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Nonlinear system dynamics of calcium and nitric oxide due to cell memory and superdiffusion in neurons

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Communications in Theoretical Physics 2024年第5期76卷 16-32页

作者： Anand Pawar Kamal Raj Pardasani department of {1. Bioinformatics and Computer ApplicationsMaulana Azad National Institute of TechnologyBhopal-462003Madhya PradeshIndia

The integer-order interdependent calcium([Ca^(2+)])and nitric oxide(NO)systems are unable to shed light on the influences of the superdiffusion and memory in triggering Brownian motion(BM)in ***,a mathematical model is constructed for the fractional-order nonlinear spatiotemporal systems of[Ca^(2+)]and NO incorporating reaction-diffusion equations in *** two-way feedback process between[Ca^(2+)]and NO systems through calcium feedback on NO production and NO feedback on calcium through cyclic guanosine monophosphate(cGMP)with plasmalemmal[Ca^(2+)]-ATPase(PMCA)was incorporated in the *** Crank–Nicholson scheme(CNS)with Grunwald approximation along spatial derivatives and L1.scheme along temporal derivatives with Gauss–Seidel(GS)iterations were *** numerical outcomes were analyzed to get insights into superdiffusion,buffer,and memory exhibiting BM of[Ca^(2+)]and NO *** conditions,events and mechanisms leading to dysfunctions in calcium and NO systems and causing different diseases like Parkinson’s were explored in neurons.

关键词： [Ca^(2+)]and nitric oxide signaling reaction-diffusion equations fractional-order systems Grunwald approximation Gauss-Seidel iterations

Equitable Cluster Partition of Planar Graphs with Girth at Least 1.

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Journal of Mathematical Research with Applications 2024年第2期44卷 152-160页

作者： Xiaoling LIU Lei SUN Wei ZHENG department of {1. and Statistics Shandong Normal University

An equitable(Ok1. Ok2,..., Okm)-partition of a graph G, which is also called a k cluster m-partition, is the partition of V(G) into m non-empty subsets V1. V2,..., Vm such that for every integer i in {1. 2,..., m}, G[Vi] is a graph with components of order at most k, and for each distinct pair i, j in {1...., m}, there is-1.≤ |Vi|-|Vj| ≤ 1. In this paper, we proved that every planar graph G with minimum degree δ(G) ≥ 2 and girth g(G) ≥ 1. admits an equitable(O71. O72,..., O7m)-partition, for any integer m ≥ 2.

关键词： equitable cluster partition planar graph girth discharging

Global Zero-relaxation Limit Problem of the Electro-diffusion Model Arising in Electro-Hydrodynamics

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Acta Mathematicae Applicatae Sinica 2024年第1期40卷 241-268页

作者： Ming-hua Yang Si-ming Huang Jin-yi Sun department of {1. Jiangxi University of Finance and EconomicsNanchang330032China School of Public Administration Guangdong University of Foreign StudiesGuangzhou510006China College of mathematics and Statistics Northwest Normal UniversityLanzhou730070China

In this paper,we study a global zero-relaxation limit problem of the electro-diffusion model arising in electro-hydrodynamics which is the coupled Planck-Nernst-Poisson and Navier-Stokes *** is,the paper deals with a singular limit problem of{u^(∈)_(t)+u^(∈)·▽u^(∈)-Δu^(∈)+▽P^(∈)=Δφ^(∈)▽φ^(∈),in R^(3)×(0,∞),▽·u^(∈)=0,in R^(3)×(0,∞),n^(∈)_(t)+u^(∈)·▽n^(∈)-Δn^(∈)=-▽·(n^(∈)▽φ^(∈)),in R^(3)×(0,∞),ct+u^(∈)·▽c^(∈)-Δc^(∈)=▽·(c^(∈)▽φ^(∈)),in R^(3)×(0,∞),∈^(-1.φ^(∈)_(t)=Δφ^(∈)-n^(∈)+c^(∈),in R^(3)×(0,∞),(u^(∈),n^(∈),c^(∈),φ^(∈))|t=0=(u0,n0,c0,φ0),in R^(3) involving with a positive,large parameter^(∈).The present work show a case that(u^(∈),n^(∈),c^(∈))stabilizes to(u^(∞),n∞,c∞):=(u,n,c)uniformly with respect to the time variable as^(∈)→+∞with respect to the strong topology in a certain Fourier-Herz space.

关键词： fourier-Herz space littlewood-Paley decomposition stability limit dissipative system

On the analytic and geometric aspects of obstruction flatness

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Acta Mathematica Sinica,English Series 2024年

作者： Peter EBENFELT Ming XIAO Hang XU department of {1. University of California at San Diego School of mathematics (Zhuhai) Sun Yat-sen University

In this paper, we investigate analytic and geometric properties of obstruction flatness of strongly pseudoconvex CR hypersurfaces of dimension 2n-1. Our first two results concern local aspects. One asserts that any strongly pseudoconvex CR hypersurface M ? Cncan be osculated at a given point p ∈ M by an obstruction flat one up to order 2n + 4 generally and 2n + 5 if and only if p is an obstruction flat point. In the other result, we show that locally there are non-spherical but obstruction flat CR hypersurfaces with transverse symmetry for n = 2. The final main result in this paper concerns the existence of obstruction flat points on compact, strongly pseudoconvex, 3-dimensional CR hypersurfaces. It asserts that the unit sphere in a negative line bundle over a Riemann surface X always has at least one circle of obstruction flat points.

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EPQ model with the effect of inflation and reliability for partial trade credit under fuzzy and cloudy fuzzy environment

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Journal of Management Analytics 2024年第1期11卷 110-134页

作者： Supriya Tiwari Kunal Shah Kajal Bhimani department of Science and Humanities Apollo Institute of Engineering&TechnologyGTUAhmedabadIndia department of {1. SMMPISRKadi Sarva VishwavidyalayaGandhinagarIndia AVAerials 401 Swarnim Business Hub-1 New Chamunda SocietyGodrej Garden CityGotaAhmedabadIndia

The proposed study offers the first-of-its-kind economic production quantity model for deteriorating items having a demand rate to be price dependent under the effect of inflation and reliability with partial trade *** model is extended under an uncertain environment by assuming inventory parameters to be triangular fuzzy numbers and cloudy triangular fuzzy *** objective of the study is to maximize the profit of the inventory system and to identify the most suitable environment for the proposed *** are verified using the numerical ***,the comparative study is presented to justify the nature of fuzzy and cloudy fuzzy *** analysis under all environments is conducted to identify the most sensitive parameters of all.

关键词： EPQ partial trade credit inflation reliability triangular fuzzy number cloudy triangular fuzzy number

Global Phase Portraits of Uniform Isochronous Centers System of Degree Six with Polynomial Commutator

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Acta Mathematicae Applicatae Sinica 2024年第3期40卷 577-599页

作者： Li-na GUO Ai-yong CHEN Shuai-feng ZHAO School of mathematics and Statistics Henan University of Science and TechnologyLuoyang 471023China department of {1. Hunan First Normal UniversityChangsha 410205China School of Mechatronics Engineering Henan University of Science and TechnologyLuoyang 471023China

This paper studies the global phase portraits of uniform isochronous centers system of degree six with polynomial *** systems have the form x=-y+xf(x,y),y=x+yf(x,y),where f(x,y)=a_(1.x+a_(2)xy+a_(3)xy^(2)+a_(4)xy^(3)+a_(5)xy^(4)=xσ(y),and any zero of 1.a_(1.y+a_(2)y^(2)+a_(3)y^(3)+a_(4)y^(4)+a_(5)y^(5),y=y is an invariant straight *** last,all global phase portraits are drawn on the Poincare disk.

关键词： global phase portraits uniform isochronous center polynomial commutator invariant straight lines

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Anomaly Detection in Imbalanced Encrypted Traffic with Few Packet Metadata-Based Feature Extraction

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Computer Modeling in Engineering & Sciences 2024年第10期141卷 585-607页

作者： Min-Gyu Kim Hwankuk Kim department of Financial Information Security Kookmin UniversitySeoul02707Republic of Korea department of Information Security Cryptography {1. Kookmin UniversitySeoul02707Republic of Korea

In the IoT(Internet of Things)domain,the increased use of encryption protocols such as SSL/TLS,VPN(Virtual Private Network),and Tor has led to a rise in attacks leveraging encrypted *** research on anomaly detection using AI(Artificial Intelligence)is actively progressing,the encrypted nature of the data poses challenges for labeling,resulting in data imbalance and biased feature extraction toward specific *** study proposes a reconstruction error-based anomaly detection method using an autoencoder(AE)that utilizes packet metadata excluding specific node *** proposed method omits biased packet metadata such as IP and Port and trains the detection model using only normal data,leveraging a small amount of packet *** makes it well-suited for direct application in IoT environments due to its low resource *** experiments comparing feature extraction methods for AE-based anomaly detection,we found that using flowbased features significantly improves accuracy,precision,F1.score,and AUC(Area Under the Receiver Operating Characteristic Curve)score compared to packet-based ***,for flow-based features,the proposed method showed a 30.1.%increase in F1.score and improved false positive rates compared to Isolation Forest and ***,the proposedmethod demonstrated a 32.43%higherAUCwhen using packet features and a 1.1.39%higher AUC when using flow features,compared to previously proposed oversampling *** study highlights the impact of feature extraction methods on attack detection in imbalanced,encrypted traffic environments and emphasizes that the one-class method using AE is more effective for attack detection and reducing false positives compared to traditional oversampling methods.

关键词： One-class anomaly detection feature extraction auto-encoder encrypted traffic CICIoT2023

Some results on probabilities of moderate deviations

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Acta Mathematica Sinica,English Series 2024年

作者： Deli LI Yu MIAO Yongcheng QI department of Mathematical Sciences Lakehead University College of mathematics and Information Science Henan Normal University department of {1. and Statistics University of Minnesota Duluth

Let{X,X_n;n≥1.be a sequence of ***-degenerate real-valued random variables with EX2<∞.Let ■ be a nondecreasing regularly varying function with indexρ≥0 and lim2t→∞g（t）=∞.Letμ=EX andσ=E（X-μ）*** this paper,on the scale g（log n）,we obtain precise asymptotic estimates for the probabilities of moderate deviations of the form ■.Unlike those known results in the literature,the moderate deviation results established in this paper depend on both the variance and the asymptotic behavior of the tail distribution of X.

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MULTIFRACTAL ANALYSIS OF CONVERGENCE EXPONENTS FOR PRODUCTS OF CONSECUTIVE PARTIAL QUOTIENTS IN CONTINUED FRACTIONS

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Acta Mathematica Scientia 2024年第4期44卷 1594-1608页

作者： Lulu FANG Jihua MA Kunkun SONG Xin YANG School of mathematics and Statistics Nanjing University of Science and TechnologyNanjing210094China School of mathematics and Statistics Wuhan UniversityWuhan 430072China Key Laboratory of Computing and Stochastic mathematics(Ministry of Education) School of Mathematics and StatisticsHunan Normal UniversityChangsha 410081China

For each real number x∈(0,1.,let[a_(1.(x),a_(2)(x),…,a_n(x),…]denote its continued fraction *** study the convergence exponent defined byτ(x)=inf{s≥0:∞∑n=1.a_(n)(x)a_(n+1.(x))^(-s)<∞},which reflects the growth rate of the product of two consecutive partial *** a main result,the Hausdorff dimensions of the level sets ofτ(x)are determined.

关键词： continued fractions product of partial quotients Hausdorff dimension