Problem Of Existence Research Articles

ON THE PERIODIC SOLUTIONS OF THE LIENARD EQUATION

Mathematical modeling of many problems of natural science leads to the need to study quasi-linear boundary value problems for functional differential equations with a linear part that is not uniquely solvable for all right-hand parts. The specificity of such problems is that the corresponding linear operator is not reversible. In the literature, such boundary value problems are usually called resonant. Since the 70s of the last century, the development of methods for studying resonant boundary value problems considered as a single operator equation has begun. A very important area of research from the point of view of applications is the application of General statements to the study of periodic boundary value problems for functional differential equations. The existence problem is considered ω - a periodic solution of the Lienard equation with a deviating argument of the form It is assumed that the function p ( t ) is measurable and Using an approach based on the application of theoretical existence for a quasilinear operator equation, sufficient conditions can be obtained in the work, at least one ω - a periodic solution must correspond to the equations. The obtained result refines some well-known results for the Lienard equations. Execution conditions decisions do not affect the existence of solutions.

J-harmonic functions on almost Hermitian manifolds

We define an operator ΔJ on any almost Hermitian manifold by first projecting the gradient of a function to the tangent space of its level set, and then taking the divergence. We call ΔJ the J-Laplacian operator. It is then shown that J-harmonic functions, which are functions H satisfying ΔJH=0, are first integrals of the vector field δω# where ω is the fundamental 2-form. This generalizes the notion of Hamiltonian functions on symplectic manifolds, and provides a refreshing way to interpret the seminal classification of almost Hermitian manifolds by Gray and Hervella. Existence and non-existence of J-harmonic functions under some conditions are explored, where a connection to the problem of existence of closed orbits in dynamical systems is revealed.

A C*-algebraic Approach to Interacting Quantum Field Theories

A novel C*-algebraic framework is presented for relativistic quantum field theories, fixed by a Lagrangean. It combines the postulates of local quantum physics, encoded in the Haag–Kastler axioms, with insights gained in the perturbative approach to quantum field theory. Key ingredients are an appropriate version of Bogolubov’s relative S-operators and a reformulation of the Schwinger–Dyson equations. These are used to define for any classical relativistic Lagrangean of a scalar field a non-trivial local net of C*-algebras, encoding the resulting interactions at the quantum level. The construction works in any number of space-time dimensions. It reduces the longstanding existence problem of interacting quantum field theories in physical spacetime to the question of whether the C*-algebras so constructed admit suitable states, such as stable ground and equilibrium states. The method is illustrated on the example of a non-interacting field and it is shown how to pass from it within the algebra to interacting theories by relying on a rigorous local version of the interaction picture.

Asymptotics of the Solutions of Boundary-Value Problems for Linear Singularly Perturbed Systems of Differential Equations in the Case of Multiple Spectrum of the Boundary Matrix

We consider the problem of existence of the solution of a boundary-value problem for a singularly perturbed linear system of differential equations in the case of multiple spectrum of the boundary matrix.

LEGAL WAYS TO COMBAT INFORMATION RARE IN UKRAINE

In the article the problem of existence of informative corporate raid is investigated in Ukraine, legal ways of overcoming (minimizations of harm) of informative corporate raid in modern realities. In the epoch of information technologies the question of defence of the information and information becomes all more actual about itself in her primitive kind. And it touches not only the certain personal data but also information of пр business reputation of legal entity. Now the question of defence of business reputation of legal entities becomes urgent, through abuse of the certain interested citizens by the rights on offering a “own opinion”. By a basic problem, that will be considered in the real article there is an invention of ways of legal counteraction to the socalled “informative corporate raid”, consideration of variants of judicial and extrajudicial defence of the broken right. Actuality of this theme consists in that an informative corporate raid does obstacle to normal economic activity of plenty of enterprises real to the sector of economy and ways of his overcoming or even. An informative corporate raid deeply got to modern realities of Ukrainian societ. Corrupted of power, to accomplish imperfection of home legislation and not desire of organs of local selfgovernment active operating under defence it basic taxpayers legal entities is a favourable environment for distribution and greater taking root of such aggressive verbal attacks Ukrainian business. Only clear legislative settlement, and the debugged work of representatives of legal entities, executive, local selfovernmentand unindifferentcitizens bodies can overcome such negative phenomenon. Eradication of informative corporate raid will assist the improvement of economic and investment climate in a country that will result in the inevitable improvement of standard of livingorate raid will assist the improvement of economic and investment climate in a country that will result in the inevitable improvement of standard of living.

Discursive loyalty in the conditions of centralization of power in Russia: nature and typology of the phenomenon

This article raises a problem of existence of the verbal political symbols of autocratic discourse in public space. The hypothesis is advanced that in the conditions of centralization of the Russian political system, forms a specific type of discursive loyalty, interpreted as communicative behavior within the framework of the structure of verbal political symbols set by the official political discourse. The object of this research is the Russian sociopolitical discourse of Russia in the early XXI century. The subject is the instruments of manifestation of discursive loyalty used by public actors. Special attention is turned to the public attitude on verbal symbols of the country’s leader, political parties and bureaucracy in the conditions of centralization and personification of power over the period from 2000 to the present. An attempt is made to formulate the typology of discursive loyalty based on the components of perception of political symbols indicated by R. Cobb and C. Elder. Three basic types of discursive loyalty are defined depending on the dominance of separate components in perception: 1) affective, based on emotional empathy with the content of the discourse of power and its source; 2) cognitive, based on recognition of the relevance of verbal symbols of the discourse of power; 3) analytical, based on rational choice of the verbal symbols of power upon availability of the alternative or evasive option. Types of loyalty are illustrated by examples of discursive behavior of the subjects of civil society of the early XXI century – presidency and prime-ministry of V. V. Putin, whose personal influence actualized the affective type of loyalty, and the results of transformation of the political system led to proliferation of analytical type of loyalty. The author believes that the prevalence of analytical type of discursive loyalty is dangerous for the political system, due to its simulated nature, which creates an illusion of public support.

The Existence of Perfect Codes in Doob Graphs

We solve the problem of existence of perfect codes in the Doob graph. It is shown that 1-perfect codes in the Doob graph D(m,n) exist if and only if 6m+3n+1 is a power of 2; that is, if the size of a 1-ball divides the number of vertices. Keywords: perfect codes, distance-regular graphs, Doob graphs, Eisenstein-Jacobi integers.

Distribution of the Number of Square-Free Divisors in Residue Classes

The notion of weekly uniform distribution of arithmetical functions was introduced by W. Narckiewicz. For many functions in various papers, the problem of existence of such distribution was solved, and asymptotic formulas for frequency of hits of function values in residue classes coprime with a module were established. These asymptotic formulas contained, as a rule, only principal part of the asymptotics. A similar problem is solved in the present paper for the function which gives the number of square-free divisors of a natural number, but the asymptotic formula is the asymptotic series.

Oscillation Equation of a Beam with Fixed and Pivotally Supporter Ends

The problem of existence of periodic solutions to a quasilinear equation of forced oscillations of an I-beam whose one end is fixed and the second one is pivotally supported is studied. Properties of the differential operator are given and the theorem on the existence of a countable number of solutions is proved in the case the nonlinear term has a power growth.

Rational Integrals of a Natural Mechanical System on the 2-Torus

Under study are the problems of existence of the first integrals rational in momenta for a natural mechanical system on the 2-torus. We prove that a rational integral with a linear numerator and denominator reduces to a linear integral. Considering the case of a quadratic numerator and linear denominator, we obtain an analogous result under some additional assumptions on the coefficients of the first integral.

The existence problem of Kähler-Einstein metrics oncompact complex manifolds with positive first Chern class

This is an expository paper. We hope to give a picture of process on the existence of Kahler-Einstein metrics on compact complex manifolds with positive first Chern class in past three decades. Our main purpose is to introduce Tians proof of Yau-Tian-Donaldson conjecture.

Local strong solutions to a quasilinear degenerate fourth-order thin-film equation

We study the problem of existence and uniqueness of strong solutions to a degenerate quasilinear parabolic non-Newtonian thin-film equation. Originating from a non-Newtonian Navier–Stokes system, the equation is derived by lubrication theory and under the assumption that capillarity is the only driving force. The fluid’s shear-thinning rheology is described by the so-called Ellis constitutive law. For flow behaviour exponents alpha ge 2 the corresponding initial boundary value problem fits into the abstract setting of Amann (Function Spaces, Differential Operators and Nonlinear Analysis, Vieweg Teubner Verlag, Stuttgart, 1993). Due to a lack of regularity this is not true for flow behaviour exponents alpha in (1,2). For this reason we prove an existence theorem for abstract quasilinear parabolic evolution problems with Hölder continuous dependence. This result provides existence of strong solutions to the non-Newtonian thin-film problem in the setting of fractional Sobolev spaces and (little) Hölder spaces. Uniqueness of strong solutions is derived by energy methods and by using the particular structure of the equation.

The human thinking and mind, information and thermodynamics

«Nothing happens accidentally» - the scientists often say. The crisis of science requires new ideas and approaches, which can ensure not only the further development of science itself, but also the solution of the problems of the optimal existence and coexistence of a man and the humanity in this vast world. The change of worldviews, scientific paradigms doesn’t always run smoothly, but the motion is inevitable these are the laws of evolution. Only the science gives the only real ways for the further evolutionary development of the mankind. The human mind and thinking still remain a mystery to science. Science has tried many times to reveal the secrets of the human thinking, but so far this mystery has not been discovered. «Everything passes, everything changes» - said the ancients and they were right. Very likely, the only things that remained invariable were the human thinking and mind; they were and always will be a convincingly changeable and constant stimulant to the development of the mankind.

On Geometric Analysis of the Dynamics of Volumetric Expansion and its Applications to General Relativity

In this paper, we discuss the global aspect of the geometric dynamics of volumetric expansion and its applications to the problem of the existence in the space-time of compact and complete spacelike hypersurfaces and to the global geometry of generalized Robertson–Walker space-times.

Brownian motion in attenuated or renormalized inverse-square Poisson potential

Nous considérons le problème parabolique d’Anderson avec potentiels aléatoires ayant des singularités en carré inverse autour des points d’un processus de Poisson standard dans $\mathbb{R}^{d}$, $d\ge 3$. Les potentiels sont obtenus par superposition de translations par les points du processus de Poisson d’un noyau $\mathfrak{K}$ satisfaisant $\mathfrak{K}(x)\approx \theta |x|^{-2}$ près de l’origine, où $\theta \in (0,(d-2)^{2}/16]$. Afin de pouvoir définir les intégrales de chemin correspondantes, nous demandons que le noyau soit ou bien atténué (intégrable à l’infini), ou, en $d=3$, renormalisé au sens de Chen et Kulik (Ann. Inst. Henri Poincaré Probab. Stat. 48 (2012) 631–660). Nous montrons l’existence et le comportement en temps long des solutions positives par représentation de Feynman–Kac, en particulier dans le cas critique $\theta =1/16$ laissé ouvert par Chen et Rosinski (Chen et Rosinski (2011)).

A Comment on a Controversial Issue: A Generalized Fractional Derivative Cannot Have a Regular Kernel

Abstract The problem whether a given pair of functions can be used as the kernels of a generalized fractional derivative and the associated generalized fractional integral is reduced to the problem of existence of a solution to the Sonine equation. It is shown for some selected classes of functions that a necessary condition for a function to be the kernel of a fractional derivative is an integrable singularity at 0. It is shown that locally integrable completely monotone functions satisfy the Sonine equation if and only if they are singular at 0.

The Existence and Legal Problems of Pak Ogah in Indonesia

Pak Ogah is a citizen, either an individual or a group that participates in regulating traffic order in the hope of being rewarded by road users who will pass or turn around at intersections in major cities in Indonesia. In this study, the issues will be presented that factors influence the emergence of Pak Ogah, and what legal problems arise from the phenomenon. The method used in this study is a qualitative research method with a juridical-empirical approach which uses facts in the field as the primary data. The results of the study stated that the emergence of the phenomenon of Pak Ogah was caused by three main factors, namely the legal substance, legal structure (law enforcement officers), and the legal culture of the Indonesian people. Furthermore, the problem arising from the phenomenon is that there is no legal guarantee and work safety for the protection of Pak Ogah if an accident occurs when regulating traffic order.

The human thinking and mind, information and thermodynamics

“Nothing happens accidentally” - the scientists often say. The crisis of science requires new ideas and approaches, which can ensure not only the further development of science itself, but also the solution of the problems of the optimal existence and coexistence of a man and the humanity in this vast world. The change of worldviews, scientific paradigms doesn’t always run smoothly, but the motion is inevitable these are the laws of evolution. Only the science gives the only real ways for the further evolutionary development of the mankind. The human mind and thinking still remain a mystery to science. Science has tried many times to reveal the secrets of the human thinking, but so far this mystery has not been discovered. “Everything passes, everything changes” - said the ancients and they were right. Very likely, the only things that remained invariable were the human thinking and mind; they were and always will be a convincingly changeable and constant stimulant to the development of the mankind.

Superlinear elliptic inequalities on manifolds

Let M be a complete non-compact Riemannian manifold and let σ be a Radon measure on M. We study the problem of existence or non-existence of positive solutions to a semilinear elliptic inequality−Δu≥σuqinM, where q>1. We obtain necessary and sufficient criteria for existence of positive solutions in terms of Green function of Δ. In particular, explicit necessary and sufficient conditions are given when M has nonnegative Ricci curvature everywhere in M, or more generally when Green's function satisfies the 3G-inequality.

Existence results for some fractional differential equations related to A ∈ B(L2[a, b

In this paper we define the (generalized) linear Volterra integral operator on L2[a, b]. Then the problem of existence and uniqueness of solutions of the second kind Volterra integral equations, corresponding to this operator, will be answered. Finally, some applications of this work to the existence of solutions of some fractional differential equations, are given.