Related papers: A non-PSLQ route to BBP-type formulas
A case-based reasoning (CBR) system solves a new problem by retrieving `cases' that are similar to the given problem. If such a system can achieve high accuracy, it is appealing owing to its simplicity, interpretability, and scalability. In…
The aim of the paper is to give an explicit description of bi-quadratic algebras on 3 generators with PBW basis.
This article defines and proves basic properties of the standard quantum circuit model of computation. The model is developed abstractly in close analogy with (classical) deterministic and probabilistic circuits, without recourse to any…
We consider M systems (each an electron in a long square cylinder) uniformly arranged on a ring and with Coulomb interactions. Exact straightforward numerical time-dependent perturbation calculation of a single N-level ($\lesssim 7$)…
We derive interesting arctangent identities involving the golden ratio, Fibonacci numbers and Lucas numbers. Binary BBP-type formulas for the arctangents of certain odd powers of the golden ratio are also derived, for the first time in the…
In this paper, a new non-search based synthesis algorithm for reversible circuits is proposed. Compared with the widely used search-based methods, our algorithm is guarantied to produce a result and can lead to a solution with much fewer…
Approximate Bayesian computation (ABC) has become an essential tool for the analysis of complex stochastic models when the likelihood function is numerically unavailable. However, the well-established statistical method of empirical…
Empirical evidence reveals existence of partial D-operators for the generalized IBP (BT) reduction algorithms that are, counterintuitively, much simpler and much easier to find than the complete D-operators from the foundational Bernstein…
The BRST structure of polynomial Poisson algebras is investigated. It is shown that Poisson algebras provide non trivial models where the full BRST recursive procedure is needed. Quadratic Poisson algebras may already be of arbitrarily high…
This short article presents a table of new equations which can be regarded as the generalized equations of the dispersionless limit of several nonlinear equations. From the definition expressed in an algebraic formula, one can get an…
Interested in formalizing the generation of fast running code for linear algebra applications, the authors show how an index-free, calculational approach to matrix algebra can be developed by regarding matrices as morphisms of a category…
In the last time some papers were devoted to the study of the con- nections between binary block codes and BCK-algebras. In this paper, we try to generalize these results to n-ary block codes, providing an algorithm which allows us to…
For a two parameter family of Bernoulli numbers $B_{n, p}$ the exponential generating function is derived by elementary methods.
The driving force in the pursuit for quantum computation is the exciting possibility that quantum algorithms can be more efficient than their classical analogues. Research on the subject has unraveled several aspects of how that can happen.…
Existence and uniqueness results for the solution of the Gibbs-type formula from non-extensive mechanics are derived rigorously. A new conditional extremal problem is proposed to get in a more simple way the Gibbs-type formula itself.
We present methods for obtaining new solutions to the bispectral problem. We achieve this by giving its abstract algebraic version suitable for generalizations. All methods are illustrated by new classes of bispectral operators.
The paper introduces a generalization for known probabilistic models such as log-linear and graphical models, called here multiplicative models. These models, that express probabilities via product of parameters are shown to capture…
We introduce an algorithm that conjectures the structure of a permutation class in the form of a disjoint cover of "rules"; similar to generalized grid classes. The cover is usually easily verified by a human and translated into an…
In this work, we present a method to generate probability distributions and classes of probability distributions, which broadens a process of probability distribution construction. In this method, distribution classes are built from…
Extensions of the $Stirling$ numbers of the second kind and $Dobinski$ -like formulas are proposed in a series of exercises for graduates. Some of these new formulas recently discovered by me are to be found in the source paper $ [1]$.…