Symmetry and Intertwining Operators for the Nonlocal Gross-Pitaevskii Equation

We consider the symmetry properties of an integro-differential multidimensional Gross-Pitaevskii equation with a nonlocal nonlinear (cubic) term in the context of symmetry analysis using the formalism of semiclassical asymptotics. This yields a semiclassically reduced nonlocal Gross-Pitaevskii equation, which can be treated as a nearly linear equation, to determine the principal term of the semiclassical asymptotic solution. Our main result is an approach which allows one to construct a class of symmetry operators for the reduced Gross-Pitaevskii equation. These symmetry operators are determined by linear relations including intertwining operators and additional algebraic conditions. The basic ideas are illustrated with a 1D reduced Gross-Pitaevskii equation. The symmetry operators are found explicitly, and the corresponding families of exact solutions are obtained

Signature Characters for A_2 and B_2

The signatures of the inner product matrices on a Lie algebra's highest weight representation are encoded in the representation's signature character. We show that the signature characters of a finite-dimensional Lie algebra's highest weight representations obey simple difference equations that have a unique solution once appropriate boundary conditions are imposed. We use these results to derive the signature characters of all $A_2$ and $B_2$ highest weight representations. Our results extend, and explain, signature patterns analogous to those observed by Friedan, Qiu and Shenker in the Virasoro algebra's representation theory.Comment: 22 p

Symmetry operators of the two-component Gross–Pitaevskii equation with a Manakov-type nonlocal nonlinearity

We consider an integro-differential 2-component multidimensional Gross-Pitaevskii equation with a Manakov-type cubic nonlocal nonlinearity. In the framework of the WKB-Maslov semiclassical formalism, we obtain a semiclassically reduced 2-component nonlocal Gross- Pitaevskii equation determining the leading term of the semiclassical asymptotic solution. For the reduced Gross-Pitaevskii equation we construct symmetry operators which transform arbitrary solution of the equation into another solution. Constructing the symmetry operator is based on the Cauchy problem solution technique and uses an intertwining operator which connects two solutions of the reduced Gross-Pitaevskii equation. General structure of the symmetry operator is illustrated with a 1D case for which a family of symmetry operators is found explicitly and a set of exact solutions is generated

Surgical treatment for septic complications in patients with duodenal perforation following endoscopic retrograde transpapillary interventions

Background. The most severe clinical cases following transpapillary endoscopic interventions are duodenal perforation with damage to the common bile duct and pancreatic duct, entrance into the abdominal cavity and retroperitoneum the aggressive contents of intestine and the infections. They usually lead to higher mortality.Aim. Evaluation of the optimal management for duodenal perforation in patients who have undergone transpapillary endoscopic interventions.Material and methods.A retrospective analysis of surgical treatment in thirty-two patients with duodenal perforation after transpapillary endoscopic interventions from the year 2007 to 2018 in one center was carried out. Nineteen cases (59.4%) were diagnosed less than 24 hours, 13 (40.6%) – more than 24 hours after injury. Twenty patients had the primary reconstruction of duodenum with various drainage options of injury area. In 19 cases there were a two-stage surgical procedure according the original method: 12 had a primary surgery, 7 were reoperated. Results. After primary reconstruction of duodenum 11 patients (55.0%) had complications, seven (63.6%) – were re-operated, in four we have applied efferent treatments and symptomatic therapy. Three patients (15.8%) died. After two-stage surgery procedure 7 patients (36.8%) had surgical complications, five (26.3%) – were re-operated. Three patients (15.8%) – were died.Conclusion. Primary duodenum reconstruction can be performed if the injury occurred less than 24 hours before surgery. Two-staged surgery is justified in cases with purulent inflammation in abdominum and reproperitoneal cavity because procedure allows reducing mortality from abdominal sepsis

Analysis of spatial humus distribution in virgin and arable Chernozems in the eroding landscapes

A statistical assessment of data on the content and spatial distribution of humus in virgin and arable Chernozems on slopes in the south of the forest-steppe zone of the Central Russian Upland was performed. The greatest number of statistically significant differences between arable and virgin Chernozems was found for the upper soil layer (0–20 cm

The evolution operator of the Hartree-type equation with a quadratic potential

Based on the ideology of the Maslov's complex germ theory, a method has been developed for finding an exact solution of the Cauchy problem for a Hartree-type equation with a quadratic potential in the class of semiclassically concentrated functions. The nonlinear evolution operator has been obtained in explicit form in the class of semiclassically concentrated functions. Parametric families of symmetry operators have been found for the Hartree-type equation. With the help of symmetry operators, families of exact solutions of the equation have been constructed. Exact expressions are obtained for the quasi-energies and their respective states. The Aharonov-Anandan geometric phases are found in explicit form for the quasi-energy states.Comment: 23 pege

Combined reactive‐separation process epoxidation of natural rubber production waste

Предложена  схема  совмещенного  реакционно‐разделительного  про‐ цесса эпоксидирования скрапа натурального каучука в cреде вода‐ксилол. Дана коли‐ чественная и качественная оценка результатов химической модификации.  The A scheme of combined reactive separation process epoxidation of natu- ral rubber scrap in water‐xylene medium was proposed. A quantitative and qualitative as‐ sessment of the results of chemical modification was given.

Competence development as a tool to ensure social projects effective management

Сучасні реалії мають багато викликів для суспільства й економіки, оскільки глобальна економічна криза та внутрішні економічні й політичні проблеми України не сприяють розвитку. На тлі цих викликів актуальною стає підтримка усього населення, прагнення покращення якості життя, зокрема в соціально вразливих верствах. Соціальні проекти в таких умовах покликані підтримувати соціальну стабільність, підвищувати якість життя населення, і, в свою чергу, потребують професійного персоналу. Досліджено суть та особливості соціальних проектів як інструменту підвищення якості життя, забезпечення соціального ефекту від реалізації, а також роль розвитку компетенцій у контексті забезпечення ефективного управління соціальними проектами. Визначено зміст управління соціальними проектами в сучасних умовах як організації, планування, керівництва, координації трудових, фінансових і матеріальнотехнічних ресурсів упродовж проектного циклу, спрямованих на ефективне досягнення їх мети й певний соціальний ефект. Визначено деякі принципи успішних соціальних проектів, що уможливлює підвищення ефективності управління ними. Сформовано певний алгоритм управління соціальними проектами, який передбачає: аналіз проблем соціальної сфери, визначення пріоритетів соціальної сфери, формування структури управління соціальними проектами, розроблення та реалізація соціальних проектів, досягнення результатів і соціального ефекту. Визначено роль компетенцій, зокрема управлінських, в забезпеченні ефективності управління соціальними проектами. На підґрунті визначення поняття «компетенція» розкрито ієрархію компетенцій управлінського персоналу соціального проекту. Визначено ключові компетенції управлінського персоналу соціальних проектів, серед яких лідерство, дисципліна, прогнозування соціального розвитку, емпатія, емоційний інтелект тощо. З урахуванням специфіки управлінських компетенцій сформовано алгоритм їх розвитку з метою забезпечення ефективності управління соціальними проектами в сучасних умовах, що передбачає певні етапи від аналізу наявних компетенцій управлінського персоналу до відповідності нових компетенцій меті і завданням соціального проекту.Modern realities have many challenges for society and the economy, as the global economic crisis and Ukraine's internal economic and political problems are not conducive to development. Against the background of these challenges, the support of the whole population, the desire to improve the quality of life, in particular in socially vulnerable groups, is becoming important. Social projects in such conditions are designed to maintain social stability, improve the quality of life, and in turn require professional staff. The article examines the essence and features of social projects as a tool to improve the quality of life, ensuring the social effect of implementation, as well as the role of competence development in the context of ensuring effective management of social projects. The content of social project management in modern conditions as organization, planning, management, coordination of labor, financial and logistical resources during the project cycle, aimed at effectively achieving their goals and a certain social effect. Some principles of successful social projects are defined, which allows to increase the efficiency of their management. A certain algorithm of social project management has been formed, which includes: analysis of social sphere problems, determination of social sphere priorities, formation of social project management structure, development and implementation of social projects, achievement of results and social effect. The role of competencies, in particular managerial ones, in ensuring the effectiveness of social project management is determined. Based on the definition of the concept of «competence», the hierarchy of management staff competencies of the social project is revealed. The key competencies of the social projects management stafff, including leadership, discipline, forecasting social development, empathy, emotional intelligence, etc. are identified. Taking into account the specifics of managerial competencies, an algorithm for their development was formed to ensure the effectiveness of social project management in modern conditions, which involves certain stages from analysis of existing competencies of management staff to new competencies goals and objectives of the social project

Kazakhstani material testing Tokamak KTM. project status

Creation of cost-efficient and safe fusion reactor will require the development of special structural materials for first wall, blanket, reactor components, which will be operated under conditions of the high heat fluxes, superconducting magnets, plasma heating systems and other elements. The existing tokamaks and other fusion facilities do not currently allow for conduction of specialized researches of plasma-facing structural materials. Kazakhstani Material Testing Tokamak (hereinafter - KTM) provides for a unique opportunity to conduct materials research and testing of separate units and components of fusion reactors..