Search Results (430)

The probability density function (PDF) of the product of two normal random variables remains an open discussion. Researchers have proposed many forms of PDFs. Among these, two notable PDFs are an analytical solution with infinite summation and an integral form with transformation. For practical computation, they must be estimated. The form with infinite summation must be truncated to a finite summation, and the form still in integration must be computed numerically. As a result of this estimation, an error occurs in the value of the estimation. This paper derives upper bounds for the estimation error resulting from truncation and numerical approximation in integral calculations. The upper bound error between the exact PDF and the truncated PDF is expressed as a geometric series using Bessel function inequality and Stirling’s approximation. The geometric formula allows the quantification of the total truncation error to be determined. For the PDF, which is still in integration form, the trapezoidal rule is used for numeric calculation. Hence, the error can be determined using the error-bound formula. The two estimated PDFs have their own advantages and disadvantages. The truncated PDF gives a relatively small upper bound value compared to the numerical calculation integral form PDF for a small value domain. However, the truncated PDF fails to perform for a large value domain, and only the integral form PDF can be used. The error for the estimation is applied to the conventional mass measurement. The results demonstrate that the error can be controlled through an analytical approach. Full article

For fractals on Riemannian manifolds, the theory of iterated function systems often does not apply well directly, as these fractal sets are often defined by relations that are multivalued or non-contractive. To overcome this difficulty, we introduce the novel notion of iterated relation systems. We study the attractor of an iterated relation system and formulate a condition under which such an attractor can be identified with that of an associated graph-directed iterated function system. Using this method, we obtain dimension formulas for the attractor of an iterated relation system on locally Euclidean Riemannian manifolds, under the graph open set condition or the graph finite type condition. This method improves the one by Ngai and Xu, which relies on knowing the specific structure of the attractor. We also study fractals generated by iterated relation systems on Riemannian manifolds that are not locally Euclidean. Full article

With reference to the widespread out-of-plane (OOP) failures of infill walls in reinforced concrete (RC) buildings during the 6 February 2023 earthquakes in Kahramanmaraş, Turkey, this paper investigates the OOP strength of unreinforced masonry (URM) infills without openings, enclosed in RC frames, while also considering the effect of prior in-plane (IP) loading. A comprehensive database has been compiled, including all available tests on infills subjected to OOP loading and sequential IP–OOP loading, as well as those on infills with gaps between the RC frame and the masonry panel. This study evaluates the effectiveness of established design models at predicting the OOP strength of infills in RC frames and proposes refinements to improve the predictive accuracy. For the OOP strength, two arch-based models are applied, and the impact of prior IP loading is addressed through a reduction factor, R. Based on test observations showing that prior IP loading disproportionately reduces the OOP strength in vulnerable infills, an improved R-factor is introduced, providing better alignment with experimental results than four existing design formulas. The influence of gaps between the infill and RC frame on the OOP behavior is also examined. The findings reveal inconsistencies and reduced reliability among the available design models, highlighting the need for further research on this critical topic. Full article

Railways are complex systems, and the braking performance of trains is crucial to ensure the line’s safety. The assessment of the stopping distance can be obtained by empirical formulas or by more sophisticated numerical models which simulate the train’s longitudinal dynamics. In both cases the level of estimation accuracy may vary a lot, depending on the numerical values attributed to several parameters related both to the train braking system and the railway. The correct identification of such parameters might be an issue in local railways. On the one hand, some widely used empirical formulas are mainly intended for national railways, thus it is critical to determine whether they are appropriate for local railways. On the other hand, the development of a good predictive simulation model requires the identification of parameters not always known for the trains in service. Starting with measurements taken from braking tests performed on a local railway, this research aims to propose an experimentally correlated dynamics model based on the train’s equation of motion that can accurately estimate the stopping distance with a reduced amount of input parameters obtainable from measurements. Several braking tests have been performed on the track to identify the model’s parameters and to enhance the numerical–experimental correlation. Meanwhile, the applicability of stopping distance empirical formulas to the case of local railways has been evaluated, and the parameters of these formulas have been identified to reduce the gap with respect to measured distance values. Even if both simulation approaches led to an accurate estimation of the stopping distance, this work highlights some distinctions. In order to match the measured distance values, some empirical formulas required the definition of doubtful input parameters values, and suggest skipping their use for local railways application. Conversely, the proposed dynamics model led to a good balance between accuracy level and the effort required for parameter identification from testing, with it being more easily applicable to different scenarios and open to the implementation of additional features in future studies. Full article

We develop a rigorous algebraic–analytic framework for multidual complex numbers ${\mathbb{DC}}_n$ within the setting of Clifford analysis and establish a comprehensive theory of hyperholomorphic multidual complex-valued functions. Our main contributions are (i) a fully coupled multidual Cauchy–Riemann system derived from the Dirac operator, yielding precise differentiability criteria; (ii) generalized conjugation laws and the associated norms that clarify metric and geometric structure; and (iii) explicit operator and kernel constructions—including generalized Cauchy kernels and Borel–Pompeiu-type formulas—that produce new representation theorems and regularity results. We further provide matrix–exponential and functional calculus representations tailored to ${\mathbb{DC}}_n$, which unify algebraic and analytic viewpoints and facilitate computation. The theory is illustrated through a portfolio of examples (polynomials, rational maps on invertible sets, exponentials, and compositions) and a solvable multidual boundary value problem. Connections to applications are made explicit via higher-order automatic differentiation (using nilpotent infinitesimals) and links to kinematics and screw theory, highlighting how multidual analysis expands classical holomorphic paradigms to richer, nilpotent-augmented coordinate systems. Our results refine and extend prior work on dual/multidual numbers and situate multidual hyperholomorphicity within modern Clifford analysis. We close with a concise summary of notation and a set of concrete open problems to guide further development. Full article

The paper advances the theory of queuing networks by presenting generalized product-form solutions that explicitly take into account the service intensity depending on the number of customers in the network nodes, including the presence of multiple service channels and multi-threaded nodes. This represents a significant extension of the classical results on the Jackson network by integrating graph-theoretic methods, including basic subgraphs with service rates depending on the number of requests. The originality of the article is in the combination of stationary and non-stationary approaches to modeling service networks within a single approach. In particular, acyclic networks with deterministic service time and non-stationary Poisson input flow are considered. Such systems present a significant difficulty, which is noted in well-known works. A stationary model of an open queuing network with service intensity depending on the number of customers in the network nodes is constructed. The stationary network model is related to the problem of marine linear navigation along a strictly defined route and schedule. A generalization of the product theorem with a new form of stationary distribution is developed for it. It is shown that even a small increase in the service intensity with a large number of requests in a queuing network node can significantly reduce its average value. A non-stationary model of an acyclic queuing network with deterministic service time in network nodes and a non-stationary Poisson input flow is constructed. The non-stationary model is associated with irregular (tramp) sea transportation. The intensities of non-stationary Poisson flows in acyclic networks are represented by product formulas using paths between the initial node and other network nodes. The parameters of Poisson distributions of the number of customers in network nodes are calculated. The simplest formulas for calculating such queuing networks are obtained for networks in the form of trees. Full article

Conventional risk assessment frameworks usually define risk as a function of vulnerabilities and threats, but they frequently lack a single quantitative model that incorporates the unique features of each element. In order to close this gap, this paper creates a flexible, open, and theoretically sound risk assessment formula that is still reliable even in the absence of complete vulnerability data. This is particularly important for financial institutions operating in emerging markets, where regulators rarely provide centralized vulnerability assessments and where Basel-type frameworks are only partially implemented. The contribution of the paper is a practically verified Bayesian network model that integrates threat likelihoods, vulnerability likelihoods, and their impacts within a probabilistic structure. Using 500 stratified Monte Carlo scenarios calibrated to real fintech and banking institutions operating under EU and national supervision, we demonstrate that excluding vulnerability impact from the model does not significantly reduce the predictive performance. These findings advance the theory of risk assessment, simplify practical implementation, and enhance the scalability of risk modeling for both traditional banks and fintech institutions in emerging economies. Full article

This study introduces YOLOv13-Cone-Lite, an enhanced algorithm based on YOLOv13s, designed to meet the stringent accuracy and real-time performance demands for traffic cone detection in autonomous formula racing cars on enclosed tracks. We improved detection accuracy by refining the network architecture. Specifically, the DS-C3k2_UIB module, an advanced iteration of the Universal Inverted Bottleneck (UIB), was integrated into the backbone to boost small object feature extraction. Additionally, the Non-Maximum Suppression (NMS)-free ConeDetect head was engineered to eliminate post-processing delays. To accommodate resource-limited onboard terminals, we minimized superfluous parameters through structural reparameterization pruning and performed 8-bit integer (INT8) quantization using the TensorRT toolkit, resulting in a lightweight model. Experimental findings show that YOLOv13-Cone-Lite achieves a mAP₅₀ of 92.9% (a 4.5% enhancement over the original YOLOv13s), a frame rate of 68 Hz (double the original model’s speed), and a parameter size of 8.7 MB (a 52.5% reduction). The proposed algorithm effectively addresses challenges like intricate lighting and long-range detection of small objects and offers the automotive industry a framework to develop more efficient onboard perception systems, while informing object detection in other closed autonomous environments like factory campuses. Notably, the model is optimized for enclosed tracks, with open traffic generalization needing further validation. Full article

This work addresses a significant gap in the existing literature by developing integral representation formulas for extended quaternion-valued functions within the framework of Clifford analysis. While classical Cauchy-type and Borel–Pompeiu formulas are well established for complex and standard quaternionic settings, there is a lack of analogous tools for functions taking values in extended quaternion algebras such as split quaternions and biquaternions. The motivation is to extend the analytical power of Clifford analysis to these broader algebraic structures, enabling the study of more complex hypercomplex systems. The objectives are as follows: (i) to construct new Cauchy-type integral formulas adapted to extended quaternionic function spaces; (ii) to identify explicit kernel functions compatible with Clifford-algebra-valued integrands; and (iii) to demonstrate the application of these formulas to boundary value problems and potential theory. The proposed framework unifies quaternionic function theory and Clifford analysis, offering a robust analytic foundation for tackling higher-dimensional and anisotropic partial differential equations. The results not only enhance theoretical understanding but also open avenues for practical applications in mathematical physics and engineering. Full article

In the development of large wireless networks, scaling law studies can provide fundamental insights. For example, is it possible to build an arbitrarily large wireless network without a wired infrastructure while maintaining a constant communication rate for each user? This is equivalent to asking if a linear scaling law is achievable for wireless networks. Whether too ambitious a goal or not, this question has attracted intensive research but still remains open. Among many proposals, the hierarchical scheme is impressive in exploiting the MIMO gain with a bootstrapping strategy. In this paper, a careful analysis of the hierarchical scheme exposes the potential influence of the pre-constant in deriving scaling laws. It is found that a modified hierarchical scheme can achieve a throughput up to an arbitrary factor higher than the original one, although it is still short of linear scaling. This study demonstrates the essential importance of the throughput formula itself, rather than the scaling laws consequently derived. Full article

Accurate path-loss characterization in the upper mid-band is critical for 5G/6G outdoor planning, yet classical deterministic expressions lose fidelity at 18 GHz, and purely data-driven regressors offer limited physical insight. We present a physics-guided residual learner that couples a calibrated two-ray model with an XGBoost regressor trained on the deterministic residuals. To enlarge the feature space without promoting overfitting, synthetic samples obtained by perturbing antenna height and ground permittivity within realistic bounds are introduced with a weight of $w=0.3$. The methodology is validated with narrowband measurements collected along two straight 25 m corridors. Under cross-corridor transfer, the hybrid predictor attains $0.59$–$0.62$ dB RMSE and $R^2\ge 0.996$, reducing the error of a pure-ML baseline by half and surpassing deterministic formulas by a factor of four. Small-scale analysis yields decorrelation lengths of 0.23 m and 0.41 m; a cross-correlation peak of unity at $\Delta =0.10$ m confirms the physical coherence of both corridors. We achieve <1 dB error using a small set of field measurements plus simple synthetic data. The method keeps a clear mathematical core and can be extended to other priors, NLOS cases, and semi-open hotspots. Full article

Background/Objectives: This study aimed to evaluate estimated pulse wave velocity (ePWV) in different glaucoma types. Methods: This was observational, cross-sectional, non-interventional study conducted on 127 primary open-angle glaucoma (POAG) patients, 59 primary angle-closure glaucoma (PACG) patients, 34 pseudoexfoliative glaucoma (PEX) patients, and 55 normotensive glaucoma (NTG) patients (total of 275 glaucoma patients). The control group (CG, 92 patients) consisted of patients with cataract. ePWV was calculated by the formula that was recommended by the Reference Values for Arterial Stiffness Collaboration from data on age and mean arterial blood pressure. The obtained results were processed by applying methods of descriptive (arithmetical mean, standard deviation) and analytical statistics, and comparisons of tested variables were performed using ANOVA. A p value less than 0.05 was considered statistically significant. Results: Statistically significant differences were found between patients with POAG and the CG (p value 0.042), and between those with NTG and the CG (p value 0.001). There was a statistically significant difference in ePWV values when comparing all tested patients with glaucoma and the control group (p = 0.001). Conclusions: Estimated pulse wave velocity may be a helpful tool in future risk assessment models for glaucoma. Full article

The longitudinal equivalent bending stiffness is a critical parameter for assessing the longitudinal responses of Double-O-Tube (DOT) shield tunnels under adjacent construction activities. Based on a longitudinal equivalent continuous model and the characteristics of the DOT shield tunnel cross-section, an analytical solution for the longitudinal equivalent bending stiffness (LEBS) of the DOT shield tunnel has been derived. Given that the cross-section of the DOT shield tunnel is an irregular structure, two scenarios are considered: one in which the neutral axis is located at the waist of the tunnel and another where it is situated at the lower arch. Using the structural design of the DOT shield tunnel for Shanghai Metro Line M8 as a case study, the effects of bolt number, segment thickness, segment width, and pillar height on the longitudinal equivalent bending stiffness have been investigated. Additionally, formulas for calculating the deformation and stress indices of the DOT shield tunnel have been established. The results indicate that increasing the number of bolts and widening the segments can enhance the longitudinal equivalent bending stiffness efficiency (LEBSE), resulting in an upward shift of the neutral axis. Conversely, as the segment thickness increases, the LEBSE decreases linearly while the neutral axis moves downward; however, the value of LEBS itself increases. With an increase in the pillar height angle, the neutral axis shifts upward, leading to an increase in the LEBS. When the pillar height angle is increased from 10° to 45°, the LEBSE decreases rapidly, followed by a gradual increase with further elevation in the pillar height angle. When the tunnel curvature radius exceeds 15,000 m, the bolts, segments, and joint openings remain in a safe state. However, when the curvature radius decreases to 5233 m, the maximum tensile stress on the bolts reaches their yield limit, and the joint openings exceed the warning threshold. Full article

Expandable polystyrene (EPS) nozzle covers can be used to replace traditional metal nozzle covers due to their excellent mechanical properties, as well as being lightweight and ablatable. As an important part of the solid rocket motor, the nozzle cover needs to be designed according to the requirements of the overall system. This study lays a theoretical foundation for the engineering design and performance optimization of the EPS nozzle cover. In this paper, the method of combining test research and numerical simulation is used to explore the pressure bearing capacity of EPS nozzle covers with different thicknesses under linear load. Firstly, the quasi-static tensile, compression and shear tests of EPS materials were carried out by universal testing machine, and the key parameters such as stress-strain curve, elastic modulus and yield strength were obtained; Based on the experimental data, the constitutive model of EPS material with respect to density is fitted and modified; The VUMAT subroutine of the material was written in Fortran language, and the mechanical properties of the nozzle cover with different material model distribution schemes and different thicknesses were explored by ABAQUS finite element numerical simulation technology. The results indicate that the EPS nozzle cover design based on the two material model allocation schemes better aligns with practical conditions; when the end thickness of the EPS nozzle cover exceeds 3 mm, the opening pressure formula for the cover based on the pure shear theory of thin-walled circular plates becomes inapplicable; the EPS nozzle cover exhibits excellent pressure-bearing capacity and performance, with its pressure-bearing capacity showing a positive correlation with its end thickness, and an EPS nozzle cover with a 9 mm end thickness can withstand a pressure of 7.58 MPa (under internal pressure conditions); the pressure-bearing capacity of the EPS nozzle cover under internal pressure conditions is higher than under external pressure conditions, and when the end pressure-bearing surface thickness increases to 9 mm, the internal pressure-bearing capacity is 3.13 MPa higher than under external pressure conditions. Full article

To investigate the movement law of top coal and the influencing factors of coal caving ratio in fully mechanized top coal caving faces, this study adopts the theory of dispersoid mechanics. First, a top coal flow model was established without considering the influence of the support. Then, the effect of the support was analyzed, and it was found that the sliding resistance of the top coal body increases with the square of both the support width and the top coal thickness. Furthermore, the positive stress on the coal particles was derived through a microelement force analysis, and a theoretical formula for arching probability was proposed. The mobility of top coal was evaluated using a flow factor, and the influence of lump size on arching tendency was quantitatively analyzed. Based on these insights, several measures to improve top coal flowability and recovery rate were proposed, including increasing mining height, enlarging the coal caving opening, enhancing the initial support force, extending the caving step, and applying multiple alternating loads to pre-break top coal. These strategies provide a theoretical basis and practical guidance for enhancing top coal caving efficiency. Full article