1,802 Results Found

Numerous formulae are available for predicting the scabbing limit and perforation limit thicknesses subjected to impact loading, but no formula has yet been proposed for estimating the scabbing depth, which is the damaged depth at the rear face when...

In current practices of determining continental shelf area, the measured sediment thickness data do not effectively reflect the distribution of sediments across the area due to its dispersed nature. This issue raises potential limitations in unknown...

This article addresses the numerical computation problem of induced inflow ratio based on the helicopter momentum theory in forward flight. The Glauert inflow formula (equation) is a nonlinear equation usually solved by the Newton–Raphson metho...

This paper presents a torque controller for the energy optimization of the powertrain of an electric Formula Student race car. Limited battery capacity within electric race car designs requires energy management solutions to minimize lap time while s...

In this paper, by virtue of the symmetry principle, we construct proper weight coefficients and use them to establish a more accurate half-discrete Hilbert-type inequality involving one upper limit function and one partial sum. Then, we prove the new...

Zeta-functions play a fundamental role in many fields where there is a norm or a means to measure distance. They are usually given in the forms of Dirichlet series (additive), and they sometimes possess the Euler product (multiplicative) when the dom...

Human milk is the healthiest option for newborns, although, under specific circumstances, infant formula is a precious alternative for feeding the baby. Except for the nutritional content, infant formulas and baby food must be pollutant-free. Thus, t...

Forming limit curve (FLC) is an important failure criterion for sheet metals in sheet metal forming, while the M-K model is widely used for the prediction of the FLC. In the M-K model, such prediction is greatly influenced by the initial thickness im...

In recent days, due to the increasing number of electric vehicle charging stations (EVCSs) and additional power consumption by domestic, commercial, and industrial consumers, the overall power system performance suffers, which further degrades voltag...

We start from a pure vector update of the concepts of complex numbers and the characteristic function of a probability distribution, free from the imaginary unit, and update some basic properties of the latter. In particular, we derive vector inverse...

The design of hybrid power units for compact racing vehicles demands optimal use of limited space while ensuring performance and regulatory compliance. This work presents a methodology for integrating a parallel P0 hybrid system into a Formula Studen...

In this paper, by means of weight coefficient methods and the Euler–Maclaurin summation formula, a half-discrete Mulholland-type inequality involving one multiple upper limit function is established, with the kernel ${(x+n^{\beta })}^{-\lambda }$ (...

The present paper revisits the determination of the semi-classical limit of the Feshbach resonances which play a role in electron impact broadening (the so-called “Stark“ broadening) of isolated spectral lines of ionized atoms. The Gailitis approxima...

With excess slurry pressures exerted on the tunnel face, slurry particles tend to infiltrate into the soil in front of the tunnel. There will be excess pore pressure ahead of the tunnel in the case of infiltration, leading to an impairment in the sup...

In our ongoing study, we explore the concepts of $\mathcal{I}$${}_3$-Cauchy and $\mathcal{I}$${}_3$-Cauchy for triple sequences in the context of random 2-normed spaces (RTNS). Moreover, we introduce and analyze the notions of $\mathcal{I}$${}_3$-convergence, $\mathcal{I}$${}_3$-convergence, $\mathcal{I}$${}_3$-limit points, and $\mathcal{I}$${}_3$-c...

The introduction of the common limit range property on $\mathcal{V}$ -fuzzy metric spaces is the foremost aim of this paper. Furthermore, significant results for coupled maps are proven by employing this property on $\mathcal{V}$ -fuzzy metric spaces. More precise...

We develop a function theory on a three-dimensional reduced quaternionic model endowed with a projected (and, therefore, non-associative) product, together with its natural dual extension generated by a nilpotent infinitesimal unit. After introducing...

This article explores the accessibility of symbolic computations, such as using the Wolfram Mathematica environment, in promoting the shift from informal experimentation to formal mathematical justifications. We investigate the accuracy of computatio...

Background: Exercise duration at maximum oxygen uptake ($\dot{\mathrm{V}}$O₂max) appears to be influenced not only by metabolic factors but also by the interplay between brain dynamics and ventilatory regulation. This study examined how cortical activity, asses...

We develop a Pizzetti calculus for the rank-one Opdam–Cherednik setting based on the Weyl symmetrized generalized translation. Its spectral multiplier is the Jacobi function, and the Jacobi differential equation yields a Darboux transmutation b...

This review is a part of the SI ‘Genome-Scale Modeling of Microorganisms in the Real World’. The goal of GEM is the accurate prediction of the phenotype from its respective genotype under specified environmental conditions. This review fo...

Big data and streaming data are encountered in a variety of contemporary applications in business and industry. In such cases, it is common to use random projections to reduce the dimension of the data yielding compressed data. These data however pos...

In the information theory community, the following “historical” statements are generally well accepted: (1) Hartley did put forth his rule twenty years before Shannon; (2) Shannon’s formula as a fundamental tradeoff between transmission rate, bandwid...

We consider a compact metric graph of size $\epsilon$ and attach to it several edges (leads) of length of order one (or of infinite length). As $\epsilon$ goes to zero, the graph ${\mathcal{G}}^{\epsilon }$ obtained in this way looks like the star-...

This research aims to study the ultimate limit state (ULS) behaviour of stiffened panel under longitudinal compression by a non-linear finite element method (NLFEM). There are different types of stiffeners mainly being used in shipbuilding, i.e., T-b...

This paper consists of three parts. In the first part, we prove that the Bekenstein-Hawking entropy is the unique expression of black hole entropy. Our proof is constructed in the framework of thermodynamics without any statistical discussion. In the...

In this paper we establish a new half-discrete Hilbert-type inequality involving the variable upper limit integral and partial sums. As applications, an inequality obtained from the special case of the half-discrete Hilbert-type inequality is further...

In the present study, a simplified and useful design formula is proposed to predict the ultimate strength of a plate under longitudinal compression. The shape of the elastic buckling strength (${\sigma }_{xE}$) equation is utilised and adjusted to predict t...

A system with two periodic directions carries two commuting holonomies $a=(u,v)\in {\mathbb{R}}^2/{\mathbb{Z}}^2$. We determine their distinguished values while separating lattice, arithmetic, and observable effects. Maximizing the lowest twisted eigenvalue places a at a de...

A lack of quality control tools limits the enforcement of fortification policies. In alignment with the World Health Organization’s ASSURED criteria (affordable, sensitive, specific, user-friendly, rapid and robust, equipment-free, and delivera...

We study truncation-compatible families $F={\left(F_m\right)}_{m\ge 1}$ over $\mathbb{Q}\left[z\right]$ through an inverse-limit formalism, and we evaluate them at the punctured cyclotomic cosine points ${\alpha }_{k,n}=cos(2\pi k/n)$ with the specialization $z=n-1$. For symmetric families of...

In this note, we study the Hopf-algebra-based (HAB) formula of Yang–Mills-Scalar (YMS) amplitudes, which expands a YMS amplitude with massive scalars as a combination of propagator matrices that mix massless scalars corresponding to gluons with...

Estimating evapotranspiration is crucial for irrigation and agricultural applications. Although the FAO-56 Penman–Monteith method is highly accurate under conditions of abundant data, its extensive requirements limit its practical application....

In this study, a new analytical model is developed for an electrostatic Microelectromechanical System (MEMS) cantilever actuator to establish a relation between the displacement of its tip and the applied voltage. The proposed model defines the micro...

Rarefication effects on jet impingement loads are studied by comparing recent new formulas at the collisionless flow limit and numerical simulations. The jet exit size is finite, and can be either planar or round. In the simulations, the jets have di...

Boundary behavior of a given important function or its limit values are essential in the whole spectrum of mathematics and science. We consider some tractable cases of limit values in which either a difference of two ingredients or a difference equat...

Background/Objective: Most weight estimation formulae developed for children from skeletal measurements are based on 20 individuals from the Denver Growth Study. This limitation is mainly due to the availability of data. The formulae produced using t...

The existing formulas for the synthetic aperture radar (SAR) Doppler centroid estimation standard deviation (STD) suffer from various limitations, especially for a dynamic sea surface. In this study, we derive an improved version of these formulas th...

The content of this study combines city safety, optimum excavation situation, mining, geology, and civil engineering principles. Tunnel boring machines (TBM) are the most commonly used machines in the excavation of urban tunnels. These machines preve...

In construction projects, dimensioning automation is now implemented with relatively high precision in both 2D CAD and 3D BIM environments when conditions are clearly defined. For identical or similar objects with the same attributes, dimension-based...

The empirical formula is one of the traditional methods used for predicting ground deformation settlement caused by tunnel excavation. Due to its rationality and simplicity, the Peck formula is widely used for predicting surface subsidence. However,...

Infant formulas are specialized foods designed for babies and toddlers who cannot be exclusively breastfed. However, acrylamide (AA) may form during the thermal processing involved in their production. Although chromatographic techniques offer high s...

Clausen’s series ₃F₂$(a,b,c;d,e;1)$, a generalized hypergeometric series with three numerator and two denominator parameters taken at unit argument, has classical closed forms when its denominator parameters exceed two of its numerator parameters by in...

Background/Objectives: The U.S. Food and Drug Administration sets nutritional standards for infant formulas. Yet, the carbohydrate components of these formulas can vary markedly in type as well as sweetness intensity. Despite evidence suggesting swee...

Patient demographic-based standard liver volume (SLV) models are widely used to estimate patient-specific hepatic metabolic demand and support future liver remnant assessment after hepatectomy. These formulae rely on anthropometric variables such as...

The mean sea level rising predicted for this century and the following centuries will make necessary to protect most of the human properties located on the coast. One of the alternatives is the construction of slope breakwaters along hundreds of kilo...

The authors reviewed the published evidence on the presence of oligosaccharides in human milk (HMO) and their benefits in in vitro and in vivo studies. The still limited data of trials evaluating the effect of mainly 2′-fucosyllactose (2′-FL) on the...

Cereulide is a heat-stable cyclic depsipeptide toxin produced by Bacillus cereus and is responsible for foodborne emetic syndrome. Recent reports of Bacillus cereus contamination and cereulide occurrence in infant formula have raised increasing food...

Purpose: The proper selection of an intraocular lens power calculation formula is an essential aspect of cataract surgery. This study evaluated the accuracy of artificial intelligence-based formulas. Design: Systematic review. Methods: This review co...

Despite its limitations, the Chezy bed shear stress formula is commonly used in depth-averaged flow numerical models as closure for estimating mutual tractive stresses with underneath boundaries. This paper proposes a novel moment-based formula that...