Search

In this paper, we consider the weakly damped wave equations with hereditary effects, and the nonlinearity f satisfies critical growth. The delay term g(t, ut) may be driven by a function with very weak assumptions, namely, just measurability. We analyze the well-posedness of solutions and verify the existence of the pullback D-attractor in CH01(Ω)×CL2(Ω) by constructing the energy functional and combining with the idea of the contractive function. [ABSTRACT FROM AUTHOR]

In this paper, we will analyze further to obtain a finer asymptotic behavior of positive solutions of semilinear elliptic equations in ℝ n by employing the Li’s method of energy function. [ABSTRACT FROM AUTHOR]

In this paper we establish two theta function identities with four parameters by the theory of theta functions. Using these identities we introduce common generalizations of Hirschhorn-Garvan-Borwein cubic theta functions, and also re-derive the quintuple product identity, one of Ramanujan’s identities, Winquist’s identity and many other interesting identities. [ABSTRACT FROM AUTHOR]

Temlyakov considered the optimal recovery on the classes of functions with bounded mixed derivative in the L p metrics and gave the upper estimates of the optimal recovery errors. In this paper, we determine the asymptotic orders of the optimal recovery in Sobolev spaces by standard information, i.e., function values, and give the nearly optimal algorithms which attain the asymptotic orders of the optimal recovery. [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 .rst derive the representation theorem of onto isometric mappings in the unit spheres ofl1(G) type spaces, and then conclude that such mappings can be extended to the whole space as real linear isometries by using a previous result of the author. [ABSTRACT FROM AUTHOR]

It is well known that the convergence of multivariate subdivision schemes with finite masks can be characterized via joint spectral radius. For nonnegative masks, we will present in this paper some computable simply sufficient conditions for the convergence, which will cover a substantially large class of schemes. [ABSTRACT FROM AUTHOR]

In this paper, we solve the problem proposed by Lan Wen for the case of dim M = 3. Roughly speaking, we prove that for fixed i, f has C1 persistently no small angles of index i if and only if f has a dominated splitting of index i on the C1 i-preperiodic set P( f). [ABSTRACT FROM AUTHOR]

This paper considers the problems of determining center or focus and isochronous centers for the planar quasi-analytic systems. Two recursive formulas to determine the focal values and period constants are given. The convergence of first integral near the center is proved. Using the general results to quasi-quadratic systems, the problem of the isochronous center of the origin is completely solved. [ABSTRACT FROM AUTHOR]

In this paper, we prove several results concerning meromorphic functions f and g of hyperorder less than one such that f ( j) and g ( j) have the same zeros and poles for j = 0, 1, 2. We provide some examples to show that our results are sharp. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the relation between the rate of convergence for the derivatives of the combinations of Baskakov operators and the smoothness for the derivatives of the functions approximated. We give some direct and inverse results on pointwise simultaneous approximation by the combinations of Baskakov operators. We also give a new equivalent result on pointwise approximation by these operators. [ABSTRACT FROM AUTHOR]

In the present paper, a problem of Ioana Mihaila is negatively answered on the invertibility of composition operators on Riemann surfaces, and it is proved that the composition operator C p is Fredholm if and only if it is invertible if and only if p is invertible for some special cases. In addition, the Toeplitz operators on $$ \Lambda _{2,a}^1 (M) $$ for Riemann surface M are defined and some properties of these operators are discussed. [ABSTRACT FROM AUTHOR]

In this paper, a cryptogroup is constructed by a band and a family of groups and homomorphisms satisfying some conditions. [ABSTRACT FROM AUTHOR]

The paper produces new versions of the minimax theorem based on original conditions. Moreover, we investigate not only the sufficiency, but also the necessity of such conditions. The proofs are very simple and preclude any topological technique. [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]

In this paper, we prove some properties of the Seneta sequences and functions, and in particular we prove a representation theorem in the Karamata sense for the sequences from the Seneta class SOc. [ABSTRACT FROM AUTHOR]

In this paper, we study a free boundary problem arising from the modeling of tumor growth. The problem comprises two unknown functions: R = R( t), the radius of the tumor, and u = u( r, t), the concentration of nutrient in the tumor. The function u satisfies a nonlinear reaction diffusion equation in the region 0 < r < R( t), t > 0, and the function R satisfies a nonlinear integrodi fferential equation containing u. Under some general conditions, we establish global existence of transient solutions, unique existence of a stationary solution, and convergence of transient solutions toward the stationary solution as t → ∞. [ABSTRACT FROM AUTHOR]

In this paper, we study the compactness of the product of a composition operator with another one’s adjoint on the Bergman space. Some necessary and sufficient conditions for such operators to be compact are given. [ABSTRACT FROM AUTHOR]

In this paper, we study one conjecture proposed by W. Bergweiler and show that any transcendental meromorphic functionsf(z) have the form exp(az+ß) iff(z)f?(z)-a(f' (z))2?0, where. Moreover, an analogous normality criterion is obtained. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we characterize the pointwise multiplier space M(D[sub tau], D[sub mu]) of Dirichlet type spaces in the unit ball of C[sup n] for the values of tau, mu in three cases: (i) tau < 0, mu < 0, (ii) tau < mu, (iii) tau >/- mu, tau > n, and construct two functions to show theft M(D[sub tau]) subset D[sub tau] properly if tau less than or equal to n and M(D[sub tau]) subset M(D[sub mu]) properly if tau > mu and tau > n 1. Keywords Dirichlet space, Pointwise multiplier Holomorphic function [ABSTRACT FROM AUTHOR]

Let u be a solution to a second order elliptic equation with singular potentials belonging to Kato–Fefferman–Phong’s class in Lipschitz domains. An elementary proof of the doubling property for u 2 over balls is presented, if the balls are contained in the domain or centered at some points near an open subset of the boundary on which the solution u vanishes continuously. Moreover, we prove the inner unique continuation theorems and the boundary unique continuation theorems for the elliptic equations, and we derive the ℬ p weight properties for the solution u near the boundary. [ABSTRACT FROM AUTHOR]

In this article, we investigate the arithmetic behavior of the function D3(n) which counts the number of 3-regular tripartitions of n. For example, we show that for α ≥ 1 and n ≥ 0, D3(32αn+11⋅32α−1−14)≡0(mod32α+3) and D3(32αn+7⋅32α−1−14)≡0(mod32α+2). [ABSTRACT FROM AUTHOR]

Let C be a nonempty closed convex subset of a real Banach space E. Let S: C → C be a quasi-nonexpansive mapping, let T: C → C be an asymptotically demicontractive and uniformly Lipschitzian mapping, and let F:= { x ε C: Sx = x and Tx = x} ≠ 0. Let { x n } n≥0 be the sequence generated from an arbitrary x 0 ε C by We prove the necessary and sufficient conditions for the strong convergence of the iterative sequence { x n } to an element of F. These extend and improve the recent results of Moore and Nnoli. [ABSTRACT FROM AUTHOR]

The author provides a finer local as well as semilocal convergence analysis of a certain class of Broyden-like methods for solving equations containing a nondifferentiable term on the m-dimensional Euclidean space ( m ≥ 1 a natural number). [ABSTRACT FROM AUTHOR]

Let R be an exchange ring with primitive factors artinian. We prove that there exists a u∈ U( R) such that 1 R ± u ∈ U( R), if and only if for any a∈ R, there exists a u ∈ U( R) such that a ± u ∈ U( R). Furthermore, we prove that, for any A ∈ M n ( R)( n ≥ 2), there exists a U ∈ GL n ( R) such that A ± U ∈ GL n ( R). [ABSTRACT FROM AUTHOR]

A new upper and lower solution theory is presented for the second order problem (G'(y))' + f(t, y) = 0 on finite and infinite intervals. The theory on finite intervals is based on a Leray-Schauder alternative, whereas the theory on infinite intervals is based on results on the finite interval and a diagonalization process. [ABSTRACT FROM AUTHOR]

We introduce the concept of ideal–comparability condition for regular rings. Let I be an ideal of a regular ring R. If R satisfies the I–comparability condition, then R is one–sided unit–regular if and only if so is R / I. Also, we show that a regular ring R satisfies the general comparability if and only if the following hold: (1) R / I satisfies the general comparability; (2) R satisfies the general I–comparability condition; (3) The natural map B( R) → B( R / I) is surjective. [ABSTRACT FROM AUTHOR]

So far the study of exponential bounds of an empirical process has been restricted to a bounded index class of functions. The case of an unbounded index class of functions is now studied on the basis of a new symmetrization idea and a new method of truncating the original probability space; the exponential bounds of the tail probabilities for the supremum of the empirical process over an unbounded class of functions are obtained. The exponential bounds can be used to establish laws of the logarithm for the empirical processes over unbounded classes of functions. [ABSTRACT FROM AUTHOR]

Let $${\fancyscript D}$$ be an increasing sequence of positive integers, and consider the divisor functions: where [ d, δ] = l.c.m.( d, δ). A probabilistic argument is introduced to evaluate the series $$ {\sum\nolimits_{n = 1}^\infty {\alpha _{n} d{\left( {n,{\fancyscript D}} \right)}} } $$ and $$ {\sum\nolimits_{n = 1}^\infty {\alpha _{n} d_{2} {\left( {n,{\fancyscript D}} \right)}} } $$ . [ABSTRACT FROM AUTHOR]

In Part I the concept of the general regular variation of n–th order is proposed and its construction is discussed. The uniqueness of the standard expression and the higher order regularity of the auxiliary functions are proved. [ABSTRACT FROM AUTHOR]

Abstract Suppose that f(x)= (f[sub 1](x),..., f[sub r](x))[sup T], x is an element of R[sup d] is a vector-valued function satisfying the refinement equation f(x) = SIGMA[sub lambda]c[sub k]f(2x-k) with finite set A of Z[sup d] and some r x r matricex c[sub k]. The requirements for Integral of to have accuracy p are given in terms of the symbol function m(xi). Keywords Accuracy, Symbol, Refinable functions [ABSTRACT FROM AUTHOR]