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SINGULARLY PERTURBED MARKOV DECISION PROCESSES WITH INCLUSION OF TRANSIENT STATES

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Journal of Systems Science & Complexity 2001年第2期14卷 199-211页

作者： R.H.Liu Q.Zhang G.Yin department of mathematics Bold GSRC The University of GeorgiaAthensGA 30602-7403USA Deportment of mathematics Wayne State UniversityDetroitMI 48202 USA

This paper is concerned with the continuous-time Markov decision processes (MDP) having weak and strong interactions. Using a hierarchical approach, the state space of the underlying Markov chain can be decomposed into several groups of recurrent states and a group of transient states resulting in a singularly perturbed MDP formulation. Instead of solving the original problem directly, a limit problem that is much simpler to handle is derived. On the basis of the optical solution of the limit problem, nearly optimal decisions are constructed for the original problem. The asymptotic optimality of the constructed control is obtained; the rate of convergence is ascertained.

关键词： Markov decision process dynamic programming asymptotically optimal control.

STOCK LOAN VALUATION UNDER A REGIME-SWITCHING MODEL WITH MEAN-REVERTING AND FINITE MATURITY

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Journal of Systems Science & Complexity 2010年第3期23卷 572-583页

作者： David PRAGER department of mathematics University of Georgia

Stock loans are business contracts between borrowers and lenders in which the borroweruses shares of stock as collateral for the *** the value of the collateral is subject to wide andfrequent price swings,valuing such a transaction behaves more like an option pricing problem thana debt valuation *** paper will list,prove,and analyze formulas for stock loan valuationwith finite horizon under various stock models,including classical geometric Brownian motion,meanreverting,and two-state regime-switching with both mean-reverting and geometric Brownian *** examples are reported to illustrate the results.

关键词： Mean reversion regime switching stock loan.

Thermal Diversities of Two Na^+/H^+ Exchanges in Guinea Pig Red Cells

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Biomedical and Environmental Sciences 2001年第3期14卷 171-179页

作者： JI HONG-LONG 1department of Cellular Biology, university of georgia, athens, georgia 30602, usa department of Cellular Biology University of Georgia Athens Georgia 30602 USA. ji@physiology.uab.edu

Objective\ To test the effect of hypothermia on Na+/H+ exchange, activated by shrinkage and cytoplasmic acidosis. Method\ Amiloride-sensitive Na+ influx in guinea pig red cells was traced with isotope 22Na and intracellular Na+ concentration was measured by emission flame photometry. Result\ Amiloride-sensitive Na+ influx decreased linearly as a function of temperatures (about 37℃) in shrunken cells, but increased in acidified cells. The up-regulation of acid-induced Na+/H+ exchange by elevated temperature was enhanced by hypo-osmolarity. Less sensitivity of intracellular H+ site at 41℃ may be the mechanism for the inhibition of shrinkage-induced Na+/H+ exchange by elevated temperature. Heating-mediated explosive increase in the activity of acid-induced Na+/H+ exchange may be due to enhanced extracellular Na+ sensitivity and lower intracellular pH caused by acidic metabolites. Acid-induced Na+/H+ ewxchange contributes to cytoplasmic Na+ accumulation. Conclusion\ These two modes of Na+/H+ exchange with different response to elevated temperature may play different roles in the cellular pathogenesis of heatstroke.

关键词： Animals Cell Culture Techniques Erythrocytes Guinea Pigs Heat Stroke Hydrogen Ion Exchange Research Support, U.S. Gov't, Non-P.H.S. Sodium Temperature

Occupation Measures of Singularly Perturbed Markov Chains with Absorbing States

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Acta Mathematica Sinica,English Series 2000年第1期16卷 161-180页

作者： G.Yin~(1)) department of mathematics,Wayne State university,Detroit,MI 48202,usaQ.Zhang~(2)) department of mathematics,university of georgia,athens,ga 30602,usaG.Badowski~(3)) department of mathematics,Wayne State university,Detroit,MI 48202,usa department of mathematics Wayne State University Detroit MI 48202 USA department of mathematics University of Georgia Athens GA 30602 USA

This paper develops asymptotic properties of singularly perturbed Markov chains with inclusion of absorbing *** focuses on both unscaled and scaled occupation *** mild conditions,a mean-square estimate is *** averaging the fast components,we obtain an aggregated *** the aggregated process itself may be non-Markovian,its weak limit is a Markov chain with much smaller state ***,a suitably scaled sequence consisting of a component of scaled occupation measures and a component of the aggregated process is shown to converge to a pair of processes with a switching diffusion component.

关键词： Singularly perturbed Markov chain Occupation measure Aggregation Absorbing state Weak convergence Switching diffusion

On the Residues of Binomial Coefficients and Their Products Modulo Prime Powers

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Acta Mathematica Sinica,English Series 2002年第2期18卷 277-288页

作者： CAI Tian Xin department of mathematics.Zhejiang university.Hangzhou 310028,P.R.China E-mail:trcai@mail.hz.zj.cnGRANVILLE Andrew department of mathematics,university of georgia.athens,ga 30602.usa E-mail:andrew@sophie.math.uga.edu department of mathematics Zhejiang University Hangzhou P. R. China department of mathematics University of Georgia Athens USA

In this paper,we show several arithmetic properties on the residues of binomial coefficients and their products modulo prime powers,e.g.. for any distinct odd primes p and *** discuss the connections with the prime r... 详细信息

关键词： Binomial coefficients Bernoulli numbers Recognizing primes

A SERENDIPITY FAMILY 0F LOCALLY SUPPORTED SPLINES IN S_8~2(△)

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Analysis in Theory and Applications 1994年第2期10卷 43-53页

作者： Lai Mingjun The university of georgia, usa department of mathematics The university of georgia athens,ga 30602 U.S.A

For a given triangulation Δ of a region R of interest, let S_8~2(Δ): = {s∈C^2(R): s|_1∈P_8,l∈Δ} be the space of all splines of degree 8 and smoothness 2, where t denotes any triangle of Δ and P_8 the space of polynomials of total degree≤8. Furthermore, let S_8~2(Δ):={s∈S_8~3(Δ):s∈C^3 at v, v∈Δ} be a super spline subspace of S_8~2(Δ). We construel a collection of locally supported splines in S_8~2(Δ) which can be used to achieve lhe full approximation order of S_8~2(Δ) and its cardinalily is less than the di- mension of super spline space space S_8~2(Δ).

关键词： A SERENDIPITY FAMILY 0F LOCALLY SUPPORTED SPLINES IN S82 Figure

SYMPLECTIC SCHEMES FOR QUASILINEAR WAVE EQUATIONS OF KLEIN-GORDON AND SINE-GORDON TYPE

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Journal of Computational mathematics 2001年第5期19卷 475-488页

作者： Xiao-wu Lu (department of mathematics and Computer Science, Emory university, Atlanta, ga 30322, usa) Emory university 美国 30322

Presents a class of finite difference methods of first and second order accuracy for the computation of solutions to the quasilinear wave equations. Overview of general symplectic schemes and generating functional; Nu... 详细信息

关键词： Symplectic integration Sine-Gordon equations Finite difference method.

Downstaging strategies for unresectable hepatocellular carcinoma

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World Journal of gastroenterology 2024年第20期30卷 2731-2733页

作者： georgia Sofia Karachaliou Nikolaos Dimitrokallis Dimitrios P Moris Division of gastroenterology Department of MedicineDuke University Medical CenterDurhamNC 27710United States First department of Surgery&Organ Transplant Unit Evangelismos General HospitalAthens 10676Greece department of Surgery Duke University Medical CenterDurhamNC 27710United States

A significant number of patients with hepatocellular carcinoma(HCC)are usually diagnosed in advanced stages,that leads to inability to achieve *** options are focusing on downstaging a locally advanced *** is wellsupported in the literature that patients with HCC who undergo successful conversion therapy followed by curative-intent surgery may achieve a significant survival benefit compared to those who receive chemotherapy alone or those who are successfully downstaged with conversion therapy but not treated with *** artery infusion chemotherapy can be a potential downstaging strategy,since recent studies have demonstrated excellent outcomes in patients with colorectal liver metastatic disease as well as primary liver malignancies.

关键词： Unresectable hepatocellular carcinoma Hepatic arterial infusion chemotherapy Downstaging Hepatocellular carcinoma

Enhancement of endogenous midbrain neurogenesis by microneurotrophin BNN-20 after neural progenitor grafting in a mouse model of nigral degeneration

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Neural Regeneration Research 2024年第6期19卷 1318-1324页

作者： Theodora Mourtzi Nasia Antoniou Christina Dimitriou Panagiotis Gkaravelas georgia Athanasopoulou Panagiota Nti Kostantzo Olga Stathi Efthymia Theodorou Maria Anesti Rebecca Matsas Fevronia Angelatou georgia Kouroupi Ilias Kazanis Laboratory of Developmental Biology Department of Biology University of Patras Laboratory of Cellular and Molecular Neurobiology-Stem Cells Hellenic Pasteur Institute 3. Department of Physiology School of Medicine University of Patras

We have previously shown the neuroprotective and pro-neurogenic activity of microneurotrophin BNN-20 in the substantia nigra of the “weaver” mouse, a model of progressive nigrostriatal degeneration. Here, we extended our investigation in two clinically-relevant ways. First, we assessed the effects of BNN-20 on human induced pluripotent stem cell-derived neural progenitor cells and neurons derived from healthy and parkinsonian donors. Second, we assessed if BNN-20 can boost the outcome of mouse neural progenitor cell intranigral transplantations in weaver mice, at late stages of degeneration. We found that BNN-20 has limited direct effects on cultured human induced pluripotent stem cell-derived neural progenitor cells, marginally enhancing their differentiation towards neurons and partially reversing the pathological phenotype of dopaminergic neurons generated from parkinsonian donors. In agreement, we found no effects of BNN-20 on the mouse neural progenitor cells grafted in the substantia nigra of weaver mice. However, the graft strongly induced an endogenous neurogenic response throughout the midbrain, which was significantly enhanced by the administration of microneurotrophin BNN-20. Our results provide straightforward evidence of the existence of an endogenous midbrain neurogenic system that can be specifically strengthened by BNN-20. Interestingly, the lack of major similar activity on cultured human induced pluripotent stem cell-derived neural progenitors and their progeny reveals the in vivo specificity of the aforementioned pro-neurogenic effect.

关键词： adult neurogenesis BNN-20 brain-derived neurotrophic factor cell replacement induced pluripotent stem cells (iPSCs) neurotrophic factors Parkinson's disease substantia