Mach's principle. Part 1. Initial state of the universe the universe

The integral formulation of equations of general relativity proposed earlier as a mathematical tool for Mach's principle forbids the conventional singular cosmologies but is compatible with the de Sitter initial space.     

Kondo temperature for the two-channel Kondo models of tunneling centers

A two-channel Kondo (2CK) non-Fermi liquid state in a metal resulting from the interaction between electrons and structural defects modeled by double-well potentials (DWP) is revisited. Account only of the two lowest states in DWP is known to lead to rather low Kondo temperature, T(K). We prove that the contribution of higher excited states reduces T(K), if all of the intermediate states are taken into account. Prefactor in T(K) is shown to be determined by the spacing between the second and the third levels epsilon(3) in DWP rather than by the electron Fermi energy epsilon(F). Since epsilon(3)相似文献   

The weakly neighborly polyhedral maps on the 2-manifold with euler characteristic −1

A weakly neighborly polyhedral map (w.n.p. map) is a two-dimensional cell-complex which decomposes a closed 2-manifold without boundary, such that for every two vertices there is a 2-cell containing them. We prove that there are just four w.n.p. maps with Euler characteristic –1 and we describe them.     

Quotient polytopes of cyclic polytopes part II: Stability of thef-vector and of thek-skeleton

This paper is the continuation of an earlier paper on quotient polytopesC(v, 2m)/F of cyclic polytopes and the associated quotient complexesC(V, 2m)/J. Here, we study mainly what changes in the faceJ do not affect thef-vector of the quotientC(V, 2m)/J. In the last section we examine the corresponding question fork-skeleta, i.e., what changes inJ do not affect the isomorphism type of skel _k C(V, 2m)/J.     

Ion-exchange selectivity of a network calixarene-containing polymer obtained by the template synthesis on Na<Superscript>+</Superscript>, K<Superscript>+</Superscript>, and Ba<Superscript>2+</Superscript> matrices

The ion-exchange equilibrium in network polymers obtained from cis-2,8,14,20-tetraphenyl-4,6,10,12,16,18,22,24-octahydroxycalix[4]arene by template synthesis on cations Na⁺, K⁺, and Ba²⁺ as matrices was studied. The selectivity coefficients of ion exchanges Ba²⁺-H⁺, Na⁺-H⁺, K⁺-H⁺, Na⁺-K⁺, and Na⁺-NH₄ ⁺ were determined. The template synthesis enhanced the affinity of the polymers to matrix-forming cations by 6–8 kJ mol⁻¹. __________ Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 8, pp. 1919–1922, August, 2005.