Spatial Central Limit Theorem for Supercritical Superprocesses

We consider a measure-valued diffusion (i.e., a superprocess). It is determined by a couple \((L,\psi )\), where L is the infinitesimal generator of a strongly recurrent diffusion in \(\mathbb {R}^{d}\) and \(\psi \) is a branching mechanism assumed to be supercritical. Such processes are known, see for example, (Englander and Winter in Ann Inst Henri Poincaré 42(2):171–185, 2006), to fulfill a law of large numbers for the spatial distribution of the mass. In this paper, we prove the corresponding central limit theorem. The limit and the CLT normalization fall into three qualitatively different classes arising from “competition” of the local growth induced by branching and global smoothing due to the strong recurrence of L. We also prove that the spatial fluctuations are asymptotically independent of the fluctuations of the total mass of the process.     

Block partitions: an extended view

Given a sequence \({S=(s_1, \ldots,s_m) \in [0, 1]^m}\), a block B of S is a subsequence \({B=(s_i,s_{i+1}, \ldots,s_j)}\). The size b of a block B is the sum of its elements. It is proved in [1] that for each positive integer n, there is a partition of S into n blocks B₁, \({\ldots,}\) B _n with \({|b_i - b_j| \le 1}\) for every i, j. In this paper, we consider a generalization of the problem in higher dimensions.     

On properties and applications of (p,q)-extended τ-hypergeometric functions

We introduce the $(p,q)$-extended τ-hypergeometric and confluent hypergeometric functions along with their integral representations. We also present closed integral expressions for the Mathieu-type a-series and for the associated alternating versions whose terms contain the $(p,q)$-extended τ-hypergeometric functions with related contiguous functional relations.     

Chemical Evolution of the Universe and its Consequences for Gravitational-Wave Astrophysics

Gravitational waves (GW) emitted by merging black holes (BH) and neutron stars are now routinely detected. Those are the afterlives of massive stars that formed all across the Universe—at different cosmic times and with different metallicities. Birth metallicity plays an important role in the evolution of massive stars. Consequently, the population properties of mergers are sensitive to the metallicity dependent cosmic star formation history (f_SFR(Z,z)). In particular, within the isolated formation scenarios (the focus of this paper), a strong low metallicity preference of the formation of BH mergers is found. The origin of this dependence and its consequences are discussed. Most importantly, uncertainty in the f_SFR(Z,z) (substantial even at low redshifts) cannot be ignored in the models. This poses a challenge for the interpretation of the observed GW source population properties. Possible improvements and the role of future GW detectors are considered. Recent efforts to determine f_SFR(Z,z) and the factors that dominate its uncertainty are summarized. Many of those factors stem from the uncertain properties of faint and distant galaxies. The fact that they leave imprint on the redshift-dependent properties of mergers makes GW a promising (and complementary to electromagnetic observations) tool to study galaxy chemical evolution.     

A direct-to-biology high-throughput chemistry approach to reactive fragment screening

Methods for rapid identification of chemical tools are essential for the validation of emerging targets and to provide medicinal chemistry starting points for the development of new medicines. Here, we report a screening platform that combines ‘direct-to-biology’ high-throughput chemistry (D2B-HTC) with photoreactive fragments. The platform enabled the rapid synthesis of >1000 PhotoAffinity Bits (HTC-PhABits) in 384-well plates in 24 h and their subsequent screening as crude reaction products with a protein target without purification. Screening the HTC-PhABit library with carbonic anhydrase I (CAI) afforded 7 hits (0.7% hit rate), which were found to covalently crosslink in the Zn²⁺ binding pocket. A powerful advantage of the D2B-HTC screening platform is the ability to rapidly perform iterative design–make–test cycles, accelerating the development and optimisation of chemical tools and medicinal chemistry starting points with little investment of resource.

A photoreactive fragment screening platform employing direct-to-biology high-throughput chemistry (D2B-HTC) for the rapid iterative synthesis and screening of libraries of photoaffinity bits.     

Quinolinesulfonamides: Interaction between bovine serum albumin,molecular docking analysis,and antiproliferative activity against human breast carcinoma cells

The complex formation of bovine serum albumin (BSA) with library of all seven regioisomeric quinolinesulfonamides (QSAs) under physiological condition is studied in this paper. The fluorescence quenching mechanism of BSA by QSAs was discussed and the association constants, as well as the number of binding sites, were calculated. In addition, a molecular docking study of the tested sulfamoylquinolines on the active site of serum albumin is performed. The experimental data and molecular docking studies reveal that sulfamoylquinolines bind in the large hydrophobic cavity of subdomain IB, and in the hydrophobic pockets of BSA subdomains IIA and IIIA by hydrophobic interactions with tryptophanyl (Trp-213) and tyrosyl residues. Moreover, the antiproliferative activity of QSAs against two human breast cancer cell lines (human adenocarcinoma (MCF-7) and human ductal carcinoma (MDA-MB-231)) and a human normal fibroblast is also studied in this paper. The antiproliferative activity of the tested QSAs was comparable to those of cisplatin. The returned data indicate that some of the tested quinolinesulfamoyl derivatives display significant cytotoxic activity.     

Empirical equations for the temperature dependence of calcite-water oxygen isotope fractionation from 10 to 70°C

Although the temperature dependence of calcite‐water oxygen isotope fractionation seems to have been well established by numerous empirical, experimental and theoretical studies, it is still being discussed, especially due to the demand for increased accuracy of paleotemperature calculations. Experimentally determined equations are available and have been verified by theoretical calculations (considered as representative of isotopic equilibrium); however, many natural formations do not seem to follow these relationships implying either that existing fractionation equations should be revised, or that carbonate deposits are seriously affected by kinetic and solution chemistry effects, or late‐stage alterations. In order to test if existing fractionation‐temperature relationships can be used for natural deposits, we have studied calcite formations precipitated in various environments by means of stable isotope mass spectrometry: travertines (freshwater limestones) precipitating from hot and warm waters in open‐air or quasi‐closed environments, as well as cave deposits formed in closed systems. Physical and chemical parameters as well as oxygen isotope composition of water were monitored for all the investigated sites. Measuring precipitation temperatures along with oxygen isotope compositions of waters and calcites yielded empirical environment‐specific fractionation–temperature equations: [1] 1000 · lnα = 17599/T – 29.64 [for travertines with a temperature range of 30 to 70°C] and [2] 1000 · lnα = 17500/T – 29.89 [for cave deposits for the range 10 to 25°C]. Finally, based on the comparison of literature data and our results, the use of distinct calcite‐water oxygen isotopic fractionation relationships and application strategies to obtain the most reliable paleoclimate information are evaluated. Copyright © 2010 John Wiley & Sons, Ltd.     

Formation of a promazine radical and promazine 5‐oxide in the reaction of promazine with hydrogen peroxide: Mechanistic insight from kinetic and EPR measurements

The kinetics of the oxidation of promazine (PMZ) by hydrogen peroxide was studied in the presence of a large excess of H₂O₂ in acidic chloride media using UV–vis spectroscopy. The reaction proceeds via two consecutive steps. In the first step, oxidation leads to formation of a promazine radical. In the second step, the promazine radical is oxidized to promazine 5‐oxide. Electron paramagnetic resonance spectroscopy (EPR) results provide clear evidence for the formation of an intermediate promazine radical. Linear dependences of the pseudo‐first‐order rate constants (k₁ and k₂) on [H₂O₂] with a nonzero intercept were established for the first and the second process, respectively. The rate of the first stage of the reaction increased slightly with increasing concentration of O₂, indicating the role of the OH^? radicals on the redox process, which are transformed into the Cl radicals. The mechanism of the overall reaction is discussed on the basis of all these kinetic measurements. © 2009 Wiley Periodicals, Inc. Int J Chem Kinet 42: 1–9, 2010     

First measurement of the linear polarization of radiative electron capture transitions

For radiative electron capture into the K shell of bare uranium ions, a study of the polarization properties has been performed. For this purpose a position sensitive germanium detector has been used as an efficient Compton polarimeter. This enabled us to measure the degree of linear polarization by analyzing Compton scattering inside the detector and to determine the orientation of the polarization plane. Depending on the observation angle and the beam energy used, the radiation is found to be linearly polarized by up to 80%. In all cases studied, the plane of polarization coincides with the collision plane. The results will be discussed in the context of rigorous relativistic calculations, showing that relativistic effects tend to lead to a depolarization of the radiation emitted.