Abstract We investigate uniform upper bounds for the number of powerful numbers in short intervals $(x, x + y]$ . obtain unconditional $O({y}/{\log y})$ and $O(\kern1.3pt y^{11/12})$ all $y^{1/2}$ -smooth numbers, respectively. Conditional on $abc$ -conjecture, we prove bound ^{1+\epsilon } squarefull y^{(2 \epsilon )/k})$ k -full when $k \ge 3$ These are related to Roth’s theorem arithmetic pr...

In 1999, Katona and Kierstead conjectured that if a k-uniform hypergraph \({\mathcal {H}}\) on n vertices has minimum co-degree \(\lfloor \frac{n-k+3}{2}\rfloor \), i.e., each set of \(k-1\) is contained in at least \) edges, then it Hamiltonian cycle. Rödl, Ruciński Szemerédi 2011 proved the conjecture true when \(k=3\) large. We show this Katona-Kierstead holds \(k=4\), large, \(V({\mathcal {...

We present in this paper an algorithm for identifying satellites in DNA sequences. Satellites (simple, micro, or mini) are repeats in number between 30 and as many as 1,000,000 whose lengths vary between 2 and hundreds of base pairs and that appear, with some mutations, in tandem along the sequence. We concentrate here on short to moderately long (up to 30-40 base pairs) approximate tandem repe...

The activity and trafficking of the Na(+),K(+)-ATPase are regulated by several hormones, including dopamine, vasopressin, and adrenergic hormones through the action of G-protein-coupled receptors (GPCRs). Arrestins, GPCR kinases (GRKs), 14-3-3 proteins, and spinophilin interact with GPCRs and modulate the duration and magnitude of receptor signaling. We have found that arrestin 2 and 3, GRK 2 a...

An epsilon number is a transfinite number which is a fixed point of an exponential map: ω ε = ε. The formalization of the concept is done with use of the tetration of ordinals (Knuth's arrow notation, ↑↑). Namely, the ordinal indexing of epsilon numbers is defined as follows: ε0 = ω ↑↑ ω, εα+1 = εα ↑↑ ω, and for limit ordinal λ: ε λ = lim α<λ εα = α<λ εα. Tetration stabilizes at ω: α ↑↑ β = α ↑...

High-resolution spectra of the ~B(2)A(1)-- ~X(2)A(1) transitions of CaCH(3) and SrCH(3) have been recorded in a molecular jet/laser ablation source using laser excitation spectroscopy. Transitions arising from the K = 0 and 1 sub-bands have been observed for both molecules. An analysis of the data using a (2)A(1) symmetric top Hamiltonian has determined rotational and spin-rotation constants fo...

The allelic frequency of the gene for the K variant of butyrylcholinesterase (BCHE-K) was 0.17 in 74 subjects with late-onset (age > 65 years) histopathologically diagnosed Alzheimer's disease (AD), which was higher than the frequencies in 104 elderly control subjects (0.09), in 14 early-onset cases of confirmed AD (0.07) and in 29 confirmed cases of other dementia (0.10). The association of BC...

A grid of bars towed through a sample of He II produces both superfluid turbulence and classical hydrodynamic turbulence. The two velocity fields-in the normal fluid and in the superfluid-have been observed to have the same energy spectral density over a large range of scales. Here, we introduce a characteristic scale l(q)=2 pi(epsilon/kappa(3))(-1/4), where epsilon is the rate of turbulent ene...