Convergence Of Sequence Research Articles

Some Topological Properties on The Cartesian Product of Fuzzy b-Metric Space

The aim of this paper is to introduce the concept of the Cartesian product of two fuzzy b-metric spaces with related properties. We have introduced the property that the Cartesian product of two complete fuzzy b-metric spaces is a complete fuzzy b-metric space in terms of the product t-norm (.), as well as the minimum t-norm (Λ). The properties of convergent and Cauchy sequence are introduced by using this concept.

Analytical solution of time-fractional Emden-Fowler equations arising in astronomy and mathematical physics

The time-fractional Emden-Fowler model is an interesting mathematical model because it is widely used and important in mathematics and applied sciences. The current investigation compiles the Elzaki transform homotopy perturbation method (ET-HPM) and the Laplace transform homotopy perturbation method (LT-HPM) for the analytical solution of the considered model. In their developments, we show that fractional orders are simple to compute, and the resulting series lead to accurate results after a few iterations. We consider the fractional orders in the context of the Caputo form. The primary aim of these approaches is to compare the analytical results of the models under consideration. These schemes do not impose any constraints on the parameters or make any assumptions that could complicate the process of obtaining the analytical results. We show that the derived outcomes are in convergent sequence with a rapid iterative formula. The iterative series and the graphical illustrations in various fractional orders confirm the efficiency of the proposed approaches. The derived results are also compared to the precise solutions, which show that our suggested approaches are simple, effective, and accurate.

Existence of normalized solutions for a fractional Kirchhoff system

In this paper, we investigate the following fractional Kirchhoff system in R N : { ( 1 + b ∫ R N | ( − Δ ) s 2 u | 2 d x ) ( − Δ ) s u + V 1 ( x ) u + λ 1 u = μ 1 | u | p 1 − 2 u + r 1 β | u | r 1 − 2 u | v | r 2 , ( 1 + b ∫ R N | ( − Δ ) s 2 v | 2 d x ) ( − Δ ) s v + V 2 ( x ) v + λ 2 v = μ 2 | v | p 2 − 2 v + r 2 β | u | r 1 | v | r 2 − 2 v , under the constraints ∫ R N | u | 2 d x = a 1 2 , ∫ R N | v | 2 d x = a 2 2 , where 0<s<1, 2s<N<4s, b, μ 1 , μ 2 , β are all positive numbers and r 1 , r 2 ≥ 1 . V 1 ( x ) , V 2 ( x ) ≥ 0 are the potential functions and a 1 , 0 $ ]]> a 2 > 0 are prescribed constants. In L 2 -critical case, we first obtain the existence of non-negative solutions through a constrained minimization problem. Then under some further assumptions on r i and V i ( x ) for i = 1, 2, we conclude the solution is Hölder continuous and decays like | x | − ( N + 2 s ) at infinity. Finally, the positivity of solutions is verified. In L 2 -supercritical case, the normalized solutions are obtained by a minimax theorem. Precisely, the theorem allows us to obtain a bounded Palais-Smale sequence satisfying the Pohozaev identity in limit sense. Further, the signs of Lagrange multipliers are determined to ensure the strong convergence of the approximate critical point sequence in H s × H s .

DIFFERENCE DOUBLE SEQUENCES OF BI-COMPLEX NUMBERS

In this article, we have introduced the notion of convergence of difference double sequences in Pringsheim’s sense, difference null in Pringsheim’s sense, bounded difference, bounded convergence differ ence, bounded null difference, regular convergence difference and reg ular null difference double sequences of bi-complex numbers. We have proved that these are linear spaces. With the help of the Euclidean norm defined on bi-complex numbers, we have established their differ ent algebraic and topological properties, as well as some of their geo metric properties. Suitable examples have been discussed to support the introduction of these classes of sequences and during the investi gation of their properties for failure cases.

Some Results on Neutrosophic I-Statistically Convergence

This paper introduces the neutrosophic -statistical convergent difference sequence spaces defined through a modulus function. Additionally, we establish new topological spaces and examine various topological properties within these neutrosophic -statistical convergent difference sequence spaces.

A New Structure of Random Approach Normed Space via Banach Space

The goal of this research is to define the convergent sequence in A-random approach space and sequentially convergent are discussed and the cluster point, open and closed ball and linear transformation. We are going to explain a new structure of Random approach normed space via Banach space in and discussed all the relations between metric space in this research.

Hyperspaces of the double arrow

Let A and S denote the double arrow of Alexandroff and the Sorgenfrey line, respectively. We show that for any n≥1, the space of all unions of at most n closed intervals of A is not homogeneous. We also prove that the spaces of non-trivial convergent sequences of A and S are homogeneous. This partially solves an open question of A. Arhangel'skiǐ [1]. In contrast, we show that the space of closed intervals of S is homogeneous.

Two remarks on properties of functions of bounded variation

In terms of variations, a sufficient condition for the uniform convergence of sequences of continuous functions is proved. Using this result, we obtain an addition to the classical Helly theorem on the selection of convergent sequences of functions with uniformly bounded variations in the case when the limit function is continuous. Also, by using an example we show that the condition of continuous differentiability of a function, ensuring the differentiability of its variation with the variable upper limit, is in a certain sense sharp.

On the Generalized Weighted Statistical Convergence

Statistical convergence and summability represent a significant generalization of traditional convergence for sequences of real or complex values, allowing for a broader interpretation of convergence phenomena. This concept has been extensively examined by numerous researchers using various mathematical tools and applied to different mathematical structures over time, revealing its relevance across multiple disciplines. In the present study, a generalized definition of the concepts of statistical convergence and summability, termed (△_v^m )_u-generalized weighted statistical convergence and (△_v^m )_u-generalized weighted by [¯N_t ]-summability for real sequences, is introduced using the weighted density and generalized difference operator. Based on this definition, several fundamental properties and inclusion results, obtained by differentiating the components used in the definitions, are provided.

Analisis Kemampuan Mahasiswa Matematika FMIPA Unimed dalam Menyelesaikan Permasalahan Konvergensi dan Divergensi Barisan Bilangan Real dengan Berbantuan Software MATLAB

This research aims to analyze the ability of FMIPA Mathematics students at Medan State University (Unimed) in solving problems of convergence and divergence of real number sequences, as well as evaluating the effectiveness of using MATLAB software in supporting understanding of these concepts. This research is based on the aim of overcoming students' difficulties in understanding the concepts of convergence and divergence. The research method used was qualitative, with a sample of 20 students selected using purposive sampling. Data was collected through written tests and observations of the use of MATLAB which were distributed via Google Form in solving questions. The results show that 55% of students are in the "very understanding" category, with MATLAB proving to be very effective in making problem solving easier and deepening understanding.

Applications of Strongly Deferred Weighted Convergence in the Environment of Uncertainty

In the context of uncertainty theory, we present strongly deferred weighted convergence of complex uncertain sequences. Also, we introduce strongly deferred weighted convergence of complex uncertain sequences in all five aspects of uncertainty, that is through almost surely, mean, measure, distribution and uniformly almost surely. Further, with the aid of interesting examples and diagram we investigate some interrelationships among these complex uncertain sequences.

Sifat Kekonvergenan Lemah pada Ruang Bernorma beserta Operator pada Ruang Barisan Konvergen Lemah

The concept of weak convergence is generated by “weakening” the existing convergence properties in normed spaces. The outcome of this article is to prove the basic properties of weak convergence, the space of weakly convergent sequence is a Banach space and the operators from the space of weakly convergent sequence to other sequence spaces (l1(X),lp(X), linfty(X),S(X) ) and vice versa are linear and bounded .

On dual Kadec norms

Let (X,‖⋅‖) be a Banach space such that all w⁎-convergent sequences in the dual unit sphere SX⁎ are also norm convergent. Then the weak⁎ and norm topologies agree on SX⁎. By known results it implies that X has a renorming whose dual is locally uniformly rotund, hence also C1-Fréchet smooth. In particular, X is an Asplund space. Our results also lend an alternative proof of the celebrated Josefson-Nissenzweig theorem.

Equilibria in matching markets with soft and hard liquidity constraints

We consider a one-to-one matching with contracts model in the presence of liquidity constraints on the buyer's side. Liquidity constraints can be either soft or hard. Competitive equilibria do exist in economies with soft liquidity constraints, but not necessarily in the presence of hard liquidity constraints. The limit of a convergent sequence of competitive equilibria in economies with increasingly stringent soft liquidity constraints may fail to be a competitive equilibrium in the limit economy with hard liquidity constraints. We establish equivalence and existence results for two alternative notions of competitive equilibrium, quantity-constrained competitive equilibrium and expectational equilibrium, together with stable outcomes and core outcomes, in economies with both types of liquidity constraints. We argue that these notions of equilibrium and stability do not suffer from discontinuity problems by showing appropriate limit results.

Wind farm cluster power prediction based on graph deviation attention network with learnable graph structure and dynamic error correction during load peak and valley periods

The power prediction accuracy of wind farm cluster (WFC) seriously affects its consumption and the safe and stable operation of power system. The fluctuation of power between wind farms (WFs) significantly affects the wind power ultra-short-term prediction (WPUP) accuracy of WFC. In this regard, this paper proposes a graph deviation attention network (GDAN) considering improved clustering distance and learnable graph structure (LGS) for predicting and correcting the wind power of WFC. And used a weighted distance function combining sequence convergence smoothing effect and correlation to dynamically divide the WFC, and to learn and construct the graph structure. Proposed the GDAN with LGS to mine the convergence correlation of WF sub-clusters and establish power prediction model. Considering the characteristics of load peak and valley periods (LPVP), introduced a power correction coefficient to reduce the error, and used the successive variational mode decomposition (SVMD) to extract its key components to achieve power prediction and correction. The proposed method is applied to the WFC in Western Inner Mongolia, China. Compared with the comparison model before correction, the RMSE, MAE and MAPE are reduced by 4.27 %, 3.55 % and 17.92 % respectively, and the R2 and Pr are increased by 11.87 % and 9.88 % respectively.

Bregman Proximal Linearized ADMM for Minimizing Separable Sums Coupled by a Difference of Functions

AbstractIn this paper, we develop a splitting algorithm incorporating Bregman distances to solve a broad class of linearly constrained composite optimization problems, whose objective function is the separable sum of possibly nonconvex nonsmooth functions and a smooth function, coupled by a difference of functions. This structure encapsulates numerous significant nonconvex and nonsmooth optimization problems in the current literature including the linearly constrained difference-of-convex problems. Relying on the successive linearization and alternating direction method of multipliers (ADMM), the proposed algorithm exhibits the global subsequential convergence to a stationary point of the underlying problem. We also establish the convergence of the full sequence generated by our algorithm under the Kurdyka–Łojasiewicz property and some mild assumptions. The efficiency of the proposed algorithm is tested on a robust principal component analysis problem and a nonconvex optimal power flow problem.

Prevalence and Detection of the Toxoplasma gondii by serological technique and making a phylogenetic in pregnant women

The study intended to inspect the prevalence of the infection in pregnant woman (Toxoplasma gondii acute and chronic stage of parasite) by rapid test and making a genetic tree after analyzing number of samples with PCR technique. This study integrated (100) blood samples taken from pregnant women in Baghdad Governorate from private laboratories and hospitals and also five uninfected samples were considered as the control group during the period of this study. The results showed that the total infected (rapid test) had a ratio of totally 27. %, acute (8 %) and chronic 19% as per table 1 in pregnant women at (p&lt;0.05) level. The parasite was PCR analysis diagnosed sample and worked in PCR product samples for sequencing analysis. It used a program Mega 6 for making a tree for this parasite and comparing to other countries for the same parasite, this program shows the mutations and convergence of the genetic sequence found in Iraq. The genotypes of this parasite were determined by the symmetry and compared to the blast analysis, showing positive examination from all samples (Toxoplasma gondii) from different hospital in Iraq.

A nested primal–dual iterated Tikhonov method for regularized convex optimization

AbstractProximal–gradient methods are widely employed tools in imaging that can be accelerated by adopting variable metrics and/or extrapolation steps. One crucial issue is the inexact computation of the proximal operator, often implemented through a nested primal–dual solver, which represents the main computational bottleneck whenever an increasing accuracy in the computation is required. In this paper, we propose a nested primal–dual method for the efficient solution of regularized convex optimization problems. Our proposed method approximates a variable metric proximal–gradient step with extrapolation by performing a prefixed number of primal–dual iterates, while adjusting the steplength parameter through an appropriate backtracking procedure. Choosing a prefixed number of inner iterations allows the algorithm to keep the computational cost per iteration low. We prove the convergence of the iterates sequence towards a solution of the problem, under a relaxed monotonicity assumption on the scaling matrices and a shrinking condition on the extrapolation parameters. Furthermore, we investigate the numerical performance of our proposed method by equipping it with a scaling matrix inspired by the Iterated Tikhonov method. The numerical results show that the combination of such scaling matrices and Nesterov-like extrapolation parameters yields an effective acceleration towards the solution of the problem.

Further remarks on absorbing Markov decision processes

In this note, based on the recent remarkable results of Dufour and Prieto-Rumeau, we deduce that for an absorbing Markov decision process with a given initial state, under a standard compactness-continuity condition, the space of occupation measures has the same convergent sequences, when it is endowed with the weak topology and with the weak-strong topology. We provided two examples demonstrating that imposed condition cannot be replaced with its popular alternative, and the above assertion does not hold for the space of marginals of occupation measures on the state space. Moreover, the examples also clarify some results in the previous literature.

A modified inertial proximal minimization algorithm for structured nonconvex and nonsmooth problem

We introduce an enhanced inertial proximal minimization algorithm tailored for a category of structured nonconvex and nonsmooth optimization problems. The objective function in question is an aggregation of a smooth function with an associated linear operator, a nonsmooth function dependent on an independent variable, and a mixed function involving two variables. Throughout the iterative procedure, parameters are selected employing a straightforward approach, and weak inertial terms are incorporated into two subproblems within the update sequence. Under a set of lenient conditions, we demonstrate that the sequence engendered by our algorithm is bounded. Furthermore, we establish the global and strong convergence of the algorithmic sequence, contingent upon the assumption that the principal function adheres to the Kurdyka–Łojasiewicz (KL) property. Ultimately, the numerical outcomes corroborate the algorithm’s feasibility and efficacy.