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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]

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]

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]

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]

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]

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 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]

Since the Leibniz–Newton formula for derivatives cannot be used in local fields, it is important to investigate the new concept of derivatives in Walsh–analysis, or harmonic analysis on local fields. On the basis of idea of derivatives introduced by Butzer, Schipp and Wade, Weisz has proved that the maximal operators of the one–dimensional dyadic derivative and integral are bounded from the dyadic Hardy space H p,q to L p,q , of weak type ( L 1 , L 1 ), and the corresponding maximal operators of the two–dimensional case are of weak type $$ {\left( {H^{\# }_{1} ,L_{1} } \right)} $$ . In this paper, we show that these maximal operators are bounded both on the dyadic Hardy spaces H p and the hybrid Hardy spaces $$ \begin{array}{*{20}c} {{H^{\# }_{p} }} & {{0 < p \leqslant 1}} \\ \end{array} $$ . [ABSTRACT FROM AUTHOR]

In this paper, we shall prove that for any orientable 3–manifold M, there is a link L = K ∪ K 1 ∪ K 2 ∪ K 3 with four components in M, such that the complement of L, say M L , contains separating essential closed surfaces of all positive genera. [ABSTRACT FROM AUTHOR]

A right R–module E over a ring R is said to be maximally injective in case for any maximal right ideal m of R, every R–homomorphism f : m → E can be extended to an R–homomorphism f' : R → E. In this paper, we first construct an example to show that maximal injectivity is a proper generalization of injectivity. Then we prove that any right R–module over a left perfect ring R is maximally injective if and only if it is injective. We also give a partial affirmative answer to Faith's conjecture by further investigating the property of maximally injective rings. Finally, we get an approximation to Faith's conjecture, which asserts that every injective right R–module over any left perfect right self–injective ring R is the injective hull of a projective submodule. [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]

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]