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Exponential localization of Steklov eigenfunctions on warped product manifolds: the flea on the elephant phenomenon
This paper is devoted to the analysis of Steklov eigenvalues and Steklov eigenfunctions on a class of warped product Riemannian manifolds ( M , g )...
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Approximate analytical solution in slow-fast system based on modified multi-scale method
A simple, yet accurate modified multi-scale method (MMSM) for an approximately analytical solution in nonlinear oscillators with two time scales...
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Internal resonance of an axially transporting beam with a two-frequency parametric excitation
This paper investigates the transverse 3:1 internal resonance of an axially transporting nonlinear viscoelastic Euler-Bernoulli beam with a...
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Some Remarks on Solvability of Dirichlet Problem for Laplace Equation in Non-standard Function Spaces
Non-standard grand-Lebesgue and Morrey spaces are considered in this work, together with grand-Sobolev and Morrey–Sobolev spaces generated by them....
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Incidence: Projective Geometry
Projective geometry is the proper domain for the notion of incidence for straight lines and points; it knows no other basic notions. The basic ideas...
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Semiclassical analysis of a nonlocal boundary value problem related to magnitude
We study a Dirichlet boundary problem related to the fractional Laplacian in a manifold. Its variational formulation arises in the study of...
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Carnot’s theory of transversals and its applications by Servois and Brianchon: the awakening of synthetic geometry in France
In this paper we discuss in some depth the main theorems pertaining to Carnot’s theory of transversals, their initial reception by Servois, and the...
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The Nonsmooth Dynamics of Combined Slip and Spin Motion Under Dry Friction
We investigate the motion of rigid bodies subject to combined slip** and spinning over a rough flat surface in the presence of dry friction....
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Quasiconformal contact foliations
We show that every quasiconformal contact foliation supports an invariant metric and characterise these foliations by the dynamical property of
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Chaotic Dynamics of Closed Cylindrical Shells Under Local Transversal Load and Temperature Field (First-Order Kirchhoff–Love Approximation Model)
This chapter is devoted to the study of chaotic vibrations of closed cylindricalShell(s)cylindrical shells subject to a local...
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Stability Theory
Stability of solutions is an important qualitative property in linear as well as nonlinear systems. The objective of this chapter is to introduce...
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Rolle Models in the Real and Complex World
Numerous problems of analysis (real and complex) and geometry (analytic, algebraic, Diophantine e.a.) can be reduced to calculation of the “number of...
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Ergodic Theorems for Laminations and Foliations: Recent Results and Perspectives
This report discusses recent results as well as new perspectives in the ergodic theory for Riemann surface laminations, with an emphasis on singular...
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Separation of Variables
Covers separable equations and Newton’s equation, both of which are solved by quadratures. Includes the Kepler problem and an introduction to...
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Attractors of Hamiltonian Nonlinear Partial Differential Equations
We survey the theory of attractors of nonlinear Hamiltonian partial differential equations since its appearance in 1990. These are results on global...
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A Local Cauchy Integral Formula for Slice-Regular Functions
We prove a local Cauchy-type integral formula for slice-regular functions. The formula is obtained as a corollary of a general integral...
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Cohomology of semisimple local systems and the decomposition theorem
In this paper, we study the cohomology of semisimple local systems in the spirit of classical Hodge theory. On the one hand, we construct a...
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The Gauss maps of Demoulin surfaces with conformal coordinates
Demoulin surfaces in the real projective 3-space are investigated. Our result enables us to establish a generalized Weierstrass type representation...
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Elements of Symplectic Geometry
The first section of this chapter is a primer on symplectic algebra and geometry in Euclidean spaces, real or complex. Concepts and results are...