相关论文: A symbolic method for k-statistics

Recently, D. S. Kim and T. Kim have studied applications of um- bral calculus associated with p-adic invariant integrals on Zp (see [6]). In this paper, we investigate some interesting properties arising from umbral calculus. These…

The paper develops a symbolic calculus for Fourier integral operators associated with canonical transformations.

We obtain a class of parametric oscillation modes that we call K-modes with damping and absorption that are connected to the classical harmonic oscillator modes through the "supersymmetric" one-dimensional matrix procedure similar to…

Differintegral methods, currently exploited in calculus, provide a fairly unexhausted source of tools to be applied to a wide class of problems involving the theory of special functions and not only. The use of integral transforms of Borel…

Recent developments in the categorical foundations of universal algebra have given fresh impetus to an understanding of the lambda calculus coming from categorical logic: an interpretation is a semi-closed algebraic theory. Scott's…

We offer new proofs, refinements as well as new results related to classical means of two variables, including the identric and logarithmic means.

Following the student t-statistic, normalization has been a widely used method in statistic and other disciplines including economics, ecology and machine learning. We focus on statistics taking the form of a ratio over (some power of) the…

We show how the use of superalgebraic methods sheds new light on some classical themes of representation theory and it leads to significant simplifications of traditional proofs.

This paper describes a new method for Symbolic Regression that allows to find mathematical expressions from a dataset. This method has a strong mathematical basis. As opposed to other methods such as Genetic Programming, this method is…

Quantum graphs have recently been introduced as model systems to study the spectral statistics of linear wave problems with chaotic classical limits. It is proposed here to generalise this approach by considering arbitrary, directed graphs…

This short note proposes a symbolic approach for representing and reasoning about quantum circuits using complex, vector or matrix-valued Boolean expressions. A major benefit of this approach is that it allows us to directly borrow the…

The umbral approach provides methods for comprehending and redefining special functions. This approach is employed efficiently in order to uncover intricacies and introduce new families of special functions. In this article, the umbral…

In this paper we use the viewpoint of the formal calculus underlying vertex operator algebra theory to study certain aspects of the classical umbral calculus and we introduce and study certain operators generalizing the classical umbral…

Clustering methods are a valuable tool for the identification of patterns in high dimensional data with applications in many scientific problems. However, quantifying uncertainty in clustering is a challenging problem, particularly when…

In this short expository article, we describe a mathematical tool called the probabilistic method, and illustrate its elegance and beauty through proving a few well-known results. Particularly, we give an unconventional probabilistic proof…

We develop a kind of quantum formalism (Hilbert space probabilistic calculus) for measurements performed over cognitive (in particular, conscious) systems. By using this formalism we could predict averages of cognitive observables.…

Dual numbers and their higher order version are important tools for numerical computations, and in particular for finite difference calculus. Based upon the relevant algebraic rules and matrix realizations of dual numbers, we will present a…

We show that, in spite of a rather common opinion, quantum mechanics can be represented as an approximation of classical statistical mechanics. The approximation under consideration is based on the ordinary Taylor expansion of physical…

Influence diagrams provide a compact graphical representation of decision problems. Several algorithms for the quick computation of their associated expected utilities are available in the literature. However, often they rely on a full…

In this work we deal with a symbolic approach to the general quadratic polynomial decomposition. By means of a symbolic implementation, we investigate some properties of the components sequences like orthogonality and symmetry. We present…