On Some “Tame” and “Wild” Aspects of the Problem of Semiscalar Equivalence of Polynomial Matrices

The problem of reducing polynomial matrices to canonical form by using semiscalar equivalent transformations is studied. This problem is wild as a whole. However, it is tame in some special cases. In the paper, classes of polynomial matrices are singled out for which canonical forms with respect to semiscalar equivalence are indicated. We use this tool to construct a canonical form for the families of coefficients corresponding to the polynomial matrices. This form enables one to solve the classification problem for families of numerical matrices up to similarity.     

Axisymmetric Collision Problem for Two Identical Elastic Solids of Revolution

A direct central collision of two identical bodies of revolution is studied. A nonstationary mixed boundary-value problem with an unknown moving boundary is formulated. Its solution is represented by a series in term of Bessel functions. An infinite system of Volterra equations of the second kind for the unknown expansion coefficients is derived by satisfying the boundary conditions. The basic characteristics of the collision process are determined depending on the curvature of the frontal surface of the bodies     

Base-Catalyzed Reaction of Cyanoalkylphosphonates with Methanol

The equilibrium conversion of nitriles in the reaction of cyanoalkylphosphonates with methanol in the presence of sodium methylate, as determined by potentiometric titration with perchloric acid in nitromethane, varies from 58 to 17.7%. The practical yields of imidates were evaluated by a preparative procedure of isolation of purified imidates from the reaction mixtures (56-14%). Because of the low conversions of nitriles, the reaction is expedient to use only for preparing alkyl (dialkoxyphosphoryl)acetimidates.     

Stability of Crystalline Ion Beams

Hyperfine Interactions - In this paper, the conditions for which three-dimensional crystalline ion beams were attained in the rf quadrupole storage ring PALLAS at a velocity of around 2800 m/s are...     

Quantum Dot and Antidot Infrared Photodetectors: Iterative Methods for Solving the Laplace Equation in Domains with Involved Geometry

We propose iteration methods for solving the Dirichlet problem in domains with involved geometry. Such problems arise in relation to the problem of optimizing quantum dot and antidot infrared detectors. We estimate the deviation of an approximate solution from the exact solution.     

Fixed point theorems for multivalued nonexpansive mappings satisfying inwardness conditions

Let X be a Banach space whose characteristic of noncompact convexity is less than 1 and satisfies the nonstrict Opial condition. Let C be a bounded closed convex subset of X, KC(X) the family of all compact convex subsets of X and T a nonexpansive mapping from C into KC(X) with bounded range. We prove that T has a fixed point. The nonstrict Opial condition can be removed if, in addition, T is an 1-χ-contractive mapping.     

Conic Formulation for l p -Norm Optimization

In this paper, we formulate the l _p -norm optimization problem as a conic optimization problem, derive its duality properties (weak duality, zero duality gap, and primal attainment) using standard conic duality and show how it can be solved in polynomial time applying the framework of interior-point algorithms based on self-concordant barriers.     

Parametric Quintic-Spline Approach to the Solution of a System of Fourth-Order Boundary-Value Problems

In this paper, we use parametric quintic splines to derive some consistency relations which are then used to develop a numerical method for computing the solution of a system of fourth-order boundary-value problems associated with obstacle, unilateral, and contact problems. It is known that a class of variational inequalities related to contact problems in elastostatics can be characterized by a sequence of variational inequations, which are solved using some numerical method. Numerical evidence is presented to show the applicability and superiority of the new method over other collocation, finite difference, and spline methods.     

Precise measurement of magnetic moment of short-lived β-emitting nuclei12B ( I π=1+, T 1/2=20.18 ms)

The spin polarized β-emitting nuclei¹²B (I ^π=1⁺,T _1/2=20.18 ms) were produced by the nuclear reaction¹¹B(d, p)¹²B and by the selection technique of the incident deuteron energy and the¹²B recoil angle following the nuclear reaction. The nuclear magnetic moment of the short-lived nuclei¹²B was measured by β-NMR with the β-NMR and β-NQR setup established for the first time in China. The nuclear magnetic moment of¹²B was determined to be μ=0.99993±0.00048 nm org=0.99993±0.00048 after the precise correction of the Knight shift.     

Insights on some chiral smectic phases

Combining layered positional order as smectic order and chirality can generate complex architectures since twist parallel to the layers is not allowed. This paper will review some new experimental results on different phases resulting from the competition between smectic positional order and twist orientational order. It concerns the TGB_A and the NL^*, that is the liquid line phase as well as the SmQ phase. Chiral effects in the isotropic phase will also be discussed.