We propose some classes of series representations for $1/\pi$ and $\pi^2$ by using a new WZ-pair. As examples, among many others, we prove that \begin{equation*} \frac{3}{2}\sum_{n=1}^{\infty}\frac{n}{16^n(n+1)(2n-1)}\binom{2n}{n}^2=\frac{1}{\pi}, \end{equation*} 1-\frac{1}{4}\sum_{n=0}^{\infty}\frac{3n+2}{(n+1)^2}\binom{2n}{n}^2 \frac{1}{16^n}=\frac{1}{\pi} $$ 4\sum_{n=0}^{\infty}\frac{1}{(n+1...

BCH codes, known for their error-correcting capability and efficient encoding decoding algorithms, are an important class of cyclic codes over finite fields. Currently, have been widely applied in consumer devices, communication systems, data storage systems. However, there is still a lot unsolved work exploring the parameters such as dimensions minimum distances. The objective this paper to st...

Let p be a rational prime, k be a perfect field of characteristic p, W = W (k) be the ring of Witt vectors, K be a finite totally ramified extension of Frac(W ) of degree e and r be a non-negative integer satisfying r < p − 1. In this paper, we prove the upper numbering ramification group G (j) K for j > 1+e(1+r/(p−1)) acts trivially on the mod p representations associated to the semi-stable p-...

We present two observations related to the application of linear (LFE) and nonlinear fractional equations (NFE). First, we give the comparison and estimates of the role of the fractional derivative term to the normal diffusion term in a LFE. The transition of the solution from normal to anomalous transport is demonstrated and the dominant role of the power tails in the long time asymptotics is ...

In an investigation of t he physical properties of hydr<;>gen isotopes it was n.ecessar.\:' t o prepare 10 liters of high-purity. hydro~en d~u.tende. TI1JS was don e ~y r eactmg IJ t hlUm aluminum hydride wit h deutenum oXIde, gly.;n~ hydro~en deutende, ]I) .t wo batch~s, ?f 98.1and 97.0-percent purity, respect ive!.\:' . .Ihls mater!ai was t hen frac t IOnated at JtqUJd hydrogen t emperature i...

A coarse-mesh finite element model of an engine cradle structure is experimentally correlated using the structural system identification technique. The coarsemesh model represents the cradle structure with beam and spring elements. The structural system identifcation code SSID is used to update the structural properties to correlate the model with measured natural frequency and modeshape data. ...

1.1 The lifting problem The problem we are concerned with in our lectures and which we shall refer to as the lifting problem was originally formulated by Frans Oort in [17]. To state it, we fix an algebraically closed field κ of positive characteristic p. Let W (κ) be the ring of Witt vectors over κ. Throughout our notes, o will denote a finite local ring extension of W (κ) and k = Frac(o) the ...

This paper presents a new partitioning scheme for fractal image coding, based on triangles and quadrilaterals. The aim is to have the advantage of the triangles over the square and rectangular blocks, in terms of adaptivity to the image (reduction of the block eeect), and to reduce the blocks number by grouping neighboring triangles into quadrilat-erals. Quadrilaterals permit a reduction of the...

Robert Pollet, MD, PhD, chief of R&D at the Atlanta VA Medical Center and an outgoing FRAC member, says the group has helped establish “an atmosphere of genuine cooperation” in support of research. esearchers at the San Francisco VA Medical Center have identified the mechanism by which minocycline, a medication being studied for the treatment of Parkinson’s disease and other neurodegenerative c...

Hough transform is a popular low-level computer vision algorithm. Its computationally effective modification, Fast Hough transform (FHT), makes use of special subsets of image matrix to approximate geometric lines on it. Because of their special structure, these subset are called dyadic patterns. In this paper various properties of dyadic patterns are investigated. Exact upper bounds on approxi...