Related papers: The Complete Characterization of Fourth-Order Symp…
If the $n-th$ order differential equation is not exact, under certain conditions, an integrating factor exists which transforms the differential equation into an exact one. Hence, its order can be reduced to the lower order. In this paper,…
We extend a factorization due to Krein to arbitrary analytic functions from the upper half-plane to itself. The factorization represents every such function as a product of fractional linear factors times a function which, generally, has…
Analytic combinatorics studies the asymptotic behaviour of sequences through the analytic properties of their generating functions. This article provides effective algorithms required for the study of analytic combinatorics in several…
To an orthogonal or unitary involution on a central simple algebra of degree 4, or to a symplectic involution on a central simple algebra of degree 8, we associate a Pfister form that characterises the decomposability of the algebra with…
A consequent approach is proposed to construct symplectic force-gradient algorithms of arbitrarily high orders in the time step for precise integration of motion in classical and quantum mechanics simulations. Within this approach the basic…
We develop the symplectic elimnation algorithm. This algorithm using simple row operations reduce a symplectic matrix to a diagonal matrix. This algorithm gives rise to a decomposition of an arbitrary matrix into a product of a symplectic…
In a recent work of Wu, Wang, Sun and Liu, a second-order explicit symplectic integrator was proposed for the integrable Kerr spacetime geometry. It is still suited for simulating the nonintegrable dynamics of charged particles moving…
We enumerate the connected graphs that contain a number of edges growing linearly with respect to the number of vertices. So far, only the first term of the asymptotics and a bound on the error were known. Using analytic combinatorics, ie…
Coherent or exact equations of motion for a post-Newtonian Lagrangian formalism are the Euler-Lagrange equations without any terms truncated. They naturally conserve energy {and} angular momentum. Doubling the phase-space variables of…
In this paper we characterize the definiteness of the discrete symplectic system, study a nonhomogeneous discrete symplectic system, and introduce the minimal and maximal linear relations associated with these systems. Fundamental…
We present a novel expression for an integrated correlation function of four superconformal primaries in $SU(N)$ $\mathcal{N}=4$ SYM. This integrated correlator, which is based on supersymmetric localisation, has been the subject of several…
In this paper we deal with symplectic Lie algebras. All symplectic structures are determined for dimension four and the corresponding Lie algebras are classified up to equivalence. Symplectic four dimensional Lie algebras are described…
The Fueter-Sce mapping theorem stands as one of the most profound outcomes in complex and hypercomplex analysis, producing hypercomplex generalizations of holomorphic functions. In recent years, delving into the factorization of the second…
A variety of problems emerged investigating electronic circuits, computer devices and cellular automata motivated a number of attempts to create a differential and integral calculus for Boolean functions. In the present article, we extend…
We show that the method of factorizing the evolution operator to fourth order with purely positive coefficients, in conjunction with Suzuki's method of implementing time-ordering of operators, produces a new class of powerful algorithms for…
In this paper, we propose a factorization of a fourth-order harmonic tensor into second-order tensors. We obtain moreover explicit equivariant reconstruction formulas, using second-order covariants, for transverse isotropic and orthotropic…
Optimization algorithms can be interpreted through the lens of dynamical systems as the interconnection of linear systems and a set of subgradient nonlinearities. This dynamical systems formulation allows for the analysis and synthesis of…
We study a class of evolutionary partial differential systems with two components related to second order (in time) non-evolutionary equations of odd order in spatial variable. We develop the formal diagonalisation method in symbolic…
We calculate the formal analytic expansions of certain formal translations in a space of formal iterated logarithmic and exponential variables. The results show how the algebraic structure naturally involves the Stirling numbers of the…
Several recent works have revealed a simplicity in equal-time correlators that is absent in their wavefunction counterparts. In this letter, we show that this arises from the simple fact that the correlator is obtained by integrating…