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A comparison of the performance on the final exam for subpopulations of students in College Algebra was used to assess the effectiveness of online homework. Data was collected for two small groups of students, one with traditional paper homework and the other with online homework. The groups of students were further classified by incoming skill level measured by a departmental placement test. The data suggests that online homework was beneficial to the incoming higher-skilled group, whereas, the lower-skilled students did not benefit from online homework. [ABSTRACT FROM PUBLISHER]

In the literature, rank-constrained Hermitian nonnegative-definite solutions to the matrix equation AXAH=B have been investigated, under the conditions that B is Hermitian and nonnegative-definite, and the matrix equation is consistent. In this paper, we discuss rank-constrained Hermitian nonnegative-definite least squares solutions to this matrix equation, in which the above conditions may not hold. We derive the rank range and expression of these least squares solutions. Therefore, the results obtained in this paper generalize those in the literature. [ABSTRACT FROM AUTHOR]

Let T and S be two self-adjoint positive invertible operators of a complex Hilbert space H. In this paper, we investigate some inequalities involving the quadratic forms of the weighted arithmetic and harmonic means of T and S. Application for operator entropies is also discussed. [ABSTRACT FROM AUTHOR]

This paper will consider the range of British participation in mathematics internationally during the nineteenth century through an analysis of British mathematical contributions to scientific journals outside of Britain. Viewing scientific papers contained in journals as significant indicators of research, we consider scientists who authored or read and responded in print to papers in a given area within a given group of journals to constitute a publication community. The extent of publication by British mathematicians in these journals can help characterize the role of foreign publication in nineteenth-century British mathematics. Moreover, the isolation of educational, societal, and personal circumstances which motivated British mathematicians to present their work to foreign journals highlights limited but concentrated groups of mathematicians committed to developing and strengthening international mathematical ties with Britain. [ABSTRACT FROM AUTHOR]

The paper reports some new solutions for heat transfer through extended surfaces or fins using the symbolic algebra package Maple 8, which is widely available. The four specific problems chosen for the present study are: (a) a rectangular convection fin with the heat transfer coefficient varying either linearly or exponentially with the distance from the base, (b) a truncated conical spine with convection at both ends, (c) a heat-generating annular fin with a constant base heat flux and an adiabatic tip, and (d) a convection fin array made of a rectangular fin and two triangular fins. Each problem is formulated in a manner that makes its solution novel and distinct from what is available in the literature. Solutions are provided in symbolic forms. Using the numerical and graphical capabilities of Maple, the results are presented in the form of numerical data as well as graphical displays. The paper demonstrates that Maple provides an effective and convenient tool for the analysis of extended surface heat transfer problems that otherwise demand tedious algebraic manipulations. [ABSTRACT FROM AUTHOR]

The Laguerre calculus is widely used for the inversion of differential operators on the Heisenberg group. Applying the Laguerre calculus established on nilpotent Lie groups of step two in Chang et al. [The Laguerre calculus on the nilpotent Lie group of step two. Preprint; 2019. Available from: ], we find the explicit formulas for the heat kernel of sub-Laplace operator and the fundamental solution of power of sub-Laplace operator on nilpotent Lie groups of step two. Calin, Chang and Markina [Generalized Hamilton–Jacobi equation and heat kernel on step two nilpotent Lie groups. In: Gustafsson B, Vasil'ev A, editors. Analysis and mathematical physics. Basel: Birkhüser; 2009 (Trends in mathematics)] also get the formulas for the heat kernel of sub-Laplace operator on nilpotent Lie groups of step two by using the Hamiltonian and Lagrangian formalisms that are related to geometric mechanics. In this paper, we use a totally different method to prove our main results by using the Laguerre calculus, which is more direct from the point of view of Fourier analysis. [ABSTRACT FROM AUTHOR]

The aim of this note is to analyse the results in the paper by D.Y. Gao and G. Strang [Geometric nonlinearity: Potential energy, complementary energy, and the gap function, Quart. Appl. Math. 47 (1989), pp. 487-504] where, according to D.Y. Gao, the complementary gap function was first introduced, and several flaws, mistakes, and inconsistencies are present, and to discuss the mathematical manner in which the mentioned paper presents itself, especially from the point of view of convex analysis. [ABSTRACT FROM AUTHOR]

Some preconditioners for accelerating the classical iterative methods are given in Zhang et al. [Y. Zhang and T.Z. Huang, A class of optimal preconditioners and their applications, Proceedings of the Seventh International Conference on Matrix Theory and Its Applications in China, 2006. Y. Zhang, T.Z. Huang, and X.P. Liu, Modified iterative methods for nonnegative matrices and M-matrices linear systems, Comput. Math. Appl. 50 (2005), pp. 1587-1602. Y. Zhang, T.Z. Huang, X.P. Liu, A class of preconditioners based on the (I+S(α))-type preconditioning matrices for solving linear systems, Appl. Math. Comp. 189 (2007), pp. 1737-1748]. Another kind of preconditioners approximating the inverse of a symmetric positive definite matrix was given in Simons and Yao [G. Simons, Y. Yao, Approximating the inverse of a symmetric positive definite matrix, Linear Algebra Appl. 281 (1998), pp. 97-103]. Zhang et al. 's preconditioners and Simons and Yao's are generalized in this paper. These preconditioners are all of low construction cost, which all could be taken as approximate inverse of M-matrices. Numerical experiments of these preconditioners applied with Krylov subspace methods show the effectiveness and performance, which also show that the preconditioners proposed in this paper are better approximate inverse for M-matrices than Simons'. [ABSTRACT FROM AUTHOR]

In this paper, the new short-term problems that are faced by a generation company in a deregulated electricity market are addressed and an optimization algorithm is proposed. Our model of the spot market explicitly represents the price of electricity as an uncertain exogenous variable. We consider a very complex problem of hydrothermal optimization with pumped-storage plants, so the problem deals with non-regular Lagrangian and non-holonomic inequality constraints. To obtain a necessary minimum condition, the problem was formulated within the framework of nonsmooth analysis using the generalized (or Clarke's) gradient and the Nonsmooth maximum principle. The optimal control problem is solved by means of an algorithm implemented in the commercial software package Mathematica. Results of the application of the method to a numerical example are presented. [ABSTRACT FROM AUTHOR]

In an earlier paper, the author introduced new upper bounds for free linear and nonlinear vibration systems; to compute the best upper bounds, the differential calculus of norms was applied. In the present paper, this work is continued for the corresponding excited systems. Some new techniques and ideas are involved. The results in the applications cannot be obtained by the methods used so far. [ABSTRACT FROM AUTHOR]

In this paper, robust regulation of stable infinite-dimensional plants with transfer functions in the H 8 -algebra is considered. The reference and disturbance signals are allowed to have an infinite number of poles on the imaginary axis, which makes it possible to consider e.g. arbitrary periodic signals. A controller depending on a positive scalar e and design parameters K k is proposed. The design parameters are matrices over H 8 , and by the main result of the paper, if the design parameters satisfy a certain condition, the proposed controller is a robust regulator for sufficiently small values of e. The only knowledge needed to verify this condition is the so-called -stability of the plant and values of the plant transfer function at the poles of the reference and disturbance signals. The analysis in this paper is in the frequency domain and it is based on the fractional representation approach. [ABSTRACT FROM AUTHOR]

Comparing the large number of research papers on the ordered weighted averaging (OWA) operator, the researches on relative quantifier are relatively rare so far. In the present paper, based on the quantifier guided aggregation method with OWA operator which was proposed by Yager [“Quantifier guided aggregation using OWA operators”, Int. J. Intell. Syst. , 11, pp. 49–73, 1996], a generating function representation method for regular increasing monotone (RIM) quantifiers is proposed. We extend the the properties of OWA operator to the RIM quantifier which is represented with a monotone function instead of the OWA weighting vector. A class of parameterized equidifferent RIM quantifier which has minimum variance generating function is proposed and its properties are also analyzed. The equidifferent RIM quantifier is consistent with its orness level for any aggregated elements, which can be used to represent the decision maker's preference. [ABSTRACT FROM AUTHOR]

In recent years, wavelet shrinkage has become a very appealing method for data de-noising and density function estimation. In particular, Bayesian modelling via hierarchical priors has introduced novel approaches for Wavelet analysis that had become very popular, and are very competitive with standard hard or soft thresholding rules. In this sense, this paper proposes a hierarchical prior that is elicited on the model parameters describing the wavelet coefficients after applying a Discrete Wavelet Transformation (DWT). In difference to other approaches, the prior proposes a multivariate Normal distribution with a covariance matrix that allows for correlations among Wavelet coefficients corresponding to the same level of detail. In addition, an extra scale parameter is incorporated that permits an additional shrinkage level over the coefficients. The posterior distribution for this shrinkage procedure is not available in closed form but it is easily sampled through Markov chain Monte Carlo (MCMC) methods. Applications on a set of test signals and two noisy signals are presented. [ABSTRACT FROM AUTHOR]

This paper deals with a fully implicit time discretization scheme with variable time-step for a nonlinear system modelling phase transition and mechanical deformations in shape memory alloys. The model is studied in the non-stationary case and accounts for local microscopic interactions between the phases introducing the gradients of the phase parameters. The resulting initial-boundary value problem has already been studied by the author who proved existence, uniqueness and continuous dependence on data for a suitable weak solution along some regularity results. A careful and detailed investigation of the variable time-step discretization is the goal of this paper. Thus, we deduce some estimates for the discretization error. These estimates depend only on data, impose no constraints between consecutive time-steps and show an optimal order of convergence. Finally, we prove another regularity result for the solution under stronger regularity assumptions on data. [ABSTRACT FROM AUTHOR]

In a recent paper by the authors, the associative and the Lie algebras of Weyl type A[D] = A ⊗ F[D] were introduced, where A is a commutative associative algebra with an identity element over a field F of any characteristic, and F[D] is the polynomial algebra of a commutative derivation subalgebra D of A. In the present paper, a class of the above associative and Lie algebras A[D] with F being a field of characteristic 0 and D consisting of locally finite derivations of A, is studied. The isomorphism classes of these associative and Lie algebras are determined. The structure of these algebras is described explicitly. [ABSTRACT FROM AUTHOR]

This paper discusses the estimation of average treatment effects in observational causal inferences. By employing a working propensity score and two working regression models for treatment and control groups, Robins et al. (1994, 1995) introduced the augmented inverse probability weighting (AIPW) method for estimation of average treatment effects, which extends the inverse probability weighting (IPW) method of Horvitz and Thompson (1952); the AIPW estimators are locally efficient and doubly robust. In this paper, we study a hybrid of the empirical likelihood method and the method of moments by employing three estimating functions, which can generate estimators for average treatment effects that are locally efficient and doubly robust. The proposed estimators of average treatment effects are efficient for the given choice of three estimating functions when the working propensity score is correctly specified, and thus are more efficient than the AIPW estimators. In addition, we consider a regression method for estimation of the average treatment effects when working regression models for both the treatment and control groups are correctly specified; the asymptotic variance of the resulting estimator is no greater than the semiparametric variance bound characterized by the theory of Robins et al. (1994, 1995). Finally, we present a simulation study to compare the finite-sample performance of various methods with respect to bias, efficiency, and robustness to model misspecification. [ABSTRACT FROM AUTHOR]

This Special Issue is dedicated to explicate and discuss methodological issues in the interdisciplinary research field of mathematical and computational approaches to music. It arose from a lively panel discussion at the third International Conference on Mathematics and Computation in Music 2011 in Paris. We have organized this panel in order to initiate the much needed interdisciplinary dialogue on the How, Why, and What of our modelling of and theorizing about music in the wide field of science, humanities and cognitive approaches to music research. From the contributions of the three panelists to this Special Issue, we extract key topics that the interdisciplinary scientific community needs to address in order to enable the different disciplines to productively complement one another in achieving a comprehensive approach to music as a complex, yet fundamental human trait. [ABSTRACT FROM PUBLISHER]

The r-component connectivity κ r (G) of the non-complete graph G is the minimum number of vertices whose deletion results in a graph with at least r components. So, κ2 is the usual connectivity. In this paper, we determine the r-component connectivity of the hypercube Q n for r=2, 3, …, n+1, and we classify all the corresponding optimal solutions. [ABSTRACT FROM PUBLISHER]

This paper deals with a construction of wavelet frame packets on the positive half-line ℝ+ using the splitting trick for frames. It is shown that, as long as finitely many splitting steps are applied, the resulting sequence of functions is a frame of L 2(ℝ+). If the matrix M(ξ) associated with the splitting is unitary, then the splitting can be applied infinitely many times to prove the existence of frame with the frame bounds as shown in Theorem 3.3. [ABSTRACT FROM AUTHOR]

Let k1≥k2≥···≥km be positive integers. In this paper, we prove that every [0, k1+···+km-n+1]-graph G contains a subgraph R such that R has a [image omitted] -factorization orthogonal to any given subgraph H with n edges for every 1≤n≤m. [ABSTRACT FROM AUTHOR]

In this paper, we deal with the multiple-objective optimization problems, considering an improved definition of generalized type I univex function. Some optimality conditions as well as some duality relations are established. [ABSTRACT FROM AUTHOR]

In this paper, we show that the widely used normalisation constraint [image omitted] does not apply to the priority vectors associated with reciprocal relations, also called fuzzy preference relations, whenever additive transitivity is involved. We show that misleading applications of this type of normalisation may lead to unsatisfactory results and we give some examples from the literature. Then, we propose an alternative normalisation procedure which is compatible with additive transitivity and leads to better results. [ABSTRACT FROM AUTHOR]

This paper considers the problem of searching for the actual time of failure for a system when the only information that is available is that it is has failed by a time t. This situation can be analyzed by using the concept of the reversed failure rate. This paper considers optimization problems that can be solved by using the reversed failure rate. When a unit is detected to have failed at time t, we discuss an optimum backward time from time t to search for its failure time which minimizes the expected cost. The recovery of a database system and of reweighing products using a scale are taken to be two typical applications of the backward time concept. Two models are proposed for appropriate maintenance actions for these situations when a unit is detected to have failed at time t. [ABSTRACT FROM AUTHOR]

In our day-to-day discourse on uncertainty, words like belief, chance, plausible, likelihood and probability are commonly encountered. Often, these words are used interchangeably, because they are intended to encapsulate some loosely articulated notions about the unknowns. The purpose of this paper is to propose a framework that is able to show how each of these terms can be made precise, so that each reflects a distinct meaning. To construct our framework, we use a basic scenario upon which caveats are introduced. Each caveat motivates us to bring in one or more of the above notions. The scenario considered here is very basic; it arises in both the biomedical context of survival analysis and the industrial context of engineering reliability. This paper is expository and much of what is said here has been said before. However, the manner in which we introduce the material via a hierarchy of caveats that could arise in practice, namely our proposed framework, is the novel aspect of this paper. To appreciate all this, we require of the reader a knowledge of the calculus of probability. However, in order to make our distinctions transparent, probability has to be interpreted subjectively, not as an objective relative frequency. [ABSTRACT FROM AUTHOR]

The k-out-of-n system structure is a very popular type of redundancy in fault-tolerant systems, with wide applications in both industrial and military systems. In this paper, the modeling, application and reliability evaluation of k-out-of-n systems are studied for the case where the components and the system have multiple performance levels. A multi-state k-out-of-n system model is proposed that allows different requirements on the number of components for different state levels, and, very importantly, more practical engineering systems can fit into this model. The multiple states in the model can be interpreted in two ways: (i) multiple levels of capacity; and (ii) multiple failure modes. Application examples of the proposed multi-state k-out-of-n system model are given under each of the interpretations. An approach is presented for efficient reliability evaluation of multi-state k-out-of-n systems with identically and independently distributed components. A recursive algorithm is proposed for reliability evaluation of multi-state k-out-of-n systems with independent components. Efficiency investigations show that both of the reliability evaluation approaches are efficient. The multi-state k-out-of-n system model with a constant k value, which is a special case of the general multi-state k-out-of-n system model, has been studied for a long time, but only on the theoretical stage. A practical application of this model is presented in this paper as well. [ABSTRACT FROM AUTHOR]

A continuous location problem in which a firm wants to set up a single new facility in a competitive environment is considered. Other facilities offering the same product or service already exist in the area. Both the location and the quality of the new facility are to be found so as to maximize the profit obtained by the firm. This is a hard-to-solve global optimization problem. An evolutionary algorithm called Universal Evolutionary Global Optimizer (UEGO) seems to be the best procedure to cope with it, but the algorithm needs several hours of CPU time for solving large instances. In this paper, four parallelizations of UEGO are presented. They all are coarse-grain methods which differ in their migratory policies. A computational study is carried out to compare the performance of the parallel algorithms. The results show that one of the parallelizations always gives the best objective function value and has an almost linear speed-up for up to 16 processing elements for large instances. [ABSTRACT FROM AUTHOR]

In this paper we present a new class of memory gradient methods for unconstrained optimization problems and develop some useful global convergence properties under some mild conditions. In the new algorithms, trust region approach is used to guarantee the global convergence. Numerical results show that some memory gradient methods are stable and efficient in practical computation. In particular, some memory gradient methods can be reduced to the BB method in some special cases. [ABSTRACT FROM AUTHOR]

This paper addresses the issue of teaching and learning engineering mathematics in order to support a future of life-long learning in the knowledge society, based on a form of understanding that goes beyond facts, theorems and algorithms. Drawing on three research studies, the importance is shown of students' experience of reflection on study, integration of mathematics into other aspects of an educational programme and into the world at large, and autonomy as a learner. Attention is then moved to implications for the processes of teaching, in order to support such understanding as a capability that students take with them from the university to the workplace. [ABSTRACT FROM AUTHOR]

In this paper, we study two types of approximate solutions for a vector optimization problem in Banach space setting. Our main concern is to define two new concepts of approximate saddle points and relate them to the above solution concepts. As a result, a dual is formulated, and duality results are established. [ABSTRACT FROM AUTHOR]

An extended Heaviside calculus proposed by Péraire in a recent paper is similar to a generalization of the Laplace transform proposed by the present author. This similarity will be illustrated by analysis of an example supplied by Péraire. [ABSTRACT FROM AUTHOR]

The principles, difficulties and challenges in control education are discussed and compared to the similar problems in the teaching of mathematics and systems science in general. The difficulties of today's students to appreciate the classical teaching of engineering disciplines, which are based on rigorous and scientifically sound grounds, are discussed. The new demands for modern engineering education assume that the mathematical skills of the students in modelling, analysis, synthesis, simulation and validation of control problems improve significantly, which sets a major challenge to the education system. To meet that challenge new activating teaching methods are needed, which together with traditional studies bring the students closer to practical applications. In the current paper two new teaching methods are presented, which are aimed at bringing the control world near the student more easily than the traditional courses do. These example cases are control courses in the net with self-study sections, interactive repetitive questions, problems with complete solutions (both pen and paper and computer problems). Also, new 'interactive laboratory exercises' have been included, where the students prepare their preliminary problems first, and after that test the controller with a real process over the net (from their home or from a computer class). [ABSTRACT FROM AUTHOR]

This paper, the first of a two-part article, follows the trail in history of the development of a graphical representation of the complex roots of a function. Root calculation and root representation are traced through millennia, including the development of the notion of complex numbers and subsequent graphical representation thereof. The concepts of the Cartesian and Argand planes prove to be central to the theme. We specifically pause to look at efforts of representing complex roots of a function on the real plane, first, by superimposing the Argand plane onto the Cartesian plane, and secondly, by keeping the planes side by side and moving between the two, and thirdly, by taking the modulus of the function value and hence eliminating one dimension to enable drawing of the complex function as a surface in three dimensions. [ABSTRACT FROM AUTHOR]

In this paper, we present a structure-preserving model-order reduction method for solving large-scale second-order MIMO dynamical systems. It is a projection method based on a block second-order Krylov subspace. We use the block second-order Arnoldi (BSOAR) method to generate an orthonormal basis of the projection subspace. The reduced system preserves the second-order structure of the original system. Some theoretical results are given. Numerical experiments report the effectiveness of this method. [ABSTRACT FROM AUTHOR]

In this paper, we suggest a new version of the Gauss-Newton method for solving a system of non-linear equations which combines the idea of sharp merit function with the idea of quadratic regularization. For this scheme, we prove general convergence results and, under a natural non-degeneracy assumption, local quadratic convergence. We analyze the behavior of this scheme on a natural problem class for which we get global and local worst-case complexity bounds. The implementation of each step of the scheme can be done by standard convex optimization technique. [ABSTRACT FROM AUTHOR]

Nonlinear systems of time dependent partial differential equations of real life phenomena tend to be very complicated to solve numerically. One common approach to solve such problems is by applying operator splitting which introduces subproblems that are easier to handle. The solutions of the subsystems are usually glued together by either the Godunov method (first-order) or the Strang method (second-order). However, the accuracy of such an approach may be very hard to analyse because of the complexity of the equations involved. The purpose of the present paper is to introduce another line of reasoning concerning the accuracy of operator splitting. Let us assume that a fully coupled and implicit discretization of the complete system has been developed. Under appropriate conditions on the continuous problem, such discretizations provide reasonable and convergent approximations. As in the continuous case, operator splitting can be utilized to obtain tractable algebraic subsystems. The problem we address in the present paper is to obtain a bound on the difference between the fully coupled implicit discrete solutions, uh, and the solutions, uh, s, obtained by applying operator splitting to these discrete equations. Suppose we know that uh converges to the analytical solution u as the grid is properly refined and, applying the results from this paper, that uh, s converges toward uh under grid refinement. Then, by the triangle inequality, also the splitting approximation uh, s converges toward the analytical solution u and convergence is thus obtained for an approximation that, from a practical point of view, is easier to compute. [ABSTRACT FROM AUTHOR]

We generalize theorems of Hardy and Miyachi for the Fourier transform on real line to the Jacobi-Dunkl transform. More precisely in the first part of this paper we give another proof of the heart of Hardy's theorem (we mean αβ=1/4), which has been obtained recently by Chouchane, Mili, and Trimèche. In the second part, we get some analog of Miyachi's theorem for the Jacobi-Dunkl transform. [ABSTRACT FROM AUTHOR]

This paper gives a quantitative control of the order of zero of a weak solution to perturbations of the Baouendi-Grushin operator, which generalizes the result due to Aronszaijn, Krzywicki, and Szarski valid for elliptic operators in divergence form with Lipschitz continuous coefficients. [ABSTRACT FROM AUTHOR]

This paper considers the problem of approximating an integrable function by piecewise linear functions that keep the integral and positivity of the original function. [ABSTRACT FROM AUTHOR]

The inverse of the risk difference, commonly referred to as the number needed to treat (NNT) has been recently proposed as a useful measure for comparing two treatments. Since its introduction, the method has been used widely to establish comparative treatment benefits, and has also been the subject of extensive discussions among statisticians. In this paper, we examine the assumptions behind the original definition of NNT, and introduce a new formulation of the method based on a random walk model. Using stopping times, we develop a paradigm for NNT that avoids some of the conceptual and inferential difficulties and pitfalls associated with the previous work on NNT. Simulation results are provided to illustrate the bias introduced by using alternative formulations of NNT, and several open problems are suggested for future research. [ABSTRACT FROM AUTHOR]

In order to get undergraduates interested in mathematics, it is essential to involve them in its ‘discovery’. In this paper, we will explain how technology and the knowledge of lower dimensional calculus can be used to help them develop intuition leading to their discovering the first derivative rule in multivariable calculus. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with the local solvability of a class of semilinear partial differential equations that are, in general, not locally solvable in C ∞ . The linear part has multiple characteristics and it is the composition of p operators, each of them contains lower order terms. We shall analyze the influence of these terms on the local solvability in Gevrey classes. [ABSTRACT FROM AUTHOR]

This paper is concerned with the stabilization problem for a class of continuous stochastic time-delay systems with nonlinear disturbances, parameter uncertainties and possible actuator failures. Both the stability analysis and synthesis problems are considered. The purpose of the stability analysis problem is to derive easy-to-test conditions for the uncertain nonlinear time-delay systems to be stochastically, exponentially stable. The synthesis problem, on the other hand, aims to design state feedback controllers such that the closed-loop system is exponentially stable in the mean square for all admissible uncertainties, nonlinearities, time-delays and possible actuator failures. It is shown that the addressed problem can be solved in terms of the positive definite solutions to certain algebraic matrix inequalities. Numerical examples are provided to demonstrate the effectiveness of the proposed design method. [ABSTRACT FROM AUTHOR]

The combination of geometrically nonlinear analysis with structural optimization against instability opens many possibilities for new formulations of the optimization problem. One of them is optimization against instability in the large. When a critical state does not exist and instability occurs at finite displacements either the lower critical loading is maximized or the generalized displacement for that load is minimized. This paper undertakes these new optimization problems providing formulations and numerical solutions for selected elements. The simple finite dimensional model is analysed first showing characteristic features of the problem, and then a real elastic element is optimized. [ABSTRACT FROM AUTHOR]

Boolean functions are widely used because they can be used to precisely describe logical circuits. Properties of Boolean functions with respect to their applications to cryptography have been studied, but relationship between Boolean functions are rarely studied. This paper studies the independence of Boolean functions, gives necessary and sufficient conditions for judging whether two given Boolean functions are independent. Some enumeration formulae are given. [ABSTRACT FROM AUTHOR]

Orthodox semigroups have been studied by many authors, in particular by Hall, Yamada and Petrich. In this paper, we give the standard representation of orthodox semigroups and investigate various e-varieties of orthodox semigroups which are determined by the standard representations. [ABSTRACT FROM AUTHOR]

In the paper, a new trust region algorithm is given for nonlinear inequality constrained optimization problems. Motivated by a dual problem introduced by Han and Mangasarian [Han, S. P., Mangasarian, O. L. (1983). A dual differentiable exact penalty function. Math. Programming 25:293-306], which is a nonnegatively constrained maximization problem, we construct a trust region algorithm for solving the dual problem. At each iteration, we only need to minimize a quadratic subproblem with simple bound constraints. Under the condition that the iterate sequence generated by the algorithm is contained in some bounded closed set, any accumulation point of the sequence is a Karush- Kuhn-Tucker point of the original problem. [ABSTRACT FROM AUTHOR]

The aim of this paper is to generalize the results of Yamada et al. [Yamada, I., Ogura, N., Yamashita, Y., Sakaniwa, K. (1998). Quadratic approximation of fixed points of nonexpansive mappings in Hilbert spaces. Numer. Funct. Anal. Optimiz. 19(l):165-190], and to provide complementary results to those of Deutsch and Yamada [Deutsch, F., Yamada, I. (1998). Minimizing certain convex functions over the intersection of the fixed point sets of nonexpansive mappings. Numer. Funct. Anal. Optim. 19(1&2):33-56] in which they consider the minimization of some function d over a closed convex set F, the nonempty intersection of N fixed point sets. We start by considering a quadratic function θ and providing a relaxation of conditions of Theorem 1 of Yamada et al. (1998) to obtain a sequence of fixed points of certain contraction maps, converging to the unique minimizer of θ over F. We then extend Theorem 2 and obtain a complementary result to Theorem 3 of Yamada et al. (1998) by replacing the condition lim n → ∞ (λn - λn+1)/λ²n+1 = 0 on the parameters by the more general condition lim n → ∞ λn / λn+1 = 1. We next look at minimizing a more general function θ than a quadratic function which was proposed by Deutsch and Yamada (1998) and show that the sequence of fixed points of certain maps converge to the unique minimizer of 9 over F. Finally, we prove a complementary result to that of Deutsch and Yamada (1998) by using the alternate condition on the parameters. [ABSTRACT FROM AUTHOR]

In many wavelets applications, a scalar product of given function with the scaling function has to be calculated. For deriving effective one point quadrature formulas, the relation among the first scaling moment and the second one is crucial. In this paper, new relations among scaling moments are deduced. [ABSTRACT FROM AUTHOR]

In this paper, an error m a well-known work which claims to prove Young's inequality is discovered and a concise proof of Young's inequality is given. [ABSTRACT FROM AUTHOR]

Whether or not there is an interaction between two factors in their effects on a dependent variable is often a central question. This paper proposes a general mechanism by which an interaction may arise: (a) the two factors are the same thing — or, at least, have a dimension in common — in the sense that it is meaningful to add (or subtract) them; (b) the sum of them (or the difference between them) is what determines the dependent variable; and (c) the relation between the sum (or difference) and the dependent variable is nonlinear. For example, if several factors contribute to arousal in an additive manner, and the relationship of performance score to arousal is inverted-U, the factors will appear to interact in their joint effect on performance. Psychological, medical, and other scientists are likely to be unfamiliar with the (nonlinear) equations used to express this type of theory. Consequently, the task of promoting and interpreting such ideas will fall to the mathematician and statistician. [ABSTRACT FROM AUTHOR]