Computing the Rank Profile Matrix

The row (resp. column) rank profile of a matrix describes the staircase shape of its row (resp. column) echelon form. In an ISSAC'13 paper, we proposed a recursive Gaussian elimination that can compute simultaneously the row and column rank profiles of a matrix as well as those of all of its leading sub-matrices, in the same time as state of the art Gaussian elimination algorithms. Here we first study the conditions making a Gaus-sian elimination algorithm reveal this information. Therefore, we propose the definition of a new matrix invariant, the rank profile matrix, summarizing all information on the row and column rank profiles of all the leading sub-matrices. We also explore the conditions for a Gaussian elimination algorithm to compute all or part of this invariant, through the corresponding PLUQ decomposition. As a consequence, we show that the classical iterative CUP decomposition algorithm can actually be adapted to compute the rank profile matrix. Used, in a Crout variant, as a base-case to our ISSAC'13 implementation, it delivers a significant improvement in efficiency. Second, the row (resp. column) echelon form of a matrix are usually computed via different dedicated triangular decompositions. We show here that, from some PLUQ decompositions, it is possible to recover the row and column echelon forms of a matrix and of any of its leading sub-matrices thanks to an elementary post-processing algorithm

Scientific, institutional and personal rivalries among Soviet geographers in the late Stalin era

Scientific, institutional and personal rivalries between three key centres of geographical research and scholarship (the Academy of Sciences Institute of Geography and the Faculties of Geography at Moscow and Leningrad State Universities) are surveyed for the period from 1945 to the early 1950s. It is argued that the debates and rivalries between members of the three institutions appear to have been motivated by a variety of scientific, ideological, institutional and personal factors, but that genuine scientific disagreements were at least as important as political and ideological factors in influencing the course of the debates and in determining their final outcome

NMR line width with allowance for the distribution of correlation times

Mathematical expressions have been derived for NMR line width on the basis of the general theory of magnetic resonance absorption described by Kubo-Tomita. Allowance is made for the distribution of correlation times of molecular motion in polymers described by the curves of Fuoss-Kirkwood, Cole-Cole, Cole-Davidson and Gavrilyaka-Negami. © 1974

Comparison of seismic signatures of flares obtained by SOHO/MDI and GONG instruments

The first observations of seismic responses to solar flares were carried out using time-distance (TD) and holography techniques applied to SOHO/MDI Dopplergrams obtained from space and un-affected by terrestrial atmospheric disturbances. However, the ground-based network GONG is potentially a very valuable source of sunquake observations, especially in cases where space observations are unavailable. In this paper we present updated technique for pre-processing of GONG observations for application of subjacent vantage holography. Using this method and TD diagrams we investigate several sunquakes observed in association with M and X-class solar flares and compare the outcomes with those reported earlier using MDI data. In both GONG and MDI datasets, for the first time, we also detect the TD ridge associated with the September 9, 2001 flare. Our results show reassuringly positive identification of sunquakes from GONG data that can provide further information about the physics of seismic processes associated with solar flares.Comment: 19 pages, 6 figures, accepted to Astrophysical Journa

Optimizing multi-inserts in routing problems with constraints

We consider a problem of sequential traversal of megalopolises (nonempty finite sets) with travel cost functions depending on the set of pending tasks and precedence constraints. Its formulation is aimed at engineering problems in fission power generation connected with minimizing the exposure of staff to radiation and in machine engineering (routing of a CNC sheet cutting machine's tool). This discrete optimization problem is assumed to be sufficiently large-scale to necessitate the use of heuristics. We consider a procedure of local improvement for heuristics through a successive application of optimizing multi-inserts-finite disjoint sets of inserts. Each insert is assumed to be optimized by means of a broadly understood dynamic programming procedure. We show that in an "additive" routing problem of this kind (with precedence constraints and complex travel cost functions) the result's improvements are also aggregated additively. The proposed construction admits a parallel implementation for multiprocessor systems; in this case, the inserts are distributed to computational nodes and formed in an independent way. © 2018 Udmurt State University.All Rights Reserved.Funding. This work was supported by the Russian Science Foundation (project no. 14–11–00109)

Принцип достоверности как методологический императив судебно-экспертной деятельности

The author reflects on whether validity can be considered both a principle of law and a functional principle of forensic expert activity. Disclosing the methodological significance of validity, which is yet to be fully and consistently incorporated in the procedural law, the author concludes that validity is understood and applied by the Russian justice and expert community precisely as a principle of law, an imperative indicator of the quality of forensic science for all its procedural forms in the legal process.Автор размышляет о том, можно ли считать достоверность одновременно и принципом права, и функциональным принципом судебно-экспертной деятельности. Раскрывая методологическое значение достоверности, которое не получило еще полного и последовательного законодательного закрепления в процессуальном праве, автор приходит к выводу, что фактически достоверность понимается и применяется российским правосудием и экспертным сообществом именно как принцип права, как императивный показатель качества судебно-экспертной деятельности всех ее процессуальных форм судопроизводства

Free nuclear induction in amorphous polymers and viscous liquids above the glass temperature

An experimental and theoretical study has been made of the temperature dependence of the form of the free induction signal (FIS) using PS and a low molecular viscous liquid, dioctylphthalate, as examples. A relationship for the form of the FIS is obtained on the basis of a hypothesis about the existence, in any viscous system, of random magnetic fields which, over a wide temperature range, are not averaged to zero by movement. © 1978

ФИЛОСОФСКО-ТЕОРЕТИЧЕСКИЕ ОСНОВЫ ПРИНЦИПА ДОСТОВЕРНОСТИ СУДЕБНО-ЭКСПЕРТНОЙ ДЕЯТЕЛЬНОСТИ

The author reflects on the philosophical problem of reliability of expert knowledge, not only as a procedural attribute of judicial proceedings, but primarily as a functional principle in building the entire system of forensic expert activity.Автор размышляет над философской проблемой достоверности экспертного знания не только как процессуального атрибута судопроизводства, но прежде всего как функционального принципа построения всей системы судебно-экспертной деятельности