A global/local analysis method for treating details in structural design

A method for analyzing global/local behavior of plate and shell structures is described. In this approach, a detailed finite element model of the local region is incorporated within a coarser global finite element model. The local model need not be nodally compatible (i.e., need not have a one-to-one nodal correspondence) with the global model at their common boundary; therefore, the two models may be constructed independently. The nodal incompatibility of the models is accounted for by introducing appropriate constraint conditions into the potential energy in a hybrid variational formulation. The primary advantage of this method is that the need for transition modeling between global and local models is eliminated. Eliminating transition modeling has two benefits. First, modeling efforts are reduced since tedious and complex transitioning need not be performed. Second, errors due to the mesh distortion, often unavoidable in mesh transitioning, are minimized by avoiding distorted elements beyond what is needed to represent the geometry of the component. The method is applied reduced to a plate loaded in tension and transverse bending. The plate has a central hole, and various hole sixes and shapes are studied. The method is also applied to a composite laminated fuselage panel with a crack emanating from a window in the panel. While this method is applied herein to global/local problems, it is also applicable to the coupled analysis of independently modeled components as well as adaptive refinement

Representation theory of finite W algebras

In this paper we study the finitely generated algebras underlying $W$ algebras. These so called 'finite $W$ algebras' are constructed as Poisson reductions of Kirillov Poisson structures on simple Lie algebras. The inequivalent reductions are labeled by the inequivalent embeddings of $sl_2$ into the simple Lie algebra in question. For arbitrary embeddings a coordinate free formula for the reduced Poisson structure is derived. We also prove that any finite $W$ algebra can be embedded into the Kirillov Poisson algebra of a (semi)simple Lie algebra (generalized Miura map). Furthermore it is shown that generalized finite Toda systems are reductions of a system describing a free particle moving on a group manifold and that they have finite $W$ symmetry. In the second part we BRST quantize the finite $W$ algebras. The BRST cohomology is calculated using a spectral sequence (which is different from the one used by Feigin and Frenkel). This allows us to quantize all finite $W$ algebras in one stroke. Explicit results for $sl_3$ and $sl_4$ are given. In the last part of the paper we study the representation theory of finite $W$ algebras. It is shown, using a quantum version of the generalized Miura transformation, that the representations of finite $W$ algebras can be constructed from the representations of a certain Lie subalgebra of the original simple Lie algebra. As a byproduct of this we are able to construct the Fock realizations of arbitrary finite $W$ algebras.Comment: 62 pages, THU-92/32, ITFA-28-9

Knaster's problem for (Z2)k(Z_2)^k-symmetric subsets of the sphere S2k−1S^{2^k-1}

We prove a Knaster-type result for orbits of the group $(Z_2)^k$ in $S^{2^k-1}$, calculating the Euler class obstruction. Among the consequences are: a result about inscribing skew crosspolytopes in hypersurfaces in $\mathbb R^{2^k}$, and a result about equipartition of a measures in $\mathbb R^{2^k}$ by $(Z_2)^{k+1}$-symmetric convex fans

Exotic Corn Lines with Increased Resistant Starch and Impact on Starch Thermal Characteristics

Ten parent corn lines, including four mutants (dull sugary2, amyloseextender sugary2, amylose-extender dull, and an amylose-extender with introgressed Guatemalen germplasm [GUAT ae]) and six lines with introgressed exotic germplasm backgrounds, were crossed with each other to create 20 progeny crosses to increase resistant starch (RS) as a dietary fiber in corn starch and to provide materials for thermal evaluation. The resistant starch 2 (RS2) values from the 10 parent lines were 18.3–52.2% and the values from the 20 progeny crosses were 16.6–34.0%. The %RS2 of parents was not additive in the offspring but greater RS2 in parents was correlated to greater RS2 in the progeny crosses (r = 0.63). Differential scanning calorimetry (DSC) measured starch thermal characteristics, revealing positive correlations of peak gelatinization temperature and change in enthalpy with %RS2 (r = 0.65 and r = 0.67, P ≤ 0.05); however, % retrogradation (a measure of RS3) and retrogradation parameters did not correlate with %RS2. The %RS2 and onset temperature increased with the addition of the ae gene, likely because RS delays gelatinization

Cohomological tautness for Riemannian foliations

In this paper we present some new results on the tautness of Riemannian foliations in their historical context. The first part of the paper gives a short history of the problem. For a closed manifold, the tautness of a Riemannian foliation can be characterized cohomologically. We extend this cohomological characterization to a class of foliations which includes the foliated strata of any singular Riemannian foliation of a closed manifold

An efficient arabinoxylan-debranching α-L-arabinofuranosidase of family GH62 from Aspergillus nidulans contains a secondary carbohydrate binding site.

An α-L-arabinofuranosidase of GH62 from Aspergillus nidulans FGSC A4 (AnAbf62A-m2,3) has an unusually high activity towards wheat arabinoxylan (WAX) (67 U/mg; k cat = 178/s, K m = 4.90 mg/ml) and arabinoxylooligosaccharides (AXOS) with degrees of polymerisation (DP) 3-5 (37-80 U/mg), but about 50 times lower activity for sugar beet arabinan and 4-nitrophenyl-α-L-arabinofuranoside. α-1,2- and α-1,3-linked arabinofuranoses are released from monosubstituted, but not from disubstituted, xylose in WAX and different AXOS as demonstrated by NMR and polysaccharide analysis by carbohydrate gel electrophoresis (PACE). Mutants of the predicted general acid (Glu(188)) and base (Asp(28)) catalysts, and the general acid pK a modulator (Asp(136)) lost 1700-, 165- and 130-fold activities for WAX. WAX, oat spelt xylan, birchwood xylan and barley β-glucan retarded migration of AnAbf62A-m2,3 in affinity electrophoresis (AE) although the latter two are neither substrates nor inhibitors. Trp(23) and Tyr(44), situated about 30 Å from the catalytic site as seen in an AnAbf62A-m2,3 homology model generated using Streptomyces thermoviolaceus SthAbf62A as template, participate in carbohydrate binding. Compared to wild-type, W23A and W23A/Y44A mutants are less retarded in AE, maintain about 70 % activity towards WAX with K i of WAX substrate inhibition increasing 4-7-folds, but lost 77-96 % activity for the AXOS. The Y44A single mutant had less effect, suggesting Trp(23) is a key determinant. AnAbf62A-m2,3 seems to apply different polysaccharide-dependent binding modes, and Trp(23) and Tyr(44) belong to a putative surface binding site which is situated at a distance of the active site and has to be occupied to achieve full activity.This work is supported by the Danish Council for Independent Research|Natural Sciences (FNU) [grant number 09-072151], by 1/3 PhD fellowship from the Technical University of Denmark (to CW) and by a Hans Christian Ørsted postdoctoral fellowship from DTU (to DC).This is the author accepted manuscript. The final version is available from Springer via http://dx.doi.org/10.1007/s00253-016-7417-