Related papers: Obstructions to Genericity in Study of Parametric …
Nonclassical symmetries and reductions of polynomial equations and systems of polynomial equations are considered. It is shown that specific polynomial equations having "hidden" symmetries can be reduced to classical symmetric systems of…
The space of polynomials in two real variables with values in a 2-dimensional irreducible module of a dihedral group is studied as a standard module for Dunkl operators. The one-parameter case is considered (omitting the two-parameter case…
In this work, we utilize discrete geometric mechanics to derive a 2nd-order variational integrator so as to simulate rigid body dynamics. The developed integrator is to simulate the motion of a free rigid body and a quad-rotor. We…
We review various combinatorial applications of field theoretical and matrix model approaches to equilibrium statistical physics involving the enumeration of fixed and random lattice model configurations. We show how the structures of the…
We briefly review the results of our paper hep-th/0009013: we study certain perturbative solutions of left-unilateral matrix equations. These are algebraic equations where the coefficients and the unknown are square matrices of the same…
The following article is an application of commutative algebra to the study of multiparameter persistent homology in topological data analysis. In particular, the theory of finite free resolutions of modules over polynomial rings is applied…
For a skew polynomial ring $R=A[X;\theta,\delta]$ where $A$ is a commutative Frobenius ring, $\theta$ an endomorphism of $A$ and $\delta$ a $\theta$-derivation of $A$, we consider cyclic left module codes $\mathcal{C}=Rg/Rf\subset R/Rf$…
Solving a polynomial system, or computing an associated Gr\"obner basis, has been a fundamental task in computational algebra. However, it is also known for its notorious doubly exponential time complexity in the number of variables in the…
In this paper we consider finite-dimensional constrained Hamiltonian systems of polynomial type. In order to compute the complete set of constraints and separate them into the first and second classes we apply the modern algorithmic methods…
In this work we consider the problem of extracting a set of interaction parameters from an high-dimensional dataset describing T independent configurations of a complex system composed of N binary units. This problem is formulated in the…
The paper presents a novel modular hybrid parallel robot for pancreatic surgery and its higher-order kinematics derived based on various formalisms. The classical vector, homogeneous transformation matrices and dual quaternion approaches…
A new convenient method of describing flat convex compact sets is proposed. It generalizes classical trigonometric functions $\sin$ and $\cos$. Apparently, this method may be very useful for explicit description of solutions of optimal…
In the present work, we demonstrate how the pseudoinverse concept from linear algebra can be used to represent and analyze the boundary conditions of linear systems of partial differential equations. This approach has theoretical and…
We study the classical problem of computing geometric thickness, i.e., finding a straight-line drawing of an input graph and a partition of its edges into as few parts as possible so that each part is crossing-free. Since the problem is…
Many problems give rise to polynomial systems. These systems often have several parameters and we are interested to study how the solutions vary when we change the values for the parameters. Using predictor-corrector methods we track the…
Many graph problems were first shown to be fixed-parameter tractable using the results of Robertson and Seymour on graph minors. We show that the combination of finite, computable, obstruction sets and efficient order tests is not just one…
This paper revisits the well-studied fixed point problem from a unified viewpoint of mathematical modeling and canonical duality theory, i.e. the original problem is first reformulated as a nonconvex optimization problem, its well-posedness…
In this chapter, we are concerned with inverse optimal control problems, i.e., optimization models which are used to identify parameters in optimal control problems from given measurements. Here, we focus on linear-quadratic optimal control…
We consider the simplest gauge theories given by one- and two- matrix integrals and concentrate on their stringy and geometric properties. We remind general integrable structure behind the matrix integrals and turn to the geometric…
The set of controllers stabilizing a linear system is generally non-convex in the parameter space. In the case of two-parameter controller design (e.g. PI control or static output feedback with one input and two outputs), we observe however…