MECHANISM OF RADIATION CROSS-LINKING OF POLYMERS AND ITS RELATIONSHIP WITH STRUCTURAL MULTIPLICITY

In an attempt to explore the effect of structural multiplicity of polymers on the mechanism of radiation crosslinking, the adaptability of the Charlesby-Pinner's equation and its various modified versions are examined. It is recognized that both chemical and morphological multiplicity of polymer structure results in the multiplicity of crosslinking mechanism, and that any single equation can only be applicable to a certain step of the whole radiation process.

Bayes and empirical-Bayes multiplicity adjustment in the variable-selection problem

This paper studies the multiplicity-correction effect of standard Bayesian variable-selection priors in linear regression. Our first goal is to clarify when, and how, multiplicity correction happens automatically in Bayesian analysis, and to distinguish this correction from the Bayesian Ockham's-razor effect. Our second goal is to contrast empirical-Bayes and fully Bayesian approaches to variable selection through examples, theoretical results and simulations. Considerable differences between the two approaches are found. In particular, we prove a theorem that characterizes a surprising aymptotic discrepancy between fully Bayes and empirical Bayes. This discrepancy arises from a different source than the failure to account for hyperparameter uncertainty in the empirical-Bayes estimate. Indeed, even at the extreme, when the empirical-Bayes estimate converges asymptotically to the true variable-inclusion probability, the potential for a serious difference remains. © Institute of Mathematical Statistics, 2010.

Fission dynamics for capture reactions in 58,64ni + 208pb systems: New results in terms of thermal energy and neutron multiplicity correlated distributions

The neutron multidetector DéMoN has been used to investigate the symmetric splitting dynamics in the reactions 58.64Ni + 208Pb with excitation energies ranging from 65 to 186 MeV for the composite system. An analysis based on the new backtracing technique has been applied on the neutron data to determine the two-dimensional correlations between the parent composite system initial thermal energy (EthCN) and the total neutron multiplicity (νtot), and between pre- and post-scission neutron multiplicities (νpre and νpost, respectively). The νpre distribution shape indicates the possible coexistence of fast-fission and fusion-fission for the system 58Ni + 208Pb (Ebeam = 8.86 A MeV). The analysis of the neutron multiplicities in the framework of the combined dynamical statistical model (CDSM) gives a reduced friction coefficient β = 23 ± 2512 × 1021 s-1, above the one-body dissipation limit. The corresponding fission time is τf = 40 ± 4620 × 10-21 s. © 1999 Elsevier Science B.V. All rights reserved.

The AstraLux large M-dwarf multiplicity survey

We present the results of an extensive high-resolution imaging survey of M-dwarf multiplicity using the Lucky Imaging technique. The survey made use of the AstraLux Norte camera at the Calar Alto 2.2m telescope and the AstraLux Sur camera at the ESO New Technology Telescope in order to cover nearly the full sky. In total, 761 stars were observed (701M-type and 60 late K-type), among which 182 new and 37 previously known companions were detected in 205 systems. Most of the targets have been observed during two or more epochs, and could be confirmed as physical companions through common proper motion, often with orbital motion being confirmed in addition. After accounting for various bias effects, we find a total M-dwarf multiplicity fraction of 27% ± 3% within the AstraLux detection range of 008-6? (semimajor axes of ~3-227 AU at a median distance of 30pc). We examine various statistical multiplicity properties within the sample, such as the trend of multiplicity fraction with stellar mass and the semimajor axis distribution. The results indicate that M-dwarfs are largely consistent with constituting an intermediate step in a continuous distribution from higher-mass stars down to brown dwarfs. Along with other observational results in the literature, this provides further indications that stars and brown dwarfs may share a common formation mechanism, rather than being distinct populations. © 2012. The American Astronomical Society. All rights reserved.

Sets of multiplicity and closable multipliers on group algebras

We undertake a detailed study of the sets of multiplicity in a second countable locally compact group G and their operator versions. We establish a symbolic calculus for normal completely bounded maps from the space B(L-2(G)) of bounded linear operators on L-2 (G) into the von Neumann algebra VN(G) of G and use it to show that a closed subset E subset of G is a set of multiplicity if and only if the set E* = {(s,t) is an element of G x G : ts(-1) is an element of E} is a set of operator multiplicity. Analogous results are established for M-1-sets and M-0-sets. We show that the property of being a set of multiplicity is preserved under various operations, including taking direct products, and establish an Inverse Image Theorem for such sets. We characterise the sets of finite width that are also sets of operator multiplicity, and show that every compact operator supported on a set of finite width can be approximated by sums of rank one operators supported on the same set. We show that, if G satisfies a mild approximation condition, pointwise multiplication by a given measurable function psi : G -> C defines a closable multiplier on the reduced C*-algebra G(r)*(G) of G if and only if Schur multiplication by the function N(psi): G x G -> C, given by N(psi)(s, t) = psi(ts(-1)), is a closable operator when viewed as a densely defined linear map on the space of compact operators on L-2(G). Similar results are obtained for multipliers on VN(C).

Sets of p-multiplicity in locally compact groups

We initiate the study of sets of p-multiplicity in locally compact groups and their operator versions. We show that a closed subset E of a second countable locally compact group G is a set of p-multiplicity if and only if E∗={(s,t):ts−1∈E} is a set of operator p-multiplicity. We exhibit examples of sets of p-multiplicity, establish preservation properties for unions and direct products, and prove a p-version of the Stone–von Neumann Theorem.

The VLT-FLAMES Tarantula Survey XXII. Multiplicity properties of the B-type stars

We investigate the multiplicity properties of 408 B-type stars observed in the 30 Doradus region of the Large Magellanic Cloud with multi-epoch spectroscopy from the VLT-FLAMES Tarantula Survey (VFTS). We use a cross-correlation method to estimate relative radial velocities from the helium and metal absorption lines for each of our targets. Objects with significant radial-velocity variations (and with an amplitude larger than 16 km s^-1) are classified as spectroscopic binaries. We find an observed spectroscopic binary fraction (defined by periods of <10^3.5 d and mass ratios >0.1) for the B-type stars, f<inf>B</inf>(obs) = 0.25 ± 0.02, which appears constant across the field of view, except for the two older clusters (Hodge 301 and SL 639). These two clusters have significantly lower binary fractions of 0.08 ± 0.08 and 0.10 ± 0.09, respectively. Using synthetic populations and a model of our observed epochs and their potential biases, we constrain the intrinsic multiplicity properties of the dwarf and giant (i.e. relatively unevolved) B-type stars in 30 Dor. We obtain a present-day binary fraction f<inf>B</inf>(true) = 0.58 ± 0.11, with a flat period distribution. Within the uncertainties, the multiplicity properties of the B-type stars agree with those for the O stars in 30 Dor from the VFTS.

Multiplicity results for some classes of Schrödinger-Poisson systems

In this thesis, we study the existence and multiplicity of solutions of the following class of Schr odinger-Poisson systems: u + u + l(x) u = (x; u) in R3; = l(x)u2 in R3; where l 2 L2(R3) or l 2 L1(R3). And we consider that the nonlinearity satis es the following three kinds of cases: (i) a subcritical exponent with (x; u) = k(x)jujp 2u + h(x)u (4 p < 2 ) under an inde nite case; (ii) a general inde nite nonlinearity with (x; u) = k(x)g(u) + h(x)u; (iii) a critical growth exponent with (x; u) = k(x)juj2 2u + h(x)jujq 2u (2 q < 2 ). It is worth mentioning that the thesis contains three main innovations except overcoming several di culties, which are generated by the systems themselves. First, as an unknown referee said in his report, we are the rst authors concerning the existence of multiple positive solutions for Schr odinger- Poisson systems with an inde nite nonlinearity. Second, we nd an interesting phenomenon in Chapter 2 and Chapter 3 that we do not need the condition R R3 k(x)ep 1dx < 0 with an inde nite noncoercive case, where e1 is the rst eigenfunction of +id in H1(R3) with weight function h. A similar condition has been shown to be a su cient and necessary condition to the existence of positive solutions for semilinear elliptic equations with inde nite nonlinearity for a bounded domain (see e.g. Alama-Tarantello, Calc. Var. PDE 1 (1993), 439{475), or to be a su cient condition to the existence of positive solutions for semilinear elliptic equations with inde nite nonlinearity in RN (see e.g. Costa-Tehrani, Calc. Var. PDE 13 (2001), 159{189). Moreover, the process used in this case can be applied to study other aspects of the Schr odinger-Poisson systems and it gives a way to study the Kirchho system and quasilinear Schr odinger system. Finally, to get sign changing solutions in Chapter 5, we follow the spirit of Hirano-Shioji, Proc. Roy. Soc. Edinburgh Sect. A 137 (2007), 333, but the procedure is simpler than that they have proposed in their paper.

The neuroprotective potential of flavonoids: a multiplicity of effects

Flavonoids exert a multiplicity of neuroprotective actions within the brain, including a potential to protect neurons against injury induced by neurotoxins, an ability to suppress neuroinflammation, and the potential to promote memory, learning and cognitive function. These effects appear to be underpinned by two common processes. Firstly, they interact with critical protein and lipid kinase signalling cascades in the brain leading to an inhibition of apoptosis triggered by neurotoxic species and to a promotion of neuronal survival and synaptic plasticity. Secondly, they induce beneficial effects on the vascular system leading to changes in cerebrovascular blood flow capable of causing angiogenesis, neurogenesis and changes in neuronal morphology. Through these mechanisms, the consumption of flavonoid-rich foods throughout life holds the potential to limit neurodegeneration and to prevent or reverse age-dependent loses in cognitive performance. The intense interest in the development of drugs capable of enhancing brain function means that flavonoids may represent important precursor molecules in the quest to develop of a new generation of brain enhancing drugs.

Style, experimentation and Jingju (Beijing Opera) as a decentered multiplicity

Jingju (Beijing Opera) is widely considered to be a fundamentally non-naturalistic practice that became known in the West after it caught the attention of western practitioners in 1935 following Mei Lanfang’s performance in Moscow. Given the implication that its importance is largely historical, some non-specialists have implied that Jingju has little relevance to contemporary modes of thinking, particularly the multiplicities of experience as outlined by philosophers such as Deleuze and Guattari. This article seeks to demonstrate the multiplicity of Jingju for a wider readership through both a historical analysis and a deconstruction of the form. It will show how, at the same time that Mei Lanfang was providing a ‘non-realistic’ model for western practitioners eager to displace the dominance of naturalism, realistic settings were becoming an integral part of Jingju performances in Shanghai. The article also engages with the various acting pai/styles that weave Jingju into a complex, multiple form. The article demonstrates how Deleuzian models actually facilitate a greater understanding of Jingju.

MULTIPLICITY OF POSITIVE SOLUTIONS FOR A CLASS OF NONLINEAR SCHRODINGER EQUATIONS

This paper proves the multiplicity of positive solutions for the following class of quasilinear problems: {-epsilon(p)Delta(p)u+(lambda A(x) + 1)vertical bar u vertical bar(p-2)u = f(u), R(N) u(x)>0 in R(N), where Delta(p) is the p-Laplacian operator, N > p >= 2, lambda and epsilon are positive parameters, A is a nonnegative continuous function and f is a continuous function with subcritical growth. Here, we use variational methods to get multiplicity of positive solutions involving the Lusternick-Schnirelman category of intA(-1)(0) for all sufficiently large lambda and small epsilon.

On the Multiplicity of Orthogonal Geodesics in Riemannian Manifold With Concave Boundary. Applications to Brake Orbits and Homoclinics

Let (M, g) be a complete Riemannian Manifold, Omega subset of M an open subset whose closure is diffeomorphic to an annulus. If partial derivative Omega is smooth and it satisfies a strong concavity assumption, then it is possible to prove that there are at least two geometrically distinct geodesics in (Omega) over bar = Omega boolean OR partial derivative Omega starting orthogonally to one connected component of partial derivative Omega and arriving orthogonally onto the other one. The results given in [6] allow to obtain a proof of the existence of two distinct homoclinic orbits for an autonomous Lagrangian system emanating from a nondegenerate maximum point of the potential energy, and a proof of the existence of two distinct brake orbits for a. class of Hamiltonian systems. Under a further symmetry assumption, it is possible to show the existence of at least dim(M) pairs of geometrically distinct geodesics as above, brake orbits and homoclinics.

Measurement of the t(t)over-bar cross section using high-multiplicity jet events

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Shape, transverse size, and charged-hadron multiplicity of jets in pp collisions at root s=7 TeV

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)