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We establish Turán-type inequalities for Bessel functions, modified Bessel functions, Krätzel function and Beta function, by using a new form of Cauchy-Bunyakovsky-Schwarz inequality. [ABSTRACT FROM AUTHOR]

Heat stress is a main threat to current and future global maize production. Adaptation of maize to future warmer conditions requires improving our understanding of crop responses to elevated temperatures. For this purpose, the same short-season (FAO 300) maize hybrid PR37N01 was grown over three years of field experiments on three contrasting Spanish locations in terms of temperature regime. The information complemented three years of greenhouse experiments with the same hybrid, applying heat treatments at various critical moments of the crop cycle. Crop phenology, growth, grain yield, and yield components were monitored. An optimized beta function improved the calculation of thermal time compared to the linear-cutoff estimator with base and optimum temperatures of 8 and 34 °C, respectively. Our results showed that warmer temperatures accelerate development rate resulting in shorter vegetative and reproductive phases ( ca . 30 days for the whole cycle). Heat stress did not cause silking delay in relation to anthesis (extended anthesis-silking interval), at least in the range of temperatures (maximum temperature up to 42.9 °C in the field and up to 52.5 °C in the greenhouse) considered in this study. Our results indicated that maize grain yield is reduced under heat stress mainly via pollen viability that in turn determines kernel number, although a smaller but significant effect of the female component has been also detected. [ABSTRACT FROM AUTHOR]

This paper proposed the distribution of Cook-Weisberg statistic used toevaluate the inuential observations in linear multiple regression analysis. The authors explored the relationship between the CW statistic and COVratio (Co-variance ratio) in terms of two independent F-ratio's and they showthe derived density function of the measure in a series expression form. More-over, the rst two moments of the distribution are derived in terms of Beta, di-gamma, poly-gamma functions, upper control limit of CW-statistic is alsoestablished and the authors computed the critical points of CW-statistic at5% and 1% signicance level for dierent sample sizes and varying no. of predictors. Finally, the numerical example shows the identication of the influential observations and the results extracted from the proposed approachesare more scientic, systematic and it's exactness outperforms the traditionalapproach. [ABSTRACT FROM AUTHOR]

We define the β -function of a perturbative quantum field theory in the mathematical framework introduced by Costello – combining perturbative renormalization and the BV formalism – as the cohomology class of a certain functional measuring scale dependence of the effective interaction. We show that the one-loop β -function is a well-defined element of the obstruction–deformation complex for translation-invariant and classically scale-invariant theories, and furthermore that it is locally constant as a function on the space of classical interactions and computable as a rescaling anomaly, or as the logarithmic one-loop counterterm. We compute the one-loop β -function in first-order Yang–Mills theory, recovering the famous asymptotic freedom for Yang–Mills in a mathematical context. [ABSTRACT FROM AUTHOR]

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For arbitrary $$f:\left( a,\infty \right) \rightarrow \left( 0,\infty \right) ,$$ $$a\ge 0,$$ the bivariable function $$B_{f}:\left( a,\infty \right) ^{2}\rightarrow \left( 0,\infty \right) ,$$ related to the Euler Beta function, is considered. It is proved that $$B_{f\text { }}$$ is a mean iff it is the harmonic mean H. Some applications to the theory of iterative functional equations are given. [ABSTRACT FROM AUTHOR]

The available evidence suggests that the current increasing trend in global surface temperatures will continue during this century, which will be accompanied by a greater frequency of extreme events. The IPCC has projected that higher temperatures may outscore the known optimal and maximum temperatures for maize. The purpose of this study was to improve the ability of the maize model CSM-IXIM to simulate crop development, growth, and yield under hot conditions, especially with regards to the impact of above-optimal temperatures around anthesis. Field and greenhouse experiments that were performed over three years (2014–2016) using the same short-season hybrid, PR37N01 (FAO 300), provided the data for this work. Maize was sown at a target population density of 5 plants m −2 on two sowing dates in 2014 and 2015 and on one in 2016 at three locations in Spain (northern, central, and southern Spain) with a well-defined thermal gradient. The same hybrid was also sown in two greenhouse chambers with daytime target temperatures of approximately 25 and above 35 °C. During the nighttime, the temperature in both chambers was allowed to equilibrate with the outside temperature. The greenhouse treatments consisted of moving 18 plants at selected phenological stages (V4, V9, anthesis, lag phase, early grain filling) from the cool chamber to the hot chamber over a week and then returning the plants back to the cool chamber. An additional control treatment remained in the cool chamber all season, and in 2015 and 2016, one treatment remained permanently in the hot chamber. Two maize models in the Decision Support System for Agrotechnology Transfer (DSSAT) V4.6 were compared, namely CERES and IXIM. The IXIM version included additional components that were previously developed to improve the crop N simulation and to incorporate the anthesis-silking interval (ASI). A new thermal time calculation, a heat stress index, the impact of pollen-sterilizing temperatures, and the explicit simulation of male and female flowering as affected by the daily heat conditions were added to IXIM. The phenology simulation in field experiments by IXIM improved substantially. The RMSE for silking and maturity in CERES were 7.9 and 13.7 days, decreasing in IXIM to 2.8 and 7.3 days, respectively. Similarly, the estimated kernel numbers, kernel weight, grain yield and final biomass were always closer to the measurements in IXIM than in CERES. The worst simulations were for kernel weight, and for that reason, the differences in grain yield between the models were small (the RMSE in CERES was 1219 kg ha −1 vs. 1082 kg ha −1 in IXIM). The greenhouse results also supported the improved estimations of crop development by IXIM (RMSE of 2.6 days) relative to CERES (7.4 days). The impact of the heat treatments on grain yield was consistently overestimated by CERES, while IXIM captured the general trend. The new IXIM model improved the CERES simulations when elevated temperatures were included in the evaluation data. Additional model testing with measurements from a wider latitudinal range and relevant heat conditions are required. [ABSTRACT FROM AUTHOR]

We study the beta functions of the quartic and Yukawa couplings of General Relativity and Unimodular Gravity coupled to the λ ϕ 4 and Yukawa theories with masses. We show that the General Relativity corrections to those beta functions as obtained from the 1PI functional by using the standard MS multiplicative renormalization scheme of Dimensional Regularization are gauge dependent and, further, that they can be removed by a non-multiplicative, though local, field redefinition. An analogous analysis is carried out when General Relativity is replaced with Unimodular Gravity. Thus we show that any claim made about the change in the asymptotic behavior of the quartic and Yukawa couplings made by General Relativity and Unimodular Gravity lack intrinsic physical meaning. [ABSTRACT FROM AUTHOR]

In this paper, we created new chaotic maps based on Beta function. The use of these maps is to generate chaotic sequences. Those sequences were used in the encryption scheme. The proposed process is divided into three stages: Permutation, Diffusion and Substitution. The generation of different pseudo random sequences was carried out to shuffle the position of the image pixels and to confuse the relationship between the encrypted the original image, so that significantly increasing the resistance to attacks. The acquired results of the different types of analysis indicate that the proposed method has high sensitivity and security compared to previous schemes. [ABSTRACT FROM AUTHOR]

In the paper, the authors survey integral representations of the Catalan numbers and the Catalan-Qi function, discuss equivalent relations between these integral representations, supply alternative and new proofs of several integral representations, collect applications of some integral representations, and present sums of several power series whose coefficients involve the Catalan numbers. [ABSTRACT FROM AUTHOR]

The authors have introduced the concept of logarithmically relative h-preinvex function which is a generalized form of previously known concepts [9, 11], and try to establish some new Hermite-Hadamard type integral inequalities for functions whose absolute values of nth derivatives are logarithmically relative h-preinvex. [ABSTRACT FROM AUTHOR]

It is well known that in, where,and. In this note we obtain a similar result in the weighted Lebesgue space. [ABSTRACT FROM PUBLISHER]

The asymptotic behavior of the Hermite-Padé approximants of the first type for two beta functions are studied. The results are expressed in terms of equilibrium problems of logarithmic potential theory and in terms of meromorphic functions on Riemann surfaces. [ABSTRACT FROM AUTHOR]

The aim of this study was to assess the dental arch curvature in subjects with normal occlusion in an Iranian population and propose a beta function formula to predict maxillary arch form using the mandibular intermolar widths (IMW) and intermolar depths (IMD). The materials used were study casts of 54 adolescents with normal occlusion and mean age of 14.1 years (25 males, 29 females, age range 12-16 years). Curve-fitting analyses were carried out and the curves passing through the facial-axis point of the canines, premolars, first molars, and the incisal edges of the anterior teeth were studied using a 3D laser scanner. Using the measured IMW and IMD of the dental arches at the maxillary and mandibular first molar region, a beta function formula proposed for predicting maxillary arch form. The accuracy of the proposed formula was assessed on 10 randomly selected dental casts. The mean (SD) of the maxillary and mandibular IMW and IMD were 57.92 (4.75), 54.19 (5.31), and 31.59 (2.90) and 28.10 (2.59) mm, respectively. There was no gender dimorphism ( P > 0.05) for both variables (IMW, IMD). There was a strong positive association ( n = 10, Pearson r = 0.98, P < 0.05) between the measured (actual) maxillary arch length and proposed arch length derived from generated formula. The goodness of fit (whole arch) for the proposed beta function formula, using adjusted r square measure and root mean square in 10 patients averaged 0.97 and 1.49 mm, respectively. The corresponding figures for the maxillary anterior arch (canine to canine) were 0.90 and 0.92 mm, respectively. The proposed beta function formula used for predicting maxillary arch form based on two mandibular measures (IMW, IMD) was found to have a high accuracy for maxillary arch prediction in the Iranian population and may be used as a guide to fabricate customized arch wires or as an aid in maxillary reconstructive surgery. [ABSTRACT FROM AUTHOR]

The main object of this paper is to present new generalizations of gamma, beta hypergeometric and confluent hypergeometric functions. Some recurrence relations, transformation formulas, operation formulas, differentiation formulas, beta distribution and integral representations are obtained for these new generalizations.

The current study was done in Patom, Namkhaneh, Gorazbon, Chelir and Baharbon districts in Kheyrud forest. A stratified sampling method based on landform was used to locate 190 0.1 ha circular sample plots in beech dominated forests. The number of Fagus orientalis Lipsky trees with DBH ≥ 7.5 cm within each plot was recorded along with elevation and slope of the ground. Also, at the center of plot, soil samples from first layer were taken for analyzing soil texture, bulk density and saturation moisture. In order to study the shape of response curve and extract the ecological optimum and amplitude in relation to the mentioned variables, beta function was used in the context of generalized linear model (GLM) with poison distribution and logarithmic link function. Gaussian Function were also applied to the data and its performance was compared to Beta Function using Deviance Test and the shape of response whether it is unimodal and symmetric or skewed. Beta function showed the response of beech to altitude is left-skewed, meaning it avoids lower elevations. This species has 1420 and 300-2150 m a.s.l for its optimum and ecological amplitude, respectively. Beech tree can distribute from gentle to steep slopes in the study area. The behavior of beech to slope is symmetric and unimodal attaining its optimum at 40% slope. Using beta function indicated that Fagus have amplitude of 0 to 80% regarding to slope percentage. In light of sand, clay and silt, Beech tree has 25, 43 and 35 % for optimum and 1-48 % for sand, 20-58% for clay and 17-55 % for silt for ecological amplitude, respectively. Using beta function showed the response of Fagus to sand and silt is unimodal and symmetric, but for clay it shows left-skewed shape. It implies that Fagus avoids soils containing low clay contents. The optimum and tolerance of saturation moisture for Fagus have been determined 50 and 17-55%, respectively. Fagus showed right-skewed response to bulk density. It gets its optimum at 1.6 g/cm3 and it can distribute from 1.3 to 2.7 g/cm3. Gaussian function always gives symmetric and bell-shaped species responses whereas the beta function has the advantage of describing either very skewed unimodal responses, or symmetric responses. It can also detect some types of bimodal. The results of this study showed although there is not much difference between Gaussian and beta functions based on deviance explained, but beta function could detect skewed response curve well, compared to Gaussian function. Beech tree has not always showed symmetric responses to the selected variables and the hypothesis implying Beech tree has unimodal and symmetric response to environmental variables can be rejected.

Carrot, a highly profitable crop in Israel, is severely damaged by Phelipanche aegyptiaca ‎parasitism. Herbicides can effectively control the parasite and prevent damage, but for ‎optimal results, knowledge about the soil-subsurface phenological stage of the parasite is ‎essential. Parasitism dynamics models have been successfully developed for the parasites P. ‎aegyptiaca, Orobanche cumana and O. minor in the summer crops, tomato, sunflower and ‎red clover, respectively. However, these models, which are based on a linear relationship ‎between thermal time and the parasitism dynamics, may not necessarily be directly ‎applicable to the P. aegyptiaca-carrot system. The objective of the current study was to ‎develop a thermal time model to predict the effect of P. aegyptiaca parasitism dynamics on ‎carrot growth. For development and validation of the models, data was collected from a ‎temperature-controlled growth experiment and from 13 plots naturally infested with P. ‎aegyptiaca in commercial carrot fields. Our results revealed that P. aegyptiaca development ‎is related to soil temperature. Moreover, unlike P. aegyptiaca parasitism in sunflower and ‎tomato, which could be predicted both a linear model, P. aegyptiaca parasitism dynamics ‎on carrot roots required a nonlinear model, due to the wider range of growth temperatures of ‎both the carrot and the parasite. Hence, two different nonlinear models were developed for ‎optimizing the prediction of P. aegyptiaca parasitism dynamics. Both models, a beta ‎function model and combined model composed of a beta function and a sigmoid curve, were ‎able to predict first P. aegyptiaca attachment. However, overall P. aegyptiaca dynamics was ‎described more accurately by the combined model (RMSE =14.58 and 10.79, respectively). ‎The results of this study will complement previous studies on P. aegyptiaca management by ‎herbicides to facilitate optimal carrot growth and handling in fields infested with P. ‎aegyptiaca. ‎

In this article, we define and study generalized forms of extended matrix variate gamma and beta functions. By using a number of results from matrix algebra, special functions of matrix arguments and zonal polynomials we derive a number of properties of these newly defined functions. We also give some applications of these functions to statistical distribution theory.

In the article the Volterra integral equations of the second kind with the given kernel are investigated. This kind of integral equations arises in the solving of some boundary value problems for essential loaded differential heat operator in an unbounded domain. The theory of boundary value problems for essential loaded differential parabolic equations is very important not only for the modeling of the physical, technical and application processes, but also in the experimental studies. The test problems are also connected with mathematical modeling of thermal processes in the electric arc of the high - current breaking devices. Experimental studies of these phenomena are difficult because of their transience and in some cases only a mathematical model is capable to provide adequate information about their dynamics, so the test material is highly relevant in modern science.