Abstract:
We introduce in this paper the concept of left rings and concern ourselves with rings containing an injective maximal left ideal. Some known results for left idempotent reflexive rings and left rings can be extended to left rings. As applications, we are able to give some new characterizations of regular left self-injective rings with nonzero socle and extend some known results on strongly regular rings. Throughout this paper, denotes an associative ring with identity, and all modules are unitary. For any nonempty subset of a ring , and denote the set of right annihilators of and the set of left annihilators of , respectively. We use , , , , , , and for the Jacobson radical, the prime radical, the set of all nilpotent elements, the left singular ideal, the set of all idempotent elements, the left socle, and the right socle of , respectively. An element of is called left minimal if is a minimal left ideal. An element of is called left minimal idempotent if is left minimal. We use and for the set of all left minimal elements and the set of all left minimal idempotent elements of , respectively. Moreover, let . A ring is called left if every minimal left ideal which is isomorphic to a summand of is a summand. Left rings were initiated by Nicholson and Yousif in [1]. In [2–6], the authors discussed the properties of left rings. In [1], a ring is called left mininjective if for every , and is said to be left minsymmetric if always implies . According to [1], left mininjective left minsymmetric left , and no reversal holds. A ring is called left universally mininjective [1] if is an idempotent left ideal of for every . The work in [2] uses the term left for the left universally mininjective. According to [1, Lemma？？5.1], left rings are left mininjective. A ring is called left min-abel [3] if for each , is left semicentral in , and is said to be strongly left min-abel [3, 7] if every element of is central in . A ring is called left if implies for and . Let be a field and . Then and is empty, so is left . Now let . Then and . Since and , is not left . Let be any ring and and . Then and are all empties, so and are all left . A ring is called left idempotent reflexive [8] if implies for all and . Clearly, is left idempotent reflexive if and only if for any and , implies if and only if for any and , implies . Therefore, left idempotent reflexive rings are left . In general, the existence of an injective maximal left ideal in a ring can not guarantee the left self-injectivity of . In [9], Osofsky proves that if is a semiprime ring containing an injective maximal

Abstract:
We show the equivalence between two notions of log moduli stacks which appear in literatures. In particular, we generalize M.Olsson's theorem of representation of log algebraic stacks and answer a question posted by him (\cite{Ol4} 3.5.3). As an application, we obtain several fundamental results of algebraic log stacks which resemble to those in algebraic stacks.

Abstract:
We report the effect of boron (nitrogen)-divacancy complex defects on the electronic properties of graphene nanoribbon by means of density functional theory. It is found that the defective subbands appear in the conduction band and valence band in accordance with boron (nitrogen)-divacancy defect, respectively; the impurity subbands don’t lead to the transition from the metallic characteristic to a semiconducting one. These complex defects affect the electronic band structures around the Fermi level of the graphene nanoribbon; the charge densities of these configurations have also changed distinctly. It is hoped that the theoretical results are helpful in designing the electronic device.

Abstract:
A novel ZnO photoanode with high specific surface area and good light scattering ability was fabricated for dye-sensitized solar cells(DSSCs).The photoanode comprised of mesoporous ZnO microspheres which were prepared by a solvothermal process.The structures and morphologies of ZnO microspheres were measured and confirmed by means of x-ray diffraction(XRD),scanning electron microscopy(SEM),energy dispersive spectrum(EDS),and multi-point Brunauer-Emmett-Teller(BET) analysis.ZnO microspheres are in sub-microm...

Abstract:
It is proved that if a ring is semiabelian, then so is the skew polynomial ring , where is an endomorphism of satisfying for all . Some characterizations and properties of semiabelian rings are studied. 1. Introduction Throughout the paper, all rings are associative with identities. We always use and to denote the set of all nilpotent elements and the set of all idempotent elements of . According to [1], a ring is called semiabelian if every idempotent of is either right semicentral or left semicentral. Clearly, a ring is semiabelian if and only if either or for every , so, abelian rings (i.e., every idempotent of is central) are semiabelian. But the converse is not true by [1, Example？2.2]. A ring is called directly finite if implies for any . It is well known that abelian rings are directly finite. In Theorem 2.7, we show that semiabelian rings are directly finite. An element of a ring is called a left minimal idempotent if and is a minimal left ideal of . A ring is called left min-abel [2] if every left minimal idempotent element of is left semicentral. Clearly, abelian rings are left min-abel. In Theorem 2.7, we show that semiabelian rings are left min-abel. A ring is called left idempotent reflexive if for any and , implies . Theorem 2.5 shows that is abelian if and only if is semiabelian and left idempotent reflexive. In [3], Wang called an element of a ring an op-idempotent if . Clearly, op-idempotent need not be idempotent. For example, let . Then is an op-idempotent, while it is not an idempotent. In [4], Chen called an element ？potent in case there exists some integer such that . We write for the smallest number of such. Clearly, idempotent is potent, while there exists a potent element which is not idempotent. For example, is a potent element, while it is not idempotent. We use and to denote the set of all op-idempotent elements and the set of all potent elements of . In Corollaries 2.2 and 2.3, we observe that every semiabelian ring can be characterized by its op-idempotent and potent elements. If is a ring and is a ring endomorphism, let denote the ring of skew polynomials over ; that is all formal polynomials in with coefficients from with multiplication defined by . In [1], Chen showed that is a semiabelian ring if and only if is a semiabelian ring. In Theorem 2.13, we show that if is a semiabelian ring with an endomorphism satisfying for all , then is semiabelian. 2. Main Results It is well known that an idempotent of a ring is left semicentral if and only if is right semicentral. Hence we have the following theorem. Theorem 2.1. The

Abstract:
Wakeup scheduling has been widely used in wireless sensor networks (WSNs), for it can reduce the energy wastage caused by the idle listening state. In a traditional wakeup scheduling, sensor nodes start up numerous times in a period, thus consuming extra energy due to state transitions (e.g., from the sleep state to the active state). In this paper, we address a novel interference-free wakeup scheduling problem called compact wakeup scheduling, in which a node needs to wake up only once to communicate bidirectionally with all its neighbors. However, not all communication graphs have valid compact wakeup schedulings, and it is NP-complete to decide whether a valid compact wakeup scheduling exists for an arbitrary graph. In particular, tree and grid topologies, which are commonly used in WSNs, have valid compact wakeup schedulings. We propose polynomial-time algorithms using the optimum number of time slots in a period for trees and grid graphs. Simulations further validate our theoretical results.

Abstract:
Given a number field $F$ with $\o_F$ its ring of integers. For certain $a,b$ and $\alpha$ in $\o_F$, we show that the Artin condition is the only obstruction to the local-global principle for integral solutions of equation $ax^2+by^2=\alpha$. Some concrete examples are presented at last.

Abstract:
Let $X$ be a smooth projective variety over an algebraically closed field $k$ of characteristic $p>0$ of $\dim X\geq 4$ and Picard number $\rho(X)=1$. Suppose that $X$ satisfies $H^i(X,F^{m*}_X(\Omg^j_X)\otimes\Ls^{-1})=0$ for any ample line bundle $\Ls$ on $X$, and any nonnegative integers $m,i,j$ with $0\leq i+j<\dim X$, where $F_X:X\rightarrow X$ is the absolute Frobenius morphism. We prove that by procedures combining taking smooth hypersurfaces of dimension $\geq 3$ and cyclic covers along smooth divisors, if the resulting smooth projective variety $Y$ has ample (resp. nef) canonical bundle $\omega_Y$, then $\Omg_Y$ is strongly stable $($resp. strongly semistable$)$ with respect to any polarization.

Abstract:
Background Streptococcus suis serotype 2 (S. suis 2, SS2) has evolved into a highly infectious entity, which caused the two recent large-scale outbreaks of human SS2 epidemic in China, and is characterized by a toxic shock-like syndrome. However, the molecular pathogenesis of this new emerging pathogen is still poorly understood. Methodology/Principal Findings 89K is a newly predicted pathogenicity island (PAI) which is specific to Chinese epidemic strains isolated from these two SS2 outbreaks. Further bioinformatics analysis revealed a unique two-component signal transduction system (TCSTS) located in the candidate 89K PAI, which is orthologous to the SalK/SalR regulatory system of Streptococcus salivarius. Knockout of salKR eliminated the lethality of SS2 in experimental infection of piglets. Functional complementation of salKR into the isogenic mutant ΔsalKR restored its soaring pathogenicity. Colonization experiments showed that the ΔsalKR mutant could not colonize any susceptible tissue of piglets when administered alone. Bactericidal assays demonstrated that resistance of the mutant to polymorphonuclear leukocyte (PMN)-mediated killing was greatly decreased. Expression microarray analysis exhibited a transcription profile alteration of 26 various genes down-regulated in the ΔsalKR mutant. Conclusions/Significance These findings suggest that SalK/SalR is requisite for the full virulence of ethnic Chinese isolates of highly pathogenic SS2, thus providing experimental evidence for the validity of this bioinformatically predicted PAI.

Abstract:
The existence of weak solutions is studied to the initial Dirichlet problem of the equation =div(|？|()？2？), with inf ()>2. We adopt the method of parabolic regularization. After establishing some necessary uniform estimates on the approximate solutions, we prove the existence of weak solutions.