Related papers: Explicit Volume-Preserving Splitting Methods for P…
Regularizing volume preserving diffeomorphism (VPD) is equivalent to a long standing problem, namely regularizing Nambu-Poisson bracket. In this paper, as a first step to regularizing VPD, we find general complete independent basis of VPD…
Previous research on exceptional units has primarily focused on the ring of rational integers or abstract finite rings, often restricted to linear or quadratic constraints. In this paper, we extend the concept of polynomial-type exceptional…
An improved characteristic set algorithm for solving Boolean polynomial systems is proposed. This algorithm is based on the idea of converting all the polynomials into monic ones by zero decomposition, and using additions to obtain…
Polytopal methods provide a flexible framework for the numerical approximation of partial differential equations on general meshes. Their convergence analysis raises specific challenges due to their inherently non-conforming nature and, in…
The wave equation for vectors and symmetric tensors in spherical coordinates is studied under the divergence-free constraint. We describe a numerical method, based on the spectral decomposition of vector/tensor components onto spherical…
In this article, discrete variants of several results from vector calculus are studied for classical finite difference summation by parts operators in two and three space dimensions. It is shown that existence theorems for scalar/vector…
In this paper, we develop a new deflation technique for refining or verifying the isolated singular zeros of polynomial systems. Starting from a polynomial system with an isolated singular zero, by computing the derivatives of the input…
In this paper, we develop a high-order adaptive virtual element method (VEM) to simulate the self-consistent field theory (SCFT) model in arbitrary domains. The VEM is very flexible in handling general polygon elements and can treat hanging…
Today, advances in medical technology extensively utilize 3D volume data for accurate and efficient diagnostics. However, sharing these data across networks in telemedicine poses significant security risks of data tampering and unauthorized…
We systematically study the splitting of vector bundles on a smooth, projective variety, whose restriction to the zero locus of a regular section of an ample vector bundle splits. First, we find ampleness and genericity conditions which…
We present counting methods for some special classes of multivariate polynomials over a finite field, namely the reducible ones, the s-powerful ones (divisible by the s-th power of a nonconstant polynomial), and the relatively irreducible…
We present a Finite Volume formulation for determining discontinuous distributions of magnetic fields within non-orthogonal and non-uniform meshes. The numerical approach is based on the discretization of the vector potential variant of the…
This paper derives numerical bounds for and implements the splitting circle method for finding roots of a univariate polynomial in the presence of fixed precision.
In this paper, we present a formalization of an algorithm to construct admissible discrete vector fields in the Coq theorem prover taking advantage of the SSReflect library. Discrete vector fields are a tool which has been welcomed in the…
This work develops advanced numerical methods for free-surface simulations of polymer mixing processes, integrating a Volume of Fluid (VOF) interface-capturing approach with a non-conforming Immersed Boundary (IB) method to model two-phase…
We develop the method of vector-fields to further study Dispersive Wave Equations. Radial vector fields are used to get a-priori estimates such as the Morawetz estimate on solutions of Dispersive Wave Equations. A key to such estimates is…
Mutual-visibility sets were motivated by visibility in distributed systems and social networks, and intertwine with several classical mathematical areas. Monotone properties of the variety of mutual-visibility sets, and restrictions of such…
The aim of the paper is twofold. Firstly, by using the constant rank level set theorem from differential geometry, we establish sharp upper bounds for the dimensions of the solution sets of polynomial variational inequalities under mild…
The use of orthonormal polynomial bases has been found to be efficient in preventing ill-conditioning of the system matrix in the primal formulation of Virtual Element Methods (VEM) for high values of polynomial degree and in presence of…
Intrinsic volumes are fundamental geometric invariants generalizing volume, surface area, and mean width for convex bodies. We establish a unified Laplace-Grassmannian representation for intrinsic and dual volumes of convex polynomial…