Abstract:
This paper surveys some recent results and progress on the extremal prob- lems in a given set consisting of all simple connected graphs with the same graphic degree sequence. In particular, we study and characterize the extremal graphs having the maximum (or minimum) values of graph invariants such as (Laplacian, p-Laplacian, signless Laplacian) spectral radius, the first Dirichlet eigenvalue, the Wiener index, the Harary index, the number of subtrees and the chromatic number etc, in given sets with the same tree, unicyclic, graphic degree sequences. Moreover, some conjectures are included.

Abstract:
The Laplacian matrix of a simple graph is the difference of the diagonal matrix of vertex degree and the (0,1) adjacency matrix. In the past decades, the Laplacian spectrum has received much more and more attention, since it has been applied to several fields, such as randomized algorithms, combinatorial optimization problems and machine learning. This paper is primarily a survey of various aspects of the eigenvalues of the Laplacian matrix of a graph for the past teens. In addition, some new unpublished results and questions are concluded. Emphasis is given on classifications of the upper and lower bounds for the Laplacian eigenvalues of graphs (including some special graphs, such as trees, bipartite graphs, triangular-free graphs, cubic graphs, etc.) as a function of other graph invariants, such as degree sequence, the average 2-degree, diameter, the maximal independence number, the maximal matching number, vertex connectivity, the domination number, the number of the spanning trees, etc.

Abstract:
In this paper, we discuss exiting roots of sub-kernel transient matrices $P$ associated with a class of $M-$ matrices which are related to generalized ultrametric matrices. Then the results are used to describe completely all links of the class of matrices in terms of structure of the supporting tree.

Abstract:
A series of three cast polyurethane elastomers were prepared from 2,4-toluene diisocyanate (TDI) and 3,5-dimethyl-thioltoluenediamine (D MTDA) chain extender, with polyethylene adi-pate (PEA), polyoxytetramethylene glycol (PTMG) and polycaprolactone (PCL) soft seg-ments. The polyol molecular weights em-ployed was 2000g/mol. The polyurethane elastomers were characterized by an elec-tronmechanical universal testing machine, an Akron abrasion loss tester, a LX-A Shore du-rometer, a rebound resilience equipment and a Dynamic- Mechanical analyzer. In addition, fractured surface of the polyurethane elas-tomers was investigated by a field emission scanning electron microscopy (SEM). The test results showed the PCL based elastomer ex-hibits the excellent tear and stress-strain properties that polyester based elastomers offer, while retaining superior compression set and resilience similar to polyether based elas-tomers. The static and dynamic properties of the PCL based elastomer were more suitable for dynamic applications. The SEM micro-graphs of all polyurethane samples indicated the existing of the microphase separation structure. Particles of the dispersed phase formed by the hard phase and crystalline part of the soft phase grows bigger with the in-creasing crystallinity of the soft segments. The hard domains are irregular shapes and with the sizes of a few micrometers.

Abstract:
Let $G$ be an unicyclic graph of order $n$ and let $Q_G(x)= det(xI-Q(G))={matrix} \sum_{i=1}^n (-1)^i \varphi_i x^{n-i}{matrix}$ be the characteristic polynomial of the signless Laplacian matrix of a graph $G$. We give some transformations of $G$ which decrease all signless Laplacian coefficients in the set $\mathcal{G}(n,m)$. $\mathcal{G}(n,m)$ denotes all n-vertex unicyclic graphs with matching number $m$. We characterize the graphs which minimize all the signless Laplacian coefficients in the set $\mathcal{G}(n,m)$ with odd (resp. even) girth. Moreover, we find the extremal graphs which have minimal signless Laplacian coefficients in the set $\mathcal{G}(n)$ of all $n$-vertex unicyclic graphs with odd (resp. even) girth.

Abstract:
Let $G$ be a graph of order $n$ and $Q_G(x)= det(xI-Q(G))= \sum_{i=1}^n (-1)^i \varphi_i x^{n-i}$ be the characteristic polynomial of the signless Laplacian matrix of a graph $G$. We give some transformations of $G$ which decrease all signless Laplacian coefficients in the set $\mathcal{B}(n)$ of all $n$-vertex bicyclic graphs. $\mathcal{B}^1(n)$ denotes all n-vertex bicyclic graphs with at least one odd cycle. We show that $B_n^1$ (obtained from $C_4$ by adding one edge between two non-adjacent vertices and adding $n-4$ pendent vertices at the vertex of degree 3) minimizes all the signless Laplacian coefficients in the set $\mathcal{B}^1(n)$. Moreover, we prove that $B_n^2$ (obtained from $K_{2,3}$ by adding $n-5$ pendent vertices at one vertex of degree 3) has minimum signless Laplacian coefficients in the set $\mathcal{B}^2(n)$ of all $n$-vertex bicyclic graphs with two even cycles.

Abstract:
Let $G$ be a graph of order $n$ and let $\mathcal{L}(G,\lambda)=\sum_{k=0}^n (-1)^{k}c_{k}(G)\lambda^{n-k}$ be the characteristic polynomial of its Laplacian matrix. Motivated by Ili\'{c} and Ili\'{c}'s conjecture [A. Ili\'{c}, M. Ili\'{c}, Laplacian coefficients of trees with given number of leaves or vertices of degree two, Linear Algebra and its Applications 431(2009)2195-2202.] on all extremal graphs which minimize all the Laplacian coefficients in the set $\mathcal{U}_{n,l}$ of all $n$-vertex unicyclic graphs with the number of leaves $l$, we investigate properties of the minimal elements in the partial set $(\mathcal{U}_{n,l}^g, \preceq)$ of the Laplacian coefficients, where $\mathcal{U}_{n,l}^g$ denote the set of $n$-vertex unicyclic graphs with the number of leaves $l$ and girth $g$. These results are used to disprove their conjecture. Moreover, the graphs with minimum Laplacian-like energy in $\mathcal{U}_{n,l}^g$ are also studied.

Abstract:
This article introduces the problems of information management in enterprises, such as information decentralization and inefficiency of data utilization

Abstract:
A new entanglement measure, which is called D-concurrence, is proposed. Then the upper and lower bounds for D-concurrence are obtained and the relationship between D-concurrence and the usual concurrence of Wootters was established. In addition, comparing with the usual concurrence, D-concurrence has some special merits.

Abstract:
We present a retrospective review of DNA immunoadsorption (DNA-IA) therapy on clinical symptoms as well as indicators in pediatric cases with systemic lupus erythematosus (SLE), and follow up the short-term curative effects. 16 SLE cases were treated by DNA-IA for 3 times every other day. We observed the changes on clinical manifestations and immunological indicators, in order to compare the alteration of these indicators including clinical manifestations, Systemic Lupus Erythematosus Disease Active Index (SLEDAI) scores, 24 hurinary protein excretion, autoantibodies, serum IgG and complement C3. 13 cases were followed up regularly, within 3 months after DNA-IA therapy, 12 cases of clinical manifestations improved (92.3%). SLEDAI scores in 10 cases decreased from (16.20 ± 12.54) to less than 5 (76.9%), 8 cases of ANA, anti-DNA antibodies were negative (61.5%), 13 cases with IgG level in serum recovered to normal (10.39 ± 4.38) g/L, C3 level rose to normal (1.06 ± 0.23) g/L. 3 to 6 months after IA, clinical manifestations and laboratory examinations in all cases got maximum improved. 9 months after IA, SLEDAI score in 2 cases (15.4%) rose to more than 5, anti-DNA antibody in 2 cases (15.4%) became positive, and 1case (7.7%) with serum C3 decreased again. 2 cases died from multiple organs dysfunction within 3 to 6 months after IA. No serious complications were found during DNA-IA. We recommend that DNA immunoadsorption is a safe and effective therapy for active childhood-onset SLE, which could improve clinical symptoms, eliminate ANA and anti-DNA antibodies. Combining with corticosteroids and immunosuppressive drugs, DNA-IA could significantly reduce the activity of disease and protect vital organs function in the short term.