Search Results (12)

This study investigates the computation of fractional and higher integer-order moments for a stochastic process governed by a one-dimensional, non-homogeneous linear stochastic differential equation (SDE) driven by fractional Brownian motion (fBm). Unlike conventional approaches relying on moment-generating functions or Fokker–Planck equations, which often yield intractable expressions, we derive explicit closed-form formulas for these moments. Our methodology leverages the Wick–Itô calculus (fractional Itô formula) and the properties of Hermite polynomials to express moments efficiently. Additionally, we establish a recurrence relation for moment computation and propose an alternative approach based on generalized binomial expansions. To validate our findings, Monte Carlo simulations are performed, demonstrating a high degree of accuracy between theoretical and empirical results. The proposed framework provides novel insights into stochastic processes with long-memory properties, with potential applications in statistical inference, mathematical finance, and physical modeling of anomalous diffusion. Full article

Steel-reinforced grout (SRG) composites are a newly developed retrofitting technique, which is considered an alternative to other fiber-reinforced composites to increase the load-carrying capacity of existing structures. This work presents an experimental campaign aimed at investigating the response of reinforced concrete (RC) beams strengthened with SRG externally applied to the tension side of the member to improve flexural capacity. The number of fiber sheet layers and fiber sheet density have been varied to evaluate the effectiveness of the retrofitting system. For some beams, different solutions of anchors at the ends of the beams have been considered to delay the premature debonding of the SRG. Moreover, single-lap direct shear tests have been carried out on concrete prisms strengthened with the same SRG composite to evaluate the bond behavior of the system. Failure modes, load responses, and corresponding flexural capacity (beam tests) and debonding loads (shear tests) are reported. The moment–curvature curves derived from cross-sectional analysis are compared with the corresponding experimental curves. The strain when the loss of composite action occurs is obtained from the curvature measured experimentally and compared with the values from formulas for the strain available in the literature and the strain at debonding in single-lap shear tests. Full article

The main recent change observed in the field of critical patient infection has been universal awareness of the need to make better use of antimicrobials, especially for the most serious cases, beyond the application of simple and effective formulas or rigid protocols. The increase in resistant microorganisms, the quantitative increase in major surgeries and interventional procedures in the highest risk patients, and the appearance of a significant number of new antibiotics in recent years (some very specifically directed against certain mechanisms of resistance and others with a broader spectrum of applications) have led us to shift our questions from “what to deal with” to “how to treat”. There has been controversy about how best to approach antibiotic treatment of complex cases of sepsis. The individualized and adjusted dosage, the moment of its administration, the objective, and the selection of the regimen are pointed out as factors of special relevance in a critically ill patient where the frequency of resistant microorganisms, especially among the Enterobacterales group, and the emergence of multiple and diverse antibiotic treatment alternatives have made the appropriate choice of antibiotic treatment more complex, requiring a constant updating of knowledge and the creation of multidisciplinary teams to confront new infections that are difficult to treat. In this article, we have reviewed the phenomenon of the emergence of resistance to antibacterials and we have tried to share some of the ideas, such as stewardship, sparing carbapenems, and organizational, microbiological, pharmacological, and knowledge tools, that we have considered most useful and effective for individualized decision making that takes into account the current context of multidrug resistance. The greatest challenge, therefore, of decision making in this context lies in determining an effective, optimal, and balanced empirical antibiotic treatment. Full article

Orthogonal generalized Laguerre moments of fractional orders (FrGLMs) are signal and image descriptors. The utilization of the FrGLMs in the analysis of big-size signals encounters three challenges. First, calculating the high-order moments is a time-consuming process. Second, accumulating numerical errors leads to numerical instability and degrades the reconstructed signals’ quality. Third, the QR decomposition technique is needed to preserve the orthogonality of the higher-order moments. In this paper, the authors derived a new recurrence formula for calculating the FrGLMs, significantly reducing the computational CPU times. We used the Schwarz–Rutishauser algorithm as an alternative to the QR decomposition technique. The proposed method for computing FrGLMs for big-size signals is accurate, simple, and fast. The proposed algorithm has been tested using the MIT-BIH arrhythmia benchmark dataset. The results show the proposed method’s superiority over existing methods in terms of processing time and reconstruction capability. Concerning the reconstructed capability, it has achieved superiority with average values of 25.3233 and 15.6507 with the two metrics PSNR and MSE, respectively. Concerning the elapsed reconstruction time, it also achieved high superiority with an efficiency gain of 0.8. The proposed method is suitable for utilization in the Internet of Healthcare Things. Full article

For massive monolithic foundation slabs, the problem of early cracking due to the intense heat release of concrete during the hardening process is relevant. The purpose of this article is to develop a simplified method for determining thermal stresses during the construction of massive monolithic foundation slabs. The proposed technique is based on the hypothesis of parabolic temperature distribution over the thickness of the structure at each moment of time. In addition to the parabolic distribution, the half-wave cosine distribution is also used. A hypothesis is also introduced about the same conditions of heat exchange with the environment on the lower and upper surfaces of the foundation. As a result, formulas are obtained that establish a direct relationship between thermal stresses and the temperature difference between the center and the surface. The solution to the test problem for the foundation slab is presented and compared with an alternative technique that does not use the hypothesis about the character of the temperature distribution over the thickness. Also, the inverse problem of determining the allowable temperature drop between the center and the surface of the structure is solved, at which the stresses on the upper surface at each moment of time will not exceed the tensile strength of concrete. Full article

Suppose that ${\xi }^{+}$ is the positive part of a random variable defined on the probability space $(\mathsf{\Omega },\mathcal{F},\mathbb{P})$ with the distribution function $F_{\xi }$. When the moment $\mathbb{E}{\left({\xi }^{+}\right)}^p$ of order $p>0$ is finite, then the truncated moment ${\overline{F}}_{\xi ,p}\left(x\right)=min\left\{1,\mathbb{E}\left({\xi }^{p}1{\mathrm{I}}_{\{\xi >x\}}\right)\right\}$, defined for all $x⩾0$, is the survival function or, in other words, the distribution tail of the distribution function $F_{\xi ,p}$. In this paper, we examine which regularity properties transfer from the distribution function $F_{\xi }$ to the distribution function $F_{\xi ,p}$ and which properties transfer from the function $F_{\xi ,p}$ to the function $F_{\xi }$. The construction of the distribution function $F_{\xi ,p}$ describes the truncated moment transformation of the initial distribution function $F_{\xi }$. Our results show that the subclasses of heavy-tailed distributions, such as regularly varying, dominatedly varying, consistently varying and long-tailed distribution classes, are closed under this truncated moment transformation. We also show that exponential-like-tailed and generalized long-tailed distribution classes, which contain both heavy- and light-tailed distributions, are also closed under the truncated moment transformation. On the other hand, we demonstrate that regularly varying and exponential-like-tailed distribution classes also admit inverse transformation closures, i.e., from the condition that $F_{\xi ,p}$ belongs to one of these classes, it follows that $F_{\xi }$ also belongs to the corresponding class. In general, the obtained results complement the known closure properties of distribution regularity classes. Full article

In this paper, a new composite floor system using cold-formed thin-walled C steel channel embedment and a foam concrete slab is developed. This new type of floor system features lightweight, high fire-resistant, and high anti-corrosion features, and can be used for multi-story buildings, providing a promising new alternative floor system for the construction market. Two four-point bending tests were carried out to investigate the flexural capacity and failure modes of this new type of composite slab. Based on the test results, a nonlinear finite element model was developed using general software package ABAQUS. The model is validated using the test results. Using this model, parametric studies were performed to study the key parameters affecting the structural behavior of this new type of composite floor system. Different parameters such as density of the foam concrete, grade of the cold-formed thin-walled C steel channel embedment, and spacing of the cold-formed thin-walled C steel channel were investigated. Their contributions to the overall moment capacity and their effect on the failure modes of this type of composite slab were discovered. Based on experimental results and FE results, design formulas for ultimate flexural capacity of this new type of composite slabs were also developed which can accurately predict their flexural capacity. Full article

This article numerically analyzes the distribution of the zeros of Riemann’s zeta function along the critical line (CL). The zeros are distributed according to a hierarchical two-layered model, one deterministic, the other stochastic. Following a complex plane anamorphosis involving the Lambert function, the distribution of zeros along the transformed CL follows the realization of a stochastic process of regularly spaced independent Gaussian random variables, each linked to a zero. The value of the standard deviation allows the possible overlapping of adjacent realizations of the random variables, over a narrow confidence interval. The hierarchical model splits the $\zeta$ function into sequential equivalence classes, with the range of probability densities of realizations coinciding with the spectrum of behavioral styles of the classes. The model aims to express, on the CL, the coordinates of the alternating cancellations of the real and imaginary parts of the $\zeta$ function, to dissect the formula for the number of zeros below a threshold, to estimate the statistical laws of two consecutive zeros, of function maxima and moments. This also helps explain the absence of multiple roots. Full article

This work is an extension of our earlier article, where a well-known integral representation of the logarithmic function was explored and was accompanied with demonstrations of its usefulness in obtaining compact, easily-calculable, exact formulas for quantities that involve expectations of the logarithm of a positive random variable. Here, in the same spirit, we derive an exact integral representation (in one or two dimensions) of the moment of a nonnegative random variable, or the sum of such independent random variables, where the moment order is a general positive non-integer real (also known as fractional moments). The proposed formula is applied to a variety of examples with an information-theoretic motivation, and it is shown how it facilitates their numerical evaluations. In particular, when applied to the calculation of a moment of the sum of a large number, n, of nonnegative random variables, it is clear that integration over one or two dimensions, as suggested by our proposed integral representation, is significantly easier than the alternative of integrating over n dimensions, as needed in the direct calculation of the desired moment. Full article

We explore a well-known integral representation of the logarithmic function, and demonstrate its usefulness in obtaining compact, easily computable exact formulas for quantities that involve expectations and higher moments of the logarithm of a positive random variable (or the logarithm of a sum of i.i.d. positive random variables). The integral representation of the logarithm is proved useful in a variety of information-theoretic applications, including universal lossless data compression, entropy and differential entropy evaluations, and the calculation of the ergodic capacity of the single-input, multiple-output (SIMO) Gaussian channel with random parameters (known to both transmitter and receiver). This integral representation and its variants are anticipated to serve as a useful tool in additional applications, as a rigorous alternative to the popular (but non-rigorous) replica method (at least in some situations). Full article

We report on a new multiscale method approach for the study of systems with wide separation of short-range forces acting on short time scales and long-range forces acting on much slower scales. We consider the case of the Poisson–Boltzmann equation that describes the long-range forces using the Boltzmann formula (i.e., we assume the medium to be in quasi local thermal equilibrium). We develop a new approach where fields and particle information (mediated by the equations for their moments) are solved self-consistently. The new approach is implicit and numerically stable, providing exact energy conservation. We test different implementations that all lead to exact energy conservation. The new method requires the solution of a large set of non-linear equations. We consider three solution strategies: Jacobian Free Newton Krylov, an alternative, called field hiding which is based on hiding part of the residual calculation and replacing them with direct solutions and a Direct Newton Schwarz solver that considers a simplified, single, particle-based Jacobian. The field hiding strategy proves to be the most efficient approach. Full article

New risk-based solvency requirements for insurance companies across European markets have been introduced by Solvency II and will come in force from 1 January 2016. These requirements, derived by a Standard Formula or an Internal Model, will be by far more risk-sensitive than the required solvency margin provided by the current legislation. In this regard, a Partial Internal Model for Premium Risk is developed here for a multi-line Non-Life insurer. We follow a classical approach based on a Collective Risk Model properly extended in order to consider not only the volatility of aggregate claim amounts but also expense volatility. To measure the effect of risk mitigation, suitable reinsurance strategies are pursued. We analyze how naïve coverage as conventional Quota Share and Excess of Loss reinsurance may modify the exact moments of the distribution of technical results. Furthermore, we investigate how alternative choices of commission rates in proportional treaties may affect the variability of distribution. Numerical results are also figured out in the last part of the paper with evidence of different effects for small and large companies. The main reasons for these differences are pointed out. Full article