RATCHETING EVALUATION OF BIOLOGICAL TISSUES OVER ASYMMETRIC LOADING CYCLES

This study intends to evaluate the ratcheting response of biological samples prepared from bovine and porcine trabecular bone, articular cartilage, meniscus, and skin tissues and tested under asymmetric (nonzero mean stress) cycles. Meniscus and skin samples were tested with stress ratios of [Formula: see text] and [Formula: see text], respectively, while other tissues were tested at [Formula: see text]. Experimental ratcheting data and related influential parameters including stress level, stress rate, and testing frequency were discussed. A parametric ratcheting equation was further calibrated to estimate the ratcheting response of tissues. The predicted ratcheting data were found to be in close agreement with the reported experimental data.

Направленные поверхностные акустические волны в нецентросимметричных решетках

Spatial distribution of surface Rayleigh acoustic wave propagating along the surface of GaAs semiconductor covered by a periodic grating of gold stripes is calculated. We demonstrated that when the lattice has no center of spatial inversion the distribution of deformation for the surface wave with the Bloch wave vector kx = 0 is asymmetric and characterized by nonzero mean momentum in the interface plane and nonzero degree of transverse polarization in the plane perpendicular to the surface. The work has been supported by the Russian Science Foundation Grant No. 20-12-00194.

DEFORMATIONS OF SURFACES FROM STATIONARY RICCI TENSOR

In this paper, we consider infinitesimal (n. m.) first-order deformations of single-connected regular surfaces in three-dimensional Euclidean space. The search for the vector field of this deformation is generally reduced to the study and solution of a system of four equations (among them there are differential equations) with respect to seven unknown functions. To avoid uncertainty, the following restriction is imposed on a given surface: the Ricci tensor is stored (mainly) on the surface. A mathematical model of the problem is created: a system of seven equations with respect to seven unknown functions. Its mechanical content is established. It is shown that each solution of the obtained system of equations will determine the field of displacement n. m. deformation of the first order of the surface of nonzero Gaussian curvature, which will be an unambiguous function (up to a constant vector). It is proved that each regular surface of nonzero Gaussian and mean curvatures allows first-order n. m. deformation with a stationary Ricci tensor. The tensor fields are found explicitly and depend on two functions, which are the solution of a linear inhomogeneous second-order differential equation with partial derivatives. The class of rigid surfaces in relation to the specified n. m. deformations. Assuming that one of the functions is predetermined, the obtained differential equation in the General case will be a inhomogeneous differential Weingarten equation, and an equation of elliptical type. The geometric and mechanical meaning of the function that is the solution of this equation is found. The following result was obtained: any surface of positive Gaussian and nonzero mean curvatures admits n. m of first-order deformation with a stationary Ricci tensor in the region of a rather small degree. Tensor fields will be represented by a predefined function and some arbitrary regular functions. Considering the Dirichlet problem, it is proved that the simply connected regular surface of a positive Gaussian and nonzero mean curvatures under a certain boundary condition admits a single first-order deformation with a stationary Ricci tensor. The strain tensors are uniquely defined.

Mean value theorems for a class of density-like arithmetic functions

This paper provides a mean value theorem for arithmetic functions [Formula: see text] defined by [Formula: see text] where [Formula: see text] is an arithmetic function taking values in [Formula: see text] and satisfying some generic conditions. As an application of our main result, we prove that the density [Formula: see text] (respectively, [Formula: see text]) of normal (respectively, primitive) elements in the finite field extension [Formula: see text] of [Formula: see text] are arithmetic functions of (nonzero) mean values.

Ghost QTL and hotspots in experimental crosses - novel solution by mixed model with nonzero mean

Abstract“Ghost-QTL” are the false discoveries in QTL mapping, that arise due to the “accumulation” of the polygenic effects, uniformly distributed over the genome. The locations on the chromosome which are strongly correlated with the summary polygenic effect depend on a specific sample correlation structure determined by the genotype at all loci. During the analysis of e-QTL data or recombinant inbred lines this correlation structure is preserved for all traits under consideration, and may lead to the so called “hot-spots” via the detection of the summary polygenic effect at exactly the same positions for most of the considered traits. We illustrate that the problem can be solved by the application of the extended mixed effect model, where the random effects are allowed to have a nonzero mean. We provide formulas for estimating the thresholds for the corresponding t-test statistics and use them in the stepwise selection strategy, which allows for a simultaneous detection of several QTL. Extensive simulation studies illustrate that our approach allows to eliminate ghost-QTL/false hot spot effects, while preserving a high power of detection of true QTL effects.

Generalized integral transforms with the translation operator on function space

Main goal of this paper is to establish various basic formulas for the generalized integral transform involving the generalized convolution product. In order to establish these formulas, we use the translation operator which was introduced in [9]. It was not easy to establish basic formulas for the generalized integral transforms because the generalized Brownian motion process used in this paper has the nonzero mean function. In this paper, we can easily establish various basic formulas for the generalized integral transform involving the generalized convolution product via the translation operator.