A new method is presented for shape sensitivity analysis of a crack in a homogeneous, isotropic, and linear-elastic body subject to mode-I loading conditions. The method involves the material derivative concept of continuum mechanics, domain integral representation of the J-integral, and direct differentiation. Unlike virtual crack extension techniques, no mesh perturbation is needed in the pro...

As the development of singular integral operators, their commutators and multilinear operators have been well studied (see [3]–[7], [18]–[20]). Let T be the Calderón-Zygmund singular integral operator and b ∈ BMO(R), a classical result of Coifman, Rochberg and Weiss (see [6]) stated that the commutator [b, T ](f) = T (bf)− bT (f) is bounded on L(R) for 1 < p <∞. The purpose of this paper is to ...

The possible identification by INTEGRAL of the EGRET source 3EG J1736 − 2908 with the active galactic nucleus GRS 1734−292 is discussed. The latter was discovered in 1990 and later identified with a Seyfert 1 galaxy. At the time of the compilation of the 3rd EGRET Catalog, it was not considered as a possible counterpart of the source 3EG J1736 − 2908, which remained unidentified. A detailed mul...

We present spectral measurements made in the soft (20–100 keV) gamma-ray band of the region containing the composite supernova remnant G11.2-0.3 and its associated pulsar PSR J1811−1925. Analysis of INTEGRAL/IBIS data allows characterisation of the system above 10 keV. The IBIS spectrum is best fitted by a power law having photon index Γ = 1.8 +0.4 −0.3 and a 20–100 keV flux of 1.5 ×10 −11 erg ...

and objectives In tutorial 2, we demonstrated the basic steps for deriving the direct boundary integral equation. In this tutorial we will explain, with more examples, the derivation of the direct boundary integral equation for systems of partial differential equations. We will consider two examples: elasticity problems and shear-deformable plate bending problems. 1 Elasticity equations In this...

In a previous paper [EG] we described an integral structure (J, E) on the exceptional Jordan algebra of Hermitian 3 × 3 matrices over the Cayley octonions. Here we use modular forms and Niemeier’s classification of even unimodular lattices of rank 24 to further investigate J and the integral, even lattice J0 = (ZE) in J . Specifically, we study ring embeddings of totally real cubic rings A into...

Strength reduction in structures like an aircraft could be resulted as cyclic loads over a period of time and is an important factor for structural life prediction. Service loads are emphasized at the regions of stress concentration, mostly at the connection of components. The initial flaw prompting the service life was expected by using the Equivalent Initial Flaw Size (EIFS) which has been re...

A graph is called integral if all its eigenvalues are integers. The quest for integral graphs was initiated by F. Harary and A. J. Schwenk [9]. All such cubic graphs were obtained by D. Cvetković and F. C. Bussemaker [2, 1], and independently by A. J. Schwenk [10]. There are exactly thirteen cubic integral graphs. In fact, D. Cvetković [2] proved that the set of regular integral graphs of a fix...