219 Results Found

Given the Yetter–Drinfeld category over any quasigroup and a braided Hopf coquasigroup in this category, we first mainly study the Radford’s biproduct corresponding to this braided Hopf coquasigroup. Then, we investigate Sweedler’s...

In this paper, a new non-linear recursive sequence is firstly introduced. Then, using this sequence, a computational problem involving the convolution of the Legendre polynomial is studied using the basic and combinatorial methods. Finally, we give a...

The main purpose of this paper is using the elementary and combinatorial methods to study the properties of the Catalan numbers, and give two new identities for them. In order to do this, we first introduce two new recursive sequences, then with the...

The aim of this paper is to research the structural properties of the Fibonacci polynomials and Fibonacci numbers and obtain some identities. To achieve this purpose, we first introduce a new second-order nonlinear recursive sequence. Then, we obtain...

This paper investigates D-finite discrete generating series and their sections. The concept of D-finiteness is extended to multidimensional discrete generating series and its equivalence to p-recursive sequences is rigorously established. It is furth...

In this paper, firstly, we introduced a second order non-linear recursive sequence, then we use this sequence and the combinatorial methods to perform a deep study on the computational problem concerning one kind sums, which includes the Chebyshev po...

For many complex industrial applications, traditional attribute reduction algorithms are often inefficient in obtaining optimal reducts that align with mechanistic analyses and practical production requirements. To solve this problem, we propose a re...

In this paper, the authors give a simple review of closed-form, explicit, and recursive formulas and related results for the nth derivative of the power-exponential function $x^x$, establish two closed-form and explicit formulas for partial Bell polynom...

In this work, we aim to study some qualitative properties of higher order nonlinear difference equations. Specifically, we investigate local as well as global stability and boundedness of solutions of this equation. In addition, we will provide solut...

In this paper, we introduce a fourth-order linear recursive sequence that is related to the concept of subbalancing numbers. This sequence is constructed by using the third balancing number in the Diophantine equation of subbalancing numbers and is c...

We investigate the multifractal geometry of irregular sets arising from weighted averages of random variables, where the weights $\left(w_n\right)$ form a positive sequence with exponential growth. Our analysis applies in particular to sequences generated by linea...

The factorization of groups into a Zappa–Szép product, or more generally into a k-fold Zappa–Szép product of its subgroups, is an interesting problem, since it eases the multiplication of two elements in a group and has rece...

In this paper, we investigate the dynamical behaviors of the rational difference equation $x_n=\left(a{x}_{n-1}\right)/\left(b+c{x}_n{x}_{n-1}\right)$ with arbitrary initial conditions, where a, b, and c are real numbers. A general solution is obtained. The asymptotic stabili...

We extend a technique recently introduced by Chen Zhuoyu and Qi Lan in order to find convolution formulas for second order linear recurrence polynomials generated by ${\left(\frac{1}{1+at+b{t}^2}\right)}^x.$ The case of generating functions containing...

Let $b$ be an odd number. By using elementary methods, we prove that: (1) When $x$ is an odd number and $y$ is an even number, the Diophantine equation $(2^x-1)(b^y-1)=$$2z^2$ has no positive integer solution except when $b$ is two special types of odd...

In this paper, we consider the solution and periodicity of the following systems of difference equations: $x_{n+1}={\displaystyle \frac{y_{n-2}}{-1+y_{n-2}{x}_{n-1}{y}_n}}$ , $y_{n+1}={\displaystyle \frac{x_{n-2}}{\pm 1\pm x_{n-2}{y}_{n-1}{x}_n}}$...

Signifiable computability aims to separate what is theoretically computable from what is computable through performable processes on computers with finite amounts of memory. Real numbers and sequences thereof, data types, and instances are treated as...

Background/Objectives: Head and neck squamous cell carcinoma (HNSCC) is a biologically heterogeneous malignancy with poor outcomes in advanced disease. Increasing evidence indicates that the tumor microenvironment, particularly cancer-associated fibr...

This paper looks into the dynamics of nonlinear systems of difference equations, with particular emphasis on fourth-order cases. Analytical solutions are derived for some cases of systems, a tedious task due to the lack of explicit mathematical techn...

The Ruler function or the Gros sequence is a classical infinite integer sequence that underlies some interesting mathematical problems. In this paper, we provide four new problems containing this type of sequence: (i) demographic discrete dynamical a...

The aim of this paper is to use elementary methods and the recursive properties of a special sequence to study the computational problem of one kind symmetric sums involving Fubini polynomials and Euler numbers, and give an interesting computational...

An algorithm for the symbolic computation of recursion operators for systems of nonlinear differential-difference equations (DDEs) is presented. Recursion operators allow one to generate an infinite sequence of generalized symmetries. The existence o...

This paper investigates nominal recursive modification (RM) in the L1 acquisition of French. Although recursion is considered the fundamental property of human languages, recursive self-embedding is found to be difficult for children in a variety of...

In this paper, a second-order nonlinear recursive sequence $M(h,i)$ is studied. By using this sequence, the properties of the power series, and the combinatorial methods, some interesting symmetry identities of the structural properties of...

In regression we can delete outliers based upon a preliminary estimator and re-estimate the parameters by least squares based upon the retained observations. We study the properties of an iteratively defined sequence of estimators based on this idea....

Recently a lot of papers have been devoted to partial infinite reciprocal sums of a higher-order linear recursive sequence. In this paper, we continue this program by finding a sequence which is asymptotically equivalent to partial infinite sums, inc...

We derive an algorithm to recursively determine the lap number (minimal number of monotonicity segments) of the iterates of twice differentiable l-modal map, enabling to numerically calculate the topological entropy of these maps. The algorithm is ob...

A data assimilation method to produce complete temporal sequences of synthetic medium-resolution images is presented. The method implements a Kalman filter recursive algorithm that integrates medium and moderate resolution imagery. To demonstrate the...

Higher-order symmetries are constructed for a linear anomalous diffusion equation with the Riemann–Liouville time-fractional derivative of order $\alpha \in (0,1)\cup (1,2)$. It is proved that the equation in question has infinite sequences of...

In this paper, we find the sequence of partial sums of the k-Fibonacci sequence, say, ${\displaystyle S_{k,n}=\sum _{j=1}^n{F}_{k,j}}$, and then we find the sequence of partial sums of this new sequence, ${\displaystyle S_{k,n}^{2)}=\sum _{j=1}^n{S}_{k,j}}$, and so on. The iterated partial sums of k-Fibonacci nu...

The main purpose of this paper is using the combinatorial method, the properties of the power series and characteristic roots to study the computational problem of the symmetric sums of a certain second-order linear recurrence sequences, and obtain s...

Accurate precipitation nowcasting is critical for many aspects of human life. A recurrent neural network (RNN) has demonstrated strong and relatively mature performance in machine learning approaches for precipitation nowcasting. However, their inher...

Brucellosis, also known as “undulant fever” is a zoonotic disease caused by Brucella, which is a facultative intracellular bacterium. Despite efforts to eradicate this disease, infection in uncontrolled domestic animals persists in severa...

Adaptive and evolutive software systems are characterized by ontologically defined non-determinism—not a defect but the primary force of their evolution. Non-determinism arises from recursion, interaction, and selection between abstract compone...

The Fibonacci sequence has broad applications in mathematics, where its inherent patterns and properties are utilized to solve various problems. The sequence often emerges in areas involving growth patterns, series, and recursive relationships. It is...

This paper explores connections between multidimensional continued fractions, specifically the Jacobi–Perron algorithm, and generalized Fibonacci and Lucas sequences of arbitrary order r. Recurrence relations are established, a sufficient crite...

Dissolved alumina concentration in the electrolyte cannot be measured continuously in aluminium reduction cells. Recursive soft sensing estimates the concentration from online process variables; however, process-condition shifts and the write-back of...

Preference optimisation improves helpfulness, but a single aggregate safety penalty lets frequent harm categories dominate the objective while rare ones bear the residual risk. This paper models post-training as a vector-constrained programme: the pa...

Aiming at the problem that sparse channel estimation in underwater acoustic communication is susceptible to complex multipath propagation, non-Gaussian impulsive noise, and channel time variations, this paper proposes a bidirectional proportionate re...

By drawing on the concepts of Jacobsthal polynomials, Jacobsthal–Lucas polynomials, and hybrid numbers, this paper constructs, for the first time, a novel class of mathematical objects with recursive properties—namely, the sequences of Ja...

Accurate state of charge (SOC) plays a vital role in battery management systems (BMSs). Among several developed SOC estimation methods, the extended Kalman filter (EKF) has been extensively applied. However, EKF cannot achieve valid estimation when t...

In this paper, we consider a company that wishes to determine the optimal reinsurance strategy minimising the total expected discounted amount of capital injections needed to prevent the ruin. The company’s surplus process is assumed to follow a Brow...

Image capture devices capture poor-quality images under low-light conditions, and the resulting images have dark areas due to insufficient exposure. Traditional Multiple Exposure Fusion (MEF) methods fuse images with different exposure levels from a...

In this paper, we prove recursive formulas for ultimate time survival probability when three random claims $X,Y,Z$ in the discrete time risk model occur in a special way. Namely, we suppose that claim X occurs at each moment of time $t\&$...

The classical Chow test for structural instability requires strictly exogenous regressors and a break-point specified in advance. In this paper, we consider two generalisations, the one-step recursive Chow test (based on the sequence of studentised r...

Let $1<a<b<c<d$ and ${\widehat{\alpha }}_{\left[5\right]}:={\left(1,\sqrt{a},\sqrt{b},\sqrt{c},\sqrt{d}\right)}^{\wedge }$ be a weighted sequence that is recursively generated by five weights $1,\sqrt{a},\sqrt{b},$ $\sqrt{c},\sqrt{d}$ . In this paper, we give suff...

We show that, for a primitive recursive function $h(\mathbf{x},t)$, where $\mathbf{x}$ is a n-tuple of natural numbers and t is a natural number, there exists a feedforward artificial neural network $\mathfrak{N}(\mathbf{x},t)$, such that for any n-tuple of natural numbers $\mathbf{z}$ and a positive nat...

Circular RNAs (circRNAs) are a novel class of non-coding RNA that, unlike linear RNAs, form a covalently closed loop without the 5′ and 3′ ends. Growing evidence shows that circular RNAs play important roles in life processes and have gre...

Instance segmentation of plant point clouds is challenging due to intricate structures, non-uniform density, and large intra-class variation. Conventional methods often suffer from blurred boundaries, instance adhesion, and insufficient coupling of s...

In this study, we present the application of a novel capillary electrophoresis (CE) method in combination with label-free quantitation and support vector machine-based feature selection (support vector machine-estimated recursive feature elimination...