相关论文: An explicit formula for a strong connection
Some special solutions to the multidimensional Lam\'e and Bourlet type equations are constructed in an explicit form.
We give an explicit formula for the Deligne pairing for a proper and flat morphisms $f:X\to S$ of schemes, in terms of the determinant of cohomology. The whole construction is justified by an analogy with the intersection theory on…
We prove an explicit version of Burgess' bound on character sums for composite moduli.
We prove the consistency of a strong polarized relation for a cardinal and its successor, using pcf and forcing
We exhibit a method to numerically compute power series expansions of modular forms on a cocompact Fuchsian group, using the explicit computation a fundamental domain and linear algebra.
We prove an explicit formula of the Berezin star product on Kaehler manifolds. The formula is expressed as a summation over certain strongly connected digraphs. The proof relies on a combinatorial interpretation of Englis' work on the…
We augment LP with a strong conditional operator, to yield a logic we call "strong LP," or LP=>. The resulting logic can speak of consistency in more discriminating ways, but introduces new possibilities for trivializing paradoxes.
We call the \emph{$p$-fundamental string} of a complex simple Lie algebra to the sequence of irreducible representations having highest weights of the form $k\omega_1+\omega_p$ for $k\geq0$, where $\omega_j$ denotes the $j$-th fundamental…
The aim of this paper is to give a new method to construct explicit formulas for algebraic differential operators of any order on a finitely generated projective module $E$ on a commutative unital ring $A$. We moreover give explicit…
This article presents an equivalent formulation of the implicit complementarity problem. We demonstrate that solution of the equivalent formulation is equivalent to the solution of the implicit complementarity problem. Moreover, we provide…
In this work we deduce explicit formulae for the elements of the matrices that represent the action of integro-differential operators over the coefficients of generalized Fourier series. Our formulae are obtained by performing operations on…
We formulate and prove a general recurrence relation that applies to integrals involving orthogonal polynomials and similar functions. A special case are connection coefficients between two sets of orthonormal polynomials, another example…
We derive and prove the connection formulas for the lambda generalized diagonal Ising model correlation functions.
We report progress in the computation and analysis of strong-coupling series of two- and three-dimensional ${\rm O}(N)$ $\sigma$ models. We show that, through a combination of long strong-coupling series and judicious choice of observables,…
A heuristic but pedagogical derivation is given of an explicit formula which accurately reproduces the period of a simple pendulum even for large amplitudes. The formula is compared with others in the literature.
An infinite dimensional algebra, which is useful for deriving exact solutions of the generalized pairing problem, is introduced. A formalism for diagonalizing the corresponding Hamiltonian is also proposed. The theory is illustrated with…
Let $\xi$ be an algebraic number and let $\alpha,\beta\in \mathbb Q[\xi]$. An explicit formula for the coordinates of the product $\alpha\beta$ is given in terms of the coordinates of $\alpha$ and $\beta$ and the companion matrix of the…
A formula for calculating Extensions of (mainly integral) Polynomial Functors is established, based upon projective resolutions. Sample computations are performed, which, in particular, exhibit a surprising non-trivial extension of Divided…
A sufficient condition of the convergence of an exotic formal series (a kind of power series with complex exponents) solution to an ODE of a general form is proposed.
We give an explicit formula for the Jones polynomial of any rational link in terms of the denominators of the canonical continued fraction of the slope of the given rational link.