1,269 Results Found

The rotational correlation times of a small compact spin probe (2,2,6,6-tetramethylpiperidin-1-yl)oxyl in isotactic polypropylene were obtained over a wide temperature range by EPR spectra simulation taking into account rotational anisotropy as well...

In this paper, a new approximation formula for the gamma function and some of its symmetric inequalities are established. We prove the superiority of our results over Yang and Tian’s approximation formula for the gamma function of order $v^{\&minus}$...

In this paper, two new approximation formulas with monotonic remainders for the gamma function have been presented. Also, we present some numerical comparisons between our new approximation formulas and some known ones, which demonstrate the superior...

Rough Heston model possesses some stylized facts that can be used to describe the stock market, i.e., markets are highly endogenous, no statistical arbitrage mechanism, liquidity asymmetry for buy and sell order, and the presence of metaorders. This...

This study establishes the new approximation formula for the Digamma function $\psi \left(s\right)=lns-{\displaystyle \frac{1}{2s}}-{\displaystyle \frac{1}{12s\sqrt{s^2+\theta \left(s\right)}}},{\displaystyle \frac{1}{36}}<\theta \left(s\right)<{\displaystyle \frac{1}{5}};s>0$, as well as some of its inequalities, where $\theta \left(s\right)$ is a continuous function. We demonstrat...

Two new approximation formulas for Bateman’s G-function are presented with strictly monotonic error functions and we deduced their sharp bounds. We also studied the completely monotonic (CM) degrees of two functions involving $G\left(r\right)$, deducing two...

We prove that the function $\sigma \left(s\right)$ defined by $\beta \left(s\right)=\frac{6s^2+12s+5}{3s^2(2s+3)}-\frac{{\psi }^{\prime }\left(s\right)}{2}-\frac{\sigma \left(s\right)}{2s^5},s>0$, is strictly increasing with the sharp bounds $0<\sigma \left(s\right)<\frac{49}{120}$, where $\beta \left(s\right)$ is Nielsen’s beta function a...

In this paper, on the basis of the Carleman matrix, we explicitly construct a regularized solution of the Cauchy problem for the matrix factorization of Helmholtz’s equation in an unbounded two-dimensional domain. The focus of this paper is on...

In this paper, we first establish an evaluation formula to calculate Wiener integrals of functionals on Wiener space. We then apply our evaluation formula to carry out easy an calculation for the analytic Fourier–Feynman transform of the functi...

In this paper, the authors briefly review some closed-form formulas of the Gauss hypergeometric function at specific arguments, alternatively prove four of these formulas, newly extend a closed-form formula of the Gauss hypergeometric function at som...

The study of thin-bed seismic phenomena is important in crustal, exploration and engineering seismology. Presently, seismic reflectivity theories based on single-interface assumption are widely used though they are only suitable for thick deposits. T...

This paper develops two novel arcsine-type analytic approximation formulas for $\mathrm{arcsl}\left(x\right)$, the Gauss lemniscate sine function, each equipped with a monotonic and bounded remainder term of order $x^{29}$ as $x\to 0$, which demonstrates the high accuracy of t...

This paper deals with a family of normalized multivariate neural network (MNN) operators of complex-valued continuous functions for a multivariate context on a box of ${\mathbb{R}}^{\overline{N}}$, $\overline{N}\in \mathbb{N}$. Moreover, we consider the case of approximation employing...

Exact interaction formulae for the plastic resistances of Z-sections under a combination of three internal forces, i.e., the bending moment about the strong axis M_y,Ed, bending moment about the weak axis M_z,Ed and bimoment B_Ed, were created and analy...

“Thin-bed” reservoirs have become important targets of seismic exploration and exploitation. However, traditional amplitude versus offset/amplitude versus angle (AVO/AVA) technologies, for example, those based on Zoeppritz equations and t...

The volatility of stock return does not follow the classical Brownian motion, but instead it follows a form that is closely related to fractional Brownian motion. Taking advantage of this information, the rough version of classical Heston model also...

In this paper, we present a Durrmeyer type generalization of parametric Bernstein operators. Firstly, we study the approximation behaviour of these operators including a local and global approximation results and the rate of approximation for the Lip...

The study shows the results of theoretical investigations into lateral torsional buckling of bisymmetric I-beams elastically restrained against warping and against rotation in the plane of lateral torsional buckling (i.e., against lateral rotation) a...

The correct evaluation of the curvatures of ball screw grooves allows the accurate design of the constructive parameters of this mechanism and enhancing its performance. The formulation commonly used in the literature, however, refers to ball bearing...

This paper presents the results of a further stage of the authors’ research into the lateral torsional buckling of hot-rolled bisymmetric I-beams, spatially elastically restrained at the support nodes, i.e., against: (1) warping, (2) rotation i...

This study presents an efficient high-order radius function Hermite finite difference (RBF-HFD) scheme for the numerical solution of Caputo time-fractional sub-diffusion equations with integral boundary conditions. The spatial derivatives are approxi...

In this paper, we propose a class of simple numerical methods for approximating solutions of one-dimensional mixed Volterra–Fredholm integral equations of the second kind. These methods are based on fixed point results for the existence and uni...

In this study, a new analytical approximation for the Bessel function of the first kind of order two $J_2\left(t\right)$, $t>0$, is produced using its power series and its asymptotic series as t tends to infinity. The absolute error between the new analytical app...

The efficient construction and employment of block operators are vital for contemporary computing, playing an essential role in various applications. In this paper, we prove a generalisation of the Frobenius formula in the setting of the theory of bl...

This paper addresses the problem of the power flow analysis of bipolar direct current (DC) networks considering unbalanced loads and the effect of a neutral wire, which may be solidly grounded or non-grounded. The power flow problem is formulated usi...

This paper presents a fast Crank–Nicolson L1 finite difference scheme for the two-dimensional time fractional mobile/immobile diffusion equation with weakly singular solution at the initial moment. First, the time fractional derivative is discr...

Solutions to problems arising from much scientific and applied research conducted at the world level lead to integral and differential equations. They are approximately solved, mainly using quadrature, cubature, and difference formulas. Therefore, in...

The parabolic trough solar collector (PTC) is the most mature solar concentrating technology, and this technology is applied in numerous thermal applications. Usually, the thermal efficiency of the PTC is expressed with the aid of polynomial expressi...

In this paper, we aim to present a novel n-point composite fractional formula for approximating a Riemann–Liouville fractional integral operator. With the use of the definite fractional integral’s definition coupled with the generalized T...

The goal of this paper is to derive closed-form approximation formulas for the spread option value and Greeks by using double integration and investigating the exercise boundary. We have found that the straight-line approximation suggested in previou...

For the calculation of thermal processes of canned food, the original formula method of Ball is still widely used for its accuracy and safety. However, it requires the consultation of tables that Ball prepared and the relative interpolation of the da...

This paper presents a geometric difficulty analysis framework for Formula 1 racing lines based on telemetry data from the 2024 season. To ensure geometric consistency across multiple laps, a representative racing line is identified using the discrete...

Based on the canonical correlation analysis, we derive series representations of the probability density function (PDF) and the cumulative distribution function (CDF) of the information density of arbitrary Gaussian random vectors as well as a genera...

In this work, we consider the properties of the two-term Machin-like formula and develop an algorithm for computing digits of $\pi$ by using its rational approximation. In this approximation, both terms are constructed by using a representation of $1/\&$...

This paper presents a closed-form quite handy formula for the local thermal resistance R_b between the temperature of the bulk heat-carrier fluid in the pipes, equally spaced on a concentric circle inside a circular energy pile, and the mean temperatu...

This paper presents an analysis of data on the cross sections of elastic and inelastic collisions of electrons with noble gases, alkali and other atoms. For the selected sets of experimental and theoretical data, optimal analytical formulas are found...

In this paper, an effective numerical approach that combines the fast L1 formula and barycentric Lagrange interpolation is proposed for solving a kind of time-fractional evolution equations. This type of equation contains a nonlocal term involving th...

In rough set theory, the multiplicity of methods of calculating neighborhood systems is very useful to calculate the measures of accuracy and roughness. In line with this research direction, in this article we present novel kinds of rough neighborhoo...

This paper studies discontinuous quasilinear sub-elliptic systems associated with Hörmander’s vector fields under controllable and natural growth conditions. By a new $\mathcal{A}$-harmonic approximation reformulation for bilinear forms $\mathcal{A}\in \mathrm{Bil}({\mathbb{R}}^{kN}$...

In this paper we obtain a best approximations theorem for multi-valued mappings in $\mathcal{G}$-convex spaces. As applications, we derive results on the best approximations in hyperconvex and normed spaces. The obtain results generalize many existing result...

Inequalities play a fundamental role in both theoretical and applied mathematics and contain many patterns of symmetries. In many studies, inequalities have been used to provide estimates of some functions based on the properties of their symmetry. I...

A computational approach with the aid of the Linear Multistep Method (LMM) for the numerical solution of differential equations with initial value problems or boundary conditions has appeared several times in the literature due to its good accuracy a...

In this paper, the Carleman matrix is constructed, and based on it we found explicitly a regularized solution of the Cauchy problem for the matrix factorization of the Helmholtz equation in a multidimensional unbounded domain in ${\mathbb{R}}^m,(m=2k,k\ge 2)$. The...

In this paper, we derive an analytical and explicit approximation for the Bessel function $J_2\left(x\right)$ for positive real x with a maximum absolute error of approximately $0.004$, which refines some new published analytic approximation. The absolute errors for...

This paper considers the Brownian perturbed Cramér–Lundberg risk model with a dividends barrier. We study various types of Padé approximations and Laguerre expansions to compute or approximate the scale function that is necessary...

When the Colebrook equation is used in its original implicit form, the unknown pipe flow friction factor can only be obtained through time-consuming and computationally demanding iterative calculations. The empirical Colebrook equation relates the un...

A high-order single-step implicit method, the Legendre–Darboux Method of order six (LDM6), is introduced for solving both linear and nonlinear initial value problems. Unlike classical Taylor expansions, LDM6 systematically constructs higher-ord...

This study proposes an L1 discretization scheme (an accurate second-order finite difference method) for time-fractional diffusion equations involving the Caputo-type Erdélyi–Kober operator, which models anomalous diffusion. Our key contr...

According to the equation for Newtonian fluids, the film thickness after spin coating is determined by five parameters: angular velocity, spin coating time, viscosity, density of the coating material, and initial thickness of the material before spin...

The conventional rolled-up model for carbon nanocones assumes that the cone is constructed from a rolled-up graphene sheet joined seamlessly, which predicts five distinct vertex angles. This model completely ignores any effects due to the changing cu...