Abstract:
Field experiments were conducted in 2011 on an experimental farm at the Cotton Research Insti-tute, Chinese Academy of Agricultural Sciences, Anyang, China. We conducted experiments with a “SPAD-502” meter to quickly measure the relative value of chlorophyll content in the leaf blades of field cotton. Our goal was to seek a suitable leaf on a cotton plant to diagnose senescence status of crop plants at later stages of growth. We began by studying the dynamic change rule of the dis-tal-most four leaves of the cotton plant during the entire growth period with two early-maturing cultivars (CCRI 36, CCRI 50) and two mid-maturing cultivars (CCRI 41, SCRC 28). We also examined the effect of different nitrogen and potassium fertilizer rates on SPAD values of the leaves of SCRC 28. Our results suggest that SPAD values of the 1st distal stem leaves from two early cultivars can act as good indicators of senescence status in the plants, if they are measured between 10 d before the boll-opening stage and 10 d after boll opening stage. Differences of SPAD values of the 3rd distal stem leaves of two mid-maturing cultivars measured between about 15 d before the boll opening stage and 15 d after the boll opening stage can also be used to measure senescence status in these cotton cultivars. The conclusion can be used for cotton producer to manage N fertilizer better at later growth stage.

Abstract:
In this paper, we want to investigate some kind of Dynkin's game under ambiguity which is represented by Backward Stochastic Differential Equation (shortly BSDE) with standard generator function g(t, y, z). Under regular assumptions, a pair of saddle point can be obtained and the existence of the value function follows. The constrained case is also treated in this paper.

Abstract:
In this paper, we solve the existence problem of optimal stopping problem under some kind of nonlinear expectation named g_\Gamma expectation which was recently introduced in Peng, S.G. and Xu, M.Y. [8]. Our method based on our preceding work on the continuous property of g_\Gamma solution. Generally, the strict comparison theorem does not hold under such nonlinear expectations any more, but we can still modify the classical method to find out an optimal stopping time via continuous property. The mainly used theory in our paper is the monotonic limit theorem of BSDE and nonlinear decomposition theorem of Doob-Meyer's type developed by Peng S.G. [6]. With help of these useful theories, a RCLL modification of the value process can also be obtained by a new approach instead of down-crossing inequality.

Abstract:
In this article, the solution of a statistical inverse problem $M = AU+\mathcal{E}$ by the Bayesian approach is studied where $U$ is a function on the unit circle $\mathbb{T}$, i.e., a periodic signal. The mapping $A$ is a smoothing linear operator and $\mathcal{E}$ a Gaussian noise. The connection to the solution of a finite-dimensional computational model $M_{kn} = A_k U_n + \mathcal{E}_k$ is discussed. Furthermore, a novel hierarchical prior model for obtaining edge-preserving conditional mean estimates is introduced. The convergence of the method with respect to finer discretization is studied and the posterior distribution is shown to converge weakly. Finally, theoretical findings are illustrated by a numerical example with simulated data.

Abstract:
Perfluorodecaline was used as a temporary retinal tamponade. Three weeks after the surgery, a residue of heavy liquid was observed in the anterior chamber, even though the patient had an intact crystalline lens without any tilt or dislocation. The remnant of the heavy liquid was taken out of the anterior chamber immediately to avoid secondary complications.Presence of heavy liquids in the anterior chamber may be associated with zonular defects even though the patient has an intact crystalline lens.Perfluorocarbon liquids (PFCLs) with high specific gravity relative to aqueous or subretinal fluid have been frequently used as intraoperative tools and a short-term tamponade in vitreoretinal surgery [1]. It is usually removed at the end of the procedure; however, occasionally residue may be retained due to hazy media. Some clinical reports have been presented in the literature about remnants of perfluorodecaline in the anterior segment [2,3].We report a case of a patient with perfluorodecaline in the anterior chamber who had an intact crystalline lens following pars plana vitrectomy.A 17-year-old male with progressive visual loss and photopsia was admitted to our ophthalmology clinic. He had a history of blunt trauma with a basketball to his right eye 6 months ago and had begun to suffer from visual disturbances since then. His visual acuity (VA) was 20/400 in his right eye. Dilated fundus exam of his right eye revealed a giant tear in the superotemporal retina with a shallow retinal detachment involving the macula (Figure 1a and 1b). His visual acuity was 20/20 and anterior and posterior segments were normal in the left eye. He underwent a three-port pars plana vitrectomy for the giant tear without crystalline lens extraction. Perfluorodecaline was used intraoperatively. Three weeks postoperatively, perfluorodecaline was observed in the anterior chamber in contact with the corneal endothelium (Figure 2). No tilt or dislocation of the crystalline lens was detected on sli

Abstract:
Verschiedene Gründe bewirken, dass Frauen h ufiger an Alzheimer-Krankheit leiden. Angesichts der langen subklinischen Entwicklung der histopathologischen Merkmale der Alzheimer-Krankheit sollten pr ventive Strategien früh eingesetzt werden. Zahlreiche In-vivo- und In-vitro-Untersuchungen belegen eine neuroprotektive Wirkung für Oestrogen. Nun substituieren Frauen vor allem in den ersten Jahren nach der Menopause Oestrogene. Dieses natürliche Experiment erlaubt nun, die Hypothese, dass Oestrogene vor Alzheimer schützen, epidemiologisch zu überprüfen. In mehreren Fallkontrollstudien und einigen Kohortenstudien wurde im allgemeinen eine protektive Wirkung von Oestrogen (ca. 30 % Risikoreduktion) festgestellt. Kurze und teilnehmerm ssig geringe Interventionsstudien bei Patientinnen mit Alzheimer-Krankheit ergaben positive Resultate. Indessen ist nicht klar, wie weit die kognitiven Verbesserungen durch die bekannte Wirkung von Oestrogen auf Affekt und Befindlichkeit bedingt sind, ohne direkt das Krankheitsgeschehen grunds tzlich zu beeinflussen. Die gegenw rtige Datenlage verlangt nach gr sseren Untersuchungen, die den Stellenwert der Hormonsubstitutionstherapie als prim re und sekund re Pr vention der Alzheimer-Krankheit besser belegen. Gegenw rtig kann Oestrogen bei Patientinnen mit famili rem Risiko, an Alzheimer-Krankheit zu erkranken, und als adjuvante Therapie bei milden Formen der Alzheimer-Krankheit im Frühstadium empfohlen werden.

Abstract:
The next generation ground-based telescopes rely heavily on adaptive optics for overcoming the limitation of atmospheric turbulence. In the future adaptive optics modalities, like multi-conjugate adaptive optics (MCAO), atmospheric tomography is the major mathematical and computational challenge. In this severely ill-posed problem a fast and stable reconstruction algorithm is needed that can take into account many real-life phenomena of telescope imaging. We introduce a novel reconstruction method for the atmospheric tomography problem and demonstrate its performance and flexibility in the context of MCAO. Our method is based on using locality properties of compactly supported wavelets, both in the spatial and frequency domain. The reconstruction in the atmospheric tomography problem is obtained by solving the Bayesian MAP estimator with a conjugate gradient based algorithm. An accelerated algorithm with preconditioning is also introduced. Numerical performance is demonstrated on the official end-to-end simulation tool OCTOPUS of European Southern Observatory.

Abstract:
A risk-neutral method is always used to price and hedge contingent claims in complete market, but another method based on utility maximization or risk minimization is wildly used in more general case. One can find all kinds of special risk measure in literature. In this paper, instead of using market modified risk measure, we use a kind of risk measure induced by g_\Gamma-solution or the minimal solution of a Constrained Backward Stochastic Differential Equation (CBSDE) directly when constraints on wealth and portfolio process comes to our consideration. Such g_\Gamma-solution and the risk measure generated by it is well defined on appropriate space under suitable conditions. We adopt the inf-convolution of convex risk measures to solve some optimization problem. A dynamic version risk measures defined through g_\Gamma-solution and some similar results about optimal problem can be got in our new framework and by our new approach.

Abstract:
In this paper, our aim is to investigate necessary conditions for optimal investment. We model the wealth process by Backward differential stochastic equations (shortly for BSDE) with or without constraints on wealth and portfolio process. The constraints can be very general thanks the non-smooth analysis method we adopted.

Abstract:
Let $G=(V,E)$ be a loopless graph and $\mathcal{T}(G)$ be the set of all spanning trees of $G$. Let $L(G)$ be the line graph of the graph $G$ and $t(L(G))$ be the number of spanning trees of $L(G)$. Then, by using techniques from electrical networks, we obtain the following formula: $$ t(L(G)) = \frac{1}{\prod_{v\in V}d^2(v)}\sum_{T\subseteq \mathcal{T}(G)}\big[\prod_{e = xy\in T}d(x)d(y)\big]\big[\prod_{e = uv\in E\backslash T}[d(u)+d(v)]\big]. $$ As a result, we provide a very simple and different proof of the formula on the number of spanning trees of some irregular line graphs, and give a positive answer to a conjecture proposed by Yan [J. Combin. Theory Ser. A 120 (2013) no. 7, 1642-1648]. By applying our formula we also derive the number of spanning trees of circulant line graphs.