This paper considers a 2-D fracture analysis of anisotropic piezoelectric solids by a boundary elementfree method. A traction boundary integral equation (BIE) that only involves the singular terms of order 1/r is first derived using integration by parts. New variables, namely, the tangential derivative of the extended displacement (the extended displacement density) for the general boundary and...

K e y w o r d s H o d g e decomposition, Quasilinear equation, Measures. 1. I N T R O D U C T I O N We give some slight new extensions of the Hodge decomposition due to Iwaniec [2] (see, also [3-5]) by proving essentially that for v E W l ' n e n ( ~ ) , ~ C R n the vector field Dv(iDv] + e)-~n can be written as D~e + K~ with ~be E W l'r~ (~), re > n and K~ is a free divergence vector and is 1-...

A linear stability analysis of the parallel uniform flow in a horizontal channel with open upper boundary is carried out. The lower boundary is considered as an impermeable isothermal wall, while the open upper boundary is subject to a uniform heat flux and it is exposed to an external horizontal fluid stream driving the flow. An eigenvalue problem is obtained for the two-dimensional transverse...

 An $(n, r)$-arc is a set of $n$ points of a projective plane such that some $r$, but no $r+1$ of them, are collinear. The maximum size of an $(n, r)$-arc in  PG(2, q) is denoted by $m_r(2,q)$. In this paper thirteen new $(n, r)$-arc in  PG(2,,29) and a table with the best known lower and upper bounds on $m_r(2,29)$ are presented. The results are obtained by non-exhaustive local computer search.

Gil Kalai introduced the shifting-theoretic upper bound relation to characterize the f -vectors of Gorenstein* complexes (or homology spheres) by using algebraic shifting. In the present paper, we study the shifting-theoretic upper bound relation. First, we will study the relation between exterior algebraic shifting and combinatorial shifting. Second, by using the relation above, we will prove ...

We first briefly survey the recent results for existence of solutions to first-order problems with fixed-time impulses. Periodic boundary conditions using upper and lower solutions were considered in [19], using degree theory. A nonlinear alternative of Leray-Schauder type was used in [15] for initial conditions or periodic boundary conditions. The monotone iterative technique was employed in [...