A new solution to Riordan's problem of combinatorial identities classification is presented. An algebgraic characterization of pairs of inverse relations of the Riordan type is given. The use of the ...integral representation approach for generating new types of combinatorial identities is demonstrated. PUBLICATION ABSTRACT
Simple formulae of similar type for the number of quadrics and symmetric forms of modules over local rings are found analytically. This simplification of known formulae of Levchuk and Starikova is ...achieved using integral representation method of combinatorial summation and leads to number-theoretical identities of new type. The problem of algebraic interpretation of new formulae is posed.
Algebra Ershov, Yu. L; Khukhro, Evgenii I; Levchuk, V. M ...
1996, 2017-03-06
eBook
The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or ...workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.
The multidimensional sum with polynomial coefficients is computed with the help of the method of integral representation and computation of combinatorial sums. This sum was obtained in the attempt to ...prove the well known Jacobian conjecture (two-dimensional case). PUBLICATION ABSTRACT
In this article the authors examine the topical nature, & sociological context of Russia within the atmosphere of the global crisis, as well as with the problems stemming from stabilization & ...modernization. The authors commence with a portrait of the nation; highlighting increasing threats of various forms & risks, which are not just connected with the global processes, but as a result of the transformation period of the 20th & 21st centuries. The article then reveals a number of complex issues related to the protection of the Russian socium, not only focusing on economic factors, but all of which effect society as a whole. Hereupon, utilizing several Russian sources; referencing some of the authors' pervious works, ie., "Zhiznennye sily cheloveka" (The Vital Power of People), "Sotsiologicheskaya kontseptsiya zhiznennykh sil cheloveka" (The Sociological Concept of the Vital Power of People), among a list of other domestic commentators, including N. Narochnitskya, & L.V. Sazhina et al. Also, of major concern, & particular to the heart of Russia; the authors focus on how this crisis affects the social-political situation, as well as the growing problem concerning socio-humanities & intellectual resources, a major fulcrum of, for, & in modern Russian society. Adapted from the source document.
The pulse forming networks (PFNs) were developed to provide a 2 kA, 20 MeV linear induction accelerator cells power supply. A PFN's and high-voltage capacitors manufacturing is organized at BINP. The ...PFN is a LC-network with nonuniform impedance made of capacitive sections with a combined paper-film dielectric filled with a castor oil in a polypropylene case. A PFN's isolation is rated at 50 kV charging voltage. The two types of PFNs are developed for 60 and 380 ns flattop duration. They are capable of producing the pulses up to 21 kV, 10 kA with a ±0.5-1% flattop voltage uniformity at a complex inductive-resistive load of the accelerating cell. The PFNs test results in the nominal regime are presented. The PFNs life test results at a higher electrical field in the dielectric are described.
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