A new modulus of smoothness based on the Euler angles is introduced on the unit sphere and is shown to satisfy all the usual characteristic properties of moduli of smoothness, including direct and inverse theorem for the best approximation by polynomials and its equivalence to a K-functional, defined via partial derivatives in Euler angles. It also leads to new moduli of smoothness and K-functi...

A method to estimate C66, which is a shear modulus of a transversely isotropic formation (with its symmetry axis parallel to the borehole), is developed and tested. The inversion for C66 is based upon a cost function which has three terms: a measure of the misfit between the observed and predicted wavenumbers, a measure of the misfit between the current estimate for CBB and the initial guess of...

Following D. B. H. Cline [Cl], we study the connections between the behavior of the spherical mean of an L modulus of continuity corresponding to the finite difference of an arbitrary order m > 0 of a function f ∈ L(R), 1 ≤ p ≤ ∞, d ∈ N, and the average decay of the Fourier transform f̂ . We obtain an estimate which refines one result from [Cl] for 1 ≤ p ≤ 2. Our main interest is in two-sided es...

There was employed the density functional theory plane-wave pseudopotential method with local density approximation and generalized gradient approximation to investigate the structural, elastic and mechanical properties of the intermetallic compound Ni3Ga. The calculated equilibrium lattice constant and bulk modulus are in good agreement with the experimental values. The elastic constants were ...

We study the evolution of the elastic shear modulus of weakly aggregated colloidal particles during the onset of a delayed collapse under gravity. The early lifetime is characterised by an elastic shear modulus that increases logarithmically in time, following which the gels experience a catastrophic failure and the elastic modulus drops dramatically. As the gel collapses, various complex behav...

Although elastography has been increasingly used for evaluating muscle shear modulus associated with age, sex, musculoskeletal, and neurological conditions, its physiological meaning is largely unknown. This knowledge gap may hinder data interpretation, limiting the potential of using elastography to gain insights into muscle biomechanics in health and disease. We derived a mathematical model f...

We develop a theory of sheaves and cohomology on the category proper modulus pairs. This complements [KMSY21], where non-proper pairs has been developed.

We study the connection between uniformly convex functions f : X → R bounded above by ‖ · ‖p, and the existence of norms on X with moduli of convexity of power type. In particular, we show that there exists a uniformly convex function f : X → R bounded above by ‖ · ‖2 if and only if X admits an equivalent norm with modulus of convexity of power type 2.