Initial Characterized L-spaces and Characterized L- topological Groups

In this research work, new topological notions are proposed and investigated. The notions are named initial characterized L-spaces and characterized L-topological groups. The properties of such notions are deeply studied. We show that the intitial characterized L-space for an characterized L-spaces exists. By this notion, the notions of characterized L-subspace and characterized product L-space are introduced and studied. More information can be found in the full paper

On Initial and Final Characterized L- topological Groups

In this research work, new topological notions are proposed and investigated. The notions are named finalcharacterized L-spaces and initial and final characterized L-topological groups. The properties of such notionsare deeply studied. We show that all the final lefts and all the final characterized L-spaces are uniquely exist inthe category CRL-Sp and hence CRL-Sp is topological category over the category SET of all sets. By the notion offinal characterized L-space, the notions of characterized qoutien pre L-spaces and characterized sum L-spacesare introduced and studied. The characterized L-subspaces together with their related inclusion mappings andthe characterized quotient pre L-spaces together with their related canonical surjections are the equalizers andco-equalizers, respectively in CRL-Sp. Moreover, we show that the initial and final lefts and then the initial andfinal characterized L-topological groups uniquely exist in the category CRL-TopGrp. Hence, the category CRLTopGrpis topological category over the category Grp of all groups. By the notion of initial and finalcharacterized L-topological groups, the notions of characterized L-subgroups, characterized product Ltopologicalgroups and characterized L-topological quotient groups are introduced and studied., we show that thecategory CRL-TopGrp is concrete and co-concrete category of the category L-Top. More details can be found in the full paper

Pitman estimator for the parameter and reliability function of the exponential distribution

The easiest and most essential distribution in reliability studies is the exponential distribution. An important issue in this area is to seek for a good estimator to estimate the parameter and reliability function of this distribution. So in this article, The Pitman method is used to derive an estimator for the parameter and reliability function of the exponential distribution, then a comparison was made with the usual methods such as maximum likelihood estimator and Bayes estimator through simulation studies with different sizes of samples. The results showed that the Pitman estimator has a good performance for the parameter of exponential distribution compared with other methods by relying on the statistical measure Mean square error. Also it showed that the Bayes estimator has a good performance compared with the other methods in estimating the reliability function by relying on the statistical measure integral mean square error

Two pressure-induced structural phase transitions in TiOCl

We studied the crystal structure of TiOCl up to pressures of $p$=25~GPa at room temperature by x-ray powder diffraction measurements. Two pressure-induced structural phase transitions are observed: At $p_{c1}$$\approx$15~GPa emerges an 2$a$$\times$2$b$$\times$$c$ superstructure with $b$-axis unique monoclinic symmetry (space group P2$_1$/$m$). At $p_{c2}$$\approx$22~GPa all lattice parameters of the monoclinic phase show a pronounced anomaly. A fraction of the sample persists in the ambient orthorhombic phase (space group $Pmmn$) over the whole pressure range.Comment: 5 pages, 5 figures; accepted for publication in Phys. Rev.

Entropy, longevity and the cost of annuities

This paper presents an extension of the application of the concept of entropy to annuity costs. Keyfitz (1985) introduced the concept of entropy, and analysed this in the context of continuous changes in life expectancy. He showed that a higher level of entropy indicates that the life expectancy has a greater propensity to respond to a change in the force of mortality than a lower level of entropy. In other words, a high level of entropy means that further reductions in mortality rates would have an impact on measures like life expectancy. In this paper, we apply this to the cost of annuities and show how it allows the sensitivity of the cost of a life annuity contract to changes in longevity to be summarized in a single figure index

IVIG (Immunoglobulin) as an Adjuvant Therapy in COVID-19

COVID-19 viral disease appeared in China in December 2019 and then spread around the world, affecting millions and causing the death of thousands of people. Its danger in simple and easy infection transmission methods. Some believe that it has moved from the bat to the human and its symptoms are high temperature, dry cough and difficulty breathing, and symptoms vary from person to person, as they may not appear on some and be severe in others.  Laboratory, in COVID-19 the rate of D-dimer increase so we recommended using of Enoxaparin sodium to raise the level of liquidity in the blood, thereby reducing the chance of thrombosis and reducing the value of D-dimer. In COVID-19 also we find the PO2 decrease in arterial blood gas analysis, increase liver enzyme levels, increase ferritin value and decrease the No of lymphocyte. Low percentage of lymphocytes is one of the predictions for infection with COVID-19 virus. Lymphocytes originate from the bone marrow and include B cells, T cells, and natural killer cells. COVID-19 binds to lymphocyte receptors and destroys them. In this case, we recommend using immunoglobulin to maintain these cells as an adjuvant therapy in COVID-19