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自动化学报 2012年第7期 1225-1228页

作者：徐宗本郭海亮王尧张海 Institute of Information and System Science Xi’an Jiaotong University department of mathematics Northwest University

Recently, regularization methods have attracted increasing attention. Lq (0 < q < 1) regularizations were proposed after L1 regularization for better solution of sparsity problems. A natural question is which is the best choice among Lq regularizations with all q in (0, 1)? By taking phase diagram studies with a set of experiments implemented on signal recovery and error correction problems, we show the following: 1) As the value of q decreases, the Lq regularization generates sparser solution. 2) When 1/2 ≤ q < 1, the L1/2 regularization always yields the best sparse solution and when 0 < q ≤ 1/2, the performance of the regularizatons takes no significant difference. Accordingly, we conclude that the L1/2 regularization can be taken as a rep- resentative of Lq (0 < q < 1) regularizations.

关键词： Lq regularization phase diagram signal recovery error correction

A Synergistic Multi-Attribute Decision-Making Method for Educational Institutions Evaluation Using Similarity Measures of Possibility Pythagorean Fuzzy Hypersoft Sets

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Computer Modeling in Engineering & Sciences 2025年第1期142卷 501-530页

作者： Khuram Ali Khan Saba Mubeen Ishfaq Atiqe Ur Rahman Salwa El-Morsy department of mathematics University of SargodhaSargodha40100Pakistan department of mathematics University of Management and TechnologyLahore54000Pakistan department of mathematics College of ScienceQassim UniversityBuraydah51452Saudi Arabia

Due to the numerous variables to take into account as well as the inherent ambiguity and uncertainty,evaluating educational institutions can be *** concept of a possibility Pythagorean fuzzy hypersoft set(pPyFHSS)is more flexible in this regard than other theoretical fuzzy set-like models,even though some attempts have been made in the literature to address such *** study investigates the elementary notions of pPyFHSS including its set-theoretic operations union,intersection,complement,OR-and *** results related to these operations are also modified for ***,the similarity measures between pPyFHSSs are formulated with the assistance of numerical examples and ***,an intelligent decision-assisted mechanism is developed with the proposal of a robust algorithm based on similarity measures for solving multi-attribute decision-making(MADM)problems.A case study that helps the decision-makers assess the best educational institution is discussed to validate the suggested *** algorithmic results are compared with the most pertinent model to evaluate the adaptability of pPyFHSS,as it generalizes the classical possibility fuzzy set-like theoretical ***,while considering significant evaluating factors,the flexibility of pPyFHSS is observed through structural comparison.

关键词： Hypersoft set Pythagorean fuzzy hypersoft set computational complexity multi-attribute decision-making optimization similarity measures uncertainty

Projective Hilbert modules and sequential approximations

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Science China mathematics 2025年第1期 137-168页

作者： Lawrence G.Brown Huaxin Lin department of mathematics Purdue University department of mathematics East China Normal University department of mathematics University of Oregon Shanghai Institute for mathematics and Interdisciplinary Sciences

We show that when A is a separable C*-algebra,every countably generated Hilbert A-module is projective（with bounded module maps as morphisms）.We also study the approximate extensions of bounded module *** the case where A is a σ-unital simple C*-algebra with strict comparison,and every strictly positive lower semicontinuous affine function on quasitraces can be realized as the rank of an element in the Cuntz semigroup,we show that the Cuntz semigroup is equivalent to unitarily equivalent classes of countably generated Hilbert A-modules if and only if A has stable rank one.

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Transport mechanism in chemically reactive hybrid nanofluid flow containing gyrotactic micro-organisms over a curved oscillatory surface

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Applied mathematics and Mechanics(English Edition) 2025年第1期46卷 177-192页

作者： M.NAVEED M.IMRAN T.ASGHAR Z.ABBAS department of mathematics Division of Science and TechnologyUniversity of Education department of mathematics The Islamia University of Bahawalpur

This paper examines the transport analysis, including both heat transfer and mass transfer, in hybrid nanofluid flow containing gyrotactic microorganisms towards a curved oscillatory surface. The influence of magnetic fields is also inspected in terms of their physical characteristics. To depict the phenomena of transport, modified versions of both Fick's and Fourier's laws are used. Additionally, the characteristics of both heterogeneous and homogeneous chemical reactions are also incorporated. Utilizing a curvilinear coordinate system, the flow problem is formulated as partial differential equations(PDEs)for momentum, concentration, microorganism field, and energy. An analytical solution to the obtained flow equations is achieved utilizing the homotopy analysis method(HAM).The effects of significant flow parameters on the pressure and microorganism fields, velocity, oscillation velocity, concentration, and temperature distributions are shown via graphs. Furthermore, the variations in skin friction, mass transfer rate, heat transfer rate, and local motile number due to different involved parameters are presented in tables and are analyzed in detail. Graphical results indicate that the curves of velocity and temperature fields are enhanced as the values of the solid volume fraction variables *** is also verified that the concentration rate field decreases as the values of the homogeneous reaction strength parameter and the radius of curvature parameter increase, and it increases with the Schmidt number and the heterogeneous reaction strength *** outcomes show a favorable response of the motile number to advanced values of the Peclet number, the Schmidt number, the microorganism difference parameter, and the bio-convective Lewis number.

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Solid Waste Management:A MADM Approach Using Fuzzy Parameterized Possibility Single-Valued Neutrosophic Hypersoft Expert Settings

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Computer Modeling in Engineering & Sciences 2025年第1期142卷 531-553页

作者： Tmader Alballa Muhammad Ihsan Atiqe Ur Rahman Noorah Ayed Alsorayea Hamiden Abd El-Wahed Khalifa department of mathematics College of SciencesPrincess Nourah bint Abdulrahman UniversityRiyadh11671Saudi Arabia 2 department of mathematics University of Management and TechnologyLahore54000Pakistan department of mathematics College of ScienceQassim UniversityBuraydah51452Saudi Arabia

The dramatic rise in the number of people living in cities has made many environmental and social problems *** search for a productive method for disposing of solid waste is the most notable of these *** scholars have referred to it as a fuzzy multi-attribute or multi-criteria decision-making problem using various fuzzy set-like approaches because of the inclusion of criteria and anticipated *** goal of the current study is to use an innovative methodology to address the expected uncertainties in the problem of solid waste site *** characteristics(or sub-attributes)that decision-makers select and the degree of approximation they accept for various options can both be indicators of these *** tackle these problems,a novel mathematical structure known as the fuzzy parameterized possibility single valued neutrosophic hypersoft expert set(ρˆ-set),which is initially described,is integrated with a modified version of Sanchez’s *** this,an intelligent algorithm is *** steps of the suggested algorithm are explained with an example that explains *** compatibility of solid waste management sites and systems is discussed,and rankings are established along with detailed justifications for their *** study’s strengths lie in its application of fuzzy parameterization and possibility grading to effectively handle the uncertainties embodied in the parameters’nature and alternative approximations,*** uses specific mathematical formulations to compute the fuzzy parameterized degrees and possibility grades that are missing from the prior *** is simpler for the decisionmakers to look at each option separately because the decision is *** the computed results,it is discovered that they are consistent and dependable because of their preferred properties.

关键词： Hypersoft expert set Sanchez’s method decision making optimization solid waste management possibility grade fuzzy parameterization

Dynamical complexity of Anosov systems driven by a quasi-periodic force

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Science China mathematics 2025年第1期 89-136页

作者： Wen Huang Zeng Lian Kening Lu department of mathematics University of Science and Technology of China School of mathematics Sichuan University

Consider C2Anosov systems on a compact manifold driven by a quasi-periodic *** study their dynamical complexity on various levels from the perspectives of both path-wise dynamics and stochastic *** that these systems are non-wandering（i.e.,every point in the phase space is nonwandering）,we prove a set of results:（1） the existence of abundance of random periodic points;（2） a random Liv?ic theorem;（3） a random Ma?é-Bousch-Conze-Guivarc'h lemma;（4） the existence of strong random ***,a concrete example constructed on a 2-dimensional torus is also given to uncover some interesting phenomena of the systems.

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Regression analysis of squeezing-induced hybrid nanofluid flow in Darcy-Forchheimer porous medium

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Applied mathematics and Mechanics(English Edition) 2025年第1期46卷 193-208页

作者： K.MUHAMMAD M.SARFRAZ department of Humanities and Sciences School of Electrical Engineering and Computer Science National University of Sciences and Technology department of mathematics Quaid-i-Azam University

This article presents a mathematical model addressing a scenario involving a hybrid nanofluid flow between two infinite parallel plates. One plate remains stationary, while the other moves downward at a squeezing velocity. The space between these plates contains a Darcy-Forchheimer porous medium. A mixture of water-based fluid with gold(Au) and silicon dioxide(Si O2) nanoparticles is formulated. In contrast to the conventional Fourier's heat flux equation, this study employs the Cattaneo-Christov heat flux equation. A uniform magnetic field is applied perpendicular to the flow direction, invoking magnetohydrodynamic(MHD) effects. Further, the model accounts for Joule heating, which is the heat generated when an electric current passes through the fluid. The problem is solved via NDSolve in MATHEMATICA. Numerical and statistical analyses are conducted to provide insights into the behavior of the nanomaterials between the parallel plates with respect to the flow, energy transport, and skin *** findings of this study have potential applications in enhancing cooling systems and optimizing thermal management strategies. It is observed that the squeezing motion generates additional pressure gradients within the fluid, which enhances the flow rate but reduces the frictional drag. Consequently, the fluid is pushed more vigorously between the plates, increasing the flow velocity. As the fluid experiences higher flow rates due to the increased squeezing effect, it spends less time in the region between the plates. The thermal relaxation, however, abruptly changes the temperature, leading to a decrease in the temperature fluctuations.

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Predicting Maximum Lifespan Limits at Mean Menopausal Age

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Journal of Mathematical Research with Applications 2025年第1期 133-142页

作者： M.SUMATHI S.ANTONY CARLA department of mathematics N.M.S.S.Vellaichamy Nadar College Research Scholar (Part-time) Madurai Kamaraj University

The age at which a woman enters natural menopause has also been associated to death from any cause. Menopause is a natural component of aging that happens between the ages of 45 and 55, with the average menopausal age being 51. Previous research has revealed the age at which women reach menopause, but there is no evidence to support the link between menopause and longevity. We made a study in assessing the limits of maximum lifespan at menopausal age in our previous article. In this paper, we aim to predict the maximum lifespan of women at mean menopausal age.

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A NOTE ON THE EXISTENCE OF STATIONARY SOLUTIONS OF THE COMPRESSIBLE EULER-POISSON EQUATIONS WITH 6/5<γ<2

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Acta Mathematica Scientia 2013年第4期33卷 936-942页

作者：向建林 department of mathematics School of Science Wuhan University of Technology

This paper is concerned with the system of Euler-Poisson equations as a model to describe the motion of the self-induced gravitational gaseous stars. When ~ 〈 7 〈 2, under the weak smoothness of entropy function, we find a sufficient condition to guarantee the existence of stationary solutions for some velocity fields and entropy function that solve the conservation of mass and energy.

关键词： Euler-Poisson equations stationary solutions existence

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Asymptotic false discovery control of the Benjamini-Hochberg procedure for pairwise comparisons

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Science China mathematics 2025年第1期 223-252页

作者： Weidong Liu Dennis Leung Qi-Man Shao School of Mathematical Sciences Shanghai Jiao Tong University School of mathematics and Statistics University of Melbourne department of Statistics and Data Science SICMSouthern University of Science and Technology

In a one-way analysis-of-variance(ANOVA) model,the number of pairwise comparisons can become large even with a moderate number of *** by this,we consider a regime with a growing number of groups and prove that,when testing pairwise comparisons,the Benjamini-Hochberg(BH) procedure can asymptotically control false discoveries,despite the fact that the involved t-statistics do not exhibit the wellknown positive dependence structure required for exact false discovery rate(FDR) *** Tukey's perspective that the difference between the means of any two groups cannot be exactly zero,our main result provides control over the directional false discovery rate and directional false discovery proportion.A key technical contribution of our work is demonstrating that the dependence among the t-statistics is sufficiently weak to establish the convergence result typically required for asymptotic FDR *** analysis does not rely on conventional assumptions such as normality,variance homogeneity,or a balanced design,thereby offering a theoretical foundation for applications in more general settings.

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