Related papers: Further study on tensor absolute value equations
We study and derive algorithms for nonlinear eigenvalue problems, where the system matrix depends on the eigenvector, or several eigenvectors (or their corresponding invariant subspace). The algorithms are derived from an implicit…
The Schwinger-Dyson Equations (SDEs) of matrix models are known to form (half) a Virasoro algebra and have become a standard tool to solve matrix models. The algebra generated by SDEs in tensor models (for random tensors in a suitable…
On the base of Lie algebraic and differential geometry methods, a wide class of multidimensional nonlinear systems is obtained, and the integration scheme for such equations is proposed.
Recent works have shown that deep neural networks can be employed to solve partial differential equations, giving rise to the framework of physics informed neural networks. We introduce a generalization for these methods that manifests as a…
A construction of differential constraints compatible with partial differential equations is considered. Certain linear determining equations with parameters are used to find such differential constraints. They generalize the classical…
For small number of equations, systems of linear (and sometimes nonlinear) equations can be solved by simple classical techniques. However, for large number of systems of linear (or nonlinear) equations, solutions using classical method…
Over the topos of sets, the notion of Lawvere theory is infinite countably-sorted algebraic but not one-sorted algebraic. Shifting viewpoint over the object-classifier topos, a finite algebraic presentation of Lawvere theories is…
Phase transitions with spontaneous symmetry breaking and vector order parameter are considered in multidimensional theory of general relativity. Covariant equations, describing the gravitational properties of topological defects, are…
We give a new theoretical tool to solve sparse systems with finitely many solutions. It is based on toric varieties and basic linear algebra; eigenvalues, eigenvectors and coefficient matrices. We adapt Eigenvalue theorem and Eigenvector…
We study a class of overdetermined algebraic systems of equations. We prove that the number of distinct solutions equals to the maximal possible if and only if certain matrices are commuting and semisimple. This gives a characterization of…
We prove a criterion for continuity of bilinear maps on countable direct sums of topological vector spaces. As a first application, we get a new proof for the fact (due to Hirai et al. 2001) that the map taking a pair of test functions on…
This paper establishes several new facts on generalized polyhedral convex sets and shows how they can be used in vector optimization. Among other things, a scalarization formula for the efficient solution sets of generalized vector…
We develop a new tool, namely polynomial and linear algebraic methods, for studying systems of word equations. We illustrate its usefulness by giving essentially simpler proofs of several hard problems. At the same time we prove extensions…
A novel approach is introduced for deriving exact solutions to nonlinear systems of ordinary differential equations. This method consists of four parts. In the initial part, the examined nonlinear differential equation system is transformed…
We establish some new common fixed point theorems of single-valued and multivalued mappings operating between complete ordered locally convex spaces under weaker assumptions. As an application, we prove a new minimax theorem of existence of…
We introduce a new approach to obtaining pointwise estimates for solutions of elliptic boundary value problems when the operator being considered satisfies a certain type of weighted integral inequalities. The method is illustrated on…
In many mathematical models of physical phenomenons and engineering fields, such as electrical circuits or mechanical multibody systems, which generate the differential algebraic equations (DAEs) systems naturally. In general, the feature…
We present some advances, both from a theoretical and from a computational point of view, on a quadratic vector equation (QVE) arising in Markovian Binary Trees. Concerning the theoretical advances, some irreducibility assumptions are…
An important problem that arises in many engineering applications is the boundary value problem for ordinary differential equations. There have been many computational methods proposed for dealing with this problem. The convergence of the…
We obtain new results on the existence and multiplicity of fixed points of Hammerstein equations in very general cones. In order to achieve this, we combine a new formulation of cones in terms of continuous functionals with fixed point…