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

Optimal clustering of a pair of irregular objects

Cutting and packing problems arise in many fields of applications and theory. When dealing with irregular objects, an important subproblem is the identification of the optimal clustering of two objects. Within this paper we consider a container (rectangle, circle, convex polygon) of variable sizes and two irregular objects bounded by circular arcs and/or line segments, that can be continuously translated and rotated. In addition minimal allowable distances between objects and between each object and the frontier of a container, may be imposed. The objects should be arranged within a container such that a given objective will reach its minimal value. We consider a polynomial function as the objective, which depends on the variable parameters associated with the objects and the container. The paper presents a universal mathematical model and a solution strategy which are based on the concept of phi-functions and provide new benchmark instances of finding the containing region that has either minimal area, perimeter or homothetic coefficient of a given container, as well as finding the convex polygonal hull (or its approximation) of a pair of objects

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

Brief Home-Based Data Collection of Low Frequency Behaviors

Data-based decision making, an important component of positive behavior support, can be difficult in brief in-home therapy due to the limited amount of time a therapist has to directly observe the child. This difficulty is exacerbated when problem behavior occurs infrequently. When a therapist cannot reliably observe problem behavior, it is often necessary to rely on parental report. The current study evaluated three approaches for parental report of low frequency problem behavior: antecedent-behavior-consequence records, incident data, and interview. Each method was analyzed with clients in home-based therapy with 2-hour weekly appointments. All clients exhibited low-frequency (i.e., less than daily) and high-intensity (i.e., causes physical harm to self/others, damage to the environment, or severe decrement to family’s quality of life) problem behavior. The treatment goal for all clients was to reduce problem behavior (most commonly aggression, disruption, or self-injury). The number of instances of problem behavior captured by each method of data-collection, quality of the data (i.e., ability to detect treatment effects using the data), and therapist and parent acceptability of each measure were analyzed. Results are discussed in terms of the relative advantages and disadvantages of each measure, clinical application of the methods, and avenues for future research

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