Abstract/Overview Approximations of fixed points have been done in different space and classes. However, characterizations in norm attainable classes remain interesting. This paper discusses approximation of nonexpansive operators in Hilbert spaces in terms of fixed points. In particular, we prove that for an invariant subspace H0 of a complex Hilbert space H; there exists a unique nonexpansive retraction R of H0 onto _(Q) and x 2 H0 such that the sequence f_ng generated by _n =_nf(_n)+(1...

Abstract/Overview In this paper we describe operator systems and elementary operators via tensor products. We also discuss norms of elementary operators.

Abstract/Overview Determining Equations are linear partial differential equations. The equation to be solved is subjected to extension generator. The coefficient of unconstrained partial derivatives is equated to zero and since the equations are homogeneous their solutions form vector space [1]. The determining equations obtained leads to n-parameter symmetries.

Abstract/Overview The equation F(x, y, y, y, y, y (4)) 0 is a one-space dimension version of wave equation. Its solutions can be classified either as analytic or numerical using finite difference approach, where the convergence of the numerical schemes depends entirely on the initial and boundary values given. In this paper, we have used Lie symmetry analysis approach to solve the wave equation given since the solution does not depend on either boundary or initial va...

Abstract/Overview In this paper, we examine conservative autonomous dynamic vibration equation, x¨ = − tanh2 x, which is time vibration of the displacement of a structure due to the internal forces, with no damping or external forcing. Numerical results using Wilson-theta method are tabulated and then represented graphically. Further the stability of the algorithms employed are also discussed.

Abstract/Overview A multiple chain pendula system constrained to move in space has been studied within the framework of a generalized coordinate system by using the Lagrangian formalism. Equations of motions for many body pendula systems have been derived .These equations concur very well with known data. We confirm that equations of motion for any values of n and l can be generated from our general equation which presents interesting characteristics. Solutions to these multi-pendula equa...

Abstract/Overview Lie symmetry analysis of Ordinary Differential Equation can be used to obtain exact solution of the equation of the form F (x, y, y’ y’’ y’’’) = 0. In this paper we use Lie Symmetry analysis approach to obtain the nonzero Lie brackets of a nonlinear Ordinary Differential Equation for heat conduction. The Lie Brackets obtained forms Lie solvable algebra that can be used to reduce the equation to lower order.

Abstract/Overview In this study Sum construction method of automorphic symmetric balanced incomplete block designs has been presented in details. Efficiency of a test design used in the Sum construction of automorphic symmetric balanced incomplete block designs has been determined alongside its existence. The process involved the application of sum construction to give new designs of parameters D (v, b, λ1+λ2) and an application of Bruck Ryser Chwola theorem extensively. A test design u...

Abstract/Overview Several construction methods have been introduced to build the elements of BIBDs’ for specific parameters, with different techniques suggested for testing their existence, still no general technique to determine the efficiencies of these designs has been realized. In this study the efficiencies and relative efficiencies of Sum constructed automorphic symmetric balanced incomplete block designs with respect to parent designs has been presented. The process involved the ...

Abstract: We propose a new generalized family of distributions called the exponentiated generalized power series (EGPS) family of distributions and study its sub-model, the exponentiated generalized logarithmic (EGL) class of distributions, in detail. The structural properties of the new model (EGPS) and its sub-model (EGL) distribution including moments, order statistics, Rényi entropy, and maximum likelihood estimates are derived. We used the method of maximum likelihood to estimate the p...

Abstract: In this thesis, we use the theory of minimal Sullivan models in rational homotopy theory to study the partial computation of the Lie bracket structure of the string homology on a formal elliptic space. In the process, we show the total space of the unit sphere tangent bundleS2m−1 → Ep→ Gk,n(C) over complex Grassmannian manifolds Gk,n(C) for 2 ≤ k ≤ n/2, where m = k(n − k) is not formal. This is done by exhibiting a non trivial Massey triple product. On the other hand, l...

Abstract: Let A and B be maximal monotone operators defined on a real Hilbert space H, and let Fix, (eqution found) and μ is a given positive number. [H. H. Bauschke, P. L. Combettes and S. Reich, The asymptotic behavior of the composition of two resolvents, Nonlinear Anal. 60 (2005), no. 2, 283-301] proved that any sequence (xn) generated by the iterative method, (eqution found) converges weakly to some point in Fix(JAμ JBμ). In this paper, we show that the modified method of alternating...

Abstract: Hierarchical multilevel multi-leader multi-follower problems are non-cooperative decision problems in which multiple decision-makers of equal status in the upper-level and multiple decision makers of equal status are involved at each of the lower-levels of the hierarchy. Much of solution methods proposed so far on the topic are either model specific which may work only for a particular sub-class of problems or are based on some strong assumptions and only for two level cases. In th...

Abstract: Tri-level optimization problems are optimization problems with three nested hierarchical structures, where in most cases conflicting objectives are set at each level of hierarchy. Such problems are common in management, engineering designs and in decision making situations in general, and are known to be strongly NP-hard. Existing solution methods lack universality in solving these types of problems. In this paper, we investigate a tri-level programming problem with quadratic fract...

Abstract: The purpose of this article is to study the method of approximation for zeros of the sum of a finite family of maximally monotone mappings and prove strong convergence of the proposed approximation method under suitable conditions. The method of proof is of independent interest. In addition, we give some applications to the minimization problems and provide a numerical example which supports our main result. Our theorems improve and unify most of the results that have been proved f...