Generalized skew derivations on triangular algebras determined by action on zero products

For a triangular algebra 𝒜 and an automorphism σ of 𝒜, we describe linear maps F,G:𝒜→𝒜 satisfying F(x)y+σ(x)G(y) = 0 whenever x,y∈𝒜 are such that xy = 0. In particular, when 𝒜 is a zero product determined triangular algebra, maps F and G satisfying the above condition are generalized skew derivations of the form F(x) = F(1)x+D(x) and G(x) = σ(x)G(1)+D(x) for all x∈𝒜, where D:𝒜→𝒜 is a skew derivation. When 𝒜 is not zero product determined, we show that there are also nonstandard solutions for maps F and G.     

Representing Sparse Gaussian DAGs as Sparse R-Vines Allowing for Non-Gaussian Dependence

Modeling dependence in high-dimensional systems has become an increasingly important topic. Most approaches rely on the assumption of a multivariate Gaussian distribution such as statistical models on directed acyclic graphs (DAGs). They are based on modeling conditional independencies and are scalable to high dimensions. In contrast, vine copula models accommodate more elaborate features like tail dependence and asymmetry, as well as independent modeling of the marginals. This flexibility comes however at the cost of exponentially increasing complexity for model selection and estimation. We show a novel connection between DAGs with limited number of parents and truncated vine copulas under sufficient conditions. This motivates a more general procedure exploiting the fast model selection and estimation of sparse DAGs while allowing for non-Gaussian dependence using vine copulas. By numerical examples in hundreds of dimensions, we demonstrate that our approach outperforms the standard method for vine structure selection. Supplementary material for this article is available online.     

Study on Synthesis and NMR Characterization of 2,3-O-Hydroxyethyl Cellulose Depending on Synthesis Conditions

The synthesis of hydroxyethyl celluloses with regioselective functionalization in position 2 and 3 starting from triphenylmethyl (trityl) cellulose is described. The effects of reaction conditions upon both the degree of substitution and the distribution of the hydroxyethyl moieties were investigated in detail. The interest was not only focused on regioselective functionalization within the anhydroglucose unit but also on the formation of oxyethylene side chains. To avoid the formation of oxyethylene side chains, 2-(2-bromoethoxy)tetrahydropyran was used as etherifying agent in comparison with 2-bromoethanol. By acidic hydrolysis, both protecting groups – trityl at 6 position and tetrahydropyran at the hydroxyethyl substituent – can be simultaneously cleaved off. The hydroxyethyl celluloses were characterized by one- and two-dimensional NMR spectroscopy in order to determine the substitution pattern.     

Closed Range Property for Holomorphic Semi-Fredholm Functions

Given Banach spaces X and Y, we show that, for each operator-valued analytic map ${\alpha \in \mathcal O (D,\mathcal L(Y,X))}$ satisfying the finiteness condition ${\dim (X/\alpha (z)Y) < \infty}$ pointwise on an open set D in ${\mathbb {C}^n}$ , the induced multiplication operator ${\mathcal O(U,Y) \stackrel{\alpha}{\longrightarrow} \mathcal O (U,X)}$ has closed range on each Stein open set ${U \subset D}$ . As an application we deduce that the generalized range ${{\rm R}^{\infty}(T) = \bigcap_{k \geq 1}\sum_{| \alpha | = k} T^{\alpha}X}$ of a commuting multioperator ${T \in \mathcal L(X)^n}$ with ${\dim(X/\sum_{i=1}^n T_iX) < \infty}$ can be represented as a suitable spectral subspace.     

Inverse temperature transition of a biomimetic elastin model: reactive flux analysis of folding/unfolding and its coupling to solvent dielectric relaxation

The inverse temperature transition (ITT) of a biomimetic model for elastin, capped GVG(VPGVG) in liquid water, is investigated by a comprehensive classical molecular dynamics study. The temperature dependence of the solvation structure and dynamics of the octapeptide are compared using three common force fields, CHARMM, GROMOS, and OPLS. While these force fields differ in quantitative detail, they all predict this octapeptide to undergo a "folding transition" to closed conformations upon heating and a subsequent "unfolding transition" to open conformations at still higher temperatures, thus reproducing the ITT scenario. The peptide kinetics is analyzed within the reactive flux formalism applied to the largest-amplitude mode extracted from principal component analysis, and the solvent's dielectric fluctuations are obtained from the total water dipole autocorrelations. Most importantly, preliminary evidence for an intimate coupling of peptide folding/unfolding dynamics, and thus the ITT, and dielectric relaxation of bulk water is given, possibly being consistent with a "slave mode" picture.     

On the Construction of Statistically Similar Representative Volume Elements Based on the Lineal-Path Function

In this contribution we propose a method for the construction of statistically similar representative volume elements (SSRVEs) which are characterized by a much less complexity than usual random RVEs and which represent quite accurately the mechanical response of the real material. For the design of such SSRVEs an objective function is minimized taking into account least-square functionals based on suitable statistical measures, that characterize the inclusion morphology. Here, we find that the incorporation of the lineal-path function leads to promising results in FE²-simulations of macroscopically homogeneous boundary value problems as well as inhomogenous ones. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Isogeometric Collocation: Cost Comparison with Galerkin Methods and Extension to Adaptive Hierarchical NURBS Discretizations

Collocation is based on the discretization of the strong form of the underlying partial differential equations, which requires basis functions of sufficient order and smoothness. Consequently, the use of isogeometric analysis (IGA) for collocation suggests itself, since splines can be readily adjusted to any order in polynomial degree and continuity required by the differential operators. In addition, they can be generated for domains of arbitrary geometric and topological complexity, directly linked to and fully supported by CAD technology. The major advantage of isogeometric collocation over Galerkin type IGA is the minimization of the computational effort for numerical quadrature. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The muon magnetic moment and new physics

The impact of the muon magnetic moment measurement on physics beyond the Standard Model is briefly reviewed. Particular emphasis is given on the case of supersymmetry. The sensitivity of g ? 2 to supersymmetry parameters and the potential for model discrimination and parameter measurements is described. The interplay between LHC data on the Higgs boson, limits on new particles, and g ? 2 is discussed.