;a_n$. In this way we obtain an extension of operators with threshold, that are obtained for n = 1. The new pair is obtained from given one.

It is shown that the problem of minimizing (maximizing) a quadratic cost functional (quadratic gain functional) given the dynamics dx = (fx + gu)dt + hdb(t, a) where b(t, a) is a fractional Brownian motion of order a, 0 < 2a < 1, can be solved completely (and meaningfully!) by using the dynamical equations of the moments of x(t). The key is to use fractional Taylor's series to obtain a relation between differential and differential of fractional order.

The temporal discretisation of a moderate semilinear parabolic problem in an abstract setting by the two-step backward differentiation formula with variable step sizes is analysed. Stability as well as optimal smooth data error estimates are derived if the ratios of adjacent step sizes are bounded from above by 1.91.

Quasigroups are algebraic structures closely related to Latin squares which have many different applications. There are several classifications of quasigroups based on their algebraic properties. In this paper we propose another classification based on the properties of strings obtained by specific quasigroup transformations. More precisely, in our research we identified some quasigroup transformations which can be applied to arbitrary strings to produce pseudo random sequences. We performed tests for randomness of the obtained pseudo-random sequences by random walks on torus. The randomness tests provided an empirical classification of quasigroups.

An efficient parallel algorithm is presented to find a maximum weight independent set of a permutation graph which takes O(log n) time using O($n^2$/ log n) processors on an EREW PRAM, provided the graph has at most O(n) maximal independent sets. The best known parallel algorithm takes O($log^2n$) time and O($n^3/log\;n$) processors on a CREW PRAM.

The present article discusses the number of empty convex 4-gons and empty convex 5-gons in a finite planar point set. New proofs are provided for the two related important results.

Motivated by the field experimental designs in agriculture, the theory of block designs has been applied to several areas such as statistics, combinatorics, communication networks, distributed systems, cryptography, etc. An explicit formula and its fast computational algorithm for a class of symmetric balanced incomplete block designs are presented. Based on the formula and the careful investigation of the modulus multiplication table, the algorithm is developed. The computational costs of the algorithm is superior to those of the conventional ones.

An f-coloring of a graph G = (V, E) is a coloring of edge set E such that each color appears at each vertex v $\in$ V at most f(v) times. The minimum number of colors needed to f-color G is called the f-chromatic index $\chi'_f(G)$ of G. Any graph G has f-chromatic index equal to ${\Delta}_f(G)\;or\;{\Delta}_f(G)+1,\;where\;{\Delta}_f(G)\;=\;max\{{\lceil}\frac{d(v)}{f(v)}{\rceil}\}$. If $\chi'_f(G)$= ${\Delta}$f(G), then G is of $C_f$ 1 ; otherwise G is of $C_f$ 2. In this paper, the classification problem of complete graphs on f-coloring is solved completely.

In this paper, we suggest and analyze a class of iterative methods for solving hemiequilibrium problems using the auxiliary principle technique. We prove that the convergence of these new methods either requires partially relaxed strongly monotonicity or pseudomonotonicity, which is a weaker condition than monotonicity. Results obtained in this paper include several new and known results as special cases.

Recently, there are some empirical Bayes procedures using NA samples. We point out a key equality which may not hold for NA samples. Thus, the results of those empirical Bayes procedures based on NA samples are dubious

The regularized structured total least norm (RSTLN) method finds an approximate solution x and error matrix E to the overdetermined linear system (H + E)x $\approx$ b, preserving structure of H. A new separation scheme by parts of variables for the regularized structured total least norm on blind deconvolution problem is suggested. A method combining the regularized structured total least norm method with a separation by parts of variables can be obtain a better approximated solution and a smaller residual. Computational results for the practical problem with Block Toeplitz with Toeplitz Block structure show the new method ensures more efficiency on image restoration.

In this paper, an adaptive trust region method based on the conic model for unconstrained optimization problems is proposed and analyzed. We establish the global and super linear convergence results of the method. Numerical tests are reported that confirm the efficiency of the new method.

We deal with the Cauchy problem for the space-time fractional diffusion equation, which is obtained from standard diffusion equation by replacing the second-order space derivative with a Caputo (or Riemann-Liouville) derivative of order ${\beta}{\in}$ (0, 2] and the first-order time derivative with Caputo derivative of order ${\beta}{\in}$ (0, 1]. The fundamental solution (Green function) for the Cauchy problem is investigated with respect to its scaling and similarity properties, starting from its Fourier-Laplace representation. We derive explicit expression of the Green function. The Green function also can be interpreted as a spatial probability density function evolving in time. We further explain the similarity property by discussing the scale-invariance of the space-time fractional diffusion equation.

In this paper, the existence of periodic positive solution and the attractivity are investigated for the rational recursive sequence $x_{n+1} = (A + ax_{n_k})/(b + x{n-l})$, where A, a and b are real numbers, k and l are nonnegative integer numbers.

In this study the optimal control of fed-batch glycerol fermentation is investigated based on an impulsive dynamical system. Considering the sudden increase of the glycerol and alkali in fed-batch culture of biodissimilation of glycerol to 1,3-propanediol, this paper proposes a non-linear impulsive system of fed-batch culture. The existence, uniqueness and regularity properties of piecewise solution for the system are proved. In view of the controllability of volumes of glycerol added to the reactor instantaneously, the paper constructs an optimal control model based on the nonlinear impulsive system and the existence of the optimal control is obtained. The control variables here are the moments and the sizes of jumps in the states at the discrete instants and the objective is to maximize the productivity of 1,3-propanediol over one cycle.

In this paper, constraint aggregation is combined with the adjoint and multiple shooting strategies for optimal control of differential algebraic equations (DAE) systems. The approach retains the inherent parallelism of the conventional multiple shooting method, while also being much more efficient for large scale problems. Constraint aggregation is employed to reduce the number of nonlinear continuity constraints in each multiple shooting interval, and its derivatives are computed by the adjoint DAE solver DASPKADJOINT together with ADIFOR and TAMC, the automatic differentiation software for forward and reverse mode, respectively. Numerical experiments demonstrate the effectiveness of the approach.

We examine the Fibonacci length of certain centro-polyhedral groups and show that in some cases the lengths depend on tribonacci sequences. Further we obtain specific examples of infinite families of three-generator groups with constant, linear and (3-step) Wall number dependent Fibonacci lengths.

In this paper, we introduce a new algebraic method to characterize rational PH plane curves. And using this method, we study the algebraic characterization of generic strongly regular rational plane PH curves expressed in the complex formalism which is introduced by R.T. Farouki. We prove that generic strongly semi-regular rational PH plane curves are completely characterized by solving a simple functional equation H(f, g) = $h^2$ where h is a complex polynomial and H is a bi-linear operator defined by H(f, g) = f'g - fg' for complex polynomials f,g.

Denote the set of n ${\times}$ n complex Hermitian matrices by Hn. A pair of n ${\times}$ n Hermitian matrices (A, B) is said to be rank-additive if rank (A+B) = rank A+rank B. We characterize the linear maps from Hn into itself that preserve the set of rank-additive pairs. As applications, the linear preservers of adjoint matrix on Hn and the Jordan homomorphisms of Hn are also given. The analogous problems on the skew Hermitian matrix space are considered.

We study the existence and nonexistence of positive periodic solutions of a non-autonomous functional differential equation with impulses. The equations we study may be of delay, advance or mixed type functional differential equations and the impulses may cause the existence of positive periodic solutions. The methods employed are fixed-point index theorem, Leray-Schauder degree, and upper and lower solutions. The results obtained are new, and some examples are given to illustrate our main results.

The purpose of this paper is to study a class of delay differential equations with two delays. First, we consider the existence of periodic solutions for some delay differential equations. Second, we investigate the local stability of the zero solution of the equation by analyzing the corresponding characteristic equation of the linearized equation. The exponential stability of a perturbed delay differential system with a bounded lag is studied. Finally, by choosing one of the delays as a bifurcation parameter, we show that the equation exhibits Hopf and saddle-node bifurcations.

The concept of the Moore-Penrose inverse in an indefinite inner product space is introduced. Extensions of some of the formulae in the Euclidean space to an indefinite inner product space are studied. In particular range-hermitianness is completely characterized. Equivalence of a weighted generalized inverse and the Moore-Penrose inverse is proved. Finally, methods of computing the Moore-Penrose inverse are presented.

The paper deals with the problem of selective harvesting in a prey-predator model with predator self limitation. Criteria for local stability and global stability for both the exploited and unexploited system are derived. The effort has been considered as a dynamic variable and taxation as a control instrument to protect the fish populations from over exploitation. Finally, the optimal taxation policy is discussed with the help of control theory.

The first part of the paper deals with a brief introduction of the plant-herbivore model system along with deterministic analysis of local stability and Hopf-bifurcations. The second part consists of stability analysis of the limit cycle arising from Hopf-bifurcation and uniqueness of limit cycle. The third part deals with the study of global stability of the model system under consideration.

An effective method for analyzing the stability of nonlinear systems is developed. After introducing a novel concept named the point- wise generalized Dahlquist constant for any mapping and presenting its useful properties, we show that the point-wise generalized Dahlquist constant is sufficient for characterizing the exponential stability of nonlinear systems.

In this paper we prove that if G is a finite group, $^2D_{n}(3)(9{\le}n = 2^m + 1\;not a prime)$, G and M have the same order components, then G$\cong$M.

In this paper, we obtain a new fixed point theorem in complete probabilistic ${\Delta}$-inner product space. As an example of applications, we utilize the results of this paper to study the existence and uniqueness of solutions for linear Valterra integral equation.

Usual symmetric duality results are proved for Wolfe and Mond-Weir type nondifferentiable nonlinear symmetric dual programs under F-convexity F-concavity and F-pseudoconvexity F-pseudoconcavity assumptions. These duality results are then used to formulate Wolfe and Mond-Weir type nondifferentiable minimax mixed integer dual programs and symmetric duality theorems are established. Moreover, nondifferentiable fractional symmetric dual programs are studied by using the above programs.

A finite element scheme is considered for the viscous Cahn-Hilliard equation with the nonconstant gradient energy coefficient. The scheme inherits energy decay property and mass conservation as for the classical solution. We obtain the corresponding error estimate using the extended Lax-Richtmyer equivalence theorem.

In the existing literature, most of the purchasing models were developed only for retailers problem ignoring the constraint of storage capacity of retailers shop/showroom. In this paper, we have developed a deterministic model of wholesaler-retailers' problem of single product. The storage capacity of wholesaler's warehouse/showroom and retailers' showroom/shop are assumed to be finite. The items are transported from wholesaler's warehouse to retailers' Own Warehouse (OW) in a lot. The customer's demand is assumed to be displayed inventory level dependent. Demands are met from OW and that spaces of OW will immediately be filled by shifting the same amount from the Rented Warehouse (RW) till the RW is empty. The time duration between selling from OW and filling up its space by new ones from RW is negligible. According to relative size of the retailers' existing (own) warehouse capacity and the demand factors, different scenarios are identified. Our objectives are to optimize the cost functions of wholesaler and two retailers separately. To solve this problem, a real coded Genetic Algorithm (GA) with roulette wheel selection/reproduction, whole arithmetic crossover and non-uniform mutation is developed. Finally a numerical example is presented to illustrate the results for different scenarios. To compare the results of GA, Generalised Reduced Gradient Method has been used for the problem. Also, a sensitivity analysis has been performed to study the variations of the optimal average cost with respect to the different parameters.

This paper outlines a reliable strategy for solving nonlinear Volterra-Fredholm integro-differential equations. The modified form of Adomian decomposition method is found to be fast and accurate. Numerical examples are presented to illustrate the accuracy of the method.

From a notion of d-pseudo-orthogonality for a sequence of poly-nomials ($d\;\in\;{2,3,\cdots}$), this paper introduces three different characterizations of natural exponential families (NEF's) with polynomial variance functions of exact degree 2d-1. These results provide extended versions of the Meixner (1934), Shanbhag (1972, 1979) and Feinsilver (1986) characterization results of quadratic NEF's based on classical orthogonal polynomials. Some news sets of polynomials with (2d-1)-term recurrence relation are then pointed out and we completely illustrate the cases associated to the families of positive stable distributions.

This paper is to investigate the approximate confidence limits of the reliability performances (such as failure rate, reliability function and average life) for a cold standby series system. The Bayesian approximate upper confidence limit of failure rate is obtained firstly, and next Bayesian approximate lower confidence limits for reliability function and average life are presented. The expressions for calculating Bayesian lower confidence limits of the reliability function and average life are also obtained, and an illustrative example is examined numerically by means of the Monte-Carlo simulation. Finally, the accuracy of confidence limits is discussed.

Given operators X and Y on a Hilbert space H, an interpolating operator is a bounded operator A such that AX = Y. In this article, we investigate compact interpolation problems for vectors in a tridiagonal algebra. Let L be a subspace lattice acting on a separable complex Hilbert space H and Alg L be a tridiagonal algebra. Let X = $(x_{ij})\;and\;Y\;=\;(y_{ij})$ be operators acting on H. Then the following are equivalent: (1) There exists a compact operator A = $(x_{ij})$ in AlgL such that AX = Y. (2) There is a sequence {$\alpha_n$} in $\mathbb{C}$ such that {$\alpha_n$} converges to zero and $$y_1\;_j=\alpha_1x_1\;_j+\alpha_2x_2\;_j\;y_{2k}\;_j=\alpha_{4k-1}x_{2k\;j}\;y_{2k+1\;j}=\alpha_{4k}x_{2k\;j}+\alpha_{4k+1}x_{2k+1\;j}+\alpha_{4k+2}x_{2k+2\;j\;for\;all\;k\;\epsilon\;\mathbb{N}$$.

It is known that the classical Fatou's lemma and Lebesgue convergence theorem do not require the assumption that J1. is finite. In this note, we show that the assumption $\mu$(X) < $\infty$ cannot be replaced with a weaker assumption to prove Fatou's lemma and Lebesgue convergence theorem for a sequence of set-valued measurable function suggested by Zhang and Wang (Fuzzy Sets and Systems 56(1993) 237-241).

In this paper we present the concepts of fuzzy submachine, which are the generalized form of crisp submachine of a fuzzy finite state machine. Also we extend the concepts of system of generators to fuzzified form.

Using the notion of intuitionistic fuzzy sets, the concept of intuitionis tic fuzzy semi-preopen sets and intuitionistic fuzzy semi-pre-continuous mappings are introduced. The relation between an intuitionistic fuzzy precontinuous ma pping and an intuitionistic semi-precontinuous mapping is given. Characterizations of intuitionistic fuzzy semi-preopen sets and intuitionist ic fuzzy semi-precontinuous mappings are given.

Let W(t) be a Wiener path, let $\xi\;:\;[0,\;{\infty})\;\to\;\mathbb{R}$ be a continuous and increasing function satisfying $\xi$(0) > 0, let $$T_{/xi}=inf\{t{\geq}0\;:\;W(t){\geq}\xi(t)\}$$ be the first-passage time of W over $\xi$, and let F denote the distribution function of $T_{\xi}$. Then the first passage problem has a unique continuous solution as following $$F(t)=u(t)+{\sum_{n=1}^\infty}\int_0^t\;H_n(t,s)u(s)ds$$, where $$u(t)=2\Psi(\xi(t)/\sqrt{t})\;and\;H_1(t,s)=d\Phi\;(\{\xi(t)-\xi(s)\}/\sqrt{t-s})/ds\;for\;0\;{\leq}\;s.

In this paper, we obtain some common fixed point theorems for fuzzy mappings in complete metric linear spaces.

In this paper, we study the behavior and sensitivity analysis of the solution set for a system of parametric generalized nonlinear mixed quasi-variational inclusions in Banach spaces. By using some new and innovative technique, existence theorem for the system of parametric generalized nonlinear mixed quasi-variational inclusions in $L_p(p\ge2$ spaces is established. Our results improve the known result of Agarwal et al.[1].

We find a condition that a graded Artinian O-sequence of codimension 4 is not level.

We calculate the normal fuzzy probability for trigonometric fuzzy numbers defined by trigonometric functions. And we study the normal probability for some operations of two trigonometric fuzzy numbers. Furthermore, we calculate the normal fuzzy probability for some fuzzy numbers generated by operations.

Case deletion diagnostic for multiple correlation coefficient is considered. A method of detecting observations that can hide or create multicollinearity is suggested. A numerical example is given for illustration.

Numerical differentiation is one of the main topics which have been studied by many researchers. If we use the forward difference scheme or the centered difference scheme, the convergence rates to the derivative are O(h) and O($h^2$), respectively. In this paper, using the Lagrange Interpolation, we construct a simple high order numerical differentiation scheme which has the convergence rate O($h^{2k}$) if we have 2k+1 equally spaced nodes. Our scheme is constructive.

A graph is k-cyclable if given k vertices there is a cycle that contains the k vertices. Sallee showed that every finite 3-connected planar graph is 5-cyclable. In this paper Sallee's result is extended to 3-connected infinite locally finite VAP-free plane graphs containing no unbounded faces.

We find a necessary and sufficient condition that the number of some Betti numbers and shifts appear in the last free module Fn of Fx based on type vectors, where X is a finite set of points in $P^n$.

Recently, there are some empirical Bayes procedures using NA samples. We point out a key equality which may not hold for NA samples. Thus, the results of those empirical Bayes procedures based on NA samples are dubious

For a positive integer k and a positive number 0 < p$\le$1, an operator T is said to be (p, k)-quasiposinormal if $T^{{\ast}k}(c^2(T^{\ast}T)P - (TT^{\ast})^P)T^k {\ge} 0$ for some c > o. In this paper we consider a structure for (p, k)-quasiposinormal.