Related papers: Disturbing the $q$-Dyson Conjecture
In this paper, I argue, contrary to the prevailing opinion in the linguistics and philosophy literature, that a sortal approach to aspectual composition can indeed be explanatory. In support of this view, I develop a synthesis of competing…
We look into computational aspects of two classical knot invariants. We look for ways of simplifying the computation of the coloring invariant and of the Alexander module. We support our ideas with explicit computations on pretzel knots.
In this article we give a survey on open problems and conjectures concerning L^2-invariants. We cover the whole portfolio and not only certain aspects as they are considered in the previous more specialized (and within their scope more…
A conjecture is given that, if true, could lead to an algorithm for computing definite sums of rational functions.
A new method for parallel generation of $q$-valued pseudorandom sequence based on the presentation of systems generating logical formulae by means of arithmetic polynomials is proposed. Fragment consisting of $k$-elements of $q$-valued…
A coherent mathematical overview of computation and its generalisations is described. This conceptual framework is sufficient to comfortably host a wide range of contemporary thinking on embodied computation and its models.
We relate the complexity of both differential and $q$-difference equations of order one and degree one and their solutions. Our point of view is to show that if the solutions are complicated, the initial equation is complicated too. In this…
Some difficulties, both numerical and conceptual, of the method to compute one dimensional wave functions by numerically integrating the quantum Hamilton-Jacobi equation, presented in the paper mentioned in the title, are analyzed. The…
We generalize the method of combinatorial telescoping to the case of multiple summations. We shall demonstrate this idea by giving combinatorial proofs for two identities of Andrews on parity indices of partitions.
We describe a variational approximation method for efficient inference in large-scale probabilistic models. Variational methods are deterministic procedures that provide approximations to marginal and conditional probabilities of interest.…
We develop an alternative approach to time independent perturbation theory in non-relativistic quantum mechanics. The method developed has the advantage to provide in one operation the correction to the energy and to the wave function,…
This paper attempts to prove the Sylvester's conjecture using Egyptian Fractions with two key ingredients. First, creating a set of operators that completely generates all possible Egyptian fraction of 1. And second, to detect patterns in…
In a recent paper published in the Philosophical Magazine [Z.-D. Zhang, Phil. Mag. 87, 5309-5419 (2007), arXiv:0705.1045], the author advances a conjectured solution for various properties of the three-dimensional Ising model. Here we…
Some conjectures and open problems in convex geometry are presented, and their physical origin, meaning, and importance, for quantum theory and generic statistical theories, are briefly discussed.
In the recent paper the interesting q-Euler numbers and polynomials introduced in JMAA. The purpose of this paper is to construct the modified q-Euler numbers and polynomiasl. Finally we will give the interesting many identities related to…
I describe my path to unconventionality in my exploration of theoretical and applied aspects of computation towards revealing the algorithmic and reprogrammable properties and capabilities of the world, in particular related to applications…
In this paper, we study a general Syracuse problem. We give some necessary conditions concerning the existence of eventual non trivial cycles. Some properties based on linear logarithmic forms are established. New general conjectures are…
An exciting new algorithmic breakthrough has been advanced for how to carry out inferences in a Dempster-Shafer (DS) formulation of a categorical data generating model. The developed sampling mechanism, which draws on theory for directed…
We extend some results about shifted Schur functions to the general context of shifted Macdonald polynomials. We obtain two explicit formulas for these polynomials: a $q$-integral representation and a combinatorial formula. Our main tool is…
We investigate the 2-dimensional jacobian conjecture via Klein's program.