In this paper we deal with monogenic and k-hypermonogenic automorphic forms on arithmetic subgroups of the Ahlfors-Vahlen group. Monogenic automorphic forms are exactly the 0-hypermonogenic automorphic forms. In the first part we establish an explicit relation to Maaß wave forms. In the second part we introduce Clifford algebra valued k-hypermonogenic cusp forms. We construct k-hypermonogenic P...

In this paper we introduce the geodesic conjugacy language and geodesic conjugacy growth series for a finitely generated group. We study the effects of various group constructions on rationality of both the geodesic conjugacy growth series and spherical conjugacy growth series, as well as on regularity of the geodesic conjugacy language and spherical conjugacy language. In particular, we show t...

Evaluations of series of the q-Watson, q-Dixon, and q-Whipple type Chuanan Wei1∗ Xiaoxia Wang2† 1 Department of Medical Informatics, Hainan Medical University, China 2 Department of Mathematics, Shanghai University, China received 16th Apr. 2016, revised 1st May 2017, accepted 6th June 2017. Using q-series identities and series rearrangement, we establish several extensions of q-Watson formulas...

We propose a generalization of a classical result on random Fourier series, namely the Billard Theorem, for random Fourier series over the d-dimensional torus. We provide an investigation of the independence with respect to a choice of a sequence of partial sums (or method of summation). We also study some probabilistic properties of the resulting sum field such as stationarity and characterist...

A method is presented (with standard examples) based on an elementary complex integral expression, for developing Frobenius series solutions for second-order linear homogeneous ordinary Fuchs differential equations. The method reduces the task of finding a series solution to the solution, instead, of a system of simple equations in a single variable. The method is straightforward to apply as an...

The control problem and Dynamic programming is a powerful tool in economics and management. We review the dynamic programming problem from its beginning up to its present stages. A problem which was involved in physics and mathematics in I 7” century led to a branch of mathematics called calculus of variation which was used in economic, and management at the end of the first quarter of the 20” ...

We provide concise series representations for various L-series integrals. Different techniques are needed below and above the abscissa of absolute convergence of the underlying L-series. 1. Preliminaries. In [8] the following odd looking integral evaluation is obtained. ∫ ∞ 0 ( 3− 2 √ 2 cos (t log 2) ) |ζ (1/2 + it)| t2 + 1/4 dt = π log 2. (1) This identity turns out—formally—to be a case of a ...

This paper discusses how young children engage with ‘control’ technology and in particular how do they attempt to control the behavior of physical and screen ‘robots’. Episodes of children-robot interactions are discussed based on data from a series of case studies where children with adults engage in specifically designed learning activities that aim to introduce young children to the basics o...

These notes provide an introduction to the mathematics used in medical imaging. In Section 6 we review the basics of calculus and multivariable calculus. In Section 2 we introduce Fourier Series, which is a premonition for the introduction of the Fourier Transform in Section 3. Finally, we will treat the mathematics of CT-Scans with the introduction of the Radon Transform in Section 4. Section ...

Aalto University, P.O. Box 11000, FI-00076 Aalto www.aalto.fi Author Olavi Nevanlinna Name of the publication Multicentric representation and von Neumann spectral sets Publisher School of Science Unit Department of Mathematics and Systems Analysis Series Aalto University publication series SCIENCE + TECHNOLOGY 11/2011 Field of research Mathematics Abstract We show how multicentric representatio...