The T ∗ ε integral was calculated numerically along an extending, tunneling crack front in an 8 mm thick, aluminum three-point bend (3PB) specimen, using a numerical model driven by experimentally obtained surface displacements. The model provided input to a contour integration for the T ∗ ε integral, via the Equivalent Domain Integral (EDI) method with incremental plasticity. Validity of the a...

In this paper, we use the parametric form of fuzzy numbers, and aniterative approach for obtaining approximate solution for a classof fuzzy nonlinear Fredholm integral equations of the second kindis proposed. This paper presents a method based on Newton-Cotesmethods with positive coefficient. Then we obtain approximatesolution of the fuzzy nonlinear integral equations by an iterativeapproach.

We apply our simultaneous contour integral method to an infinite sum in Prudnikov et al. and use it derive the of Incomplete gamma function terms Hurwitz zeta function. then evaluate this formula new series special functions fundamental constants. All results work are new.

We study the numerical approximation of a time dependent equation involving fractional powers of an elliptic operator L defined to be the unbounded operator associated with a Hermitian, coercive and bounded sesquilinear form on H 0 (Ω). The time dependent solution u(x, t) is represented as a Dunford Taylor integral along a contour in the complex plane. The contour integrals are approximated usi...

In this paper, 2D boundary element stress analysis is carried out to obtain the T-stress for multiple internal edge cracks in thick-walled cylinders for a wide range of cylinder radius ratios and relative crack depth. The T-stress, together with the stress intensity factor K, provides amore reliable two-parameter prediction of fracture in linear elastic fracture mecha...

The flicker response contour for the isopod Asellus is a simple probability integral (F - log I) over the whole determinable range (F = 1 to 51). This contrasts with the "distorted" asymmetrical curves obtained with Apis, Anax, and other arthropods with large convex eyes. The explanation of the distortion as due to mechanical conditions affecting photoreception is therefore confirmed, as the st...

High order differences of simple number sequences may be analysed asymptotically by means of integral representations, residue calculus, and contour integration. This technique, akin to Mellin transform asymptotics, is put in perspective and illustrated by means of several examples related to combinatorics and the analysis of algorithms like digital tries, digital search trees, quadtrees, and d...

Two approaches for the efficient rational approximation of the Fermi-Dirac function are discussed: one uses the contour integral representation and conformal mapping and the other is based on a version of the multipole representation of the Fermi-Dirac function that uses only simple poles. Both representations have logarithmic computational complexity. They are of great interest for electronic ...

In this paper, interval Legendre wavelet method is investigated to approximated the solution of the interval Volterra-Fredholm-Hammerstein integral equation. The shifted interval Legendre polynomials are introduced and based on interval Legendre wavelet method is defined. The existence and uniqueness theorem for the interval Volterra-Fredholm-Hammerstein integral equations is proved. Some examp...