相关论文: A Holonomic Ideal Annihilating the Fisher-Bingham …

In this paper, we discuss a system of differential equations for the Fisher integral on the special orthogonal group. Especially, we explicitly give a set of linear differential operators which generates the annihilating ideal of the Fisher…

We give a new algorithm to find local maximum and minimum of a holonomic function and apply it for the Fisher-Bingham integral on the sphere $S^n$, which is used in the directional statistics. The method utilizes the theory and algorithms…

The Fisher-Bingham system is a system of linear partial differential equations satisfied by the Fisher-Bingham integral for the $n$-dimensional sphere $S^n$. The system is given in [Nakayama et al. (2011), Theorem 2] and it is shown that it…

In this paper we implement the holonomic gradient method to exactly compute the normalising constant of Bingham distributions. This idea is originally applied for general Fisher-Bingham distributions in Nakayama et al. (2011). In this paper…

We present a novel algorithm for constructing differential operators with respect to external variables that annihilate Feynman-like integrals and give rise to the associated $\mathcal{D}$-modules, based on Griffiths-Dwork reduction. By…

This work continues the research of generalized Heisenberg algebras connected with several orthogonal polynomial systems. The realization of the annihilation operator of the algebra corresponding to a polynomial system by a differential…

We present an algorithm for computing a holonomic system for a definite integral of a holonomic function over a domain defined by polynomial inequalities. If the integrand satisfies a holonomic difference-differential system including…

We present an algorithm to compute the annihilator of (i.e., the linear differential equations for) the logarithm of a polynomial in the ring of differential operators with polynomial coefficients. The algorithm consists of differentiation…

We study a generalized Chebyshev oscillator [1] associated with a point interaction for the discrete Schr\"odinger equation. Our goal is to find a realization of the annihilation operator for this oscillator by a differential operator. This…

We develop the theory of Hodge ideals for Q-divisors by means of log resolutions, extending our previous work on reduced hypersurfaces. We prove local (non-)triviality criteria and a global vanishing theorem, as well as other analogues of…

Let $O_X$ (resp. $D_X$) be the sheaf of holomorphic functions (resp. the sheaf of linear differential operators with holomorphic coefficients) on $X$ (=the complex affine n-space). Let $Y$ be a locally weakly quasi-homogeneous free divisor…

We consider {\em discretized} Hamiltonian PDEs associated with a Hamiltonian function that can be split into a linear unbounded operator and a regular nonlinear part. We consider splitting methods associated with this decomposition. Using a…

We study {\it non-holonomic} overideals of a left differential ideal $J\subset F[\partial_x, \partial_y]$ in two variables where $F$ is a differentially closed field of characteristic zero. The main result states that a principal ideal $J=<…

We show that for each Banach ideal of homogeneous polynomials, there exists a (necessarily unique) Banach operator ideal compatible with it. Analogously, we prove that any ideal of $n$-homogeneous polynomials belongs to a coherent sequence…

After sketching the basic theory of injective ideals of homogeneous polynomials, we characterize injective polynomial ideals by means of a domination property and applications of this characterization to some classical operator ideals and…

Without any restrictions on the base field, we compute the hull and prove a conjecture of Eisenbud and Sturmfels giving an unmixed decomposition of a cellular binomial ideal. Over an algebraically closed field, we further obtain an explicit…

In this paper we generalize the involutive methods and algorithms devised for polynomial ideals to differential ones generated by a finite set of linear differential polynomials in the differential polynomial ring over a zero characteristic…

A dynamic iteration scheme for linear infinite-dimensional port-Hamiltonian systems is proposed. The dynamic iteration is monotone in the sense that the error is decreasing, it does not require any stability condition and is in particular…

An ideal of a local polynomial ring can be described by calculating a standard basis with respect to a local monomial ordering. However standard basis algorithms are not numerically stable. Instead we can describe the ideal numerically by…

We investigate properties of differential and difference operators annihilating certain finite-dimensional subspaces of exponential functions in two variables that are connected to the representation of real-valued trigonometric and…