Deformations of Fuchsian Systems of Linear Differential Equations and the Schlesinger System

We consider holomorphic deformations of Fuchsian systems parameterized by the pole loci. It is well known that, in the case when the residue matrices are non-resonant, such a deformation is isomonodromic if and only if the residue matrices satisfy the Schlesinger system with respect to the parameter. Without the non-resonance condition this result fails: there exist non-Schlesinger isomonodromic deformations. In the present article we introduce the class of the so-called isoprincipal deformations of Fuchsian systems. Every isoprincipal deformation is also an isomonodromic one. In general, the class of the isomonodromic deformations is much richer than the class of the isoprincipal deformations, but in the non-resonant case these classes coincide. We prove that a deformation is isoprincipal if and only if the residue matrices satisfy the Schlesinger system. This theorem holds in the general case, without any assumptions on the spectra of the residue matrices of the deformation. An explicit example illustrating isomonodromic deformations, which are neither isoprincipal nor meromorphic with respect to the parameter, is also given

Zeros of the Jimbo, Miwa, Ueno tau function

We introduce a family of local deformations for meromorphic connections on the Riemann sphere in the neighborhood of a higher rank (simple) singularity. Following a scheme introduced by Malgrange we use these local models to prove that the zeros of the tau function introduced by Jimbo, Miwa and Ueno occur precisely at those points in the deformation space at which a certain Birkhoff-Riemann- Hilbert problem fails to have a solution.Comment: 59 page

Isomonodromic deformatiion with an irregular singularity and hyperelliptic curve

In this paper, we extend the result of Kitaev and Korotkin to the case where a monodromy-preserving deformation has an irregular singularity. For the monodromy-preserving deformation, we obtain the $\tau$-function whose deformation parameters are the positions of regular singularities and the parameter $t$ of an irregular singularity. Furthermore, the $\tau$-function is expressed by the hyperelliptic $\Theta$ function moving the argument \z and the period \B, where $t$ and the positions of regular singularities move $z$ and \B, respectively.Comment: 23 pages, 2 figure

Schlesinger transformations for elliptic isomonodromic deformations

Schlesinger transformations are discrete monodromy preserving symmetry transformations of the classical Schlesinger system. Generalizing well-known results from the Riemann sphere we construct these transformations for isomonodromic deformations on genus one Riemann surfaces. Their action on the system's tau-function is computed and we obtain an explicit expression for the ratio of the old and the transformed tau-function.Comment: 19 pages, LaTeX2

Radiation effects on silver and zinc battery electrodes, III Interim report, Oct. 1965 - Jan. 1966

Radiation effects on silver-zinc battery electrode

PO and ID BCG vaccination in humans induce distinct mucosal and systemic immune responses and CD4(+) T cell transcriptomal molecular signatures.

Protective efficacy of Bacillus Calmette-Guérin (BCG) may be affected by the methods and routes of vaccine administration. We have studied the safety and immunogenicity of oral (PO) and/or intradermal (ID) administration of BCG in healthy human subjects. No major safety concerns were detected in the 68 healthy adults vaccinated with PO and/or ID BCG. Although both PO and ID BCG could induce systemic Th1 responses capable of IFN-γ production, ID BCG more strongly induced systemic Th1 responses. In contrast, stronger mucosal responses (TB-specific secretory IgA and bronchoalveolar lavage T cells) were induced by PO BCG vaccination. To generate preliminary data comparing the early gene signatures induced by mucosal and systemic BCG vaccination, CD4(+) memory T cells were isolated from subsets of BCG vaccinated subjects pre- (Day 0) and post-vaccination (Days 7 and 56), rested or stimulated with BCG infected dendritic cells, and then studied by Illumina BeadArray transcriptomal analysis. Notably, distinct gene expression profiles were identified both on Day 7 and Day 56 comparing the PO and ID BCG vaccinated groups by GSEA analysis. Future correlation analyses between specific gene expression patterns and distinct mucosal and systemic immune responses induced will be highly informative for TB vaccine development.Mucosal Immunology advance online publication 30 August 2017; doi:10.1038/mi.2017.67

A Decathlon in Multidimensional Modeling: Open Issues and Some Solutions

The concept of multidimensional modeling has proven extremely successful in the area of Online Analytical Processing (OLAP) as one of many applications running on top of a data warehouse installation. Although many different modeling techniques expressed in extended multidimensional data models were proposed in the recent past, we feel that many hot issues are not properly reflected. In this paper we address ten common problems reaching from defects within dimensional structures over multidimensional structures to new analytical requirements and more

Non-Fermi liquid behavior of SrRuO_3 -- evidence from infrared conductivity

The reflectivity of the itinerant ferromagnet SrRuO_3 has been measured between 50 and 25,000 cm-1 at temperatures ranging from 40 to 300 K, and used to obtain conductivity, scattering rate, and effective mass as a function of frequency and temperature. We find that at low temperatures the conductivity falls unusually slowly as a function of frequency (proportional to \omega^{-1/2}), and at high temperatures it even appears to increase as a function of frequency in the far-infrared limit. The data suggest that the charge dynamics of SrRuO_3 are substantially different from those of Fermi-liquid metals.Comment: 4 pages, 3 postscript figure