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.     

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.     

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   

Residual conductance fluctuations of tiny disordered conductors

Conductances of the equivalent samples differ randomly (Stone 1985). At zero temperature these fluctuations were found to be of the order ofe ²/h for samples of arbitrary size and form (Altshuler 1985; Lee and Stone 1985). Experimentally such fluctuations manifest themselves as e.g. the reproducible aperiodic oscillations of the given sample conductance in magnetic field (Webbet al 1985; Stone 1985). These oscillations can be understood in terms of the correlation function (Lee and Stone 1985; Altshuler and Khmel’nitskii 1985) of the conductances in different fields. The characteristic field scale of the aperiodic oscillations corresponds to the unit magnetic flux through the sample. Conductance fluctuations decrease with the growth of temperature if the sample size is larger than the diffusion length within the timeh/T (Stone 1985; Lee and Stone 1985; Webbet al 1984, 1985; Altshuler and Khmel’nitskii 1985). These fluctuations are proportional toT ^?1/4,T ^?1/2 logT, andT ^?1/2 in the 3-d, 2-d and 1-d cases, respectively (Altshuler and Khmel’nitskii 1985) (the experiments of Webbet al 1984, 1985 correspond to the latter case). Random potential in tiny samples breaks all space symmetries. All effects which are forbidden in the average by these symmetries should manifest themselves by (i) conductance anisotropy, (ii) its dependence on the electric field direction and (iii) giant generation of the second harmonic in the granular sample under light radiation (Altshuler and Khmel’nitskii 1985). Conductance changes aperiodically with variation of the chemical potential (Lee and Stone 1985). Because of this thermopower fluctuations are much larger than its average value (Altshuler and Khmel’nitskii 1985). Conductance fluctuations are very sensitive to the random impurity potential variations (Altshuler and Spivak 1985). For instance, the change of the film conductance due to the shift ofone impurity isfinite for any film size. This effect can be used for the super flow impurity diffusion investigations. Variations of the localized spins realization in spin glasses change the conductance. This can explain (Altshuler and Spivak 1985) the conductance dependence on the magnetic field direction observed by Webbet al (1984, 1985).