For the lack of formula of linear range for S-shaped MEMS planar micro-spring, this paper establishes physical and mathematical model and analysis the material stress-strain angle. The formula is deduced by calculating the strain and rotation of the basic unit of micro-spring tension. Compared with the results of the tests on micro-spring which produced by UV-LIGA process, the formula results i...

For positive C 0 C_0 -semigroups S"> S encoding="application/x-tex">S</mml:an...

2 Ito-Doeblin’s formula(s) 7 2.1 First formulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2 Generalizations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.3 Continuous semi-martingales . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.4 Integration by parts formula . . . . . . . . . . . ...

Let S be a polynomial of degree 2n + 2, that is, positive on the real axis, and let w = 1/S on (−∞,∞). We present an explicit formula for the nth orthogonal polynomial and related quantities for the weight w. This is an analogue for the real line of the classical Bernstein-Szegő formula for (−1, 1). 1. The result The Bernstein-Szegő formula provides an explicit formula for orthogonal polynomial...

We calculate the linear response thermopower S of a quantum point contact using the Landauer formula and therefore assume non-interacting electrons. The purpose of the paper, is to compare analytically and numerically the linear thermopower S of non-interacting electrons to the low temperature approximation, S = (π/3e)k BT∂μ[lnG(μ, T = 0)], and the so-called Mott expression, S M = (π/3e)k BT∂μ[...

The formula mentioned in the title is proved. Introduction Let S, T be complete nonsingular surfaces over an algebraically closed field k of any characteristic, and let h : T → S be a finite separable morphism of degree n. We establish a formula that expresses the Euler characteristic (understood as the degree of the second Chern class ∫ c2,T ) of T via the Euler characteristic of S and some lo...

We analyze four-dimensional symplectic manifolds of type X = S 1 × M</mm...

Mixtures of silicone elastomer and silicone oil were prepared and the values of their Young's moduli, E, determined in compression. The mixtures had volume fractions, [Formula: see text], of silicone oil in the range of 0-0.73. Measurements were made, under displacement control, for strain rates, [Formula: see text], in the range of 0.04-3.85 s(-1). The behaviour of [Formula: see text] as a fun...