One class of linear Fredholm integral equations with functionals and parameters

The theory of linear Fredholm integral-functional equations of the second kind with linear functionals and with a parameter is considered. The necessary and sufficient conditions are obtained for the coefficients of the equation and those parameter values, in the nighbohood of which the equation has solutions. The leading terms of the asymptotics of the solutions are constructed. The constructive method is proposed for constructing a solution both in the regular case and in the irregular one. In the regular case, the solution is constructed as a Taylor series in powers of the parameter. In the irregular case, the solution is constructed as a Laurent series in powers of the parameter. Constructive theory and method is demonstrated on the model example

Theoretical and experimental study of high-pressure synthesized B20-type compounds Mn1−x_{1-x}(Co,Rh)x_xGe

The search and exploration of new materials not found in nature is one of modern trends in pure and applied chemistry. In the present work, we report on experimental and \textit{ab initio} density-functional study of the high-pressure-synthesized series of compounds Mn$_{1-x}$(Co,Rh)$_x$Ge. These high-pressure phases remain metastable at normal conditions, therewith they preserve their inherent noncentrosymmetric B20-type structure and chiral magnetism. Of particular interest in these two isovalent systems is the comparative analysis of the effect of $3d$ (Co) and $4d$ (Rh) substitution for Mn, since the $3d$ orbitals are characterized by higher localization and electron interaction than the $4d$ orbitals. The behavior of Mn$_{1-x}$(Co,Rh)$_x$Ge systems is traced as the concentration changes in the range $0 \leq x \leq 1$. We applied a sensitive experimental and theoretical technique which allowed to refine the shape of the temperature dependencies of magnetic susceptibility $\chi(T)$ and thereby provide a new and detailed magnetic phase diagram of Mn$_{1-x}$Co$_x$Ge. It is shown that both systems exhibit a helical magnetic ordering that very strongly depends on the composition $x$. However, the phase diagram of Mn$_{1-x}$Co$_x$Ge differs from that of Mn$_{1-x}$Rh$_x$Ge in that it is characterized by coexistence of two helices in particular regions of concentrations and temperatures.Comment: 12 pages, 11 figure

Possibility of local pair existence in optimally doped SmFeAsO(1-x) in pseudogap regime

We report the analysis of pseudogap Delta* derived from resistivity experiments in FeAs-based superconductor SmFeAsO(0.85), having a critical temperature T_c = 55 K. Rather specific dependence Delta*(T) with two representative temperatures followed by a minimum at about 120 K was observed. Below T_s = 147 K, corresponding to the structural transition in SmFeAsO, Delta*(T) decreases linearly down to the temperature T_AFM = 133 K. This last peculiarity can likely be attributed to the antiferromagnetic (AFM) ordering of Fe spins. It is believed that the found behavior can be explained in terms of Machida, Nokura, and Matsubara (MNM) theory developed for the AFM superconductors.Comment: 5 pages, 2 figure

Strong-Coupling Superconductivity of CeIrSi3_3 with the Non-centrosymmetric Crystal Structure

We studied the pressure-induced superconductor CeIrSi$_3$ with the non-centrosymmetric tetragonal structure under high pressure. The electrical resistivity and ac heat capacity were measured in the same run for the same sample. The critical pressure was determined to be $P_{\rm c}$ = 2.25 GPa, where the antiferromagnetic state disappears. The heat capacity $C_{\rm ac}$ shows both antiferromagnetic and superconducting transitions at pressures close to $P_{\rm c}$. On the other hand, the superconducting region is extended to high pressures of up to about 3.5 GPa, with the maximum transition temperature $T_{\rm sc}$ = 1.6 K around $2.5-2.7$ GPa. At 2.58 GPa, a large heat capacity anomaly was observed at $T_{\rm sc}$ = 1.59 K. The jump of the heat capacity in the form of ${\Delta}{C_{\rm ac}}/C_{\rm ac}(T_{\rm sc})$ is 5.7 $\pm$ 0.1. This is the largest observed value among previously reported superconductors, indicating the strong-coupling superconductivity. The electronic specific heat coefficient at $T_{\rm sc}$ is, however, approximately unchanged as a function of pressure, even at $P_{\rm c}$.Comment: This paper will be published in J. Phys. Soc. Jpn. on the August issue of 200

High pressure investigation of the heavy-fermion antiferromagnet U_3Ni_5Al_19

Measurements of magnetic susceptibility, specific heat, and electrical resistivity at applied pressures up to 55 kbar have been carried out on single crystals of the heavy-fermion antiferromagnet U_3Ni_5Al_19, which crystallizes in the Gd_3Ni_5Al_19 orthorhombic structure with two inequivalent U sites. At ambient pressure, a logarithmic T-dependence of the specific heat and T-linear electrical resistivity below 5 K indicates non-Fermi liquid (NFL) behavior in the presence of bulk antiferromagnetic order at T_N=23 K. Electrical resistivity measurements reveal a crossover from non-Fermi liquid to Fermi liquid behavior at intermediate pressures between 46 kbar and 51 kbar, followed by a return to NFL T^{3/2} behavior at higher pressures. These results provide evidence for an ambient pressure quantum critical point and an additional antiferromagnetic instability at P_c=60 kbar.Comment: 12 pages, 5 figure

A Novel Dielectric Anomaly in Cuprates and Nickelates: Signature of an Electronic Glassy State

The low-frequency dielectric response of hole-doped insulators La_{2}Cu_{1-x}Li_{x}O_{4} and La_{2-x}Sr_{x}NiO_{4} shows a large dielectric constant \epsilon ^{'} at high temperature and a step-like drop by a factor of 100 at a material-dependent low temperature T_{f}. T_{f} increases with frequency and the dielectric response shows universal scaling in a Cole-Cole plot, suggesting that a charge glass state is realized both in the cuprates and in the nickelates.Comment: 5 pages, 4 figure