This paper is concerned with elastic local buckling of rectangular plates subjected to intermediate and end inplane loads. Since closed form solution for buckling analysis of plates with different end conditions and subjected to intermediate loads is complicated, numerical methods are more useful. Because of restrictions on the two finite strip methods, the longitudinal B3 spline expressions co...

This paper is concerned with elastic local buckling of rectangular plates subjected to intermediate and end inplane loads. Since closed form solution for buckling analysis of plates with different end conditions and subjected to intermediate loads is complicated, numerical methods are more useful. Because of restrictions on the two finite strip methods, the longitudinal B3 spline expressions co...

In process multi-input multi-output (MIMO) systems are observed that are dominated by interactions between input and outputs. Process decouplers are synthesized to reduce these interactions before controller design. In this work analytical expressions for closed-loop interactive transfer functions are found and interaction reducers (IR) are designed (as process decouplers) for closed-loop contr...

‎Complex-valued harmonic functions that are univalent and‎ ‎sense-preserving in the open unit disk $U$ can be written as form‎ ‎$f =h+bar{g}$‎, ‎where $h$ and $g$ are analytic in $U$‎. ‎In this paper‎, ‎we introduce the class $S_H^1(beta)$‎, ‎where $1<betaleq 2$‎, ‎and‎ ‎consisting of harmonic univalent function $f = h+bar{g}$‎, ‎where $h$ and $g$ are in the form‎ ‎$h(z) = z+sumlimits_{n=2}^inf...

The article is devoted to classification of close sets of functions in k-valued logic. We build the classification of finite closed sets. The sets contain only constants and unary functions since sets containing even a two-ary function are infinite. Formulas of the number of finite sets and minimal sets exist for all natural k. We find the numbers of closed sets containing the identity function...

Infinite series of the type ∞ ∑ n=1 ( 2 )n n 1 n! 2F1(−n, b; γ; y) are investigated. Closed-form sums are obtained for α a positive integer α = 1, 2, 3, . . . . The limiting case of b → ∞, after y is replaced with x2/b, leads to ∞ ∑ n=1 ( 2 )n n 1 n! 1F1(−n, γ, x2). This type of series appears in the first-order perturbation correction for the wavefunction of the generalized spiked harmonic osc...

We investigate the notion of K-triviality for closed sets and continuous functions in 2N. For every K-trivial degreee d, there exists a closed set of degree d and a continuous function of degree d. Every K-trivial closed set contains a K-trivial real. There exists a K-trivial Π1 class with no computable elements. A closed set is K-trivial if and only if it is the set of zeroes of some K-trivial...

Let X be a definably compact definable C manifold and 2 ≤ r < ∞. We prove that the set of definable Morse functions is open and dense in the set of definable C functions on X with respect to the definable C topology.

In this paper we investigate the generalisation of Wendland’s compactly supported radial basis functions to the case where the smoothness parameter is not assumed to be a positive integer or half-integer and the parameter l, which is chosen to ensure positive definiteness, need not take on the minimal value. We derive sufficient and necessary conditions for the generalised Wendland functions to...

Classes of functions of several variables on arbitrary non-empty domains that are closed under permutation of variables and addition of dummy variables are characterized in terms of generalized constraints, and hereby Hellerstein’s Galois theory of functions and generalized constraints is extended to infinite domains. Furthermore, classes of operations on arbitrary non-empty domains that are cl...