Auxiliary information is used to estimate population parameters and enhance the efficiency of estimators. However, when such information is partially or entirely unavailable, or when surveying a large sample is prohibitively expensive, two-phase sampling becomes practical. Unlike previous approaches, this study introduces a generalised hybrid estimator that integrates ratio, product and exponential-type strategies to achieve consistently lower mean squared errors. This unified framework extends existing variance estimation methods in two-phase sampling and demonstrates clear efficiency gains over conventional estimators. Therefore, this study aims at addressing the problem of variance estimation under such a context. This study suggests a class of efficient hybrid estimators for estimating finite population variance in two-phase sampling. The bias and mean squared error expressions are derived up to the first order of approximation and compared with those of existing estimators. A special case of the proposed class of estimators is also discussed. The performance of the proposed estimator is evaluated empirically using two real-world data sets. A simulation study is conducted using three bivariate normal populations with varying correlations between the auxiliary and study variables. To evaluate estimator performance, theoretical percentage relative efficiencies are computed. The results of both simulation and empirical studies demonstrate significant efficiency gains of the proposed estimator over existing approaches.
Based on hydrogen and oxygen isotopes and hydrochemical composition data, this paper discusses the sources, genesis and geochemical changes of geothermal fluids in the south-eastern Gansu province.Water from six hot springs (Tongwei bathing pool River Hot Spring, Qingshui seismostation, Tianshui seismostation, Wushan seismostation, Chengxian seismostation and Wudu seismostation) was collected in triplicate from July to September in the wet season. The measurement results showed that total dissolved solids of the water samples ranged from 456-2823 mg/L.The water samples can be classified into four hydrochemical types: Na+-Cl-, Ca2+/Na+-HCO3-, Ca2+-SO(4)(2-)and Na+-HCO3-. The hydrogen and oxygen isotopic composition indicates that the hot spring water in the region originates from atmospheric precipitation, undergoes water-rock interactions during its circulation, and may mix with surface water. The chemical composition of the water across different water bodies is primarily influenced by water-rock interactions and evaporation-crystallisation processes. Using the Gaillardet model, it is concluded that most ions result from the combined weathering and dissolution of silicate and evaporite rocks. The depth of hot water circulation exceeds 3 km, and significant changes in circulation depth have occurred since the Wenchuan earthquake.
This study addresses the challenge of outliers in sample surveys, a common issue that can distort results and lead to inaccurate conclusions. To tackle this problem, researchers have developed various robust regression techniques including least trimmed squares, least median of squares, least absolute deviations, Huber's, Hample's and Tukey's maximum likelihood estimators, and Huber's maximum likelihood estimator for location and scale estimators. We propose a new approach: minimum covariance determinant-based ratio estimators for estimating the population mean in sample surveys. To assess the performance of the proposed minimum covariance determinant-based estimators, we derive their mean square error expressions and determine the conditions under which they surpass existing estimators in efficiency. To validate our theoretical findings, we conduct a numerical illustration using real-world data and perform simulations with R-Programme software. The results demonstrate that our method effectively handles outliers and improves the overall accuracy of survey-based estimations, making it a valuable tool for researchers working with sample survey data.
The associations of cardiac function of patients with dilated cardiomyopathy (DCM) and chronic heart failure (CHF) with kidney injury molecule-1 (KIM-1) and renal and vascular endothelial functions were explored. The subjects (80 in total) were recruited from patients undergoing treatment between June 2020 and July 2022. A retrospective analysis was implemented on their clinical data, and grade-I group (n=16), grade-II group (n=36) and grade-III group (n=28) were set up in accordance with New York Heart Association classification standards for cardiac function. The levels of endothelin-1, thromboxane B2, serum creatinine, blood urea nitrogen, cystatin C, glomerular filtration rate and KIM-1 were higher in grade-II and grade-III groups than in the grade-I group and also higher in the grade III group than in the grade-II group (P<0.05). This study comprehensively analyses the association of KIM-1, vascular endothelial function and renal function with cardiac functional status in DCM-related CHF. The findings suggest that these biomarkers may serve as sensitive indicators for early detection of cardiac dysfunction and guide timely clinical interventions.
The current study addresses a significant gap in sampling theory by introducing novel ratio-type estimators for finite population mean under circular systematic sampling using a quantile regression approach. We derive the theoretical mean squared error expressions for the proposed estimators and conduct comparative analyses against existing estimators. The results clearly demonstrate that our estimators outperform traditional ones in terms of efficiency. To validate our findings, we present numerical illustrations based on a real-life data set. Moreover, a Monte Carlo simulation study based on real-life data set is also included to check the performance of the proposed estimators. Numerical findings endorse the potential of the proposed estimators. The findings may help the researchers to get more estimates that are precise for population mean, which is widely applicable in different fields.
This paper comprehensively investigates the statistical continuity of functions taking values in uniform spaces. It aims to demonstrate how classical continuity can be characterised and extended by replacing traditional sequence convergence with statistically structured sequences defined via natural density. Thus, the concept of continuity is reinterpreted through statistical convergence, offering a more profound and comprehensive theoretical contribution to the study of continuity in uniform spaces.
This study presents an efficient method for estimating the population mean of a study variable using a Searls exponential ratio estimator. The approach is based on simple random sampling and leverages known population parameters of an auxiliary variable for enhanced estimation of population mean. Using large sample approximations up to the first order, the expressions for the bias and mean squared error of the proposed estimator are derived. To evaluate its performance, the estimator is compared conceptually and mathematically with several existing estimators. Theoretical results are further validated through both simulated and real-world data sets. Findings from these evaluations demonstrate that the proposed estimator consistently outperforms many competing estimators, particularly at higher population mean values. Therefore, it holds promise for improving population mean estimation across a range of practical applications.
This study aims to investigate the impact of follow-up frequency on prenatal processes and maternal behaviours in pregnant rats. A total of 16 primigravida Wistar albino rats were used in the study. The pregnant rats were randomly divided into 4 groups: control group (C), group followed up every 2 days (IG1), group followed up every 4 days (IG2) and group followed up every 6 days (IG3). The daily feed intake, water consumption, weight gain and fasting blood glucose levels of the rats in the groups were determined during the study period. In addition, the birth weight and daily weight gain of the pups were recorded. The open-field test was administered to the pregnant rats and social preference tests were conducted on the maternal rats at post-birth, with locomotor activities evaluated using Python programming. The weight, food and water intake in the IG3 group significantly increased while the IG2 group showed a decrease. The highest offspring weights were recorded in the IG2 group while the lowest were observed in the IG3 group. The longest time spent in the centre of the test maze was recorded in the IG2 group at 39.33 +/- 5.50 sec. while the shortest time was recorded in the control group at 21.66 +/- 2.88 sec. The follow-up procedure applied every 4 days to pregnant rats was found to decrease food and water intake and weight gain while leading to the highest weights of the offspring, indicating positive effects on behavioural parameters, particularly stress.
This retrospective study examines the optimal timing for Mycoplasma pneumoniae (MP) IgM detection in children with clinical symptoms such as cough and fever, and evaluates the diagnostic value of MP-IgM levels with routine blood tests. Clinical data from 149 children with MP IgM positivity were analysed, focusing on symptom onset times and changes in IgM levels, white blood cell (WBC), neutrophil-to-lymphocyte ratio (NLR) and platelet-to-lymphocyte ratio (PLR) at varying symptom durations. Coughing appeared as early as 24 hr after infection, with fever following 12 hr later. The median cough duration was 7 days, with 54.4% of children testing IgM positive within this period, while fever was present in 59.1% of cases. IgM, WBC, NLR and PLR levels were significantly higher than those in the control group in children with cough durations of 8-15 days, and prolonged fever (>3 days) correlated with higher IgM and PLR levels. It is concluded that for children with suspected MP infection, quantitative MP-IgM testing combined with routine blood parameters (WBC, NLR, PLR) is recommended for rapid diagnosis, particularly in those with cough persisting >7 days or fever lasting >3 days.
In this article deferred density is employed to introduce new generalisations of topological convergence, boundedness and Cauchiness for sequences in a locally solid Riesz space. Along with investigating the fundamental properties and inclusion theorems of these newly introduced concepts, the notion of statistical continuity is extended for functions using the deferred Ces & agrave;ro mean in locally solid Riesz spaces.
In the present study ruled surfaces generated by Darboux and instantaneous Pfaff vectors of Salkowski curves in Euclidean 3-space are considered. Some geometric properties of these surfaces such as striction curves, surface normal vectors, tangent and asymptotic planes, distribution parameters, Gaussian and mean curvatures and fundamental forms are investigated. Some results and interpretations of these surfaces are obtained.
Fractional versions of graph-theoretic invariants have expanded their applicability to diverse fields such as connectivity, scheduling, assignment and operational research. Building on this extension of fractional graph theory, we introduce the local fractional metric dimension (LFMD) of non-planar networks. For a given network G, the local resolving neighbourhood LR(uw) of an edge uw is defined as the set of vertices in G that distinguish between u and w. A function rho:V(G)->[0,1] is considered a local resolving function if rho(LR(uw))>= 1 for every edge uw in G. The LFMD of G is then defined as the minimum value of rho(V(G)) taken over all possible local resolving functions. In this paper we compute the exact values of the LFMD for two non-planar, structurally symmetric network families- generalised gear and generalised helm networks-each constructed with a finite number of levels and characterised by distinct types of vertices. We compare the results for both networks and analyse the impact of pendant vertices in the context of bipartite and non-bipartite structures. Furthermore, we investigate the asymptotic behaviour as the order of the networks approaches infinity and present an emergency exit planning scenario to illustrate the practical significance of our findings.
Bucephalandra is a genus of endemic plants in Borneo. It is highly valued in the aquascape community because of its significant economic potential. This study aims to identify the species type of six Bucephalandra sp. accessions from Borneo through morphological characterisation, and evaluate their genetic diversity using maturase K (matK), internal transcribed spacer (ITS) and ribulose-biphosphate carboxylase/oxygenase large subunit (rbcL) markers. The observed characters include the morphology of the leaf, stem and root. Phylogenetic trees were constructed using the unweighted pair group method with arithmetic mean based on each matrix of the respective marker and on the concatenated matrix of all markers. The characteristics of the leaves, stems and roots vary among the six accessions. All accessions exhibit similar leaf colours, except for B. diabolica, which has reddish leaves. The accessions are identified as B. goliath, B. forcipula, B. diabolica, B. kishii, B. pubes and B. minotaur. Based on respective ITS and matK sequences, the tree clusters all Bucephalandra species into three groups. The tree, based on concatenated sequences, not only clusters them into three groups but also differentiates B. motleyana (as reference accession) from other Bucephalandra species. The concatenated data set has a haplotype diversity of 1 and a high level of Pi of 0.10917. It indicates that using matK, ITS and rbcL in combination is an optimal and efficient method for differentiating and clustering the Bucephalandra species.
We propose the neutrosophic Poisson moment exponential distribution (NPMExD) as an extension of the Poisson moment exponential distribution (PMExD) originally developed by Ahsan-ul Haq. We detail the application of neutrosophic logic to the PMExD framework, enhancing its capability to handle uncertainty and indeterminacy. The study explores various statistical and mathematical properties of the NPMExD, including the survival function, moment generating function, hazard rate function, order statistics distribution, cumulative hazard function, index of dispersion, and related measures. Parameter estimation is performed using the maximum likelihood estimation method, followed by a comprehensive simulation study to assess the estimator performance. Finally, the practical efficacy of the proposed distribution is demonstrated through the analysis of two real-world data sets: remission times (in weeks) for 20 leukemia patients and 59 months of actual tax revenue (monthly) data from Egypt. The results indicate that the NPMExD provides a superior fit compared to the neutrosophic discrete Ramos-Louzada distribution for these data sets.
Regression analysis plays a significant role in statistics by identifying the relationship between variables. However, when the assumptions of ordinary least squares are violated, non-parametric regression becomes a preferable approach. In the field of non-parametric regression, Nadaraya-Watson (NW) kernel regression estimators have gained popularity in recent decades. The adaptive NW kernel regression estimator is considered one of the best and most effective estimators for non-parametric regression due to its varying bandwidth. The effective utilisation of the bandwidth factor is a key aspect of kernel regression. This article proposes the use of probability-weighted moments (PWMs) to enhance the bandwidth factor of the kernel regression estimator. The novelty of this approach lies in replacing traditional measures of central tendency and dispersion with PWMs to introduce a new family of NW kernel regression estimators that are more robust to outliers. Monte Carlo simulation studies are conducted to compare the performance of existing and proposed kernel regression estimators. The simulations use a data set of COVID-19 cases from Africa, highlighting the severity of the current pandemic. The results of the simulations demonstrate that the proposed family of estimators is more robust than existing estimators.
This study introduces a derivative concept that integrates the q-derivative and the Fr & eacute;chet derivative, aiming to overcome the limitations associated with non-linear operators. The theoretical foundation for the newly defined quantum Fr & eacute;chet derivative is presented, supported by definitions, properties and illustrative examples. In particular, this derivative maintains consistency with classical definitions in finite-dimensional cases, while offering generalisability for applications in infinite-dimensional spaces.
The present study evaluates the nephroprotective effect and molecular function of miRNA-1906 stimulation on ischemia/reperfusion (I/R)-induced acute kidney injury (AKI) in mice. Clamping kidney tissues caused I/R-induced renal injury. In this study, 18 mice were divided into three distinct groups (n = 6): control group, AKI group and miRNA-1906 agomir Test group. The miRNA-1906 group received 500 nmol/kg of miRNA-1906 agomir administered intrathecally for 24 hrs before the induction of ischemia. The effects of miRNA-1906 stimulation on kidney function, oxidative stress and mediators of inflammation were evaluated. The expressions of Slit Guidance Ligand 2 (SLIT2), Roundabout homolog 1 (ROBO1), desmin, caspase-3, Transient Receptor Potential Canonical 6 (TRPC6), phosphorylated Akt (p-Akt) and nephrin in renal tissues were measured by western blot to investigate the impact of miRNA-1906 stimulation on podocyte damage. Histopathological changes were assessed with hematoxylin and eosin staining. The miRNA-1906 agomir reduced the serum levels of creatinine and blood urea nitrogen, as well as the excretion of microalbumin, in the AKI group. The treatment with miRNA-1906 agomir also lowered levels of oxidative stress and inflammatory mediators in the kidney tissues of mice that I/R had injured. In comparison to the AKI group, the miRNA-1906 agomir treatment also resulted in a notable upregulation of desmin, caspase-3, and Transient Receptor Potential Cation Channel 6 (TRPC-6), as well as a significant reduction in nephrin. The miRNA-1906 agomir also reduced SLIT2/ROBO1 circuit modification, restoring podocyte function. The I/Rinduced AKI was resolved by stimulating miRNA-1906 with miRNA-1906 agomir. This controls podocyte damage by blocking the SLIT2/ROBO1 pathway.
This study presents a simple and rapid method for the simultaneous determination of folate (FA), also known as vitamin B9 and its derivatives, namely 5-methyltetrahydrofolate (5-MTHF), tetrahydrofolate (THF) and 10-formylfolic acid (10-CHOFA), in Thai rice grains. Chromatographic separation was conducted using a C18 column with isocratic elution and a mixture of 0.1% formic acid and acetonitrile (85:15 v/v) as the mobile phase. The flow rate was maintained at 0.70 mL/min. and detection was performed using a photodiode array detector at a wavelength of 267 nm. The calibration curves for FA and its derivatives demonstrated excellent linearity (R > 0.9990) over the following concentration ranges: 0.50-50.0 mu g/mL for FA, 0.50-200.0 mu g/mL for 5-MTHF, 0.50-50.0 mu g/mL for THF and 5.0-100.0 mu g/mL for 10-CHOFA. The limits of detection ranged from 0.09 to 0.15 mu g/mL while the limits of quantification were between 0.30 - 0.50 mu g/mL. Recoveries at concentrations of 5, 20, 60 and 90 mu g/mL were found to be between 91% and 104%. In the samples analysed the concentrations of FA and its derivatives ranged from 0.19 to 27.10 mg/100 g dry weight. This method demonstrates high reliability and practicality for the simultaneous determination of FA and its derivatives in rice.
Co-coatomically ss-supplemented modules are identified by extending the concept of ss-supplemented modules, and certain characteristics of co-coatomically ss-supplemented modules are demonstrated. It is established that the sum of a finite set of co-coatomically ss-supplemented modules remains co-coatomically ss-supplemented. Moreover, it is proven that any quotient module of a co-coatomically ss-supplemented module is also co-coatomically ss-supplemented. It is observed that if G is a co-coatomically ss-supplemented submodule of a module E with the condition that E/G lacks a maximal submodule, then E is co-coatomically ss-supplemented. It is demonstrated that the ring S is semi-perfect and Rad(S) subset of Soc( sS) if and only if S is semi-local and Rad(S) subset of Soc( sS) if and only if each left S-module is cocoatomically ss-supplemented. Furthermore, specific characteristics of co-coatomically ss-supplemented modules over Dedekind rings are examined.
The multiplication operator M (u) f = u. f within the bicomplex Lorentz space L-p,L-q (BC) (Omega, R, theta), is investigated. It is initially established that M-u is D-bounded if and only if the function u is essentially D-bounded. Subsequently, it is proved that the collection of all Dbounded multiplication operators on BC-Lorentz spaces forms a maximal abelian sub-algebra within the Banach algebra of all bounded linear operators on L-p,L-q (BC) (Omega, R, theta). Additionally, a necessary and sufficient condition for the compactness of M-u is provided. Finally, by introducing a condition for a multiplication operator to exhibit a closed range, the author identifies some conditions equivalent to M-u being a Fredholm operator.
