Linear superposition in nonlinear wave dynamics

We study nonlinear dispersive wave systems described by hyperbolic PDE's in R^{d} and difference equations on the lattice Z^{d}. The systems involve two small parameters: one is the ratio of the slow and the fast time scales, and another one is the ratio of the small and the large space scales. We show that a wide class of such systems, including nonlinear Schrodinger and Maxwell equations, Fermi-Pasta-Ulam model and many other not completely integrable systems, satisfy a superposition principle. The principle essentially states that if a nonlinear evolution of a wave starts initially as a sum of generic wavepackets (defined as almost monochromatic waves), then this wave with a high accuracy remains a sum of separate wavepacket waves undergoing independent nonlinear evolution. The time intervals for which the evolution is considered are long enough to observe fully developed nonlinear phenomena for involved wavepackets. In particular, our approach provides a simple justification for numerically observed effect of almost non-interaction of solitons passing through each other without any recourse to the complete integrability. Our analysis does not rely on any ansatz or common asymptotic expansions with respect to the two small parameters but it uses rather explicit and constructive representation for solutions as functions of the initial data in the form of functional analytic series.Comment: New introduction written, style changed, references added and typos correcte

Far-off-resonant wave interaction in one-dimensional photonic crystals with quadratic nonlinearity

We extend a recently developed Hamiltonian formalism for nonlinear wave interaction processes in spatially periodic dielectric structures to the far-off-resonant regime, and investigate numerically the three-wave resonance conditions in a one-dimensional optical medium with $\chi^{(2)}$ nonlinearity. In particular, we demonstrate that the cascading of nonresonant wave interaction processes generates an effective $\chi^{(3)}$ nonlinear response in these systems. We obtain the corresponding coupling coefficients through appropriate normal form transformations that formally lead to the Zakharov equation for spatially periodic optical media.Comment: 14 pages, 4 figure

Global attractors for strongly damped wave equations with displacement dependent damping and nonlinear source term of critical exponent

In this paper the long time behaviour of the solutions of 3-D strongly damped wave equation is studied. It is shown that the semigroup generated by this equation possesses a global attractor in H_{0}^{1}(\Omega)\times L_{2}(\Omega) and then it is proved that this global attractor is a bounded subset of H^{2}(\Omega)\times H^{2}(\Omega) and also a global attractor in H^{2}(\Omega)\cap H_{0}^{1}(\Omega)\times H_{0}^{1}(\Omega)

КАЧЕСТВО ОБРАЗОВАНИЯ В СВЕТЕ КОМПЕТЕНТНОСТНОЙ ПАРАДИГМЫ РАЗВИТИЯ ВЫСШЕЙ ШКОЛЫ

The problem of ensuring the relevance of educational processes of socio-economic and cultural needs of society has become a serious challenge for traditional approaches in higher education. Higher professional education can no longer remain in a state of substantial isolation from the needs of the labour market and changes in systems of communication in society as a whole, one of the conditions for the effective functioning of the system is the balance of interests of subjects of educational process in diversified innovative environment with a new type of relations between participants. Focus on learning outcomes in the design, implementation and evaluation of educational program quality involves changing paradigm of the educational process as a system. So you need an awareness of the complexity of the competence approach on the basis of which it is planned to improve the functioning of the system of higher education and increase the quality of professional training of graduates. Modernization of Russian education in accordance with these requirements increases the importance of orientation to the process of self-development and realization of personal potential of teachers in professional education in training activities, but this form of organization of educational work, which aims, contents, requirements to get results close to future professional activity. This article describes the features of competence-based paradigm of development of modern higher education; justifies essential changes in objectives, principles, contents, forms and methods of training and assessment of its quality; the factors, due to increased importance of self-actualization, defining the approach to the full development of the potential capabilities and its successful preparation for professional activities.Проблема обеспечения релевантности образовательных процессов социально-экономическим и культурным потребностям общества стала серьезным вызовом для традиционных подходов в высшей школе. Высшее профессиональное образование уже не может оставаться в состоянии значительного отрыва от потребностей рынка труда и изменений в системах коммуникаций в обществе в целом. Одним из условий эффективного функционирования системы является сбалансированность интересов субъектов образовательного процесса в диверсифицированной инновационной среде с новым типом отношений между участниками. Ориентация на результаты обучения при разработке, реализации и оценке качества образовательных программ предполагает смену парадигмы образовательного процесса как системы. Поэтому необходимо осознание многоаспектности компетентностного подхода, на основе которого планируется обеспечить улучшение функционирования системы высшей школы и рост качества профессиональной подготовки выпускников. Модернизация российского образования в соответствии с этими требованиями увеличивает значимость ориентации на процесс саморазвития и реализации личностного потенциала преподавателей – в профессиональной, студентов – в учебной деятельности, но с такой формой организации учебной работы, которая по целям, содержанию, требованиям к получаемым результатам приближена к будущей профессиональной деятельности. В данной статье раскрываются особенности компетентностной парадигмы развития современной высшей школы; обоснованы сущностные изменения, происходящие в целях, принципах, содержании, формах и методах обучения и оценки его качества; исследованы факторы, обусловленные усилением значимости самоактуализации личности, определяющей подход к всестороннему развитию потенциала человека и его успешной подготовке к профессиональной деятельности

ФИНАНСОВАЯ ДОСТУПНОСТЬ ДЛЯ ЛЮДЕЙ С ИНВАЛИДНОСТЬЮ: ОТ НОРМАТИВНО-ПРАВОВОЙ ОСНОВЫ К АДАПТАЦИИ СИСТЕМЫ ПРОФЕССИОНАЛЬНОЙ ПОДГОТОВКИ СПЕЦИАЛИСТОВ ФИНАНСОВОГО РЫНКА

Тhe article is devoted to the formation and development of the system of social protection of disabled people in Russia in terms of providing equal access to financial services. Modern social policy of the country focuses on ensuring equality of rights and opportunities in realization of needs and individual resources of each member of society. The relevance of the topic is explained by the consistently higher number of people with disabilities. People with disabilities as a special social category of consumers of financial services need significant measures of social protection and the adaptation of the classical approach to financial services. In Russia there is a certain system of bodies and institutions of civil society represented by various organizations, whose functions include the protection of the rights of consumers of financial services. It is planned to overcome the shortcomings of the existing supervision in the field of consumer protection by introducing behavioral supervision of the financial services market by the Bank of Russia. The existing legal and regulatory framework includes measures aimed at encouraging financial market participants to take active socially useful actions, which, in our opinion, cannot be effective without removing one of the obstacles to ensuring financial accessibility-the mental barrier caused by the lack of experience of interaction between individual groups of citizens with the financial sector. In this regard, currently in modern Russia there is a need to form a scientific concept of professional training, based on psychology and understanding of the social status of people with disabilities who need full integration into society.Статья посвящена вопросу становления и развития системы социальной защиты инвалидов в России в аспекте предоставления равного доступа к финансовым услугам. Современная социальная политика страны ориентирована на обеспечение равенства прав и возможностей в реализации потребностей и индивидуальных ресурсов каждого члена общества. Актуальность выбранной темы обусловлена неизменно высоким числом лиц с ограниченными возможностями здоровья. Инвалиды как особая социальная категория потребителей финансовых услуг нуждаются в значительных мерах социальной защиты и, как следствие, адаптации классического подхода в финансовом обслуживании. В России сложилась определенная система органов и институтов гражданского общества, представленных различными организациями, в функции которых входит решение вопросов по защите прав потребителей финансовых услуг. Преодолеть недостатки действующего надзора в области защиты прав потребителей планируется с помощью внедрения поведенческого надзора Банком России рынка финансовых услуг. Существующая нормативно-правовая основа включает меры, направленные на стимулирование участников финансового рынка к активным общественно-полезным действиям, которые, на наш взгляд, не могут быть эффективными без устранения одного из препятствий в обеспечении финансовой доступности – ментального барьера, обусловленного недостатком опыта взаимодействия отдельных групп граждан с финансовым сектором. В связи с эти, в настоящее время в современной России назрела необходимость формирования научной концепции профессиональной подготовки специалистов, основанной на психологии и понимании социального статуса людей с ограниченными возможностями здоровья, которые нуждаются в полноценной интеграции в общество

The laminar-turbulent transition in a fibre laser

Studying the transition from a linearly stable coherent laminar state to a highly disordered state of turbulence is conceptually and technically challenging, and of great interest because all pipe and channel flows are of that type. In optics, understanding how a system loses coherence, as spatial size or the strength of excitation increases, is a fundamental problem of practical importance. Here, we report our studies of a fibre laser that operates in both laminar and turbulent regimes. We show that the laminar phase is analogous to a one-dimensional coherent condensate and the onset of turbulence is due to the loss of spatial coherence. Our investigations suggest that the laminar-turbulent transition in the laser is due to condensate destruction by clustering dark and grey solitons. This finding could prove valuable for the design of coherent optical devices as well as systems operating far from thermodynamic equilibrium

Nonlinear beam cleanup in Yb-doped GRIN multimode fiber taper

We demonstrate beam self-cleaning in a tapered Ytterbium-doped graded- index multimode fiber in both active and passive configurations, without accompanying self-phase modulation induced spectral broadening or frequency conversio

Variations in concerns reported on the Patient Concerns Inventory (PCI) in head and neck cancer patients from different health settings across the world

Background: The aim was to collate and contrast patient concerns from a range of different head and neck cancer follow-up clinics around the world. Also, we sought to explore the relationship, if any, between responses to the patient concerns inventory (PCI) and overall quality of life (QOL). Methods: Nineteen units participated with intention of including 100 patients per site as close to a consecutive series as possible in order to minimize selection bias. Results: There were 2136 patients with a median total number of PCI items selected of 5 (2-10). “Fear of the cancer returning” (39%) and “dry mouth” (37%) were most common. Twenty-five percent (524) reported less than good QOL. Conclusion: There was considerable variation between units in the number of items selected and in overall QOL, even after allowing for case-mix variables. There was a strong progressive association between the number of PCI items and QOL