Abstract:
The optimal geometric mean return is an important property of an asset. As a derivative of the underlying asset, the option also has this property. In this paper, we show that the optimal geometric mean returns of a stock and its option are the same from Kelly criterion. It is proved by using binomial option pricing model and continuous stochastic models with self-financing assumption. A simulation study reveals the same result for the continuous option pricing model. 1. Introduction The original question of Kelly criterion [1] is how to bet the fraction of your total wealth to maximize your long-term wealth when the odds and probabilities of a gambling game are known. Latane [2] first introduced the geometric mean investment strategy into finance and economics. As an application of generalized Kelly criterion, Latane and Tuttle [3] proposed a wealth maximizing model for building portfolios using geometric mean return. Bickel [4] discovered the relationship between optimal long run growth rate and the efficient portfolios based on the minimum variance criterion. Weide et al. [5] and Maier et al. [6] developed a strategy which maximizes the geometric mean return on portfolio investment. Similar research can be found by Ziemba [7], Elton and Gruber [8], and Bernstein and Wilkinson [9]. How to optimize the geometric mean return by the Kelly criterion becomes an important question faced by many portfolio managers and researchers. In the literature, Kelly criterion is also known as growth optimal portfolio, capital growth theory of investment, geometric mean strategy, investment for the long run, and maximum expected log. Estrada [10] used it as geometric mean maximization (GMM) and compared the popular mean variance analysis and Kelly criterion from an empirical perspective. Merton [11] was the first one to address the dynamic portfolio choice problem using the idea from Kelly criterion, which becomes a well-known topic in finance. McEnally [12] provided an overview of Kelly criterion, and MacLean et al. [13] summarized desirable and undesirable properties of Kelly criterion. Stock options are popular in many financial markets. An option is a contract between a buyer and a seller that gives the buyer right to buy or to sell a particular stock at a later day with a fixed price. A call option gives buyers right to buy stock and a put option gives buyers right to sell stock. The theoretical value of an option can be evaluated according to several models. Most of the theorems and models assume that market is free of arbitrage. Arbitrage is to make a guaranteed

Abstract:
In this paper, we give the first detailed proof of the short-time existence of Deane Yang's local Ricci flow. Then using the local Ricci flow, we prove short-time existence of the Ricci flow on noncompact manifolds, whose Ricci curvature has global lower bound and sectional curvature has only local average integral bound. The short-time existence of the Ricci flow on noncompact manifolds with bounded curvature was studied by Wan-Xiong Shi in 1990s. As a corollary of our main theorem, we get the short-time existence part of Shi's theorem in this more general context.

Abstract:
Let $(M^n, g)$ be a complete Riemannian manifold with $Rc\geq -Kg$, $H(x, y, t)$ is the heat kernel on $M^n$, and $H= (4\pi t)^{-\frac{n}{2}}e^{-f}$. Nash entropy is defined as $N(H, t)= \int_{M^n} (fH) d\mu(x)- \frac{n}{2}$. We studied the asymptotic behavior of $N(H, t)$ and $\frac{\partial}{\partial t}\Big[N(H, t)\Big]$ as $t\rightarrow 0^{+}$, and got the asymptotic formulas at $t= 0$. In the Appendix, we got Hamilton-type upper bound for Laplacian of positive solution of the heat equation on such manifolds, which has its own independent interest.

Abstract:
$\mathscr{W}$-entropy and reduced volume for the Ricci flow were introduced by Perelman, which had proved their importance in the study of the Ricci flow. L. Ni studied the analogous concepts for the linear heat equation on the static manifolds, and established an equation which links the large time behavior of these two. Due to the surprising similarity between those concepts in the Ricci flow and the linear heat equation, a natural question whether such equation holds for the Ricci flow ancient solution was asked by L. Ni. In this paper, we gave an alternative proof to L. Ni's original equation based on a new method. And following the same philosophy of this method, we answer L. Ni's question positively for Type I $\kappa$-solutions of the Ricci flow.

Abstract:
Let $(M^n, g)$ be a compact $n$-dim ($n\geq 2$) manifold with nonnegative Ricci curvature, and if $n\geq 3$ we assume that $(M^n, g)\times \mathbb{R}$ has nonnegative isotropic curvature. The lower bound of the Ricci flow's existence time on $(M^n, g)$ is proved. This provides an alternative proof for the uniform lower bound of a family of closed Ricci flows' maximal existence times, which was firstly proved by E. Cabezas-Rivas and B. Wilking. We also get an interior curvature estimates for $n= 3$ under $Rc\geq 0$ assumption among others. Combining these results, we proved the short time existence of the Ricci flow on a large class of $3$-dim open manifolds, which admit some suitable exhaustion covering and have nonnegative Ricci curvature.

Abstract:
In this paper, we study the large time behavior of the heat kernel on complete Riemannian manifolds with nonnegative Ricci curvature, which was studied by P. Li with additional maximum volume growth assumption. Following Y. Ding's original strategy, by blowing down the metric, using Cheeger and Colding's theory about limit spaces of Gromov-Hausdorff convergence, combining with the Gaussian upper bound of heat kernel on limit spaces, we succeed in reducing the limit behavior of the heat kernel on manifold to the values of heat kernels on tangent cones at infinity of manifold with renormalized measure. As one application, we get the consistent large time limit of heat kernel in more general context, which generalizes the former result of P. Li. Furthermore, by choosing different sequences to blow down the suitable metric, we show the first example manifold whose heat kernel has inconsistent limit behavior, which answers an open question posed by P. Li negatively.

Abstract:
As part of our ongoing efforts to sequence and map the watermelon (Citrullus spp.) genome, we have constructed a high density genetic linkage map. The map positioned 234 watermelon genome sequence scaffolds (an average size of 1.41 Mb) that cover about 330 Mb and account for 93.5% of the 353 Mb of the assembled genomic sequences of the elite Chinese watermelon line 97103 (Citrullus lanatus var. lanatus). The genetic map was constructed using an F8 population of 103 recombinant inbred lines (RILs). The RILs are derived from a cross between the line 97103 and the United States Plant Introduction (PI) 296341-FR (C. lanatus var. citroides) that contains resistance to fusarium wilt (races 0, 1, and 2). The genetic map consists of eleven linkage groups that include 698 simple sequence repeat (SSR), 219 insertion-deletion (InDel) and 36 structure variation (SV) markers and spans ~800 cM with a mean marker interval of 0.8 cM. Using fluorescent in situ hybridization (FISH) with 11 BACs that produced chromosome-specifc signals, we have depicted watermelon chromosomes that correspond to the eleven linkage groups constructed in this study. The high resolution genetic map developed here should be a useful platform for the assembly of the watermelon genome, for the development of sequence-based markers used in breeding programs, and for the identification of genes associated with important agricultural traits.

Abstract:
We performed half Roche/454 GS-FLX run for each of the four watermelon fruit developmental stages (immature white, white-pink flesh, red flesh and over-ripe) and obtained 577,023 high quality ESTs with an average length of 302.8 bp. De novo assembly of these ESTs together with 11,786 watermelon ESTs collected from GenBank produced 75,068 unigenes with a total length of approximately 31.8 Mb. Overall 54.9% of the unigenes showed significant similarities to known sequences in GenBank non-redundant (nr) protein database and around two-thirds of them matched proteins of cucumber, the most closely-related species with a sequenced genome. The unigenes were further assigned with gene ontology (GO) terms and mapped to biochemical pathways. More than 5,000 SSRs were identified from the EST collection. Furthermore we carried out digital gene expression analysis of these ESTs and identified 3,023 genes that were differentially expressed during watermelon fruit development and ripening, which provided novel insights into watermelon fruit biology and a comprehensive resource of candidate genes for future functional analysis. We then generated profiles of several interesting metabolites that are important to fruit quality including pigmentation and sweetness. Integrative analysis of metabolite and digital gene expression profiles helped elucidating molecular mechanisms governing these important quality-related traits during watermelon fruit development.We have generated a large collection of watermelon ESTs, which represents a significant expansion of the current transcript catalog of watermelon and a valuable resource for future studies on the genomics of watermelon and other closely-related species. Digital expression analysis of this EST collection allowed us to identify a large set of genes that were differentially expressed during watermelon fruit development and ripening, which provide a rich source of candidates for future functional analysis and represent a valuable incre

Abstract:
为明确黄瓜绿斑驳花叶病毒(Cucumber green mottle mosaic virus,CGMMV)在葫芦上的种传规律,以西瓜砧木葫芦种子为材料,采用双抗体夹心酶联免疫吸附测定法(DAS-ELISA)、反转录聚合酶链式反应(RT-PCR)与生物学检测相结合的方法研究葫芦种子的带毒率和传毒率的关系,并评价了干热处理对病毒的钝化效果。结果表明,DAS-ELISA灵敏度检测种子时,在感染种子研磨液:健康种子研磨液为1:1 000时,带毒量仍能检测出阳性,RT-PCR和DAS-ELISA 两种方法均能准确检测葫芦种子的带毒情况;6个批次的葫芦种子有4个批次呈阳性,带毒率在0~100%之间,贮藏1年后的传毒率在0~5.6%之间;4个为CGMMV阳性的种子批经干热处理后,仅1株实生苗呈阳性。研究表明,CGMMV在葫芦作物上的隐性带毒现象非常普遍;种子的带毒率高而传毒率低,以表面带毒为主,且非常稳定;72℃ 72 h干热处理葫芦种子能有效地钝化CGMMV。 The relationship between the rate of seed contamination and seed-to-seedling transmission of Cucumber green mottle mosaic virus (CGMMV) on gourd seeds was studied and the effect of dry heat treatment on the virus passivation process was evaluated by using DAS-ELISA, RT-PCR and biological detection methods. The results showed that the sensitivity of DAS-ELISA detection was a ratio of 1/1 000 of CGMMV infected/healthy seeds in the grinding fluid mixtures. Both DAS-ELISA and RT-PCR methods could accurately detect CGMMV from gourd seed soaking liquid. Among six batches of gourd seeds, four batches of seeds were positive, and the contamination rates were between 0-100%. After one year of storage, the seed-to-seedling transmission rates were between 0-5.6%. Four batches of commercial gourd seeds infested with CGMMV were treated by dry heat treatment (DHT), only one seedling appeared positive. This study indicated that CGMMV hidden poison phenomenon was very common on the gourd crop. The transmission rate of gourd seed-to-seedling was low while the contamination rate was high, which indicated that the virus mainly distributed on the surface of the seeds and they were very stable. CGMMV could be effectively passivated on gourd seeds treated by DHT method at 72℃ for 72 h.