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In this paper, we introduce the probabilistic Bernstein polynomials and derive new and interesting correlations among several special functions and special number sequences such as Euler polynomials, Bernoulli polynomials of higher order, Frobenius–Euler polynomials of higher order, Stirling numbers of the second kind and Bell polynomials subject to several special random variables. [ABSTRACT FROM AUTHOR]

The transportation sector is undergoing an ever-increasing fast development, shifting from traditional fossil fuel-based transport to ultra-low emission electrified transport. To accelerate this transformation, appropriate planning and operation of charging stations (CSs) especially fast and ultra-fast CSs is of utmost importance. The initial and most important step toward optimum planning of CSs is to develop models for the prediction of electric vehicle (EV) load demand in order to estimate future charging profiles. Thus, a stochastic EV load model should be employed to get an accurate estimation of the total EV charging load regrading numerous interdependent uncertainties. The paper specially provides a critical review regarding different uncertainties related to EV load demand and various stochastic modeling approaches. For this purpose, related research works reported between 2005 and 2023 were gathered, screened, and summarized. Then, selected research papers are evaluated in terms of stochastic modeling of EV load demand. The stochastic approaches were categorized in two main groups of conventional and fast charging modes with regard to probability density functions, Monte Carlo Simulation, Fuzzy method, Markov chain, artificial neural networks, Copulas, and hybrid modes. Next, details of each methodology by highlighting related cons and pros were provided. It was obtained that most research works took into account three to five random variables (RVs) in-average for stochastic studies. In addition, various test and real-world networks throughout the world were employed to validate the obtained results. Finally, some potential future research areas in the field of stochastic CS planning and operation are presented. HIGHLIGHTS: A comprehensive review of the different types of EVs and CSs, A technical review of different RVs and uncertainties related to stochastic EV load demand, A complete review of various stochastic methods for EV load demand modeling, and An outlook on identifying future research perspectives in the field. [ABSTRACT FROM AUTHOR]

In current researches on belief rule base (BRB), input parameters are tended to be expressed in the form of quantitative values through expert knowledge combined with optimization methods. A singular quantitative value fails to capture the statistical properties, leading to irrational outcomes. Therefore, an attempt on attribute weights is made in this paper, and a new model with probability distribution attribute weights (pdw) called BRB-pdw is proposed. The combination of two attributes is in detail discussed, where attribute weights are described as random variables with specific probability distribution. To characterize the output of probability distribution attribute weight, a new concept of expectation of activation weight is proposed. In addition, the BRB-pdw is extended to multiple attributes to demonstrate its universality. Furthermore, fundamental properties and characteristics of the BRB-pdw are further validated by rigorous mathematical derivation. Finally, practicability of the BRB-pdw is validated with NASA lithium battery open dataset, and experiments show that the BRB-pdw model is more robust while maintaining precision. [ABSTRACT FROM AUTHOR]

In this paper, we present the concept of being monotonic in sequence according to a specific direction for a collection of random variables. This concept broadens the existing notions of multivariate dependence, such as sequential left-tail and right-tail dependence. Furthermore, we explore connections with other multivariate dependence concepts, highlight key properties, and analyze the new concept within the framework of copulas. Several examples are provided to demonstrate our findings. [ABSTRACT FROM AUTHOR]

This paper compares the probabilistic analysis results of earth slopes using Random Variable (RV) and Random Field (RF) approaches, with a focus on potential differences in the mobilized sliding mass. The Finite Element Method (FEM) with Shear Strength Reduction (SSR) is utilized to determine Pore Water Pressure (PWP) and the Factor of Safety (FoS). In the RF approach, random FEM is conducted using "crude" Monte Carlo Simulation (MCS) and the Karhunen–Loève expansion, while the RV approach employs the First-Order Reliability method (FORM) and Importance Sampling Monte Carlo Simulation (IMCS). Sensitivity analysis was performed to reveal the most important parameters. The RV results may either underestimate or overestimate the probability of failure (Pf) compared to those obtained by the RF approach. Smaller Pf values are observed in RF with smaller correlation lengths (L) of soil properties. The mean value of the factor of safety (µFoS) closely matches the deterministic FoS when L is largest, while the coefficient of variation of FoS (COVFoS) increases. Finally, in the RF analysis, it was found that intermediate sliding volumes carry higher risks, with smaller volumes having higher occurrence probabilities and larger volumes having much lower probabilities. [ABSTRACT FROM AUTHOR]

The characterization of the cyclic resistance of soils is more important for the prediction of the liquefaction potential and the safety of the buildings. Thus, various cyclic resistance curves had been proposed in the literature and improved regularly. The hyperbolic boundary function (HBF) model based on standard penetration test (SPT) data was developed from a database of 669 sets, which includes 302 sets of Chi-Chi earthquake data and 367 sets of data collected by Youd and his colleagues. This model is based on the Seed and Idris hypothesis, which states that the peak shear stress induced at a given depth is always less than that deduced from the simplified procedure of Seed and Idriss. Filali and Sbartai, based on a suite of equivalent linear site response analyses, showed that the peak shear stress induced by an earthquake can in many cases be greater than the simplified peak shear stress; it means that the rd factor became greater than 1. In this case, the assumption on which is based the simplified procedure is not always verified. For this reason, Filali and Sbartai proposed an earthquake corrector factor (RC) in the range where the shear stress reduction factor (rd) is greater than 1 to adjust the deformable and rigid body. In this paper, we will perform a probabilistic analysis to evaluate the liquefaction potential using a database based on standard penetration test collected after the Chi-Chi Taiwan earthquake with a cyclic stress ratio computed using the proposed corrector factor. This paper presents an adjusted model of the Bayesian mapping function that relates deterministic factor of safety to probability of liquefaction (PL) using the corrected version of the simplified method. In this study, probability boundary curves derived from a Bayesian mapping function are presented based on the original and the corrected version of the simplified method in order to show, in each case, the position of the deterministic boundary curve defined by the hyperbolic function (HBF) model with respect to the probability of liquefaction. The paper also presents an updated form of the hyperbolic function (HBF) model based on the true position of the probabilistic boundary curve according to the corrected version of the simplified method. [ABSTRACT FROM AUTHOR]

In this paper, three-dimensional nonlinear dynamic finite-element analyses are conducted to examine the effect of soil property variability on the lateral displacement (D) of liquefiable ground reinforced by granular columns. A suite of 20 ground motions is selected from the NGA-West2 database as input. A soil-granular column ground system consisting of an intermediate liquefiable layer is modeled in OpenSees. Both the random variable (RV) and random filed (RF) methods are adopted to model the variability of soil property parameters. Dynamic analyses are then conducted to estimate the earthquake-induced deformation of the soil-granular column system. It is found that modeling the variability of soil parameters based on the RV method generally increases the geometric mean and standard deviation (σlnD) of D for the soil-granular column system. Enlarging the spatial correlation of soil parameters in the RF model brings in a slight increase of the mean D and comparable σlnD values, respectively. Hence, incorporating the spatially correlated soil property parameters may not be necessarily increase the variation of D for the soil-granular column system. Specifically, the statistical distribution of D is more sensitive to the vertical scale of fluctuation rather than the horizontal one. The results presented could aid in addressing the variability issue for performance-based design of granular column-reinforced liquefiable ground in engineering applications. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Mathematical Physics, Analysis, Geometry (18129471) is the property of B Verkin Institute for Low Temperature Physics & Engineering and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In the present paper, we study a set that can be treated as a generalised set of subsums for a geometric series. This object was discovered independently in various mathematical aspects. For instance, it is closely related to various systems of representation of real numbers. The main object of this paper was particularly studied by R. Kenyon, who brought up a question about the Lebesgue measure of the set and conjectured that it is positive. Further, Z. Nitecki confirmed the hypothesis by using nontrivial topological techniques. However, the aforementioned result is quite limited, as this particular case should satisfy a rigid condition of homogeneity. Despite the limited progress, the problem remained understudied in a general framework. The study of topological, metric, and fractal properties of the set of subsums for a numerical series is a separate research direction in mathematics. On the other hand, the topic is related to another modern mathematical problem, namely, deepening of the Jessen-Wintner theorem for infinite Bernoulli convolutions and their generalisations. The essence of the problem is to reveal the necessary and sufficient conditions for the probability distribution of a random subsum of a geometric series to be absolutely continuous or singular. The Jessen-Wintner theorem guarantees that the distribution is pure (pure discrete, pure singular, or pure absolutely continuous). Meanwhile, the L'evy theorem gives us the necessary and sufficient condition for the distribution to be discrete. Since the set of subsums for an absolutely convergent series coincides with the set of possible outcomes of the corresponding probability distribution, under certain conditions, it allows us to apply various probability techniques for its further investigation. In particular, some techniques help us to prove that the above sets have a positive Lebesgue measure and allow to deepen the Jessen-Wintner theorem under certain conditions. [ABSTRACT FROM AUTHOR]

L. Klebanov proved the following theorem. Let ξ 1 , ⋯ , ξ n be independent random variables. Consider linear forms L 1 = a 1 ξ 1 + ⋯ + a n ξ n , L 2 = b 1 ξ 1 + ⋯ + b n ξ n , L 3 = c 1 ξ 1 + ⋯ + c n ξ n , L 4 = d 1 ξ 1 + ⋯ + d n ξ n , where the coefficients a j , b j , c j , d j are real numbers. If the random vectors (L 1 , L 2) and (L 3 , L 4) are identically distributed, then all ξ i for which a i d j - b i c j ≠ 0 for all j = 1 , n ¯ are Gaussian random variables. The present article is devoted to an analog of the Klebanov theorem in the case when random variables take values in a locally compact Abelian group and the coefficients of the linear forms are integers. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to give some strong laws of large numbers for arrays of -exchangeable random sets and fuzzy random sets in a separable Banach space. To get convergence theorems for multi-valued random variables, we also improve some results in the case of single-valued random variables taking values in a Banach space. Our results extend some related results in literature. Some typical examples illustrating this study are provided. [ABSTRACT FROM AUTHOR]

This paper examines the Wasserstein metric between the empirical probability measure of n discrete random variables and a continuous uniform measure in the d-dimensional ball, providing an asymptotic estimation of their expectations as n approaches infinity. Furthermore, we investigate this problem within a mixed process framework, where n discrete random variables are generated by the Poisson process. [ABSTRACT FROM AUTHOR]

The article discusses the qualimetric method of assessing the quality of any product. One of the promising areas of development of quality assessment is associated with the use of a generalized quality parameter. This approach achieves a number of advantages, including increasing the methodological reliability of quality assessment, reducing the list of controlled parameters, the possibility of unifying diagnostics, etc. However, this raises certain difficulties associated with the introduction of a generalized quality parameter. Building a generalized product quality assessment is associated with the creation of a single assessment that quantifies quality through its parameters. The difficulties encountered can be resolved by introducing an artificial metric that is common to all parameters. The set of values of each parameter should be matched with some standard analog, with a single scale of quality assessment from zero to one. This scale should be the same for all parameter values. The construction of this scale is related to the distribution of parameter quality. To find the quality assessment of a single indicator and the entire product, it is necessary to consider a set of estimates of the values of factors with different distributions. The solution to the problem is found by introducing an artificial metric that is uniform for all factors. This means that the set of values of each factor must be matched to a certain standard, for example, a rating scale from zero to one. This scale should be the same for all factor values. One important issue is the choice of the type of product quality assessment. Assessments can be point and interval. A quantitative assessment determined by a single number, the so-called point estimate, can be erroneous, especially when the value is determined by expert methods. Therefore, it is proposed that, in addition to the point estimate of quality, its interval estimate should also be found. This will allow for more reasonable quality management. [ABSTRACT FROM AUTHOR]

Purpose – This paper aims to obtain the evolution law of dynamic performance of CR400BF electric multiple unit (EMU). Design/methodology/approach – Using the dynamic simulation based on field test, stiffness of rotary arm nodes and damping coefficient of anti-hunting dampers were tested. Stiffness, damping coefficient, friction coefficient, track gauge were taken as random variables, the stochastic dynamics simulation method was constructed and applied to research the evolution law with running mileage of dynamic index of CR400BF EMU. Findings – The results showed that stiffness and damping coefficient subjected to normal distribution, the mean and variance were computed and the evolution law of stiffness and damping coefficient with running mileage was obtained. Originality/value – Firstly, based on the field test we found that stiffness of rotary arm nodes and damping coefficient of anti-hunting dampers subjected to normal distribution, and the evolution law of stiffness and damping coefficient with running mileage was proposed. Secondly stiffness, damping coefficient, friction coefficient, track gauge were taken as random variables, the stochastic dynamics simulation method was constructed and applied to the research to the evolution law with running mileage of dynamic index of CR400BF EMU.

In this paper, we introduce the concept of monotonicity according to a direction for a set of random variables. This concept extends well-known multivariate dependence notions, such as corner set monotonicity, and can be used to detect dependence in multivariate distributions not detected by other known concepts of dependence. Additionally, we establish relationships with other known multivariate dependence concepts, outline some of their salient properties, and provide several examples. [ABSTRACT FROM AUTHOR]

In this article, we establish a new auxiliary identity on fractal sets for twice local differentiable function involving extended fractal integral operators. Testing this identity together with generalized fractal Hölder’s and Power-mean integral inequalities, we develop some new fractal–fractional Simpson’s type inequalities. Furthermore, we use modified Yang Hölder’s and Power-mean inequality to create new fractal estimates. We also give comparison analysis of bounds and show how the modified form of Yang Hölder’s and Powermean integral inequalities can result in improved lower upper bounds. We also provide concrete examples to examine the validity of obtain results numerically and also justify them by 2D and 3D graphical analysis. As implementations, we operate our findings to get new applications in form of ζ-type special means, moment of random variables and wave equations. [ABSTRACT FROM AUTHOR]

Copyright of Revista Gestão & Tecnologia is the property of Revista Gestao & Tecnologia and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Let (Ω , Σ , p) be a probability measure space and let X : Ω → R k be a (vector valued) random variable. We suppose that the probability pX induced by X is absolutely continuous with respect to the Lebesgue measure on R k and set fX as its density function. Let ϕ : R k → R n be a C1-map and let us consider the new random variable Y = ϕ (X) : Ω → R n. Setting m : = max { rank (J ϕ (x)) : x ∈ R k } , we prove that the probability pY induced by Y has a density function fY with respect to the Hausdorff measure H m on ϕ (R k) which satisfies f Y (y) = ∫ ϕ − 1 (y) f X (x) 1 J m ϕ (x) d H k − m (x) , for H m − a. e. y ∈ ϕ (R k). Here J m ϕ is the m-dimensional Jacobian of ϕ. When J ϕ has maximum rank we allow the map ϕ to be only locally Lipschitz. We also consider the case of X having probability concentrated on some m-dimensional sub-manifold E ⊆ R k and provide, besides, several examples including algebra of random variables, order statistics, degenerate normal distributions, Chi-squared and "Student's t" distributions. [ABSTRACT FROM AUTHOR]

This research incorporates an electricity market model based on a stochastic allocation of distributed resources and the analysis of an optimal demand response for a smart microgrid. This research develops a methodology that allows the application and comparison of various demand-response mechanisms and the analysis of the differences between them and the case of no-demand response, emphasizing economics, environmental care, demand curves, and other factors. By enabling more active participation by residential users of the smart microgrid, these demand-response methods help to flatten the demand curve and support the goals set by the electricity market model. Both conventional and non-conventional generators compete in the electricity market, with renewable energy sources preferred to encourage green generation. Conventional generators are required to supply electricity gradually, starting with the lowest pollution level. In addition, conventional generators are compensated for dispatch, system reliability, and availability. In addition, random variables are used in this study to predict initial load, solar radiation analysis, and biomass input before resources are optimized to meet demand. [ABSTRACT FROM AUTHOR]

Convex and preinvex functions are two different concepts. Specifically, preinvex functions are generalizations of convex functions. We created some intriguing examples to demonstrate how these classes differ from one another. We showed that Godunova-Levin invex sets are always convex but the converse is not always true. In this note, we present a new class of preinvex functions called $ (\mathtt{h_1}, \mathtt{h_2}) $-Godunova-Levin preinvex functions, which is extensions of $ \mathtt{h} $-Godunova-Levin preinvex functions defined by Adem Kilicman. By using these notions, we initially developed Hermite-Hadamard and Fejér type results. Next, we used trapezoid type results to connect our inequality to the well-known numerical quadrature trapezoidal type formula for finding error bounds by limiting to standard order relations. Additionally, we use the probability density function to relate trapezoid type results for random variable error bounds. In addition to these developed results, several non-trivial examples have been provided as proofs.

The article provides proof that the diagnostics of marine internal combustion engines and other ship power plant machines should take into account the randomness and unpredictability of certain events, such as wear, damage, the variations of mechanical and thermal loads, etc., which take place during machine operation. In the article, the energy E, like the other forms (methods) that it can be converted into (heat and work), is considered the random variable Et; at time t, this variable has the mean value E¯t{\bar E_t}, which is the observed value of the statistic E¯st{\bar E_{st}} with an asymptotically normal distribution N(E(Et),σtn)N\left( {E\left( {{E_t}} \right),{{{\sigma _t}} \over {\sqrt n }}} \right), irrespective of the functional form of the random variable Et. A proof is given that shows that the expected value estimated in the above way, considering the time t of the performance of task Z by a marine internal combustion engine or other ship power plant machine, can be used to determine the machine’s possible action (DM). When compared to the required action (DW) needed for task Z to be performed, this possible action makes it possible to formulate an operating diagnosis concerning whether the engine or machine of concern is able to perform task Z. It is assumed that an energy device of this type is able to perform a given task when the inequality DM≥DW holds. Otherwise, when DM < DW, the device cannot perform the task for which it was adopted in the design and manufacturing phase, which means that it is in the incapability state, although it still can be started and convert energy into the form of heat or work..

In this comprehensive study, we delve deeply into the concept of multivariate total positivity, defining it in accordance with a direction. We rigorously explore numerous salient properties, shedding light on the nuances that characterize this notion. Furthermore, our research extends to establishing distinct forms of dependence among the order statistics of a sample from a distribution function. Our analysis aims to provide a nuanced understanding of the interrelationships within multivariate total positivity and its implications for statistical analysis and probability theory.

Copyright of Machine Tool & Hydraulics is the property of Guangzhou Mechanical Engineering Research Institute (GMERI) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this paper, the existence, uniqueness, compactness, and stability of a coupled random diffierential equations involving the Hilfer fractional derivatives with nonlocal boundary conditions are discussed. Arguments are discussed via some random fixed point theorems in a separable vector Banach spaces and Ulam type stability. Some examples are presented to ensure the abstract results. [ABSTRACT FROM AUTHOR]

In this paper we prove the existence of solutions for fractional order functional and neutral functional differential equations with infinite delay principles combined with a technique based on vector-valued metrics and convergent to zero matrices. [ABSTRACT FROM AUTHOR]

We investigate random variables for which the variance and the information potential satisfy a preservation law. [ABSTRACT FROM AUTHOR]

In this comprehensive study, we delve deeply into the concept of multivariate total positivity, defining it in accordance with a direction. We rigorously explore numerous salient properties, shedding light on the nuances that characterize this notion. Furthermore, our research extends to establishing distinct forms of dependence among the order statistics of a sample from a distribution function. Our analysis aims to provide a nuanced understanding of the interrelationships within multivariate total positivity and its implications for statistical analysis and probability theory. [ABSTRACT FROM AUTHOR]

An improvement of methods and models for preliminary estimation of the performance of harvesters in timber production intends to support better justification of the use of certain harvester types and technologies for specific natural and production conditions. It is possible to increase the accuracy of calculation models with a more complete and realistic description of the production environment and operational processes. The article presents a modelling of the harvester’s movements across cutting areas for selecting a position with the highest number of accessible trees. The investigational process involved the creation of an algorithm along with a simulation model and the statistical processing of the results. The problem-solving process required consideration of the tree’s distribution within the cutting region. The data arrays, which were necessary for efficiency evaluation in the simulation model and its software implementation, were the following: the distance between the working stands of the machine with the maximum number of available trees, the time of cyclic processing, and the number of trees in the area. The results of the statistical analysis of the data are presented with justification from the theoretical laws of probability distribution. The choice of machine working stands, which considered the arrangement of the trees, was estimated using the productivity per hour index. The index was calculated with a constant distance parameter that is equal to the difference between the maximum and the minimum manipulator’s movement, and it was also calculated for a stand with a maximum number of accessible trees. The calculation function for the index involves random variables that characterize the working conditions of the stand. The index itself is conceded as a random variable. The values for it were found by statistical data processing. A comparison of the values determined a high probability of a significant increase in the productivity of the harvester. At the stand with the maximum number of trees, it is estimated at around 8 % with a standard deviation of 0.199. For citation: Makarenko A.V. Effective Positioning in Cutting Area of a Harvester Using Computer Modelling. Lesnoy Zhurnal = Russian Forestry Journal, 2023, no. 4, pp. 120–135. (In Russ.). https://doi.org/10.37482/0536-1036-2023-4-120-135

Abstract Water meter measurement error is considered as one important component of non-revenue water by International Water Association. Its magnitude depends combinedly on users’ consumption behaviors (intake spectrum) and metrological characteristics of water meters (meter error curve). Most published researches have only analyzed the meter error curves without taking the users’ consumption behaviors into consideration. This study developed a practical approach by using the relative difference chart of master-meters and sub-meters groupings (i.e., RM-μz chart) to identify average metering errors for a major water utility company in Taiwan. About 120,000 sets of “master-meter and sub-meter grouping” data of Taipei Water Department were analyzed. The approach successfully estimated average metering errors of its 99.6% domestic meters (around 1.6 million water meters), the results are 9.9, 6.1, and 10.0% less than the actual water consumption recorded by the sub-meters, master-meters, and direct-meters, respectively.

We consider an analog of the problem of the existence of the summable distributional density of a random variable in the form of power series on the dyadic half-line which was originally proposed and partially solved by Erdös on the standard real line. Given a random variable as a series of the powers of , we address the question of such that the density of belongs to the space of the function whose modulus is summable on the dyadic half-line. We answer the question for some values of , and consider the so-called dual problem when is fixed, but the coefficients of the formula for have more degrees of freedom. Also we obtain some criteria for the existence of density in terms of the solution of the refinement equation tied directly to as well as in terms of the coefficients defining . [ABSTRACT FROM AUTHOR]

On the basis of a deterministic electrodynamic model, a probabilistic model of microwave ferromagnetic resonance (FMR) in 3D magnetic nanocomposites based on opal matrices has been developed assuming that the FMR magnetic field of each of the magnetic nanoparticles (MNPs) is a random variable distributed according to the normal law. The results of calculating the values of the mathematical expectation of random values of the real and imaginary parts of the diagonal and off-diagonal components of the effective permeability tensor of a 3D magnetic nanocomposite are obtained depending on the strength of the bias field for several values of the dissipation parameter of MNPs at different values of the standard deviation of the random value of the FMR magnetic field of the nanoparticles at frequency f= 26 GHz. The results are compared with the experiment. [ABSTRACT FROM AUTHOR]

Objective Ever since Harry Markowitz's groundbreaking paper on the mean-variance model was published in 1952, numerous efforts have been dedicated to exploring the applications and advancements of classical models. Following the development of financial markets, active portfolio optimization has become one of the most important topics in finance. This study aimed to examine active portfolio management, a critical and delicate choice for investors, particularly concerning overall portfolio risk. The determination of an optimal stock portfolio that offers both a substantial return rate and controlled risk is consistently a subject of keen interest for analysts, investors, and even portfolio managers. Methods Many methods have been developed to measure investment risk, and the price of risky assets changes rapidly and randomly due to the complexity of the financial market. A random interval is a suitable tool for describing uncertainty with randomness and imprecision. Given the uncertainty in financial markets, this study used stochastic intervals to describe the returns of risky assets and the tail sequence risk, called the interval-valued conditional value at risk (ICVaR). The interval value in this model is an extension of the classic portfolio model, which can comprehensively reflect the complexity of the financial market and the risk-taking behavior of investors. Results Following the findings from the real data of 10 out of 30 large corporates listed on the Tehran Stock Exchange, the ICVaR model is interpretable and compatible with the practical scenario and can be used to choose the optimal portfolio at different levels of risk and depending on the risk-taking degree of the investor. The present study used the portfolio optimization approach under a new criterion of ICVaR through the closing price, the highest price, and the lowest price on each trading day. In this model, the return range of the risky asset is taken as a random variable with an interval value. Besides, CVaR with an interval value is used to describe the risk instead of the variance at a certain level of return. Conclusion Uncertainties induced by asset transactions affect the predictions of investment plans. To address such challenging uncertainties in this study, a stable stochastic optimization approach was presented based on the range of optimal solutions produced by the proposed model to determine different operational options. Finally, the model developed in this study showed that investors' subjective risk preference or aversion can be described by observing the principle of portfolio diversification, which reflects an innovation different from the classic portfolio model. Furthermore, the worst possible case was optimized in all scenarios in the model by robust optimization. The findings indicated that a narrower range corresponds to a higher level of risk aversion among investors. [ABSTRACT FROM AUTHOR]

Abstract We give new inequalities involving the expectation and variance of a random variable defined on a finite interval and having an essentially bounded probability density function. Our inequalities sharpen previous inequalities by N.S. Barnett and S.S. Dragomir. We prove our bounds are optimal, and we explicitly give the cases in which equality occurs.

The paper presents a novel analysis of interrelations between ordinary (crisp) $ \sigma $-algebras and soft $ \sigma $-algebras. It is known that each soft $ \sigma $-algebra produces a system of crisp (parameterized) $ \sigma $-algebras. The other way round is also possible. That is to say, one can generate a soft $ \sigma $-algebra from a system of crisp $ \sigma $-algebras. Different methods of producing soft $ \sigma $-algebras are discussed by implementing two formulas. It is demonstrated how these formulas can be used in practice with the aid of some examples. Furthermore, we study the fundamental properties of soft $ \sigma $-algebras. Lastly, we show that elements of a soft $ \sigma $-algebra contain information about a specific event.

Water meter measurement error is considered as one important component of non-revenue water by International Water Association. Its magnitude depends combinedly on users' consumption behaviors (intake spectrum) and metrological characteristics of water meters (meter error curve). Most published researches have only analyzed the meter error curves without taking the users' consumption behaviors into consideration. This study developed a practical approach by using the relative difference chart of master-meters and sub-meters groupings (i.e., RM-μz chart) to identify average metering errors for a major water utility company in Taiwan. About 120,000 sets of "master-meter and sub-meter grouping" data of Taipei Water Department were analyzed. The approach successfully estimated average metering errors of its 99.6% domestic meters (around 1.6 million water meters), the results are 9.9, 6.1, and 10.0% less than the actual water consumption recorded by the sub-meters, master-meters, and direct-meters, respectively. [ABSTRACT FROM AUTHOR]

A new time‐dependent reliability analysis model with a mixture of random variables and interval variables is proposed in this paper. First, samples of random variables are generated according to their probability density functions. Then, the samples are substituted into the performance function to obtain the interval processes corresponding to these samples. The reliability index of each interval process is computed to finally obtain the upper and lower bounds of failure probability. The adaptive Kriging surrogate model based on the global addition strategy is used in the calculation process to increase the computational efficiency. The accuracy of the computational strategy is demonstrated by a mathematical example and three engineering practical cases. The proposed new hybrid time‐dependent reliability model is compared to the conventional hybrid reliability model. The comparison results show that the proposed model is more convenient to implement than the conventional reliability model. It can accurately evaluate the reliability of the structure and can be applied to real‐world engineering practice thereby providing assistance and guidance for hybrid time‐dependent reliability analysis of structures. [ABSTRACT FROM AUTHOR]

To decrease thermal conductivities of ceramic materials applied to thermal barrier coatings (TBCs), substitutional elements are introduced into ceramic materials through defect engineering. However, predicting what substitutional elements are more efficient for decreasing a given TBC ceramic material's thermal conductivity among potential substitutional elements is still a challenge. In this work, a novel approach for predicting the most efficient substitutional elements is presented. It avoids the experimental trial-and-error method and optimizes computational processes, thus saving computational cost. The core part of the approach is the phonon relaxation time expression for a doped ceramic material, which was obtained through the introduction of random variables in the work. Besides, an application of the expression in combination with software Vienna Ab-initio Simulation Package (VASP) for doped SrZrO 3 with rare earth elements is given. It is found that La and Eu elements most efficiently decrease the thermal conductivity of SrZrO 3 . To validate the correctness of the expression and the model, the thermal conductivities of all doped SrZrO 3 are calculated using Slack method. The doped SrZrO 3 with La and Eu has lower thermal conductivities of 1.2 W/(mK) and 1.3 W/(mK), respectively, compared to doped SrZrO 3 with other rare earth elements. Furthermore, it is found that variation trends of various doped materials' reciprocal relative phonon relaxation time obtained by the expression and reciprocal thermal conductivities obtained by Slack method are the same, which suggests our model and expression are reasonable. [ABSTRACT FROM AUTHOR]