How long is the convex minorant of a one-dimensional random walk?

We prove distributional limit theorems for the length of the largest convex minorant of a one-dimensional random walk with independent identically distributed increments. Depending on the increment law, there are several regimes with different limit distributions for this length. Among other tools, a representation of the convex minorant of a random walk in terms of uniform random permutations is utilized

Theory of temperature dependence of the Fermi surface-induced splitting of the alloy diffuse-scattering intensity peak

The explanation is presented for the temperature dependence of the fourfold intensity peak splitting found recently in diffuse scattering from the disordered Cu3Au alloy. The wavevector and temperature dependence of the self-energy is identified as the origin of the observed behaviour. Two approaches for the calculation of the self-energy, the high-temperature expansion and the alpha-expansion, are proposed. Applied to the Cu3Au alloy, both methods predict the increase of the splitting with temperature, in agreement with the experimental results.Comment: 4 pages, 3 EPS figures, RevTeX, submitted to J. Phys. Condens. Matter (Letter to the Editor

Perfect magnetohydrodynamics as a field theory

We propose the generally covariant action for the theory of a self-coupled complex scalar field and electromagnetism which by virtue of constraints is equivalent, in the regime of long wavelengths, to perfect magnetohydrodynamics (MHD). We recover from it the Euler equation with Lorentz force, and the thermodynamic relations for a prefect fluid. The equation of state of the latter is related to the scalar field's self potential. We introduce 1+3 notation to elucidate the relation between MHD and field variables. In our approach the requirement that the scalar field be single valued leads to the quantization of a certain circulation in steps of $\hbar$; this feature leads, in the classical limit, to the conservation of that circulation. The circulation is identical to that in Oron's generalization of Kelvin's circulation theorem to perfect MHD; we here characterize the new conserved helicity associated with it. We also demonstrate the existence for MHD of two Bernoulli-like theorems for each spacetime symmetry of the flow and geometry; one of these is pertinent to suitably defined potential flow. We exhibit the conserved quantities explicitly in the case that two symmetries are simultaneously present, and give examples. Also in this case we exhibit a new conserved MHD circulation distinct from Oron's, and provide an example.Comment: RevTeX, 16 pages, no figures; clarifications added and typos corrected; version to be published in Phys. Rev.

Mechatronical Module Development on the Basis of Wave Rack Gear for Working Members Drive of Automatized Machines

Peculiarities of geometry elements synthesis of wave transmission with a rolling (cog) rack, its kinematics and simulation interaction of discrete wedge pushers with rolling rack are considered here. Principles of drive creation and systems of microprocessor control of the mechatronical module of the translation by using wave transmission with the rolling rack as well as the main appraches in design-technological preparation of its making are presented.Рассмотрены особенности синтеза геометрии элементов волновой передачи с роликовой (цевочной) рейкой, ее кинематики и моделирование взаимодействия дискретных клиновых толкателей с роликовой рейкой. Изложены принципы создания привода и системы микропроцессорного управления мехатронного модуля поступательного перемещения с использованием волновой передачи с роликовой рейкой, а также основные подходы в конструкторско-технологической подготовке его производства

Antigen-Specific versus Non-Antigen-Specific Immunoadsorption in ABO-Incompatible Renal Transplantation

Introduction: ABO-incompatible (ABOi) renal transplantation (RTx) from living donors is an established procedure to expand the donor pool for patients with end stage renal disease. Immunoadsorption (IA) is a standard procedure for the removal of preformed antibodies against the allograft. In this study, antigen-specific and non-antigen-specific IA in ABOi RTx were compared. Patients and Methods: 10 patients underwent antigen-specific IA (Glycosorb group) and 13 patients non-antigen-specific IA (Immunosorba group). The effects of both procedures regarding antibody reduction, number of treatments, complications, costs, as well as the allograft function and patient survival were compared between both groups. Results: Although the IgG levels were reduced equally by both procedures (p=0.82), the reduction of the IgM level was more effective in the Glycosorb group (p=0.0172). Patients in both groups required a median number of 6 IA before ABOi RTx. Allograft function at one year after AB0i RTx was similar in both groups (estimated glomerular filtration rate: 66 vs. 64 ml/min/1.73m² respectively), with a death-censored graft survival of 90.0% and 92.3% respectively. Complication rates did not differ between procedures. Due to the reuse of non-antigen-specific Immunosorba columns, costs were considerably lower in this group; however, the use of the Immunosorba-based IA was less time-efficient. Conclusion: Considering upcoming alternatives as simultaneous performance of dialysis and IA or a possible reuse of Glycosorb columns, this might become less relevant in the future

Charged multifluids in general relativity

The exact 1+3 covariant dynamical fluid equations for a multi-component plasma, together with Maxwell's equations are presented in such a way as to make them suitable for a gauge-invariant analysis of linear density and velocity perturbations of the Friedmann-Robertson-Walker model. In the case where the matter is described by a two component plasma where thermal effects are neglected, a mode representing high-frequency plasma oscillations is found in addition to the standard growing and decaying gravitational instability picture. Further applications of these equations are also discussed.Comment: 14 pages (example added), to appear in Class. Quantum Gra