Abstract-The one-speed critical problem is solved for a two-region sphere, where the total cross section is common, but different multiplication parameters in the two zones are permitted. A transform procedure is used to reduce the integral transport equation to a pseudo problem in slab geometry. This, in turn, is solved by Case’s method of normal modes. The analysis leads to a Fredholm integra...

This paper concerns a rather concrete phenomenon in abstract operator algebras. The main examples of the algebras we study are algebras of singular integral operators (pseudo-differential operators of order zero). As everyone knows, the Fredhohn index of a pseudo-differential operator depends only on its symbol and the Atiyah-Singer Index Theorem gives an explicit formula for computing the depe...

Pseudo interface waves can exist at the interface of a fluid and a fluid-saturated poroelastic solid. These waves are typically related to the pseudo-Rayleigh pole and the pseudo-Stoneley pole in the complex slowness plane. It is found that each of these two poles can contribute (as a residue) to a full transient wave motion when the corresponding Fourier integral is computed on the principal R...

This manuscript contains several new notions including intuitionistic fuzzy Nb metric space, quasi-Sb-metric pseudo-Sb-metric quasi-N-metric space and pseudo space. We prove decomposition theorem fixed-point results in the setting of Further, we provide non-trivial examples to show validity introduced results. At end, solve an integral equation, system linear equations nonlinear fractional diff...

the aim of this paper is to generalize the‎‎notion of pseudo-almost valuation domains to arbitrary‎ ‎commutative rings‎. ‎it is shown that the classes of chained rings‎ ‎and pseudo-valuation rings are properly contained in the class of‎ ‎pseudo-almost valuation rings; also the class of pseudo-almost‎ ‎valuation rings is properly contained in the class of quasi-local‎ ‎rings with linearly ordere...

In a recent article, the first and second kinds of multivariate Chebyshev polynomials fractional degree, relevant integral repesentations, have been studied. this we introduce pseudo-Lucas functions show possible applications these new functions. For kind, compute Newton sum rules any orthogonal polynomial set starting from entries Jacobi matrix. representation formulas for powers r×r matrix, a...

Fatigue damage of engineering materials severely affects the serviceability their structures. It is impracticable to accurately predict fatigue process due variability material properties, microstructure heterogeneity and others. This study aims track entire viscoelastic by coupling with mechanism. A typical material, asphalt binder, widely used in pavement selected for investigation this study...