INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES最新文献

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Investigation of Magnetized Casson Nanofluid Flow along Wedge: Gaussian Process Regression 磁化卡松纳米流体沿楔形流的研究：高斯过程回归

IF 1.2 Q1 MATHEMATICS

INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES

Pub Date : 2024-01-08 DOI: 10.1155/2024/2880748

M. Shanmugapriya, R. Sundareswaran, S. G. K. Subramanian, A. Alameri

An unsteady two-dimensional magnetized Casson nanofluid flow model is constructed over a wedge under the effect of thermal radiation and chemical reaction. The multiple slip effects are also assumed near the surface of the wedge along with the convective boundary restrictions. This study investigates the application of soft computing techniques to address the challenges posed by the complexity of problem modeling and numerical methods. Traditional approaches incorporating various model factors may struggle to provide accurate solutions. To resolve this issue, Gaussian process regression (GPR) is employed to predict the solution of the proposed flow model. With the help of the numerical shooting method together with Runge–Kutta–Fehlberg fourth-fifth-order (RKF-45) reference data, the GPR model is trained. The numerical simulation illustrated that the Casson fluid parameter β and the unsteadiness parameter S strengthen the friction factor, and the heat transfer rate is enhanced as the radiation parameter Rd becomes larger. In addition, the Biot numbers Bi1 & Bi2 lead to strengthen nanoparticle temperature; an opposite behavior is noticed with the skin friction coefficient S˜fxRex0.5, heat transfer rate H˜tx Rex0.5, and nanoparticle transfer rate C˜txRex0.5. The GPR model with the exponential Kernel function provided better performance than other functions on both training and checking datasets to predict S˜fxRex0.5,H˜tx Rex0.5, and C˜txRex0.5. Statistical metrics including RMSE, MAE, MAPE, MSE, R2, and R are employed to check the accuracy and convergences of the predicted and numerical solutions obtained through GPR and RKF-45. It is observed that all three GPR models had an R2 value of higher than 0.9. The proposed study demonstrates the advantages of employing soft computing methods (GPR) to effectively analyse the behavior of complex flow models.

在热辐射和化学反应的作用下，构建了楔形上的非稳态二维磁化卡松纳米流体流动模型。在楔形表面附近还假设了多重滑移效应以及对流边界限制。本研究探讨了软计算技术的应用，以应对问题建模和数值方法的复杂性所带来的挑战。包含各种模型因素的传统方法可能难以提供精确的解决方案。为解决这一问题，采用了高斯过程回归（GPR）来预测所提出的流动模型的解。在数值射击法和 Runge-Kutta-Fehlberg 四阶-五阶 (RKF-45) 参考数据的帮助下，对 GPR 模型进行了训练。数值模拟结果表明，卡松流体参数 β 和不稳定性参数 S 可增强摩擦因数，辐射参数 Rd 越大，传热速率越高。此外，Biot 数 Bi1 和 Bi2 会使纳米粒子温度升高；而皮肤摩擦系数 S˜fxRex0.5、传热速率 H˜txRex0.5 和纳米粒子传热速率 C˜txRex0.5 则与之相反。在预测 S˜fxRex0.5、H˜tx Rex0.5 和 C˜txRex0.5 时，使用指数核函数的 GPR 模型在训练数据集和检验数据集上的性能均优于其他函数。采用 RMSE、MAE、MAPE、MSE、R2 和 R 等统计指标来检查通过 GPR 和 RKF-45 获得的预测解和数值解的准确性和收敛性。结果表明，所有三个 GPR 模型的 R2 值均高于 0.9。拟议的研究证明了采用软计算方法（GPR）有效分析复杂流动模型行为的优势。

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引用次数: 0

Horadam Polynomials and a Class of Biunivalent Functions Defined by Ruscheweyh Operator 霍拉达姆多项式和一类由 Ruscheweyh 算子定义的双等价函数

IF 1.2 Q1 MATHEMATICS

INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES

Pub Date : 2023-12-29 DOI: 10.1155/2023/2573044

Waleed Al-Rawashdeh

In this paper, we introduce and investigate a class of biunivalent functions, denoted by Hn,r,α, that depends on the Ruscheweyh operator and defined by means of Horadam polynomials. For functions in this class, we derive the estimations for the initial Taylor–Maclaurin coefficients a2 and a3. Moreover, we obtain the classical Fekete–Szegö inequality of functions belonging to this class.

在本文中，我们介绍并研究了一类双等价函数，用 Hn,r,α 表示，它依赖于 Ruscheweyh 算子，并通过霍拉达姆多项式定义。对于该类函数，我们得出了初始泰勒-麦克劳林系数 a2 和 a3 的估计值。此外，我们还得到了属于这一类函数的经典费克特-塞戈不等式。

引用次数: 0

The Fuzzy Prime Spectrum of Partially Ordered Sets 部分有序集合的模糊质谱

IF 1.2 Q1 MATHEMATICS

INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES

Pub Date : 2023-12-15 DOI: 10.1155/2023/4526348

Derso Abeje Engidaw, Gezahagne Mulat Addis, Wondwosen Zemene Norahun, Dereje Kifle Boku, Habtu Bayafers Demrew, T. Degefa

We study the space of prime fuzzy ideals (and the space of maximal fuzzy ideals as a subspace) equipped with the hull-kernel topology in partially ordered sets. Mainly, we investigate the conditions for which the fuzzy prime spectrum of a poset is compact, Hausdorff, and normal, respectively.

我们研究了部分有序集合中带有赫尔核拓扑的素模糊理想空间（以及作为子空间的最大模糊理想空间）。我们主要研究了正集的模糊素谱分别是紧凑的、豪斯多夫的和正态的条件。

引用次数: 0

Improved Finite Difference Technique via Adomian Polynomial to Solve the Coupled Drinfeld’s–Sokolov–Wilson System 通过阿多米亚多项式改进有限差分技术求解德林菲尔德-索科洛夫-威尔逊耦合系统

IF 1.2 Q1 MATHEMATICS

INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES

Pub Date : 2023-12-06 DOI: 10.1155/2023/6916596

Israa Th. Younis, Ekhlass S. Al-Rawi

This study presents a new algorithm for effectively solving the nonlinear coupled Drinfeld’s–Sokolov–Wilson (DSW) system using a hybrid explicit finite difference technique with the Adomian polynomial (EFD-AP). The suggested approach addresses the problem of accurately solving the DSW system. Numerical results are obtained by comparing the exact solution with absolute and mean square errors using a test problem to assess the EFD-AP accuracy against the exact solution and the conventional explicit finite difference (EFD) method. The results exhibit excellent agreement between the approximate and exact solutions at different time values, and the results showed that the proposed EFD-AP method achieves superior accuracy and efficiency compared to the EFD method, which makes it a promising method for solving nonlinear partial differential systems of higher order.

本文提出了一种利用Adomian多项式混合显式有限差分技术有效求解非线性耦合Drinfeld - sokolov - wilson (DSW)系统的新算法。该方法解决了DSW系统的精确求解问题。通过一个测试问题，将精确解与绝对误差和均方误差进行比较，以评估EFD- ap与精确解和传统显式有限差分(EFD)方法的精度，从而获得数值结果。结果表明，该方法在求解高阶非线性偏微分系统时具有较好的精度和效率，是一种很有前途的求解方法。

引用次数: 0

On Properties of Graded Rings with respect to Group Homomorphisms 论分级环关于群同态的性质

IF 1.2 Q1 MATHEMATICS

INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES

Pub Date : 2023-11-15 DOI: 10.1155/2023/3803873

A. Alshehry, R. Abu-Dawwas, Muhsen Al-Bashayreh

Let <math xmlns="http://www.w3.org/1998/Math/MathML" id="M1"> <mi>G</mi> </math> be a group and <math xmlns="http://www.w3.org/1998/Math/MathML" id="M2"> <mi>R</mi> </math> be a <math xmlns="http://www.w3.org/1998/Math/MathML" id="M3"> <mi>G</mi> </math> -graded ring with non-zero unity. The goal of our article is reconsidering some well-known concepts on graded rings using a group homomorphism <math xmlns="http://www.w3.org/1998/Math/MathML" id="M4"> <mi>α</mi> <mo>:</mo> <mi>G</mi> <mo>⟶</mo> <mi>G</mi> </math> . Next is to examine the new concepts compared to the known concepts. For example, it is known that <math xmlns="http://www.w3.org/1998/Math/MathML" id="M5"> <mfenced open="(" close=")" separators="|"> <mrow> <mi>R</mi> <mo>,</mo> <mi>G</mi> </mrow> </mfenced> </math> is weak if whenever <math xmlns="http://www.w3.org/1998/Math/MathML" id="M6"> <mi>g</mi> <mo>∈</mo> <mi>G</mi> </math> such that <math xmlns="http://www.w3.org/1998/Math/MathML" id="M7"> <msub> <mrow> <mi>R</mi> </mrow> <mrow> <mi>g</mi> </mrow> </msub> <mo>=</mo> <mn>0</mn> </math> , then <math xmlns="http://www.w3.org/1998/Math/MathML" id="M8"> <msub> <mrow> <mi>R</mi> </mrow> <mrow> <msup> <mrow> <mi>g</mi> </mrow>

同样，我们建立并研究了 α 非退化环、α 规则环、α 强环、α 第一强级环和α 弱交叉积的概念。

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引用次数: 0

Some Inequalities Involving the Derivative of Rational Functions 涉及有理函数导数的几个不等式

Q1 MATHEMATICS

INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES

Pub Date : 2023-10-11 DOI: 10.1155/2023/5541585

Arnisa Rasri, Jiraphorn Somsuwan Phanwan

In this paper, we establish some inequalities involving the modulus of the derivative of rational functions with prescribed poles and restricted zeros. The obtained results generalize some known inequalities for rational functions. Moreover, our results also contain certain known polynomial inequalities.

本文建立了具有规定极点和限制零点的有理函数导数的模的几个不等式。所得结果推广了有理函数的一些已知不等式。此外，我们的结果还包含某些已知的多项式不等式。

引用次数: 0

Censoring Balancing Functions for Undetected Probably Significant Effects in Cox Regression Cox回归中未检测到的可能显著效应的审查平衡函数

Q1 MATHEMATICS

INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES

Pub Date : 2023-09-26 DOI: 10.1155/2023/6676767

Ildephonse Nizeyimana, George Otieno Orwa, Michael Arthur Ofori, Samuel Musili Mwalili

Weighted Cox regression models were proposed as an alternative to the standard Cox proportional hazards models where consistent estimators can be obtained with more relative strength compared to unweighted cases. We proposed censoring balancing functions which can be built in a way that allows us to obtain the maximum possible significant treatment effects that may have gone undetected due to censoring. The harm caused by this is compensated and new weighted parameter estimates are found. These functions are constructed to be monotonic because even the hazard ratios are not exactly constant as in the ideal case, but are violated by monotonic deviations in time. For more than one covariate, even the interaction between covariates in addition to censoring can lead to the loss of significance for some covariates’ effects. Undetected significant effects of one covariate can be obtained, still keeping the significance and approximate size of the remaining one(s). This is performed by keeping the consistency of the parameter estimates. The results from both the simulated datasets and their application to real datasets supported the importance of the suggested censoring balancing functions in both one covariate and more than one covariate cases.

加权Cox回归模型被提出作为标准Cox比例风险模型的替代方案，与未加权的情况相比，可以获得相对强度更高的一致估计。我们提出了审查平衡功能，该功能可以通过一种方式构建，使我们能够获得最大可能的显著处理效果，这些效果可能由于审查而未被发现。对由此造成的危害进行了补偿，并找到了新的加权参数估计。这些函数被构造为单调的，因为即使是风险比也不像在理想情况下那样完全恒定，而是被时间上的单调偏差所违背。对于一个以上的协变量，即使是协变量之间的相互作用，除了审查之外，也会导致一些协变量的影响失去显著性。可以获得一个协变量未检测到的显著效应，但仍然保持其余协变量的显著性和近似大小。这是通过保持参数估计的一致性来实现的。模拟数据集的结果及其在实际数据集上的应用支持了所建议的审查平衡函数在单协变量和多协变量情况下的重要性。

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引用次数: 0

On Parametric and Matrix Solutions to the Diophantine Equation

x^{2} + d y^{2} - z^{2} = 0

Where

d

Is a … Diophantine方程x 2 + d y 2−z 2 = 0的参数解和矩阵解

Q1 MATHEMATICS

INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES

Pub Date : 2023-09-25 DOI: 10.1155/2023/1505337

James D. Shaw, James Guyker

The well‐known matrix‐generated tree structure for Pythagorean triplets is extended to the primitive solutions of the Diophantine equation

x^{2} + d y^{2} - z^{2} = 0

where

d

is a positive square‐free integer. The proof is based on a parametrization of these solutions as well as on a dual version of the Fermat’s method of descent.

众所周知，毕达哥拉斯三元组的矩阵生成树形结构被推广到丢芬图方程x2 + d2 - z2 = 0的原始解中，其中d是一个正的无平方整数。证明是基于这些解的参数化以及费马下降法的对偶版本。

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引用次数: 0

Unique Common Fixed Points for Expansive Maps 独特的公共固定点扩展地图

Q1 MATHEMATICS

INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES

Pub Date : 2023-09-11 DOI: 10.1155/2023/6689743

Hadeel Z. Alzumi, Hakima Bouhadjera, Mohammed S. Abdo

In this work, we establish three common fixed point results for expansive maps satisfying implicit relations in metric and dislocated metric spaces. We do this by utilizing recently developed concept of occasionally weakly biased maps of type

(A)

. These studies about the theory of common fixed points refine several earlier ones. Some illustrative examples are offered to support our theorems, and even better, a pertinent application is supplied to demonstrate the viability and applicability of one of these results.

本文建立了在度量空间和错位度量空间中满足隐式关系的扩展映射的三个公共不动点结果。我们利用最近发展的A类偶尔弱偏映射的概念来做到这一点。这些关于公共不动点理论的研究完善了先前的一些研究。提供了一些说明性的例子来支持我们的定理，甚至更好的是，提供了一个相关的应用来证明这些结果之一的可行性和适用性。

引用次数: 0

Atezolizumab in Combination with Bevacizumab for the Management of Patients with Hepatocellular Carcinoma in the First-Line Setting: Systematic Literature Review and Meta-Analysis. Atezolizumab联合贝伐单抗治疗一线肝癌患者:系统文献综述和荟萃分析

IF 11.6 Q1 MATHEMATICS

INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES

Pub Date : 2023-07-29 eCollection Date: 2023-12-01 DOI: 10.1159/000533166

Arndt Vogel, Richard S Finn, Marie-Hélène Blanchet Zumofen, Carolina Heuser, Javier Sanchez Alvarez, Michael Leibfried, Catherine R Mitchell, Sarah Batson, Gabrielle Redhead, Vincent E Gaillard, Masatoshi Kudo

Background: In 2020, atezolizumab-bevacizumab became the new standard of care (SOC) for first-line unresectable hepatocellular carcinoma (HCC) patients, following a decade where sorafenib was the preferred first-line treatment. In the last few years, a number of novel systemic treatments with non-inferiority and superiority to sorafenib have been approved as first-line treatments.

Objectives: The objective of this systematic literature review (SLR) and network meta-analysis (NMA) was to compare randomised controlled trial evidence for atezolizumab-bevacizumab with globally relevant pharmacological comparators for first-line treatment of patients with unresectable HCC.

Methods: Randomised controlled trials investigating first-line treatment of HCC in adults with no prior systemic treatment were eligible for inclusion into the SLR and were retrieved from Embase, MEDLINE, and Evidence-Based Medicine (EBM) Reviews. Interventions of interest for the NMA included atezolizumab-bevacizumab, sorafenib, lenvatinib, durvalumab (including in combination with tremelimumab), cabozantinib (including in combination with atezolizumab), camrelizumab (including in combination with rivoceranib), pembrolizumab (including in combination with lenvatinib), and tislelizumab. Random effects NMA was conducted for survival endpoints within a Bayesian framework with an informative prior distribution for between-study heterogeneity. The hazard ratios for relative treatment effect were estimated with 95% credible intervals (CrIs).

Results: The SLR identified 49 studies, of which eight formed a connected evidence network permitting the indirect treatment comparison of atezolizumab-bevacizumab with comparators of interest. The indirect comparisons suggested an improved overall survival (OS) with atezolizumab-bevacizumab versus most comparators. All indirect treatment comparison results for atezolizumab-bevacizumab included the null value within the 95% CrI (n = 1) for OS and progression-free survival (PFS).

Conclusions: The results of the NMA indicate atezolizumab-bevacizumab is associated with superior or comparable OS and PFS together with a manageable safety profile compared with globally relevant comparators in the unresected HCC indication. The findings support that atezolizumab-bevacizumab remains SOC for the management of first-line unresectable HCC patients.

背景:2020年，阿特唑单抗-贝伐单抗成为一线不可切除肝细胞癌(HCC)患者的新护理标准(SOC)，此前10年，索拉非尼是首选的一线治疗方案。在过去的几年中，一些新的系统性治疗与索拉非尼相比具有非劣效性和优越性，已被批准作为一线治疗。目的:本系统文献综述(SLR)和网络荟萃分析(NMA)的目的是比较atezolizumab-bevacizumab的随机对照试验证据与全球相关的药理学比较物，用于一线治疗不可切除的HCC患者。方法:研究未接受过全身治疗的成人HCC一线治疗的随机对照试验符合纳入SLR的条件，并从Embase、MEDLINE和循证医学(EBM)综述中检索。NMA感兴趣的干预措施包括atezolizumab-bevacizumab, sorafenib, lenvatinib, durvalumab(包括与tremelimumab合用)，cabozantinib(包括与atezolizumab合用)，camrelizumab(包括与rivoeranib合用)，pembrolizumab(包括与lenvatinib合用)和tislelizumab。随机效应NMA是在贝叶斯框架内对生存终点进行的，具有研究间异质性的信息先验分布。相对治疗效果的风险比以95%可信区间(CrIs)估计。结果:SLR确定了49项研究，其中8项形成了一个连接的证据网络，允许将atezolizumab-bevacizumab与感兴趣的比较物进行间接治疗比较。间接比较表明，与大多数比较药物相比，atezolizumab-bevacizumab的总生存期(OS)有所改善。atezolizumab-bevacizumab的所有间接治疗比较结果包括OS和无进展生存期(PFS)的95% CrI (n = 1)内的零值。结论:NMA的结果表明，在未切除的HCC适应症中，与全球相关的比较药相比，atezolizumab-bevacizumab具有优越或可比的OS和PFS，以及可管理的安全性。研究结果支持atezolizumab-bevacizumab仍然是一线不可切除HCC患者的SOC治疗方案。

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