Matroid bases with cardinality constraints on the intersection

Mathematical Programming - Given two matroids $$\mathcal {M}_{1} = (E, \mathcal {B}_{1})$$ and $$\mathcal {M}_{2} = (E, \mathcal {B}_{2})$$ on a common ground set E with base sets $$\mathcal...     

Asymmetric Information in a Capital Accumulation Differential Game with Spillover and Learning Effects

Journal of Optimization Theory and Applications - This paper considers a capital accumulation game where the installation costs of investments are lowered by the firm’s own capital stock...     

?*-extensions of tori, higher chow groups and applications to incidence equivalence relations for algebraic cycles

LetX be a smooth projective variety over an algebraically closed fieldk. We repeat Bloch's construction of aG _m -biextension (torseur)E over CH _hom ^p (X)×CH _hom ^q (X) forp+q=dim(X)+1. First we show that in characteristic zeroE comes via pullback from the Poincaré biextension over the corresponding product of intermediate Jacobians which has been conjectured by Bloch and Murre. Then the relations betweenE and various equivalence relations for algebraic cycles are studied. In particular we reprove Murre's theorem stating that Griffiths' conjecture holds for codimension 2 cycles, i.e. every 2-codimensional cycle which is algebraically and incidence equivalent to zero has torsion Abel-Jacobi invariant.     

Nonreciprocal effects in light reflection by a moving medium

Nonreciprocal effects in light reflection by a medium moving along an interface are considered in a weakly relativistic approximation. It is found that nonreciprocal effects are anomalously large in the vicinity of the Brewster and the total-internal-reflection (TIR) angles when light is reflected by transparent moving media. These effects exceed considerably (by several orders of magnitude) the ratio of the velocity of the reflecting medium to the velocity of light and can be proportional to rather than to under certain conditions. We show new possibilities for the creation a method for investigation of the structure of nonuniform flows with a very small spatial scale (less than one millimeter). This method is based on measurement of amplitude and phase nonreciprocities in light reflection by these flows.Institute of Applied Physics, Russian Academy of Sciences, Nizhny Novgorod. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 38, No. 11, pp. 1146–1157, November, 1995.     

Change in structure and properties of carbon steels bombarded by a 10−5 to 10−4 second high-energy electron beam

We consider the hardening characteristics and features of the structural and phase transformations in carbon steel (0.7% C) quenched from the melt using an electron beam with electron energy 130–180 keV, pulse duration 10–200 msec and power density 10⁶ to 10⁷ W/cm². We have observed that maximum hardening is achieved for pulse duration 40 msec. The nonmonotonic character of the dependence of the degree of hardening on the pulse duration is connected with the substantial effect of the beam parameters on the phase composition and morphology of the rapidly quenched structures.Institute of Power Electronics, Siberian Branch, Russian Academy of Sciences; Tomsk State Architectural Design Academy. Institute of the Physics of Strength and Materials Science, Siberian Branch, Russian Academy of Sciences. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, p. 42–50, October, 1995.     

On stable geometries

Within the concept of projective lattice geometry we are considering the class of stable geometries which have also been introduced in [14]. The investigation of their basic properties will result in fundamental structure theorems which especially give a lattice-geometric characterization of free left modules of rank 6 over proper right Bezout rings of stable rank 2. This yields a proper generalization of previous results of ours.     

A new heuristic algorithm solving the linear ordering problem

The linear ordering problem is an NP-hard combinatorial problem with a large number of applications. Contrary to another very popular problem from the same category, the traveling salesman problem, relatively little space in the literature has been devoted to the linear ordering problem so far. This is particularly true for the question of developing good heuristic algorithms solving this problem.In the paper we propose a new heuristic algorithm solving the linear ordering problem. In this algorithm we made use of the sorting through insertion pattern as well as of the operation of permutation reversal. The surprisingly positive effect of the reversal operation, justified in part theoretically and confirmed in computational examples, seems to be the result of a unique property of the problem, called in the paper the symmetry of the linear ordering problem. This property consists in the fact that if a given permutation is an optimal solution of the problem with the criterion function being maximized, then the reversed permutation is a solution of the problem with the same criterion function being minimized.     

On the maximum principle for doubly nonlinear parabolic equations

For a general class of doubly nonlinear parabolic equations, some versions of the maximum principle are established. They play an important role in studying the regularity of generalized solutions of such equations. In particular, the results obtained can be used in studying equations of the form $$\frac{{\partial u}}{{\partial t}} - div\{ |u|^l |\nabla u\} = 0, m > 1, l > 1 - m.$$ which have numerous applications in the mechanics of continuous media. Bibliography: 17 tiles.