This article deals with the general linearization problem of Jacobi polynomials. We provide two approaches for finding closed analytical forms of the linearization coefficients of these polynomials. The first approach is built on establishing a new f...
This paper investigates a class of Jacobsthal-type polynomials (JTPs) that involves one parameter. We present several new formulas for these polynomials, including expressions for their derivatives, moments, and linearization formulas. The key idea b...
The principal objective of this article is to develop new formulas of the so-called Chebyshev polynomials of the fifth-kind. Some fundamental properties and relations concerned with these polynomials are proposed. New moments formulas of these polyno...
This paper introduces new formulas for non-symmetric Jacobi polynomials of specific parameters, focusing specifically on the subclasses where the difference between the two parameters of Jacobi polynomials is two or three. First, several key expressi...
This paper investigates certain Jacobi polynomials that involve one parameter and generalize the well-known orthogonal polynomials called Chebyshev polynomials of the third-kind. Some new formulas are developed for these polynomials. We will show tha...
This work delves deeply into convolved Fibonacci polynomials (CFPs) that are considered generalizations of the standard Fibonacci polynomials. We present new formulas for these polynomials. An expression for the repeated integrals of the CFPs in term...
We present a novel proof, using group theory, for a Meijer transform formula. This proof reveals the formula as a specific case of a broader generalized result. The generalization is achieved through a linear operator that intertwines two representat...
A Riemannian manifold endowed with
In this paper, new formulas for the Fibonacci polynomials, including high-order derivatives and repeated integrals of them, are derived in terms of the polynomials themselves. The results are then used to solve connection problems between the Fibonac...
This paper explores the Schröder polynomials, a class of polynomials that produce the famous Schröder numbers when
In this article, we present new theoretical findings on specific polynomials that generalize the concept of telephone numbers, namely, Telephone polynomials (TelPs). Several new formulas are developed, including expressions for higher-order derivativ...
Upon ligand binding or during chemical reactions the state of a molecular system changes in time. Usually we consider a finite set of (macro-) states of the system (e.g., ‘bound’ vs. ‘unbound’), although the process itself takes place in a continuous...
In this contribution, we first present a new recursion relation fulfilled by the linearization coefficients of Bessel polynomials (LCBPs), which is different than the one presented by Berg and Vignat in 2008. We will explain why this new recursion fo...
Computed X-ray tomography (CT), together with pulse and pressure decay permeability methods were used to evaluate a formula for absolute reservoir permeability. For this reason, 62 core samples representing geological material of tight, gas-bearing s...
A very recent article delved into and expanded the four parametric linear Euler sums, revealing that two well-established subjects—Euler sums and series involving the zeta functions—display particular correlations. In this study, we prese...
The connectivity index χ can be regarded as the sum of bond contributions. Inthis article, boiling point (bp)-oriented contributions for each kind of bond are obtainedby decomposing the connectivity indices into ten connectivity character bases and t...
This paper establishes symmetric inequalities for the reciprocal sums of Fibonacci numbers. By using elementary methods, recurrence properties, Cassini’s identity, and the Fibonacci–Lucas connection, we deduce the precise bounds for these...
The object of investigation in this paper is a scalar linear fractional differential equation with generalized proportional derivative of Riemann–Liouville type (LFDEGD). The main goal is the obtaining an explicit solution of the initial value proble...
Let
Energy auctions are commonly used to contract energy projects and are extensively studied from the regulator’s perspective. However, analyzing auctions from the stakeholders’ perspective is critical to determine the impact of regulatory d...
In this paper, we discuss several shift retrieval problems, both classical and compressed, and provide connections between them using the general framework of circulant matrices. We review the properties of circulant matrices necessary for our calcul...
During the water injection development process of highly deviated wells in low-permeability reservoirs, the water flooding distance between different layers of the same oil and water well is different due to the deviation of the well. In addition, th...
This paper explains the mathematical foundations of a method for modelling semi-rigid unions. The unions are modelled using rotational rather than linear springs. A nonlinear second-order analysis is required, which includes both the effects of the f...
In this study, we define a new family of Gaussian polynomials, called Gaussian Chebyshev polynomials, by extending classical Chebyshev polynomials into the complex domain. These polynomials are characterized by second-order linear recurrence relation...
In this paper, we establish new hypergeometric representations for two classical integer sequences, namely the Pell and Jacobsthal sequences. Motivated by Dilcher’s hypergeometric formulations of the Fibonacci sequence, we extend this framework...
The present work highlights a new general method devoted to computations of the clamped linear electro-optical coefficients from the measured fundamental vibrational frequencies and the nonlinear dielectric susceptibility constants. The calculations...
Correlation in cyber risk represents an additional source of concern for utility and industrial infrastructures, where risks may be introduced by connected systems. A major means of reducing risk is to transfer it through insurance. In this paper, we...
This paper investigates a class of nonlinear rational difference equations with delayed terms, which often arise in various mathematical models. We analyze the iterative behavior of these rational functions and show how their iterations can be repres...
While synchronization in the brain neural networks has been studied, the emergency of the main oscillation frequency and its evolution at different normal and pathological states remains poorly investigated. We propose a new concept of the formation...
Complexity (number of spanning trees) is an essential and significant component in the design of communication networks (graphs). To ensure strong resistance and stiffness and to enhance the probability of a connection between two vertices, improveme...
In this paper, a simple and effective numerical approach is presented on the basis of the Member Discrete Element Method (MDEM) to investigate static and dynamic responses of steel frames with semi-rigid joints. In the MDEM, structures are discretize...
Since head-related transfer functions (HRTFs) represent the interactions between sounds and physiological structures of listeners, anthropometric parameters represent a straightforward way to customize (or predict) individualized HRTFs. This paper pr...
It is well known that the conformable and the symmetric differential operators have formulas in terms of the first derivative. In this document, we combine the two definitions to get the symmetric conformable derivative operator (SCDO). The purpose o...
The article considers a non-stationary three-dimensional spatial mathematical model of biological kinetics and geochemical processes with nonlinear coefficients and source functions. Often, the step of analytical study in models of this kind is skipp...
For a nonnegative integer p, we give explicit formulas for the p-Frobenius number and the p-genus of generalized Fibonacci numerical semigroups. Here, the p-numerical semigroup
A binary, three-dimensional (3D), foldable, Metal–Organic Framework (MOF) of formula {[trans-Ni(H2O)2(μ-4,4′-bpy)2](ClO4)2}n (1), with CdSO4 (65 8), cds, topology, based on four-connected (4-c) square-planar single Ni2+ ion nodes and t...
Due to the limitations of processing errors, test conditions and other factors, geometric similarity errors in scale tests of steel structure joints are difficult to avoid, but the research on this error is little known. Based on the similarity theor...
The universal hinge support (UHS) is a new connection system for the tower and pier of a single-tower cable-stayed bridge (STCSB), which could conform the multi-direction rotation of the tower and release the bending moment at the bottom of the tower...
In this paper, the
This study addresses the challenges of setting segmentation points in the membership function and determining appropriate weights for different types of information within a fuzzy logic algorithm for map matching. We use linear fitting to derive an e...
In this paper we consider the problem of an insurance company where the wealth of the insurer is described by a Cramér-Lundberg process. The insurer is allowed to invest in a risky asset with stochastic volatility subject to the influence of an econo...
Designing antennas for vehicular communication systems presents several unique challenges due to the dynamic nature of vehicular environments, mobility, and the need for reliable connectivity. A wider bandwidth is a critical requirement of vehicular...
Microseismic monitoring systems (MMS) have become increasingly crucial in detecting tremors in coal mining. Microseismic sensors (MS), integral components of MMS, profoundly influence positioning accuracy and energy calculations. Hence, calibrating t...
Laminated bamboo (LB) has shown enough exceptional performance to be used in constructions, but the performance of the bolted connections remains to be explored. To meet the criteria of low-carbon construction and fill the research gap in LB dowel em...
To reduce the cast in place work of concrete and realize the industrial production of a bamboo–concrete composite (BCC), innovative connection systems composed of an assembled bamboo–lightweight concrete composite (ABLCC) structure featur...
Hybrid grid-connected renewable energy systems have gained significant importance in sustainably responding to an increased electrical energy demand. These are time-varying nonlinear dynamical plants, where the value of their parameters depends on ch...
This research examines the structural and magnetic properties of monodomain cobalt ferrite nanoparticles with the formula (Co1−xFex)A[Fe2−xCox]BO4. The particles were synthesized using various methods, including coprecipitation (with and...
This paper presents a comprehensive introduction and systematic derivation of the evolutionary equations for absolute entropy H and relative entropy D, some of which exist sporadically in the literature in different forms under different subjects, wi...
The shear connector of a steel composite bridge is designed by predicting fatigue life using the fatigue strength curves (S-N curve) based on push-out test results. The fatigue strength curves of the current design codes present only a linear relatio...
28 September 2022
In this work, we describe the synthesis, crystal structure and magnetic properties of the neutral hexacopper(II) complex of formula {[Cubpca)]2[Cu(dmopba)(H2O)]}2·4H2O (1), where Hbpca = bis(2-pyridylcarbonyl)-amide and dmopba = 4,5-dimethyl-1...
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