Abstract:
Apple is one of the most important fruit trees in
temperate zones, and is cultivated widely throughout the world. Drought stress
affects the normal growth of apple tree, and further affects fruit yield and
quality. The present study examined the effects of drought on photosynthesis
and water use efficiency (WUE) of two apple cultivars (Honeycrisp and Yanfu 3)
that differ in drought tolerance. The results showed that the photosynthetic
rate decreased in response to drought stress for both cultivars, with
significant differences in intensity. Values for net photosynthetic rate (Pn)
in stressed Yanfu 3 remained significantly lower than in the controls, while, forHoneycrisp, only a slight drop in photosynthesis.
Similarly, stomatal conductance (Gs), intercellular CO_{2} concentration (Ci), transpiration rate (Tr) were markedly reduced inYanfu
3 under drought stress. However,
Honeycrisp showed only minor changes. Under drought stress, the contents of Chl
a, Chl b and Chl t in
Yanfu 3 were all decreased significantly compared with the control. However,
little difference in Honeycrisp was noted between stressed plants and controls.
Values for WUE in stressed Yanfu 3 remained higher than in the controls from
day 3 until the end of the experiment, while no significant difference was
observed in Honeycrisp. Furthermore, Honeycrisp also exhibited superior
physiological traits, as indicated by its anatomical and morphological
characteristics. Therefore, we conclude that the superior drought tolerance of
Honeycrisp was due to its anatomical and morphological characteristics, which
possibly contributed to the maintenance of higher photosynthetic capacity than
Yanfu 3.

Abstract:
Whole-rock and mineral separate Ar-Ar dating was carried out for the Linzizong volcanic rocks at Linzhou Basin in Tibet to constrain the time span of volcanism and the corresponding stratigraphic sequence. Sampling was based on detailed geologic mapping and stratigraphic sequence of Dianzhong, Nianbo, Pana Formations, systematically from the bottom to near the top. The results indicate that the Linzizong volcanic rocks erupted from Paleocene to middle of Eocene (64.43· 43.93 Ma). Among them, the Pana Formation formed from ca. 48.73 to 43.9 Ma, the Nianbo Formation around 54 Ma and the Dianzhong Formation from 64.4 to 60.6 Ma. In combination with evidence from the geochemical characteristics of the volcanic rocks, and from stratigraphy in southern Tibet, it is postulated that the age of the lowest member in the Dianzhong Formation of the Linzizong volcanic rock, which overlies unconformably the Late Cretaceous Shexing Formation, likely corresponds to the inception of the collision between Indian and Asian continents in southern Tibet.

Abstract:
A proper vertex coloring of a graph is equitable if the sizes of color classes differ by at most one. The equitable chromatic number of a graph $G$, denoted by $\chi_=(G)$, is the minimum $k$ such that $G$ is equitably $k$-colorable. The equitable chromatic threshold of a graph $G$, denoted by $\chi_=^*(G)$, is the minimum $t$ such that $G$ is equitably $k$-colorable for $k\ge t$. We develop a formula and a linear-time algorithm which compute the equitable chromatic threshold of an arbitrary complete multipartite graph.

Abstract:
A proper vertex coloring of a graph is equitable if the sizes of color classes differ by at most 1. The equitable chromatic number of a graph $G$, denoted by $\chi_=(G)$, is the minimum $k$ such that $G$ is equitably $k$-colorable. The equitable chromatic threshold of a graph $G$, denoted by $\chi_=^*(G)$, is the minimum $t$ such that $G$ is equitably $k$-colorable for $k \ge t$. In this paper, we give the exact values of $\chi_=(K_{m_1,..., m_r} \times K_n)$ and $\chi_=^*(K_{m_1,..., m_r} \times K_n)$ for $\sum_{i = 1}^r m_i \leq n$.

Abstract:
A proper vertex coloring of a graph is equitable if the sizes of color classes differ by at most 1. The equitable chromatic threshold of a graph $G$, denoted by $\chi_=^*(G)$, is the minimum $k$ such that $G$ is equitably $k^\prime$-colorable for all $k^\prime \ge k$. Let $G\times H$ denote the direct product of graphs $G$ and $H$. For $n\ge m\ge 2$ we prove that $\chi_=^*(K_{m} \times K_n)$ equals $\lceil\frac{mn}{m+1}\rceil$ if $n\equiv 2,...,m (\textup{mod} m+1)$, and equals $m\lceil\frac{n}{s^\star}\rceil$ if $n\equiv 0,1 (\textup{mod} m+1)$, where $s^\star$ is the minimum positive integer such that $s^\star \nmid n$ and $s^\star\ge m+2.$

Abstract:
In this article, we introduce a recurrence formula which only involves two adjacent values of the Riemann zeta function at integer arguments. Based on the formula, an algorithm to evaluate $\zeta$-values(i.e. the values of Riemann zeta function) at odd-integers from the two nearest $\zeta$-values at even-integers is posed and proved. The behavior of the error bound is $O(10^{-n})$ approximately where $n$ is the argument. Our method is especially powerful for the calculation of Riemann zeta function at large argument, while for smaller ones it can also reach spectacular accuracies such as more than ten decimal places.

Abstract:
Let $\kappa(G)$ be the connectivity of $G$. The Kronecker product $G_1\times G_2$ of graphs $G_1$ and $G_2$ has vertex set $V(G_1\times G_2)=V(G_1)\times V(G_2)$ and edge set $E(G_1\times G_2)=\{(u_1,v_1)(u_2,v_2):u_1u_2\in E(G_1),v_1v_2\in E(G_2)\}$. In this paper, we prove that $\kappa(G\times K_2)=\textup{min}\{2\kappa(G), \textup{min}\{|X|+2|Y|\}\}$, where the second minimum is taken over all disjoint sets $X,Y\subseteq V(G)$ satisfying (1)$G-(X\cup Y)$ has a bipartite component $C$, and (2) $G[V(C)\cup \{x\}]$ is also bipartite for each $x\in X$.

Abstract:
Let $\kappa'(G)$ be the edge connectivity of $G$ and $G\times H$ the direct product of $G$ and $H$. Let $H$ be an arbitrary dense graph with minimal degree $\delta(H)>|H|/2$. We prove that for any graph $G$, $\kappa'(G\times H)=\textup{min}\{2\kappa'(G)e(H),\delta(G)\delta(H)\}$, where $e(H)$ denotes the number of edges in $H$. In addition, the structure of minimum edge cuts is described. As an application, we present a necessary and sufficient condition for $G\times K_n(n\ge3)$ to be super edge connected.

Abstract:
The Nimu metamorphic rocks are mainly composed of garnet biotite gneiss and biotite-plagioclase hornblende hornfels, which are exposed on the north side of Yarlung suture zone, southern Tibet. Our studies show that the rocks have metamorphosed to hornblende hornfels facies-pyroxene hornfels facies; garnet porphyroblasts with growth zonation, amphiboles are calcic amphiboles, most of the biotites are ferrobiotites and siderophyllites, most of the feldspars are oligoclases and andesine, with a small amount of...