Related papers: Quadratic Vector Equations
We study quadratic optimization with indicator variables and an M-matrix, i.e., a PSD matrix with non-positive off-diagonal entries, which arises directly in image segmentation and portfolio optimization with transaction costs, as well as a…
In this short review we first recall combinatorial or ($0-$dimensional) quantum field theory (QFT). We then give the main idea of a standard QFT method, called the intermediate field method, and we review how to apply this method to a…
In this paper, we analyze nonlinear differential equations subject to generalized boundary conditions. More specifically, we provide a framework from which we can provide conditions, which are straightforward to check, for the solvability…
The classical quadratic formula and some of its lesser known variants for solving the quadratic equation are reviewed. Then, a new formula for the roots of a quadratic polynomial is presented.
These lecture notes focus on some numerical linear algebra algorithms in scientific computing. We assume that students are familiar with elementary linear algebra concepts such as vector spaces, systems of equations, matrices, norms,…
This paper proposes new quadratic constraints (QCs) to bound a quadratic polynomial. Such QCs can be used in dissipation ineqaulities to analyze the stability and performance of nonlinear systems with quadratic vector fields. The proposed…
Quantum monodromy matrices coming from a theory of two coupled (m)KdV equations are modified in order to satisfy the usual Yang-Baxter relation. As a consequence, a general connection between braided and {\it unbraided} (usual) Yang-Baxter…
We show the validity of select existence results for a vector optimization problem, and a variational inequality. More generally, we consider generalized vector quasi-variational inequalities, as well as, fixed point problems on genuine…
We present here the necessary and sufficient conditions for the invertibility of tridiagonal matrices, commonly named Jacobi matrices, and explicitly compute their inverse. The techniques we use are related with the solution of…
We consider three key properties of Metzler and nonnegative matrices and extensions of these to classes of self-dual proper convex cones. Specifically, we study mappings that are quasi-monotone (QM) with respect to a cone $K$ and discuss…
Using parafermionic field theoretical methods, the fundamentals of 2d fractional supersymmetry ${\bf Q}^{K} =P$ are set up. Known difficulties induced by methods based on the $U_{q}(sl(2))$ quantum group representations and non commutative…
The existence problem for mutually unbiased bases is an unsolved problem in quantum information theory. A related question is whether every pair of bases admits vectors that are unbiased to both. Mathematically this translates to the…
We investigate convexification for convex quadratic optimization with step function penalties. Such problems can be cast as mixed-integer quadratic optimization problems, where binary variables are used to encode the non-convex step…
The present author recently proposed and proved a relationship theorem between nonlinear polynomial equations and the corresponding Jacobian matrix. By using this theorem, this paper derives a Newton iterative formula without requiring the…
We show that a class of divergence-form elliptic problems with quadratic growth in the gradient and non-coercive zero order terms are solvable, under essentially optimal hypotheses on the coefficients in the equation. In addition, we prove…
We analyze certain stationary fields with linear regressions and quadratic conditional variances. This classic probabilistic problem leads somewhat unexpectedly to stationary Markov processes closely tied to non-commutative probability…
Recent work in the field of signal processing has shown that the singular value decomposition of a matrix with entries in certain real algebras can be a powerful tool. In this article we show how to generalise the QR decomposition and SVD…
Algebraic lambda-calculi have been studied in various ways, but their semantics remain mostly untouched. In this paper we propose a semantic analysis of a general simply-typed lambda-calculus endowed with a structure of vector space. We…
In a previous paper the generator matrix elements and (dual) vector reduced Wigner coefficients (RWCs) were evaluated via the polynomial identities satisfied by a certain matrix constructed from the $R$-matrix $R$ and its twisted…
The use of quadratic residues to construct matrices with specific determinant values is a familiar problem with connections to many areas of mathematics and statistics. Our research has focused on using cubic residues to construct matrices…