We discuss a number of techniques for determining the Minkowski dimension of bounded subsets of some Euclidean space of any dimension, including: the box-counting dimension and equivalent definitions based on various box-counting functions; the similarity dimension via the Moran equation (at least in the case of self-similar sets); the order of the (box-)counting function; the classic result on...

The opioid growth factor, [Met5]-enkephalin, is an inhibitory agent of cell proliferation and maturation that interacts with the zeta (zeta) opioid receptor to modulate growth. In order to learn more about this receptor, polyclonal and monoclonal antibodies were raised against binding subunits identified on two-dimensional gels by ligand blotting. Using Western blotting, the polyclonal antibodi...

This paper extends tools developed in [10, 8] to study character polylogarithms. These objects are used to compute Mordell-Tornheim-Witten character sums and to explore their connections with multiple-zeta values (MZVs) and with their character analogues [17].

background: isolating sperms with normal chromatin content is considered vital in intra cytoplasmic sperm injection treatment. today, researchers are trying to find new procedures to select sperms with normal chromatin content and morphology. this study examines the effectiveness of zeta, density gradient centrifugation (pure sperm) and combination of pure- zeta procedures in selecting sperms w...

Objective Selection of sperm for intra-cytoplasmic sperm injection (ICSI) is usually considered as the ultimate technique to alleviate male-factor infertility. In routine ICSI, selection is based on morphology and viability which does not necessarily preclude the chance injection of DNA-damaged or apoptotic sperm into the oocyte. Sperm with high negative surface electrical charge, named “Zeta p...

The 90K solid-state structures, room temperature absorption, and room temperature and 17 K emission spectra of seven different salts of [Cu(I)(bfp)(2)](+) (bfp = 2,9-bis(trifluoromethyl)-1,10-phenanthroline) have been determined. To quantify the distortion of the Cu coordination environment, a distortion parameter zeta is defined that is a combined measure of the flattening, rocking, and waggin...

1. Classical motivation 2 1.1. Some classical identities 2 1.2. Riemann’s zeta function 2 1.3. Dedekind zeta functions 3 1.4. Higher regulators 4 2. Motivic L-functions 4 2.1. Realizations of motives 4 2.2. L-functions 6 3. Beilinson’s conjectures on special values of L-functions 7 3.1. Elementary reduction 7 3.2. The regulator map 8 3.3. The conjectures 8 3.4. Known cases 9 4. Motivic cohomolo...

1. In t roduc t ion . Several recently invented number-theoretic algorithms are sketched below. They all have the common feature that they rely on bounded precision computations of analytic functions. The main one of these algorithms is a new method of calculating values of the Riemann zeta function at multiple points. This method enables one to verify the truth of the Riemann Hypothesis (RH) f...

From the point of view of differential geometry and mathematical physics, the Riemann zeta function appears as the operator zeta function associated to the Laplacian operator on the line segment [18] [17] [5] [6] [14]. A natural generalisation of this setting, is to consider a Sturm Liouville operator instead, i.e. a singularity at one of the end points [9] [10] [11] [7] [8][16]. This leads aga...