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Fuzzy Dynamic Optimal Model for COVID-19 Epidemic in India Based on Granular Differentiability 认领 引用
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作者 KHATUA Debnarayan DE Anupam +3 位作者 KAR Samarjit SAMANTA Eshan SEKH Arif Ahmed GUHA ADHYA Debashree 《Journal of Shanghai Jiaotong university(Science)》 EI 2025年第3期545-560,共16页
The pandemic SARS-CoV-2 has become an undying virus to spread a sustainable disease named COVID-19 for upcoming few years.Mortality rates are rising rapidly as approved drugs are not yet available.Isolation from the i... The pandemic SARS-CoV-2 has become an undying virus to spread a sustainable disease named COVID-19 for upcoming few years.Mortality rates are rising rapidly as approved drugs are not yet available.Isolation from the infected person or community is the preferred choice to protect our health.Since humans are the only carriers,it might be possible to control the positive rate if the infected population or host carriers are isolated from each other.Isolation alone may not be a proper solution.These are the resolutions of previous research work carried out on COVID-19 throughout the world.The present scenario of the world and public health is knocking hard with a big question of critical uncertainty of COVID-19 because of its imprecise database as per daily positive cases recorded all over the world and in India as well.In this research work,we have pre-sented an optimal control model for COVID-19 using granular differentiability based on fuzzy dynamical systems.In the first step,we created a fuzzy Susceptible-Exposed-Infected-Asymptomatic-Hospitalized-Recovered-Death(SEIAHRD)model for COVID-19,analyzed it using granular differentiability,and reported disease dynamics for time-independent disease control parameters.In the second step,we upgraded the fuzzy dynamical system and granular differentiability model related to time-dependent disease control parameters as an optimal control problem invader.Theoretical studies have been validated with some practical data from the epidemic COVID-19 related to the Indian perspective during first wave and early second wave. 展开更多
关键词 COVID-19 asymptomatic susceptible fuzzy dynamical system granular differentiability
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GÂTEAUX DIRECTIONAL DIFFERENTIABILITY OF THE GENERALIZED METRIC PROJECTION IN BANACH SPACES 认领 引用
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作者 Jinlu LI 《Acta Mathematica Scientia》 SCIE CSCD 2025年第4期1597-1618,共22页
Let X be a real uniformly convex and uniformly smooth Banach space and C a nonempty closed and convex subset of X.Let ΠC:X→C denote the generalized metric projection operator introduced by Alber in[1].In this pap... Let X be a real uniformly convex and uniformly smooth Banach space and C a nonempty closed and convex subset of X.Let ΠC:X→C denote the generalized metric projection operator introduced by Alber in[1].In this paper,we define the Gâteaux directional differentiability of ΠC.We investigate some properties of the Gâteaux directional differentiability of ΠC.In particular,if C is a closed ball,or a closed and convex cone(including proper closed subspaces),or a closed and convex cylinder,then,we give the exact representations of the directional derivatives of ΠC.By comparing the results in[12]and this paper,we see the significant difference between the directional derivatives of the generalized metric projection operator ΠC and the Gâteaux directional derivatives of the standard metric projection operator PC. 展开更多
关键词 uniformly convex and uniformly smooth Banach space the generalized metric projection directional differentiability of the generalized metric projection directional derivative of the generalized metric projection
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Some Equivalent Conditions for the Differentiability of Continuous Gauge Functions on Banach Space 认领 引用
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作者 南朝勋 《Chinese Quarterly Journal of Mathematics》 1992年第4期84-88,共5页
In this paper,some equivalent conditions for differentiability of condtinuous gauge function are given.
关键词 gauge function subgradient Gauteaux differentiability Frechet differentiability
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DIFFERENTIABILITY OF CONVEX FUNCTIONS AND ASPLUND SPACES 认领 引用 被引量：3
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作者 程立新 张风 《Acta Mathematica Scientia》 SCIE 1995年第2期171-179,共9页
Characterizations of differentiability are obtained for continuous convex functions defined on nonempty open convex sets of Banach spaces as a generalization and application of a mumber of mathematicians several years... Characterizations of differentiability are obtained for continuous convex functions defined on nonempty open convex sets of Banach spaces as a generalization and application of a mumber of mathematicians several years effort, and a characteristic theorem is given for Banach spaces which are (weak) Asplund spaces. 展开更多
关键词 CONVEX FUNCTION DIFFERENTIABILITY BANACH SPACE ASPLUND SPACE
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ON THE CONTINUITY AND DIFFERENTIABILITY OF AKIND OF FRACTAL INTERPOLATION FUNCTION 认领 引用
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作者 李红达 叶正麟 高行山 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2002年第4期471-478,共8页
The sufficient conditions of Holder continuity of two kinds of fractal interpolation functions defined by IFS (Iterated Function System) were obtained. The sufficient and necessary condition for its differentiability ... The sufficient conditions of Holder continuity of two kinds of fractal interpolation functions defined by IFS (Iterated Function System) were obtained. The sufficient and necessary condition for its differentiability was proved. Its derivative was a fractal interpolation function generated by the associated IFS, if it is differentiable. 展开更多
关键词 fractal interpolation function Holder continuity differentiability
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HOLDER CONTINUITY AND DIFFERENTIABILITY ON CONVERGING SUBSEQUENCES 认领 引用
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作者 Volker Elling 《Acta Mathematica Scientia》 SCIE CSCD 2012年第1期75-83,共9页
It is shown that an arbitrary function from D Rn to Rm will become C0,a-continuous in almost every x∈ D after restriction to a certain subset with limit pointx. For n 〉 m differentiability can be obtained. Examples ... It is shown that an arbitrary function from D Rn to Rm will become C0,a-continuous in almost every x∈ D after restriction to a certain subset with limit pointx. For n 〉 m differentiability can be obtained. Examples show the Ho1der exponent a=min{1,n/m}is optimal. 展开更多
关键词 Ho1der continuity Lipschitz continuity differentiability restriction weaksolution
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ON THE PRODUCT OF GTEAUX DIFFERENTIABILITY LOCALLY CONVEX SPACES 认领 引用 被引量：1
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作者 沈喜生 程立新 《Acta Mathematica Scientia》 SCIE 2005年第3期395-400,共6页
A locally convex space is said to be a Gateaux differentiability space (GDS) provided every continuous convex function defined on a nonempty convex open subset D of the space is densely Gateaux differentiable in .D.Th... A locally convex space is said to be a Gateaux differentiability space (GDS) provided every continuous convex function defined on a nonempty convex open subset D of the space is densely Gateaux differentiable in .D.This paper shows that the product of a GDS and a family of separable Prechet spaces is a GDS,and that the product of a GDS and an arbitrary locally convex space endowed with the weak topology is a GDS. 展开更多
关键词 Convex function locally convex space Gateaux differentiability space
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DIFFERENTIABILITY FOR THE HIGH DIMENSIONAL POLYNOMIAL-LIKE ITERATIVE EQUATION 认领 引用 被引量：12
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作者 李晓培 邓圣福 《Acta Mathematica Scientia》 SCIE 2005年第1期130-136,共7页
This paper studies the smoothness of solutions of the higher dimensional polynomial-like iterative equation. The methods given by Zhang Weinian([7]) and by Kulczvcki M, Tabor j.([3]) are improved by constructing a new... This paper studies the smoothness of solutions of the higher dimensional polynomial-like iterative equation. The methods given by Zhang Weinian([7]) and by Kulczvcki M, Tabor j.([3]) are improved by constructing a new operator for the structure of the equation in order to apply fixed point theorems. Existence, uniqueness and stability of continuously differentiable solutions are given. 展开更多
关键词 iteration fixed point theorem differentiable solutions existence uniqueness stability
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The differentiability of solutions for elliptic equations which degenerate on part of the boundary of a convex domain 认领 引用
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作者 SONG Jia-xin CAO Yi 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2018年第4期421-435,共15页
In this paper,we study the differentiability of solutions on the boundary for equartions of type L_λu=~2u/x^2+|x|2λ~2u/y^2=f(x,y),whereλis an arbitrary positive number.By introducing a proper metric that... In this paper,we study the differentiability of solutions on the boundary for equartions of type L_λu=~2u/x^2+|x|2λ~2u/y^2=f(x,y),whereλis an arbitrary positive number.By introducing a proper metric that is related to the elliptic operator L_λ,we prove the differentiability on the boundary when some well-posed boundary conditions are satisfied.The main difficulty is the construction of new barrier functions in this article. 展开更多
关键词 elliptic equations convex domain differentiability
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Differentiability of Functions on Spheres and Criterions of Convexity 认领 引用
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作者 CHEN Tingting GUO Qi 《Wuhan University Journal of Natural Sciences》 CAS CSCD 2022年第4期273-280,共8页
Some basic concepts for functions defined on subsets of the unit sphere,such as the s-directional derivative,s-gradient and s-Gateaux and s-Frechet differentiability etc,are introduced and investigated.These concepts ... Some basic concepts for functions defined on subsets of the unit sphere,such as the s-directional derivative,s-gradient and s-Gateaux and s-Frechet differentiability etc,are introduced and investigated.These concepts are different from the usual ones for functions defined on subsets of Euclidean spaces,however,the results obtained here are very similar.Then,as applications,we provide some criterions of s-convexity for functions defined on unit spheres which are improvements or refinements of some known results. 展开更多
关键词 spherical convexity spherically convex function Gateaux and Frechet differentiability criterion of convexity
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ON TERM BY TERM DYADIC DIFFERENTIABILITY OF WALSH-KACZMARZ SERIES 认领 引用 被引量：2
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作者 Gyorgy Gdt 《Analysis in Theory and Applications》 2003年第1期55-75,共21页
The aim of this paper is to prove the following theorem concerning the term by term differentiation the-orem of Walsh-Kaczmarz series. Let (ck) be a decreasing real sequence withare integrable functions and f(x) is a.... The aim of this paper is to prove the following theorem concerning the term by term differentiation the-orem of Walsh-Kaczmarz series. Let (ck) be a decreasing real sequence withare integrable functions and f(x) is a. e. dyadic (or Butzer and Wagner) differentiate withThe function Kk means the kth Walsh-Kaczmarz function. 展开更多
关键词 dyadic (Butzer and Wagner) differentiability Walsh-Kaczmarz series monotone coefficients Fejer kernels
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Differentiability of Convex Functions in Locally Convex Spaces(Ⅰ)──Continuous Convex Functions and Gateaux Differentiability 认领 引用 被引量：3
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作者 吴从 程立新 《Journal of Harbin Institute of Technology(New Series)》 CAS 1994年第1期7-12,共6页
The aim of this paper is to investigate the differentiability(Gateaux differentiabllity and subdifferentiability) of continuous convex functions on locally convex spaces and to study the behaviour of some important re... The aim of this paper is to investigate the differentiability(Gateaux differentiabllity and subdifferentiability) of continuous convex functions on locally convex spaces and to study the behaviour of some important results for this research area in locally convex spaces. 展开更多
关键词 ss: Differentiability convex function locally convex space
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DIFFERENTIABILITY OF C_0-SEMIGROUPS WITH APPLICATION  认领 引用
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作者 金振东 喻文焕 +1 位作者 靳展 王辅敏 《Transactions of Tianjin University》 CAS 1999年第2期25-29,共5页
This paper considers the differentiability of C 0 semigroups with respect to (w.r.t.) parameters contained in their infinitesimal generators.It is proved that the generalized continuity and strong differentiability of... This paper considers the differentiability of C 0 semigroups with respect to (w.r.t.) parameters contained in their infinitesimal generators.It is proved that the generalized continuity and strong differentiability of their infinitesimal generators w.r.t.parameters imply the differentiability of the C 0 semigroups.The results are applied to the differentiability of the solution of a linear delay differential equation w.r.t.its delays. 展开更多
关键词 C 0 semigroup infinitesimal generator generalized continuity strongly Frechet differential dalay equation
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Differentiability of the Pritchard-Salamon systems with admissible state-feedback 认领 引用
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作者 于欣 《Journal of Zhejiang University-SCIENCE A》 CAS 2005年第4期311-314,共4页
Many papers on a wide range of control problems for Pritchard-Salamon systems have appeared and many of its important mathematical and system theoretical properties have been revealed. This paper deals with the differ... Many papers on a wide range of control problems for Pritchard-Salamon systems have appeared and many of its important mathematical and system theoretical properties have been revealed. This paper deals with the differentiability of the Pritchard-Salamon system with admissible state-feedback. Spectrum analysis showed that under definite condition, the unbounded perturbation semigroup of the Pritchard-Salamon system is eventually differentiable. 展开更多
关键词 C_0-semigroup Differentiability Admissible operator Pritchard-Salamon systems Perturbation
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Smulyan Lemma and Differentiability of the Support Function 认领 引用
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作者 Ildar Sadeqi Sima Hassankhali 《Analysis in Theory and Applications》 CSCD 2018年第4期348-357,共10页
The purpose of this paper is to verify the Smulyan lemma for the support function, and also the Gateaux differentiability of the support function is studied on its domain. Moreover, we provide a characterization of Fr... The purpose of this paper is to verify the Smulyan lemma for the support function, and also the Gateaux differentiability of the support function is studied on its domain. Moreover, we provide a characterization of Frechet differentiability of the support function on the extremal points. 展开更多
关键词 Frechet and Gateaux differentiability support function strict convexity Smulyan lemma
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Differentiability of Convex Functions in Locally Convex Spaces(Ⅱ)──Frechet 认领 引用
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作者 王晓敏 程立新 《Journal of Harbin Institute of Technology(New Series)》 CAS 1997年第1期1-4,共4页
DifferentiabilityofConvexFunctionsinLocallyConvexSpaces（II）──FrechetDifferentiabilityWUCongxinWANGXiaominCHENGLixin吴从aaay，王晓敏...
关键词 王晓 Differentiability of Convex Functions in Locally Convex Spaces Frechet
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Characterizations of Differentiability Points of Norms on c0(Г)and l∞(Г) 认领 引用
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作者 Wu Congxin Cheng Lixin Yao Xiaobo 《Northeastern Mathematical Journal》 1996年第2期153-160,共8页
Characterizations of Frechet(Gateaux)differentiability points of the original norms of co(Г)and l∞(Г)and Day’s norm on c0(Г)are given.
关键词 Banach Space Asplund Space Differentiability Point of Norm
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Infinite Differentiability of the Free Energy for a Derrida–Retaux System 认领 引用
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作者 Xinxing Chen 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2026年第6期1457-1480,共24页
We consider a recursive system which was introduced by Derrida and Retaux(J.Stat.Phys.,156,268-290(2014))as a toy model to study the depinning transition in presence of disorder.Derrida and Retaux predicted the free e... We consider a recursive system which was introduced by Derrida and Retaux(J.Stat.Phys.,156,268-290(2014))as a toy model to study the depinning transition in presence of disorder.Derrida and Retaux predicted the free energy F∞(p)of the system exhibit quite an unusual physical phenomenon which is an infinite order phase transition.Hu and Shi(J.Stat.Phys.,172,718-741(2018))studied a special situation and obtained other behavior of the free energy,while insisted on p=pc being an essential singularity.Recently,Chen,Dagard,Derrida,Hu,Lifshits and Shi(Ann.Probab.,49,637-670(2021))confirmed the Derrida-Retaux conjecture under suitable integrability condition.However,from a mathematical point of view,it is still unknown whether the free energy is infinitely differentiable at the critical point.So we continue to study the infinite differentiability of the free energy in this paper. 展开更多
关键词 Derrida–Retaux system infinite differentiability infinite order phase transition free energy recursive distribution equation
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CpMYB114-like enhances CpNADP-ME2 expression to induce malate reduction and sugar accumulation during papaya ripening 认领 引用 被引量：2
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作者 Chenping Zhou Ruibin Kuang +5 位作者 Xiaming Wu Ze Xu Han He Chuanhe Liu Yuerong Wei Min Yang 《Horticultural Plant Journal》 SCIE CAS CSCD 2026年第8期1810-1826,共17页
Sugars and organic acids form the core fundamental flavor foundation of ripe papaya fruit.Although R2R3-type v-myb myeloblastosis viral oncogene homolog transcription factors(R2R3-MYB TFs)have been reported to play im... Sugars and organic acids form the core fundamental flavor foundation of ripe papaya fruit.Although R2R3-type v-myb myeloblastosis viral oncogene homolog transcription factors(R2R3-MYB TFs)have been reported to play important roles in regulating the primary and secondary metabolism in fruits.However,the functions and underlying regulatory mechanisms of R2R3-MYB TFs in the metabolism of sugars and organic acids during papaya ripening remain unclear.In this study,through RNA sequencing(RNA-seq)coupled with quantitative real-time polymerase chain reaction(qRT-PCR)validation,a novel ethylene-responsive R2R3-MYB TF gene,CpMYB114-like(CpMYB114L),was identified.Transcriptome analysis and ethylene induction assays highlighted CpMYB114L as the key MYB gene activated during papaya ripening.Subcellular localization experiments confirmed that CpMYB114L was localized in the nucleus.Analyses of transgenic papaya fruits and calli,demonstrated that CpMYB114L promoted the accumulation of glucose,fructose,and sucrose,while simultaneously accelerating malate degradation.DNA Affinity Purification sequencing(DAP-seq)combined with yeast one-hybrid(Y1H)assays identified that CpMYB114L directly bound to the promoters of two sugar/organic acid metabolism-related genes,Isocitrate dehydrogenase 5(CpIDH5)and NADP-dependent malic enzyme 2(CpNADP-ME2).Electrophoretic mobility shift(EMSA),dual-luciferase reporter(Dual-LUC)and chromatin immunoprecipitation-quantitative PCR(ChIP-qPCR)assays further confirmed that CpMYB114L positively activated the expression of CpIDH5 and CpNADP-ME2 by directly binding to the specific regions of their promoters.Notably,transient overexpression of CpNADP-ME2 in papaya fruits and calli recapitulated decreased malate levels and increased sugar content,whereas CpIDH5 overexpression did not exhibit any functional relevance.This study elucidates a regulatory module,CpMYB114L-CpNADP-ME2,linking malate catabolism and sugar accumulation,offering valuable insights into flavor improvement strategies for papaya. 展开更多
关键词 Carica papaya Differentially expressed genes Ethylene Fruit quality Malic enzyme MYB transcription factor
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Stemness CD24 activation promotes hepatocellular carcinoma progression via an immune escape mechanism 认领 引用 被引量：2
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作者 Yin Cai Lu-Yin Liu +5 位作者 Xiao-Xiao Xia Hao Tang Min Xu Wen-Li Sai Deng-Fu Yao Min Yao 《World Journal of Gastroenterology》 SCIE CAS 2026年第3期143-156,共14页
BACKGROUND Cluster of differentiation 24(CD24)serves as a liver cancer stem cell marker,and its upregulation is related to chronic liver disease malignancy.However,the exact relationship between CD24 expression and he... BACKGROUND Cluster of differentiation 24(CD24)serves as a liver cancer stem cell marker,and its upregulation is related to chronic liver disease malignancy.However,the exact relationship between CD24 expression and hepatocarcinogenesis remains unknown.AIM To investigate CD24 levels among individuals with chronic liver diseases and confirm the alterations in CD24 and programmed death-ligand 1(PD-L1)expression in a dynamic model of rat hepatocarcinogenesis.METHODS Approved by the ethics committee,CD24 levels were detected in the serum of 129 patients with hepatocellular carcinoma(HCC),72 patients with chronic hepatitis(CH),60 patients with liver cirrhosis(LC)and 111 normal control(NC).Receiver operating characteristic curves and clinicopathological characteristics of CD24 were used to evaluate the diagnostic or prognostic value for HCC,and the CD24+T lymphocyte ratio and dynamic alterations in CD24 and PD-L1 expression were confirmed in a rat HCC model.RESULTS Compared with those in the CH,LC and NC groups,the average CD24 level in the HCC group was significantly greater(P<0.01).The CD24+T-cell ratio in the HCC group was greater than that in the CH or NC group.Clinicopathological characteristics of high CD24 in HCC patients included hepatitis B virus infection,single/multicenter status,tumor size,lymph node or extrahepatic metastasis,differentiation degree,tumor-node-metastasis grade,Child-Pugh score,portal vein tumor thrombus and poor prognosis.Mechanistically,CD24 is dynamically upregulated during hepatocarcinogenesis and closely positively correlated with PD-L1 for immune escape,metastasis(CD44),and with respect to HCC markers(Wnt3a,GPC-3 and alpha-fetoprotein).CONCLUSION Activated CD24 promoted HCC formation through programmed death-ligand 1 signaling and could be a valuable biomarker for monitoring chronic liver disease malignancy. 展开更多
关键词 Clusters of differentiation 24 Hepatocarcinogenesis Programmed death-ligand 1 Biomarker Chronic liver disease
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