Formula For Density Research Articles

On the asymptotic density of states in solvable models of strings

We present a closed formula for the asymptotic density of states for a class of solvable superstring models on curved backgrounds. The result accounts for the effects of the curvature of the target space in a concise way.

Observing and identifying fouled ballast bed using infrared thermography (IRT): A real-time temperature prediction study based on an enhanced BiGRU model

The ballast bed constitutes the cornerstone of the ballasted track. A fouled ballast bed poses a significant threat to its performance, potentially resulting in severe consequences. In recent years, studies have shown that infrared thermography (IRT) technology has emerged as a promising method for detecting the fouled ballast bed. The surface temperatures of clean and fouled ballast beds differ because of their distinct thermodynamic properties. To effectively utilize temperature for identifying the fouled ballast bed, it is essential to accurately predict surface temperatures for two threshold levels of fouling in real-time. To address the issue, this paper proposes an improved BiGRU model (CBGA), and the main contributions are as follows. First, a formula for the surface heat flux density of the ballast bed was derived. In conjunction with existing research findings, the key factors affecting its surface temperature were identified as inputs to the neural network, including the solar radiation intensity, air temperature, wind speed, and humidity. Next, thermodynamic finite element models were established based on a field experiment, which can be utilized to expand the sample library. Leveraging this groundwork, 430 days of temperature data and meteorological data were acquired to train the neural network. Before inputting data into the BiGRU model, CNN and Attention mechanisms were employed to extract local and significant features. Furthermore, a residual network was introduced to ensure the model’s performance. It exhibits superior performance compared to other models. Subsequently, the CBGA model was used to study the impact of different time steps on the prediction accuracy. It was found that a time step of 660 minutes resulted in the best predictive performance. At this time, the evaluation indicators on the testing dataset were: MSE = 0.057, RMSE = 0.238, MAE = 0.168, and MAPE = 0.008. Finally, the reliability and feasibility of the CBGA model were validated using experimental data. These findings demonstrate that the proposed method can achieve real-time prediction of the ballast surface temperature, laying a solid foundation for the practical application of IRT technology in railway maintenance.

Assesment of wind potential energy of four major cities in Cote d’ivoire using satellite data from 2015 to 2022

In Côte d’Ivoire, the use of renewable energy is becoming a major challenge in the context of climate change and global warming. Therefore, the aim of this study is to characterize the wind profile for potential energy in Abidjan, Man, Bouaké and Korhogo of Côte d’Ivoire using satellite data. Wind speed and direction data from Copernicus Centre from 2015 to 2022 are used for these major cities. The frequency method is used to build wind rose and power density formula to estimate the potential energy for each city, at ground level (10 m) and in particular level at 100 m and 500 m. The results showed a slightly wind speed and direction variation from 2015 to 2022. This suggests that wind has a seasonal (wet and dry) evolution over the year. However, wind speeds increase for each city with the altitude. The higher average wind speed is observed in Abidjan with a power density of 58 W/m2. The lower wind speed and power density are observed in Man, Bouaké and Korhogo. So, the coastline of Côte d’Ivoire has the higher wind energy resource than the inland regions of the country.

Halbach structure parameter optimization by Maxwell tensor method for PML in manned hybrid maglev

This paper presents an optimization of the Halbach structure parameters for the permanent magnetic levitation (PML) component in manned hybrid maglev system using Maxwell tensor method. The focus is on enhancing the levitation force and reducing the lateral stiffness, which are important for improving the system’s load capacity and lateral stability. Based on the analysis of the magnetic flux density formula as presented by Halbach (1985), seven structural parameters were reduced to four independent variables. The Maxwell tensor formulation enabled the derivation of analytical expressions for the levitation force and stiffness, leading to identification of parametier conbinations that maximize magneitc properties. Contour plots were constructed to visually demonstrate the impact of parameter variations on magnetic characteristics, including magnetic flux density, levitation force, and lateral stiffness. Ultimately, a series of optimization cases for structural parameters were proposed in accordance with the design requirements of the manned hybrid Maglev system, and these cases were comprehensively evaluated through contour plot analysis. Furthermore, the finite element software FEMM was utilized to model and validate the optimal cases, thereby confirming the effectiveness of the analytical expressions for magnetic properties and the optimization strategy. This research not only provides theoretical support for the design of PML components but also offers new insights into the optimization of magnetic characteristics for hybrid maglev systems.

Asymptotic behavior of heat kernels and Green functions on affine buildings

We compute asymptotic formulas for the transition densities p(n;x,y) of finite range isotropic random walks on affine buildings. We also describe the asymptotic behavior of the corresponding Green functions.

Marcus Stochastic Differential Equations: Representation of Probability Density

Marcus stochastic delay differential equations are often used to model stochastic dynamical systems with memory in science and engineering. It is challenging to study the existence, uniqueness, and probability density of Marcus stochastic delay differential equations, due to the fact that the delays cause very complicated correction terms. In this paper, we identify Marcus stochastic delay differential equations with some Marcus stochastic differential equations without delays but subject to extra constraints. This helps us to obtain the following two main results: (i) we establish a sufficient condition for the existence and uniqueness of the solution to the Marcus delay differential equations; and (ii) we establish a representation formula for the probability density of the Marcus stochastic delay differential equations. In the representation formula, the probability density for Marcus stochastic differential equations with memory is analytically expressed in terms of probability density for the corresponding Marcus stochastic differential equations without memory.

Evaluation of the relative density based on flat dilatometer test

Abstract Overseeing the relative density of soils in all types of earth structures during both construction and operation is crucial to ensure that these structures attain the necessary density and strength. Especially in linear structures that extend over significant lengths, geotechnical investigations should include planning tests that allow for determining the maximum number of geotechnical parameters, such as cone penetration tests (CPTU) or Marchetti dilatometer tests (DMT). The article presents the in situ tests aimed at assessing the relative density of sandy soils. Empirical formulas available in the literature for determining the relative density Dr from DMT gave inconsistent results compared to those obtained from dynamic soundings, especially in the near-surface zone, where high KD readings significantly overestimate relative density values. Assuming the results of DPL probe tests as reference values, a formula for the compaction index based on DMT soundings has been proposed. In contrast to the formulas commonly used in the literature, the proposed formula for the relative density depends not only on the horizontal stress index KD, but also on the dilatometer modulus ED.

Localized density-based K-means UAV communication coverage algorithm for UV collaboration

In response to the problem of UAV-assisted communication, utilizing the characteristics of wireless ultraviolet with strong anti-jamming performance and good confidentiality, providing emergency communication services by covering ground users with UAVs as aerial base stations is crucial. A K-means clustering coverage algorithm based on the local density is proposed, which increases the connectivity term of UAVs on the basis of minimizing the squared error; secondly, the definition formula of the local density is proposed, and a heuristic decision function is used to determine the selection of the initial cluster center. The simulation results show that the initial coverage of the initial cluster center selected by the heuristic function is increased by 31.6%. Compared to the standard K-means algorithm and FSFDP algorithm, the coverage rate of the proposed algorithm in this paper is improved by 7.2% and 4.3%, respectively.

Random anti-commuting Hermitian matrices

We consider pairs of anti-commuting [Formula: see text]-by-[Formula: see text] Hermitian matrices that are chosen randomly with respect to a Gaussian measure. Generically such a pair decomposes into the direct sum of [Formula: see text]-by-[Formula: see text] blocks on which the first matrix has eigenvalues [Formula: see text] and the second has eigenvalues [Formula: see text]. We call [Formula: see text] the skew spectrum of the pair. We derive a formula for the probability density of the skew spectrum, and show that the elements are repelling.

Inference for the Parameters of a Zero-Inflated Poisson Predictive Model

In the insurance sector, Zero-Inflated models are commonly used due to the unique nature of insurance data, which often contain both genuine zeros (meaning no claims made) and potential claims. Although active developments in modeling excess zero data have occurred, the use of Bayesian techniques for parameter estimation in Zero-Inflated Poisson models has not been widely explored. This research aims to introduce a new Bayesian approach for estimating the parameters of the Zero-Inflated Poisson model. The method involves employing Gamma and Beta prior distributions to derive closed formulas for Bayes estimators and predictive density. Additionally, we propose a data-driven approach for selecting hyper-parameter values that produce highly accurate Bayes estimates. Simulation studies confirm that, for small and moderate sample sizes, the Bayesian method outperforms the maximum likelihood (ML) method in terms of accuracy. To illustrate the ML and Bayesian methods proposed in the article, a real dataset is analyzed.

Probability density of the solution to nonlinear systems driven by Gaussian and Poisson white noises

A new method is proposed to compute the probability density of the multi-dimensional nonlinear dynamical system perturbed by a combined excitation of Gaussian and Poisson white noises. We first deduce a probability-density solver from the Euler–Maruyama scheme of the stochastic system and the corresponding Chapman–Kolmogorov equation. This solver actually is an explicit numerical formula of the probability density of the solution to this stochastic system. To compute the probability density, we propose an efficient algorithm for this solver, which actually is the implementation of a numerical integration. Furthermore, we prove this solver is an approximated solution of the corresponding forward Kolmogorov equation. Numerical examples are conducted to illustrate our probability-density solver.

Thermo-osmosis of a near-critical binary fluid mixture: A general formulation and universal flow direction.

We consider a binary fluid mixture, which lies in the one-phase region near the demixing critical point, and study its transport through a capillary tube linking two large reservoirs. We assume that short-range interactions cause preferential adsorption of one component onto the tube's wall. The adsorption layer can become much thicker than the molecular size, which enables us to apply hydrodynamics based on a coarse-grained free-energy functional. For transport processes induced by gradients of the pressure, composition, and temperature along a cylindrical tube, we obtain the formulas of the Onsager coefficients to extend our previous results on isothermal transport, assuming the critical composition in the middle of each reservoir in the reference equilibrium state. Among the processes, we focus on thermo-osmosis-mass flow due to a temperature gradient. We explicitly derive a formula for the thermal force density, which is nonvanishing in the adsorption layer and causes thermo-osmosis. This formula for a near-critical binary fluid mixture is an extension of the conventional formula for a one-component fluid, expressed in terms of local excess enthalpy. We predict that the direction of thermo-osmotic flow of a mixture near the upper (lower) consolute point is the same as (opposite to) that of the temperature gradient, irrespective of which component is adsorbed on the wall. Our procedure would also be applied to dynamics of a soft material, whose mesoscopic inhomogeneity can be described by a coarse-grained free-energy functional.

Estimation Formula of Unmanned Aerial Vehicle Base Stations Density for Required Line-of-Sight Probability in Urban Environments

Estimation Formula of Unmanned Aerial Vehicle Base Stations Density for Required Line-of-Sight Probability in Urban Environments

Nonparametric kernel estimation of conditional copula density

This paper introduces a new mathematical formula for the bivariate conditional copula density and proposes kernel-type estimators for it. We demonstrate the consistency and asymptotic normality of these estimators, which also exhibit the best quadratic mean convergence rate when the optimal theoretical bandwidth is selected.

Credit default swap pricing with counterparty risk in a reduced form model with Hawkes process

Credit default swap pricing with counterparty risk in a reduced form model with Hawkes process

Absolutely continuous invariant measures for random dynamical systems of beta-transformations

We consider an independent and identically distributed (i.i.d.) random dynamical system of simple linear transformations on the unit interval Tβ(x)=βx (mod 1), x∈[0,1] , β > 0, which are the so-called beta-transformations. For such a random dynamical system, including the case that it is generated by uncountably many maps, we give an explicit formula for the density function of a unique stationary measure under the assumption that the random dynamics is expanding in mean. As an application, in the case that the random dynamics is generated by finitely many maps and the maps are chosen according to a Bernoulli measure, we show that the density function is analytic as a function of parameter in the Bernoulli measure and give its derivative explicitly. Furthermore, for a non-i.i.d. random dynamical system of beta-transformations, we also give an explicit formula for the random densities of a unique absolutely continuous invariant measure under a certain strong expanding condition or under the assumption that the maps randomly chosen are close to the beta-transformation for a non-simple number in the sense of parameter β.

A prediction model of maximum dry density of over coarse-grained soil

The control of maximum dry density is an important issue for over coarse-grained soil. A theoretical formula of the maximum dry density for over coarse-grained soil was derived, which is related to the maximum dry density of the original soil, particle density, and mass fraction of giant particles in the mixed soil. Maximum dry densities of seven groups of mixed soil were calculated by the discrete element method (DEM) and theoretical formula, and the results showed that the maximum dry densities obtained from the DEM were always lower than the results calculated by theoretical formula, and the difference increased with the increase in giant particle proportion. The volume growth coefficient was proposed to describe the increase in pore volume of the mixed soil caused by the embedding of giant particles, and the maximum dry density model for over coarse-grained soil was proposed. The results showed that the model fitted well to the DEM results, validating the high rationality and reliability.

An Application of Interacting Boson Fermion-Fermion Model (IBFFM) for <sup>134</sup>Cs Nucleus

This work concerns the calculations of interacting boson fermion-fermion model (IBFFM) for the odd-odd nucleus <sup>134</sup>Cs. The energy levels (positive and negative parity states), electric transition probability B(E2), magnetic transition probability B(M1), quadrupole and magnetic dipole moments have been studied in this work. The IBFFM results are compared with the available experimental data. In the present work, the IBFFM pattern of total and parametric dependent level densities for the odd-odd nucleus <sup>134</sup>Cs is investigated and compared to the pattern found in previous investigations in the framework of combinatorial and spectral distribution approaches. When comparing the theoretical values with the available experimental values, it was found that there is a good match between them. This is due to the values of the Hamiltonian parameters that were found accurately, so this IBFFM model is considered one of the effective models in studying the nuclear structure of odd-odd nuclei. The level density of the odd-odd nucleus <sup>196</sup>Au is investigated in the interacting boson-fermion-fermion model (IBFFM) which accounts for collectivity and complex interaction between quasiparticle and collective modes. The IBFFM spin-dependent level densities show high-spin reduction with respect to Bethe formula. This can be well accounted for by a modified spin-dependent level density formula.

Depth of focus and intensity distribution of a lensacon illuminated by a partially coherent Gaussian Schell vortex beam

Using the extended Huygens–Fresnel principle, a cross-spectral density formula was developed for a Gaussian Schell model vortex (PCGSMV) beam diffracted through a lensacon (lens with an axicon). The intensity and depth of focus (DOF) shaped by the lensacon were calculated. Our numerical results show the relationship between the intensity distribution and depth of focus with the beam waist width as well as the spatial correlation of the coherence length. Furthermore, the relationship between the beam spot size and propagation distance was investigated. In the case of the lensacon tandem, the maximum intensity was greater than that attained by the axicon alone for the same beam parameters, and the DOF was smaller than that of the axicon alone. The vortex structure canceled out the low value of the spatial degree of coherence length. Our numerical model exhibited high-intensity values and high-quality Bessel rings along the DOF, which are critical for various applications.

Asymmetric cosine-Gaussian Schell-model sources

We introduce a new class of Schell-model source whose spatial correlation function carries a finite series of nontrivial phases and is modulated by cosine function. The propagating formula for the cross-spectral density (CSD) function of the beams generated by this new source in free space is derived and used to investigate the characteristics of the light fields for different modulation parameters. The results show that the appearance of the modulating function and the nontrivial phase sequence cause the radiated fields with extraordinary characteristics during propagation, such as self-splitting and self-interfering in an asymmetric manner. This method of jointly controlling the magnitude and phase of the source complex coherence state provides a new approach for achieving beam shaping.