Related papers: Computing standard canonical forms of regular line…

We consider the canonical fundamental systems of solutions of linear homogeneous Caputo fractional differential equations with continuous variable coefficients. Here we gained a series-representation of the canonical fundamental system by…

Paul Van Dooren [Linear Algebra Appl. 27 (1979) 103-140] constructed an algorithm for the computation of all irregular summands in Kronecker's canonical form of a matrix pencil. The algorithm is numerically stable since it uses only unitary…

Semidefinite programs (SDPs) -- some of the most useful and versatile optimization problems of the last few decades -- are often pathological: the optimal values of the primal and dual problems may differ and may not be attained. Such SDPs…

Heisenberg's matrix formulation of quantum mechanics can be generalized to relativistic systems by evolving in light-front time tau = t+z/c. The spectrum and wavefunctions of bound states, such as hadrons in quantum chromodynamics, can be…

The matrix of canonical differential equations consists of the 1-$\mathrm{d}\log$-form coefficients obtained by projecting ($n$+1)-$\mathrm{d}\log$-forms onto $n$-$\mathrm{d}\log$-form master integrands. With dual form in relative…

For a normal subvariety $V$ of ${\bf C}^n$ with a good ${\bf C}^*$-action we give a simple characterization for when it has only log canonical, log terminal or rational singularities. Moreover we are able to give formulas for the…

The canonical tensor model, which is a tensor model in the Hamilton formalism, can be straightforwardly quantized and has an exactly solved physical state. The state is expressed by a wave function with a generalized form of the Airy…

In this article, we present a structured Kalman filter associated with the transformation matrix for observable Kalman canonical decomposition from conventional Kalman filter (CKF) in order to generate a more accurate time scale. The…

This paper presents the general theory of canonical transformations of coordinates in quantum mechanics. First, the theory is developed in the formalism of phase space quantum mechanics. It is shown that by transforming a star-product, when…

We give a rigorous formulation of the intuitive idea that a differentiable map should be thesame thing as a locally, or infinitesimally, linear map: just as a linear map respects the operations of addition and multiplication by scalars ina…

This paper presents a unifying theory of Linear second order systems that allows time-varying and time invariant systems to be treated in the same way for the first time. In the process, a transformation is given that diagonalizes an…

For any quantum group of finite ADE type, we prove a new formula for the standard bilinear form evaluated at monomials. Combining this with ideas from the Lusztig-Shoji algorithm, we obtain a new algorithm that computes the canonical basis.…

We derive the canonical forms for a pair of $n\times n$ complex matrices $(E,Q)$ under transformations $(E,Q) \rightarrow (UEV,U^{-T}QV)$, and $(E,Q) \rightarrow (UEV,U^{-*}QV)$, where $U$ and $V$ are nonsingular complex matrices. We, in…

Classifying phase transitions is a fundamental and complex challenge in condensed matter physics. This work proposes a framework for identifying quantum phase transitions by combining classical shadows with unsupervised machine learning. We…

Many areas of science and engineering encounter data defined on spherical manifolds. Modelling and analysis of spherical data often necessitates spherical harmonic transforms, at high degrees, and increasingly requires efficient computation…

In this article, we establish an average behaviour of the normalised Fourier coefficients of the Hecke eigenforms supported at the integers represented by any primitive integral positive definite binary quadratic form of fixed discriminant…

We argue that reducing nonlinear programming problems to a simple canonical form is an effective way to analyze them, specially when the problem is degenerate and the usual linear independence hypothesis does not hold. To illustrate this…

We consider compositions of the transformations of the time variable and canonical transformations of the other coordinates, which map completely integrable system into other completely integrable system. Change of the time gives rise to…

Let $\mathbb{F}$ be an algebraically closed field of characteristic $0$. Given a square matrix $A \in \mathbb{F}^{n \times n}$ and a polynomial $f \in \mathbb{F}[w]$, we determine the Jordan canonical form of the formal Fr\'{e}chet…

We introduce canonical coordinates on minimal time-like surfaces in the n-dimensional Minkowski space and prove the existence and the uniqueness of these parameters. With respect to these coordinates the coefficients of the first…