Darboux transformation for classical acoustic spectral problem

We study discrete isospectral symmetries for the classical acoustic spectral problem in spatial dimensions one and two, by developing a Darboux (Moutard) transformation formalism for this problem. The procedure follows the steps, similar to those for the Schr\"{o}dinger operator. However, there is no one-to-one correspondence between the two problems. The technique developed enables one to construct new families of integrable potentials for the acoustic problem, in addition to those already known. The acoustic problem produces a non-linear Harry Dym PDE. Using the technique, we reproduce a pair of simple soliton solutions of this equation. These solutions are further used to construct a new positon solution for this PDE. Furthermore, using the dressing chain approach, we build a modified Harry Dym equation together with its LA-pair. As an application, we construct some singular and non-singular integrable potentials (dielectric permitivity) for the Maxwell equations in a 2D inhomogeneous medium.Comment: 16 pages; keywords Darboux (Moutard) transformation, Classical acoustic spectral problem, Reflexionless potentials, Soliton

Multilevel Clustering Fault Model for IC Manufacture

A hierarchical approach to the construction of compound distributions for process-induced faults in IC manufacture is proposed. Within this framework, the negative binomial distribution is treated as level-1 models. The hierarchical approach to fault distribution offers an integrated picture of how fault density varies from region to region within a wafer, from wafer to wafer within a batch, and so on. A theory of compound-distribution hierarchies is developed by means of generating functions. A study of correlations, which naturally appears in microelectronics due to the batch character of IC manufacture, is proposed. Taking these correlations into account is of significant importance for developing procedures for statistical quality control in IC manufacture. With respect to applications, hierarchies of yield means and yield probability-density functions are considered.Comment: 10 pages, the International Conference "Micro- and Nanoelectronics- 2003" (ICMNE-2003),Zvenigorod, Moscow district, Russia, October 6-10, 200

ОТНОСИТЕЛЬНЫЙ ПОДХОД К ВЫЯВЛЕНИЮ ПРИМЕСЕЙ ПАРАФИНА В ПЧЕЛИНОМ ВОСКЕ

The article deals with modern methods of identifying paraffin wax admixtures in bee wax. It proves the efficiency of the approach which uses a k coefficient as a criteria to show wax content changes in the mixture with paraffin, k coefficient is a ratio of n-alkanes with even and odd number of carbon atoms. The identification of paraffin was conducted with the use of gas chromatography method without the use of an internal standard. The article considers the capacity of using this method to study paraffin - wax mixtures in a wide contents range of components. The difference in k coefficient values for the paraffin content varying from 0 to 10 % (of the mass) amounted to over 10 units. For the studied sample of pure wax the coefficient was 13.0, and for a 10 %o-admixture ofparaffin it was 2.8. The further increase in paraffin content resulted in a less intensive change of the coefficient value - up to the value of 1.5 with the paraffin content of 43 %. The identification margin in this approach can be estimated at less than 3 % of the mass.Розглянуто сучасні методи виявлення домішок парафіну в бджолиному воску. Доведена ефективність підходу, що використовує відношення вмісту н-алканів з парною і непарною кількістю атомів вуглецю, до встановлення наявності та кількісної оцінки вмісту парафіну у воску. Виявлення парафіну проводилося методом газової хроматографії без використання внутрішнього стандарту. Розглянуто можливість дослідження цим способом сумішей парафін-воск у широкому концентраційному діапазоні компонентів

Creation of Supply Chain Management Aimed At Improving the Quality and Accessibility of Municipal Services

Abstract— Supply chain management of regulation are mainly used in the field of municipal services management. Coordination between local governments and other organizations that control the provision of municipal services is poorly developed on the territory of municipal entities. The solution to this problem becomes particularly relevant in the context of creating the supply chain system for the management.  It is quite obvious that a review of approaches and methods in organizing the provision of municipal services is necessary under supply chain strategy. First of all, we implemented the effective supply chain for allocation of resources in the context of the transition to medium-term budget planning, and also to the integration of supply chain mechanism for organizing the provision of municipal services in the existing territorial development management system. This article provides an insight into supply chain management practices in a municipal context. It highlights the status, challenges and way forward for the implementation of supply chain management in a municipal environment

Continuation of the exponentially small transversality for the splitting of separatrices to a whiskered torus with silver ratio

We study the exponentially small splitting of invariant manifolds of whiskered (hyperbolic) tori with two fast frequencies in nearly-integrable Hamiltonian systems whose hyperbolic part is given by a pendulum. We consider a torus whose frequency ratio is the silver number $\Omega=\sqrt{2}-1$. We show that the Poincar\'e-Melnikov method can be applied to establish the existence of 4 transverse homoclinic orbits to the whiskered torus, and provide asymptotic estimates for the tranversality of the splitting whose dependence on the perturbation parameter $\varepsilon$ satisfies a periodicity property. We also prove the continuation of the transversality of the homoclinic orbits for all the sufficiently small values of $\varepsilon$, generalizing the results previously known for the golden number.Comment: 17 pages, 2 figure

LATE PALEOZOIC CONTRASTING MAGMATISM OF THE EASTERN KAAKHEM MAGMATIC AREA (CENTRAL ASIAN OROGENIC BELT)

Based on the isotope-geochronological (zircons, U-Pb method), petrogeochemical, and structural and petrologic data, the following paper provides a detailed description of the characteristics of the Late Paleozoic basic and granitoid magmatism in the eastern part of the Kaakhem magmatic area (Eastern Tuva). During the formation of the Shivey alkaline-granitoid and Chadal gabbroid massifs in the period of 292–283 Ma, there were revealed two stages of contrasting magmatism. The early stage is characterized by the formation of plutonic mingling structures and intermediate rocks. Deformation structures, widespread in the early-mingling rocks, are superimposed and formed in extensional regime. At a later stage, there occurred a sequential intrusion of salic and mafic magmas into the zones of local extension in the early-mingling host rocks. A similar petrogeochemical composition of basic rocks of the early and late mingling indicates that they all formed from enriched magma. Granosyenites and granites are derived from melting of tonalities and metasedimentary rocks with a significant contribution of the mantle component. The simultaneous formation of the Chadal gabbroid and Shivei granitoid massifs took place at the intraplate stage of the development of geological structures of Eastern Tuva in the Late Paleozoic