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In this paper, we investigate the existence and multiplicity of nontrivial solutions for poly-Laplacian system on a finite graph G=(V,E), which is a generalization of the Yamabe equation on a finite graph. When the nonlinear term F satisfies the super-(p,q)-linear growth condition, by using the mountain pass theorem we obtain that the system has at least one nontrivial solution, and by using the symmetric mountain pass theorem, we obtain that the system has at least dim W nontrivial solutions, where W is the working space of the poly-Laplacian system. We also obtain the corresponding result for the poly-Laplacian equation. In some sense, our results improve some results in (Grigor’yan et al. in J. Differ. Equ. 261(9):4924–4943, 2016).

Objective The study aimed to investigate the role of nutrition‐sensitive and specific interventions along with nutrition education on child stunting during the first 1000 days in Ethiopia. Methods An adequacy evaluation study was used to see changes between the baseline and end‐line data after following for 1 year. A sample of 170 mother‐child pairs who had a 1‐year followed up was used to detect differences. We performed structural equation modeling to elucidate changes in feeding behaviors, socioeconomic status, water, sanitation and hygiene on child linear growth. Furthermore, the independent effect of covariates on child linear growth was handled using a general linear model. Results A total of 170 and 270 mother‐child dyads were interviewed at baseline and end‐line surveys, respectively. After about 1 year of intervention, the annual rate of stunting prevalence declined from 29.3% (95% confidence interval [CI] = 18.6, 42.7) to 16.4% (95% CI = 10.7, 24.2). There was a significant change in the mean of length‐for‐age Z‐score which changed from −1.18 to −0.45 (P < .034). Adjusting for the different constructs of the health belief model, child sex, age, feeding behaviors, and dietary diversity, one egg consumption per day was responsible for the most significant variability explained (36%) for stunting reduction. Conclusions Sustainable access to egg consumption for children below 2 years experienced a substantial reduction in childhood stunting. A combination of nutrition‐sensitive agricultural and direct nutrition interventions along with behavioral‐based education is a sustainable strategy in reducing and preventing child growth from faltering in the early life stages.

We propose a Bayesian non-linear hierarchical model that addresses some of the major challenges that non-life insurance companies face when forecasting the outstanding claim amounts for which they will ultimately be liable. This approach is distinctive in several ways. First, data from individual companies are treated as repeated measurements of various cohorts of claims, thus respecting the correlation between successive observations. Second, non-linear growth curves are used to model the loss development process in a way that is intuitively appealing and facilitates prediction and extrapolation beyond the range of the available data. Third, a hierarchical structure is employed to reflect the natural variation of major parameters between the claim cohorts, accounting for their heterogeneity. This approach enables us to carry out inference at the level of industry, company and/or accident year, based on the full posterior distribution of all quantities of interest. In addition, prior experience and expert opinion can be incorporated in the analyses through judgementally selected prior probability distributions. The ability of the Bayesian framework to carry out simultaneous inference based on the joint posterior is of great importance for insurance solvency monitoring and industry decision making.

We consider a class of convex integral functionals composed of a term of linear growth in the gradient of the argument, and a fidelity term involving L² distance from a datum. Such functionals are known to attain their infima in the BV space. Under the assumption that the domain of integration is convex, we prove that if the datum is in W 1,1, then the functional has a minimizer in W 1,1. In fact, the minimizer inherits W 1,p regularity from the datum for any p ∈ [1,+∞]. We also obtain a quantitative bound on the singular part of the gradient of the minimizer in the case that the datum is in BV. We infer analogous results for the gradient flow of the underlying functional of linear growth. We admit any convex integrand of linear growth.

Folate and vitamin B 12 are essential for growth. Our objective was to estimate their long-term effects on linear growth in North Indian children. This is a follow-up study of a factorial designed, double-blind, randomised, placebo-controlled trial in 1000 young children. Starting at 6–30 months of age, we gave folic acid (approximately 2 RDA), vitamin B 12 (approximately 2 RDA), both vitamins or a placebo daily for 6 months. Six years after the end of supplementation, we measured height in 791 children. We used the plasma concentrations of cobalamin, folate and total homocysteine to estimate vitamin status. The effect of the interventions, the association between height-for-age z-scores (HAZ) and baseline vitamin status, and the interactions between supplementation and baseline status were estimated in multiple regression models. Mean ( sd ) age at follow-up was 7·4 (0·7) years (range 6 to 9 years). There was a small, non-significant effect of vitamin B 12 on linear growth and no effect of folic acid. We observed a subgroup effect of vitamin B 12 supplementation in those with plasma cobalamin concentration < 200 pmol/l ( P for interaction = 0·01). The effect of vitamin B 12 supplementation in this group was 0·34 HAZ (95 % CI 0·11, 0·58). We found an association between cobalamin status and HAZ in children not given vitamin B 12 ( P for interaction = 0·001). In this group, each doubling of the cobalamin concentration was associated with 0·26 (95 % CI 0·15, 0·38) higher HAZ. Suboptimal vitamin B 12 status in early childhood seemingly limits linear growth in North Indian children.

We discuss several variants of the TV-regularization model used in image recovery. The proposed alternatives are either of nearly linear growth or even of linear growth, but with some weak ellipticity properties. The main feature of the paper is the investigation of the analytic properties of the corresponding solutions.

An annualised linear growth velocity (LGV) reference can identify groups of children at risk of growing poorly. As a single velocity reference for all preschool ages does not exist, we present an interim tool, derived from published, normative growth studies, for detecting growth faltering, illustrating its use in Nepali preschoolers. The WHO Child Growth Velocity Standard was adapted to derive 12-month increments and conjoined to the Tanner-Whitehouse Height Velocity Reference data yielding contiguous preschool linear growth annualised velocities. Linear restricted cubic spline regressions were fit to generate sex-specific median and standard normal deviate velocities for ages 0 through 59 months. LGV -scores (LGVZ) were constructed, and growth faltering was defined as LGVZ < –2. Use of the reference was illustrated with data from Nepal’s region. Children contributing the existing growth references and a cohort of 4276 Nepali children assessed from 2013 to 2016. Fitted, smoothed LGV reference curves displayed monotonically decreasing 12-month LGV, exemplified by male/female annual medians of 26·4/25·3, 12·1/12·7, 9·1/9·4, 7·7/7·8 and 7/7 cm/years, starting at 0, 12, 24, 36 and 48 months, respectively. Applying the referent, 31·1 %, 28·6 % and 29·3 % of Nepali children <6, 6–11 and 12–23 months of age, and ∼6 % of children 24–59 months, exhibited growth faltering. Under 24 months, faltering velocities were more prevalent in girls (34·4 %) than boys (25·3 %) ( < 0·05) but comparable (∼6 %) in older preschoolers. A LGV reference, concatenated from extant data, can identify preschool groups at-risk of growth faltering. Application and limitations are discussed.

Background: Poor postnatal weight gain in very low birth weight (VLBW) preterm infants has been shown to have a negative effect on neurodevelopment. However, the dose-dependent neurodevelopmental consequences of linear stunting in this population have not previously been assessed. Understanding this relationship is important because organ growth and differentiation are more tightly linked to lean body mass and thus linear growth. Objective: To assess the duration and clinical determinants of poor linear growth and its relationship to neurodevelopment in preterm infants. Methods: Weight, recumbent length and head circumference were recorded at birth, hospital discharge, and at 4, 12 and 24 months corrected age (CA) in 62 VLBW infants. Standardized Z-scores for weight (WZ), length (LZ) and head circumference (HCZ) were calculated and assessed as a function of inpatient clinical factors using linear regression models. Twenty-four-month neurodevelopmental function was analyzed as a function of growth status. Results: Mean LZ was lower than WZ (p = 0.004) at hospital discharge, was related in part to illness severity and remained lower than baseline LZ until 24 months CA. Controlling for WZ and HCZ at each age, lower LZ at 4 and 12 months CA was associated with lower cognitive function scores at 24 months CA (p ≤ 0.03). Conclusions: Nutritional and nonnutritional factors influenced the degree of pre- and postdischarge linear growth suppression in VLBW infants, which in turn was negatively associated with developmental outcomes at 24 months CA. Since linear growth correlates with brain growth and indexes a number of clinical factors, it is an important biomarker that can be used in VLBW infants to predict long-term developmental outcomes.

The objective of study designed to concur whether micronutrient concentration change reduces the high burden of growth defect of young children age 6 to 59 after nutrition behavior exertions end in Central highland Ethiopia. We used a cluster parallel, non-inferiority randomized control trial. “Kebeles” [lower administrations] selected from central highland districts randomly assigned to either the intervention or the control cluster. At the baseline survey, 1012 children aged 6-59 months and paired mothers were selected from randomly assigned kebeles using a systematic sampling method. The intervention cluster was appointed to exploit nutrition behavior intervention through 15 months. The baseline and end-line data contained median urine iodine, hemoglobin, anthropometry, and other variables analyzed using independent t-test and Generalized Estimate Equation (GEE) using SPSS version 21 software. At the end-line, about 715 study participants completed the nutrition Behavior Change Communication (BCC) intervention. A very high (42.1%) prevalent growth defect observed at baseline and reduced to high level (28.67%) at the end-line. Baseline iodine concentration by 0.69 cm (B=0.69, P < 0.05) and end-line by 0.271 cm (B=0.271, P < 0.05) somewhat increased average end-line height compared to iron concentration. The difference of height (Ht) baseline – end-line between intervention and control group was 0.51 cm. Being in the intervention cluster increased Ht by 10.8 cm (beta [β] = 10.8, standard error [SE] = 1.023) than other predictors of growth of children. This community-based study implied the need for efforts to improve the linear growth of children at an early age through inspiring nutrition behavior.

Coronavirus has long been considered a global epidemic. It caused the deaths of nearly 7.01 million individuals and caused an economic downturn. The number of verified coronavirus cases is increasing daily, putting the whole human race at danger and putting strain on medical experts to eradicate the disease as rapidly as possible. As a consequence, it is vital to predict the upcoming coronavirus positive patients in order to plan actions in the future. Furthermore, it has been discovered all across the globe that asymptomatic coronavirus patients play a significant part in the disease’s transmission. This prompted us to incorporate similar examples in order to accurately forecast trends. A typical strategy for analysing the rate of pandemic infection is to use time-series forecasting technique. This would assist us in developing better decision support systems. To anticipate COVID-19 active cases for a few countries, we recommended a hybrid model utilizing a fuzzy time series (FTS) model mixed with a non-linear growth model. The coronavirus positive case outbreak has been evaluated for Italy, Brazil, India, Germany, Pakistan, and Myanmar through June 5, 2020 in phase-1, and January 15, 2022 in phase-2, and forecasts active cases for the next 26 and 14 days respectively. The proposed framework fitting effect outperforms individual logistic growth and the fuzzy time series techniques, with R-scores of 0.9992 in phase-1 and 0.9784 in phase-2. The proposed model provided in this article may be utilised to comprehend a country’s epidemic pattern and assist the government in developing better effective interventions.