STUDY OF ENERGETIC TRANSIENTS USING TOOLS LIKE MESA & SNEC, MOSFIT AND SNCOSMO

We explore the study of energetic transients including core-collapse supernovae using various publicly available analysis tools like MESA & SNEC, MOSFiT and SNCOSMO. We used MESA to evolve a star having zero age main sequence mass (Mzams) of 24 M⊙ until the onset of core-collapse. Then we exploded this model using openly available explosion codes, STELLA & SNEC and obatined various observable parameters such as bolometric luminosity and photospheric velocities etc. We also used MOSFiT to model the light curve of a type Ic supernova, SN1999ex and obtained various physical parameters. SNCOSMO is used for template fitting of various supernovae by varying various parameters such as red shift, dust map, stretch factor of light curve, explosion epoch of supernova etc.

Lyapunov exponents for the Lorentz transformations

We calculate the Lyapunov exponents of the stretch factor $f^-(x)=(1-x^2)^{-1/2}$ from the Lorentz transformations and of its reciprocal $f^+(x)=(1-x^2)^{+1/2}$ as well.

Flaccid penile length and stretch factor in the newborn

Objective: Little is known about the flaccid penile length in the newborn and the degree of stretch of the penis among investigators while measuring the stretched penile length. This study aimed to document the flaccid penile length and the stretch factor in the newborn.Methods: This cross-sectional study was carried out on 200 term male infants within the first 72 hours of life. The flaccid penile length and the stretched penile length were measured with a wooden spatula and the stretch factor was calculated.Results: The mean (±SD) flaccid and stretched penile length were 30.9 ± 3.8 mm and 38.9 ± 4.0 mm respectively. The mean stretch factor was 26.4 %. Both testes had the same mean volume of 1.6 ± 0.5 ml. There was a significant correlation between flaccid and stretched penile lengths (r = 0.775, p = 0.000). The flaccid penile length was a significant predictor of the stretched penile length.Conclusion: This study has been able to determine the stretch factor while measuring the flaccid and stretch penile lengths in Nigerian newborn infants. It is recommended that the flaccid penile length be measured along with the stretched penile length and determine the stretch factor in order to compare how much investigators stretch the penis during measurement. This will allow for detailed comparison of penile anthropometry across different ethnic groups and races. Keywords: flaccid penile length, newborn, stretch factor, stretched penile length.

T-Spanner Problem

The t-spanner problem is a popular combinatorial optimization problem and has different applications in communication networks and distributed systems. This chapter considers the problem of constructing a t-spanner subgraph H in a given undirected edge-weighted graph G in the sense that the distance between every pair of vertices in H is at most t times the shortest distance between the two vertices in G. The value of t, called the stretch factor, quantifies the quality of the distance approximation of the corresponding t-spanner subgraph. This chapter studies two variations of the problem, the Minimum t-Spanner Subgraph (MtSS) and the Minimum Maximum Stretch Spanning Tree(MMST). Given a value for the stretch factor t, the MtSS problem asks to find the t-spanner subgraph of the minimum total weight in G. The MMST problem looks for a tree T in G that minimizes the maximum distance between all pairs of vertices in V (i.e., minimizing the stretch factor of the constructed tree). It is easy to conclude from the literatures that the above problems are NP-hard. This chapter presents genetic algorithms that returns a high quality solution for those two problems.

The approximately universal shapes of epidemic curves in the Susceptible-Exposed-Infectious-Recovered (SEIR) model

Compartmental transmission models have become an invaluable tool to study the dynamics of infectious diseases. The Susceptible-Infectious-Recovered (SIR) model is known to have an exact semi-analytical solution. In the current study, the approach of Harko et al. (Appl. Math. Comput. 236:184–194, 2014) is generalised to obtain an approximate semi-analytical solution of the Susceptible-Exposed-Infectious-Recovered (SEIR) model. The SEIR model curves have nearly the same shapes as the SIR ones, but with a stretch factor applied to them across time that is related to the ratio of the incubation to infectious periods. This finding implies an approximate characteristic timescale, scaled by this stretch factor, that is universal to all SEIR models, which only depends on the basic reproduction number and initial fraction of the population that is infectious.

Stretch factor in a planar Poisson–Delaunay triangulation with a large intensity

Let X := X n ∪ {(0, 0), (1, 0)}, where X n is a planar Poisson point process of intensity n. We provide a first nontrivial lower bound for the distance between the expected length of the shortest path between (0, 0) and (1, 0) in the Delaunay triangulation associated with X when the intensity of X n goes to ∞. Simulations indicate that the correct value is about 1.04. We also prove that the expected length of the so-called upper path converges to 35 / 3π2, yielding an upper bound for the expected length of the smallest path.