Related papers: Evolution equation in Hilbert-Mumford calculus
We consider the links between consistent and approximate descriptions of the quantum-classical systems, i.e. systems are composed of two interacting subsystems, one of which behaves almost classically while the other requires a quantum…
Curve evolution is often used to solve computer vision problems. If the curve evolution fails to converge, we would not be able to solve the targeted problem in a lifetime. This paper studies the theoretical aspect of the convergence of a…
We derive effective recursion formulae of top intersections in the tautological ring $R^*(M_g)$ of the moduli space of curves of genus $g\geq 2$. As an application, we prove a convolution-type tautological relation in $R^{g-2}(M_g)$.
Crossover and mutation are the two main operators that lead to new solutions in evolutionary approaches. In this article, a new method of performing the crossover phase is presented. The problem of choice is evolutionary decision tree…
We consider a one dimensional evolution problem modeling the dynamics of an acoustic field coupled with a set of mechanical oscillators. We analyze solutions of the system of ordinary and partial differential equations with time-dependent…
In the work two ways of evolutionary interpretation of entropy model for correspondence matrix calculation are proposed. Both approaches based on the stochastic chemical kinetic evolution under the detailed balance condition. The first…
In this paper, we introduce the concept of Developmental Partial Differential Equation (DPDE), which consists of a Partial Differential Equation (PDE) on a time-varying manifold with complete coupling between the PDE and the manifold's…
The paper presents the results of numerical solution of the evolution law for the constrained mean-curvature flow. This law originates in the theory of phase transitions for crystalline materials and describes the evolution of closed…
We study the gradient flow of an energy with mixed homogeneity which is at the interface of Finsler and sub-Riemannian geometry
We extend a contraction mapping argument for ordinary state-dependent delay differential equations to evolutionary partial differential equations in the sense of R. Picard, that is, to equations of the form $\bigl(\partial_{t}…
We propose a numerical method for approximate calculations of the time evolution of point particle systems given only the system's Hamiltonian function and initial conditions. The method both generates and solves the equations of motion…
This paper investigates type isomorphism in a lambda-calculus with intersection and union types. It is known that in lambda-calculus, the isomorphism between two types is realised by a pair of terms inverse one each other. Notably,…
We give a Lie-algebraic classification of third order quasilinear equations which admit non-trivial Lie point symmetries.
A program dedicated to the numerical solution of the evolution equations for twist-three multiparton correlation functions is presented. The solutions are obtained by direct integration on a discretized momentum fraction grid. Both flavor…
By the work of J.Huh, one can interpret binomial coefficients as a solution to an intersection problem on a permutohedral variety $X_E$. Applying Hirzebruch-Riemann-Roch, this intersection problem is equivalent to computing Euler…
The issue of so-called maximal regularity is discussed within a Hilbert space framework for a class of evolutionary equations. Viewing evolutionary equations as a sums of two unbounded operators, showing maximal regularity amounts to…
This paper studies the Hilbert scheme of a curve on a complete-intersection K-trivial threefold, in the case in which the curve is unobstructed in the ambient variety in which the threefold lives. The basic result is that the obstruction…
The goal of this very short note is to give a new proof of Faber's formula for the socle intersection numbers in the tautological ring of $\mathcal{M}_g$. This new proof exhibits a new beautiful tautological relation that stems from the…
We reconsider the deterministic haploid mutation-selection equation with two types. This is an ordinary differential equation that describes the type distribution (forward in time) in a population of infinite size. This paper establishes…
A modification of the symmetry approach for the classification of integrable differential-difference equations of the form $$ u_{n,t} = f_n(u_{n-1}, u_n, u_{n+1}), $$ where $n$ is a discrete integer variable, is presented (the well-known…