Let ~ be a (possibly infinite) projective plane, and G a collineation group of ~ . Suppose temporarily that ~ is a translation plane with respect to L, and G is the group of collineations fixing L. Then G=TGx, where T is the translation group with respect to L, and x is an affine point. If, moreover, the characteristic of ~ is not 2, then Gx= CG(t) and G= TCa(t), where t is an involutory homolo...

Nomenclature A k , a k Fourier series coefficients, d mean difference between theoretical and experimental stress values, i square root of –1, m mapping function shape descriptor, r, θ polar coordinates in the mapping plane, s standard deviation in the difference between stress values, t distance from the crack tip, x, y Cartesian coordinates in the physical plane, z complex coordinate in the p...

Consider convex plane domains D(t) = (1− t)D0 + tD1, 0 ≤ t ≤ 1. We first prove that the 1/4-power of the polar moment of inertia about the centroid of D(t) is concave in t. From this we deduce some isoperimetric inequalities.

In this note we aim to study plane-wave limits of the solutions of type II superstring theories. We consider Freund-Rubin type dS5 ×H5 solutions of type IIB theory and obtain a new kind of plane-wave solutions, we refer them as de Sitter plane-waves or Dpp-waves. Considering Hull’s time-like T-duality we are able to map the Dpp wave solution to maximally supersymmetric Hpp-wave in IIB string th...

A r e c o g n i t i o n procedure w i t h a range f i n d e r presented i n t h i s paper i s developed f o r the eye of the i n t e l l i g e n t robo t s t u d i e d i n the E l e c t r o t e c h n i c a l L a b o r a t o r y . The range f i n d e r employs a v e r t i c a l s l i t p r o j e c t e r which p r o j e c t s a . l i g h t beam on the o b j e c t s . Whi le the beam is moved in a...

Thermoelectric materials can recover electrical energy from waste heat and vice versa, which are of great significance in green harvesting solid state refrigerator. The thermoelectric figure merit (zT) quantifies the conversion efficiency, a large Seebeck or Nernst effect is crucial for development devices. Here we present significantly thermopower topological semimetal ZrTe5, attributed to bot...

The theorem in question gives a sufficient condition for a quadratic space over a local ring R to contain a hyperbolic plane over R. Our main aim in this paper is to prove the following result, which is a variant of the Springer theorem [La] for quadratic spaces over local rings. Theorem. Let R be a local Noetherian domain that has an infinite residue field of characteristic different from 2. L...