Abstract:
A proper edge t-coloring of a graph G is a coloring of its edges with colors ？1, 2,..., t,？such that all colors are used, and no two adjacent edges receive the same color. A cyclically interval t-coloring of a graph G is a proper edge t-coloring of G such that for each vertex, either the set of colors used on edges incident to x or the set of colors not used on edges incident to x forms an interval of integers. In this paper, we provide a new proof of the result on the colors in cyclically interval edge colorings of simple cycles which was first proved by Rafayel R. Kamalian in the paper “On a Number of Colors in Cyclically Interval Edge Colorings of Simple Cycles, Open Journal of Discrete Mathematics, 2013, 43-48”.

Abstract:
For a given graph G, a k-role assignment of G is a surjective function ？such that , where N(x) and N(y) are the neighborhoods of x and y, respectively. Furthermore, as we limit the number of different roles in the neighborhood of an individual, we call r a restricted size k-role assignment. When the hausdorff distance between the sets of roles assigned to their neighbors is at most 1, we call r a k-threshold close role assignment. In this paper we study the graphs that have k-role assignments, restricted size k-role assignments and k-threshold close role assignments, respectively. By the end we discuss the maximal and minimal graphs which have k-role assignments.

Abstract:
A total coloring of a graph G is a functionsuch that no adjacent vertices, edges, and no incident vertices and edges obtain the same color. A k-interval is a set of k consecutive integers. A cyclically interval total t-coloring of a graph G is a total coloring a of G with colors 1,2,...,t, such that at least one vertex or edge of G is colored by i,i=1,2,...,t, and for any, the set is a -interval, or is a -interval, where d_{G}(x) is the degree of the vertex x in G. In this paper, we study the cyclically interval total colorings of cycles and middle graphs of cycles.

Abstract:
A total coloring of a graph G with colors 1, 2, ..., t is called a cyclically interval total t-coloring if all colors are used, and the edges incident to each vertex v∈V(G) together with v are colored by (dG(v)+1) consecutive colors modulo t, where dG(v) is the degree of the vertex v in G. The one point union ？of k-copies of cycle Cn is the graph obtained by taking v as a common vertex such that any two distinct cycles？ and？ are edge disjoint and do not have any vertex in common except v. In this paper, we study the cyclically interval total colorings of , where n≥3 and k≥2.

In this paper, we propose a cross-layer design combining
adaptive modulation coding (AMC) and automatic repeat request (ARQ) to minimize
the bit energy consumption under both packet loss rate and retransmission delay
constraints. We analyze the best constellation size of M-ary square quadrature
amplitude modulation (MQAM) in different distance, and give advice on
retransmission limits under different packet loss rates. The impacts of path
loss fading and additive white Gaussian noise (AWGN)are taken into
consideration. The computation of energy consumption includes the circuit,
transmission and retransmission energies at both transmitter and receiver
sides. Numerical results are obtained to verify the validity of our design. We
also show that the retransmission benefit varies with the packet loss rate
constraint.

Abstract:
It is hard to compute the competition number for a graph in general and characterizing a graph by its competition number has been one of important research problems in the study of competition graphs. Sano pointed out that it would be interesting to compute the competition numbers of some triangulations of a sphere as he got the exact value of the competition numbers of regular polyhedra. In this paper, we study the competition numbers of several kinds of triangulations of a sphere, and get the exact values of the competition numbers of a 24-hedron obtained from a hexahedron by adding a vertex in each face of the hexahedron and joining the vertex added in a face with the four vertices of the face, a class of dodecahedra constructed from a hexahedron by adding a diagonal in each face of the hexahedron, and a triangulation of a sphere with 3n (n≥2) vertices.

Abstract:
For an uncontrollable system, adding leaders and adjusting edge weights are two methods to improve controllability. In this paper, controllability of multi-agent systems under directed topologies is studied, especially on leader selection problem and weight adjustment problem. For a given system, necessary and sufficient algebraic conditions for controllability with fewest leaders are proposed. From another perspective, when leaders are fixed, controllability could be improved by adjusting edge weights, and therefore the system is supposed to be structurally controllable, which holds if and only if the communication topology contains a spanning tree. It is also proved that the number of fewest edges needed to be assigned on new weights equals the rank deficiency of controllability matrix. An algorithm on how to perform weight adjustment is presented. Simulation examples are provided to illustrate the theoretical results.

Abstract:
Mitogen-activated
protein kinases (MAPKs) are important components in signal transduction modules
which play crucial roles in regulation of many biological processes in plants.
Although genome-wide analysis of MAPK and MAPKK family has been carried out in
poplar species, few data about the biological function analysis of this gene
family are available to date. In this study, a group C MAPK
gene 84KMPK14was
cloned from hybrid poplar (Populus alba×P.
glandulosa cv. “84K”). It
contained a typical protein kinase domain, a conserved TEY-motif and an atypical
conserved common docking (CD) domain. Sequence alignment revealed that 84KMPK14 was the most homologous to Populus
trichocarpa PtMPK14. Expression
analysis indicated

Abstract:
Self-assembled complexes between cage compounds cucurbit[n = 5–8]urils and hexamethylenetetramine were studied by using NMR techniques. Experimental results reveal that hexamethylenetetramine can lid cucurbit [5] uril to forming self-assembled capsules in which nothing is encapsulated yet; the cavity of the cucurbit[7]uril can accommodate a hexamethylenetetramine molecule to form a selfassembled host-guest inclusion. Moreover, both the cavity interaction of the cucurbit[7]uril with hexamethylenetetramine·HCl and the portal interaction of the dipole carbonyl of the cucurbit[7]uril with hexamethylenetetramine·HCl lead to form self-assembled capsules in which the hexamethylenetetramine·HCl are encapsulated in the hexamethylenetetramine·HCl “lidded” cucurbit[7]uril. Although the structures of the portal and cavity to cucurbit[5]uril are similar, there is no obvious interaction between decamethylcucurbit[5]uril and hexamethylenetetramine, and also between cucurbit [6]uril or cucurbit[8]uril and hexamethylenetetramine.

Abstract:
For the instrument limitation and imperfect imaging optics, it is difficult to acquire high spatial resolution hyperspectral imagery. Low spatial resolution will result in a lot of mixed pixels and greatly degrade the detection and recognition performance, affect the related application in civil and military fields. As a powerful statistical image modeling technique, sparse representation can be utilized to analyze the hyperspectral image efficiently. Hyperspectral imagery is intrinsically sparse in spatial and spectral domains, and image super-resolution quality largely depends on whether the prior knowledge is utilized properly. In this article, we propose a novel hyperspectral imagery super-resolution method by utilizing the sparse representation and spectral mixing model. Based on the sparse representation model and hyperspectral image acquisition process model, small patches of hyperspectral observations from different wavelengths can be represented as weighted linear combinations of a small number of atoms in pre-trained dictionary. Then super-resolution is treated as a least squares problem with sparse constraints. To maintain the spectral consistency, we further introduce an adaptive regularization terms into the sparse representation framework by combining the linear spectrum mixing model. Extensive experiments validate that the proposed method achieves much better results.