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.     

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.     

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.     

Novel network polymers based on calixresorcinarenes

The novel network polymers 2a-2d based on calix[4]resorcinarene derivatives were obtained with yields 2a: 80%, 2b: 90%, 2c: 70%, 2d: 70%. Polymers 2a and 2b containing fragments of tetramethylcalix[4]resorcinarene or tetraphenylcalix[4]resorcinarene as a repeating units were synthesized by condensation cis-tetramethylcalix[4]resorcinarene or cis-tetraphenylcalix[4]resorcinarene with formaldehyde. Polymers 2c and 2d containing fragments of furylcalix[4]resorcinarene were obtained by condensation of formaldehyde with products of calix[4]resorcinarene and furfural interaction. The IR spectra and sorption properties of the polymers were researched. It is found out that 2a-2d can participate in the cation-exchange reaction.     

Electron spin resonance studies at the phase transition in YbInCu4

In the intermetallic compound YbInCu₄ the Gd³⁺-ESR and the static susceptibility were measured in the temperature range 1.5K–300 K, i.e. both below and above the valence phase transition which occurs in this material at T_ph≈50 K. The Gd³⁺ resonance is mainly determined by exchange interaction of Gd³⁺ ions with fluctuating Yb³⁺ ions via conduction electrons (RKKY coupling) both below and above this transition. Arguments are presented that at low temperature YbInCu₄ is a dense Kondo system (mixed valent state).