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In this paper, we study the L p -boundedness of the commutator [ b , S R δ (H) ] (f) = b S R δ (H) f - S R δ (H) (b f) of a BMO function b and the Bochner–Riesz means S R δ (H) for Hermite operator H = - Δ + | x | 2 on R n , n ≥ 2 . We show that if δ > δ (q) = n (1 / q - 1 / 2) - 1 / 2 , the commutator [ b , S R δ (H) ] is bounded on L p (R n) whenever q < p < q ′ and 1 ≤ q ≤ 2 n / (n + 2) . [ABSTRACT FROM AUTHOR]

We are concerned with the following class of equations with exponential nonlinearities: which is related to the Tzitzéica equation. Here $$h_1, h_2$$ are two smooth positive functions. The purpose of the paper is to initiate the analytical study of the above equation and to give a quite complete picture both for what concerns the blow-up phenomena and the existence issue. In the first part of the paper we provide a quantization of local blow-up masses associated to a blowing-up sequence of solutions. Next we exclude the presence of blow-up points on the boundary under the Dirichlet boundary conditions. In the second part of the paper we consider the Tzitzéica equation on compact surfaces: we start by proving a sharp Moser-Trudinger inequality related to this problem. Finally, we give a general existence result. [ABSTRACT FROM AUTHOR]

In this paper, we consider the conjecture that \sigma2^{t+1l-1,2^t} are the only nonlinear balanced elementary symmetric Boolean functions where t and l are positive integers. We prove if n=2^t+1l-1, l odd and 2^t+1\nmid d, \sigman,d is balanced if and only if d=2^k, 1\leq k\leq t. Our results verify most cases of the conjecture for n\equiv3\ (mod\ 4). [ABSTRACT FROM AUTHOR]

Two recent studies have suggested that neural network modelling offers no worthwhile improvements in comparison to the application of weighted linear transfer functions for capturing the non-linear nature of hydrological relationships. The potential of an artificial neural network to perform simple non-linear hydrological transformations under controlled conditions is examined in this paper. Eight neural network models were developed: four full or partial emulations of a recognised non-linear hydrological rainfall-runoff model; four solutions developed on an identical set of inputs and a calculated runoff coefficient output. The use of different input combinations enabled the competencies of solutions developed on a reduced number of parameters to be assessed. The selected hydrological model had a limited number of inputs and contained no temporal component. The modelling process was based on a set of random inputs that had a uniform distribution and spanned a modest range of possibilities. The initial cloning operations permitted a direct comparison to be performed with the equation-based relationship. It also provided more general information about the power of a neural network to replicate mathematical equations and model modest non-linear relationships. The second group of experiments explored a different relationship that is of hydrological interest; the target surface contained a stronger set of non-linear properties and was more challenging. Linear modelling comparisons were performed against traditional least squares multiple linear regression solutions developed on identical datasets. The reported results demonstrate that neural networks are capable of modelling nonlinear hydrological processes and are therefore appropriate tools for hydrological modelling. [ABSTRACT FROM AUTHOR]

In this paper, we focus on the Schrödinger-Kirchhoff-type equation [ABSTRACT FROM AUTHOR]

In this paper we study a nonlocal singularly perturbed Choquard type equation -ε2Δu + V (x)u = εµ-2[1/|x|µ*(P(x)G(u))]P(x)g(u) in R2, where e is a positive parameter, 1/|x|µ with 0 < µ < 2 is the Riesz potential, * is the convolution operator, V (x), P(x) are two continuous real functions and G(s) is the primitive function of g(s). Suppose that the nonlinearity g is of critical exponential growth in R2 in the sense of the Trudinger-Moser inequality, we establish some existence and concentration results of the semiclassical solutions of the Choquard type equation in the whole plane. As a particular case, the concentration appears at the maximum point set of P(x) if V (x) is a constant. [ABSTRACT FROM AUTHOR]

In this paper, we prove that, if Deligne's “petits camarades conjecture” holds, then a Langlands type correspondence holds also for p-adic coefficients on a smooth curve over a finite field. As an application, we prove that any overconvergent F -isocrystal of rank less than or equal to 2 on a smooth curve is ı-mixed. [ABSTRACT FROM AUTHOR]

In this paper, we firstly give the definition of dispersionless bigraded Toda hierarchy (dBTH) and introduce some Sato theory on dBTH. Then we define Orlov-Schulman's ML, MR operator and give the additional Block symmetry of dBTH. Meanwhile we give tau function of dBTH and some related dispersionless bilinear equations. [ABSTRACT FROM AUTHOR]

Let X be a normed space, V be an open convex subset of X and let be a given function. A function is called -midconvex if By the result of Tabor and Tabor, we know that under respective conditions on , if f is -midconvex and locally bounded above at a point then there exists a continuous function such that In this paper we determine the smallest function satisfying the above inequality. The required conditions on are such that the functions , satisfy them. As the main tool we use de Rham theorem. [ABSTRACT FROM AUTHOR]

This paper describes a new algorithm for calculating all equations (direct and inverse transformation, convergence of meridians, linear distortion, calculus of surfaces, and arc-to-chord correction) for the Gauss-Krüger projection. Instead of using different equations for each problem, all the calculi are based on the equations used to obtain the direct transformation. These equations are also more accurate than previous ones and can be extended to an arbitrary width. This paper also explains how the Gauss-Krüger projection may satisfy the needs and requirements of civil engineers as well as Geographical Information Systems (GIS) users, particularly if extended beyond its usual 4° longitudinal range, and therefore can be used as a global reference system for GIS. [ABSTRACT FROM AUTHOR]

We will show in this paper that if λ is very close to 1, then can be attained, where M is a compact–manifold with boundary. This result gives a counter–example to the conjecture of de Figueiredo and Ruf in their paper titled "On an inequality by Trudinger and Moser and related elliptic equations" ( Comm. Pure. Appl. Math., 55, 135–152, 2002). [ABSTRACT FROM AUTHOR]

In this paper we present a novel treatment of the inspection-system design problem when inspection is unreliable and subject to classification errors. Our approach. based on the theory of Error-Correcting Codes (ECC). leads to the development of a Self- Correcting Inspection (SC) decision rule that does not require complete knowledge of inspection error probabilities. We show that the proposed rule assures correct classification, if the number of inspection errors is less than a certain number. We analyze the performance of the SCI decision rule under different inspection situations, including sonic situations that are uncommon in the field of error-correcting codes. Then, we show how the underlying mathematical structure can be applied to determine the number of inspections and the level of inspection reliability in order to minimize the sum of inspection-related costs. The practical contribution of this work lies in that it expands the ability of the designer of inspection systems to deal with cases where there is very little or no information regarding the reliability of the inspection operations. [ABSTRACT FROM AUTHOR]

In this paper we examine a number of different definitions of strategic stability and the relations among them. In particular, we show that the stability requirement given by Hillas (1990) is weaker than the requirements involved in the various definitions of stability in Mertens' reformulation of stability (Mertens 1989,1991). To this end, we introduce a new definition of stability and show that it is equivalent to (a variant of ) the definition given by Hillas (1990). We also use the equivalence of our new definition with the definition of Hillas to provide correct proofs of some of the results that were originally claimed (and incorrectly 'proved') in Hillas (1990). [ABSTRACT FROM AUTHOR]

In this paper we investigate the properties of multimodular functions. In doing so we give elementary proofs for properties already established by Hajek and we generalize some of his results. In particular, we extend the relation between convexity and multimodularity to some convex subsets of Zm. We also obtain general optimization results for average costs related lo a sequence of multimodular functions rather than to a single function. Under this general context, we show that the expected average cost problem is optimized by using regular sequences. We finally illustrate the usefulness of this theory in admission control into a D/D/1 queue with fixed batch arrivals, with no state information. We show that the regular policy minimizes the average queue length for the case of an infinite queue, but not for the case of a finite queue. When further adding a constraint on the losses, it is shown that a regular policy is also optimal for the finite queue case. [ABSTRACT FROM AUTHOR]

This paper analyzes the equilibrium of an economy where economic agents differ with respect to their information gathering and processing abilities. Our results depend on the magnitude of the relative risk aversion. We show that the unsophisticated (with respect to their information processing abilities) agents are disproportionately important in the cases of both large and small risk aversion. In the case of the relative risk aversion measure being greater than unity volatility of aggregate consumption is reduced. This supports the view that observed consumption in many countries fluctuates less than predicted by models with fully rational agents only. [ABSTRACT FROM AUTHOR]

This paper presents a quantitative discussion on the stability of the second-order periodic difference equation, which characterizes the discrete periodic time-varying system. The periodic parameter discrete system, which corresponds to Mathieu's equation in the continuous system, is represented by a second-order linear difference equation with a small parameter E in the varying term. The parameter E plays an important role in the determination of the stability. By applying McLachlan's method, the expression for the boundary between the stability and the instability can be determined analytically with regard to the parameters contained in the equation. For the case where the periodic parameter of the difference equation is represented as a sum of two even functions, the boundary between stability and instability is determined. The stability can be analyzed in a similar way for the case where the periodic parameter is represented as a sum of N even functions in Fourier series. [ABSTRACT FROM AUTHOR]

In a previous paper, the authors presented the minimax block search strategy for locating the maximum of unimodal functions of one variable by a sequence of simultaneous function evaluations. In the present work the nearly optimal minimax golden block search method is developed which has the advantage that the number of function evaluations need not be specified in advance. For one experiment per block it reduces to the well known golden section method. It is shown that this method is an excellent approximation of the block search strategy and that for a certain marginal resolution the two methods become identical. [ABSTRACT FROM AUTHOR]

In this paper, we deduce new conditions for the existence of ground state solutions for the $p$-Laplacian equation $$\begin{equation*} \left \{ \begin{array}{@{}ll} -\mathrm {div}(\nabla u^{p-2}\nabla u)+V(x)u^{p-2}u=f(x, u), \quad x\in {\mathbb {R}}^{N},\\[5pt] u\in W^{1, p}({\mathbb {R}}^{N}), \end{array} \right . \end{equation*}$$ which weaken the Ambrosetti–Rabinowitz type condition and the monotonicity condition for the function $t\mapsto f(x, t)/t^{p-1}$. In particular, both $tf(x, t)$ and $tf(x, t)-pF(x, t)$ are allowed to be sign-changing in our assumptions. [ABSTRACT FROM AUTHOR]

The paper deals with solutions to Emden-Fowler-type equations of any arbitrary order. The asymptotic properties of solutions to these equations are studied, and a systematic survey of numerous uncoordinated results of analysis of continuable and noncontinuable solutions is given. [ABSTRACT FROM AUTHOR]

This paper deals with the Schrödinger equation $i{\partial }_{s} u(\mathbf{z} , t; s)- \mathcal{L} u(\mathbf{z} , t; s)= 0, $ where $ \mathcal{L} $ is the sub-Laplacian on the Heisenberg group. Assume that the initial data $f$ satisfies $\vert f(\mathbf{z} , t)\vert \lesssim {q}_{\alpha } (\mathbf{z} , t), $ where ${q}_{s} $ is the heat kernel associated to $ \mathcal{L} . $ If in addition $\vert u(\mathbf{z} , t; {s}_{0} )\vert \lesssim {q}_{\beta } (\mathbf{z} , t), $ for some ${s}_{0} \in \mathbb{R} \setminus \{ 0\} , $ then we prove that $u(\mathbf{z} , t; s)= 0$ for all $s\in \mathbb{R} $ whenever $\alpha \beta \lt { s}_{0}^{2} . $ This result holds true in the more general context of $H$-type groups. We also prove an analogous result for the Grushin operator on ${ \mathbb{R} }^{n+ 1} . $ [ABSTRACT FROM AUTHOR]

For a positive integer k, a total {k}-dominating function of a graph G without isolated vertices is a function f from the vertex set V(G) to the set {0,1,2, . . . ,k} such that for any vertex v ∊ V(G), the condition Σu∊N(v) f (u) ≥ k is fulfilled, where N(v) is the open neighborhood of v. The weight of a total {k}-dominating function f is the value ω(f) = Σv∊V f (v). The total {k}-domination number, denoted by γt{k} (G), is the minimum weight of a total {k}-dominating function on G. A set {f1, f2, . . . , fd} of total {k}-dominating functions on G with the property that Σdi =1 fi(v) ≤ k for each v ∊ V(G), is called a total {k}-dominating family (of functions) on G. The maximum number of functions in a total {k}-dominating family on G is the total {k}-domatic number of G, denoted by dt{k} (G). Note that dt{1} (G) is the classic total domatic number dt(G). In this paper, we present bounds for the total {k}-domination number and total {k}-domatic number. In addition, we determine the total {k}-domatic number of cylinders and we give a Nordhaus-Gaddum type result. [ABSTRACT FROM AUTHOR]

In this paper, we give some necessary conditions on the existence of meromorphic solutions on Fermat type difference equations. We also consider the properties of transcendental entire solutions on the systems of Fermat type differential-difference equations. [ABSTRACT FROM AUTHOR]

The theorems of continuous dependence of bounded Φ-variation solutions on parameters for Kurzweil equations are established through making use of the functions of bounded Φ-variation were introduced by Musiclak and Orlicz in paper [2]. The results are essential generalization of continuous dependence of bounded variation solutions on parameters for Kurzweil equations in paper [6]. [ABSTRACT FROM AUTHOR]

Let E be a cookie-cutter set with dim H E = s. It is known that the Hausdorff s-measure and the packing s-measure of the set E are positive and finite. In this paper, we prove that for a gauge function g the set E has positive and finite Hausdorff g-measure if and only if 0 < lim inf t→0 $$ \tfrac{{g(t)}} {{t^s }} $$ < ∞. Also, we prove that for a doubling gauge function g the set E has positive and finite packing g-measure if and only if 0 < lim sup t→0 $$ \tfrac{{g(t)}} {{t^s }} $$ < ∞. [ABSTRACT FROM AUTHOR]

In this paper we study some applications of the Levy logarithmic Sobolev inequality to the study of the regularity of the solution of the fractal heat equation, i.e. the heat equation where the Laplacian is replaced with the fractional Laplacian. It is also used to the study of the asymptotic behaviour of the Levy-Ornstein-Uhlenbeck process. [ABSTRACT FROM AUTHOR]

A free boundary problem that arises from the physical phenomenon of "peeling a thin tape from a domain" is treated. In this phenomenon, the movement of the tape is governed by a hyperbolic equation and is affected by the peeling front. We are interested in the behavior of the peeling front, especially, the phenomenon of self-excitation vibration. In the present paper, a mathematical model of this phenomenon is proposed. The cause of this vibration is discussed in terms of adhesion. [ABSTRACT FROM AUTHOR]

The basic rules of elementary algebra can often appear beyond the grasp of many students. Even though most subjects, including calculus, prove to be more difficult, it is the simple rules of algebra that continue to be the “thorn in the side” of many mathematics students. In this paper we present a result intended to help students achieve a greater understanding of a familiar algebraic error. [ABSTRACT FROM AUTHOR]

In this paper, we establish the generalized Hyers–Ulam–Rassias stability of C*-ternary ring homomorphisms associated to the Trif functional equation [ABSTRACT FROM AUTHOR]

In this paper, it is proved that with at most $$ O{\left( {N^{{\frac{{65}} {{66}}}} } \right)} $$ exceptions, all even positive integers up to N are expressible in the form $$ p^{2}_{2} + p^{3}_{3} + p^{4}_{4} + p^{5}_{5} $$ . This improves a recent result $$ O{\left( {N^{{\frac{{19193}} {{19200}} + \varepsilon }} } \right)} $$ due to C. Bauer. [ABSTRACT FROM AUTHOR]

The main result of the paper is a theorem, using which a new proof of Roth’s theorem is obtained, a new solvability criterion for the matrix equation AX-YB = C is proved, a formula for a particular solution of the latter is derived, and the least of the orders of square nonsingular matrices containing a given rectangular matrix as a submatrix is determined. Bibliography: 5 titles. [ABSTRACT FROM AUTHOR]

Let p be a prime, m ≥ 2, and ( m, p( p – 1)) = 1. In this paper, we will calculate explicitly the Gauss sum $$ G{\left( \chi \right)} = {\sum {_{{x \in \mathbb{F}^{ * }_{q} }} \chi {\left( x \right)}\zeta ^{{T{\left( x \right)}}}_{p} } } $$ in the case of [ (ℤ/ mℤ)* : 〈 p〉] = 4, and −1 ∉ 〈 p〉, where q = p f , $$ f = \frac{{\varphi {\left( m \right)}}} {4} $$ , χ is a multiplicative character of $${\Bbb F}$$ q with order m, and T is the trace map for $${\Bbb F}$$ q / $${\Bbb F}$$ p . Under the assumptions [ (ℤ/ mℤ)* : 〈 p〉] = 4 and −1 ∉ 〈 p〉, the decomposition field of p in the cyclotomic field ℚ(ζ m ) is an imaginary quartic (abelian) field. And G (χ) is an integer in K. We deal with the case where K is cyclic in this paper and leave the non–cyclic case to the next paper. [ABSTRACT FROM AUTHOR]

In this paper, a class of global optimization problems is considered. Corresponding to each local minimizer obtained, we introduced a new modified function and construct a corresponding optimization subproblem with one constraint. Then, by applying a local search method to the one-constraint optimization subproblem and using the local minimizer as the starting point, we obtain a better local optimal solution. This process is continued iteratively. A termination rule is obtained which can serve as stopping criterion for the iterating process. To demonstrate the efficiency of the proposed approach, numerical examples are solved. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we will establish some oscillation criteria for the second-order nonlinear neutral delay dynamic equation on a time scale ; here is a quotient of odd positive integers with and real-valued positive functions defined on . To the best of our knowledge nothing is known regarding the qualitative behavior of these equations on time scales, so this paper initiates the study. [Copyright &y& Elsevier]

This paper proposes a movement trajectory planning model, which is a maximum task achievement model in which signal-dependent noise is added to the movement command. In the proposed model, two optimization criteria are combined, maximum task achievement and minimum energy consumption. The proposed model has the feature that the end-point boundary conditions for position, velocity, and acceleration need not be prespecified. Consequently, the method can be applied not only to the simple point-to-point movement, but to any task. In the method in this paper, the hand trajectory is derived by a psychophysical experiment and a numerical experiment for the case in which the target is not stationary, but is a moving region. It is shown that the trajectory predicted from the minimum jerk model or the minimum torque change model differs considerably from the results of the psychophysical experiment. But the trajectory predicted from the maximum task achievement model shows good qualitative agreement with the hand trajectory obtained from the psychophysical experiment. © 2004 Wiley Periodicals, Inc. Syst Comp Jpn, 35(11): 48–58, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/scj.10377 [ABSTRACT FROM AUTHOR]

In this paper, a new method for the computation of the infimum for a large class of continuous-time H∞ optimal control problem by state feedback is presented. The main ingredients of the new method include three generalized eigenvalue problems whose coefficient matrices are from a condensed form of the given system. This condensed form is computed using only orthogonal transformations which can be implemented via a numerically stable way. The superiority of the new method over the existing one given in Chen (H∞Control and its Applications, Chapter 5. Springer: Berlin, 1997) is verified by some numerical examples. Copyright © 2004 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The central result of this paper is a new nonlinear equation which describes the evolution of the oriented distance function b... of a set ... with thin boundary under the influence of a velocity field. We relate it to equations and constructions used in the context of level set methods. We further introduce a new moving narrow-band method which not only can be readily implemented to solve our evolution equation, but could also be used for equations of motion by curvatures. In the process we review and sharpen the characterization of smooth sets and manifolds and sets of positive reach (e.g., local semiconvexity in an extended sense of the oriented distance function of the closure of the set). For W2,p-Sobolev domains a new characterization and a compactness theorem are given in terms of the Laplacian of the oriented distance function rather than its whole Hessian matrix. [ABSTRACT FROM AUTHOR]

The paper addresses the dynamic stability of random systems. The dynamic stability bounds are established on the basis of the definition of stability with respect to moment functions. The differential equations for these functions are derived by approximating an exponentially correlated normal random process by a random process with a finite number of states. These results are shown to agree with the well-known results for parametric white noise excitation [ABSTRACT FROM AUTHOR]

In this paper, we investigate a decidable case of the term semiunification problem. In our case, the arity of any functional symbol in terms equals one (with a possible exception for outer symbols of terms, for which no restrictions are imposed). We propose an algorithm constructing the most general solution of the semiunification problem. In addition, we prove an upper bound on the height of this solution; this upper bound is linear with respect to heights of terms in the initial problem. Our method reduces the problem for terms to a special system of equations in free semigroups and solves the latter system. Bibliography: 10 titles. [ABSTRACT FROM AUTHOR]

The paper sets forth a method of successive approximations along loading paths. The method is used to determine the thermoelastoplastic stress–strain state of laminated shells under axisymmetric complex loading. Deformation-type constitutive equations describing loading along arbitrary plane paths are employed. A numerical example is presented [ABSTRACT FROM AUTHOR]

Revision can be seen as any operation which turns a cognitive state CSt into a subsequent cognitive state CSt'. Two kinds of change can be considered: in the "belief change" case, the cognitive states represent beliefs on a world; they art revised in response to the getting of new information about a static world. In the "world change" case, the cognitive states represent known facts on a real world; they are revised in response to change in this dynamic world. We focus in the following on world change case and propose a way to keep up to date with a dynamic world. Reasoning about change requires predicting how the world will change along dine. In absence of a predictive model of evolution, the commonsense law of inertia has been currently used and justifies the minimal change approach to the frame problem. We propose here to use an explicit transition model, which will be used as a predictive evolution model. Dean and Kanazawa propose to use a probabilistic model of persistence and causation. We propose in this paper to use a symbolic model of transition by directly encoding expectations. In the first two sections, we describe the formalism that we propose to explicitly encode the transition model and its axiomatisation. We give then a formal definition of the revision operation using a transition model and discuss what can be a contraction operation in the context of world change. An illustrative example is presented and in the last section, our approach is compared to other related works. [ABSTRACT FROM AUTHOR]

The paper proposes a parallel survey of revision and updating operations available in the probability theory and in the possibility theory frameworks. In these two formalisms the current state of knowledge is generally represented by a [0,l]-avalued function whose domain is art exhaustive set of mutually exclusive possible states of the world. However, in possibility theory, IS unit-interval can be viewed as a purely ordinal scale. Two general kinds of operations can be defined on this assignment function: conditioning, and imaging (or "projection"). The difference between these two operations is analogous to the one made between belief revision à la Gärdenfors and updating à la Kaisuno rid Mendelzon in the logical framework. In the probabilistic framework these two operations are respectively Bayesian conditioning and Lewis' imaging. Counterparts to these operations are presented for the ponibilistic framework including the cue of conditioning upon uncertain observations, and justifications we given which parallel the ones existing for the probabilistic operations. More particularly, it is recalled that pouibilistic conditioning satisfies all the postulates proposed by Alchounón, Gärdenfors and Makinson for belief revision (stated in possibilistic terms), and it is proved that possibilistic imaging satisfies all the postulates proposed by Katsuno and Mendelzon. The situation where our current knowledge is stated in terms of weighted logical propositions is discussed in connection to possibility theory. Revision in other more complex numerical furmalisms, namely belief and plausibility functions, and upper and lower probabilities is also surveyed. Recent results on the revision of conditional knowledge bases are also reviewed. The frameworks of belief functions, upper and lower probabilities and conditional bases we more sophisticated than the previous ones because they enable to distinguish between factual evidence and generic knowledge in a cognitive state. This framework leads to two forms of belief revision respectively taking care of the revision of evidence and the revision of knowledge. [ABSTRACT FROM AUTHOR]

This article focuses on the computational aspects of dynamic programming. Dynamic programming is a method of solving multi-stage decision-process problems. Several computational difficulties are characteristic of all dynamic-programming solutions. In the theory of dynamic programming one find dealing with functions whose arguments are states of a system and whose values are optimal yields. In dynamic programming of low dimension the functions are generally defined by a table of values calculated at a grid of points. For problems of increased complexity it may prove desirable to approximate these functions. In this way only the appropriate coefficients need be computed at each iteration of the recurrence relation. The evaluation of a 10-dimensional function at only 10 grid points in each dimension would generate or 10 billion numbers. Yet this same function might be adequately defined by only 100 parameters of a suitably chosen approximating form. Furthermore, if one is dealing with analytic functions rather than tabular ones, tools of mathematical analysis such as calculus can be used to determine the maximum required by equation otherwise slower search techniques must be employed.

To resist algebraic attacks, Boolean functions should possess high algebraic immunity. In 2003, Courtois and Meier showed that the algebraic immunity of an n-variable Boolean function is upper bounded by [n/2]. And then several papers studied how to find symmetric Boolean functions with maximum algebraic immunity. In this correspondence, we prove that for each odd n, there is exactly one trivially balanced n-variable symmetric Boolean function achieving the maximum algebraic immunity. [ABSTRACT FROM AUTHOR]

In this paper, some Hardy and Rellich type inequalities on complete non-compact smooth metric measure spaces have been established. Moreover, based on the main results about the Hardy and Rellich type inequalities, several inequalities of the Hardy–Poincaré type or the Heisenberg–Pauli–Weyl type can also be given as byproducts. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and study a new multivalued mapping in R-trees, called k-strictly pseudononspreading. We also introduce a new two-step iterative process for two k-strictly pseudononspreading multivalued mappings in R-trees. Strong convergence theorems of the proposed iteration to a common fixed point of two k-strictly pseudononspreading multivalued mappings in R-trees are established. Our results improve and extend the corresponding results existing in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we present the error control techniques for the error correction methods (ECM) which is recently developed by P. Kim et al. [8, 9]. We formulate the local truncation error at each time and calculate the approximated solution using the solution and the formulated truncation error at previous time for achieving uniform error bound which enables a long time simulation. Numerical results show that the error controlled ECM provides a clue to have uniform error bound for well conditioned problems [1]. [ABSTRACT FROM AUTHOR]

In [9], the author extends the definition of lifting and supplemented modules to δ-lifting and δ-supplemented by replacing "small submodule" with "δ-small submodule" introduced by Zhou in [13]. The aim of this paper is to show new properties of δ-lifting and δ-supplemented modules. Especially, we show that any finite direct sum of δ-hollow modules is δ-supplemented. On the other hand, the notion of amply δ-supplemented modules is studied as a generalization of amply supplemented modules and several properties of these modules are given. We also prove that a module M is Artinian if and only if M is amply δ-supplemented and satisfies Descending Chain Condition (DCC) on δ-supplemented modules and on δ-small submodules. Finally, we obtain the following result: a ring R is right Artinian if and only if R is a δ-semiperfect ring which satisfies DCC on δ-small right ideals of R. [ABSTRACT FROM AUTHOR]