The invariants of the Weil representation of SL2(Z)\mathrm{SL}_2(\mathbb{Z})

The transformation behaviour of the vector valued theta function of a positive definite even lattice under the metaplectic group $\mathrm{Mp}_2(\mathbb{Z})$ is described by the Weil representation. This representation plays an important role in the theory of automorphic forms. We show that its invariants are induced from $5$ fundamental invariants

A Comparative Study

Background: The Narcissism Inventory (NI) is a frequently used German inventory for measuring narcissism in clinical settings; an additional short version (NI-90) also exists. Psychometric properties of the NI-90 scales were examined in clinical and non-clinical adolescent samples. Methods: Two adolescent samples were assessed with the NI-90: a non-clinical sample (n = 439, mean age ± SD = 15.05 ± 1.77 years) and a clinical sample (n = 235, 18.26 ± 0.77 years). Confirmatory factor analysis and principle component analysis were used to scrutinize the structure of the scales. Multiple regression analysis was used to predict the scores on two scales (helpless self; negative body self). Results: This study revealed heterogeneity in the NI-90 scales, which in turn explains the wide range seen in Cronbach’s α (from 0.53 to 0.93). The postulated 4-factor structure could not be replicated in both samples. Multiple regression analysis revealed that personality disorder did not significantly predict negative body self or helpless self scores, whereas eating, mood, as well as somatoform and conversion disorders did. One NI-90 scale (greedy for praise and reassurance) showed sufficient psychometric quality for the measurement of narcissism in both samples. Conclusion: Based on the results, the authors recommend revising the NI-90. Items that may be useful for measuring aspects related to affective and body image complaints are presented. The greedy for praise and reassurance scale may be valuable for measuring features of ‘overt’ narcissism

BKM Lie superalgebra for the Z_5 orbifolded CHL string

We study the Z_5-orbifolding of the CHL string theory by explicitly constructing the modular form tilde{Phi}_2 generating the degeneracies of the 1/4-BPS states in the theory. Since the additive seed for the sum form is a weak Jacobi form in this case, a mismatch is found between the modular forms generated from the additive lift and the product form derived from threshold corrections. We also construct the BKM Lie superalgebra, tilde{G}_5, corresponding to the modular form tilde{Delta}_1 (Z) = tilde{Phi}_2 (Z)^{1/2} which happens to be a hyperbolic algebra. This is the first occurrence of a hyperbolic BKM Lie superalgebra. We also study the walls of marginal stability of this theory in detail, and extend the arithmetic structure found by Cheng and Dabholkar for the N=1,2,3 orbifoldings to the N=4,5 and 6 models, all of which have an infinite number of walls in the fundamental domain. We find that analogous to the Stern-Brocot tree, which generated the intercepts of the walls on the real line, the intercepts for the N >3 cases are generated by linear recurrence relations. Using the correspondence between the walls of marginal stability and the walls of the Weyl chamber of the corresponding BKM Lie superalgebra, we propose the Cartan matrices for the BKM Lie superalgebras corresponding to the N=5 and 6 models.Comment: 30 pages, 2 figure

Analytical Solution for the Deformation of a Cylinder under Tidal Gravitational Forces

Quite a few future high precision space missions for testing Special and General Relativity will use optical resonators which are used for laser frequency stabilization. These devices are used for carrying out tests of the isotropy of light (Michelson-Morley experiment) and of the universality of the gravitational redshift. As the resonator frequency not only depends on the speed of light but also on the resonator length, the quality of these measurements is very sensitive to elastic deformations of the optical resonator itself. As a consequence, a detailed knowledge about the deformations of the cavity is necessary. Therefore in this article we investigate the modeling of optical resonators in a space environment. Usually for simulation issues the Finite Element Method (FEM) is applied in order to investigate the influence of disturbances on the resonator measurements. However, for a careful control of the numerical quality of FEM simulations a comparison with an analytical solution of a simplified resonator model is beneficial. In this article we present an analytical solution for the problem of an elastic, isotropic, homogeneous free-flying cylinder in space under the influence of a tidal gravitational force. The solution is gained by solving the linear equations of elasticity for special boundary conditions. The applicability of using FEM codes for these simulations shall be verified through the comparison of the analytical solution with the results gained within the FEM code.Comment: 23 pages, 3 figure

484pretrospective ras analysis of the epic trial cetuximab plus irinotecan vs irinotecan in patients pts with second line metastatic colorectal cancer mcrc

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Antibacterial 45S5 Bioglass®-based scaffolds reinforced with genipin cross-linked gelatin for bone tissue engineering

45S5 Bioglass® (BG) scaffolds with high porosity (>90%) were coated with genipin cross-linked gelatin (GCG) and further incorporated with poly(p-xylyleneguanidine) hydrochloride (PPXG). The obtained GCG coated scaffolds maintained the high porosity and well interconnected pore structure. A 26-fold higher compressive strength was provided to 45S5 BG scaffolds by GCG coating, which slightly retarded but did not inhibit the in vitro bioactivity of 45S5 BG scaffolds in SBF. Moreover, the scaffolds were made antibacterial against both Gram-positive and Gram-negative bacteria by using polyguanidine, i.e. PPXG, in this study. Osteoblast-like cells (MG-63) were seeded onto PPXG and GCG coated scaffolds. PPXG was biocompatible with MG-63 cells at a low concentration (10 μg mL−1). MG-63 cells were shown to attach and spread on both uncoated and GCG coated scaffolds, and the mitochondrial activity measurement indicated that GCG coating had no negative influence on the cell proliferation behavior of MG-63 cells. The developed novel antibacterial bioactive 45S5 BG-based composite scaffolds with improved mechanical properties are promising candidates for bone tissue engineering

BKM Lie superalgebras from counting twisted CHL dyons

Following Sen[arXiv:0911.1563], we study the counting of (`twisted') BPS states that contribute to twisted helicity trace indices in four-dimensional CHL models with N=4 supersymmetry. The generating functions of half-BPS states, twisted as well as untwisted, are given in terms of multiplicative eta products with the Mathieu group, M_{24}, playing an important role. These multiplicative eta products enable us to construct Siegel modular forms that count twisted quarter-BPS states. The square-roots of these Siegel modular forms turn out be precisely a special class of Siegel modular forms, the dd-modular forms, that have been classified by Clery and Gritsenko[arXiv:0812.3962]. We show that each one of these dd-modular forms arise as the Weyl-Kac-Borcherds denominator formula of a rank-three Borcherds-Kac-Moody Lie superalgebra. The walls of the Weyl chamber are in one-to-one correspondence with the walls of marginal stability in the corresponding CHL model for twisted dyons as well as untwisted ones. This leads to a periodic table of BKM Lie superalgebras with properties that are consistent with physical expectations.Comment: LaTeX, 32 pages; (v2) matches published versio