Interpolation with Specified Error of a Point Series Belonging to a Monotone Curve

The paper addresses the problem of modeling a smooth contour interpolating a point series belonging to a curve containing no special points, which represents the original curve with specified accuracy. The contour is formed within the area of possible location of the parts of the interpolated curve along which the curvature values are monotonously increased or decreased. The absolute interpolation error of the point series is estimated by the width of the area of possible location of the curve. As a result of assigning each intermediate point, the location of two new sections of the curve that lie within the area of the corresponding output section is obtained. When the interpolation error becomes less than the given value, the area of location of the curve is considered to be formed, and the resulting point series is interpolated by a contour that lies within the area. The possibility to shape the contours with arcs of circles specified by characteristics is investigated.

Anisotropic Antiplane Elastoplastic Problem

In this work we solve an anisotropic antiplane elastoplastic problem about stress state in a body weakened by a hole bounded by a piecewise-smooth contour. We give the conservation laws which allowed us to reduce calculations of stress components to a contour integral over the contour of the hole. The conservation laws allowed us to find the boundary between the elastic and plastic areas

Determination of the Conditions of an Effective Functioning of Elongated Cumulative Charges in Processing the Marble Stone

The study of the effect of Elongated Cumulative Charges (ECC) on rock formations has an important scientific and practical significance for solving a number of process problems in mining practice. The use of charges with a longitudinal concavity for a directional destruction (presplit blasting, “smoothwall” chipping) involves reducing the explosives consumption, preserving the aquifer rock mass from additional explosion-caused cracks, obtaining a smooth contour and reducing the volume of drilling works. It is noted that one of the options that provides the explosion energy redistribution in a destructible medium is the use of elongated cumulative charges with a damping core. Experimental evidences on the dynamic loading of model blocks by an explosion of an elongated cumulative charge with an inert pad of various acoustic stiffness are reported.

A RECIPROCITY THEOREM FOR BUCKLING STATES OF VAT (STEERED FIBER) COMPOSITE PLATES

In the present paper the flat composite plates in buckling are studied. The plates have a symmetric lay-up and loaded along their piecewise-smooth contour by the in-plane forces. The consideration employs the Classical Lamination Plate Theory. A reciprocity theorem for the buckling states of the plate is derived and analyzed. The theorem may be used as a benchmark for the structural analysis and the optimization software.

Generalized Cauchy integrals on the plane

The integrals with homogeneous-difference kernels are considered on a smooth contour. The boundary properties of the integrals are described in the H?lder space. An analogue of the known Sokhotski-Plemelj formula is obtained. Moreover, the differentiation formula of these integrals is also given.

Fluctuations of the membrane with piecewise smooth contour and mixed boundary conditions

The eigenvalue problem for the two-dimensional operator Laplace is classical in mathematics and physics. However, computing methods for calculation of eigenvalues have still many problems, especially in applications to acoustic and electromagnetic wave guides. The investigated below two-dimensional spectral for the Laplace operator have been previously considered by the author only in smooth areas. The solutions of these tasks (eigen functions) are infinitely differentiated or. even analytical and therefore in order to create effective algorithms it is necessary to consider this enormous a priori information. Traditional methods of finite differences and finite elements almost do not practically use the information on smoothness of the decision, i.e. these are methods with saturation. The term “saturation” was entered by K.I. Babenko. Using the method of computing experiment the author investigates the task about fluctuations of the membrane with the piecewise smooth contour for two-dimensional area, obtained by conformal representation of the square. It is shown that eigen functions are infinitely differentiated. Therefore, numerical algorithms without saturation are applicable. In article the calculation algorithm of eigenvalues in this two-dimensional area is developed, which allows determining up to 10 natural frequencies with the accuracy acceptable for practice on the grid 10×10.

Chondrodermatitis nodularis chronica helicis excision and reconstruction

Background:Chondrodermatitis nodularis chronica helicis is a common benign condition of the pinna. It presents as a painful, well demarcated nodule on the pinna that may be associated with surrounding erythema or an overlying crust.Methods:This paper describes techniques for the excision of chondrodermatitis nodularis chronica helicis on both the helix and anti-helix, and reconstruction of the defect.Conclusion:Both methods give an excellent cosmetic result and can be performed under local anaesthetic. Excising and smoothing down the cartilage decreases the likelihood of recurrence as a smooth contour to the ear is achieved.