Abstract:
To analyze extreme climatic change features and effects on runoff in the Manas River basin, Xinjiang, data were collected including daily mean temperature, daily highest and lowest temperatures, and daily precipitation from six meteorological stations in the Manas River basin as well as daily runoff data from the Kensiwate hydrologic stations during 1960-2010. By adopting the threshold value of extreme climatic events defined by ET ALDDMI and with the aid of nonparametric statistical tests, Pearson III methods, and others, the effect of extreme climatic events on extreme runoff in the past 50 years in the Manas River basin, Xinjiang, was analyzed. The results showed that in the past 50 years, 1) extreme warming events (annual extreme maximum temperature, warm-day and warm-night index) have risen significantly (P < 0.05). Among these the warm-day and warm-night indices decreased abruptly in 2001 and 1996, respectively. With respect to extreme cold events (annual extreme minimum temperature, cold-day and cold-night indices), the extreme minimum temperature was high after 1976, and the cold-day index weakened significantly, similar to the cold-night index. 2) Except for the continuous drought days (CDD), the other five indices of extreme precipitation events appeared to trend upward, with an abrupt change around 1993. 3) Flood events in 1990, mostly in summer, accounted for 42.9% of the total number of floods since 1960. Floods increased mainly because extremely high summer temperatures increased snowmelt, increasing inflow to the rivers, which combined with more precipitation to cause the increase in summer peak flood discharge.

Abstract:
InConsumer to Business (C2B)mode driven by consumer demand, enterprises must not
only meet the requirements of individual customers, but also take into account
the trade-off between cost and profit. Customization-massing becomes the core
model successfully
implementing the C2B.This articleanalyses and expounds the principle and the main way
of realizing C2B by customization-massing from two aspects “personalized marketing” and “flexible production”, and proposes “Intelligent manufacturing” and “3D technology” will be the future direction of C2B development in
China.

Abstract:
In this paper, we construct families of irreducible representations for a class of quantum groups $U_{q}(f_{m}(K))$. First, we give a natural construction of irreducible weight representations for $U_{q}(f_{m}(K))$ using methods in spectral theory developed by Rosenberg. Second, we study the Whittaker model for the center of $U_{q}(f_{m}(K))$. As a result, the structure of Whittaker representations is determined, and all irreducible Whittaker representations are explicitly constructed. Finally, we prove that the annihilator of a Whittaker representation is centrally generated.

Abstract:
Starting from a Hecke $R-$matrix, Jing and Zhang constructed a new deformation $U_{q}(sl_{2})$ of $U(sl_{2})$, and studied its finite dimensional representations in \cite{JZ}. Especically, this algebra is proved to be just a bialgebra, and all finite dimensional irreducible representations are constructed in \cite{JZ}. In addition, an example is given to show that not every finite dimensional representation of this algebra is completely reducible. In this note, we take a step further by constructing more irreducible representations for this algebra. We first construct points of the spectrum of the category of representations over this new deformation by using methods in noncommutative algebraic geometry. Then applied to the study of representations, our construction recovers all finite dimensional irreducible representations as constructed in \cite{JZ}, and yields new families of infinite dimensional irreducible weight representations of this new deformation $U_{q}(sl_{2})$.

Abstract:
Motivated by the study of invariant rings of finite groups on the first Weyl algebras $A_{1}$ (\cite{AHV}) and finding interesting families of new noetherian rings, a class of algebras similar to $U(sl_{2})$ were introduced and studied by Smith in \cite{S}. Since the introduction of these algebras, research efforts have been focused on understanding their weight modules, and many important results were already obtained in \cite{S} and \cite{Ku}. But it seems that not much has been done on the part of nonweight modules. In this note, we generalize Kostant's results in \cite{K} on the Whittaker model for the universal enveloping algebras $U(\frak g)$ of finite dimensional semisimple Lie algebras $\frak g$ to Smith's algebras. As a result, a complete classification of irreducible Whittaker modules (which are definitely infinite dimensional) for Smith's algebras is obtained, and the submodule structure of any Whittaker module is also explicitly described.

Abstract:
We study algebra endomorphisms and derivations of some localized down-up algebras $\A$. First, we determine all the algebra endomorphisms of $\A$ under some conditions on $r$ and $s$. We show that each algebra endomorphism of $\A$ is an algebra automorphism if $r^{m}s^{n}=1$ implies $m=n=0$. When $r=s^{-1}=q$ is not a root of unity, we give a criterion for an algebra endomorphism of $\A$ to be an algebra automorphism. In either case, we are able to determine the algebra automorphism group for $\A$. We also show that each surjective algebra endomorphism of the down-up algebra $A(r+s, -rs)$ is an algebra automorphism in either case. Second, we determine all the derivations of $\A$ and calculate its first degree Hochschild cohomology group.

Abstract:
In this paper, we study a class of down-up algebras $\A$ defined over a polynomial base ring $\K[t_{1}, \cdots, t_{n}]$ and establish several analogous results. We first construct a $\K-$basis for the algebra $\A$. As a result, we prove that the Gelfand-Kirillov dimension of $\A$ is $n+3$ and completely determine the center of $\A$ when $char\K=0$. Then, we prove that the algebra $\A$ is a noetherian domain if and only if $\beta\neq 0$; and $\A$ is Auslander-regular when $\beta \neq 0$. We also prove that the global dimension of $\A$ is $n+3$; and the algebra $\A$ is a prime ring except $\alpha=\beta=\phi=0$. Moreover, we obtain some results on the Krull dimension, isomorphisms, and automorphisms of the algebra $\A$.

Abstract:
We determine the group of algebra automorphisms for the two-parameter quantized enveloping algebra $\V$. As an application, we prove that the group of Hopf algebra automorphisms for $\V$ is isomorphic to a torus of rank two.

Abstract:
In this paper, we completely determine the group of algebra automorphisms for the two-parameter Hopf algebra ${\check U}_{r,s}^{\geq 0}({\mathfrak sl_{3}})$. As a result, the group of Hopf algebra automorphisms is determined for $\V$ as well. We further characterize all the derivations of the subalgebra $U^{+}_{r,s}({\mathfrak sl_{3})}$, and calculate its first degree Hochschild cohomology group.