Abstract:
Let $\mathcal{S}$ be a finite commutative semigroup. The Davenport constant of $\mathcal{S}$, denoted ${\rm D}(\mathcal{S})$, is defined to be the least positive integer $\ell$ such that every sequence $T$ of elements in $\mathcal{S}$ of length at least $\ell$ contains a proper subsequence $T'$ ($T'\neq T$) with the sum of all terms from $T'$ equaling the sum of all terms from $T$. Let $q>2$ be a prime power, and let $\F_q[x]$ be the ring of polynomials over the finite field $\F_q$. Let $R$ be a quotient ring of $\F_q[x]$ with $0\neq R\neq \F_q[x]$. We prove that $${\rm D}(\mathcal{S}_R)={\rm D}(U(\mathcal{S}_R)),$$ where $\mathcal{S}_R$ denotes the multiplicative semigroup of the ring $R$, and $U(\mathcal{S}_R)$ denotes the group of units in $\mathcal{S}_R$.

Abstract:
Let $\mathcal{S}$ be a finite semigroup, and let $E(\mathcal{S})$ be the set of all idempotents of $\mathcal{S}$. Gillam, Hall and Williams in 1972 proved that every sequence of terms from the semigroup $\mathcal{S}$ of length at least $|\mathcal{S}|-|E(\mathcal{S})|+1$ contains a nonempty subsequence whose product is idempotent, which affirmed a question proposed by Erd\H{o}s. They also gave a sequence of terms from a particular semigroup to show the value $|\mathcal{S}|-|E(\mathcal{S})|+1$ is best possible. Motivated by this work, in this paper we completely determined the structure of the extremal sequence $T$ provide that $T$ is a sequence of terms from any finite commutative semigroup $\mathcal{S}$ of length exactly $|\mathcal{S}|-|E(\mathcal{S})|$ such that $T$ contains no nonempty subsequence whose product is idempotent. Moreover, we introduced two combinatorial constants for finite semigroups associated with this Erd\H{o}s' question.

Abstract:
Let $\mathcal{S}$ be a commutative semigroup, and let $T$ be a sequence of terms from the semigroup $\mathcal{S}$. We call $T$ an (additively) {\sl irreducible} sequence provided that no sum of its some terms vanishes. Given any element $a$ of $\mathcal{S}$, let ${\rm D}_a(\mathcal{S})$ be the largest length of the irreducible sequence such that the sum of all terms from the sequence is equal to $a$. In case that any ascending chain of principal ideals starting from the ideal $(a)$ terminates in $\mathcal{S}$, we found the sufficient and necessary conditions of ${\rm D}_a(\mathcal{S})$ being finite, and in particular, we gave sharp lower and upper bounds of ${\rm D}_a(\mathcal{S})$ in case ${\rm D}_a(\mathcal{S})$ is finite. We also applied the result to commutative unitary rings. As a special case, the value of ${\rm D}_a(\mathcal{S})$ was determined when $\mathcal{S}$ is the multiplicative semigroup of any finite commutative principal ideal unitary ring.

Abstract:
Distributed Compressed Sensing (DCS) is an emerging field that exploits both intra- and inter-signal correlation structures and enables new distributed coding algorithms for multiple signal ensembles in wireless sensor networks. The DCS theory rests on the joint sparsity of a multi-signal ensemble. In this paper we propose a new mobile-agent-based Adaptive Data Fusion (ADF) algorithm to determine the minimum number of measurements each node required for perfectly joint reconstruction of multiple signal ensembles. We theoretically show that ADF provides the optimal strategy with as minimum total number of measurements as possible and hence reduces communication cost and network load. Simulation results indicate that ADF enjoys better performance than DCS and mobile-agent-based full data fusion algorithm including reconstruction performance and network energy efficiency.

Abstract:
Studies on Agrobacterium tumefaciens-mediated transformation of wild tobaccos Nicotiana debneyi, Nicotiana clevelandii, and Nicotiana glutinosa were conducted. Leaf disks were infected and
co-cultivated with A. tumefaciens strain EHA105 carrying the binary vector pBISN1 with an intron
interrupted β-glucuronidase (GUS) reporter gene (gusA) and the neomycin phosphotransferase
gene (nptII). Selection and regeneration of kanamycin resistant shoots were conducted on regeneration
medium containing 8.88 μM 6-benzylaminopurine (BAP), 0.57 μM indole-3-acetic acid
(IAA), 50 mg·L^{-1} kanamycin and 250 mg·L^{-1} timentin. Kanamycin resistant shoots were rooted
Murashige and Skoog (MS) medium containing 100 mg·L^{-1} kanamycin and 250 mg·L^{-1} timentin.
Using this protocol, kanamycin-resistant plants were obtained from all three wild tobaccos at frequencies
of 75.6% for N. debneyi, 25.0% for N. clevelandii, and 2.8% for N. glutinosa. Transcripts of nptII and gusA were detected in kanamycin-resistant T0 transformants (i.e., 2 for N. glutinosa and
5 for each of the N. debneyi and N. clevelandii) by the reverse transcript polymerase chain reaction
(RT-PCR), and histochemical GUS assays confirmed expression of gusA in both T_{0} plants and T_{1} seedlings. The results indicate that the protocols are efficient for transformation of wild tobacco N.
debneyi and N. clevelandii.

Abstract:
Let $G$ be a finite abelian group, and let $m>0$ with $\exp(G)\mid m$. Let $s_{m}(G)$ be the generalized Erd\H{o}s-Ginzburg-Ziv invariant which denotes the smallest positive integer $d$ such that any sequence of elements in $G$ of length $d$ contains a subsequence of length $m$ with sum zero in $G$. For any integer $r>0$, let $\mathcal{I}_m^{(r)}$ be the collection of all $r$-uniform intersecting families of size $m$. Let $R(\mathcal{I}_m^{(r)},G)$ be the smallest positive integer $d$ such that any $G$-coloring of the edges of the complete $r$-uniform hypergraph $K_{d}^{(r)}$ yields a zero-sum copy of some intersecting family in $\mathcal{I}_m^{(r)}$. Among other results, we mainly prove that $\Omega(s_{m}(G))-1\leq R (\mathcal{I}_{m}^{(r)}, \ G)\leq \Omega(s_{m}(G)),$ where $\Omega(s_{m}(G))$ denotes the least positive integer $n$ such that ${n-1 \choose r-1}\geq s_{m}(G)$, and we show that if $r\mid \Omega(s_{m}(G))-1$ then $R (\mathcal{I}_{m}^{(r)}, \ G)= \Omega(s_{m}(G))$.

Abstract:
With continuously increasing of photovoltaic (PV) plant’s penetration, it has become a critical issue to improve the fault ride-through capability of PV plant. This paper refers to the German grid code, and the PV system is controlled to keep grid connected, as well as inject reactive current to grid when fault occurs. The mathematical model of PV system is established and the fault characteristic is studied with respect to the control strategy. By analyzing the effect of reactive power supplied by the PV system to the point of common coupling (PCC) voltage, this paper proposes an adaptive voltage support control strategy to enhance the fault ride-through capability of PV system. The control strategy fully utilizes the PV system’s capability of voltage support and takes the safety of equipment into account as well. At last, the proposed control strategy is verified by simulation.

Abstract:
This paper presents a study carried out at Beijing Normal University with the aim of investigating whether semi-finished products could affect liberal arts students’？mastery of knowledge,？mastery of operational skills？and？ICT self-efficacy？in multimedia creation. The literature has argued that obstacles in creating multimedia artifacts lead liberal arts students to have low ICT self-efficacy. Semi-finished products are used as a scaffolding to facilitate liberal arts students’ creation of multimedia artifacts, such as Flash animations and interactive web-pages. However, empirical research on the effects of such scaffolding is lacking. We conducted a quasi-experiment in which we compared an experimental class of 117 students majoring in History with a control class of 102 students majoring in Chinese Language and Literature who took a Multimedia Technology and Webpage Producing (MTWP) course. The experimental？class (revising condition) used semi-finished products to develop animations and web-pages while the control class (creating condition) developed animations and web-pages from scratch. Data were collected through a Knowledge and Skill Test and a Scale on ICT self-efficacy. T-tests were used to compare outcomes of the two conditions. Results revealed that students’？mastery of knowledge？in the revising condition was significantly higher than students in the creation condition, but there were no significant differences between the two conditions in terms of students’？mastery of operational skills. Results also showed that there were significant differences between the two conditions in terms of students’？

Abstract:
The {\it crossing number} of a graph $G$ is the minimum number of pairwise intersections of edges in a drawing of $G$. In this paper, we give the exact values of crossing numbers for some variations of hypercube with order at most four, including crossed cube, locally twisted cube and M\"{o}bius cube.

Abstract:
Rituximab, the first monoclonal antibody against CD20 molecule, has revolutionized lymphoma therapy [1,2]. More monoclonal antibodies targeting different antigens are being developed for lymphoma therapy [3]. CD19 is specifically expressed in normal and neoplastic lymphoid cells. This review summarizes the molecular structure and functions of CD19 antigen as well as the clinical development of CD19 monoclonal antibodies for lymphoma therapy.The human CD19 antigen is a 95 kd transmembrane glycoprotein belonging to the immunoglobulin (Ig) superfamily [4,5]. It is encoded by the 7.41 kilobite cd19 gene located on the short arm of chromosome 16, 16p11.2 [6]. The gene contains 15 exons and codes for the CD19 molecule with 556 amino acids (Figure？1). There are more than one mRNA transcripts, though only two transcript isoforms have been isolated in vivo[5-7]. Structurally, the gene contains an unusually short 5'-untranslated region. The proximal cd19 promoter lacks a TATA box, and its major start sites are found within 50 bp of the initiation codon [8].CD19 is classified as a type I transmembrane protein, with a single transmembrane domain, a cytoplasmic C-terminus, and extracellular N-terminus. No significant homology exists between CD19 and other known proteins [9]. The extracellular element contains two C2-type Ig-like domains divided by a smaller potential disulfide linked non-Ig-like domain, as well as N-linked carbohydrate addition sites (Figure？2). The highly conserved cytoplasmic domain consists of 242 amino acids with nine tyrosine residues near the C-terminus [9-11]. Multiple studies have come to suggest that the biologic functions of CD19 are dependent on three cytoplasmic tyrosine residues – Y391, Y482 and Y513. Experiments have shown that substitution of phenylalanine for tyrosine at two of the positions, Y482 and Y513, leads to inhibited phosphorylation of the other seven tyrosines [12-14].CD19 was first identified as the B4 antigen of human B lymphocytes th