Related papers: Exact equations for structure functions and equati…
(1) There is a finitely presented group with a word problem which is a uniformly effectively inseparable equivalence relation. (2) There is a finitely generated group of computable permutations with a word problem which is a universal…
We propose a simple algebraic method for constructing exact solutions of equations of two-dimensional hydrodynamics of an incompressible fluid. The problem reduces to consecutively solving three linear partial differential equations for a…
In this paper, we deal with the notions of naturality from category theory and definablity from model theory and their interactions. In this regard, we present three results. First, we show, under some mild conditions, that naturality…
The Degasperis-Procesi equation with self-consistent sources(DPESCS) is derived. The Lax representation and the conservation laws for DPESCS are constructed. The peakon solution of DPESCS is obtained.
We provide the analytic expressions of the totally symmetric and anti-symmetric structure constants in the $\mathfrak{su}(N)$ Lie algebra. The derivation is based on a relation linking the index of a generator to the indexes of its non-null…
A systematic method to derive the Hamiltonian and Nambu form for the shallow water equations, using the conservation for energy and potential enstrophy, is presented. Different mechanisms, such as vortical flows and emission of gravity…
Deformation theory is treated for locally notherian formal schemes (non necessarily smooth). The cotangent complex is defined in the derived category through the homology localization functor. The basic properties and results of a…
To account for phenomenological theories and a set of invariants, stress and strain are usually decomposed into a pair of pressure and deviatoric stress and a pair of volumetric strain and deviatoric strain. However, the conventional…
We study the rate of decay of the energy functional of solutions of the wave equation with localized damping and a external force. We prove that the decay rates of the energy functional is determined from a forced differential equation.
We introduce structured decompositions, category-theoretic structures which simultaneously generalize notions from graph theory (including treewidth, layered treewidth, co-treewidth, graph decomposition width, tree independence number,…
We consider possibly degenerate and singular elliptic equations in a possibly anisotropic medium. We obtain monotonicity results for the energy density, rigidity results for the solutions and classification results for the…
In this article, we consider inverse problems of determining a source term and a coefficient of a first-order partial differential equation and prove conditional stability estimates with minimum boundary observation data and relaxed…
Recent atomic force microscopy (AFM) can measure force curves between a probe and a sample surface in several solvents. The force curve is thought as the solvation structure in some cases, because its shape is generally oscilltive and pitch…
We present a numerical kinetic scheme for an unsteady mixed pressurised and free surface model. This model has a source term depending on both the space variable and the unknown, U, of the system. The source term is composed by a…
A matrix (and any associated linear system) will be referred to as structured if it has a small displacement rank. It is known that the inverse of a structured matrix is structured, which allows fast inversion (or solution), and reduced…
Improved model independent upper bounds on the weak transition form factors are derived using inclusive sum rules. Comparison of the new bounds with the old ones is made for the form factors h_{A_1} and h_V in B -> D* decays.
Interrelation between Thom's catastrophes and differential equations revisited. It is shown that versal deformations of critical points for singularities of A,D,E type are described by the systems of Hamilton-Jacobi type equations. For…
The $\imath$-divided powers (depending on a parity) form the $\imath$canonical basis for the split rank 1 $\imath$quantum group and they are a basic ingredient for $\imath$quantum groups of higher rank. We obtain closed formulae for the…
The equations of hydrodynamics including mass, linear momentum, angular momentum, and energy are derived by coarse-graining the microscopic equations of motion for systems consisting of rotary dumbbells driven by internal torques.
We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part we discus the main structures…