For all positive even integers \(n\), graphs of order \(n\) with degree sequence \(S_{n}:1,2,\dots,n/2,n/2,n/2+1,n/2+2,\dots,n-1\) naturally arose in the study of a labeling problem in [1].This fact motivated the authors of the aforementioned paper to study these sequences and as a result of this study they proved that there is a unique graph of order \(n\) realizing \(S_{n}\) for every even integer \(n\). The main goal of this paper is to generalize this result.

The Sombor index has gained lot of attention in the recent days for its mathematical properties and chemical applicabilities. Here, we initiated the novel block number version of the classical Sombor index and its matrix representation of a graph. The Block Sombor index \(BS(G)\) is defined as the sum total of square root of the sum of squares of block numbers of adjacent vertices, where the block number of a vertex is the number of blocks to which that vertex belongs to. The main purpose of this paper is to obtain some bounds and characterizations of \(BS(G)\) and its Block Sombor energy \(E_{BS}\). Also, we estimate some properties of spectral radius of Block Sombor matrix \(A_{BS}(G)\).

This study aims to model the statistical behaviour of extreme maximum temperature values in Rwanda. To achieve such an objective, the daily temperature data from January 2000 to December 2017 recorded at nine weather stations collected from the Rwanda Meteorological Agency were used. The two methods, namely the block maxima (BM) method and the Peaks Over Threshold (POT), were applied to model and analyse extreme temperatures in Rwanda. Model parameters were estimated, while the extreme temperature return periods and confidence intervals were predicted. The model fit suggests that Gumbel and Beta distributions are the most appropriate for the annual maximum daily temperature. Furthermore, the results show that the temperature will continue to increase as estimated return levels show it.

Using the Kudryashov and Tanh methods, we have obtained novel exact solutions for the Paraxial Wave Dynamical Equation with Kerr law, including various types of wave solutions. These distinct types of wave solutions have important applications in physics and engineering, and their physical characteristics are well defined. These outcomes are a substantial innovation in the study of water waves in mathematical physics and engineering phenomena. The results we have acquired demonstrate the power and effectiveness of the present techniques.

In this work, the effect of suction/injection on transient free convective flow in vertical porous (suction/injection on the channel surfaces) channel filled with porous material in the presence of thermal dispersion was studied. The Boussinesq assumption is applied and the nonlinear governing equations of motion and energy are developed. The time dependent problem is solved using implicit finite difference method while steady state problem is solved by perturbation technique method. The solution obtained is graphically represented and the effects of suction/injection, time, Darcy number, thermal dispersion, and Prandtl number on the fluid flow and heat transfer characteristics. During the course of computation, an excellent agreement was found between the well-known steady state solutions sand transient solutions at large value of time. Furthermore, the time required to reach steady state velocity and temperature field strongly dependent on suction/injection parameter, Prandtl number and thermal dispersion parameter. The introduction of suction/injection has distorted the symmetric nature of the flow formation.

In this paper we establish the existence of monads on cartesian products of projective spaces. We give the necessary and sufficient conditions for the existence of monads on \(\mathbf{P}^1\times\cdots\times \mathbf{P}^1\). We construct vector bundles associated to monads on \(X=\mathbf{P}^n\times\mathbf{P}^n\times\mathbf{P}^m\times\mathbf{P}^m\). We study these vector bundles associated to monads on \(X\) and prove their stability and simplicity.

In this paper, we established a new integral identity for twice partially differentiable functions. As a consequence, we established some new Simpson’s type integral inequalities for functions of two independent variables whose mixed partial derivative is bounded and \((\alpha_1, m_1)-(\alpha_2, m_2)\)-preinvex on the coordinates in both the first and second sense.

Motivated by Euler-Goldbach and Shallit-Zikan theorems, we introduce zeta-one functions with infinite sums of \(n^{s}\pm1\) as an analogy of the Riemann zeta function. Then we compute values of these functions at positive even integers by the residue theorem.

In this article, we focus on developing new results regarding normed quasilinear spaces. We provide a definition for soft homogenized quasilinear spaces and obtain some related results. Furthermore, we explore the floor of soft normed quasilinear spaces. Using some soft linearity and soft quasilinearity methods, we derive new results and examples. Finally, we also obtain some new consequences that we believe will facilitate the development of quasilinear functional analysis in a soft inner product quasilinear space.

Context: HIV/AIDS is known to affect an individual not only physically but also mentally, socially, and financially. It is a syndrome that builds a vacuum in a person affecting his/her life as a whole. Quality of life (QOL) of human immunodeficiency virus/acquired immuno deficiency syndrome (HIV/AIDS) patients has emerged as a significant medical outcome measure in recent times.
Aims: The purpose of the present observational study is to evaluate the quality of life (QOL) of people living with HIV/AIDS (PLHIV) receiving ART and its association with different social and clinical variables.
Materials and Methods: 140 patients of \(\geq\)18 years with HIV attending the tertiary level ante-retroviral treatment (ART) center were interviewed with using a validated standard version of the World Health Organization QOL (WHO-QOL BREF). Data on sociodemographic and clinical profile e.g., BMI, and CD4 were gathered. Mean scores were calculated in each domain. Descriptive statistics, independent t test, ANOVA and logistic regression were done to analyze the results.
Results: The overall QOL score of the subjects was moderate; Mean quality of life score was highest in the environmental domain (Mean=13.2\(\pm\)4.2). PLHIV with lower BMI also had poorer QOL (P<0.05). Employment significantly affected the social health domain and psychological domains of the subjects. Men reported poorer level of independence and physical health while women reported poorer social relationships and environment. All the six domains correlated significantly with the overall QOL indicated by the G-facet.
Conclusion: Attention toward improving the social status by enhancing sociopsychological supports such as social sensitization, mental health care of patients, and interventions to reduce stigma of PLHIV should be accorded with high priority to ensure improvement in the overall QOL of PLHIV.