973 research outputs found
The invariants of the Weil representation of
The transformation behaviour of the vector valued theta function of a
positive definite even lattice under the metaplectic group
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 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 Cronbachâs 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 âovertâ 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 BioglassÂź-based scaffolds reinforced with genipin cross-linked gelatin for bone tissue engineering
45S5 BioglassÂź (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 ÎŒg mLâ1). 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
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