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Sufficient conditions for the existence of solutions of nonlinear boundary value problems for higher-order functional difference equations with p-Laplacian are established by making of continuation theorems. We allow f to be at most linear, superlinear, or sublinear in obtained results. [ABSTRACT FROM AUTHOR]

In this article, we investigate the chaotic behaviours in the fractional-order Lorenz system. By utilizing the fractional calculus techniques, we found that chaos exists in the fractional-order Lorenz system of order less than 3. The lowest order we found to have chaos in this system is 2.97. [ABSTRACT FROM AUTHOR]

In this paper, we establish some inequalities of Fejér type for g-convex dominated functions. [ABSTRACT FROM AUTHOR]

The article reports on the nature of projectile motion in a uniform, downward gravitational field and resisted by a drag force due to the air through which it moves. It states that the nature of the projectile motion lies near the heart of the scientific revolution. The drag force is assumed to act in a direction opposite to that of the projectile's velocity and to depend only on its magnitude, therefore, Coriolis forces and Earth's curvature are ignored. The author notes that the projectile motion under quadratic drag was at the center of an episode in the calculus priority dispute.

Abstract: The paper presents a new method introducing an anchored discrete convolution for calculating the length of a digital curve. The method is based on discrete convolution by using convolution masks and point anchoring in the pixel. The use of ordinary convolution distorts the curve shape and gives large errors in length calculation. The advantage of anchoring is that it limits the point shifting into the pixel during the calculation of the curve length. The method is applied to an analytical arc and various calculations are performed. In addition different methods from the literature were compared and a real sample was tested. [Copyright &y& Elsevier]

Abstract: In this paper, a further improved extended Fan sub-equation method is used to construct exact solutions of the (2+1)-dimensional breaking soliton equations. As a result, many new and more general non-travelling wave and coefficient function solutions are obtained including soliton-like solutions, triangular-like solutions, single and combined non-degenerate Jacobi elliptic wave function-like solutions, Weierstrass elliptic doubly-like periodic solutions, each of which contains an arbitrary function of two variables. The results show the proposed method give new and more general exact solutions. More importantly, the method with the aid of symbolic computation provides a very effective and powerful mathematical tool for solving a great many non-linear partial differential equations in mathematical physics. [Copyright &y& Elsevier]

Abstract: This paper deals with a nonlinear parabolic equation with a more complicated source term, which is a product of localized source u q (0, t), local source u p (x, t), and weight function a(x). We investigate how the three factors influence the asymptotic behavior of solutions. It is shown that the blow-up set consists of single point {x =0} if p >1. When 0⩽ p ⩽1 with p + q >1, the blow-up take place everywhere in B. Moreover, the blow-up rate estimate is established with more precise coefficients determined. [Copyright &y& Elsevier]

The purpose of this paper is to give a q-analogue of the p-adic twisted l-function, which is an answer to a part of the problem in a previous publication( see J. Math. Anal. Appl. (in press) ). [ABSTRACT FROM AUTHOR]

Abstract: In this paper, characterizations of the existence of the directional derivative and second-order parabolic directional derivative of a locally Lipschitzian function are established. These characterizations involve the adjacent cone and second-order adjacent set of the graph of the function. [Copyright &y& Elsevier]

Abstract: Let and be analytic in the unit disk. The Hadamard product of f and g is defined by . This paper gives some characterizations of functions in spaces in terms of the Hadamard products. [Copyright &y& Elsevier]

This article claims to have established several existence theorems of positive solutions for nonlinear m-point boundary value problem for several dynamic equations on time scales. These equations include (φ(u&Delta))&nabla + α(t) f (t, u(t)) = 0, t ... (0,T), φ(uΔ(0)) = Σ i=1m-2 αiφ(uΔ(...i, u(T) = Σi=1m-2biu(...i, where φ : R &rar; R is an increasing homoemorphism and homomorphism and φ(0) = 0. It provides example calcalations using these equations.

Abstract: In an earlier paper [D. Richards, Q. Zheng, Determinant formulas for multidimensional hypergeometric period matrices, Adv. in Appl. Math. 29 (2002) 137–151] on the determinants of certain period matrices, we formulated a conjecture about the determinant of a certain hypergeometric matrix. In this article, we establish this conjecture by constructing a system of linear equations in which that determinant is one of the variables. As a consequence, we obtain the value of an integral which generalizes the well-known multidimensional beta integral of A. Selberg [A. Selberg, Bemerkninger om et multipelt integral, Norsk. Mat. Tidsskr. 26 (1944) 71–78] and some hypergeometric determinant formulas of A. Varchenko [A. Varchenko, The Euler beta-function, the Vandermonde determinant, the Legendre equation, and critical values of linear functions on a configuration of hyperplanes. I, Izv. Akad. Nauk SSSR Ser. Mat. 53 (1989) 1206–1235, English translation, Math. USSR-Izv. 35 (1990) 543–571; A. Varchenko, The Euler beta-function, the Vandermonde determinant, the Legendre equation, and critical values of linear functions on a configuration of hyperplanes. II, Izv. Akad. Nauk SSSR Ser. Mat. 54 (1990) 146–158, English translation, Math. USSR-Izv. 36 (1991) 155–167]. [Copyright &y& Elsevier]

The transformer diagnostic methods are systematically being improved and extended due to growing requirements for reliability of power systems in terms of uninterrupted power supply and avoidance of blackouts. Those methods are also driven by longer lifetime of transformers and demand for reduction of transmission and distribution costs. Hence, the detection of winding faults in transformers, both in exploitation or during transportation is an important aspect of power transformer failure prevention. The frequency response analysis method (FRA), more and more frequently used in electric power engineering, has been applied for investigations and signature analysis based on the admittance and transfer function. The paper presents a novel approach to the identification of typical transformer winding problems such as axial or radial movements or turn-to-turn faults. The proposed transfer function discrimination (TFD) criteria are based on the derived transfer function ratios, manifesting higher sensitivity. [ABSTRACT FROM AUTHOR]

Abstract  The χ calculus is a model of concurrent and mobile systems. It emphasizes that communications are information exchanges. In the paper, two constructions are incorporated into the framework of the chi calculus, which are asymmetric communication and mismatch condition widely used in applications. Since the barbed bisimilarity has proved its generality and gained its popularity as an effective approach to generating a reasonable observational equivalence, we study both the operational and algebraic properties of the barbed bisimilarity in this enriched calculus. The investigation supports an improved understanding of the bisimulation behaviors of the model. It also gives a general picture of how the two constructions affect the observational theory. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we study the normality of a family of meromorphic functions and obtain some normality results for meromorphic functions, which improve and generalize the related results of Gu, Bergweiler and Lin. [Copyright &y& Elsevier]

Abstract: The persistence of some stage structured predator–prey model with finite and infinite delay was studied in this paper. By analyzing right-hand functions and using the comparison theorem, some sufficient conditions for the persistence of populations with finite and infinite delay were derived. [Copyright &y& Elsevier]

Abstract: This paper discusses a kind of bent functions that have some symmetric properties about some variables. Section 2 mainly discusses the bent functions symmetric about some two variables and gives the necessary and sufficient condition for these functions. Section 3 gives algebraic expressions of some bent functions. [Copyright &y& Elsevier]

Abstract: This paper investigates the decentralized control of LTI continuous-time plants using generalized sampled-data hold functions (GSHF). GSHFs can be used to modify the structure of the digraph of the resultant discrete plant, by removing certain interconnections in the discrete-time equivalent model to form a hierarchical system model of the plant. This is a new application of discretization and has, as its motivation, the design of decentralized controllers using centralized methods. [Copyright &y& Elsevier]

Abstract: In this paper we study the problem where are positive radial functions, and . We give existence and nonexistence results, depending on the parameters p and λ. It turns out that is a critical value for the existence of solutions. [Copyright &y& Elsevier]

In this paper, we study the problem of uniqueness of meromorphic functions sharing small functions with their derivatives, partly answer the conjecture of R. Brüch, and obtain some results which improve the theorems of K. Yu et al. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, harmonic wavelets, which are analytically defined and band limited, are studied, together with their differentiable properties. Harmonic wavelets were recently applied to the solution of evolution problems and, more generally, to describe evolution operators. In order to consider the evolution of a solitary profile (and to focus on the localization property of wavelets), it seems to be more expedient to make use of functions with limited compact support (either in space or in frequency). The connection coefficients of harmonic wavelets are explicitly computed (in the following) at any order, and characterized by some recursive formulas. In particular, they are functionally and finitely defined by a simple formula for any order of the basis derivatives. [Copyright &y& Elsevier]

By employing a novel idea and simple techniques, we substantially generalize the Turán type inequality for rational functions with real zeros and prescribed poles established by Min [5] to include L pspaces for 1≤ p≤∞while loosing the restriction ρ > 2 at the same time. [ABSTRACT FROM AUTHOR]

In what follows two curious generalizations of four-element matrixes for first-degree relevant logic will be presented. The first part of the paper deals with the semantic consideration and algebraic analysis of inconsistent logic PR (P for paraconsistent, and R for relevant), to be result of combining matrixes for the system FDE with the matrix for classical implication. In the second part the variant of propositional logic with certain "non-monotonic" properties is considered. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the author investigates two-species nonautonomous delay diffusive preypredator models with Michaelis-Menten functional response. Sufficient conditions are derived for permanence of the species. Further, the author also establishs the sufficient conditions that guarantee the arbitrary positive periodic solution of the systems is global attractive. [Copyright &y& Elsevier]

Abstract: In this paper, nutrient-phytoplankton-zooplankton interaction with general uptake functions in which nutrient recycling is either instantaneous or delayed is considered. To account for higher predation, zooplankton''s death rate is modeled by a quadratic term instead of the usual linear function. Persistence conditions for each of the delayed and nondelayed models are derived. Numerical simulations with data from the existing literature are explored to compare the two models. It is demonstrated numerically that increasing zooplankton death rate can eliminate periodic solutions of the system in both the instantaneous and the delayed nutrient recycling models. However, the delayed nutrient recycling can actually stabilize the nutrient-plankton interaction. [Copyright &y& Elsevier]

In this paper, in the setting of sequential spaces, we consider the value functions vS and vI defined by vS(x)=supy∈K(x)f(x,y) and vI(x)=infy∈K(x)f(x,y), and we introduce sufficient conditions on the value functions and on the data, weaker than upper semicontinuity, which guarantee the existence of maximum for such functions. Various examples illustrate the results and the connections with previous results. [Copyright &y& Elsevier]

In this paper, the lower bounds of Bloch constants Bn, for functions with multiplicity at least n, are improved by showing [Copyright &y& Elsevier]

Let Σ(p, k)(p, k ∈ N) be the class of functions f(z) = z-p+ak-p²k-p+... analytic in 0 < |z| < 1. A subclass M(p, k, α, λ) of Σ(p, k) is introduced. The object of the present paper is to investigate convolution properties for the class M(p, k, α, λ). Also a property of the partial sums of certain functions in this class is given. [ABSTRACT FROM AUTHOR]

The aim of this paper is to investigate homomorphisms which reserve square-free languages or primitive languages. A characterization of square-free-preserving homomorphisms is presented. We show that every square-free-preserving homomorphism is primitive-preserving. Strongly cube-free-preserving homomorphisms are also studied. [ABSTRACT FROM AUTHOR]

In [2, Theorem 3], Bell and Kappe proved that if d is a derivation of a prime ring R which acts as a homomorphism or an anti-homomorphism on a nonzero right ideal I of R, then d = 0 on R. In the present paper our objective is to extend this result to Lie ideals. The following result is proved: Let R be a 2-torsion free prime ring and U a nonzero Lie ideal of R such that u2 ε U, for all u ε U. If d is a derivation of R which acts as a homomorphism or an anti-homomorphism on U, then either d=0 or U &subE; Z(R). [ABSTRACT FROM AUTHOR]

This paper gives some characterizations of strongly θ-precontinuous functions. [ABSTRACT FROM AUTHOR]

In this paper, a mortar finite element method for parabolic problem is presented. Multigrid method is used for solving the resulting discrete system. It is shown that the multigrid method is optional, i.e., the convergence rate is independent of the mesh size L and the time step parameter Τ. [ABSTRACT FROM AUTHOR]

This paper presents the problem of aggregation over individual agents as a basic identification problem inherent to interpreting relationships between averaged economic variables. The concept of a complete aggregation structure is introduced, which embodies the correct condition for identification. Several examples of complete aggregation structures are provided by previous work on the aggregation problem in economics. Examples are also provided by work on complete distribution families in statistics, which in turn provide the correct conceptual framework for developing a theory of parameter estimation and tests of specific aggregation assumptions. The potential lack of correspondence between microeconomic behavior and estimated relations between averaged data is illustrated by distribution families obeying linear probability movement, which induce an extreme failure of the completeness property. Certain topics regarding empirical applications of aggregation results are reviewed. [ABSTRACT FROM AUTHOR]

Let L be a degree-2L-function associated to a Maass cusp form. We explore an algorithm that evaluates t values of L on the critical line in time O(t1+𝜖). We use this algorithm to rigorously compute an abundance of consecutive zeros and investigate their distribution. [ABSTRACT FROM AUTHOR]

A function $f:X\rightarrow X$ determines a topology $P(f)$ on $X$ by taking the closed sets to be those sets $A\subseteq X$ with $f(A)\subseteq A$. The topological space $(X,P(f))$ is called a functionally Alexandroff space. We completely characterise the homogeneous functionally Alexandroff spaces. [ABSTRACT FROM AUTHOR]

We consider the localization problem for control robust invariant compact sets of a continuous dynamical system with perturbation and control. The solution method generalizes the functional localization method, which was earlier used in localization problems for continuous autonomous and nonautonomous systems as well as in discrete systems. The properties of the corresponding localizing sets are described. [ABSTRACT FROM AUTHOR]

We study the strong type and weak type estimates of intrinsic square functions including the Lusin area integral, Littlewood-Paley g-function and -function on the generalized Morrey spaces for , where Φ is a growth function on satisfying the doubling condition. The boundedness of commutators generated by functions and intrinsic square functions is also obtained. [ABSTRACT FROM AUTHOR]

In [`Robin function and conformal welding - A new proof of the existence', submitted] a new proof of the existence of the Robin function is given using conformal welding. This proof is essentially based on the simply connected case and a conformal mapping which maps the domain onto a complement of a disk and a system of radial spires. The aim of this note is to show that this proof also has a wider meaning, namely that this mapping is the unique solution of extremal problems, which minimizes the length or the diameter of a subset of the boundary curve. As a consequence we obtain sharp inequalities for the Robin capacity and the logarithmic capacity. [ABSTRACT FROM AUTHOR]

In this article, we consider a general modification of the Kohn–Nirenberg domain in ℂn, namely,. In particular, we study the existence of support surface and the regularity of peak function at the point 0∈∂Ωk. [ABSTRACT FROM AUTHOR]

It has been shown that every n-person, perfect information game with no chance moves and bounded, lower semicontinuous payoffs has a subgame perfect-equilibrium in pure strategies. Here the same is proved when the payoffs are bounded and upper semicontinuous. [ABSTRACT FROM AUTHOR]

We investigate the Extended Proximal Auxiliary Problem Principle (EPAPP) [A. Kaplan and R. Tichatschke, Extended Auxiliary Problem Principle using Bregman distances, Optimization 53 (2004), pp. 603-623, A. Kaplan and R. Tichatschke, Bregman functions and auxiliary problem principle, Optim. Methods Softw. 23, 1 (2008), pp. 95-107] for solving variational inequalities whose operator - here called the main operator - is the sum of a maximal monotone and a continuous operator. As usual for proximal methods using Bregman distances, Kalpan and Tichatschke required that the main operator is paramonotone. There are two main purposes of the present article. First, we establish the convergence of the EPAPP method without the use of paramonotonicity by replacing the latter assumption by other (partly rather natural) ones. An example showing that the main operator does not even have to be monotone is also given. Second, we discuss the EPAPP method with a stopping criterion of fixed-relative-error type by Solodov and Svaiter [An inexact hybrid generalized proximal point algorithm and some new results on the theory of Bregman functions, Math. Oper. Res. 25 (2000), pp. 214-230]. Kaplan and Tichatschke used a stopping criterion of summable-error type was used to admit an inexact solution of the corresponding auxiliary problems. To our knowledge, such a stopping criterion has not been applied to an extended APP yet; also in this situation, the paramonotonicity hypothesis is avoided. Independent of the stopping criterion under consideration, we admit an outer approximation of the set-valued component of the main operator. Owing to the use of Bregman-like functions to construct the symmetric components of the auxiliary operators, an interior-point effect is provided, meaning that - with a certain precaution - the auxiliary problems can be treated as unconstrained ones. [ABSTRACT FROM AUTHOR]

We obtain an exact estimate for a nonincreasing uniform rearrangement of a function of two variables from the Muckenhoupt class A. [ABSTRACT FROM AUTHOR]

Let f: ℝ+ → ℝ. The subject is the trace inequality Tr f( A) + Tr f( P2 AP2) ≦ Tr f( P12 AP12) + Tr f( P23 AP23), where A is a positive operator, P1; P2; P3 are orthogonal projections such that P1 + P2 + P3 = I, P12 = P1 + P2 and P23 = P2 + P3. There are several examples of functions f satisfying the inequality (called (SSA)) and the case of equality is described. [ABSTRACT FROM AUTHOR]

This study examines how students in the early stages of learning about the concept of functions, describe a curve and, in particular, evaluate the appropriateness of their argument about the representation of a function. Students are offered a message game which is related to a curve drawn on a coordinate system, representing an 'imaginary function'. In this message game, one half of the class must describe a curve to the other half who will then try to reproduce it as similarly as possible. Data analysis indicates that the idea of the curve that consists of series of points is very effective, while the idea of variation does not exist or is too limited among students at the beginning of learning functions. Thus, the concept of variation is not used as a criterion to describe a curve. More surprisingly, the students are working on the curve as if it was just a picture on a grid regardless of the representation of the function. [ABSTRACT FROM AUTHOR]