Abstract In this note we establish a necessary and sufficient condition for solvability of the homogeneous Riemann boundary problem with infinity index on rectifiable open curve. The deal considers influence requirement solutions problem, degree non-smoothness curve at endpoints as well behavior coefficient these points.

— We prove the modulo p and modulo p 2 cases of the Igusa conjecture on exponential sums. This conjecture predicts specific uniform bounds in the homogeneous polynomial case of exponential sums modulo p m when p and m vary. We introduce the motivic oscillation index of a polynomial and prove the possibly stronger, analogue bounds for m = 1, 2 using this index instead of the bounds of the conjec...

Chondrocytes are the living cells in articular cartilage (AC). They synthesize and maintain the extracellular matrix. Their activity is regulated by the interplay of genetic and environmental factors, such as soluble mediators, extracellular matrix composition, and mechanical factors. The mechanical environment of the chondrocytes has a significant influence on the health of the joint. In past ...

In the present paper, an asymptotic model is constructed for the short-time deformation of an articular cartilage layer modeled as transversely isotropic, transversely homogeneous (TITH) biphasic material. It is assumed that the layer thickness is relatively small compared with the characteristic size of the normal surface load applied to the upper surface of the cartilage layer, while the bott...

The standard scalar paraxial parabolic (Fock–Leontovich) propagation equation is generalized to include allorder nonparaxial corrections in the significant case of a tensorial refractive-index perturbation on a homogeneous isotropic background. In the resultant equation, each higher-order nonparaxial term (associated with diffraction in homogeneous space and scaling as the ratio between beam wa...

Using the Fresnel relations as axioms, we derive a generalized electromagnetic momentum for a piecewise homogeneous medium and a different generalized momentum for a medium with a spatially varying refractive index in the Wentzel-Kramers-Brillouin (WKB) limit. Both generalized momenta depend linearly on the field, but the refractive index appears to different powers due to the difference in tra...

what we mean by alliteration of homogeneous words is that such alliteration is based on two or more lexical basis that is conspicuously coordinative and homogeneous with each other. they are homogeneous in that their form, structure, and tone, are similar. we can name two homogeneous words, two bases of homonym. it is evident that such words, though homogeneous from one hand, should necessarily...