### Extending Utility Representations of Partial Orders

, 2005

"... The problem is considered as to whether a monotone function defined on a subset P of Euclidean space IR k can be strictly monotonically extended to IR k. It is proved that this is the case if and only if the function is separably increasing. Explicit formulas are given for a class of extensions whic ..."

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The problem is considered as to whether a monotone function defined on a subset P of Euclidean space IR k can be strictly monotonically extended to IR k. It is proved that this is the case if and only if the function is separably increasing. Explicit formulas are given for a class of extensions which involves an arbitrary function. Similar results are obtained for utility functions that represent strict partial orders on abstract sets X. The special case where P is a Pareto subset of IR k (or of X) is considered.

### Comparison of Mumijo (Shilajit) and Humic Acids (HA) Chemical Composition Using FTICR Mass-Spectrometry

"... Humic substances (HS) are complex mixtures formed during decay of plant and animal materials. HS are generically classified into fulvic and humic acid fractions according to their solubility properties. The particular features of HS are polydispersity and extreme structural heterogeneity. The biolog ..."

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Humic substances (HS) are complex mixtures formed during decay of plant and animal materials. HS are generically classified into fulvic and humic acid fractions according to their solubility properties. The particular features of HS are polydispersity and extreme structural heterogeneity. The biological effects of humic substances can be

### Characterization of Mumijo (Shilajit) from Different Regions by FTICR Mass-Spectrometry

"... Native Mumijo is a blackish-brown exudation, of variable consistencies, obtained from steep rocks of different formations found in the Himalayas at altitudes between 1000-5000 m, from Arunachal Pradesh in the East, to Kashmir in the West. Mumijo also is found in other mountain ranges of the world, e ..."

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Native Mumijo is a blackish-brown exudation, of variable consistencies, obtained from steep rocks of different formations found in the Himalayas at altitudes between 1000-5000 m, from Arunachal Pradesh in the East, to Kashmir in the West. Mumijo also is found in other mountain ranges of the world, e.g. Afganisthan (Hindukush, Badakh-Shan),

### CLUSTER-LEVEL TUNING OF A SHALLOW WATER EQUATION SOLVER ON THE INTEL MIC ARCHITECTURE

, 2014

"... The paper demonstrates the optimization of the execution en-vironment of a hybrid OpenMP+MPI computational fluid dynamics code (shallow water equation solver) on a cluster enabled with Intel Xeon Phi coprocessors. The discussion includes: 1. Controlling the number and affinity of OpenMP threads to o ..."

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The paper demonstrates the optimization of the execution en-vironment of a hybrid OpenMP+MPI computational fluid dynamics code (shallow water equation solver) on a cluster enabled with Intel Xeon Phi coprocessors. The discussion includes: 1. Controlling the number and affinity of OpenMP threads to optimize access to memory bandwidth; 2. Tuning the inter-operation of OpenMP and MPI to partition the problem for better data locality; 3. Ordering the MPI ranks in a way that directs some of the traffic into faster communication channels; 4. Using efficient peer-to-peer communication between Xeon Phi coprocessors based on the InfiniBand fabric. With tuning, the application has 90 % percent efficiency of par-allel scaling up to 8 Intel Xeon Phi coprocessors in 2 compute

### SPECTRA OF MAGNETIC FLUCTUATIONS AND RELATIVISTIC PARTICLES PRODUCED BY A NONRESONANT WAVE INSTABILITY IN SUPERNOVA REMNANT SHOCKS

, 2009

"... We model strong forward shocks in young supernova remnants with efficient particle acceleration where a nonresonant instability driven by the cosmic ray current amplifies magnetic turbulence in the shock precursor. Particle injection, magnetic field amplification (MFA), and the nonlinear feedback of ..."

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We model strong forward shocks in young supernova remnants with efficient particle acceleration where a nonresonant instability driven by the cosmic ray current amplifies magnetic turbulence in the shock precursor. Particle injection, magnetic field amplification (MFA), and the nonlinear feedback of particles and fields on the bulk flow are derived consistently. The shock structure depends critically on the efficiency of turbulence cascading. If cascading is suppressed, MFA is strong, the shock precursor is stratified, and the turbulence spectrum contains several discrete peaks. These peaks, as well as the amount of MFA, should influence synchrotron X-rays, allowing observational tests of cascading and other assumptions intrinsic to the nonlinear model of nonresonant wave growth. Key words: acceleration of particles – cosmic rays – instabilities – magnetic fields – shock waves – supernova remnants 1.

### Preprint typeset using L ATEX style emulateapj v. 03/07/07 SPECTRA OF MAGNETIC FLUCTUATIONS AND RELATIVISTIC PARTICLES PRODUCED BY A NONRESONANT WAVE INSTABILITY IN SUPERNOVA REMNANT SHOCKS

, 2009

"... We model strong forward shocks in young supernova remnants with efficient particle acceleration where a nonresonant instability driven by the cosmic ray current amplifies magnetic turbulence in the shock precursor. Particle injection, magnetic field amplification (MFA) and the nonlinear feedback of ..."

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We model strong forward shocks in young supernova remnants with efficient particle acceleration where a nonresonant instability driven by the cosmic ray current amplifies magnetic turbulence in the shock precursor. Particle injection, magnetic field amplification (MFA) and the nonlinear feedback of particles and fields on the bulk flow are derived consistently. The shock structure depends critically on the efficiency of turbulence cascading. If cascading is suppressed, MFA is strong, the shock precursor is stratified, and the turbulence spectrum contains several discrete peaks. These peaks, as well as the amount of MFA, should influence synchrotron X-rays, allowing observational tests of cascading and other assumptions intrinsic to the nonlinear model of nonresonant wave growth. Subject headings: acceleration of particles – shock waves – cosmic rays – supernova remnants – magnetic field – instabilities 1.

### Vibrodynamics of a Submerged Solid Affected by a Pulsating Singlet.

"... Summary. This paper3 provides a new insight into the classical Björkness problem. We examine system ‘solid+fluid ’ forced by an immobile singlet whose intensity is given at every time. We show that this system is governed by the Least Action Principle. The related Largangian is written out almost e ..."

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Summary. This paper3 provides a new insight into the classical Björkness problem. We examine system ‘solid+fluid ’ forced by an immobile singlet whose intensity is given at every time. We show that this system is governed by the Least Action Principle. The related Largangian is written out almost explicitly up to the Green function of the solid. In particular, there is a linear in velocity term. We show that it is integrable only in the case of spherical particle. We make a special accent on the case of high-frequency pulsating singlet. To construct the high-frequency asymptotic we employ a very natural formalism recently proposed by V. Yudovich. It makes us capable to obtain the Lagrangian governing ‘averaged ’ motions directly from Hamilton’s principle. We present such ‘slow ’ Lagrangian for the solid of general form. In more details, we study ‘averaged ’ dynamics of the spherical solid which can be homogeneous or not, and then discuss the related ‘buoyancy ’ effect for the solid of general form. Key words: Björkness forces, analytical dynamics 1

### and

, 807

"... The highly amplified magnetic fields suggested by observations of some supernova remnant (SNR) shells are most likely an intrinsic part of efficient particle acceleration by shocks. This strong turbulence, which may result from cosmic ray driven instabilities, both resonant and non-resonant, in the ..."

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The highly amplified magnetic fields suggested by observations of some supernova remnant (SNR) shells are most likely an intrinsic part of efficient particle acceleration by shocks. This strong turbulence, which may result from cosmic ray driven instabilities, both resonant and non-resonant, in the shock precursor, is certain to play a critical role in self-consistent, nonlinear models of strong, cosmic ray modified shocks. Here we present a Monte Carlo model of nonlinear diffusive shock acceleration (DSA) accounting for magnetic field amplification through resonant instabilities induced by accelerated particles, and including the effects of dissipation of turbulence upstream of a shock and the subsequent precursor plasma heating. Feedback effects between the plasma heating due to turbulence dissipation and particle injection are strong, adding to the nonlinear nature of efficient DSA. Describing the turbulence damping in a parameterized way, we reach two important results: first, for conditions typical of supernova remnant shocks, even a small amount of dissipated turbulence energy ( ∼ 10%) is sufficient

### Eurasian Geogr Copyright © 20 Ukraine’s Geopolitical Choice, 2009

"... Abstract: A noted specialist in international affairs and former U.S. ambassador to Ukraine revie follo facet tion vola a ran men Ukra early com tive ture, Ukra ovyc early 1 Ukrain its geopolitic foreign polic its need to m Many be tion as presid the Euro-Atl stymied the c idential elect policies th ..."

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Abstract: A noted specialist in international affairs and former U.S. ambassador to Ukraine revie follo facet tion vola a ran men Ukra early com tive ture, Ukra ovyc early 1 Ukrain its geopolitic foreign polic its need to m Many be tion as presid the Euro-Atl stymied the c idential elect policies than The Uni linked to the Ukrainians c adopt a more ing greater s supporters i