609 Results Found

We consider real trigonometric polynomial Bernoulli equations of the form $A\left(\theta \right)y^{\prime }=B_1\left(\theta \right)+B_n\left(\theta \right)y^n$ where $n\ge 2$, with $A,B_1,B_n$ being trigonometric polynomials of degree at most $\mu \ge 1$ in variables $\theta$ and $B_n\left(\theta \right)\not\equiv 0$...

In this paper, algorithms for different types of trigonometric power sums are developed and presented. Although interesting in their own right, these trigonometric power sums arise during the creation of an algorithm for the four types of twisted tri...

By means of the Lagrange interpolation, we derive two trigonometric identities that are utilized to evaluate, in closed forms, eight classes of power sums of trigonometric functions over equally distributed angles around the unit circle. When the mth...

Copulas are useful functions for modeling multivariate distributions through their univariate marginal distributions and dependence structures. They have a wide range of applications in all fields of science that deal with multivariate data. While th...

This paper introduces new trigonometric basis functions (TBF) in polynomial and rational form with two shape parameters (SPs). Some classical characteristics, such as the partition of unity, positivity, symmetry, CHP, local control and invariance und...

This work is intended to directly supplement the previous work by Coutsias and Kazarinoff on the foundational understanding of lacunary trigonometric systems and their relation to the Fresnel integrals, specifically the Cornu spirals [Physica 26D (19...

In this paper, we introduce and prove several generalized algebraic-trigonometric inequalities by considering negative exponents in the inequalities.

In this paper, the constructions of both open and closed trigonometric Hermite interpolation curves while using the derivatives are presented. The combination of tension, continuity, and bias control is used as a very powerful type of interpolation;...

In this paper, under the framework of Extended Chebyshev space, four new generalized quasi cubic trigonometric Bernstein basis functions with two shape functions $\alpha \left(t\right)$ and $\beta \left(t\right)$ are constructed in a generalized quasi cubic trigonometric space span$\{1,{\mathrm{si}}^{}$...

The symmetric-convolution multiplication (SCM) property of discrete trigonometric transforms (DTTs) based on unitary transform matrices is developed. Then as the reciprocity of this property, the novel multiplication symmetric-convolution (MSC) prope...

This paper presents a new recursive trigonometric (RT) technique for Field-Programmable Gate Array (FPGA) design implementation. The traditional implementation of trigonometric functions on FPGAs requires a significant amount of data storage space to...

Recent advances in mathematical inequalities suggest that bounds of polynomial-exponential-type are appropriate for evaluating key trigonometric functions. In this paper, we innovate in this sense by establishing new and sharp bounds of the form $(1-\alpha$...

Proposing new families of probability models for data modeling in applied sectors is a prominent research topic. This paper also proposes a new method based on the trigonometric function to derive the updated form of the existing probability models....

Copulas are important probabilistic tools to model and interpret the correlations of measures involved in real or experimental phenomena. The versatility of these phenomena implies the need for diverse copulas. In this article, we describe and invest...

This paper proposes a novel hybrid arithmetic–trigonometric optimization algorithm (ATOA) using different trigonometric functions for complex and continuously evolving real-time problems. The proposed algorithm adopts different trigonometric fu...

This paper proposes a new approach to define two frequency trigonometric spline curves with interesting shape preserving properties. This construction requires the normalized B-basis of the space $U_4\left(I_{\alpha }\right)=\mathrm{span}\{1,cost,sint,cos2t,sin2t\}$ defined on...

Copula analysis was created to explain the dependence of two or more quantitative variables. Due to the need for in-depth data analysis involving complex variable relationships, there is always a need for new copula models with original features. As...

We construct one-frequency trigonometric spline curves with a de Boor-like algorithm for evaluation and analyze their shape-preserving properties. The convergence to quadratic B-spline curves is also analyzed. A fundamental tool is the concept of the...

Here, we study the extension of p-trigonometric functions $\mathrm{sinp}$ and $\mathrm{cosp}$ family in complex domains and p-hyperbolic functions $\mathrm{sinhp}$ and the $\mathrm{coshp}$ family in hyperbolic complex domains. These functions satisfy analogous relations as their classical coun...

The generalized trigonometric functions called Ateb-functions are considered. On this basis, a generalization of the Fourier transform is constructed and called the Ateb-transform. From the operator theory point of view, the Ateb-transform is conside...

We establish precise exponential tail estimates for lacunary trigonometric sums of the form $f_N\left(x\right)={\sum }_{k=1}^N{c}_k\cos \left(2\pi n_{k}x\right)$, under the Hadamard gap condition. Using cumulant expansions and moment-generating function techniques, we obtain non-asymptoti...

We establish new simple bounds for the quotients of inverse trigonometric and inverse hyperbolic functions such as $\frac{{sin}^{-1}x}{{sinh}^{-1}x}$ and $\frac{{tanh}^{-1}x}{{tan}^{-1}x}$. The main results provide polynomial bounds using even quadratic functions and...

Explicit links of the multivariate discrete (anti)symmetric cosine and sine transforms with the generalized dual-root lattice Fourier–Weyl transforms are constructed. Exact identities between the (anti)symmetric trigonometric functions and Weyl...

The choice of an appropriate regression model for econometric modeling minimizes information loss and also leads to sound inferences. In this study, we develop four quantile regression models based on trigonometric extensions of the unit generalized...

Many variations of the multiple zeta values have been found to play important roles in different branches of mathematics and theoretical physics in recent years, such as the cyclotomic/color version, which appears prominently in the computation of Fe...

Investigation of the generalized trigonometric and hyperbolic functions containing two parameters has been a very active research area over the last decade. We believe, however, that their monotonicity and convexity properties with respect to paramet...

Supersymmetric quantum mechanics has wide applications in physics. However, there are few potentials that can be solved exactly by supersymmetric quantum mechanics methods, so it is undoubtedly of great significance to find more potentials that can b...

The average deformed fiber is a continuous and smooth function of the fourth order. The deflection and rotation of beams can be determined by various methods available in the literature. Thus, in this paper, the expression of the average deformed fib...

This paper introduces a new approach for the fabrication of generalized developable cubic trigonometric Bézier (GDCT-Bézier) surfaces with shape parameters to address the fundamental issue of local surface shape adjustment. The GDCT-B&e...

In the present paper we study the generalized Hyers–Ulam stability of the generalized trigonometric functional equations $$f(xy)+\mu (y)f(x\sigma (y))=2f(x)g(y)+2h(y),x,y\in S;$$ $$f(xy)+\mathrm{\&mu}$$...

A novel category of convex functions, termed multiplicatively trigonometric convex functions, are introduced in this paper. We explore their algebraic characteristics and establish connections between such functions and other forms of convex function...

This paper presents the cubic trigonometric interpolation curves with two parameters generated over the space {1, sint, cost, sin²t, sin³t, cos³t}. The new curves can not only automatically interpolate the given data points without solving equation s...

Trigonometric B-spline curves with shape parameters are equally important and useful for modeling in Computer-Aided Geometric Design (CAGD) like classical B-spline curves. This paper introduces the cubic polynomial and rational cubic B-spline curves...

In modern computers, complicated signal processing is highly optimized with the use of compilers and high-speed processing using floating-point units (FPUs); therefore, programmers have little opportunity to care about each process. However, a highly...

The ruin probability is used to determine the overall operating risk of an insurance company. Modeling risks through the characteristics of the historical data of an insurance business, such as premium income, dividends and reinvestments, can usually...

This paper proposes a Hybrid Recursive Trigonometric (HRT) technique for FPGA-based direct digital frequency synthesizers. The HRT technique integrates a recursive cosine generator with periodic reinitialization via a second-order Taylor polynomial t...

This paper presents a novel recursive trigonometry (RT) technique for direct digital frequency synthesizer (DDFS) implementations. Traditional DDFS systems on field programmable gate arrays (FPGAs) either require a substantial amount of read-only mem...

In this paper, we establish two new inequalities of the Masjed Jamei type for inverse trigonometric and inverse hyperbolic functions and apply them to obtain some refinement and extension of Mitrinović–Adamović and Lazarević ineq...

This study presents a novel fifth-order unequal-sized trigonometric weighted essentially non-oscillatory (US-TWENO) scheme and a novel hybrid US-TWENO (HUS-TWENO) scheme with a novel troubled cell indicator in a finite difference framework to address...

The concept of linear Diophantine fuzzy set (LDFS) theory with its control parameters is a strong model for machine learning and data-driven multi-criteria decision making (MCDM). The sine-trigonometric function (STF) has two significant features, pe...

Despite being heavily used in the training of deep neural networks (DNNs), multipliers are resource-intensive and insufficient in many different scenarios. Previous discoveries have revealed the superiority when activation functions, such as the sigm...

This paper presents a second examination of trigonometric step sizes and their impact on Warm Restart Stochastic Gradient Descent (SGD), an essential optimization technique in deep learning. Building on prior work with cosine-based step sizes, this s...

Tidal open boundary conditions (OBCs) of the M₂ tidal constituent in the Bohai and Yellow Seas (BYS) are estimated via the assimilation of multi-satellite altimeter data to optimize regional tidal numerical simulation. A two-dimensional adjoint assim...

This paper’s main goal is to introduce left and right exponential trigonometric convex interval-valued mappings and to go over some of their important characteristics. Additionally, we demonstrate the Hermite–Hadamard inequality for inter...

The main objective of this paper is to construct the various shapes and font designing of curves and to describe the curvature by using parametric and geometric continuity constraints of generalized hybrid trigonometric Bézier (GHT-Bézi...

In the present work, a neotype chaotic product trigonometric map (PTM) system is proposed. We demonstrate the chaotic characteristics of a PTM system by using a series of complexity criteria, such as bifurcation diagrams, Lyapunov exponents, approxim...

For some highly nonlinear problems, the general second-order response surface method (RSM) cannot satisfy the accuracy requirement. To improve accuracy, the highest order number has to be determined in advance. Thus, a progressive trigonometric mixed...

This paper proposes a numerical method to obtain an approximation solution for the time-fractional Schrödinger Equation (TFSE) based on a combination of the cubic trigonometric B-spline collocation method and the Crank-Nicolson scheme. The fract...

This study is intended as a note and provides an extension to a much-used and established test for portfolio efficiency, the Gibbons, Ross, and Shanken GRS-Wald test. Tests devised to measure portfolio efficiency are crucial to the theoretical issues...

In this study, we research the univariate quantitative symmetrized approximation of complex-valued continuous functions on a compact interval by complex-valued symmetrized and perturbed neural network operators. These approximations are derived by es...