AN EFFECTIVE APPROACH OF FOUR-STEP METHOD FOR OPTIMAL SOLUTION OF TRANSPORTATION PROBLEM

Transportation problem (TP) in operation research is one of the most in use optimization technique to deal the problems that are related with transportation of goods from sources to destinations. Initial Basic Feasible Solution (IBFS) plays a vital role in TP which offers a way to obtain the optimal solution. The objective is to prevail the total transportation cost equivalent or nearer to optimal solution. In this paper, an effective approach of Four Step Method (FSM) for optimal solution of TP has been brought up in order to get optimal solution of TPs. In this method we construct the Maximum Column Table (MCT) and Maximum Row Table (MRT). Several problems has been solved using this method to get the optimal solution. The outcomes of proposed method are contrasted with results of North West Corner Method (NWCM), Least Cost Method (LCM) and Vogal’s Approximation Method (VAM). It is observed that the proposed method is not only achieving better results but also overcoming the limitation of VAM. Key Words: Transportation problem, Initial Basic Feasible Solution, Optimal solution, Linear programming proble

Convergence rate for the hybrid iterative technique to explore the real root of nonlinear problems

This study explored the convergence rate of the hybrid numerical iterative technique (HNIT) for the solution of nonlinear problems (NLPs) of one variable ( f (x) = 0) . It is sightseen that convergence rate is two for the HNIT. By the HNIT, several algebraic and transcendental NLPs of one variable have been illustrated as an approximate real root for efficient performance. In many instances, HNIT is more vigorous and attractive than well-known conventional iterative techniques (CITs). The computational tool MATLAB has been used for the solution of iterative techniques

Combined variational iteration method with chebyshev wavelet for the solution of convection-diffusion-reaction problem

The goal of the work is to solve the nonlinear convection-diffusion-reaction problem using the variational iteration method with the combination of the Chebyshev wavelet. This work developed a hybrid iterative technique named as Variational iteration method with the Chebyshev wavelet for the solutions of nonlinear convection-diffusion-reaction problems. The aim of applying the derived algorithm is to achieve fast convergence. During the solution of the given problem, the restricted variations will be mathematically justified. The effects of the scaling and other parameters like diffusion parameter, convection parameter, and reaction parameter on the solution are also focused on by their suitable selection. The approximate results include the error profiles and the simulations. The results of variational iteration with the Chebyshev wavelet are compared with variational iteration method, the Modified variational iteration method, and the Variational iteration method with Legendre wavelet. The error profiles allow us to compare the results with well-known existing schemes

Analysis of Inertia Effect on Axisymmetric Squeeze Flow of Slightly Viscoelastic Fluid Film between Two Disks by Recursive Approach

In this study, we analyzed the inertia effect on the axisymmetric squeeze flow of slightly viscoelastic fluid film between two disks. A system of nonlinear partial differential equations (PDEs) in cylindrical coordinates, along with nonhomogenous boundary conditions, illustrates the phenomenon of fluid flow caused by squeezing with the inertia effect. The Langlois recursive approach was applied to obtain the analytical solution of the system having a stream function, axial and radial velocities, pressure distribution, normal and tangential stresses and normal squeeze force. These flow variables are also portrayed graphically to describe the effects of the Reynolds number and slightly viscoelastic parameter. The results show that by increasing the Reynolds number, the velocity profile decreases, and both the pressure distribution and shear stresses increase. Moreover, there is a small increase in normal squeeze force. When the slightly viscoelastic parameter approaches zero, the obtained solution of flow variables matches with the classical results. This study can be applied to understand the mechanism of load-bearing features in thrust bearings and in arthrodial human joint (knee and hip) diseases.Basque Government Grants IT1555-22 and KK-2022/00090; and MCIN/AEI 269.10.13039/501100011033 for Grant PID2021-1235430B-C21/C22

Measuring routine childhood vaccination coverage in 204 countries and territories, 1980-2019 : a systematic analysis for the Global Burden of Disease Study 2020, Release 1

Background Measuring routine childhood vaccination is crucial to inform global vaccine policies and programme implementation, and to track progress towards targets set by the Global Vaccine Action Plan (GVAP) and Immunization Agenda 2030. Robust estimates of routine vaccine coverage are needed to identify past successes and persistent vulnerabilities. Drawing from the Global Burden of Diseases, Injuries, and Risk Factors Study (GBD) 2020, Release 1, we did a systematic analysis of global, regional, and national vaccine coverage trends using a statistical framework, by vaccine and over time. Methods For this analysis we collated 55 326 country-specific, cohort-specific, year-specific, vaccine-specific, and dosespecific observations of routine childhood vaccination coverage between 1980 and 2019. Using spatiotemporal Gaussian process regression, we produced location-specific and year-specific estimates of 11 routine childhood vaccine coverage indicators for 204 countries and territories from 1980 to 2019, adjusting for biases in countryreported data and reflecting reported stockouts and supply disruptions. We analysed global and regional trends in coverage and numbers of zero-dose children (defined as those who never received a diphtheria-tetanus-pertussis [DTP] vaccine dose), progress towards GVAP targets, and the relationship between vaccine coverage and sociodemographic development. Findings By 2019, global coverage of third-dose DTP (DTP3; 81.6% [95% uncertainty interval 80.4-82 .7]) more than doubled from levels estimated in 1980 (39.9% [37.5-42.1]), as did global coverage of the first-dose measles-containing vaccine (MCV1; from 38.5% [35.4-41.3] in 1980 to 83.6% [82.3-84.8] in 2019). Third- dose polio vaccine (Pol3) coverage also increased, from 42.6% (41.4-44.1) in 1980 to 79.8% (78.4-81.1) in 2019, and global coverage of newer vaccines increased rapidly between 2000 and 2019. The global number of zero-dose children fell by nearly 75% between 1980 and 2019, from 56.8 million (52.6-60. 9) to 14.5 million (13.4-15.9). However, over the past decade, global vaccine coverage broadly plateaued; 94 countries and territories recorded decreasing DTP3 coverage since 2010. Only 11 countries and territories were estimated to have reached the national GVAP target of at least 90% coverage for all assessed vaccines in 2019. Interpretation After achieving large gains in childhood vaccine coverage worldwide, in much of the world this progress was stalled or reversed from 2010 to 2019. These findings underscore the importance of revisiting routine immunisation strategies and programmatic approaches, recentring service delivery around equity and underserved populations. Strengthening vaccine data and monitoring systems is crucial to these pursuits, now and through to 2030, to ensure that all children have access to, and can benefit from, lifesaving vaccines. Copyright (C) 2021 The Author(s). Published by Elsevier Ltd.Peer reviewe

Some New Integral Inequalities Involving Fractional Operator with Applications to Probability Density Functions and Special Means

Fractional calculus manages the investigation of supposed fractional derivatives and integrations over complex areas and their applications. Fractional calculus is the purported assignment of differentiations and integrations of arbitrary non-integer order. Lately, it has attracted the attention of several mathematicians because of its real-life applications. More importantly, it has turned into a valuable tool for handling elements from perplexing frameworks within different parts of the pure and applied sciences. Integral inequalities, in association with convexity, have a strong relationship with symmetry. The objective of this article is to introduce the notion of operator refined exponential type convexity. Fractional versions of the Hermite–Hadamard type inequality employing generalized R–L fractional operators are established. Additionally, some novel refinements of Hermite–Hadamard type inequalities are also discussed using some established identities. Finally, we present some applications of the probability density function and special means of real numbers

Some New Integral Inequalities Involving Fractional Operator with Applications to Probability Density Functions and Special Means

Fractional calculus manages the investigation of supposed fractional derivatives and integrations over complex areas and their applications. Fractional calculus is the purported assignment of differentiations and integrations of arbitrary non-integer order. Lately, it has attracted the attention of several mathematicians because of its real-life applications. More importantly, it has turned into a valuable tool for handling elements from perplexing frameworks within different parts of the pure and applied sciences. Integral inequalities, in association with convexity, have a strong relationship with symmetry. The objective of this article is to introduce the notion of operator refined exponential type convexity. Fractional versions of the Hermite–Hadamard type inequality employing generalized R–L fractional operators are established. Additionally, some novel refinements of Hermite–Hadamard type inequalities are also discussed using some established identities. Finally, we present some applications of the probability density function and special means of real numbers

Perception and practices regarding cannabis consumption in Karachi, Pakistan: A cross-sectional study

Several studies have been carried out regarding the awareness and usage of cannabis around the world, especially in developed countries. Pakistan ranks amongst the top nations in regards to cannabis consumption. However, the amount of literature shedding light on people\u27s perception, knowledge and practices are scarce. Therefore, the authors sought to establish a baseline study to ignite the discussion on the possibility of cannabis\u27 induction in the medical field in Pakistan, and additionally provide a foundation for further research. The purpose of this study was to investigate the level of understanding and consumption practices in Karachi with respondents from different socio-economic backgrounds, age groups and gender regarding cannabis use and assessing the awareness of the general population. The null hypothesis is that the usage of cannabis does not have a significant correlation with age, gender, or socio-economic status of a population. We conducted a cross-sectional study in November 2018 using convenience sampling and interviewed 518 individuals for their gender, age, and socio-economic status, to determine their knowledge, attitudes, and practices regarding cannabis usage. The participants were questioned about their knowledge and its source. Attitudes were judged using three and five-point Likert scales while questions regarding practices centered upon the past and current usage of cannabis. One-way analysis of variance and chi-square tests were used as the primary statistical tests. Out of the 518 people who responded, more than half of the respondents were males (n = 340, 65.6%). The majority was familiar with the use of cannabis (n = 514, 99.2%), and the different ways in which it is consumed (n = 435, 84%). About one-third of the participants happened to consume cannabis (n = 168, 32.4%), and a quarter mentioned recreational use/curiosity as the principal reason (n = 134, 25.9%). Majority of the respondents agreed upon the harmful effects of consuming cannabis (n = 364, 70.3%), while when compared to other inimical drugs, half of them believed it to be less harmful (n = 259, 50%). Besides, an overwhelming majority stated, that if they were to consume cannabis, they would not consider taking permission from their parents/guardians (n = 441, 85.2%). Concerning legality, three-fifths of the participants chose cannabis to remain illegal in Pakistan (n = 307, 59.3%) and, for not consuming/quitting cannabis, the primary reason chosen was its harmful consequences (n = 210, 40.5%). Our study revealed that knowledge about usage of cannabis still requires a great deal of attention. Only individuals from higher socio-economic backgrounds have a positive attitude towards cannabis usage and are aware of it. There is an urgent need for awareness programs that especially reach out to the lower socio-economic status population, who otherwise do not have access to essential information resources. We also found that males were more likely to be consumers and to have more knowledge about cannabis, therefore, it is equally important to educate females about this topic so that an informed discussion about cannabis use and its medical benefits can be generated in Pakistan