Improved exponential type variance estimators for population utilizing supplementary information.

This paper contributes to the existing literature on variance estimators by utilizing supplementary information. The variance estimation problem of a finite population is a significant matter as sometimes, it is tough to control the variation. For this purpose, an optimum family of exponential variance estimators is suggested under simple random sampling. Moreover, different specific members of the proposed estimators are identified by incorporating various known characteristics of the supplementary variable in the suggested generalized class of estimators. The derivations for the expressions of bias as well as mean square error (MSE) of the proposed estimators are conducted. The suggested family of estimators is studied in different situations by using sets of real data and simulation studies for their performance. To evaluate the efficiency of the suggested estimators, R software is used for the analysis. The study compares the performance of the proposed estimators against the traditional estimators. The theoretical and numerical comparisons show that the estimators suggested in the study are superior in efficiency as compared to the existing estimators.

Pyridine-2,6-Dicarboxylic Acid As a Facile and Highly Selective "Turn-Off" Fluorimetric Chemosensor for Detection of Cu (II) Ions in Aqueous Media.

Copper metal is third most abundant trace element in human body. Determination of Cu (II) ions is a burning topic in field of environment protection and food safety because of its significant impact on ecosystem. In this study, 2,6-pyridine dicarboxylic acid (PDA) has been explored as "turn-off" florescent probe for florescent detection of Cu (II) ions. This sensor showed highly selective complexing ability towards Cu (II) ions. Addition of aqueous solution of Cu (II) ions remarkably quenched the fluorescence intensity of PDA while, on contrary, there was no any prominent fluorescence quenching interference on addition of various metal ions. The binding mode of PDA and Cu (II) ions was determined as stoichiometry of 1:1 and it was further confirmed by single crystal XRD analysis. Mechanisms of static and dynamic quenching were confirmed by stern-volmer plot. Limit of detection (LOD) and limit of quantification (LOQ) for Cu (II) ions was calculated as 3.6 µM and 1.23 µM respectively, which is far below the acceptable value (31.5µM) according to the World Health Organization. The use of the sensor for detection of Cu (II) ions in real samples in aqueous media was also performed.

Cattano Christov double diffusion model for third grade nanofluid flow over a stretching Riga plate with entropy generation analysis.

The current investigation delves into the convective heat and mass transfer characteristics of third-grade radiative nanofluid flow within a porous medium over a Riga plate configuration. The Riga plate structure incorporates magnets and electrodes strategically arranged on a plate surface. To enhance the accuracy of energy and concentration expressions within the third-grade fluid flow, the Cattano Christov Double Diffusion model is employed. Entropy generation analysis is conducted by applying the second law of thermodynamics, and Darcy's model is employed to characterize the behavior of a porous medium. Appropriate similarity transformations have been used to convert the partial differential equations monitoring the fluid flow model into dimensionless ordinary differential equations. The Galerkin weighted residual method is employed to resolve these equations numerically. The findings contain detailed explanations of how relevant factors affect the temperature field, concentration field, velocity field, entropy generation, and Bejan number, in addition to graphic representations of the results. The findings indicate that the medium's porosity and Brinkman number promote entropy generation. The Bejan number and entropy production is affected by the thermal radiation parameter, which first rises and then declines after a certain distance.

Multiwaves, breathers, lump and other solutions for the Heimburg model in biomembranes and nerves.

In this manuscript, a mathematical model known as the Heimburg model is investigated analytically to get the soliton solutions. Both biomembranes and nerves can be studied using this model. The cell membrane's lipid bilayer is regarded by the model as a substance that experiences phase transitions. It implies that the membrane responds to electrical disruptions in a nonlinear way. The importance of ionic conductance in nerve impulse propagation is shown by Heimburg's model. The dynamics of the electromechanical pulse in a nerve are analytically investigated using the Hirota Bilinear method. The various types of solitons are investigates, such as homoclinic breather waves, interaction via double exponents, lump waves, multi-wave, mixed type solutions, and periodic cross kink solutions. The electromechanical pulse's ensuing three-dimensional and contour shapes offer crucial insight into how nerves function and may one day be used in medicine and the biological sciences. Our grasp of soliton dynamics is improved by this research, which also opens up new directions for biomedical investigation and medical developments. A few 3D and contour profiles have also been created for new solutions, and interaction behaviors have also been shown.

The development of an extended Weibull model with applications to medicine, industry and actuarial sciences.

This paper delves into the theoretical and practical exploration of the complementary Bell Weibull (CBellW) model, which serves as an analogous counterpart to the complementary Poisson Weibull model. The study encompasses a comprehensive examination of various statistical properties of the CBellW model. Real data applications are carried out in three different fields, namely the medical, industrial and actuarial fields, to show the practical versatility of the CBellW model. For the medical data segment, the study utilizes four data sets, including information on daily confirmed COVID-19 cases and cancer data. Additionally, a Group Acceptance Sampling Plan (GASP) is designed by using the median as quality parameter. Furthermore, some actuarial risk measures for the CBellW model are obtained along with a numerical illustration of the Value at Risk and the Expected Shortfall. The research is substantiated by a comprehensive numerical analysis, model comparisons, and graphical illustrations that complement the theoretical foundation.

The Role of Gut-derived Short-Chain Fatty Acids in Multiple Sclerosis.

Multiple sclerosis (MS) is a chronic condition affecting the central nervous system (CNS), where the interplay of genetic and environmental factors influences its pathophysiology, triggering immune responses and instigating inflammation. Contemporary research has been notably dedicated to investigating the contributions of gut microbiota and their metabolites in modulating inflammatory reactions within the CNS. Recent recognition of the gut microbiome and dietary patterns as environmental elements impacting MS development emphasizes the potential influence of small, ubiquitous molecules from microbiota, such as short-chain fatty acids (SCFAs). These molecules may serve as vital molecular signals or metabolic substances regulating host cellular metabolism in the intricate interplay between microbiota and the host. A current emphasis lies on optimizing the health-promoting attributes of colonic bacteria to mitigate urinary tract issues through dietary management. This review aims to spotlight recent investigations on the impact of SCFAs on immune cells pivotal in MS, the involvement of gut microbiota and SCFAs in MS development, and the considerable influence of probiotics on gastrointestinal disruptions in MS. Comprehending the gut-CNS connection holds promise for the development of innovative therapeutic approaches, particularly probiotic-based supplements, for managing MS.

Mathematical modeling and dynamics of immunological exhaustion caused by measles transmissibility interaction with HIV host.

This paper mainly addressed the study of the transmission dynamics of infectious diseases and analysed the effect of two different types of viruses simultaneously that cause immunodeficiency in the host. The two infectious diseases that often spread in the populace are HIV and measles. The interaction between measles and HIV can cause severe illness and even fatal patient cases. The effects of the measles virus on the host with HIV infection are studied using a mathematical model and their dynamics. Analysing the dynamics of infectious diseases in communities requires the use of mathematical models. Decisions about public health policy are influenced by mathematical modeling, which sheds light on the efficacy of various control measures, immunization plans, and interventions. We build a mathematical model for disease spread through vertical and horizontal human population transmission, including six coupled nonlinear differential equations with logistic growth. The fundamental reproduction number is examined, which serves as a cutoff point for determining the degree to which a disease will persist or die. We look at the various disease equilibrium points and investigate the regional stability of the disease-free and endemic equilibrium points in the feasible region of the epidemic model. Concurrently, the global stability of the equilibrium points is investigated using the Lyapunov functional approach. Finally, the Runge-Kutta method is utilised for numerical simulation, and graphic illustrations are used to evaluate the impact of different factors on the spread of the illness. Critical factors that effect the dynamics of disease transmission and greatly affect the rate and range of the disease's spread in the population have been determined through a thorough analysis. These factors are crucial in determining the expansion of the disease.

Role of dietary fiber and lifestyle modification in gut health and sleep quality.

Dietary fiber has an immense role in the gut microbiome by modulating juvenile growth, immune system maturation, glucose, and lipid metabolism. Lifestyle changes might disrupt gut microbiota symbiosis, leading to various chronic diseases with underlying inflammatory conditions, obesity, and its associated pathologies. An interventional study of 16 weeks examined the impact of psyllium husk fiber with and without lifestyle modification on gut health and sleep quality in people with central obesity (men = 60 and women = 60), those aged from 40 to 60 years, those having WC ≥ 90 cm (men) and WC ≥ 80 cm (women), and no history of any chronic disease or regular medication. The participants were subgrouped into three intervention groups, namely, the psyllium husk fiber (PSH) group, the lifestyle modification (LSM) group, and the LSM&PSH group and control group with equal gender bifurcation (men = 15 and women = 15). A 24-h dietary recall, gastrointestinal tract (GIT) symptoms, and sleep quality analysis data were collected on validated questionnaires. The analyses of variance and covariance were used for baseline and post-intervention, respectively. Student's t-test was applied for pre- and post-intervention changes on the variable of interest. The intervention effect on GIT health was highly significant (P < 0.001). The mean GIT scores of the LSM, PSH, and LSM&PSH groups were 2.99 ± 0.14, 2.49 ± 0.14, and 2.71 ± 0.14, respectively, compared to the mean GIT scores of the control group. No significant (P = 0.205) effect of either intervention was observed on sleep quality. The study concluded that psyllium husk fiber significantly improved the GIT symptoms, while no significant effect of the intervention was observed on sleep quality analysis.

A fair bed allocation during COVID-19 pandemic using TOPSIS technique based on correlation coefficient for interval-valued pythagorean fuzzy hypersoft set.

The relationship between two variables is an essential factor in statistics, and the accuracy of the results depends on the data collected. However, the data collected for statistical analysis can be unclear and difficult to interpret. One way to predict how one variable will change about another is by using the correlation coefficient (CC), but this method is not commonly used in interval-valued Pythagorean fuzzy hypersoft set (IVPFHSS). The IVPFHSS is a more advanced and generalized form of the Pythagorean fuzzy hypersoft set (PFHSS), which allows for more precise and accurate analysis. In this research, we introduce the correlation coefficient (CC) and weighted correlation coefficient (WCC) for IVPFHSS and their essential properties. To demonstrate the applicability of these measures, we use the COVID-19 pandemic as an example and establish a prioritization technique for order preference by similarity to the ideal solution (TOPSIS) model. The technique is used to study the problem of optimizing the allocation of hospital beds during the pandemic. This study provides insights into the importance of utilizing correlation measures for decision-making in uncertain and complex situations like the COVID-19 pandemic. It is a robust multi-attribute decision-making (MADM) methodology with significant importance. Subsequently, it is planned to increase a dynamic bed allocation algorithm based on biogeography to accomplish the superlative decision-making system. Moreover, numerical investigations deliberate the best decision structures and deliver sensitivity analyses. The efficiency of our encouraged algorithm is more consistent than prevalent models, and it can effectively control and determine the optimal configurations for the study.

Improved exponential type mean estimators for non-response case using two concomitant variables in simple random sampling.

This paper addresses new exponential estimators for population mean in case of non-response on both the study and the concomitant variables using simple random sampling. The expressions for theoretical bias and mean square error of new estimators are derived up to first-order approximation and comparisons are made with the existing estimators. The proposed estimators are observed more efficient as compared to the considered estimators in the literature. For instance, the classical [4] unbiased estimator, the estimator of [9], and other existing estimators under the explained conditions. The theoretical results are supported numerically by using real-life data sets, under the criteria of bias, mean square error, percent relative efficiency and mathematical conditions. It is also clear from the numerical results that the suggested exponential estimators performed better than the estimators in the literature.

Deciphering the functional landscape and therapeutic implications of noncoding RNAs in the TGF-ß signaling pathway in colorectal cancer: A comprehensive review.

Colorectal cancer (CRC) remains a major global health concern, necessitating an in-depth exploration of the intricate molecular mechanisms underlying its progression and potential therapeutic interventions. Transforming Growth Factor-ß (TGF-ß) signaling, a pivotal pathway implicated in CRC plays a dual role as a tumor suppressor in the early stages and a promoter of tumor progression in later stages. Recent research has shed light on the critical involvement of noncoding RNAs (ncRNAs) in modulating the TGF-ß signaling pathway, introducing a new layer of complexity to our understanding of CRC pathogenesis. This comprehensive review synthesizes the current state of knowledge regarding the function and therapeutic potential of various classes of ncRNAs, including microRNAs (miRNAs), long noncoding RNAs (lncRNAs), and circular RNAs (circRNAs), in the context of TGF-ß signaling in CRC. The intricate interplay between these ncRNAs and key components of the TGF-ß pathway is dissected, revealing regulatory networks that contribute to the dynamic balance between tumor suppression and promotion. Emphasis is placed on how dysregulation of specific ncRNAs can disrupt this delicate equilibrium, fostering CRC initiation, progression, and metastasis. Moreover, the review provides a critical appraisal of the emerging therapeutic strategies targeting ncRNAs associated with TGF-ß signaling in CRC. The potential of these ncRNAs as diagnostic and prognostic biomarkers is discussed, highlighting their clinical relevance. Additionally, the challenges and prospects of developing RNA-based therapeutics, such as RNA interference and CRISPR/Cas-based approaches, are explored in the context of modulating TGF-ß signaling for CRC treatment. In conclusion, this review offers a comprehensive overview of the intricate interplay between ncRNAs and the TGF-ß signaling pathway in CRC. By unraveling the functional significance of these regulatory elements, we gain valuable insights into the molecular landscape of CRC, paving the way for the development of novel and targeted therapeutic interventions aimed at modulating the TGF-ß signaling cascade through the manipulation of ncRNAs.

Functionalization of Shorea faguetiana biochar using Fe2O3 nanoparticles and MXene for rapid removal of methyl blue and lead from both single and binary systems.

The synthesis of polymeric magnetic composites is a promising strategy for the rapid and efficient treatment of wastewater. Lead and methyl blue are extremely hazardous to living organisms. The sorption of Pb2+ and the dye methyl blue (MB) by biochar is an ecologically sustainable method to remediate this type of water pollution. We functionalized Shorea faguetiana biochar with Fe2O3 and MXene, resulting in Fe2O3/BC/MXene composites with an efficient, rapid, and selective adsorption performance. Based on X-ray photoelectron and Fourier transform infrared spectrometry, we found that the Fe2O3/BC/MXene composites had an increased number of surface functional groups (F-, C[double bond, length as m-dash]O, CN, NH, and OH-) compared with the original biochar. The batch sorption findings showed that the maximum sorption capacities for Pb2+ and MB at 293 K were 882.76 and 758.03 mg g-1, respectively. The sorption phenomena obeyed a pseudo-second-order (R2 = 1) model and the Langmuir isotherm. There was no competition between MB and Pb2+ in binary solutions, indicating that MB and Pb2+ did not influence each other as a result of their different adsorption mechanisms (electrostatic interaction for Pb2+ and hydrogen bonding for MB). This illustrates monolayer sorption on the Fe2O3/BC/MXene composite governed by chemical adsorption. Thermodynamic investigations indicated that the sorption process was spontaneous and exothermic at 293-313 K, suggesting that it is feasible for practical applications. Fe2O3/BC/MXene can selectively adsorb Pb2+ ions and MB from wastewater containing multiple interfering metal ions. The sorption capacities were still high after five reusability experiments. This work provides a novel Fe2O3/BC/MXene composite for the rapid and efficient removal of Pb2+ and MB.

Critical analysis for nonlinear oscillations by least square HPM.

In this study, a novel adapted homotopy perturbation method (HPM) is used to treat the nonlinear phenomena of free vibration in a system with one degree of freedom. This adaptation involves the integration of HPM with a least-squares optimizer, resulting in a hybrid method called the least square homotopy perturbation method (LSHPM). The LSHPM is tested on various nonlinear problems documented in the existing literature. To evaluate the effectiveness of the proposed approach, the identified problems are also tackled using HPM and the MATLAB built-in function bvp5c, and then the results are compared with those obtained using LSHPM. In addition, a comparative analysis is carried out with the results of the AG method as found in the literature. The results show that LSHPM is a reliable and efficient method suitable for solving more complicated initial value problems in the fields of science and engineering.

Impact of chemical reaction on Eyring-Powell fluid flow over a thin needle with nonlinear thermal radiation.

The thin needle is viewed as a revolutionary object since it has a thinner thickness than a boundary layer. As a consequence, scientific and engineering applications for instance electrical equipment, hot wire anemometers and geothermal power generation are significantly impacted by the flow deformed by a thin moving needle. MHD Eyring-Powell fluid flow over a thin needle perceiving heat source, chemical reaction and nonlinear thermal radiation is the subject of the current investigation. In addition, the present study utilizes the Buongiorno model to examine the special effects of the fluid's Brownian and thermophoretic forces. The solution of the dimensionless form of ODEs is produced by applying exact renovations to the given problem, which is determined by the structure of PDEs. The bvp4c algorithm, based on the finite difference approach is utilized to numerically solve such modified ODEs. For validation, the results obtained indicate good agreement when compared to the literature. Finally, a detailed graphical analysis of key parameters is shown and explained while keeping in mind the physical significance of flow parameters. The results show that as magnetic and fluid parameter values improve, the velocity gradient falls. Increasing heat source and radiation parameters optimises heat transfer rate. The augmentation of the Lewis number and chemical reaction accelerates the rate of mass transfer on the surface. Brownian motion and thermophoresis provide enhanced thermal performance for the fluid temperature. Growing the thermophoresis parameter from 0.1 to 0.3 upsurges the Nusselt number by 5.47% and the Sherwood number by 12.26%.

An enhanced estimator of finite population variance using two auxiliary variables under simple random sampling.

In this article, we have suggested a new improved estimator for estimation of finite population variance under simple random sampling. We use two auxiliary variables to improve the efficiency of estimator. The numerical expressions for the bias and mean square error are derived up to the first order approximation. To evaluate the efficiency of the new estimator, we conduct a numerical study using four real data sets and a simulation study. The result shows that the suggested estimator has a minimum mean square error and higher percentage relative efficiency as compared to all the existing estimators. These findings demonstrate the significance of our suggested estimator and highlight its potential applications in various fields. Theoretical and numerical analyses show that our suggested estimator outperforms all existing estimators in terms of efficiency. This demonstrates the practical value of incorporating auxiliary variables into the estimation process and the potential for future research in this area.

The hydrodyanamics of gravity-driven vessel drainage of third order fluid using perturbation method.

In this work, tank drainage phenomena for in-compressible and isothermal fluid having unsteady fluid flow for third order fluid is studied. Analytical solution of the proposed problem is obtained using perturbation method subject to proper boundary conditions. No-slip condition is used because of fluid will have zero velocity relative to a solid boundary. Object of this work is to find out the velocity profile, flow rate, time required to empty a tank (time efflux) and mathematical relation of time and depth of the tank. Influence of different parameter over velocity profile, effect of radius of the tank over depth, effect of radius of piper over flow rate and effect of depth over flow rate are examined graphically using mathematica. Velocity profile of this model is compared with newtonian fluid's while assuming epsilon as a zero using graph and table from which it is clear that third order fluid posses greater velocity then Newtonian fluid.

Extension of correlation coefficient based TOPSIS technique for interval-valued Pythagorean fuzzy soft set: A case study in extract, transform, and load techniques.

Correlation is an essential statistical concept for analyzing two dissimilar variables' relationships. Although the correlation coefficient is a well-known indicator, it has not been applied to interval-valued Pythagorean fuzzy soft sets (IVPFSS) data. IVPFSS is a generalized form of interval-valued intuitionistic fuzzy soft sets and a refined extension of Pythagorean fuzzy soft sets. In this study, we propose the correlation coefficient (CC) and weighted correlation coefficient (WCC) for IVPFSS and examine their necessary properties. Based on the proposed correlation measures, we develop a prioritization technique for order preference by similarity to the ideal solution (TOPSIS). We use the Extract, Transform, and Load (ETL) software selection as an example to demonstrate the application of these measures and construct a prioritization technique for order preference by similarity to the ideal solution (TOPSIS) model. The method investigates the challenge of optimizing ETL software selection for business intelligence (BI). This study offers to illuminate the significance of using correlation measures to make decisions in uncertain and complex settings. The multi-attribute decision-making (MADM) approach is a powerful instrument with many applications. This expansion is predicted to conclude in a more reliable decision-making structure. Using a sensitivity analysis, we contributed empirical studies to determine the most significant decision processes. The proposed algorithm's productivity is more consistent than prevalent models in controlling the adequate conformations of the anticipated study. Therefore, this research is expected to contribute significantly to statistics and decision-making.

Behavior of higher-order MDD on energy ratios at the interface of thermoelastic and piezothermoelastic mediums.

This paper investigates the intricate energy distribution patterns emerging at an orthotropic piezothermoelastic half-space interface by considering the influence of a higher-order three-phase lags heat conduction law, accompanied by memory-dependent derivatives (referred to as HPS) within the underlying thermoelastic half-space (referred to as TS). This study explores the amplitude and energy ratios of reflected and transmitted waves. These waves span various incident types, including longitudinal, thermal, and transversal, as they propagate through the TS and interact at the interface. Upon encountering the interface, an intriguing dynamic unfolds: three waves experience reflection within the TS medium, while four waves undergo transmission into the HPS medium. A graphical representation effectively illustrates the impact of higher-order time differential parameters and memory to offer comprehensive insights. This visual representation reveals the nuanced fluctuations of energy ratios with the incidence angle. The model astutely captures diverse scenarios, showcasing its ability to interpret complex interface dynamics.