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L1/2正则子在Lq(0 徐宗本1郭海亮1王尧1张海1,2 1. Institute of Information and System Science, Xi'an Jiaotong University2. department of Mathematics, Northwest University

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自动化学报 2012年第7期38卷 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

Global Stability to Steady Supersonic Rayleigh Flows in One-Dimensional Duct

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Chinese Annals of mathematics,Series B 2024年第2期45卷 279-296页

作者： Fenglun WEI Jianli LIU department of Mathematics Shanghai University Newtouch Center for mathematics of Shanghai University

Heat exchange plays an important role in hydrodynamical systems,which is an interesting topic in theory and application.In this paper,the authors consider the global stability of steady supersonic Rayleigh flows for the one-dimensional compressible Euler equations with heat exchange,under the small perturbations of initial and boundary conditions in a finite rectilinear duct.

关键词： Compressible Euler equations Heat exchange Supersonic Rayleigh fow Steady solution Classical solution

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On Modules Satisfying S-Noetherian Spectrum Condition

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Communications in mathematics and Statistics 2023年第3期11卷 649-662页

作者： MehmetÖzen Osama A.Naji Ünsal Tekir Suat Koç department of Mathematics Sakarya UniversitySakaryaTurkey department of Mathematics Marmara UniversityIstanbulTurkey

Let R be a commutative ring having nonzero identity and M be a unital R-module.Assume that S⊆R is a multiplicatively closed subset of R.Then,M satisﬁes S-Noetherian spectrum condition if for each submodule N of M,there exist s∈S and aﬁnitely generated submodule F⊆N such that sN⊆radM(F),where radM(F)is the prime radical of F in the sense(McCasland and Moore in Commun Algebra 19(5):1327–1341,1991).Besides giving many properties and characterizations of S-Noetherian spectrum condition,we prove an analogous result to Cohen’s theorem for modules satisfying S-Noetherian spectrum condition.Moreover,we characterize modules having Noetherian spectrum in terms of modules satisfying the S-Noetherian spectrum condition.

关键词： Noetherian modules S-Noetherian modules Noetherian spectrum S-Noetherian spectrum condition

On the Structure of Quantum Toroidal Superalgebra εm|n

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Acta Mathematica Sinica,English Series 2023年第11期39卷 2117-2138页

作者： Xiang Hua WU Hong Da LIN Hong Lian ZHANG department of Mathematics Shanghai University Newtouch Center for mathematics of Shanghai University

Recently the quantum toroidal superalgebra εm|nassociated with glm|nwas introduced by L. Bezerra and E. Mukhin, which is not a quantum Kac-Moody algebra. The quantum toroidal superalgebra εm|nexploits infinite sequences of generators and relations of the form, which are called Drinfeld realization. In this paper, we use only finite set of generators and relations to define an associative algebra ε’m|nand show that there exists an epimorphism from ε’m|nto the quantum toroidal superalgebra εm|n. In particular, the structure of ε’m|nenjoys some properties like Drinfeld-Jimbo realization.

关键词： Quantum toroidal superalgebra Drinfeld realization Lie superalgebra 17B37 17B67

Study of bending angle and shadow in a new Schwarzschild-like black hole affected by plasma and non-plasma mediums

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Chinese Physics C 2024年第5期48卷 309-318页

作者： Riasat Ali Tiecheng Xia Muhammad Awais Rimsha Babar department of Mathematics Newtouch Center for Mathematics of Shanghai UniversityShanghai 200444China department of Mathematics University of Engineering and Technology Lahore-54890Pakistan department of Mathematics GC University Faisalabad Layyah CampusLayyah-31200Pakistan

In this study,we analyze the models of the deflection angle of a new Schwarzschild-like black hole(BH)and employ the optical metric of the BH.To achieve this,we use the Gaussian curvature of the optical metric and the Gauss-Bonnet theorem,known as the Gibbons-Werner technique,to determine the deflection angle.Furthermore,we examine the deflection angle in the presence of a plasma medium and the effect of the plasma medium on the deflection angle.The deflection angle of the BH solution in the gauged super-gravity is computed using the Keeton-Petters approach.Utilizing the ray-tracing technique,we investigate the shadow of the corresponding BH and analyze the plots of the deflection angle and shadow to verify the influence of the plasma and algebraic thermodynamic parameters on the deflection angle and shadow.

关键词： new Schwarzschild-like black hole Gibbons-Werner and Keeton-Petters techniques deflection angle ray-tracing approach shadow

Hopf bifurcation and synchronisation of afractional-order butterfly-fish chaotic system

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Journal of Control and Decision 2022年第1期9卷 117-128页

作者： P.Ramesh M.Sambath K.Balachandran department of Mathematics Periyar UniversitySalemIndia department of Mathematics Bharathiar UniversityCoimbatoreIndia

Our aim is to study the Hopf bifurcation and synchronisation of a fractional-order butterfly-fishchaotic system. First, we derived the existence of a chaotic attractor in the fractional-order systemand also synchronisation problem between two identical fractional-order chaotic systems isstudied. Also, control design for the synchronisation with a suitable linear controller is tested inthe response system. Finally, numerical simulation results are provided to confirm the theoreticalanalysis.

关键词： Stability Hopf bifurcation chaotic attractor synchronisation fractional dynamical system

The effect of supply disruption in a two-layer supply chain with one retailer and two suppliers with promotional effort under random demand

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Journal of Management Analytics 2023年第1期10卷 22-37页

作者： Totan Garai Arpita Paul department of Mathematics Syamsundar CollegeShyamsundarIndia department of Mathematics Dinhata CollegeCooch BeharIndia

This paper considers a closed-loop supply chain comprising one retailer and two suppliers.It assumes one supplier as the main supplier and another as the backup.The coordination issue of the supply chain has been discussed in this work.The main supplier’s yield is considered subject to disruption.The demand considered here is stochastic.We aim to calculate the supplier’s optimum production quantity.Similarly,the retailer’s optimal ordering quantity is found out.Additionally,in the centralized supply chain model,we want to maximize the expected profit under certain restriction.Numerical illustrations are discussed to the benefit some characteristic insights over the supply chain model.

关键词： Supply chain management random supply uncertain demand disruption

An EOQ model with backordering for perishable items under multiple advanced and delayed payments policies

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Journal of Management Analytics 2022年第3期9卷 403-434页

作者： Prasanta Kumar Ghosh Amalesh Kumar Manna Jayanta Kumar Dey Samarjit Kar department of Mathematics National Institute of Technology DurgapurDurgapurIndia department of Mathematics The University of BurdwanBurdwanIndia department of Mathematics Mahishadal Raj CollegePurba MedinipurIndia department of Mathematics Y.S.Palpara MahavidyalayaPurba MedinipurIndia

This study investigated an economic order quantity (EOQ) model with completebackorder for fixed lifetime perishable items under multiple advance and delayedpayments policies. Here, a new type of business policy is consideredwhere supplieroffers the retailer to pay a fraction of the purchasing cost before the order deliverybymultiple equal installments starting from the ordering time and the rest amountafter the delivery by multiple equal installments. Here, some theoretical results areillustrated to determine the conditions of existence and uniqueness of the optimalsolutions. A closed form solution is determined to solve the proposed model underapproximation. Some numerical examples are provided to examine the validity ofthe proposed model. Finally, sensitivity analyses are presented to obtain the effectof optimal policy and provide some managerial insights of the model.

关键词： inventory perishable item expiry date advance payment delayed payment

Nonlinear Inverse Relations of the Bell Polynomials via the Lagrange Inversion Formula (Ⅱ)

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Journal of Systems Science & Complexity 2023年第1期36卷 96-116页

作者： MA Xinrong WANG Jin department of Mathematics Soochow UniversitySuzhou 215006China department of Mathematics Zhejiang Normal UniversityJinhua 321004China

In this paper,by means of the classical Lagrange inversion formula,the authors establish a general nonlinear inverse relation as the solution to the problem proposed in the paper[J.Wang,Nonlinear inverse relations for the Bell polynomials via the Lagrange inversion formula,J.Integer Seq.,Vol.22(2019),Article 19.3.8].As applications of this inverse relation,the authors not only find a short proof of another nonlinear inverse relation due to Birmajer,et al.(2012),but also set up a few convolution identities concerning the Mina polynomials.

关键词： Bell polynomial convolution identity formal power series Lagrange inversion formula Mina polynomial nonlinear inverse relation recurrence relation

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