Arithmetic properties of blocks of consecutive integers

This paper provides a survey of results on the greatest prime factor, the number of distinct prime factors, the greatest squarefree factor and the greatest m-th powerfree part of a block of consecutive integers, both without any assumption and under assumption of the abc-conjecture. Finally we prove that the explicit abc-conjecture implies the Erd\H{o}s-Woods conjecture for each k>2.Comment: A slightly corrected and extended version of a paper which will appear in January 2017 in the book From Arithmetic to Zeta-functions published by Springe

What we don't know about time

String theory has transformed our understanding of geometry, topology and spacetime. Thus, for this special issue of Foundations of Physics commemorating "Forty Years of String Theory", it seems appropriate to step back and ask what we do not understand. As I will discuss, time remains the least understood concept in physical theory. While we have made significant progress in understanding space, our understanding of time has not progressed much beyond the level of a century ago when Einstein introduced the idea of space-time as a combined entity. Thus, I will raise a series of open questions about time, and will review some of the progress that has been made as a roadmap for the future.Comment: 15 pages; Essay for a special issue of Foundations of Physics commemorating "Forty years of string theory

Negative Energy, Superluminosity and Holography

The holographic connection between large $N$ Super Yang Mills theory and gravity in anti deSitter space requires unfamiliar behavior of the SYM theory in the limit that the curvature of the AdS geometry becomes small. The paradoxical behavior includes superluminal oscillations and negative energy density. These effects typically occur in the SYM description of events which take place far from the boundary of AdS when the signal from the event arrives at the boundary. The paradoxes can be resolved by assuming a very rich collection of hidden degrees of freedom of the SYM theory which store information but give rise to no local energy density. These degrees of freedom, called precursors, are needed to make possible sudden apparently acausal energy momentum flows. Such behavior would be impossible in classical field theory as a consequence of the positivity of the energy density. However we show that these effects are not only allowed in quantum field theory but that we can model them in free quantum field theory.Comment: Expanded version replacing earlier hep-th/990218

Influence of Processing Parameters in Sicp - Aluminium Alloy Composite Produced by Stir Casting Method

Metal matrix composites are gaining wider acceptance in aerospace and defence industries due to their starving need for lightweight — high strength materials. The control of processing parameters is very important in order to obtain good quality casing with minimal defects. In this study the influence of processing parameters on the properties of SiC particle reinforced aluminium alloy (Al- 10%Si- 0.6%Mg) composite was investigated. The composites are prepared by stir casting method. This method involves mixing of SiC in the molten aluminium alloy aided with mechanical agitation. The processing parameters that were investigated include melt temperature and stirring speed. Specimens produced were subjected to mechanical testing. Microstructure observed through scanning electron microscope and optical microscope was correlated to the observed mechanical behavior. The results show that the melt temperature appears to have little effect on the mechanical properties and particle settling. SEM photographs show that there is particle clustering at low melt temperature

Generalized iterated wreath products of cyclic groups and rooted trees correspondence

Consider the generalized iterated wreath product $\mathbb{Z}_{r_1}\wr \mathbb{Z}_{r_2}\wr \ldots \wr \mathbb{Z}_{r_k}$ where $r_i \in \mathbb{N}$. We prove that the irreducible representations for this class of groups are indexed by a certain type of rooted trees. This provides a Bratteli diagram for the generalized iterated wreath product, a simple recursion formula for the number of irreducible representations, and a strategy to calculate the dimension of each irreducible representation. We calculate explicitly fast Fourier transforms (FFT) for this class of groups, giving literature's fastest FFT upper bound estimate.Comment: 15 pages, to appear in Advances in the Mathematical Science

Deconstruction and Holography

It was recently pointed out that the physics of a single discrete gravitational extra dimension exhibits a peculiar UV/IR connection relating the UV scale to the radius of the effective extra dimension. Here we note that this non-locality is a manifestation of holography, encoding the correct scaling of the number of fundamental degrees of freedom of the UV theory. This in turn relates the Wilsonian RG flow in the UV theory to the effective gravitational dynamics in the extra dimension. The relevant holographic c-function is determined by the expression for the holographic bound. Holography in this context is a result of the requirements of unitarity and diffeomorphism invariance. We comment on the relevance of this observation for the cosmological constant problem.Comment: 11 pages, LaTe

Evaluation of existing limited sampling models for busulfan kinetics in children with beta thalassaemia major undergoing bone marrow transplantation

Busulfan pharmacokinetic parameters are useful in predicting the outcome of allogeneic bone marrow transplantation (BMT). Standard pharmacokinetic measurements require multiple blood samples. Various limited sampling models (LSM) have been proposed for reducing the sample number required for these measurements, essentially for patients with malignant disorders undergoing BMT. This study was undertaken to evaluate the existing LSM for busulfan pharmacokinetics to find out the most suitable method for patients with thalassaemia major undergoing BMT. Busulfan levels in plasma samples were analysed by HPLC. The AUC calculated by non-compartmental analysis using the program 'TOPFIT' was compared with previously published LSMs. Our seven sample pharmacokinetic data for AUC calculation was compared with the published LSMs. The three sample models suggested by Chattergoon et al and Schuler et al showed significant agreement with AUC TOPFIT (R2 = 0.98 and 0.94, respectively) in our clinical context. Other models resulted in significant over or under representation of observed values (Vassal's model R2 = 0.61; Chattergoon's two sample model R2 = 0.84; four sample model R2 = 0.83; Schuler's two sample model R2 = 0.79). By these data the three sample LSM proposed by Chattergoon et al and Schuler et al are suitable for calculation of the AUC in patients with thalassaemia major undergoing BMT conditioned with oral busulfan

Risk Factors for Non-adherence to Directly Observed Treatment (DOT) in a Rural Tuberculosis Unit, South India

Objective: To identify risk factors for non-adherence of tuberculosis (TB) patients to DOT. Methods: Retrospective study of TB patients by logistic regression analysis to identify risk factors for non-adherence. Results: Of the 1666 patients interviewed, 1108 (67%) adhered and 558 (33%) did not adhere to DOT. Of 558 patients, the risk factors associated with non-adherence were illiteracy (39%), difficulty in accessing health facility (57%), and nongovernment DOT centre (43%). Conclusion: Patients should be educated about tuberculosis and importance of DOT. All DOT centres, including Nongovernment DOT centres, should be made more accessible and patient-friendly