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Abstract: In this paper, we focus on the proposed algorithms to solve a linear programming problem with the convex combination of the max–min and the max–average composition and the max–star composition, respectively. They have been proposed by Ghodousian and Khorram [A. Ghodousian, E. Khorram, Solving a linear programming problem with the convex combination of the max–min and the max–average fuzzy relation equations, Appl. Math. Comput. 180 (2006) 411–418] and Khorram et al. [E. Khorram, A. Ghodousian, A. Abbasi Molai, Solving linear optimization problems with max–star composition equation constraints, Appl. Math. Comput. 179 (2006) 654–661], respectively. Firstly, we show that the “Tabular method algorithm” in the first paper and the “First procedure” in the second paper may not lead to the optimal solutions of the two models in some cases. Secondly, we generalize the proposed algorithm by Abbasi Molai and Khorram [A. Abbasi Molai, E. Khorram, A modified algorithm for solving the proposed models by Ghodousian and Khorram and Khorram and Ghodousian, Appl. Math. Comput. 190 (2007) 1161–1167] to solve the two models. In fact, it modifies the presented algorithms in the two papers. Finally, some numerical examples are given to illustrate the purposes. [Copyright &y& Elsevier]

Abstract: In this paper, we present some sixth-order class of modified Ostrowski’s methods for solving nonlinear equations. Per iteration each class member requires three function and one first derivative evaluations, and is shown to be at least sixth-order convergent. Several numerical examples are given to illustrate the performance of some of the presented methods. [Copyright &y& Elsevier]

Abstract: The aim of this short note is to show on a numerical example that one of the two optimization algorithms proposed in [E. Khorram, A. Ghodousian, Linear objective function optimization with fuzzy relation equation constraints regarding max-av composition, Appl. Math. Comput. 173 (2006) 872–886] may not lead to the optimal solution in some cases. Besides it will be pointed out that the other algorithm (correct, but unfortunately ineffective for larger problems) proposed in [E. Khorram, A. Ghodousian, Linear objective function optimization with fuzzy relation equation constraints regarding max-av composition, Appl. Math. Comput. 173 (2006) 872–886] can be extended to a wider class of non-convex optimization problems. [Copyright &y& Elsevier]

Abstract: A integro-differential equation (IDE) model of a cyclic competitive system is analyzed. Linear stability analysis are performed about the spatial constant solutions, and conditions are derived under which they are stable or unstable. Spatial patterns along with the instability of the nontrivial equilibrium are also observed. [Copyright &y& Elsevier]

Most of the published results on solving operator equations are very restrictive i.e. they have been proved under certain additional assumptions and in fact we do not have general solvability conditions. There are many reasons why this is so, one of them being the fact that the usual methods employed when solving these equations involve the use of generalized inverses which exist and are bounded in the case of operators only under certain special conditions such as closedness of the range of operators. Using two previously considered systems of operator equations as examples, we will show that using a particular general approach we can give necessary and sufficient solvability conditions without any additional assumptions. We will consider the system A X C = C = C X A and generalize recent particular results from the paper C. Deng, et al. (Appl. Math. Letters 81, 86–92 (2018)), as well as B A X = B = X A B for which the particular results are given in the paper C. Deng, (J. Math. Anal. Appl. 398 (2013) 664–670). We intend to use our approach to initiate formulating various general solvability conditions for other systems of operator equations. [ABSTRACT FROM AUTHOR]

• We disprove a conjecture proposed by Fiedorowicz, Sidorowicz, Sopena (Appl. Math. Comput. 410 (2021) 126253). • In addition, we find a result of the above paper is not correct. • Two sufficient conditions are given for a hamiltonian digraph D with w c → (D) = 2. Under an arc-coloring c of a digraph D , if for each pair of vertices (u , v) , there exists a directed walk from u to v satisfying that any two consecutive arcs of it have different colors, we say that D is properly-walk connected, and c is a proper-walk coloring of D. The proper-walk connection number w c → (D) of D is the least integer k such that D has a proper-walk coloring with k colors. Fiedorowicz, Sidorowicz, Sopena (Appl. Math. Comput. 410 (2021) 126253) conjectured that if D is a hamiltonian digraph with δ (D) ≥ 2 , then w c → (D) ≤ 2. In this paper, we disprove the conjecture by constructing two families of counterexamples. Also, we present some cases for a hamiltonian digraph D having w c → (D) = 2. In addition, we find that Observation 15 is not true in the same paper. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce a new class of the generalized mixed equilibrium problems with a new definition of the relaxed monotonicity for bi-functions in topological vector spaces. By employing the KKM technique and under some appropriate assumptions on the considering nonlinear mappings, we obtain the existence of a solution for the generalized mixed equilibrium problems with the new concept of the relaxed monotonicity and coercivity condition(in order to relax the compactness of the domains of the nonlinear mappings) in the setting of topological vector spaces. Moreover, the compactness and convexness of the solution set are investigated. The results in the paper extend and generalize the corresponding results, especially Sintunavarat (2013) [20] in this area by providing mild assumptions in order to guarantee the existence of a solution for the generalized mixed equilibrium problem. [ABSTRACT FROM AUTHOR]

In this paper, to analyze the effect of the cross patch infection between different groups to the spread of gonorrhea in a community, we establish the complete global dynamics of a multi-group SIS epidemic model with varying total population size by a threshold parameter. In the proof, we use special Lyapunov functional techniques, not only one proposed by the paper [Prüss et al., 2006], but also the other one for a varying total population size with some ideas specified to our model and no longer need a grouping technique derived from the graph theory which is commonly used for the global stability analysis of multi-group epidemic models. [ABSTRACT FROM AUTHOR]

In this paper, the underlying general linear methods (GLMs) are adapted to linear neutral multidelay-integro-differential equations (NMIDEs). In order to obtain stability criteria of the extended GLMs, the corresponding results in paper of Zhang and Vandewalle (2008) are generalized. Based on the concepts of A( α )-stability and A-stability of the underlying GLMs, a serial of asymptotic stability criteria of the extended GLMs are obtained. [ABSTRACT FROM AUTHOR]

The generalized k -connectivity κ k (G) of a graph G , introduced by Hager in 1985, is a natural generalization of the concept of connectivity κ (G) , which is just for k = 2. Rongxia Hao et al. determined the generalized 4-connectivity of the total graphs of the complete equipartition bipartite graph and conjectured that κ 4 (T (K m , m + 1)) = 2 m − 1 and κ 4 (T (K m , n)) = 2 m for n > m + 1 and m ≥ 4 in [Appl. Math. Comput. 422 (2022)]. In this paper, we solved this conjecture. [ABSTRACT FROM AUTHOR]

• The minimum over all maximum number of edge-disjoint paths to connect any 3-subset θ of V (G) is given. • The compact upper bound of 3-path connectivity π 3 (G) for a general graph G is gotten. • The structural proprieties of line graphs L (K m , n) and total graphs T (K m , n) of complete bipartite graphs K m , n are deeply explored. • The 3-path connectivity π 3 (L (K m , n)) and π 3 (T (K m , n)) are determined. Let θ be a subset of vertex set V (G) of a simply connected graph G , two θ -trees P 1 and P 2 of G are said to be internally disjoint if V (P 1) ∩ V (P 2) = θ and E (P 1) ∩ E (P 2) = ∅. For an integer k ≥ 2 , the k -path connectivity π k (G) (resp. k -tree connectivity κ k (G)) of a graph G is defined as min { π G (θ) | θ ⊆ V (G) and | θ | = k } (resp. min { κ G (θ) | θ ⊆ V (G) and | θ | = k }), where π G (θ) (resp. κ G (θ)) is the maximum number of pairwise internally disjoint θ -paths (resp. θ -trees) in G. The 3-tree connectivity of the line graph L (K m , n) and total graph T (K m , n) of the complete bipartite graph K m , n are gotten in [Appl. Math. Comput. 347(2019) 645-652]. In this paper, these results are improved from trees to paths. The exact values of the 3-path connectivity for L (K m , n) and T (K m , n) are gotten. That is, π 3 (L (K m , n)) = ⌊ 3 m + 2 n − 3 4 ⌋ − 1 for m = 3 and odd n , otherwise, π 3 (L (K m , n)) = ⌊ 3 m + 2 n − 3 4 ⌋ unless m = 1 and n = 1 , 2 ; π 3 (T (K m , n)) = m + ⌊ m 4 ⌋ for n ≥ m ≥ 1. In addition, the compact upper bound of π 3 (G) for a general graph G are gotten. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we give some necessary and sufficient conditions for the solvability to the system of matrix equations and provide an expression of the general solution to (0.1). Furthermore, we obtain the maximal and minimal ranks of and in (0.1). The findings of this paper extend the known results in the literatures. [Copyright &y& Elsevier]

Abstract: This paper presents new results on delay-dependent stability and stabilization for linear systems with interval time-varying delays. Some less conservative delay-dependent criteria for determining the stability of the time-delay systems are obtained in this paper. Based on the stability conditions, we propose a new state transformation technology to facilitate controller designing efficiently and computationally. The method is also applicable to the existing stability conditions reported by now, while the existing technologies may fail to derive computational control procedures from the stability conditions. Finally, some numerical examples well illustrate the effectiveness of the proposed method. [Copyright &y& Elsevier]

Abstract: This paper investigates the problem of chaos and hyper-chaos control, and proposes a simple adaptive feedback control method for chaos control under a reasonable assumption. In comparison with previous methods, the present control technique is simple both in the form of the controller and its application. Several illustrative examples with numerical simulations are studied by using the results obtained in this paper. Study of examples shows that our control method works very well in chaos control. [Copyright &y& Elsevier]

Abstract: In this paper, the super-linearly and quadratically convergent strong sub-feasible method [J.L. Li, J.B. Jian, A superlinearly and quadratically convergent strongly subfeasible method for nonlinear inequality constrained optimization, OR Transactions, 7 (2) (2003) 21–34] for nonlinear inequality constrained optimization is improved, such that the iterative points can get into the feasible region after a finite number of iterations. As a result, a strict restricted condition can be overcome. Another two contributions of this paper are that a new bidirectional Armijo line search is presented and a lot of numerical comparison results are reported. [Copyright &y& Elsevier]

Abstract: In this paper, a Volterra model with mutual interference and Beddington–DeAngelis functional response is investigated, some sufficient conditions which guarantee the existence and global attractivity of positive periodic solution for the system are obtained. Furthermore, our results improve the main results of paper . [Copyright &y& Elsevier]

Abstract This paper briefly surveys Markov’s theorem related to zeros of orthogonal polynomials. Monotonicity of zeros of some families of orthogonal polynomials are reviewed in detail. [ABSTRACT FROM AUTHOR]

Abstract The trinomial coefficient (n k) 2 is given by ∑ k = − n n (n k) 2 x k = (1 + x + x − 1) n. In this paper, we obtain the explicit formulas for the lacunary sum ∑ − n ≤ k ≤ n k ≡ r (mod m) (n k) 2. For example, ∑ − n ≤ k ≤ n k ≡ 1 (mod 12) (n k) 2 = 2 n + 3 n − (− 1) n + 6 H n 12 , where H 0 = 0 , H 1 = 1 and H n = 2 H n − 1 + 2 H n − 2 for n ≥ 2. [ABSTRACT FROM AUTHOR]

Abstract Let Δ k be the unique normalized cusp form of level one and weight k with k = 16 , 18 , 20 , 22 , 26. In this paper, we describe a method to achieve the explicit bounds B k of n such that the Fourier coefficients a n (Δ k) ≠ 0 for all n < B k. [ABSTRACT FROM AUTHOR]

Abstract: This paper shows some elementary facts on simple games with respect to blockability relations. It is verified in this paper that fundamental concepts on simple games as null players, dictators, veto players, and so on can be expressed in terms of blockability relations. More, some new concepts as “conflict-free” and so on, are introduced from the viewpoint of blockability relations into the framework of simple games. [Copyright &y& Elsevier]

Abstract: In the paper finite-dimensional stationary dynamical control systems described by linear stochastic ordinary differential state equations with multiple point delays in the control are considered. Using notations, theorems and methods taken directly from deterministic controllability problems for linear dynamical systems with delays in control, necessary and sufficient conditions for different kinds of stochastic relative controllability in a given time interval are formulated and proved. It will be proved that under suitable assumptions relative controllability of a deterministic linear associated dynamical system is equivalent to stochastic relative exact controllability and stochastic relative approximate controllability of the original linear stochastic dynamical system. As a special case relative stochastic controllability of dynamical systems with single point delay is also considered. Some remarks and comments on the existing results for stochastic controllability of linear dynamical systems are also presented. In the second part of the paper minimum energy control problem is considered. Under the assumption that system is stochastically relatively exactly controllable analytical formula for minimum energy control is given. [Copyright &y& Elsevier]

Abstract: A variety of rank formulas of some matrix expressions and certain partitioned matrices with respect to the generalized inverse are established. Some necessary and sufficient conditions are given by using the rank formulas presented in this paper for two, three and four ordered matrices to be independent in the generalized inverse . As special cases, necessary and sufficient conditions are derived for two, three and four ordered matrices to be independent in the weighted Moore–Penrose inverse and the Drazin inverse. Some known results can be regarded as the special cases of the results in this paper. [Copyright &y& Elsevier]

Abstract: In this paper, we firstly make some corrections for typos errors on our paper “Nontrivial Solution of Third-order Nonlinear Eigenvalue Problems, Appl. Math. Comput. 176(2006), 714–721”. And then, we supplement some cases which have not been studied in the above paper. [Copyright &y& Elsevier]

Abstract: In the present paper, we estimate the rate of convergence on functions of polynomial type for some variant of the Baskakov operators. The form of the operator discussed in the present paper makes results helpful from the computational point of view. [Copyright &y& Elsevier]

Abstract: In a recent paper [M.A. Noor, K.I. Noor, Three-step iterative methods for nonlinear equations, Applied Mathematics and Computation 183 (2006) 322–327], a three-step iterative method with third-order convergence for solving nonlinear equations has been presented. In this paper, we show that the iterative method given by the authors has quadratic convergence, not the third-order one suggested in their work. [Copyright &y& Elsevier]

Abstract: This paper is an attempt to stress the usefulness of the multi-variable special functions. In this paper, we derive generating relations involving multi-variable Tricomi and Hermite–Tricomi functions by using Lie-algebraic method. Further, we derive certain new and known generating relations involving other forms of Tricomi, Hermite–Tricomi and Bessel functions as applications. [Copyright &y& Elsevier]

Abstract: This paper presents a survey of error-free algorithms to solve various systems of linear equations. The presented algorithms do not introduce computational errors into the solution and thus they are well suited to solve ill-conditioned linear systems. The error-free algorithms are based on modulo arithmetic. Two basic approaches have been investigated in the paper. The first one is based on iterative scheme using one modulus only. The other one is parallel and uses several moduli and the Chinese theorem. It is based on polynomial algebra operations that allow to express the operation of deconvolution as a sequence of convolutions of both response and output signals. [Copyright &y& Elsevier]

Abstract: This paper is concerned with a new type of the classical Bernstein operators where the function is evaluated at intervals . We also make extensive study simultaneous approximation by the linear combination of these new Bernstein type operators . At the end of this paper we have given an other modification of these operators. [Copyright &y& Elsevier]

Abstract: Some methods have been presented for ranking efficient decision making units (DMUs) in data envelopment analysis (DEA). This paper addresses the ranking of interval data by using Monte Carlo method. This method is based on a paper [G.R. Jahanshahloo, F. Hosseinzadeh Lotfi, H. Zhiani Rezai, F. Rezai Balf, Using Monte Carlo method for ranking efficient DMUs, Applied Mathematics and Computation 162 (2005) 371–379]. The worthwhile this method is its ability in ranking of extreme and non-extreme efficient DMUs. [Copyright &y& Elsevier]

Abstract: Orthogonal systems of trigonometric polynomials of semi-integer degree with respect to a weight function w(x) on [0,2π) have been considered firstly by Turetzkii in [A.H. Turetzkii, On quadrature formulae that are exact for trigonometric polynomials, East J. Approx. 11 (2005) 337–359 (Translation in English from Uchenye Zapiski, Vypusk 1(149), Seria math. Theory of Functions, Collection of Papers, Izdatel’stvo Belgosuniversiteta imeni V.I. Lenina, Minsk (1959) 31–54)]. It is proved that such orthogonal trigonometric polynomials of semi-integer degree satisfy five-term recurrence relation. In this paper we present explicit formulas for five-term recurrence coefficients for some weight functions. [Copyright &y& Elsevier]

Abstract: In this paper, we formulate a new robust two-species nonautonomous predator–prey model with multi-delays and impulsive effects and perform a systematic mathematical and ecological study. Our results in this paper indicate that under the appropriate linear periodic impulsive perturbations, the system is permanent and has a unique positive globally attractive semi-trivial periodic solution. By using the Brouwer fixed point theorem, we prove that if the periodic system is permanent, then there is at least one positive periodic solution of the system. We show that the conditions for global attractivity of the positive semi-trivial periodic solution and permanence of the population of the model depend on time delay, so, we call it “profitless”. In this paper, the main feature is that we introduce multi-delays and impulses into the predator–prey model, exhibit a new modeling method which is applied to investigate multi-species impulsive multi-delays differential equations. [Copyright &y& Elsevier]

Abstract: In the present paper, the authors introduce identities for the -transform which yield a Parseval type relationship for the -transform. The Parseval type relationship proven in this paper give rise to useful corollaries for evaluating indefinite integrals of special functions. Some examples are also given as illustrations of the results presented here. [Copyright &y& Elsevier]

Abstract: In this paper, we first define some generalized Schur complements, then we study the representation of M–P inverse group inverse and Drazin for the partitioned matrix . Based on this, we give three kind quotient identities of generalized Schur complement about the partitioned matrix and develops the results in paper [M. Redivo-Zaglia, Pseudo-Schur complement and their applications, Appl. Num. Math. 50 (2004) 511–519; K. Jbilou, A. Messaoudi, K. Tabaâ, Some Schur complement identities and applications to matrix exatrapolation methods, Linear Algebra Appl. 392 (2004) 195–210]. In the end of the paper, we give the application of these generalized Schur complement in solution of linear equation, and give numerical example to show our results. [Copyright &y& Elsevier]

Abstract: In this paper, we establish the formulas of the maximal and minimal ranks of the quaternion matrix expression where X is a variant quaternion matrix subject to quaternion matrix equations . As applications, we give a new necessary and sufficient condition for the existence of solutions to the system of matrix equations , which was investigated by Wang [Q.W. Wang, A system of four matrix equations over von Neumann regular rings and its applications, Acta Math. Sin., 21(2) (2005) 323–334], by rank equalities. In addition, extremal ranks of the generalized Schur complement with respect to an inner inverse A − of A, which is a common solution to quaternion matrix equations , are also considered. Some previous known results can be viewed as special cases of the results of this paper. [Copyright &y& Elsevier]

Abstract: This paper presents an alternative and efficient method for solving a class of constraint parametric optimization problems using particle swarm optimization algorithm (PSO). In this paper, for the first time PSO is used for solving convex parametric programming, but PSO must be adaptive for doing it. So, for obtaining particles velocities, adaptation weight and velocity boundaries in the updating of velocities are calculated in the recursive form. Computational complexity of the PSO algorithm is decreased based on uniformity of population of particles, the uniformity of which is obtained using eigenvalue spread of covariance of population. Two simple examples are provided for showing the efficiency of the proposed method. For solving these examples, eigenvalue spread criteria applied in the PSO algorithm decrease 78% of computations. [Copyright &y& Elsevier]

Abstract: In this paper, a filled function with one-parameter is proposed for solving unconstrained global optimization problems. This filled function is modified from the previously reported one (see paper [Y.J. Yang, Y.L. Shang, A new filled function method for unconstrained global optimization, Applied Mathematics and Computations 173 (1) (2006) 501–512]). The properties of the filled function are discussed in this paper. An algorithm for unconstrained global optimization is developed from this new filled function. The computational results show that this algorithm is efficient and reliable. [Copyright &y& Elsevier]

Abstract: For a signal control road network subject to equilibrium flows, the maximum possible increase in travel demands is considered in this paper. Using the concept of reserve capacity of signal-controlled junctions, the problem of finding the maximum increase in traffic demands can be formulated as a mathematical program with equilibrium constraints (MPEC). In this paper, we present a projected gradient approach to obtain the maximum increase in travel demands based on the TRANSYT traffic model. Numerical computations are made on a grid network where good results are obtained. [Copyright &y& Elsevier]

Abstract: In this paper, we introduce a new three-step iterative scheme for finding the common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality using the technique of updating the solution. We show that the sequence converges strongly to a common element of two sets under some control conditions. Results proved in this paper may be viewed as an improvement and refinement of the recent results of Noor and Huang [M. Aslam Noor, Z. Huang, Three-step methods for nonexpansive mappings and variational inequalities, Appl. Math. Comput., in press] and Yao and Yao [Y. Yao, J.C. Yao, On modified iterative method for nonexpansive mappings and monotone mappings, Appl. Math. Comput., in press]. [Copyright &y& Elsevier]

Abstract: In this paper, we focus on the proposed algorithm for optimizing the linear function with fuzzy relation equation constraints regarding max-prod composition that it has been proposed by Ghodousian and Khorram [A. Ghodousian, E. Khorram, An algorithm for optimizing the linear function with fuzzy relation equation constraints regarding max-prod composition, Appl. Math. Comput. 178 (2006) 502–509]. Firstly, we show that the algorithm may not lead to the optimal solution in some cases. Secondly, we propose a new algorithm for solving the presented model by Ghodousian and Khorram (2006), as mentioned above. In fact, it modifies the presented algorithm in the Ghodousian and Khorram’s paper. Also, this algorithm is extended to the presented model by Khorram and Ghodousian [E. Khorram, A. Ghodousian, Linear objective function optimization with fuzzy relation equation constraints regarding max-av composition, Appl. Math. Comput. 173 (2006) 872–886.] with max-av composition. Finally, some numerical examples are given for illustrating the purposes. [Copyright &y& Elsevier]

Abstract: Since Cook introduced the notion of local influence in 1986 a great number of papers have appeared in statistics handling this topic in a wide variety of areas. However, until we know, there is no paper focussed on local influence in survey sampling. This paper assesses the local influence through the curvature of the perturbation-formed surface of the ratio estimator in a simple random sampling without replacement and the Horvitz–Thompson estimator in an inclusion proportional to size sampling design. Both estimators use auxiliary information (x) and can be obtained through a model-assisted reasoning where the ratio model with variance proportional to x plays an important role. Two perturbation schemes are considered, a model perturbation and an auxiliary variable perturbation. We illustrate the effectiveness of the method in order to identify influential points with two real examples. [Copyright &y& Elsevier]

Abstract: In this paper, our main purpose is to establish the existence of positive bounded entire solutions of second-order quasilinear elliptic systems. The main results of the present paper are new and extend the previously known results. [Copyright &y& Elsevier]

Abstract: In this paper, our main purpose is to establish the existence of singular positive radial solutions of second order quasilinear elliptic equations. The main results of the present paper are new and extend the previously known results. [Copyright &y& Elsevier]

Abstract: In this paper, on basis of other related works (see [R. Scott, Optimal L ∞ estimates for the finite element method on irregular meshes, Math. Comp. V 30 (1976) 681–697; Qun Lin, Qi-ding Zhu, The Preprocessing and Postprocessing for FEM, Shanghai Science Press, China, 1994; I. Babuska, A. Miller, The post-processing in the finite element method, Parts I–II, Internat. J. Numer. Methods Engrg. 20 (1984) 1085–1109, 1111–1129]), we will continue to study the theory of FEM for elliptic problems with singular righthand side. The main difference between this paper and other related works (see Scott, 1976; Lin and Zhu, 1994; Babuska and Miller, 1984) is that it will present some local estimates for FEM of elliptic problems with singular righthand side. Of course, some numerical examples will be given to investigate those error estimates. [Copyright &y& Elsevier]

Abstract: This paper presents the new convergence analysis for the Newton-like method proposed by [Xinyuan Wu, A new continuation Newton-like method and its deformation, Appl. Math. Comput. 112 (2000) 75–78.] Compared with the original version of the convergence analysis, the restriction imposed on f″(x) is removed thoroughly. In order to guarantee the quadratic convergence of the Newton-like method, it is suffices to suppose that f′(x ∗)≠0 and f′(x) is local Lipschitz near x ∗, where x ∗ is a solution of nonlinear equation f(x)=0. Moreover, some comments are given with examples for the Newton-like method, in comparison with Newton’s method. It can be concluded that the new algorithm is more feasible, effective than Newton’s method. In particularly, when it happens that, the derivative of the function f(x) at an iterate is singular or almost singular, the Newton-like method is vast superior to the classical Newton method. The numerical results of the paper strongly support the conclusion. [Copyright &y& Elsevier]

Abstract: In this paper, weak and strong convergence theorems of three-step iterations are established for asymptotically nonexpansive mappings in Banach spaces. The results obtained in this paper extend and improve the recent ones announced by Xu and Noor [B.L. Xu, M.A. Noor, Fixed point iterations for asymptotically nonexpansive mappings in Banach spaces, J. Math. Anal. Appl. 267 (2002) 444–453], Suthep Suantai [S. Suantai, Weak and strong convergence criteria of Noor iterations for asymptotically nonexpansive mappings, J. Math. Anal. Appl. 311 (2005) 506–517], Weerayuth Nilsrakoo and Satit Saejung [W. Nilsrakoo, S. Saejung, A new three-step fixed point iteration scheme for asymptotically nonexpansive mappings, Appl. Math. Comput., in press, doi:10.1016/j.amc.2006.01.063] and others. [Copyright &y& Elsevier]

Abstract: Evaluating the efficiency of organizational units continues to be a difficult problem to solve, especially when the multiplicity of inputs (resources, costs) and outputs (services, products) associated with these units is considered. This paper considers a previous article published by Wang and Luo [Y. Wang, Y. Luo, DEA efficiency assessment using ideal and anti-ideal decision-making units, Applied Mathematics and Computation 173 (2) (2006) 902–915] in the journal of Applied Mathematics and Computation where data envelopment analysis (DEA) and the technique for order preference by similarity to ideal solution (TOPSIS) are integrated in ranking of decision-making units (DMUs). Wang and Luo (2006) contribute to a very interesting topic by showing that the TOPSIS idea can be combined to DEA for a comprehensive ranking of DMUs. However, this paper finds that their approach is problematic in employing the negative ideal point (NIP) for DEA computation. Their ideal point based models rely on using conflicting efficiency concepts. We slightly revised the models so that a DEA analysis using TOPSIS idea can be performed. Numerical demonstration reveals that our approach produces a ranking result that is consistent with that in previous studies. [Copyright &y& Elsevier]

Abstract: Changing economic conditions make the selling price and demand quantity more and more uncertain in the market. The conventional inventory models determine the selling price and order quantity for a retailer’s maximal profit with exactly known parameters. This paper develops a solution method to derive the imprecise profit of the inventory model when the demand quantity and unit cost are imprecise. Since imprecise parameters contained in the inventory model lie in intervals, the profit value calculated from the model should be in a range as well. We formulate a pair of two-level mathematical programming model to derive the upper bound and lower bound of the profit. Based on the duality theorem of geometric programming, the pair of two-level mathematical programs is transformed into a pair of conventional geometric programs. Solving the corresponding pair of geometric programs produces the interval of profit. An example illustrates the idea in this paper. That example also shows that the interval profit contains more information for determining inventory policy. [Copyright &y& Elsevier]

Abstract: A Cramer rule for solving a kind of restricted matrix equationsis presented in [G. Wang, Jie Sun, A Cramer rule for solution of the general restricted matrix equation, Appl. Math. Comput. 154 (2004) 415–422]. This paper gives a more condensed Cramer rule for the solution of the matrix equations. The results in [G. Wang, Z.L. Xu, Solving a kind of restricted matrix equations and Cramer rule, Appl. Math. Comput. 162 (2005) 329–338, Chao Gu, G.R. Wang, Z.L. Xu, PCR Algorithm for the Parallel Computation of the Solution of a class of Singular linear Systems, Appl. Math. Comput. 176 (2006) 237–244] are partially the special cases in our paper. [Copyright &y& Elsevier]

Abstract: Tien D. Kieu, in 10 papers posted to the quant-ph section of the xxx.lanl.gov preprint archive [some of which were also published in printed journals such as Proc. Royal Soc. A 460 (2004) 1535] had claimed to have a scheme showing how, in principle, physical “quantum adiabatic systems” could be used to solve the prototypical computationally undecidable problem, Turing’s “halting problem”, in finite time, with success probability >2/3 (where this 2/3 is independent of the input halting problem). There were several errors in those papers, most which ultimately could be corrected. More seriously, we here exhibit counterexamples to a crucial step in Kieu’s argument. The counterexamples are small quantum adiabatic systems in which “decoy” nonground states arise with high probability (>99.999%). Kieu had wrongly claimed no decoy state could ever acquire occupation probability greater than 50%. These counterexamples destroy Kieu’s entire plan and there seems no way to correct the plan to escape them. Nevertheless, there are some important consequences salvageable from Kieu’s idea: we can prove that the “halflife” of Kieu’s quantum systems is uncomputably large and no fully general form of the quantum adiabatic theorem can exist that yields computable upper bounds on adiabatic convergence times (both unless Church’s thesis is false so that finite time adiabatic quantum system evolution is unsimulable); and we can prove that no algorithm exists to find the ground-state energy of Kieu’s class of quantum Hamiltonians and hence their long-term thermal behavior is uncomputable. [Copyright &y& Elsevier]

Abstract: In this paper, our main purpose is to establish the existence of positive bounded entire solutions of second order quasilinear elliptic equations under new conditions. The main results of the present paper are new and extend the previously known results. [Copyright &y& Elsevier]