Search

In this paper, we propose to study the asymptotic properties of some conditional functional parameters, such as the distribution function, the density, and the hazard function, for an explanatory variable with values in a Hilbert space (infinite dimension) and a response variable real in a quasi-associated dependency framework. We consider the non parametric estimation of the conditional distribution function by the kernel method in the presence of the quasi-associated dependence, and we establish under general hypotheses the almost complete convergence with speed of the estimator built in the associated case. The estimation of the conditional hazard function will be conducted by utilizing the two outcomes of the conditional distribution function and the conditional density. We establish the asymptotic normality of the kernel estimator as the conditional risk function of a properly normalized functional. We explicitly give the asymptotic variance. Simulation studies were conducted to investigate the behavior of the asymptotic property in the context of finite sample data. All the statistical analyses were performed using R software. [ABSTRACT FROM AUTHOR]

Ceramic grinding, which in this paper is defined as a method of using ceramic materials as grinding media, is favored by many processing plants as an emerging high-efficiency and energy-saving grinding method. This paper investigates the effect of slurry mass concentration on the grinding characteristics of magnetite by taking the feed of the secondary ball mill for processing magnetite as the research object. The study results show that the slurry mass concentration significantly affects the ceramic ball grinding characteristics of magnetite, especially for coarse particles. When the grinding concentration is higher than 50%, the breakage rate of magnetite plummets to 1/3 of the value at low mass concentrations. The standard deviation of the breakage rate relative to the concentration gradually decreases as the feed size falls, indicating that the coarser the feed size, the more sensitive the ceramic ball grinding is to the concentration, and thus industrial secondary ceramic ball mills need to avoid grinding under high-quality concentrations. The change in the consistency parameter of distribution function and zero-order output characteristics signals a radical variation in the grinding characteristics of magnetite using the ceramic ball grinding method compared to conventional grinding. Because the ceramic ball grinding method can greatly reduce energy consumption while lowering the chance of overgrinding, this grinding method deserves more attention as the world works to reach carbon neutrality and emissions peak. [ABSTRACT FROM AUTHOR]

The paper proves a theorem about the structure of the distribution function on which the extremum of the fractionally linear functional is reached in the presence of an uncountable number of linear constraints. The problem of finding an extremal distribution function arises when determining the optimal control strategy in a class of Markov homogeneous randomized control strategies. The structure of extremal functions is described by a finite number of parameters; hence, the problem is greatly simplified since it is reduced to the search for an extremum of some function. [ABSTRACT FROM AUTHOR]

This article deals with the analysis of the multi-cell association setup, and it exploits the possibility of enhancing coverage in the envisioned sixth generation (6G) large-scale cellular networks. Specifically, we propose a simple, effective approach for finding a closed-form solution to the coverage probability of a given user in a multi-cell association regime of downlink multiple-user multiple-input multiple-output (MU-MIMO) systems. In particular, a Rayleigh fading channel is considered, wherein the transmitter has only the knowledge of the second-order statistics of the channel. The proposed work uses an indefinite quadratic formulation method and thereby investigates the effect of cell association in a correlated downlink broadcast channel with co-channel interference, additive white noise, and multiple transceiver antenna elements. In the results, we show that a predefined signal-to-interference-plus-noise ratio (SINR) threshold dictates an effective multi-cell association setup, and we identify the region in which a multi-cell association performs better that a single association-based network. The derived theoretical expressions in this paper are validated by the same means of simulation. [ABSTRACT FROM AUTHOR]

Knowable moments, abbreviated as K-moments, are redefined as expectations of maxima or minima of a number of stochastic variables that are a sample of the variable of interest. The new definition enables applicability of the concept to any type of variable, continuous or discrete, and generalization for transformations thereof. While K-moments share some characteristics with classical and other moments, as well as with order statistics, they also have some unique features, which make them useful in relevant applications. These include the fact that they are knowable, i.e., reliably estimated from a sample for high orders. Moreover, unlike other moment types, K-moment values can be assigned values of distribution function by making optimal use of the entire dataset. In addition, K-moments offer the unique advantage of considering the estimation bias when the data are not an independent sample but a time series from a process with dependence. Both for samples and time series, the K-moment concept offers a strategy of model fitting, including its visualization, that is not shared with other methods. This enables utilization of the highest possible moment orders, which are particularly useful in modelling extremes that are closely associated with high-order moments. [ABSTRACT FROM AUTHOR]

A detailed statistical description of the evolution of supersaturated-by-gas solution at degassing has been presented on the basis of finding the time-dependent distribution in radii of overcritical gas bubbles. The influence of solution viscosity and capillarity via internal pressure in the bubbles on this distribution has been considered until the moment when the gas supersaturation drops due to depletion and stops nucleation of new overcritical gas bubbles. This study is based on our previous results for the nonstationary growth rates of overcritical bubbles depending on gas supersaturation, diffusivity and solubility in solution, solution viscosity, and surface tension on bubble surface. Other important factors are linked with the initial rate of homogeneous gas bubble nucleation and coupling between diffusivity and viscosity in the solution. Here, we numerically studied how all these factors affect the time-dependent distribution function of overcritical bubbles in their radii, maximal and mean bubble radii, and the time-dependent swelling ratio of a supersaturated-by-gas solution in a wide range of solution viscosities. [ABSTRACT FROM AUTHOR]

Whilst several methods exist to provide sample estimates of the probability distribution function at several points, for the probability density of continuous stochastic variables, only a gross representation through the histogram is typically used. It is shown that the newly introduced concept of knowable moments (K-moments) can provide smooth empirical representations of the distribution function, which in turn can yield point and interval estimates of the density function at a large number of points or even at any arbitrary point within the range of the available observations. The proposed framework is simple to apply and is illustrated with several applications for a variety of distribution functions. [ABSTRACT FROM AUTHOR]

We presented a method based on multigraphs to mathematically define a distribution function in time for the generation of data exchange in a special-purpose communication network. This is needed for the modeling and design of communication networks (CNs) consisting of integrated telecommunications and computer networks (ITCN). Simulation models require a precise definition of network traffic communication. An additional problem for describing the network traffic in simulation models is the mathematical model of data distribution, according to which the generation and exchange of certain types and quantities of data are realized. The application of multigraphs enabled the time and quantity of the data distribution to be displayed as operational procedures for a special-purpose communication unit. A multigraph was formed for each data-exchange time and allowed its associated adjacency matrix to be defined. Using the matrix estimation method allowed the mathematical definition of the distribution function values. The application of the described method for the use of multigraphs enabled a more accurate mathematical description of real traffic in communication networks. [ABSTRACT FROM AUTHOR]

The double exponential WJ distribution has been shown to competently describe extreme events and critical phenomena, while the Gaussian function has celebrated rich applications in many other fields. Here we present the analysis that the WJ distribution may be properly treated as an extended Gaussian function. Based on the Taylor expansion, we propose three methods to formulate the WJ distribution in the form of Gaussian functions, with Method I and Method III being accurate and self-consistent, and elaborate the relationship among the parameters of the functions. Moreover, we derive the parameter scaling formula of the WJ distribution to express a general Gaussian function, with the work illustrated by a classical case of extreme events and critical phenomena and application to topical medical image processing to prove the effectiveness of the WJ distribution rather than the Gaussian function. Our results sturdily advocate that the WJ distribution can elegantly represent a Gaussian function of arbitrary parameters, whereas the latter usually is not able to satisfactorily describe the former except for specific parameter sets. Thus, it is conclusive that the WJ distribution offers applicability in extreme events and critical phenomena as well as processes describable by the Gaussian function, namely, implying plausibly a unifying approach to the pertinent data processing of those quite distinct areas and establishing a link between relevant extreme value theories and Gaussian processes. [ABSTRACT FROM AUTHOR]

This article presents a methodological approach to modeling the processes of changing the dispersed composition of solid phase particles, such as granulation, crystallization, pyrolysis, and others. Granulation is considered as a complex process consisting of simpler (elementary) processes such as continuous particle growth, agglomeration, crushing and abrasion. All these elementary processes, which are also complex in themselves, usually participate in the formation of the dispersed composition of particles and proceed simultaneously with the predominance of one process or another, depending on the method of its organization and the physicochemical properties of substances. A quantitative description of the evolution of the dispersed composition of the solid phase in technological processes in which the particle size does not remain constant is proposed. Considering the stochastic nature of elementary mass transfer events in individual particles, the methods of the theory of probability are applied. The analysis of the change in the dispersed composition is based on the balanced equation of the particle mass distribution function. The equation accounts for all possible physical mechanisms that effect changes in particle size during chemical and technological processes. Examples of solutions to this equation for specific processes of practical importance are provided. The obtained analytical solutions are of independent interest and are in good agreement with the experimental data, which indicates the adequacy of the proposed approach. These solutions can also be used to analyze similar processes. The effectiveness has been confirmed during the analysis and calculation of the processes of granulation of various solutions and disposal of oil-containing waste to obtain a granular mineral additive. [ABSTRACT FROM AUTHOR]

In this study, the problem of conditional density estimation of a scalar response variable, given a functional covariable, is considered. A new estimator is proposed by combining the k-nearest neighbors (k-N-N) procedure with the local linear approach. Then, the uniform consistency in the number of neighbors (UNN) of the proposed estimator is established. Such result is useful in the study of some data-driven rules. As a direct application and consequence of the conditional density estimation, we derive the UNN consistency of the conditional mode function estimator. Finally, to highlight the efficiency and superiority of the obtained results, we applied our new estimator to real data and compare it to its existing competitive estimator. [ABSTRACT FROM AUTHOR]

Making cities smart represents a major potential for sustainable development, where both the quality of life and the economy improve. Implementing new and efficient solutions in a smart city involves a large spectrum of uncertainties related to the size and project complexity. Characterization and assessment of the variables uncertainty in planning methodology seem necessary to reach the best decision about the best approach to achieve favorable realization outcomes for planned projects. By including uncertainties in the planning, assessment makes it possible to calculate result uncertainties for all expectations, and project cost-effectiveness. In this way, planning can be improved, if the most important parameters of result uncertainties are identified, better defined, and controlled. This study describes a parameter uncertainty characterization methodology applied on the cost-benefit analysis of smart city development with a case study, focused on smart metering infrastructure. Parameter uncertainty characterization is performed based on its variable nature (epistemic and aleatory), time-dependency, and the available information. Cost-benefit analysis results are given as both point value and as uncertainties. Uncertainty is considered for 25 variables of investment and operating costs, and benefits estimation. The presented methodology in smart city planning provides a way to better identify the critical parameters for achieving the defined objectives. [ABSTRACT FROM AUTHOR]

In this work, we revisit Boltzmann's distribution function, which, together with the Boltzmann equation, forms the basis for the kinetic theory of gases and solutions to problems in hydrodynamics. We show that magnetic fields may be included as an intrinsic constituent of the distribution function by theoretically motivating, deriving and analyzing its complex-valued version in its most general form. We then validate these considerations by using it to derive the equations of ideal magnetohydrodynamics, thus showing that our method, based on Boltzmann's formalism, is suitable to describe the dynamics of charged particles in magnetic fields. [ABSTRACT FROM AUTHOR]