Hasil untuk "q-fin.PR"

F. Arecchi, R. Meucci, G. Puccioni et al.

W. Al-salam

Arun Rai, Ilgaz Arikan, J. Pye et al.

A. Crofts, S. Meinhardt, Kevin R. Jones et al.

A. Bayad, Taekyun Kim

In this paper, we give relations involving values of q-Bernoulli, q-Euler, and Bernstein polynomials. Using these relations, we obtain some interesting identities on the q-Bernoulli, q-Euler, and Bernstein polynomials.

M. Aredes, Hirofumi Akagi, Edson H. Watanabe et al.

Vijay Gupta

A. Rodolakis

F. Atici, P. Eloe

Abstract The study of fractional q-calculus in this paper serves as a bridge between the fractional q-calculus in the literature and the fractional q-calculus on a time scale , where to ∈ ℝ and 0 < q < 1. By use of time scale calculus notation, we find the proof of many results more straight forward. We shall develop some properties of fractional q-calculus, we shall develop some properties of a q-Laplace transform, and then we shall employ the q-Laplace transform to solve fractional q-difference equations.

D. Funder, R. Furr, C. R. Colvin

Taekyun Kim

H. Gauchman

Abstract In this paper, q -calculus analogues of some classical and some recent integral inequalities are found. Applications to estimation of sums of some convergent series are also given.

T. Laakso

Tiffany Barnes

S. Ostrovska

Eric Wiewiora

Shaping has proven to be a powerful but precarious means of improving reinforcement learning performance. Ng, Harada, and Russell (1999) proposed the potential-based shaping algorithm for adding shaping rewards in a way that guarantees the learner will learn optimal behavior. In this note, we prove certain similarities between this shaping algorithm and the initialization step required for several reinforcement learning algorithms. More specifically, we prove that a reinforcement learner with initial Q-values based on the shaping algorithm's potential function make the same updates throughout learning as a learner receiving potential-based shaping rewards. We further prove that under a broad category of policies, the behavior of these two learners are indistinguishable. The comparison provides intuition on the theoretical properties of the shaping algorithm as well as a suggestion for a simpler method for capturing the algorithm's benefit. In addition, the equivalence raises previously unaddressed issues concerning the efficiency of learning with potential-based shaping.

A. Sole, V. Kac

We study q-integral representations of the q-gamma and the q-beta functions. This study leads to a very interesting q-constant. As an application of these integral representations, we obtain a simple conceptual proof of a family of identities for Jacobi triple product, including Jacobi's identity, and of Ramanujan's formula for the bilateral hypergeometric series.

P. Fournier, D. Raoult

Stuart J. Russell, A. Zimdars

David S. Leslie, E. J. Collins