Model of free charge generation in polymers

A time solution of the excimer-ion pair system is presented here with a special attention to the time asymptote. Presented at the Czech-Israeli-German Symposium “Dynamical Processes in Condensed Molecular Systems”, Prague, Czech Republic, 26–30 May 1997. This work was supported by the grant No. C 1050601 of the Grant Agency of the Academy of Sciences of the Czech Republic.     

Interpolation by a Game

We introduce a notion of a real game (a generalisation of the Karchmer-Wigderson game (cf. [3]) and of real communication complexity, and relate this complexity to the size of monotone real formulas and circuits. We give an exponential lower bound for tree-like monotone protocols (defined in [4, Definition 2.2]) of small real communication complexity solving the monotone communication complexity problem associated with the bipartite perfect matching problem. This work is motivated by a research in interpolation theorems for prepositional logic (by a problem posed in [5, Section 8], in particular). Our main objective is to extend the communication complexity approach of [4, 5] to a wider class of proof systems. In this direction we obtain an effective interpolation in a form of a protocol of small real communication complexity. Together with the above mentioned lower bound for tree-like protocols this yields as a corollary a lower bound on the number of steps for particular semantic derivations of Hall's theorem (these include tree-like cutting planes proofs for which an exponential lower bound was demonstrated in [2]).     

On a certain two-sided symmetric condition in magnetic field analysis and computations

A special two-sided condition for the incremental magnetic reluctivity is introduced which guarantees the unique existence of both the weak and the approximate solutions of the nonlinear stationary magnetic field distributed on a region composed of different media, as well as a certain estimate of the error between the two solutions. The condition, being discussed from the physical as well as the mathematical point of view, can be easily verified and is fulfilled for various magnetic reluctivity models used in electrotechnical practice.     

Invariant Subspaces for Semigroups of Algebraic Operators

T. Laffey showed (Linear and Multilinear Algebra6(1978), 269–305) that a semigroup of matrices is triangularizable if the ranks of all the commutators of elements of the semigroup are at most 1. Our main theorem is an extension of Hthis result to semigroups of algebraic operators on a Banach space. We also obtain a related theorem for a pair {A, B} of arbitrary bounded operators satisfying rank (AB−BA)=1 and several related conditions. In addition, it is shown that a semigroup of algebraically unipotent operators of bounded degree is triangularizable.     

Homomorphic images of finite subdirectly irreducible unary algebras

We prove that a finite unary algebra with at least two operation symbols is a homomorphic image of a (finite) subdirectly irreducible algebra if and only if the intersection of all its subalgebras which have at least two elements is nonempty. While working on this paper the first and the third authors were partially supported by the Grant Agency of the Czech Republic, grant #201/02/0594, and by the institutional grant MSM0021620839; the second author was supported by the Ministry of Science, Technologies and Development of Republic of Serbia, grant no. 1227.     

Magnetization and Specific Heat of UCo0.95T0.05Al (T = Fe, Ni) Single Crystals

We present the first single-crystal study of Fe and Ni doped U(Co_1-x T _x )Al compounds in comparison to the parent compound, the itinerant 5f-electron metamagnet UCoAl. Magnetization and specific-heat data measured in the temperature range of (1.8-300) K and in fields up to 10 T are analyzed and discussed. Both compounds exhibit a strong uniaxial anisotropy with the dominating magnetic response along the c-axis of the hexagonal ZrNiAl-type structure. Ni substitution yields an increase of the critical field for metamagnetism; UCo_0.95Fe_0.05Al is ferromagnetic below 30 K. Temperature evolution of the entropy change between 0 and 10 T points to involvement of magnetic correlations or spin fluctuations in the paramagnetic compounds UCoAl and UCo_0.95Ni_0.05Al.