An analysis of mean life and lifetime of unstable elementary particles

A theoretical analysis of the concept of lifetime and mean life of unstable elementary particles is presented. New analytic formulas for lifetime and mean life as a function of decay width and the mass of unstable particle are derived for Breit-Wigner and Matthews-Salam energy distributions. It is demonstrated that, for unstable particles with a larger width or decay energy threshold, the deviation from the generally accepted mean life ^m = ^–1 is significant. The behavior of the decay law P(t) for small times is analyzed, and it is shown that the Breit-Wigner distribution violates the condition P(t = 0) = 0, whereas the Matthews-Salam distribution satisfies it.     

Brownian dynamics simulations on CPU and GPU with BD_BOX

There has been growing interest in simulating biological processes under in vivo conditions due to recent advances in experimental techniques dedicated to study single particle behavior in crowded environments. We have developed a software package, BD_BOX, for multiscale Brownian dynamics simulations. BD_BOX can simulate either single molecules or multicomponent systems of diverse, interacting molecular species using flexible, coarse-grained bead models. BD_BOX is written in C and employs modern computer architectures and technologies; these include MPI for distributed-memory architectures, OpenMP for shared-memory platforms, NVIDIA CUDA framework for GPGPU, and SSE vectorization for CPU.     

The continuous solution of a functional equation of Abel

Summary The functional equation(x) + (y) = (xf(y) + yf(x)) (1) for the unknown functionsf, and mapping reals into reals appears in the title of N. H. Abel's paper [1] from 1827 and its differentiable solutions are given there. In 1900 D. Hilbert pointed to (1), and to other functional equations considered by Abel, in the second part of his fifth problem. He asked if these equations could be solved without, for instance, assumption of differentiability of given and unknown functions. Hilbert's question was recalled by J. Aczél in 1987, during the 25th International Symposium on Functional Equations in Hamburg-Rissen. In particular Aczél asked for all continuous solutions of (1). An answer to his question is contained in our paper. We determine all continuous functionsf: I ,: A _f (I × I) and: I that satisfy (1). HereI denotes a real interval containing 0 andA _f (x,y) := xf(y) + yf(x), x, y I. The list contains not only the differentiable solutions, implicitly described by Abel, but also some nondifferentiable ones.Applying some results of C. T. Ng and A. Járai we are able to obtain even a more general result. For instance, the assertion (i.e. the list of solutions) remains unchanged if we replace continuity of and by local boundedness of orf(0)I from above or below. Strengthening a bit the assumptions onf we can preserve a large part of the assertion requiring only the measurability of either orf(0)I.     

The synthesis and characterisation of some nickel(0) complexes with π-bounded vinylsilicon ligands; the molecular structure of [Ni{P(C6H5)3}2{η-CH2CHSi(CH3)3}]

Reactions of the nickel(0) complexes [Ni(cod)₂] (in the presence of PP or [Ni(PPh₃)₂C₂H₄] with vinyl-siloxanes, -silanes or -silazanes yield, by displacement of alkene ligand, the new nickel π-complexes [Ni(PPh₃)₂(η-CH₂CHSi(OSiMe₃)₃)] (2), [{Ni(PPh₃)}₂{μ-(η-{(CH₂CH)₂SiMe}₂O})] (4), [Ni(PPh₃){η⁴-CH₂CHSi(Me)(μ-O)}₃] (5), [{Ni(η-CH₂CHSiMe₂)₂O}(η-CH₂CHSiMe₃)] (7) and the known complexes [Ni(PPh₃)₂(η-CH₂CHSiMe₃)] (1), [{Ni(PPh₃)}₂{μ-(η-(CH₂CH)₄Si})] (3), [{Ni(PPh₃)(η-CH₂CHSiMe₂)₂NH}] (6) obtained by a simple one pot synthesis, more efficiently than in hitherto published reports. The X-ray crystal structure of (1) shows a trigonal planar environment around the nickel atom.     

A look at multiparticle production via modified combinants

The European Physical Journal A - The transverse momentum ($$p_{T}$$) distribution of strange hadrons ($$K_{S}^{0}$$ and $$\varLambda $$) and multi-strange hadrons( $$\varXi $$ and $$\varOmega $$)...     

Two 1-substituted 4-nitro­imidazoles

Crystalline 4-nitro-1-phenyl­imidazole, C₉H₇N₃O₂, (I), and 4′-­nitro-1-phenyl-4,1′-bii­imidazole, C₁₂H₉N₅O₂, (II), contain C—H⃛O and C—H⃛N hydrogen bonds, connecting the mol­ecules into infinite chains. The aromatic fragments in both compounds are nearly planar. The dihedral angles between the benzene and imidazole rings are 26.78 (5)° in (I) and 29.36 (8)° in (II).     

Synthesis of new 2-oxosparteine derivatives

For the first time, substituents to the 3-position of 2-oxosparteine have been introduced. The synthesis of 3-phenylthiolupanine, 3,3-di(phenylthio)lupanine, 3-dehydrolupanine, 3-bromodehydro-lupanine and 2-thiono-3-dehydrosparteine has been described. The stereochemistry of these compounds has been determined and by NMR spectroscopy and X-ray crystallography.     

Analysis of the normal modes of molecules with D3h symmetry: Infrared spectra of monomeric s-triazine and cyanuric acid

Normal modes of s-triazine and cyanuric acid were calculated at the DFT(B3LYP)/6-311++G(d,p) level. These modes were analyzed in terms of potential energy distribution (PED), computed using a specially designed set of symmetry coordinates. The normal-mode analysis was described in detail and the PED matrix definition used in the calculations was provided. Particular attention has been devoted to the degenerate vibrations. The experimental infrared spectra of s-triazine and cyanuric acid isolated in low-temperature Ar matrices have been recorded and interpreted by comparison with the theoretically predicted normal modes. In the spectrum of matrix-isolated s-triazine, the IR bands originating from ¹³C and ¹⁵N isotopologues with one of the ring atoms substituted by a rare isotope were detected. These bands were identified thanks to the excellent agreement between the experimentally observed and theoretically predicted isotope shifts.     

Simultaneous confidence bands for the integrated hazard function

The construction of the simultaneous confidence bands for the integrated hazard function is considered. The Nelson–Aalen estimator is used. The simultaneous confidence bands based on bootstrap methods are presented. Four methods of construction of such confidence bands are proposed. The weird and conditional bootstrap methods are used for resampling. Simulations are made to compare the actual coverage probability of the bootstrap and the asymptotic simultaneous confidence bands. It is shown that the equal-tailed bootstrap confidence band has the coverage probability closest to the nominal one. We also present application of our confidence bands to the data regarding survival after heart transplant. This research was partly supported by AGH grant No. 10.420.03.