Nonvanishing cohomology and classes of Gorenstein rings

We give counterexamples to the following conjecture of Auslander: given a finitely generated module M over an Artin algebra Λ, there exists a positive integer n_M such that for all finitely generated Λ-modules N, if Ext_Λⁱ(M,N)=0 for all i?0, then Ext_Λⁱ(M,N)=0 for all i?n_M. Some of our examples moreover yield homologically defined classes of commutative local rings strictly between the class of local complete intersections and the class of local Gorenstein rings.     

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...     

Chaos-controlling technique for suppressing self-modulation in backward-wave tubes

A method for suppressing self-modulation in backward-wave tubes is proposed. Additional delay is introduced into the feedback circuit, owing to which the output signal amplitude affects the electron beam current that enters into the interaction space. Numerical simulations demonstrate that the operating current in the single-frequency oscillation mode may be increased roughly twofold.     

Recognition of the Finite Simple Groups F 4(2m) by Spectrum

The spectrum of a finite group is the set of its element orders. A finite group G is said to be recognizable by spectrum, if every finite group with the same spectrum as G is isomorphic to G. The purpose of the paper is to prove that for every natural m the finite simple Chevalley group F ₄(2 ^m ) is recognizable by spectrum.     

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.     

Stratifiable Families of Extremals and Sufficient Conditions for Optimality in Optimal Control Problems

It is shown that, if a parametrized fämily of extremals F can be stratified in a way compatible with the flow map generated by F, then those trajectories of the family which realize the minimal values of the cost in F are indeed optimal in comparison with all trajectories which lie in the region R covered by the trajectories of F. It is not assumed that F is a field covering the state space injectively. As illustration, an optimal synthesis is constructed for a system where the flow of extremals exhibits a simple cusp singularity.     

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.     

Synthesis and electrical characteristics of polyaniline nanoparticles and their polymeric composite

Monodisperse polyaniline nanoparticles (PAPSSA) were synthesized from an oxidative dispersion polymerization using poly(sodium 4-styrenesulfonate) (PSSA) as both a polymeric stabilizer and a dopant agent due to its acidity. The nanoparticles were being stabilized with two different molecular weight of PSSA. Size effect of PAPSSA particles were examined by scanning electron microscopy (SEM), transmission electron microscopy (TEM) and dynamic light scattering (DLS). The d.c. electrical conductivity of composite films on the glass substrate was measured by a four-probe method. It was found that the electrical properties of the composite films are affected by the content of nano-sized polyaniline and different molecular weights of stabilizer in the poly(vinyl alcohol) (PVA) matrix.     

An effect of application of chiral aluminium alkoxides and amides as adducts to zirconium catalyzed carbo- and cycloalumination of olefins

This paper is dedicated to a study of properties of the following novel optically active organoaluminium compounds (OACs): (1S,2S)-l,7,7-trimethyl-2-[(dialkylalumina)oxy]-bicyclo[2.2.1]heptanes and (1S)-N-(dialkylalumina)-6,7-dimethoxy-1-methyl-1,2,3,4- tetrahydroisoquinolines. The synthesis of the chiral OACs was carried out in the reaction of either natural camphor or salsolidine with both AlEt₃ and i-Bu₂AlH. The main goal of the research was to investigate the stereodifferentiating activity of the chiral OACs in the olefin carbo- and cycloalumination reactions, catalyzed by Cp₂ZrCl₂.