Module Correspondences for Twisted Group Algebras

Abstract

Let G and A be finite groups such that (|G|, |A|) = 1. Let K be an algebraically closed field with Char K = 0. Denote by K ^α G the twisted group algebra of G over K with factor set α. In this paper we prove that if A acts homogeneously on K ^α G, then there exists an action of A on G, and there is a one-to-one correspondence between the set of A-invariant irreducible K ^α G-modules and the set of irreducible K ^α C _G (A)-modules.     

New lower bounds on 2-spontaneous emission error designs

The combinatorial object named $t$-spontaneous emission error design ($t$-SEED) was proposed by Beth et al. in 2003 in order to correct errors caused by quantum jumps. The newly rising category of $t$-SEEDs has been studied extensively in recent years. Especially, the maximal possible dimensions for 2-SEEDs with block size 3 were determined completely; lower bounds on 2-SEEDs were established by applying affine groups. In this paper we utilize the action of twisted affine groups on finite fields and obtain new lower bounds on the dimensions of 2-$(q^2,k;m)$ SEEDs, some of which outperform the known ones.     

Inducing a high twisted conformation in the polyimide structure by bulky donor moieties for the development of non-volatile memory

Two polyimides, PI(DAT-6FDA) and PI(DAPT-6FDA), from N-(2,4-diaminophenyl)-N,N-diphenylamine (DAT) or N-(4-(2′,4′-diaminophenoxy)phenyl-N,N-diphenylamine (DAPT) and 4,4′-(hexafluoroisopropylidene)diphthalic anhydride (6FDA) were prepared to clarify the structural effect on the resulting memory properties. The memory device based on PI(DAT-6FDA) showed an unstable volatile behavior, while the device based on PI(DAPT-6FDA) with a more bulky donor (D) unit exhibited a stable non-volatile FLASH type memory characteristic with a long retention time over 10⁴ s. The theoretical simulation based on the density functional theory (DFT) suggested that the greater distinct charge separation between the ground and charge transfer (CT) states led to a highly stable memory behavior. Also, it was clarified that PI(DAPT-6FDA) had a highly twisted conformation compared to PI(DAT-6FDA) in the ground state, and a more twisted dihedral angle between the D and acceptor (A) units was induced in the CT state, which led to the non-volatile memory characteristic.     

Synthesis and reconstruction of computer generated holograms by a double pass technique on a twisted nematic-based liquid crystal spatial light modulator

Achieving phase only modulation from a spatial light modulator (SLM) is useful for many optical processing tasks. In this paper, we demonstrate a simple method of decoupling phase and amplitude modulation in a twisted nematic liquid crystal (TNLC) SLM using a double pass technique. A Jones calculus model is developed which matches our experimental data.     

TritonX-100 selective chemosensor based on β-cyclodextrin modified by anthracene derivative

β-Cyclodextrin (CD) modified by 2-(9-anthracenecarboxamido)phenyl group (Ant-CD) was synthesized and their complexation behavior was investigated by UV and fluorescence spectroscopy. Fluorescence intensity of Ant-CD was dramatically enhanced ca. 10-fold by the addition of TritonX-100 (TX-100) in water below the critical micelle concentration. Ant-CD also showed ca. 4-fold fluorescence increasing in the addition of analogous materials, n-octylbenzenesulfonate in water. These results indicate that Ant-CD can act as a highly sensitive and selective chemosensor for TX-100. Ant-CD and TX-100 formed a pseudorotaxane supramolecular complex. This result was supported by ¹H-¹H NOESY NMR measurement.     

Fixed points of involutive automorphisms of the Bruhat order

Applying a classical theorem of Smith, we show that the poset property of being Gorenstein^* over Z₂ is inherited by the subposet of fixed points under an involutive poset automorphism. As an application, we prove that every interval in the Bruhat order on (twisted) involutions in an arbitrary Coxeter group has this property, and we find the rank function. This implies results conjectured by F. Incitti. We also show that the Bruhat order on the fixed points of an involutive automorphism induced by a Coxeter graph automorphism is isomorphic to the Bruhat order on the fixed subgroup viewed as a Coxeter group in its own right.     

Experiments on snap buckling, hysteresis and loop formation in twisted rods

We give the results of large deflection experiments involving the bending and twisting of 1 mm diameter nickel-titanium alloy rods, up to 2 m in length. These results are compared to calculations based on the Cosserat theory of rods. We present details of this theory, formulated as a boundary value problem. The mathematical boundary conditions model the experimental setup. The rods are clamped in aligned chucks and the experiments are carried out under rigid loading conditions. An experiment proceeds by either twisting the ends of the rod by a certain amount and then adjusting the slack, or fixing the slack and varying the amount of twist. In this way, commonly encountered phenomena are investigated, such as snap buckling, the formation of loops, and buckling into and out of planar configurations. The effect of gravity is discussed.