A novel idea to construct flat-top partition of unity functions in a closed form on a general (structured or unstructured) finite element mesh is presented. An efficient and practical construction method of a flat-top partition of unity function is important in the generalized finite element method (GFEM). Details on how to construct flat-top partition of unity functions on a provided mesh are ...

Vedic literature in Sanskrit has been serving the entire world humanistic efforts. Sri Lanka is a nation of different religions and diverse cultures tradition going back to several centuries The treated be oldest world. Objective this study identify some evidences Social Harmony concepts Rig Literature. This Study focused on Rigveda considering its early origin recognition among scholars. Mixed...

In this paper a new mathematical procedure is presented for combining different pieces of evidence which are represented in the interval form to reflect our knowledge about the truth of a hypothesis. Evidences may be correlated to each other (dependent evidences) or conflicting in supports (conflicting evidences). First, assuming independent evidences, we propose a methodology to construct comb...

The notion that science is unified in one way or another dates back at least to Aristotle, though unity claims since then have been diverse and variously motivated. By way of introduction to the modern discussion of unity, disunity, and integration, in this first section we examine five historical attempts to unify knowledge: Aristotle’s metaphysical and hierarchical unity; the Enlightenment pr...

Let p ≡ 1 (mod 4) be a prime number and let ζ = e be a primitive root of unity. Then there exists a unique biquadratic extension eld Q(y)/Q that is a sub eld of Q(ζ). The aim of this work is to construct an algorithm for nding such y explicitly. Finally we state a general conjecture about the y we found.

Recently, the authors introduced two new second-order single-resistance-controlled oscillators (SRCO) employing four/three unity-gain cells (unity-gain voltage followers and unity-gain current followers). In this communication, a novel family of SRCOs has been presented which employ a reduced number of (only two) unity-gain cells as active elements. The workability of the new circuits has been ...

The partition of unity is an essential ingredient for meshless methods named by GFEM, PUFEM (partition of unity FEM), XFEM(extended FEM), RKPM(reproducing kernel particle method), RPPM(reproducing polynomial particle method), the method of clouds in the literature. There are two popular choices for partition of unity: a piecewise linear FEM mesh and the Shepard-type partition of unity. However,...

7 Periodic Series and Functions 128 7.1 Basic Trigonometric Identities . . . . . . . . . . . . . . . . . . 128 7.2 Basic Trigonometric Integrals . . . . . . . . . . . . . . . . . . 130 7.3 Basic Properties of Complex Numbers . . . . . . . . . . . . . 131 7.4 Complex Numbers and Trigonometrical Identities . . . . . . . 133 7.5 The Exponential of a Complex Number . . . . . . . . . . . . . 133 7.6...

In this paper, we show that the problem of computing the complex roots of unity is not as simple as it seems at rst. In particular, the formulas given in a standard programmer's reference book Knuth, Seminumerical Algorithms, 1981] are shown to be numerically unstable , giving unacceptably large error for moderate sized sequences. We give alternative formulas, which we show to be superior both ...