Asymptotic Behaviour of the Proper Length and Volume of the Schwarzschild Singularity

Though popular presentations give the Schwarzschild singularity as a point it is known that it is spacelike and not timelike. Thus it has a "length" and is not a "point". In fact, its length must necessarily be infinite. It has been proved that the proper length of the Qadir-Wheeler suture model goes to infinity [1], while its proper volume shrinks to zero, and the asymptotic behaviour of the length and volume have been calculated. That model consists of two Friedmann sections connected by a Schwarzschild "suture". The question arises whether a similar analysis could provide the asymptotic behaviour of the Schwarzschild black hole near the singularity. It is proved here that, unlike the behaviour for the suture model, for the Schwarzschild essential singularity $\Delta s$ $\thicksim$ $K^{1/3}\ln K$ and $V\thicksim$ $K^{-1}\ln K$, where $K$ is the mean extrinsic curvature, or the York time.Comment: 13 pages, 1 figur

Gravitational wave scintillation by a stellar cluster

The diffraction effects on gravitational waves propagating through a stellar cluster are analyzed in the relevant approximation of Fresnel diffraction limit. We find that a gravitational wave scintillation effect - similar to the radio source scintillation effect - comes out naturally, implying that the gravitational wave intensity changes in a characteristic way as the observer moves.Comment: 9 pages, in press in IJMP

Weyl collineations that are not curvature collineations

Though the Weyl tensor is a linear combination of the curvature tensor, Ricci tensor and Ricci scalar, it does not have all and only the Lie symmetries of these tensors since it is possible, in principle, that "asymmetries cancel". Here we investigate if, when and how the symmetries can be different. It is found that we can obtain a metric with a finite dimensional Lie algebra of Weyl symmetries that properly contains the Lie algebra of curvature symmetries. There is no example found for the converse requirement. It is speculated that there may be a fundamental reason for this lack of "duality".Comment: 9 page

Multipliers for p-Bessel sequences in Banach spaces

Multipliers have been recently introduced as operators for Bessel sequences and frames in Hilbert spaces. These operators are defined by a fixed multiplication pattern (the symbol) which is inserted between the analysis and synthesis operators. In this paper, we will generalize the concept of Bessel multipliers for p-Bessel and p-Riesz sequences in Banach spaces. It will be shown that bounded symbols lead to bounded operators. Symbols converging to zero induce compact operators. Furthermore, we will give sufficient conditions for multipliers to be nuclear operators. Finally, we will show the continuous dependency of the multipliers on their parameters.Comment: 17 page

How gender- and violence-related norms affect self-esteem among adolescent refugee girls living in Ethiopia.

BACKGROUND: Evidence suggests adolescent self-esteem is influenced by beliefs of how individuals in their reference group perceive them. However, few studies examine how gender- and violence-related social norms affect self-esteem among refugee populations. This paper explores relationships between gender inequitable and victim-blaming social norms, personal attitudes, and self-esteem among adolescent girls participating in a life skills program in three Ethiopian refugee camps. METHODS: Ordinary least squares multivariable regression analysis was used to assess the associations between attitudes and social norms, and self-esteem. Key independent variables of interest included a scale measuring personal attitudes toward gender inequitable norms, a measure of perceived injunctive norms capturing how a girl believed her family and community would react if she was raped, and a peer-group measure of collective descriptive norms surrounding gender inequity. The key outcome variable, self-esteem, was measured using the Rosenberg self-esteem scale. RESULTS: Girl's personal attitudes toward gender inequitable norms were not significantly predictive of self-esteem at endline, when adjusting for other covariates. Collective peer norms surrounding the same gender inequitable statements were significantly predictive of self-esteem at endline (ß = -0.130; p  =  0.024). Additionally, perceived injunctive norms surrounding family and community-based sanctions for victims of forced sex were associated with a decline in self-esteem at endline (ß = -0.103; p  =  0.014). Significant findings for collective descriptive norms and injunctive norms remained when controlling for all three constructs simultaneously. CONCLUSIONS: Findings suggest shifting collective norms around gender inequity, particularly at the community and peer levels, may sustainably support the safety and well-being of adolescent girls in refugee settings

Feasibility of Serverless Cloud Services for Disaster Management Information Systems

Serverless is the new generation of cloud services that supports the pay-per-use policy in true spirit by charging only for the execution time of the hosted code. Amazon introduced serverless service of Lambda in 2014 and it is consider as the most popular serverless cloud service till date. This paper focuses on the serverless cloud services of Lambda and elaborates the importance of Lambda based serverless cloud services for hosting the disaster management information systems (DMIS). We have identified two repeatedly occurring phases of the life cycle of a DMIS viz. low activity phase and high activity phase. Our findings state that serverless cloud services are well-suited for both of these phases of a DMIS. Serverless reduces the operational cost during the low activity phase by detaching the code from running containers and it improves the scalability during the high activity phase by quickly assigning the already available containers from the container pool. However, this all comes with the price of reduced QoS (Quality of Service) for initial requests after specific idle duration and our experimental results report the QoS degradation with respect to idle time for Lambda service

Use of Complex Lie Symmetries for Linearization of Systems of Differential Equations - II: Partial Differential Equations

The linearization of complex ordinary differential equations is studied by extending Lie's criteria for linearizability to complex functions of complex variables. It is shown that the linearization of complex ordinary differential equations implies the linearizability of systems of partial differential equations corresponding to those complex ordinary differential equations. The invertible complex transformations can be used to obtain invertible real transformations that map a system of nonlinear partial differential equations into a system of linear partial differential equation. Explicit invariant criteria are given that provide procedures for writing down the solutions of the linearized equations. A few non-trivial examples are mentioned.Comment: This paper along with its first part ODE-I were combined in a single research paper "Linearizability criteria for systems of two second-order differential equations by complex methods" which has been published in Nonlinear Dynamics. Due to citations of both parts I and II these are not replaced with the above published articl

Small nerve fiber damage and Langerhans cells in type 1 and type 2 diabetes and LADA measured by corneal confocal microscopy

Purpose: Increased corneal and epidermal Langerhans cells (LCs) have been reported in patients with diabetic neuropathy. The aim of this study was to quantify the density of LCs in relation to corneal nerve morphology and the presence of diabetic neuropathy and to determine if this differed in patients with type 1 diabetes mellitus (T1DM), type 2 diabetes mellitus (T2DM), and latent autoimmune diabetes of adults (LADA). Methods: Patients with T1DM (n = 25), T2DM (n = 36), or LADA (n = 23) and control subjects (n = 23) underwent detailed assessment of peripheral neuropathy and corneal confocal microscopy. Corneal nerve fiber density (CNFD), branch density (CNBD), length (CNFL) and total, immature and mature LC densities were quantified. Results: Lower CNFD (P < 0.001), CNBD (P < 0.0001), and CNFL (P < 0.0001) and higher LC density (P = 0.03) were detected in patients with T1DM, T2DM, and LADA compared to controls. CNBD was inversely correlated with mature (r = -0.5; P = 0.008), immature (r = -0.4; P = 0.02) and total (r = -0.5; P = 0.01) LC density, and CNFL was inversely correlated with immature LC density (r = -0.4; P = 0.03) in patients with T1DM but not in patients with T2DM and LADA. Conclusions: This study shows significant corneal nerve loss and an increase in LC density in patients with T1DM, T2DM, and LADA. Furthermore, increased LC density correlated with corneal nerve loss in patients with T1DM