Search Results (15)

White clover (Trifolium repens L.) is known for its ability to fix nitrogen biologically, its high nutritional value, and its adaptability to livestock systems. However, excessive fertilization with synthetic nitrogen alters its symbiosis with Rhizobium and reduces the protein content of the forage. The objective of this study was to evaluate the interaction between nitrogen fertilization (0 and 60 kg N ha⁻¹), cutting time, and post-cutting evaluation on the morphology, yield, and nutritional composition of white clover. A completely randomized block experimental design with three factors, distributed in three blocks, was used. Within each block, three replicates of each treatment were assigned (six interactions), giving a total of 54 experimental units. The data were analyzed using a three-way analysis of variance and Tukey’s multiple comparison test. Exponential models and generalized additive models (GAMs) were applied to the morphology and yield data to identify the best fit. The treatment with 60 kg N ha⁻¹ and cutting at 30 days showed significant increases in plant height (47.42%), fresh weight (59.61%), dry weight (98.41%), and leaf width (27.55%) compared to the control. It also produced the highest protein content (28.44%) compared to the other treatments with fertilization, without negatively affecting digestibility. The GAMs best fit most morphological and yield parameters (except leaf height and width). All fertilized treatments had higher fresh and dry weight yields. In conclusion, applying 60 kg N ha⁻¹ after cutting at 30 days, followed by harvesting between 54 and 60 days, improved both the quality and yield of white clover, which favored sustainable pasture management and reduced excessive nitrogen use. Full article

The cure kinetics in frontal polymerization (FP) of short carbon-fiber-reinforced composites are investigated numerically, focusing on the influence of fiber aspect ratio, volume fraction, and orientation. A classical heat conduction equation is used in FP, where the enthalpic reaction generates heat. The heat generation term is expressed in terms of the rate of degree of cure ($\mathrm{d}\mathsf{\alpha }/\mathrm{d}\mathrm{t}$) in thermoset resin. A rate equation of the degree of cure for epoxy is established in terms of a pre-exponential factor, activation energy, Avogadro’s gas constant, and temperature. The cure kinetics parameters for epoxy resin used in this study are determined using the Ozawa method. The numerical model was validated with experimental data. The results reveal that the aspect ratio of fibers has a minimal effect on the polymerization time. The volume percentage of fibers significantly influences the curing time and temperature distribution, with higher fiber volume fractions leading to faster curing due to enhanced heat transfer. Additionally, fiber orientation plays a critical role in cure kinetics, with specific angles facilitating more effective heat transfer, thereby influencing the curing rate and frontal velocity. The results offer valuable insights into optimizing the design and manufacturing processes for high-performance epoxy-based composites through FP, where precise control over curing is critical. Full article

In regions with severe cold and high latitudes, concrete structures are susceptible to cracking and displacement due to uneven temperature stress, which directly impacts their normal utilization. Therefore, to investigate the temperature distribution characteristics of concrete box girders under the combined influence of low temperatures and cold waves, a temperature test was conducted on a model of concrete box girders in Xinjiang Province, China. Based on the measured data, the distribution pattern of the most unfavorable negative temperature differential observed in high-latitude regions was determined. Long-term numerical simulation and extreme value analysis were performed using historical meteorological data, revealing that the vertical negative temperature gradient in the concrete box girder structures follows a composite exponential distribution. The temperature differential at the top complies with Chinese code requirements, while at the bottom, it aligns more closely with British standard BS5400. Statistical analysis of historical meteorological data predicts that the 50-year temperature differential will result in a drop amplitude of 26.42 °C, which is 1.44 times higher than measured values obtained from experiments. The proposed negative temperature gradient pattern for concrete box girders presented in this study can encompass general design codes and provide guidance for designing concrete bridges in severe cold areas. Full article

Paratemporal methods based on tree expansion have proven to be effective in efficiently generating the trajectories of stochastic systems. However, combinatorial explosion of branching arising from multiple choice points presents a major hurdle that must be overcome to implement such techniques. In this paper, we tackle this scalability problem by developing a systems theory-based framework covering both conventional and proposed tree expansion algorithms for speeding up discrete event system stochastic simulations while preserving the desired accuracy. An example is discussed to illustrate the tree expansion framework in which a discrete event system specification (DEVS) Markov stochastic model takes the form of a tree isomorphic to a free monoid over the branching alphabet. We derive the computation times for baseline, non-merging, and merging tree expansion algorithms to compute the distribution of output values at any given depth. The results show the remarkable reduction from exponential to polynomial dependence on depth effectuated by node merging. We relate these results to the similarly reduced computation time of binomial coefficients underlying Pascal’s triangle. Finally, we discuss the application of tree expansion to estimating temporal distributions in stochastic simulations involving serial and parallel compositions with potential real-world use cases. Full article

This study explored the complex interplay and potential risk of financial contagion across major financial indices, focusing on the Bucharest Exchange Trading Investment Funds Index (BET-FI), along with global indices like the S&P 500, Nasdaq Composite (IXIC), and Dow Jones Industrial Average (DJIA). Our analysis covered an extensive period from 2012 to 2023, with a particular emphasis on Romania’s financial market. We employed Autoregressive Distributed Lag (ARDL) modeling to examine the interrelations among these indices, treating the BET-FI index as our primary variable. Our research also integrated Exponential Curve Fitting (EXCF) and Generalized Supremum Augmented Dickey–Fuller (GSADF) models to identify and scrutinize potential price bubbles in these indices. We analyzed moments of high volatility and deviations from typical market trends, influenced by diverse factors like government policies, presidential elections, tech sector performance, the COVID-19 pandemic, and geopolitical tensions, specifically the Russia–Ukraine conflict. The ARDL model revealed a stable long-term relationship among the variables, indicating their interconnectedness. Our study also highlights the significance of short-term market shifts leading to long-term equilibrium, as shown in the Error Correction Model (ECM). This suggests the existence of contagion effects, where small, short-term incidents can trigger long-term, domino-like impacts on the financial markets. Furthermore, our variance decomposition examined the evolving contributions of different factors over time, shedding light on their changing interactions and impact. The Cholesky factors demonstrated the interdependence between indices, essential for understanding financial contagion effects. Our research thus uncovered the nuanced dynamics of financial contagion, offering insights into market variations, the effectiveness of our models, and strategies for detecting financial bubbles. This study contributes valuable knowledge to the academic field and offers practical insights for investors in turbulent financial environments. Full article

The deterioration of the surrounding rock at the tunnel bottom is a damage mechanics issue that occurs under disturbance load. To investigate the anisotropic characteristics of mechanical behavior and the AE response mechanism of layered sandstone, uniaxial compression tests and acoustic emission (AE) monitoring were conducted. The results show that the layer structure causes remarkable anisotropic characteristics in the wave velocities. The strain characteristics and mechanical parameters of layered sandstone exhibit obvious deterioration effects. The local strain and overall strain show a synergistic feature, with the local strain path being more complex and the deformation response being extremely sensitive. The peak stress and elastic modulus both exhibit V-type distribution rules, slowly decreasing first, then rapidly decreasing, and finally increasing rapidly, with the boundary points of the layer angle being 45° and 67.50°. The peak stress and elastic modulus show a nonlinear exponential correlation with the layer angle, and the sandstone belongs to the intermediate anisotropy level. The rupture pattern shows significant anisotropic characteristics, with the failure modes including tension failure, including tension failure I and tension failure Ⅱ, shear failure, and tension–shear composite failure. The fractal dimension shows a negative correlation with the layer deterioration effect. The AE activity exhibits a phased response characteristic to the aging deformation of layer structure. The more obvious the layer deterioration effect is, the longer the AE delay is. The AE intensity of tensile failure sandstone is generally greater than that of oblique shear failure. Full article

Constructing an accurate model for insurance losses is a challenging task. Researchers have developed various methods to model insurance losses, such as composite models. Composite models combine two distributions: one for part of the data with small and high frequencies and the other for large values with low frequencies. The purpose of this article is to consider a mixture of prior distributions for exponential–Pareto and inverse-gamma–Pareto composite models. The general formulas for the posterior distribution and the Bayes estimator of the support parameter $\theta$ are derived. It is shown that the posterior distribution is a mixture of individual posterior distributions. Analytic results and Bayesian inference based on the proposed mixture prior distribution approach are provided. Simulation studies reveal that the Bayes estimator with a mixture distribution outperforms the Bayes estimator without a mixture distribution and the ML estimator regarding their accuracies. Based on the proposed method, the insurance losses from natural events, such as floods from 2000 to 2019 in the USA, are considered. As a measure of goodness-of-fit, the Bayes factor is used to choose the best-fitted model. Full article

In this article, a new modification of the Weibull model with three parameters, the new exponential Weibull distribution (E-WD), is defined. The new model has many statistical advantages, the heavy-tailed behavior and the regular variation property were offered. Many of the important statistical functions of the modified model are presented in closed forms. The flexibility of E-WD has been improved. The proposed model can be used to fit data with different shapes, it can be right-skewed, left-skewed, decreasing, curved and symmetric. Some distribution properties of the proposed model, including moment generating function, characteristic function, moment, quantile and identifiability property, have been derived. In addition to the information generating function, the Shannon entropy and information energy are also discussed. The maximum likelihood approach and Bayesian estimation are used to estimate the distribution parameters. In the Bayesian method, three different loss functions are used. The calculations show the biases and estimated risks to obtain the best estimator. The bootstrap confidence intervals, the asymptotic confidence intervals and the observed variance-covariance matrix are obtained. Metropolis Hastings’ MCMC procedure is used for the calculations. We apply the composite distribution to stock data for four variables. The goodness-of-fit results show that the model performs well compared to its competitors. The proposed model can be used for forecasting and decision making. Full article

It is observed that, for some of the data in engineering and medical fields, the hazard rates increase to a high peak at the beginning and quickly decrease to a low level. In the context of survival analysis, such a hazard rate is called a upside-down bathtub hazard rate. In this paper, we investigated the properties of a model named exponentiated exponential-Pareto distribution. The model was recently proposed and applied to insurance data. We demonstrated that the model has upside-down bathtub-shaped hazard rates with specific choices of parameters. The theoretical properties such as moments, survival functions, and hazard functions were derived. The parameter estimation procedures were also introduced. We then briefly discussed the goodness-of-fit tests of the model with the simulations. Finally, we applied the model to a specific time-to-event data set along with a comparison of the performances with previous existing models. When compared to previous proposed models, the exponentiated exponential-Pareto model demonstrated good performance when fitting to such data sets. Full article

The generalized likelihood ratio test (GLRT) for composite hypothesis testing problems is studied from a geometric perspective. An information-geometrical interpretation of the GLRT is proposed based on the geometry of curved exponential families. Two geometric pictures of the GLRT are presented for the cases where unknown parameters are and are not the same under the null and alternative hypotheses, respectively. A demonstration of one-dimensional curved Gaussian distribution is introduced to elucidate the geometric realization of the GLRT. The asymptotic performance of the GLRT is discussed based on the proposed geometric representation of the GLRT. The study provides an alternative perspective for understanding the problems of statistical inference in the theoretical sense. Full article

The rock acoustic emission (AE) technique has often been used to study rock destruction properties and has also been considered an important measure for simulating earthquake foreshock sequences. Among them, the AE b value is an essential parameter for the size distribution characteristics and probabilistic hazard analysis of rock fractures. Variations in b values obtained in rock AE tests and earthquakes are often compared to establish analogies in the damage process and precursory analysis. Nevertheless, because the amplitudes measured on the sample boundary by an acoustic sensor (apparent amplitude) are often used to estimate the b value, which cannot descript the source size distribution, it is necessary to develop a method to obtain the size distribution characteristics of the real source from the apparent amplitude in doubly truncated distribution. In this study, we obtain AE apparent amplitudes by applying an attenuation operator to source amplitudes generated by a computer with an underlying exponential distribution and then use these simulated apparent amplitudes to perform a comparative analysis of various b value estimation methods that are used in earthquakes and propose an optimal b value estimation procedure for rock AE tests through apparent amplitudes. To further verify the reliability of the newly proposed procedure, a b value characteristics analysis was carried out on a non-explosive expansion agent rock AE test and transparent refractive index experiment with red sandstone, marble, granite, and limestone. The results indicate that mineral grains of different sizes and compositions and different types of discontinuities of rock specimens determine the rock fracture characteristics, as well as the b value. The dynamic b values decreased linearly during the loading process, which confirms that variations in the b value also depend on the stress. These results indicate that the newly proposed procedure for estimating the b value in rock AE tests based on apparent amplitudes has high reliability. Full article

In this paper, we propose a new family of distributions, by exponentiating the random variables associated with the probability density functions of composite distributions. We also derive some mathematical properties of this new family of distributions, including the moments and the limited moments. Specifically, two special models in this family are discussed. Three real datasets were chosen, to assess the performance of these two special exponentiated-composite models. When fitting to these three datasets, these three special exponentiated-composite distributions demonstrate significantly better performance, compared to the original composite distributions. Full article

Evaluation of images of special functions under operators of fractional calculus has become a hot topic with hundreds of recently published papers. These are growing daily and we are able to comment here only on a few of them, including also some of the latest of 2019–2020, just for the purpose of illustrating our unified approach. Many authors are producing a flood of results for various operators of fractional order integration and differentiation and their generalizations of different special (and elementary) functions. This effect is natural because there are great varieties of special functions, respectively, of operators of (classical and generalized) fractional calculus, and thus, their combinations amount to a large number. As examples, we mentioned only two such operators from thousands of results found by a Google search. Most of the mentioned works use the same formal and standard procedures. Furthermore, in such results, often the originals and the images are special functions of different kinds, or the images are not recognized as known special functions, and thus are not easy to use. In this survey we present a unified approach to fulfill the mentioned task at once in a general setting and in a well visible form: for the operators of generalized fractional calculus (including also the classical operators of fractional calculus); and for all generalized hypergeometric functions such as ${}_p{\mathsf{\Psi }}_q$ and ${}_p{F}_q$, Fox H- and Meijer G-functions, thus incorporating wide classes of special functions. In this way, a great part of the results in the mentioned publications are well predicted and appear as very special cases of ours. The proposed general scheme is based on a few basic classical results (from the Bateman Project and works by Askey, Lavoie–Osler–Tremblay, etc.) combined with ideas and developments from more than 30 years of author’s research, and reflected in the cited recent works. The main idea is as follows: From one side, the operators considered by other authors are cases of generalized fractional calculus and so, are shown to be (m-times) compositions of weighted Riemann–Lioville, i.e., Erdélyi–Kober operators. On the other side, from each generalized hypergeometric function ${}_p{\mathsf{\Psi }}_q$ or ${}_p{F}_q$ ($p\le q$ or $p=q+1$) we can reach, from the final number of applications of such operators, one of the simplest cases where the classical results are known, for example: to ${}_0{F}_{q-p}$ (hyper-Bessel functions, in particular trigonometric functions of order $(q-p)$), ${}_0{F}_0$ (exponential function), or ${}_1{F}_0$ (beta-distribution of form ${(1-z)}^{\alpha }{z}^{\beta })$. The final result, written explicitly, is that any GFC operator (of multiplicity $m\ge 1$) transforms a generalized hypergeometric function into the same kind of special function with indices p and q increased by m. Full article

In this paper, a new heavy-tailed distribution, the mixture Pareto-loggamma distribution, derived through an exponential transformation of the generalized Lindley distribution is introduced. The resulting model is expressed as a convex sum of the classical Pareto and a special case of the loggamma distribution. A comprehensive exploration of its statistical properties and theoretical results related to insurance are provided. Estimation is performed by using the method of log-moments and maximum likelihood. Also, as the modal value of this distribution is expressed in closed-form, composite parametric models are easily obtained by a mode matching procedure. The performance of both the mixture Pareto-loggamma distribution and composite models are tested by employing different claims datasets. Full article

Functionally graded composite materials may constitute an advantageous alternative to engineering applications, allying a customized tailoring capability to its inherent continuous properties transition. However, these attractive characteristics must account for the uncertainty that affects these materials and their structures’ physical quantities. Therefore, it is important to analyze how this uncertainty will modify the foreseen deterministic response of a structure that is built with these materials, identifying which of the parameters are responsible for a greater impact. To pursue this main objective, the material and geometrical parameters that characterize a plate made of an exponentially graded material are generated according to a random multivariate normal distribution, using the Latin hypercube sampling technique. Then, a set of finite element analyses based on the first-order shear deformation theory are performed to characterize the linear static responses of these plates, which are further correlated to the input parameters. This work also considers the constitution of statistic models in order to allow their use as alternative prediction models. The results show that for the plates that were analyzed, the uncertainty associated with the elasticity modulus of both phases is mainly responsible for the maximum transverse deflection variability. The effectiveness of the statistical models that are built are also shown. Full article