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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]

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]

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]

The article investigates some delay integral inequalities on time scales which provide explicit bounds on unknown functions. Researchers have used Gronwall's inequality and comparison theorem. Results of the study unify and extend some delay integral inequalities and their corresponding discrete analogues. It was found that the numerical solution agrees with the analytical solution for some discrete inequalities. The inequalities given can be used as handy tools in the qualitative theory of certain classes of delay dynamic equations on time scales.

The article presents a study on the superlinear equations with nonlinearities f with functions that are limited and do not satisfy the classical Ambrosetti-Rabinowitz type condition. The existence of superlinear equations with blowup arguments and nonexistence results are also mentioned. The article also mentions the variational methods, morse's index and blowup methods. Asymptotically homogenous nonlinearities, topological techniques and blowup methods necessary to the subcritical growth of nonlinearities are also presented.

In the present work converse theorems of trigonometric approximation of functions and its fractional derivatives in certain Orlicz spaces are improved with respect to the fractional moduli of smoothness. An improved Marchaud inequality is also given. [ABSTRACT FROM AUTHOR]

Radius constants for several classes of analytic functions on the unit disk are obtained. These include the radius of starlikeness of a positive order, radius of parabolic starlikeness, radius of Bernoulli lemniscate starlikeness, and radius of uniform convexity. In the main, the radius constants obtained are sharp. Conjectures on the non-sharp radius constants are given. [ABSTRACT FROM AUTHOR]

The article analyzes the boundary asymptotic behavior of solutions for weighted p(x)-Laplacian equations that take infinite value on a bounded domain. It was found that the boundary asymptotic of solutions of the Laplacian function is continuous and positive. The p(x)-Laplacian possesses more complicated inhomogeneous nonlinearities, thus, some special techniques are needed. Its main difficulty arises from the lack of compactness. The uniqueness and asymptotic behavior of solutions for problem is a nonnegative function which is allowed to vanish on the boundary.

The article examines the regularity criterion for weak solutions to the Navier-Stokes equations in terms of the gradient of the pressure. An interpolation inequality was used to refine when the solution is smooth. Deriving a priori estimates for smooth solutions is measured through multiplying the regularity condition of weak solutions to the Navier-Stokes equations by the interpolation inequality. Since the Leray weak solution satisfies the energy inequality, Serrin's uniqueness criterion can be applied.

The article focuses on the characteristic quantiities associated with homogenous P-type and m-type functions. For any given P-matrix, M ∈ RnXn, Mathias and Pang introduced a quantity a( M ), where there is a bound for the solution of the linear complementarity problem ( M, q ) with a P-matrix M. Fundamental quantity a { A, B } associated with a pair { A, B } having v-column P-property, where A, B ∈ RmXn is established with global error bounds for the vertical and horizontal linear complementarity problems. Concepts of P-type and M-type functions, as well as quantities for homogenous P-type and M-type functions are presented.

The article focuses on reverse Hardy-Hilbert-type inequality, proven to estimate the weight coefficient. The extension of Yang's work on inequalities involving n for 1.5 < ʎ < 3, by estimating the weight coefficient with the expression of the β function. Weight coefficient ɷʎ ( n ) is defined, with N0 as the set of nonnegative integers, N as the set of positive integers, and R as the set of real numbers. Since for 1.5 ⩽ ʎ < 3, 2( n + 1 )2-ʎ / ( ʎ - 1 ) ( 2n + 3 - ʎ ) > 0, ( 2ʎ - 3) ( ʎ - 1 )/12( n + 1 )2 ⩾ 0, ʎ ( ʎ - 1 )2/24( n + 1 )3 > 0, then it results to ( 2.2 ), in which the lemma is proved.

The article presents a discussion that focuses on the Kantorovich and the Durrmeyer-type modifications of the generalized favard operators. The discussion is also said to be aimed at proving an inverse approximation theorem for functions f. An analogous inequality for the rth weighted modulus of smoothness of the function f is also presented. The theorems, equations, and calculations associated with such mathematical concept are also included in the discussion. Mathematical proofs linked to such equations are also provided.

In this paper we study fair division problems with the special feature that there exists only one transferable good that everyone likes. This good will be used to compensate some individuals for their differences in other non-transferable resources (like talents or handicaps). In this context we test the traditional no-envy solution and we verify that: 1) its ethical content can be a matter of discussion, and 2) frequently it does not select a non-empty set of allocations. We propose an extension of this criterion that partially solves the existence problem while also retaining the main ethical properties of the preceding solution. [ABSTRACT FROM AUTHOR]