Proof. First suppose that a ∼H b, so that a = bk for some k ∈ H, and let ah (with h ∈ H) be an artibrary element of aH. Then we have ah = bkh = b(kh) ∈ bH, hence aH ⊆ bH. The proof of bH ⊆ aH is similar. Conversely, suppose that aH = bH. Since a ∈ aH = bH we have a = bk for some k ∈ H. Then a−1b = k−1 ∈ H, hence a ∼H b. (d) Prove that the map g 7→ ag is a bijection from H to aH. Proof. Consider...

The potential energy surfaces (PESs) of Lin(BH)5(n-6) systems (where n = 5, 6, and 7) were explored using the gradient embedded genetic algorithm (GEGA) program, in order to find their global minima conformations. This search predicts that the lowest-energy isomers of Li6(BH)5 and Li7(BH)5(+) contain a (BH)5(6-) pentagonal fragment, which is isoelectronic and structurally analogous to the proto...

We present results for two colliding black holes (BHs), with angular momentum, spin, and unequal mass. For the first time, gravitational waveforms are computed for a grazing collision from a full 3D numerical evolution. The collision can be followed through the merger to form a single BH, and through part of the ringdown period of the final BH. The apparent horizon is tracked and studied, and p...

In this article we look at the well-studied upper bounds for |A|, where A ⊂ N is a Bh sequence, and generalise these to the case where A ⊂ N d. In particular we give d-dimensional analogues to results of Chen, Jia, Graham and Green.

A set A of positive integers is a Bh-set if all the sums of the form a1+ · · ·+ah, with a1, . . . , ah ∈ A and a1 ≤ · · · ≤ ah, are distinct. We provide asymptotic bounds for the number of Bh-sets of a given cardinality contained in the interval [n] = {1, . . . , n}. As a consequence of our results, we address a problem of Cameron and Erdős (1990) in the context of Bh-sets. We also use these re...

We examined effects of an angiotensin converting-enzyme inhibitor, benazepril hydrochloride (BH), on renal hypertension and chronic renal failure (CRF) in cats. For experimental CRF, healthy cats (n=5) underwent 7/8 renal ablation. After renal insufficiency and hypertension were confirmed by blood urea nitrogen (BUN), serum creatinine, creatinine clearance and telemetric recording of systemic b...

According to recent simulations, the coalescence of two spinning black holes (BHs) could lead to a BH remnant with recoil speeds of up to thousands of km s(-1). Here we examine the circumstances resulting from a gas-rich galaxy merger under which the ejected BH would carry an accretion disk and be observable. As the initial BH binary emits gravitational radiation and its orbit tightens, a hole ...

Long oligopeptides (>10 residues) are generated during the catabolism of cellular proteins in the cytosol. To be presented to T cells, such peptides must be trimmed by aminopeptidases to the proper size (typically 8-10 residues) to stably bind to MHC class I molecules. Aminopeptidases also destroy epitopes by trimming them to even shorter lengths. Bleomycin hydrolase (BH) is a cytosolic aminope...

We describe the successful synthesis of the first mixed-cation (pseudoternary) amidoborane, Na[Li(NH(2)BH(3))(2)], with theoretical hydrogen capacity of 11.1 wt%. Na[Li(NH(2)BH(3))(2)] crystallizes triclinic (P1) with a = 5.0197(4) Å, b = 7.1203(7) Å, c = 8.9198(9) Å, α = 103.003(6)°, β = 102.200(5)°, γ = 103.575(5)°, and V = 289.98(5) Å(3) (Z = 2), as additionally confirmed by Density Function...

The production rate of compact objects, i.e. neutron stars (NS) and black holes (BH), in active galactic nuclei (AGN) and quasars (QSO), where the frequent supernova explosion is used to explain the high metallicity, is very high due to the interaction between the accretion disk and main sequence stars in the nucleus of the quasar. The compact object-red giant star (RG) binaries can be easily f...