Sufficient conditions for the invertibility of adapted perturbations of identity on the Wiener space

Let (W, H, μ) be the classical Wiener space. Assume that U = I _W  + u is an adapted perturbation of identity, i.e., u : W → H is adapted to the canonical filtration of W. We give some sufficient analytic conditions on u which imply the invertibility of the map U. In particular it is shown that if ${u\in {\rm ID}_{p,1}(H)}$ is adapted and if ${\exp(\frac{1}{2}\|\nabla u\|_2^2-\delta u)\in L^q(\mu)}$ , where p ^?1 + q ^?1 = 1, then I _W  + u is almost surely invertible. With the help of this result it is shown that if ${\nabla u\in L^\infty(\mu,H\otimes H)}$ , then the Girsanov exponential of u times the Wiener measure satisfies the logarithmic Sobolev inequality and this implies the invertibility of U = I _W  +  u . As a consequence, if, there exists an integer k ≥  1 such that ${\|\nabla^k u\|_{H^{\otimes(k+1)}}\in L^\infty(\mu)}$ , then I _W  +  u is again almost surely invertible under the almost sure continuity hypothesis of ${t\to\nabla^i \dot{u}_t}$ for i ≤  k ? 1.     

Prediction of Yield‐line Geometries for Arbitrary Simply Supported Slabs

The calculation of limit loads of slabs using the yield‐line theory requires the assumption of a kinematical collapse mechanism. In recent years several approaches concerning the optimization of predefined mechanisms have been introduced. Usually they contain semi‐automatic procedures which depend on user‐defined yield‐line predictions. This paper presents a systematic approach and a numerical procedure to find yield‐line predictions for arbitrary all‐side supported slabs. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Die Irrtumswahrscheinlichkeit des χ 2-Testes im Grenzfall der Poissonverteilung

Summary If the expectations of two Poisson distributions are compared by means of the x ²-test, the probability of an error of the first kind is never much larger than the asymptotic value 0.01 or 0.02 or 0.05 on the three most usual levels.     

Synthesis and mass spectral study of new phenylsulfonyl substituted isoxazolidines

st001.gif" data-lg-src="/cms/attachment/bf9b81ab-4d0a-495d-94bb-31ac451664a2/must001.jpg" alt="chemical structure image" title="chemical structure image"> Ten 2,3‐disubstituted 4‐phenylsulfonyl isoxazolidines ( 3a‐j ) were prepared by 1,3‐dipolar cycloaddition reaction of substituted nitrones ( 1a‐j ) with phenyl vinyl sulfone ( 2 ). The reaction products were identified by means of IR, NMR, and MS data. In addition, the factors influencing on the electron ionization induced mass spectral fragmentation of the title products are discussed in detail.     

Optimized Wang-Landau sampling of lattice polymers: Ground state search and folding thermodynamics of HP model proteins

Coarse-grained (lattice-) models have a long tradition in aiding efforts to decipher the physical or biological complexity of proteins. Despite the simplicity of these models, however, numerical simulations are often computationally very demanding and the quest for efficient algorithms is as old as the models themselves. Expanding on our previous work [T. Wu?st and D. P. Landau, Phys. Rev. Lett. 102, 178101 (2009)], we present a complete picture of a Monte Carlo method based on Wang-Landau sampling in combination with efficient trial moves (pull, bond-rebridging, and pivot moves) which is particularly suited to the study of models such as the hydrophobic-polar (HP) lattice model of protein folding. With this generic and fully blind Monte Carlo procedure, all currently known putative ground states for the most difficult benchmark HP sequences could be found. For most sequences we could also determine the entire energy density of states and, together with suitably designed structural observables, explore the thermodynamics and intricate folding behavior in the virtually inaccessible low-temperature regime. We analyze the differences between random and protein-like heteropolymers for sequence lengths up to 500 residues. Our approach is powerful both in terms of robustness and speed, yet flexible and simple enough for the study of many related problems in protein folding.     

Random rotations of the Wiener path

Summary Let (W, H, ) be an abstract Wiener space and letR(w) be a strongly measurable random variable with values in the set of isometries onH. Suppose that Rh is smooth in the Sobolev sense and that it is a quasi-nilpotent operator onH for everyhH. It is shown that (R(w)h) is again a Gaussian (0, |h| _H ² )-random variable. Consequently, if (e _i ,i)W ^* is a complete, orthonormal basis ofH, then defines a measure preserving transformation, a rotation, onW. It is also shown that if for some strongly measurable, operator valued (onH) random variableR, (R(w+k)h) is (0, |h| _H ² )-Gaussian for allk, hH, thenR is an isometry and Rh is quasi-nilpotent for allHH. The relation between the stochastic calculi for these Wiener pathsw and , as well as the conditions of the inverbibility of the map are discussed and the problem of the absolute continuity of the image of the Wiener measure under Euclidean motion on the Wiener space (i.e. composed with a shift) is studied.The research of the second author was supported by the Fund for the Promotion of Research at the TechnionDedicated to the memory of Albert Badrikian     

Global stability of a multistrain SIS model with superinfection and patch structure

We study the global stability of a multistrain SIS model with superinfection and patch structure. We establish an iterative procedure to obtain a sequence of threshold parameters. By a repeated application of a result by Takeuchi et al. [Nonlinear Anal Real World Appl. 2006;7:235–247], we show that these parameters completely determine the global dynamics of the system: for any number of patches and strains with different infectivities, any subset of the strains can stably coexist depending on the particular choice of the parameters.     

Characterization of a 2‐Benzo[c]cinnoline Modified Glassy Carbon Electrode by Raman Spectroscopy,Electrochemical Impedance Spectroscopy,and Ellipsometry

This work describes the characterization of the grafted 2‐benzo[c]cinnoline (2BCC) molecules at a glassy carbon (GC) electrode surface by voltammetry and spectroscopy. Attachment of the molecule to the carbon substrate was achieved by the electrochemical reduction of 2‐benzo[c]cinnoline diazonium salt (2BCC‐DAS). GC electrode modification was carried out in aprotic solution with 2BCC diazonium salt. Dopamine (DA) and ascorbic acid (AA) were used to prove the surface modification to see the blockage of the electron transfer. The presence of 2BCC at the GC electrode surface was characterized by cyclic voltammetry and Raman spectroscopy. Raman spectroscopy was used to monitor molecular bound properties of the adsorbates at the 2BCC‐GC surface and confirm the attachment of 2BCC molecules onto the GC surface. The thickness of the 2BCC film on GC was also investigated by ellipsometric measurement.