On escape criterion of an orbit with s-convexity and illustrations of the behavior shifts in Mandelbrot and Julia set fractals.

Our study presents a novel orbit with s-convexity, for illustration of the behavior shift in the fractals. We provide a theorem to demonstrate the escape criterion for transcendental cosine functions of the type Tα,β(u) = cos(um)+αu + β, for [Formula: see text] and m ≥ 2. We also demonstrate the impact of the parameters on the formatted fractals with numerical examples and graphical illustrations using the MATHEMATICA software, algorithm, and colormap.

A bibliometric analysis of health systems research in Pakistan.

Background: Health systems research and publication are vital for improving healthcare at all levels of care. They provide evidence for policy and for better service outcomes.

Aims: To assess published health systems research in Pakistan from 2011 to 2020 and to model and forecast the publication trend.

On optimal fuzzy best proximity coincidence points of fuzzy order preserving proximal (, )-lower-bounding asymptotically contractive mappings in non-Archimedean fuzzy metric spaces.

This paper discusses some convergence properties in fuzzy ordered proximal approaches defined by —sequences of pairs, where is a surjective self-mapping and where and are nonempty subsets of and abstract nonempty set and is a partially ordered non-Archimedean fuzzy metric space which is endowed with a fuzzy metric , a triangular norm * and an ordering The fuzzy set takes values in a sequence or set where the elements of the so-called switching rule are defined from to a subset of Such a switching rule selects a particular realization of at the th iteration and it is parameterized by a growth evolution sequence and a sequence or set which belongs to the so-called -lower-bounding mappings which are defined from [0, 1] to [0, 1]. Some application examples concerning discrete systems under switching rules and best approximation solvability of algebraic equations are discussed.

High prevalence of HIV infection among injection drug users (IDUs) in Hyderabad and Sukkur, Pakistan.

Objective: To estimate size of injection drug users (IDU), determine their high risk behaviours and assess the prevalence of HIV.

Method: As part of second generation surveillance (SGS), we investigated specific demographic and behavioural characteristics of IDUs in Hyderabad and Sukkur in 2005. It was a cross sectional study.

Risky sexual behavior, knowledge of sexually transmitted infections and treatment utilization among a vulnerable population in Rawalpindi, Pakistan.

As a part of a second generation surveillance, we investigated the sociodemographics, risky sexual behavior, knowledge of HIV and sexually transmitted infections (STIs) and treatment seeking behavior among a vulnerable population. A cross-sectional study preceded by mapping, was conducted in Rawalpindi, Pakistan during 2005. Subjects were recruited through snowball, time location cluster and cluster sampling techniques.