Estimates on Green functions of second order differential operators with singular coefficients

We investigate the Green functions G(x,x^{\prime}) of some second order differential operators on R^{d+1} with singular coefficients depending only on one coordinate x_{0}. We express the Green functions by means of the Brownian motion. Applying probabilistic methods we prove that when x=(0,{\bf x}) and x^{\prime}=(0,{\bf x}^{\prime}) (here x_{0}=0) lie on the singular hyperplanes then G(0,{\bf x};0,{\bf x}^{\prime}) is more regular than the Green function of operators with regular coefficients.Comment: 16 page

Trimethyl-3-meth­oxy-4-oxo-5-triphenyl­phospho­ranyl­idene­cyclo­pent-1-ene-1,2,3-tricarboxyl­ate

The title compound, C30H27O8P (2), was formed as one of two products {(1) [Krawczyk et al. (2010 ▶). Acta Cryst. E66 (cv2752)] and (2)} in the reaction of dimethyl acetyl­enedicarboxyl­ate with triphenyl­phosphine. The mol­ecule of (2) consists of a five-membered carbocyclic ring. The P atom is a part of a triphenylphosphoranylidene substituent. In contrast to (1), the five-membered ring of (2) is planar, the r.m.s. deviation being only 0.009 (2) Å

On the existence of effective potentials in time-dependent density functional theory

We investigate the existence and properties of effective potentials in time-dependent density functional theory. We outline conditions for a general solution of the corresponding Sturm-Liouville boundary value problems. We define the set of potentials and v-representable densities, give a proof of existence of the effective potentials under certain restrictions, and show the set of v-representable densities to be independent of the interaction.Comment: 13 page

Implication of the PAMELA antiproton data for dark matter indirect detection at LHC

Since the PAMELA results on the "anomalously" high positron fraction and the lack of antiproton excess in our Galaxy, there has been a tremendous number of studies advocating new types of dark matter, with larger couplings to electrons than to quarks. This raises the question of the production of dark matter particles (and heavy associated coloured states) at LHC. Here, we explore a very simple benchmark dark matter model and show that, in spite of the agreement between the PAMELA antiproton measurements and the expected astrophysical secondary background, there is room for large couplings of a WIMP candidate to heavy quarks. Contrary to what could have been naively anticipated, the PAMELA pbar/p measurements do not challenge dark matter model building, as far as the quark sector is concerned. A quarkophillic species is therefore not forbidden.Owing to these large couplings, one would expect that a new production channel opens up at the LHC, through quark--quark and quark--gluon interactions. Alas, when the PDF of the quark is taken into account, prospects for a copious production fade away.Comment: 7 pages, 2 figures, captions of some figures modified, main conclusion unchange

Tetra­methyl 1,1,2-triphenyl-2H-1λ5-phosphole-2,3,4,5-tetra­carboxyl­ate

The title compound, C30H27O8P (1), was formed as one of two products {(1) and (2) [Krawczyk et al. (2010 ▶). Acta Cryst. E66 (cv2753)]} in the reaction of dimethyl acetyl­enedicarboxyl­ate with triphenyl­phosphine. The mol­ecule of (1) consists of a five-membered ring, in which the P atom is incorporated. One of the phenyl groups of the triphenyl­phosphine migrated to a vicinal C atom during the reaction. The five-membered ring of (1) is corrugated [r.m.s. deviation = 0.0719 (8) Å], whereas that in compound (2) is planar, the r.m.s. deviation being only 0.009 (2) Å

Translation Representations and Scattering By Two Intervals

Studying unitary one-parameter groups in Hilbert space (U(t),H), we show that a model for obstacle scattering can be built, up to unitary equivalence, with the use of translation representations for L2-functions in the complement of two finite and disjoint intervals. The model encompasses a family of systems (U (t), H). For each, we obtain a detailed spectral representation, and we compute the scattering operator, and scattering matrix. We illustrate our results in the Lax-Phillips model where (U (t), H) represents an acoustic wave equation in an exterior domain; and in quantum tunneling for dynamics of quantum states

Theoretical and experimental investigation of thiourea derivatives: synthesis, crystal structure, in-silico and in-vitro biological evaluation

ABSTRACT. In this study, five different thiourea derivatives were synthesized from aryl amines according to the reported method. 1-Benzoyl-3-(4-methoxyphenyl)thiourea (2) was confirmed with single crystal XRD analysis while 1-benzoyl-3-phenylthiourea (1), 1-benzoyl-3-(4-hydroxyphenyl)thiourea (3), 1-benzoyl-3-(2-nitrophenyl) thiourea (4) and 1-benzoyl-3-p-tolylthiourea (5) were elucidated with FTIR and NMR techniques. The geometry optimization of the targeted molecules was accomplished with density functional theory applying B3LYP function. The experimental (XRD) and calculated (DFT) bond angles and bond lengths were compared. The frontier molecular orbitals and molecular electrostatic potential were computed to determine the charge density distribution and possible sites for electrophilic and nucleophilic reactions of the crystalline compound. The synthesized compounds were evaluated as an anti-radical scavenger and enzyme (esterases and protease) inhibitor using in-vitro models. The results confirmed that the synthesized molecules have good anti-oxidant property while a moderate enzyme inhibiting activity. Docking study was conducted with acetylcholine and butyrylcholine esterase which suggested that molecules under study have a potential to inhibit these esterases and protease enzymes. On the basis of in-vitro studies, it is concluded that compound 2 is most active against all tested assays.                     KEY WORDS: Thiourea, 2,2-Diphenyl-1-picrylhydrazyl, Enzyme inhibition, Density functional theory, Docking studies   Bull. Chem. Soc. Ethiop. 2021, 35(3), 587-600. DOI: https://dx.doi.org/10.4314/bcse.v35i3.1

Cosmic ray electrons and positrons from discrete stochastic sources

The distances that galactic cosmic ray electrons and positrons can travel are severely limited by energy losses to at most a few kiloparsec, thereby rendering the local spectrum very sensitive to the exact distribution of sources in our galactic neighbourhood. However, due to our ignorance of the exact source distribution, we can only predict the spectrum stochastically. We argue that even in the case of a large number of sources the central limit theorem is not applicable, but that the standard deviation for the flux from a random source is divergent due to a long power law tail of the probability density. Instead, we compute the expectation value and characterise the scatter around it by quantiles of the probability density using a generalised central limit theorem in a fully analytical way. The uncertainty band is asymmetric about the expectation value and can become quite large for TeV energies. In particular, the predicted local spectrum is marginally consistent with the measurements by Fermi-LAT and HESS even without imposing spectral breaks or cut-offs at source. We conclude that this uncertainty has to be properly accounted for when predicting electron fluxes above a few hundred GeV from astrophysical sources.Comment: 16 pages, 8 figures; references and clarifying comment added; to appear in JCA

“Clicking“ fragment leads to novel dual-binding cholinesterase inhibitors

Cholinesterase inhibitors are potent therapeutics in the treatment of Alzheimer's disease. Among them, dual binding ligands have recently gained a lot of attention. We discovered novel dual-binding cholinesterase inhibitors, using “clickable” fragments, which bind to either catalytic active site (CAS) or peripheral anionic site (PAS) of the enzyme. Copper(I)-catalyzed azide-alkyne cycloaddition allowed to effectively synthesize a series of final heterodimers, and modeling and kinetic studies confirmed their ability to bind to both CAS and PAS. A potent acetylcholinesterase inhibitor with IC50 = 18 nM (compound 23g) was discovered. A target-guided approach to link fragments by the enzyme itself was tested using butyrylcholinesterase

Atmospheric and Galactic Production and Propagation of Light Antimatter Nuclei

The production and propagation of light antimatter nuclei has been calculated using inclusive antiproton production cross sections from a new data analysis, and coalescence models for the production of composite particles. Particles were propagated using recently proven phenomenological approaches. The atmospheric secondary flux is evaluated for the first time. The Galactic flux obtained are larger than those obtained previously in similar calculations. The non-annihilating scattering contributions of the propagated particles are introduced. The preliminary results are shown and discussed.Comment: 4 pages, Contribution to the ICRC 200