bluuebunny/crossref_metadata_2025 huggingface dataset:
Practice-Oriented Strategies of Student Immersion in the Artistic World of Musical Compositions
Authors: Reva Valentin P.
Published: November 2019

Music perception is a multi-level system of creative activity carried out in a unity of emotional and rational, collective and individual, physical and spiritual, conscious and intuitive, linear and non-linear mechanisms and actions. When a person perceives music, he cognizes not only the content, but also himself, realizes personal potential. In the article practice-oriented strategies for immersion into the artistic world of musical works: intonational-plastic, intonational-genre, intonational-contemplative, intonational-stylistic were grounded and experimentally tested. Covering a wide area of music content, they can be added, improved are considered as the basic foundations of the education of music perception, on which students can rely in their lives. None of the stated approaches gave direct instructions on what specifically needs to be heard in a piece of music. The methods of unobtrusive targeting of attention to the disclosure of musical content, its projection on life experience (speech, physical, kinesthetic, somatic, plastic, gestural) were prevailed. Incomparable results of perception arise in situations of subject-visual or emotional-figurative disclosure of the content of music, retelling it by a teacher or establishing links with students’ intonation experience (prototypes of speech, bodily movements); while listening to music, or its active experience, suspended, immersed in the emotionally saturated world of musical images. Attempts to overcome the spiritual and physical level of perception, to approach the content of music, bypassing these processes, do not lead to any meaningful pedagogical results.
Conceptual Foundations of the Academic Course “Traditional Music in Culture of Peoples of the World”
Authors: Ovchinnikova Yulia S.
Published: November 2019

In Russia the teaching of traditional music of peoples of the world is realized in higher education institutions with specialization in musicology, performing art and in solitary cases in music pedagogics. The actual dialogue between sound and musical traditions and acquisition of musical polylingualism of the world by nonprofessional musicians shows a clear need for including into the variable component of higher humanitarian education a subject focused on complex, interdisciplinary study of world music with orientation on development of intercultural competence of future specialists. The author generalizes her 12 years’ experience in teaching the course “Traditional music in culture of peoples of the world” at the Faculty of Foreign Languages and Area Studies of Lomonosov Moscow State University for students of the following educational programs: “Linguistics and Intercultural Communication”, “Area Studies and International Relations”, “Culture Studies”. Also the experience of teaching this course as interfaculty subject (2019) is recognized. The theoretical foundations of the course, culture study approach to the world music, pedagogical technics, music and cultural content, results of the work are regarded.
Technological Terms of Monitoring the Readiness of Musician Students for Artistic-Interpretational Activities
Authors: Molostvova Irina Ye.
Published: November 2019

The article describes the requirements for a man of the new time, expressed in the need for his personal self-development, the full disclosure of creative potential. The specificity of the professional activity of a teacher-musician as a subject of culture capable of establishing a spiritual level interaction with students is determined, which is based on the actualization of the creative self-consciousness of all subjects of the educational process. The author considers the possibility of the technologization of the process of mastering the teacher-musician artistic and interpretative activities as a necessary component of his professional training, starting with the development of diagnostics of the success of mastering it. For this purpose, the concept of “artistic and interpretational competence of a teacher-musician” is introduced, and the stages of mastering it are defined: motivational-indicative, procedural-activity-related, and effective-corrective. The article proposes a detailed description of these stages in terms of content and diagnosis of the achievement of the appropriate level. In accordance with this, to diagnose the process of forming artistic and interpretative competence, the author proposes a level principle of diagnosis and an exemplary system of tasks that reveal knowledge and skills that are characterized as standard, key or leading.
To the History of the National Programmes of Music Therapy: V. M. Bekhterev – A Multidisciplinary Approach in Science and Education
Authors: Orlova Ekaterina M.
Published: November 2019

The article analyzes the valuable, organizational and scientific approaches by V. M. Bekhterev to the issues related to the study of the influence of music on the somatic and mental sphere of man. The versatile problems of researches of school of the scientist in this direction characterizing its scientific programme, historical and philosophical and theoretical and methodological bases are presented. Of particular interest are the little-known archival documents related to the creation of a special Commission to study the influence of music and the activities of the State Institute of music education, which was part of the Psychoneurological Academy established by V. M. Bekhterev. An attempt is made to comprehend the value of the personal potential of the scientist in the development of the domestic musical-therapeutic, musical-psychological and musical-pedagogical knowledge from the perspective of the present time, from the point of view of modern problems of science and education. It is shown that the contributions of the scientist in this direction are to direct methodology of these researches on the materialistic base, to attract experimental methods of research of musical influence, to involve the synthesis of natural science and social and humanitarian disciplines with musicology, to uphold the principles of complexity and interdisciplinary, unity of theory, experiment and practice, individual approach to the study of the influence of music on the person in medical and educational contexts.
The Holizm and Organic Philosophy in Modern Muzykologiya: Search of New Relevant Methodology
Authors: Koptelova Tatyana I.
Published: November 2019

Object of research is the Philosophical Paradigm of modern methodology of pedagogics of music education. Methodological opportunities of a Holism and Organic Philosophy are analyzed; features of their application in a musicology. At the same time the Organic Philosophy is considered as the system of knowledge and also the intellectual tradition focusing attention on functional integrity of objects of reality and laws of wildlife. It is about need of studying of music as the phenomenon of spiritual culture assuming unity of human mind, imagination and experience. Scientific potential of Organic Philosophy which allows to investigate all set of the national Cultural Paradigms reflected in modern musical art is realized and to find ways of overcoming such difficulty as the irrational maintenance of music. Contradictions of a Holism and ways of their permission in Organic Philosophy are investigated. The expediency of the appeal to Organic Philosophy is proved in the sphere of formation of new methodology of pedagogics of music education which main task is development of creative identity and disclosure of performing talent. In this regard the integrating potential of Organic Philosophy, her ability through a phenomenon of life to connect all available and inaccessible to human consciousness is shown in the scientific article. The Organic Philosophy allows art to speak about science not only language of artistic image, but also from a position of conscious feeling (an altruistic love).
History and Theory of Musical Writing as an Academic Discipline
Authors: Englin Stanislav E.
Published: November 2019

The article outlines the reasons why the modern musicologist must be competent in matters of history and theory of a notation. Results of research of the systems of graphical writing of music are proposed to be used in educational purposes. This is due to the fact that the notation is reflected some of the most important features of the musical thinking of the era of its formation. Therefore, knowledge of specific types of music semiography is a tool of obtaining objective data on the deep principles of music of the specific historical period (time of creation and at least, the initial existence of this notation). The interconnected subjects analyze the study of the notation and the basic tasks of musicology. Introduction of training course of music semiography be seen in the light of the multidimensional problem of music education and science. It is concluded that the implementation of educational subject “History and theory of musical writing” provided the coordination of efforts of scientists aimed at creating a modern concept of semiography, contributes to the attainment the essence of musical writing on the basis of generalization of the results of semiography studies. In turn, this will be a significant step on the path of knowledge absolutely patterns, reflected in the variety notations.
The efficacy and safety of a proprietary onion-pumpkin extract (OPtain120) on blood pressure: an open-label study
Authors: Yoshinari Orie , Udani Jay , Moriyama Hiroyoshi , Shiojima Yoshiaki , Chien Xiaoming
Published: December 2019

Background: Nutraceuticals and functional foods are increasingly being used to help manage hypertension. Treatment with either pumpkin or onion can significantly lower systolic and diastolic blood pressure in animal studies. Traditionally, pumpkin has been used to support healthy blood pressure, glucose tolerance and lipid levels. Onion contains high levels of flavonoids, including quercetin, which decreases blood pressure and promotes restoration of healthy endothelial function. However, human trials on these food sources are limited, and the combined effects of pumpkin and onion have not been examined yet.Objective: We performed an open-label clinical study to evaluate the effects of a proprietary onion-pumpkin extract (OPtain120) on systolic and diastolic blood pressure.Methods: Healthy adults with systolic blood pressure (SBP) and diastolic blood pressure (DBP) in the elevated range of 140-159 and 80-90 mmHg, respectively, were enrolled in this study. Subjects consumed one capsule of onion-pumpkin extract twice daily for 12 weeks. Daily Home Blood Pressure Measurement (HBPM) was taken upon waking and before bed. Office Blood Pressure Measurement (OBPM) was taken in-clinic at Week 0, 6, and 12.Results:  52 subjects were screened and 12 were enrolled in the study, with a total of 10 subjects completing the study. Systolic HBPM taken before bed demonstrated a statistically significant reduction from baseline (147.23 mmHg) to Week 12 (138.14 mmHg), representing a reduction of 9.09 mmHg (6.17%, p=0.021). Diastolic HBPM taken before bed demonstrated a decrease of 4.06 mmHg (4.46%, p=0.085), a significant reduction from baseline (91.07 mmHg) at Week 12 (87.02 mmHg). Non-statistically significant reductions were seen in the early morning Systolic (3.14%) and Diastolic (2.57%) HBPM and in the Systolic (1.36%) OBPM.Conclusion: OPtain120 was safely consumed over a 12-week period. OPtain120 appears to be effective in lowering Systolic Blood Pressure at bedtime in healthy individuals with slightly elevated blood pressure. This study suggests that onion-pumpkin extract may aid individuals who manage their cardiovascular risk factors with diet and lifestyle.Key Words: pumpkin, onion, extract, blood pressure
On the asymptotic behavior of transmission thin shell problems
Authors: Merabet I. , Nicaise S. , Chacha D.A.
Published: November 2019

In this paper we study the asymptotic behavior of two-dimensional transmission problems for the linear Koiter model of an elastic multi-structure composed of two thin shells with the same thickness ε<<1. Contrary to the case of membrane shells, the formal limit problem, i.e., for ε=0, fails to give a convenient approximate solution, as the limit problem is ill posed. An appropriate dilation leads to an equivalent problem, for which we prove its strong convergence towards some finite limit.
Numerical microlocal analysis of 2-D noisy harmonic plane and circular waves
Authors: Benamou J.-D. , Collino F. , Marmorat S.
Published: November 2019

We present a mathematical and numerical analysis of the stability and accuracy of the NMLA (Numerical MicroLocal Analysis) method [J. Comput. Phys. 199(2) (2004), 717–741] and its discretization. We restrict to homogeneous space and focus on the two simplest cases: (1) Noisy plane wave packets, (2) Noisy point source solutions. A stability result is obtained through the introduction of a new “impedance” observable. The analysis of the point source case leads to a modified second order (curvature dependent) correction of the algorithm. Since NMLA is local, this second order improved version can be applied to general data (heterogeneous media). See [J. Comput. Phys. 231(14) (2012), 4643–4661] for a an application to a source discovery inverse problem.
First-order expansion for the Dirichlet eigenvalues of an elliptic system with oscillating coefficients
Authors: Prange Christophe
Published: November 2019

This paper is concerned with the homogenization of the Dirichlet eigenvalue problem, posed in a bounded domain Ω⊂R2, for a vectorial elliptic operator −∇·Aε(·)∇ with ε-periodic coefficients. We analyse the asymptotics of the eigenvalues λε,k when ε→0, the mode k being fixed. A first-order asymptotic expansion is proved for λε,k in the case when Ω is either a smooth uniformly convex domain, or a convex polygonal domain with sides of slopes satisfying a small divisors assumption. Our results extend those of Moskow and Vogelius in Proc. Roy. Soc. Edinburgh Sect. A 127(6) (1997), 1263–1299 restricted to scalar operators and convex polygonal domains with sides of rational slopes. We take advantage of the recent progress due to Gérard-Varet and Masmoudi [J. Eur. Math. Soc. 13 (2011), 1477–1503; Acta Math. 209 (2012), 133–178] in the homogenization of boundary layer type systems.
The second grade fluid flow problem in an infinite pipe
Authors: Klovienė N. , Pileckas K.
Published: November 2019

The non-stationary equations describing the motion of the second grade fluid are studied in an infinite three-dimensional pipe of arbitrary cross-section. For sufficiently small data the existence of the unique Poiseuille type solution having a given time-dependent flow rate (flux) is proved. The velocity field U has all three components. However, we show that components U1, U2 are secondary in comparison with the axial velocity U3.
High-frequency uniform asymptotics for the Helmholtz equation in a quarter-plane
Authors: Huang Min-Hai , Zhao Yu-Qiu
Published: November 2019

We demonstrate an approach to derive uniform and point-wise asymptotic formulas based on Fokas' transform method. To this aim, we study the high-frequency uniform asymptotics for the solution of the Helmholtz equation, in a quarter plane and subject to a specific Neumann condition. The analysis is based on the integral representation of the solution derived via Fokas' transform method. In the case of piecewise constant boundary data, full point-wise asymptotic expansions of the solution are obtained by using the method of steepest descents for definite integrals. A uniform asymptotic expansion, holding in the whole quadrant, is also derived in terms of the complementary error function. The uniform expansion exhibits smooth transitions across certain critical vertical lines, along which the point-wise asymptotic approximations have jumps.
Stabilization by switching time-delay
Authors: Ammari Kaïs , Nicaise Serge , Pignotti Cristina
Published: November 2019

In this paper we consider some stabilization problems for the wave equation with switching time-delay. We prove exponential stability results for appropriate damping coefficients. The proof of the main results is based on D'Alembert formula, observability inequality and some energy estimates. More general problems, like the Petrovsky system, are also discussed.
Vorticity layers of the 2D Navier–Stokes equations with a slip type boundary condition
Authors: Gie Gung-Min , Jung Chang-Yeol
Published: November 2019

We study the asymptotic behavior, at small viscosity ε, of the Navier–Stokes equations in a 2D curved domain. The Navier–Stokes equations are supplemented with the slip boundary condition, which is a special case of the Navier friction boundary condition where the friction coefficient is equal to two times the curvature on the boundary. We construct an artificial function, which is called a corrector, to balance the discrepancy on the boundary of the Navier–Stokes and Euler vorticities. Then, performing the error analysis on the corrected difference of the Navier–Stokes and Euler vorticity equations, we prove convergence results in the L2 norm in space uniformly in time, and in the norm of H1 in space and L2 in time with rates of order ε3/4 and ε1/4, respectively. In addition, using the smallness of the corrector, we obtain the convergence of the Navier–Stokes solution to the Euler solution in the H1 norm uniformly in time with rate of order ε1/4.
A rigorous derivation of the time-dependent Reynolds equation
Authors: Fabricius John , Koroleva Yulia , Wall Peter
Published: November 2019

We study the asymptotic behavior of solutions of the evolution Stokes equation in a thin three-dimensional domain bounded by two moving surfaces in the limit as the distance between the surfaces approaches zero. Using only a priori estimates and compactness it is rigorously verified that the limit velocity field and pressure are governed by the time-dependent Reynolds equation.
Dispersion estimates for 2D Dirac equation
Authors: Kopylova E.A.
Published: November 2019

We obtain a dispersion long-time decay in weighted norms for solutions of the 2D Dirac equation with generic potentials. For high energy component we develop the approach of Boussaid relying on the Mourre estimates and the minimal escape velocity estimates of Hunziker, Sigal and Soffer. For the low energy component we obtain the asymptotics of the resolvent near the thresholds in the nonsingular case and apply 2D version of Jensen–Kato lemma on “one-and-half partial integration”.

The results can be applied to the study of asymptotic stability and scattering of solitons for nonlinear 2D Dirac equations.
Uniform stability of (a,k)-regularized families
Authors: Lizama Carlos , Miana Pedro J. , Poblete Felipe
Published: November 2019

In this article we study the uniform stability of an (a,k)-regularized family {S(t)}t≥0 generated by a closed operator A. We give sufficient conditions, on the scalar kernels a, k and the operator A, to ensure the uniform stability of the family {S(t)}t≥0 in Hilbert spaces. Our main result is a generalization of Theorem 1 in [Proc. Amer. Math. Soc. 132(1) (2004), 175–181], concerning the stability of resolvent families, and can be seen as a substantial generalization of the Gearhart–Greiner–Prüss characterization of exponential stability for strongly continuous semigroups.
The Oberbeck–Boussinesq approximation in critical spaces
Authors: Danchin Raphaël , He Lingbing
Published: November 2019

In this paper we study the validity of the so-called Oberbeck–Boussinesq approximation for compressible viscous perfect gases in the whole three-dimensional space. Both the cases of fluids with positive heat conductivity and zero conductivity are considered. For small perturbations of a constant equilibrium, we establish the global existence of unique strong solutions in a critical regularity functional framework. Next, taking advantage of Strichartz estimates for the associated system of acoustic waves, and of uniform estimates with respect to the Mach number, we obtain all-time convergence to the Boussinesq system with a explicit decay rate.
Variational resolution for some general classes of nonlinear evolutions. Part I
Authors: Poliakovsky Arkady
Published: November 2019

We develop a variational technique for some wide classes of nonlinear evolutions. The novelty here is that we derive the main information directly from the corresponding Euler–Lagrange equations. In particular, we prove that not only the minimizer of the appropriate energy functional but also any critical point must be a solution of the corresponding evolutional system.
Global solution to the drift-diffusion-Poisson system for semiconductors with nonlinear recombination-generation rate
Authors: Wu Hao , Jiang Jie
Published: November 2019

In this paper, we study the Cauchy problem of a time-dependent drift-diffusion-Poisson system for semiconductors. Existence and uniqueness of global weak solutions are proven for the system with a higher-order nonlinear recombination-generation rate R. We also show that the global weak solution will converge to a unique equilibrium as time tends to infinity.
From two-fluid Euler–Poisson equations to one-fluid Euler equations
Authors: Li Yachun , Peng Yue-Jun , Wang Ya-Guang
Published: November 2019

We consider quasi-neutral limits in two-fluid isentropic Euler–Poisson equations arising in the modeling of unmagnetized plasmas and semiconductors. For periodic smooth solutions, we justify an asymptotic expansion in a time interval independent of the Debye length. This implies the convergence of the equations to compressible Euler equations. The proof is based on energy estimates for symmetrizable hyperbolic equations and on the exploration of the coupling between the Euler equations and the Poisson equation.
Evolution parabolic inequalities for pseudo-monotone operators
Authors: Pham Phuong Nguyen
Published: November 2019

In this article, we prove the existence of weak solutions of variational parabolic inequalities with pseudo-monotonicity and nonzero initial data using finite differences in time.
Some properties of solutions of some semilinear elliptic singular problems and applications to the G-convergence
Authors: Boccardo Lucio , Casado-Díaz Juan
Published: November 2019

This paper concerns some semilinear elliptic singular problems. The aim is twofold: the study of some properties of the solutions and the study of the G-convergence.
Long-time behavior of bounded global solutions to systems of nonlinear integro-differential equations
Authors: Sánchez Justino , Vergara Vicente
Published: November 2019

We study the long-time behavior of bounded solutions of certain systems of nonlinear integro-differential equations, including differential equations of fractional order between 1 and 2. We obtain appropriate Lyapunov functions for this system and prove that any bounded global solution converges to a steady state if the nonlinear potential E occurring in the system satisfies the Łojasiewicz inequality.
Exponential stability for linear evolutionary equations
Authors: Trostorff Sascha
Published: November 2019

We give an approach to exponential stability within the framework of evolutionary equations due to Picard [Math. Methods Appl. Sci. 32(14) (2009), 1768–1803]. We derive sufficient conditions for exponential stability in terms of the material law operator which is defined via an analytic and bounded operator-valued function and give an estimate for the expected decay rate. The results are illustrated by three examples: differential-algebraic equations, partial differential equations with finite delay and parabolic integro-differential equations.
Asymptotics of eigenstates of elliptic problems with mixed boundary data on domains tending to infinity
Authors: Chipot Michel , Roy Prosenjit , Shafrir Itai
Published: November 2019

We analyze the asymptotic behavior of eigenvalues and eigenfunctions of an elliptic operator with mixed boundary conditions on cylindrical domains when the length of the cylinder goes to infinity. We identify the correct limiting problem and show in particular, that in general the limiting behavior is very different from the one for the Dirichlet boundary conditions.
Large-time behavior of small solutions of a two-dimensional semilinear elliptic equation with a dynamical boundary condition
Authors: Fila Marek , Ishige Kazuhiro , Kawakami Tatsuki
Published: November 2019

We consider the following initial value problem for a two-dimensional semilinear elliptic equation with a dynamical boundary condition:

−Δu=up, x∈R2+, t>0,

∂tu+∂νu=0, x∈∂R2+, t>0,

u(x,0)=φ(x1)≥0, x=(x1,0)∈∂R2+,

where u=u(x,t), ∂t:=∂/∂t, ∂ν:=−∂/∂x2, R2+:={(x1,x2): x1∈R,x2>0} and p>1. We show that small solutions behave asymptotically like suitable multiples of the Poisson kernel. This is an extension of previous results of the authors of this paper to the two-dimensional case.
Approximative composition of Wick symbols and applications to the time dependent Hartree–Fock equation
Authors: Amour L. , Khodja M. , Nourrigat J.
Published: November 2019

In this paper, we derive a semiclassical asymptotic expansion of the Wick symbol, for the product of two operators, when the first one is a Weyl pseudodifferential operator in the class of Calderón–Vaillancourt and the second one is trace class in L2(Rn). This result is extended in the direction of Schatten classes. We also report a corresponding result in the context of anti-Wick operators. The Wick expansion is used to derive an equation satisfied, up to an arbitrary small error term, by the Wick symbol of density operators governed by the time dependent Hartree–Fock (TDHF) equation. Still in the situation of the TDHF dynamics, we prove the finiteness of the Ehrenfest time.
Small mass asymptotics of a charged particle in a variable magnetic field
Authors: Lee Jong Jun
Published: November 2019

We consider small mass asymptotics of the motion of a charged particle in a noisy force field combined with a variable magnetic field. The Smoluchowski–Kramers approximation does not hold in this case. We show that after a regularization of noise, a Smoluchowski–Kramers type approximation works.
Asymptotic analysis for Schrödinger Hamiltonians via Birkhoff–Gustavson normal form
Authors: Ghomari Kaoutar , Messirdi Bekkai , Vũ Ngọc San
Published: November 2019

This article reviews the Birkhoff–Gustavson normal form theorem (BGNF) near an equilibrium point of a quantum Hamiltonian. The BGNF process is thereafter used to investigate the spectrum of Schrödinger operators in the 1:1, 1:2 and 1:3 resonances. A computer program is proposed to compute the coefficients of the BGNF up to any order.
Crack propagation in anisotropic composite structures
Authors: Nazarov S.A. , Specovius-Neugebauer M. , Steigemann M.
Published: November 2019

A crack approaching a material interface between two elastic materials may stop or may advance by either penetrating the interface or deflecting into the interface (cf. N.Y. He and J.W. Hutchinson, Int. J. Solids Struct. 25 (1989), 1053–1067). Mathematical models for crack path prediction are based on the asymptotic behavior near the crack tip. In this work, an idea to compute the asymptotic expansion of the displacement field for structures composed of two dissimilar elastic anisotropic materials is shown, if the crack impinges the material interface. In contrast to the well-known case of isotropic materials, logarithmic terms can appear in the asymptotic decomposition of the displacement field in anisotropic composites. Based on this results, the energy release rate is calculated for different scenarios of crack propagation in composite structures.
Random homogenization for a fluid flow through a membrane
Authors: Maris F. , Vernescu B.
Published: November 2019

Effective boundary conditions for the flow of a viscous fluid across randomly leaky permeable membranes are studied. Threshold leak conditions of subgradient type, introduced by Fujita [Res. Inst. Math. Sci. Kokyuroku 888 (1994), 199–216, J. Comp. Appl. Math. 149(1) (2002), 56–79], are considered on the randomly distributed solid part of the membrane. The effective conditions are of subgradient type with an effective yield limit, in the case of a densely distributed solid part, or of Navier slip type, in the critical case; in the dilute case the tangential slip cancels, whereas the normal velocity and stress are continuous. We thus extend our results [Complex Variables and Elliptic Equations 57(2–4) (2012), 437–453], from the periodic permeable membrane, to a randomly permeable membrane model.
Homogenization of diffusion–deformation in dual-porous medium with discontinuity interfaces
Authors: Griso Georges , Rohan Eduard
Published: November 2019

Models of homogenized fluid-saturated dual-porous media with weak, or strong discontinuity interfaces (resembling fissures) are derived using the periodic unfolding method. Stress discontinuities at the interfaces are admitted, requesting further restrictions on the applied external forces. The limit models, obtained by a rigorous asymptotic analysis, reflect some non-local effects inherited from the microstructural interactions. In view of obtaining the a priori estimates, standard approaches based on smooth extensions, well fitted for perforated or high-contrast media, cannot be adopted for fissured domains. Therefore, a new approach is developed which enables to control the norm of some “off-diagonal” terms which in the model equations are generated by the interfaces and are not involved in the energy-related expressions.
On the wave operator for dissipative potentials with small imaginary part
Authors: Wang Xue Ping , Zhu Lu
Published: November 2019

We determine the range of the incoming wave operator for the pair of operators (−Δ,−Δ+V1(x)−iεV2(x)) on L2(Rn) under the conditions n≥3 and 0 is a regular point of −Δ+V1, V2≥0 and ε>0 is small enough. This implies that the dissipative scattering operator is bijective.
Improved decay rates for solutions for a multidimensional generalized Benjamin–Bona–Mahony equation
Authors: Said-Houari Belkacem
Published: November 2019

In this paper, we study the decay rates of solutions for the generalized Benjamin–Bona–Mahony equation in multi-dimensional space. For initial data in some L1-weighted spaces, we prove faster decay rates of the solutions. More precisely, using the Fourier transform and the energy method, we show the global existence and the convergence rates of the solutions under the smallness assumption on the initial data and we give better decay rates of the solutions. This result improves early works in J. Differential Equations 158(2) (1999), 314–340 and Nonlinear Anal. 75(7) (2012), 3385–3392.
Magneto-resistance in three-dimensional composites
Authors: Briane Marc , Pater Laurent
Published: November 2019

In this paper we study the magneto-resistance, i.e. the second-order term of the resistivity perturbed by a low magnetic field, of a three-dimensional composite material. Extending the two-dimensional periodic framework of [Mathematical Models and Methods in Applied Sciences 20(7) (2010), 1161–1177], it is proved through a H-convergence approach that the dissipation energy induced by the effective magneto-resistance is greater or equal to the average of the dissipation energy induced by the magneto-resistance in each phase of the composite. This inequality validates for a composite material the Kohler law which is known for a homogeneous conductor. The case of equality is shown to be very sensitive to the magnetic field orientation. We illustrate the result with layered and columnar periodic structures.
Asymptotic controllability and asymptotic synchronization for a coupled system of wave equations with Dirichlet boundary controls
Authors: Li Tatsien , Rao Bopeng
Published: November 2019

In this paper, the asymptotic null controllability and various kinds of asymptotic synchronization, as some sorts of weakened controllability and synchronization, are introduced and studied for a coupled system of wave equations with Dirichlet boundary controls. Equivalent properties of observability are established and several examples of explanation are also given.
On the rate of convergence of solutions in domain with random multilevel oscillating boundary
Authors: Chechkin G.A. , D'Apice C. , De Maio U. , Piatnitski A.L.
Published: November 2019

In the paper we deal with the homogenization problem for the Poisson equation in a singularly perturbed domain with multilevel oscillating boundary. This domain consists of the body, a large number of thin periodically situated cylinders joining to the body through thin random transmission zone with rapidly oscillating boundary. Inhomogeneous Fourier boundary conditions with perturbed coefficients are set on the boundaries of the thin cylinders and on the boundary of the transmission zone. We prove the homogenization theorems. Moreover we derive estimates of deviation of the solution to initial problem from the solution to the homogenized problem in different cases.

It appears that depending on small parameters in Fourier boundary conditions of initial problem one can obtain Dirichlet, Neumann or Fourier boundary conditions in the homogenized problem. We estimate the convergence of solutions in these three cases.
A phase transition model for the helium supercooling
Authors: Bonetti Elena , Frémond Michel
Published: November 2019

We build a predictive theory for the evolution of mixture of helium and supercooled helium at low temperature. The absolute temperature θ and the volume fraction β of helium, which is dominant at temperature larger than the phase change temperature, are the state quantities. The predictive theory accounts for local interactions at the microscopic level, involving the gradient of β. The nonlinear heat flux in the supercooled phase results from a Norton–Hoff potential. We prove that the resulting set of partial differential equations has solutions within a convenient analytical frame.
Energy decay to Timoshenko's system with thermoelasticity of type III
Authors: Fatori L.H. , Muñoz Rivera J.E. , Nunes Monteiro R.
Published: November 2019

We consider the thermoelastic beam system when the oscillations are defined by the Timoshenko's model and the heat conduction is given by Green and Naghdi theories. Our main result is that the corresponding semigroup is exponentially stable if and only if the wave speeds associated to the hyperbolic part of the system are equal. In the case of lack of exponential stability we show that the solution decays polynomially and we prove that the rate of decay is optimal.
Random perturbations of dynamical systems with reflecting boundary and corresponding PDE with a small parameter
Authors: Hu Wenqing , Tcheuko Lucas
Published: November 2019

We study the asymptotic behavior of a diffusion process with small diffusion in a domain D. This process is reflected at ∂D with respect to a co-normal direction pointing inside D. Our asymptotic result is used to study the long time behavior of the solution of the corresponding parabolic PDE with Neumann boundary condition.
Large deviations for multi-scale Markovian switching systems with a small diffusion
Authors: He Qi , Yin G.
Published: November 2019

This work develops asymptotic properties of randomly switching and time inhomogeneous dynamic systems under Brownian perturbation with a small diffusion. The switching process is modeled by a continuous-time Markov chain, which portraits discrete events that cannot be modeled by a diffusion process. In the model, there are two small parameters. One of them is ε associated with the generator of the continuous-time, inhomogeneous Markov chain, and the other is δ=δε signifies the small intensity of the diffusion. Assume ε→0 and δε→0 as ε→0. This paper focuses on large deviations type of estimates for such Markovian switching systems with small diffusions. The ratio ε/δε can be a nonzero constant, or equal to 0, or ∞. These three different cases yield three different outcomes. This paper analyzes the three cases and present the corresponding asymptotic properties.
Characterization of the orbit of standing waves of Hartree-type equations with external Coulomb potential
Authors: Hajaiej H.
Published: November 2019

We prove the orbital stability and then characterize the orbit of standing waves of Schrödinger equation of Hartree type.
Error estimates in periodic homogenization with a non-homogeneous Dirichlet condition
Authors: Griso G.
Published: November 2019

In this paper we investigate the homogenization problem with a non-homogeneous Dirichlet condition. Our aim is to give error estimates with boundary data in H1/2(∂Ω). The tools used are those of the unfolding method in periodic homogenization.
Spectral asymptotics, instability and Riesz basis property of root vectors for Rayleigh beam model with non-dissipative boundary conditions
Authors: Shubov Marianna A.
Published: November 2019

In this paper we investigate the Rayleigh beam model with non-dissipative boundary conditions recently considered in the literature. The beam is clamped at the left end and subject to a feedback control type boundary conditions at the right. The components of the 2-dim input vector are shear and moment at the right end and the components of the observation vector are time derivatives of displacement and slope at the right end. The input is related to the observation through a co-diagonal matrix depending on two non-negative control parameters. The paper contains two main results. First we derive the leading term, the second order term, and the remainder in the asymptotic representation of the eigenmodes of the system. It follows from spectral asymptotics that the system has an infinite alternating sequence of stable and unstable eigenmodes. This type of instability has been recently obtained in the literature by a different method. The instability result might be of interest for energy harvesting models where destabilization of a system is desirable. The second result is the fact that the generalized eigenvectors of the dynamics generator of the system form a Riesz basis in the state space equipped with the energy metric. This result implies, in particular, that the system generates a C0-semigroup in the state space.
Scaling limits and exit law for multiscale diffusions
Authors: Almada Sergio Angel , Spiliopoulos Konstantinos
Published: November 2019

In this paper we study the fluctuations from the limiting behavior of small noise random perturbations of diffusions with multiple scales. The result is then applied to the exit problem for multiscale diffusions, deriving the limiting law of the joint distribution of the exit time and exit location. We apply our results to the first order Langevin equation in a rough potential, studying both fluctuations around the typical behavior and the conditional limiting exit law, conditional on the rare event of going against the underlying deterministic flow.
Smooth attractors for the quintic wave equations with fractional damping
Authors: Savostianov Anton , Zelik Sergey
Published: November 2019

Dissipative wave equations with critical quintic nonlinearity and damping term involving the fractional Laplacian are considered. The additional regularity of energy solutions is established by constructing the new Lyapunov-type functional and based on this, the global well-posedness and dissipativity of the energy solutions as well as the existence of a smooth global and exponential attractors of finite Hausdorff and fractal dimension is verified.
Analysis of an enhanced approximate cloaking scheme for the conductivity problem
Authors: Heumann Holger , Vogelius Michael S.
Published: November 2019

We extend and analyse an enhanced approximate cloaking scheme, which was recently introduced by Ammari, Kang, Lee and Lim [Comm. Math. Phys. 317(1) (2013), 253–266] to cloak a domain with a fixed, homogeneous Neumann boundary condition. Subject to the solvability of a finite set of algebraic equations we construct an approximate cloak for the two dimensional transmission case, which achieves invisibility of the order ρ2N+2 while maintaining the same level of local anisotropy as earlier schemes of order ρ2 [Inverse Problems 24(1) (2008), 015016]. The approximate cloak and the invisibility estimate is independent of the objects being cloaked. Finally, we present analytical as well as numerical evidence for the solvability of the required algebraic equations.
On lacunary Toeplitz determinants
Authors: Kozlowski K.K.
Published: November 2019

By using Riemann–Hilbert problem based techniques, we obtain the asymptotic expansion of lacunary Toeplitz determinants det N[cℓa−mb[f]] generated by holomorphic symbols, where ℓa=a (resp. mb=b) except for a finite subset of indices a=h1,…,hn (resp. b=t1,…,tr). In addition to the usual Szegö asymptotics, our answer involves a determinant of size n+r.
Concentration–diffusion phenomena of heat convection in an incompressible fluid
Authors: Farwig Reinhard , Schulz Raphael , Yamazaki Masao
Published: November 2019

We study in the whole space Rn the behaviour of solutions to the Boussinesq equations at large distances. Therefore, we investigate the solvability of these equations in weighted L∞-spaces and determine the asymptotic profile for sufficiently fast decaying initial data. For n=2,3 we are able to construct initial data such that the velocity exhibits an interesting concentration–diffusion phenomenon.
A novel generalized solution expansion for the Lagerstrom model
Authors: Ou Chunhua , Wong R.
Published: November 2019

In this paper we re-visit the Lagerstrom problem

y" + (n-1)/r y' + εyy' = 0,

y(1) = 0, y(∞) = 1,

where ε is a small positive real number and n is a positive integer (or any real number greater than 2). Using rigorous analysis, a generalized asymptotic expansion, as ε→0, is derived for the solution of this problem. A trans-series expansion of the solution for large values of r is also presented; the leading term coefficient is determined by a connection formula between the values of the solution at the two points r=1 and r=∞. An extension and a discussion of the problem for n∈[1,2) is also given.
Asymptotic analysis for Volterra difference equations
Authors: Cuevas Claudio , Choquehuanca Mario , Soto Herme
Published: November 2019

Let X be an arbitrary Banach space. This work deals with the asymptotic behavior, the continuity and the compactness properties of solutions of the non-linear Volterra difference equation in X described by u(n+1)=λΣj=−∞na(n−j)u(j)+f(n,u(n)), n∈Z, for λ in a distinguished subset of the complex plane, where a(n) is a complex summable sequence and the perturbation f is a non-Lipschitz nonlinearity. Concrete applications to control systems and integro-difference equations are given.
A curious instability phenomenon for a rounded corner in presence of a negative material
Authors: Chesnel Lucas , Claeys Xavier , Nazarov Sergey A.
Published: November 2019

We study a 2D scalar harmonic wave transmission problem between a classical dielectric and a medium with a real-valued negative permittivity/permeability which models a metal at optical frequency or an ideal negative metamaterial. We highlight an unusual instability phenomenon for this problem when the interface between the two media presents a rounded corner. To establish this result, we provide an asymptotic expansion of the solution, when it is well-defined, in the geometry with a rounded corner. Then, we prove error estimates. Finally, a careful study of the asymptotic expansion allows us to conclude that the solution, when it is well-defined, depends critically on the value of the rounding parameter. We end the paper with a numerical illustration of this instability phenomenon.
Decay estimates of solutions for mildly degenerate Kirchhoff type dissipative wave equations in unbounded domains
Authors: Ono Kosuke
Published: November 2019

We consider the Cauchy problem for mildly degenerate Kirchhoff type dissipative wave equations: ρu″+‖A1/2u(t)‖2γAu+u′=0 in RN×R+, u(x,0)=u0(x), u′(x,0)=u1(x) in RN, with ρ>0, γ≥1, and ‖A1/2u0‖>0. When either the coefficient ρ or the initial data {u0,u1} are small, we prove the existence of global solutions by using several identities for energies. Moreover, we derive lower decay estimates of the solutions, and upper decay estimates of their second order derivatives.
Weakly and strongly singular solutions of semilinear fractional elliptic equations
Authors: Chen Huyuan , Véron Laurent
Published: November 2019

Let Ω⊂RN (N≥2) be a bounded C2 domain containing 0, 0<α<1 and 0
0, we prove that the weakly singular solution uk of (Ek) (−Δ)αu+up=kδ0 in Ω, which vanishes in Ωc, is a classical solution of (E*) (−Δ)αu+up=0 in Ω\{0} with the same outer data. Let A=[N/2α,1+2α/N) for N=2,3 and (√5−1)/4N<α<1, otherwise, A=∅; we derive that uk converges to ∞ in whole Ω as k→∞ for p∈(0,1+2α/N)\A, while the limit of uk is a strongly singular solution of (E*) for 1+2α/N<p<N/(N−2α).
A model of individual clustering with vanishing diffusion
Authors: Nasreddine Elissar
Published: November 2019

We consider a model of individual clustering with two specific reproduction rates and small diffusion parameter in one space dimension. It consists of a drift–diffusion equation for the population density coupled to an elliptic equation for the velocity of individuals. We prove the convergence (in suitable topologies) of the solution of the problem to the unique solution of the limit transport problem, as the diffusion coefficient tends to zero.
Uniform asymptotics for orthogonal polynomials with exponential weight on the positive real axis
Authors: Dai Dan , Qiu Weiyuan , Wang Jun
Published: November 2019

We consider the uniform asymptotics of polynomials orthogonal on [0,∞) with respect to the exponential weight w(x)=xαe−Q(x), where α>−1 and Q(x) is a polynomial with positive leading coefficient. In this paper, we have obtained two types of asymptotic expansions in terms of Laguerre polynomials and elementary functions for z in different overlapping regions, respectively. These two regions together cover the whole complex plane. Our approach is based on the steepest descent method for Riemann–Hilbert problems introduced by Deift and Zhou [Ann. Math. 137 (1993), 295–368].
Smoluchowski–Kramers approximation and large deviations for infinite dimensional gradient systems
Authors: Cerrai Sandra , Salins Michael
Published: November 2019

In this paper, we explicitly calculate the quasi-potentials for the damped semilinear stochastic wave equation when the system is of gradient type. We show that in this case the infimum of the quasi-potential with respect to all possible velocities does not depend on the density of the mass and does coincide with the quasi-potential of the corresponding stochastic heat equation that one obtains from the zero mass limit. This shows in particular that the Smoluchowski–Kramers approximation can be used to approximate long time behavior in the zero noise limit, such as exit time and exit place from a basin of attraction.
Homogenization of random diffusions in non-stationary environments
Authors: Boryc Marcin , Komorowski Tomasz
Published: November 2019

In the present paper we prove homogenization for diffusions and the solutions of their corresponding Kolmogorov's equation with random, non-stationary, but locally ergodic coefficients. The results generalizes earlier work of Papanicolaou and Varadhan [in: Statistics and Probability: Essays in Honor of C.R. Rao, North-Holland, 1982, pp. 547–552] and Yurinskii [Sibirsk. Mat. Zh. 23(2) (1982), 176–188].