here we consider all finite non-abelian 2-generator $p$-groups ($p$ an odd prime) of nilpotency class two and study the probability of having $n^{th}$-roots of them. also we find integers $n$ for which, these groups are $n$-central.

Nonlinear Time History (NTH) analysis is currently the most reliable method for estimating structural behavior. Considerable computational demand and complexity of this method may cause difficulty for its routine practical application. Based on the Methodology of Endurance Time (ET) method, it can estimate the nonlinear response of structures with a much lower computational cost. In this resear...

We show that two knots have matching Vassiliev invariants of order less than n if and only if they are equivalent modulo the nth group of the lower central series of some pure braid group, thus characterizing Vassiliev’s knot invariants in terms of the structure of the braid groups. We also prove some results about knots modulo the nth derived subgroups of the pure braid groups, and about knots...

This paper presents a classification of Cellular Automata rules based on its properties at the nth iteration. Elaborate computer program has been designed to get the nth iteration for arbitrary 1-D or 2-D CA rules. Studies indicate that the figures at some particular iteration might be helpful for some specific application. The hardware circuit implementation can be done using opto-electronic c...

Autocorrelation is a common method to estimate the duration of ultrashort laser pulses. In the ultraviolet (UV) regime it is challenging to employ the process of second-harmonic generation, most prominently due to absorption in nonlinear crystals at very short wavelengths. Here we show how to utilize spontaneous parametric down-conversion (SPDC) to generate an autocorrelation signal in the infr...

The notation G/G/1 queue is usually referred to a single-server queue with first-in-first-out discipline and with a general distribution of the sequences of inter-arrival and service times (which are the “driving sequences” of the system). Customers are numbered n = 0, 1, . . .. We assume that customer 0 arrives to a system at time t = 0 and finds there an initial amount of work, so has to wait...

We initiate the study of classical knots through the homotopy class of the nth evaluation map of the knot, which is the induced map on the compactified n-point configuration space. Sending a knot to its nth evaluation map realizes the space of knots as a subspace of what we call the nth mapping space model for knots. We compute the homotopy types of the first three mapping space models, showing...

In this set of lecture notes we focus on the point-value representation obtained by looking at a particular set of points, the nth roots of unity. In the field of complex numbers C, there are exactly n different solutions to the equation x = 1. We call these solutions the n-th roots of unity. One of these roots of unity is ωn = cos(2π/n)+ i sin(2π/n), and this is called the principal nth root o...

OBJECTIVES To present and compare antibiotic prescribing for inpatients among the most common non-bacterial diagnoses groups at medicine departments of a teaching (TH) and a non-teaching hospital (NTH) in central India. SETTING An observational cross-sectional study was conducted at two tertiary care settings in Ujjain district, Madhya Pradesh, India. DATA AND PARTICIPANTS The data were col...

Activation of oxidative stress-responses and downregulation of insulin-like signaling (ILS) is seen in Nucleotide Excision Repair (NER) deficient segmental progeroid mice. Evidence suggests that this is a survival response to persistent transcription-blocking DNA damage, although the relevant lesions have not been identified. Here we show that loss of NTH-1, the only Base Excision Repair (BER) ...