Using Rounding Function in the Problems of Finite-Element Analysis

This work offers to supplement polynomial elements used by the step function of Heaviside and rounding functions which allows to simplify and formalise the record of test piecewise continuous function applying it for continual problems solution by the method of Galerkin.Key words: Finite element method; Galerkin; Rounding functio

Multivariate risks and depth-trimmed regions

We describe a general framework for measuring risks, where the risk measure takes values in an abstract cone. It is shown that this approach naturally includes the classical risk measures and set-valued risk measures and yields a natural definition of vector-valued risk measures. Several main constructions of risk measures are described in this abstract axiomatic framework. It is shown that the concept of depth-trimmed (or central) regions from the multivariate statistics is closely related to the definition of risk measures. In particular, the halfspace trimming corresponds to the Value-at-Risk, while the zonoid trimming yields the expected shortfall. In the abstract framework, it is shown how to establish a both-ways correspondence between risk measures and depth-trimmed regions. It is also demonstrated how the lattice structure of the space of risk values influences this relationship.Comment: 26 pages. Substantially revised version with a number of new results adde

Determination of thermophysical properties of oil-acetone miscella based on the peng-robinson equation of state

The article is devoted to the determination of thermophysical properties of oil-acetone miscella based on the Peng-Robinson equation of state. The data of the thermophysical properties of the oil-acetone miscella allow to simulate processes of separation of oil-acetone miscella in extraction technology

Multivariate Lorenz dominance based on zonoids

Multivariate Lorenz order, Directional majorization, Price Lorenz order, Generalized Lorenz function, Multidimensioned Gini index,

Evaluation of saturated porous material extraction in a multistage counterflow process

A mathematical description of the extraction process with impregnation of a porous raw material in a multistage countercurrent cascade is give, which led to the conclusion that the increased porosity of the extracted material leads to a decrease in the extraction depth at other equal conditions

Axon tracking in serial block-face scanning electron microscopy

Electron microscopy is an important modality for the analysis of neuronal structures in neurobiology. We address the problem of tracking axons across large distances in volumes acquired by serial block−face scanning electron microscopy (SBFSEM). Tracking, for this application, is defined as the segmentation of an axon that spans a volume using similar features between slices. This is a challenging problem due to the small cross−sectional size of axons and the low signal−to−noise ratio in our SBFSEM images. A carefully engineered algorithm using Kalman−snakes and optical flow computation is presented. Axon tracking is initialized with user clicks or automatically using the watershed segmentation algorithm, which identifies axon centers. Multiple axons are tracked from slice to slice through a volume, updating the positions and velocities in the model and providing constraints to maintain smoothness between slices. Validation results indicate that this algorithm can significantly speed up the task of manual axon trackin

Modeling of rheological dependencies of the process of oil material extruding

The aim of the research is to develop rheological dependences of the oil material during extrusion and to simulate viscosity of the material when producing vegetable oil by pressing in an extruder during the flow of a plastically deformable porous medium. Methods of mathematical modeling of structural models of viscosity have been used to describe both non-linear plastic and pseudo-plastic flows. The technique is based on the fact that the viscoplastic properties of the Bingham flow are taken into account. An approximation of the flow equations has been presented within the Bingham rheological model, taking into account the experimentally established effect of hydrostatic pressure on the shear stress of the sunflower pulp entering the extruder. Plastic viscosity remains almost constant.The effective viscosity has been considered as consisting of two components: the plastic viscosity, that corresponds to the Newtonian fluid viscosity, and the structural viscosity, which characterizes the shear resistance caused by the tendency of the solid particles contained in the Bingham fluid to form a structure. As a result of the studies, the influence of the main parameters of the extrusion process on the effective viscosity of the oil material has been assessed. The need to use the most theoretically substantiated Bingham equation has been substantiated, which allows you to determine the effective viscosity over a sufficiently large interval of shear rates in the extruder channel.As a result, rheological models of the shear flow have been determined that describe both plastic and pseudo plastic flows with fairly good accuracy