In this paper we construct sampling sets over the rotation group SO(3). The proposed construction is based on a parameterization, which reflects the product nature S2 × S1 of SO(3) very well, and leads to a spherical Pythagorean-like formula in the parameter domain. We prove that by using uniformly distributed points on S2 and S1 we obtain uniformly sampling nodes on the rotation group SO(3). F...

A new technique utilizing theoretical wave forms has been developed to determine precise shear wave travel times. This technique was applied to long-period World-Wide Standard Seismograph Network and Canadian network seismograms of five large nuclear explosions to obtain a surface focus shear wave data set containing about 100 travel times for distances greater than 30 ø. Very little scatter is...

There are developed many topological methods which are powerful tools in the theory of critical points of functionals; see for example [2], [3], [5], [6], [9], [13]–[20], [22]–[25], [27]–[29], [32], [33], [43]–[45], [47], [48], [51], [59]. It happens quite often that functionals whose critical points are important in the theory of differential equations are invariant under an action of a compac...

This communication reports a numerical simulation of reentry induction by successive stimulation (S1-S2) that does not require an S1 gradient of refractoriness. The S1 action potential is uniform in space, so before the S2 stimulus there is no refractory gradient. Nevertheless, a unipolar S2 stimulus initiates quatrefoil reentry. The result supports the growing realization that virtual electrod...

In this communication, we describe several features of the D. melanogaster gene which codes for ribosomal protein 49 (rp49). Nucleotide sequence analysis in conjunction with primer extension and S1 nuclease protection experiments show that the structure of the rp49 gene consists of a 102 bp 5' exon, a single 59 bp intron, and a 420 bp 3' exon, encoding a total of 132 amino acids. The rp49 gene ...

Helicobacter pylori is a gram-negative rod associated with gastroduodenal pathologies, such as gastritis, peptic ulcer, and gastric adenocarcinoma. Although most H. pylori infections are clinically silent, the organism is associated with substantial morbidity and mortality. It is unknown why the bacteria are able to produce severe disease in some hosts and be innocuous in others. Different viru...

Given an undirected graph G = (V,E), the max-cut problem asks for the partition S1, S2 ⊆ V , s.t., the number of edges going from S1 to S2 are maximized. Remember that since S1, S2 is a partition, so S1∪S2 = V and S1 ∩ S2 = ∅. Clearly this is an optimization problem. It is known to be NP-hard and so not expected to have a polynomial time algorithm. We are interested in finding an approximation ...

I have 50 pairs of socks of which 30 are black and 35 are cotton. How many pairs of socks are black and cotton? If I call the set of black socks A and the set of cotton socks B, we are looking at |A ∩ B|. It is not hard to see that: |A ∪ B| = |A| + |B| − |A ∩ B| because every element that belongs to both A and B is counted twice by |A|+|B|, so we subtract the size of the intersection once. Ther...

Cross-linking of myosin subfragment 1 (S1) with a molar excess of actin in vitro reveals the presence of an actin-S1-actin complex. It is absolutely essential that actin be present in molar excess over S1 so that the decoration of F-actin with S1 be incomplete. However, the excess of actin may not be available in the overlap zone of sarcomeres of skeletal muscle. We therefore found it necessary...