Two types of the effective mass divergence and the Grüneisen ratio in heavy-fermion metals

The behavior of the specific heat c_p, effective mass M^*, and the thermal expansion coefficient of a Fermi system located near the fermion condensation quantum phase transition (FCQPT) is considered. We observe the first type behavior if the system is close to FCQPT: the specific heat , , while the thermal expansion coefficient . Thus, the Grüneisen ratio Γ(T)=/c_p does not diverges. At the transition region, where the system passes over from the non-Fermi liquid to the Landau Fermi liquid, the ratio diverges as . When the system becomes the Landau Fermi liquid, Γ(T,r)∝1/r, with r being a distance from the quantum critical point. Provided the system has undergone FCQPT, the second type takes place: the specific heat behaves as , M^*∝1/T, and =a+bT with a,b being constants. Again, the Grüneisen ratio diverges as .     

X-ray fluorescence determination of bromine in halogenated organic compounds using quasisolid emitters

A series of quasi-solid emitters is proposed for the X-ray fluorescence determination of bromine in different bromine-containing compounds. It is shown that sucrose-based glasses are the best emitters for analyzing alkali solutions of halogenated organic compounds, saccharose-based glasses and polymer films are best for analyzing powder samples, and organic gels offer most promise for analyzing liquid (at normal conditions) samples. It is noted that the proposed method can expand the possibilities of commercially produced element analyzers, which are currently intended for determining only C, H, O, N, and S in organic compounds and cannot be used for determining halogens.     

Structure of the attraction zones of the final states in the presence of dynamical period doubling bifurcations

The structure of the attraction zones of the final states associated with dynamical period doubling bifurcations is investigated. It is found that on the “initial value—transition rate” plane the attraction zones of the two possible final states alternate with each other and that a subdivision of the attraction regions occurs with a decrease in the transition rate. It is shown that the boundaries of the attraction zones are smeared out because of the effect of noise and in this situation the fine structure of the attraction zones is destroyed. As analytical and numerical calculations have shown, the critical value of the noise variance, corresponding to the boundary between the dynamical (or predictable) and stochastic (or unpredictable) modes, has a power-law dependence on the transition rate with a typical exponent value of one. The existence of “noise” invariants is also observed: the integrated (over all initial values) probability of achieving the final state is invariant with respect to the noise level. Zh. éksp. Teor. Fiz. 113, 369–380 (January 1998)     

Application of a double insulated probe for the investigation of charged-particle beams in plasmas

It is shown that the existence of a current in the external circuit of a double insulated probe without electrical bias between its electrodes is evidence of the presence of a stream (beam) of charged particles in a plasma. The species of particles forming a beam in a plasma, the direction and divergence of the beam, and information on the distribution of the current density over the beam cross section in the plasma can be obtained by determining the direction and strength of the current in the external circuit of the probe as it is positioned at various sites in the investigated system. Zh. Tekh. Fiz. 68, 121–123 (October 1998)     

Isospectrality and galois projective geometries

We construct a series of pairs of domains in the plane and pairs of surfaces with boundary that are isospectral but not isometric. The construction is based on the existence of finite transformation groups that are spectrally equivalent but not isomorphic. Translated fromMatematicheskie Zametki, Vol. 63, No. 5, pp. 660–664, May, 1998. This research was partially supported by the Russian Foundation for Basic Research and by INTAS under joint grant No. 96-01-00043.     

Vector Lattices on a Set of Two Generators

It is proved that the center of an automorphism group Aut(FVL2) of a free vector lattice FVL2 on a set of two free generators is isomorphic to a multiplicative group of positive reals. It is shown that the free vector lattice FVL2 has an isomorphic representation by continuous piecewise linear functions of the real line; as a consequence, the ideal lattice and the root system for rectifying ideals in FVL2 are amply described. Similar results are obtained for a free vector lattice FVL2 _Q 2 generated by two elements over a field of rational numbers.     

On fundamental groups of compact Hausdorff spaces

We discuss which groups can be realized as the fundamental groups of compact Hausdorff spaces. In particular, we prove that the claim ``every group can be realized as the fundamental group of a compact Hausdorff space' is consistent with the Zermelo-Fraenkel-Choice set theory.

     

Solid-phase extraction on alkyl-bonded silica gels in inorganic analysis.

Solid-phase extraction (SPE) is an effective tool for the preconcentration of trace elements and their separation from various sample constituents. Octadecyl and other alkyl-bonded silica gels are most widely used for these purposes. The fundamentals of the SPE of inorganic ions are reviewed and compared with those of related techniques (liquid-liquid extraction and reversed-phase liquid chromatography). The extraction of ions in the form of chelate compounds, inorganic salts solvated by neutral reagents, and ion-pair compounds is considered. Numerous applications of SPE to the separation and preconcentration of different elements and their species, including on-line combinations with instrumental determination techniques, are described and tabulated.