Properties of a class of groups on <Emphasis Type="Italic">Z</Emphasis><Subscript><Emphasis Type="Italic">m</Emphasis></Subscript>

In this paper, we obtain the factorization of direct production and order of group GL(n, Z _m ) in a simple method. Then we generalize some properties of GL(2, Z _p ) proposed by Huppert, and prove that the group \(GL\left( {2,{Z_{{z^\lambda }}}} \right)\) is solvable. We also prove that group GL(n, Z _p ) is solvable if and only if GL(n, Z _p ) is solvable, and list the generators of groups GL(n, Z _p ) and SL(n, Z _p ). At last, we prove that PSL(2, Z _p )(p > 3) and PSL(n, Z _p )(n > 3) are simple.     

Explicit breather-type and pure <Emphasis Type="Italic">N</Emphasis>-soliton solution of DNLS<Superscript>+</Superscript> equation with nonvanishing boundary condition

Based on a newly revised inverse scattering transform for the derivative nonlinear Schrödinger (DNLS⁺) equation with nonvanishing boundary condition (NVBC), the explicit breather-type and pure N-soliton solution has been derived by some algebra techniques. The two-breather solution and the pure double-soliton solution have been given as two typical examples in illustration of the general formula of the multi-soliton solution. The asymptotic behaviors of the N-soliton solution are discussed in detail.     

A new second-order Mehrotra-type predictor-corrector algorithm for SDO

In Zhang's recent works,a second-order Mehrotra-type predictor-corrector algorithm for linear optimization was extended to semidefinite optimization and derived that the algorithm for semidefinite optimization had O(n~(3/2)log(X~0)~T·S~0/ε) iteration complexity based on the NT direction as Newton search direction. In this paper, we extend the second-order Mehrotra-type predictor-corrector algorithm for linear optimization to semidefinite optimization and discuss the polynomial convergence of the algorithm by modifying the corrector direction and new iterates. It is proved that the iteration complexity is reduced to O(n~(3/2)log(X~0)~T·S~0/ε), which coincides with the currently best iteration bound of Mehrotra-type predictor-corrector algorithm for semidefinite optimization.     

Multi-pattern matching algorithm with wildcards based on bit-parallelism

Multi-pattern matching with wildcards is a problem of finding the occurrence of all patterns in a pattern set{p~1,---,p~k}in a given text t. If the percentage of wildcards in pattern set is not high,this problem can be solved using finite automata. We introduce a multi-pattern matching algorithm with a fixed number of wildcards to overcome the high percentage of the occurrence of wildcards in patterns. In our proposed method,patterns are matched as bit patterns using a sliding window approach. The window is a bit window that slides along the given text,matching against stored bit patterns. Matching process is executed using bit wise operations. The experimental results demonstrate that the percentage of wildcard occurrence does not affect the proposed algorithm's performance and the proposed algorithm is more efficient than the algorithms based on the fast Fourier transform. The proposed algorithm is simple to implement and runs efficiently in O(n+d(n/σ)(m/w))time,where n is text length,d is symbol distribution over k patterns,m is pattern length,and σ is alphabet size.     

Parameter-Dependent Third-Order Susceptibility of InxGa1-xN/GaN Parabolic Quantum Dots

The electron states confined in wurtzite InxGa1-xN/GaN strained quantum dots （QDs） have been investigated in the effective -mass approximation by solving the Schrtdinger equation, in which parabolic confined potential and strong built-in electric field effect （due to the piezoelectricity and spontaneous polarization） have been taken into account. The real part Rex^（3）（0,0,ω） and the imaginary part Imx^（3）（0,0,ω） of the third-order susceptibil- ity describe quadratic electro-optic effects and electro-absorption process of the QDs respectively. And both of them have been calculated in directions parallel and vertical to z axis. Furthermore, the study shows Rex^（3）（0,0,ω） and Imx^（3）（0,0,ω） increase under resonant conditions with the QDs＇ radius and height increase, and the same results occur when the content increase. In addition, the resonant position shift to the lower energy region when the parabolic frequencies increase.     

Glass-forming ability,microhardness, corrosion resistance,and dealloying treatment of Mg60-xCu40Ndx alloy ribbons

The influence of Nd addition on the glass-forming ability (GFA), microhardness, and corrosion resistance of Mg_60-xCu₄₀Nd_x (x=5, 10, 15, 20, and 25, at%) alloys were investigated by differential scanning calorimetry, Vickers-type hardness tests, and electrochemical methods. The results suggest that the GFA and microhardness of the amorphous alloys increase until the Nd content reaches 20at%. The corrosion potential and corrosion current density obtained from the Tafel curves indicate that the Mg₃₅Cu₄₀Nd₂₅ ternary alloy exhibits the best corrosion resistance among the investigated alloys. Notably, nanoporous copper (NPC) was synthesized through a single-step dealloying of Mg_60-xCu₄₀Nd_x (x=5, 10, 15, 20, and 25) ternary alloys in 0.04 mol·L-1 H₂SO₄ solution under free corrosion conditions. The influence of dealloying process parameters, such as dealloying time and temperature, on the microstructure of the ribbons was also studied using the surface diffusivity theory. The formation mechanism of dealloyed samples with a multilayered structure was also discussed.     

A wide neighborhood arc-search interior-point algorithm for convex quadratic programming

In this paper, we propose an arc-search interior-point algorithm for convex quadratic programming with a wide neighborhood of the central path, which searches the optimizers along the ellipses that approximate the entire central path. The favorable polynomial complexity bound of the algorithm is obtained, namely O(nlog(( x~0)~TS~0/ε)) which is as good as the linear programming analogue. Finally, the numerical experiments show that the proposed algorithm is efficient.     

Mg<Superscript>2+</Superscript>-Triggered and pH-Tuned <Emphasis Type="Italic">in vitro</Emphasis> Assembly of Trehalose-6-Phosphate Synthase

The enzyme OtsA (trehalose-P synthase) plays a critical role in the biosynthesis of trehalose, which is a nonreducing disaccharide that plays important functions in many organisms. By using light scattering technique, we discovered that OtsA in Arthrobacter strain A3 polymerized in the presence of divalent metal ions (Mg²⁺ or Ca²⁺), and the kinetics of the assembly was dependent on their concentrations. We identified potential compounds that can affect the kinetics of the polymerization, particularly, heparin, which acts as a very promising inhibitor of the polymerization. The OtsA assembly turns out to be a very delicate process that is finely regulated by pH. OtsA may be in the polymerized form at physiological pH in vivo, suggesting a more complicated mechanism of the enzyme. These unique properties of OtsA provide novel insights into the molecular mechanism of the biosynthesis of trehalose.     

Gracefulness of several unconnected graphs with wheel

In the paper, we study the gracefulness of several unconnected graphs related to wheel. For natural number p ≥1,t ≥1, let n =2t +3, 2t +4, which proved W_n∪K_(p,t)~(1)∪K_(p,t)~(2) is graceful; for p ≥1, t ≥1,let n=2t+3,2t+4, then W_(n,2n+1)∪K_(p,t)~(1)∪K_(p,t)~(2) is graceful and for m≥1,r ≥1, let n =2m +5, W_(n,2n+1) ∪( C_3∨K m) U St( r)is graceful.     

Ranks of repeated-root constacyclic code

By the discussion of division in \(F_{^{^{^{_2 m} } } } \left[ u \right]/\left\langle {u^4 } \right\rangle \), the minimal spanning set and the rank of a (1 + u + u ²) - constacyclic code with an arbitrary length N = 2 ^e n over \(\Phi \) are determined based on the factorization of (x ⁿ - 1) over \({F_{{2^m}}}\).     

Analysis of type II toxin-antitoxin genes <Emphasis Type="Italic">all</Emphasis> 3211-<Emphasis Type="Italic">asl</Emphasis> 3212 in <Emphasis Type="Italic">Anabaena</Emphasis> PCC 7120

The type II toxin-antitoxin genes are responsible for the phenotypic switch to a quasi-dormant state that enables cell survival under stresses, a similar function to heterocyst of cyanobacteria. In this paper, we particularly study the role of gene pair all3211-asl3212 under Spectinomycin stress to reveal how the type II toxin-antitoxin involved in environmental stress responses. Bioinformatics prediction shows that toxin protein gene All3211 is homologous to MazF, a member of mazEF family that encoding nucleases. We clone gene all3211-asl3212 into expression vectors to identify its molecular characteristics. Deletion mutant strains of all3211-asl3212 are selected in a tri-parental mating screen. Phenotype comparisons of mutant and wild type reveals no difference of single-deletion-mutants in pigment integrity, the sensitivity to antibiotics, and heterocyst formation. The results show that deletion mutation of single TAS gene pair all3211-asl3212 results in limited effects on the cellular growth of PCC 7120. Thus, we suggest that dosage compensating might be provided from redundant genes or bypass pathways to offset obvious phenotypic differences.     

An Algorithm for the Spectral Immunity of Binary Sequence with Period 2~n

To resist the fast algebraic attack and fast selective discrete Fourier transform attacks, spectral immunity of a sequence or a Boolean function was proposed. At the same time, an algorithm to compute the spectral immunity of the binary sequence with odd period N was presented, here N is a factor of 2~n-1, where n is an integer. The case is more complicated when the period is even. In this paper, we compute linear complexity of every orthogonal sequence of a given sequence using Chan-Games algorithm and k- error linear complexity algorithm. Then, an algorithm for spectral immunity of binary sequence with period N=2~n is obtained. Furthermore, the time complexity of this algorithm is proved to be O(n).     

A new quantum algorithm for computing RSA ciphertext period

Shor proposed a quantum polynomial-time integer factorization algorithm to break the RSA public-key cryptosystem. In this paper, we propose a new quantum algorithm for breaking RSA by computing the order of the RSA ciphertext C. The new algorithm has the following properties: 1) recovering the RSA plaintext M from the ciphertext C without factoring n; 2) avoiding the even order of the element; 3) having higher success probability than Shor’s; 4) having the same complexity as Shor’s.     

On the Dual <Emphasis Type="Italic">p</Emphasis>-Measures of Asymmetry for Star Bodies

Recently, the connection between p-measures of asymmetry and the L_p -mixed volumes for convex bodies was found soon after the p-measure of asymmetry was proposed, and the Orlicz-measures of asymmetry was proposed inspired by such a kind of connection. In this paper, by a similar way the dual p -measures of asymmetry for star bodies (naturally for convex bodies) is introduced first. Then the connection between dual p -measures of asymmetry and L_p -dual mixed volumes is established. Finally, the best lower and upper bounds of dual p-measures and the corresponding extremal bodies are discussed.     

A generalized funk’s section theorem for measures

If L is a star body in R~n whose central(n-i)-slices have the same(n-i)-dimensional measure μ_(n-i)(with appropriate density)as the central(n-i)-slices of an origin-symmetric star body K,then the corresponding n-dimensional measures μ_n of K and L satisfy μ_n(K)≤μ_n(L).This extends a generalized Funk’s section theorem for volumes to that for measures.     

Molecular phylogenetics of <Emphasis Type="Italic">Gymnocypris</Emphasis> (Teleostei: Cyprinidae) in Lake Qinghai and adjacent drainages

149 complete mitochondrial DNA (mtDNA) cytochrome b (Cyt b) genes (1140 bp) of Gymnocypris przewalskii, Gymnocypris eckloni and Gymnocypris scolistomus from the Lake Qinghai, Yellow River and Qaidam Basin were sequenced and analyzed. Consistent dendrogram indicated that the samples collected from the same species do not constitute a separate monophyletic group and all the samples were grouped into three highly divergent lineages (A, B and C). Among them, Lineage A contained all samples of G. przewalskii from the Lake Qinghai and partial samples of the G. eckloni from the Yellow River. Lineage B contained the remaining samples of G. eckloni from the Yellow River. Lineage C was composed of a monophyletic group by G. eckloni from the Qaidam Basin. Analysis of molecular variance (AMOVA) indicated that most of genetic variations were detected within these three mtDNA lineages (93.12%), suggesting that there are three different lineages of Gymnocypris in this region. Our Cyt b sequence data showed that G. przewalskii was not a polytypic species, and G. scolistomus was neither an independent species nor a subspecies of G. eckloni. The divergent mtDNA lineages of G. eckloni from the Yellow River suggested that gene flow between the different populations was restricted to a certain extent by several gorges on the upper reach of the Yellow River. Lineage B of G. eckloni might be the genetic effect from the ancestor which was incorporated with the endemic schizothoracine fishes when the headward erosion of the Yellow River reached to its current headwaters of late. The G. eckloni from Basin Qaidam was a monophyletic group (lineage C) and F_st values within G. eckloni from the Yellow River were higher than 0.98, suggesting that the gene flow has been interrupted for a long time and the G. eckloni from Basin Qaidam might have been evolved into different species by ecology segregation. The correlation between the rakers number of Gymnocypris and population genetic variation was not significant. All Gymnocypris populations exhibited a low nucleotide diversity (π = 0.00096–0.00485). Therefore the Gymnocypris populations from Basin Qaidam could have experienced severe bottleneck effect in history. Our result suggested Gymnocypris populations of Basin Qaidam should give a high priority in conservation programs.     

Lüroth Expansion Digits and Maclaurin's Inequality

It is well known that for almost all real number x, the geometric mean of the first n digits d_i(x) in the Lüroth expansion of x converges to a number K_0 as n→∞. On the other hand, for almost all x, the arithmetric mean of the first n Lüroth expansion digits d_i(x) approaches infinity as n→∞. There is a sequence of refinements of the AM-GM inequality, Maclaurin's inequalities, relating the 1/k-th powers of the k-th elementary symmetric means of n numbers for 1≤k≤n. In this paper, we investigate what happens to the means of Lüroth expansion digits in the limit as one moves f(n) steps away from either extreme. We prove sufficient conditions on f(n) to ensure divergence when one moves away from the arithmetic mean and convergence when one moves f(n) steps away from geometric mean.     

Enhanced antioxidant capacities <Emphasis Type="Italic">in vivo</Emphasis> caused by the change in key constituent of <Emphasis Type="Italic">Terminalia chebula</Emphasis> Retz. treated with Tibet traditional process

In order to investigate the chemical-biological relationship caused by the special processing technology, the constituent’s content and antioxidant capacity in vivo of Euphorbia fischeriana Steud processing Terminalia chebula Retz. have been tested. Taking T. chebula Retz. as control, the content of gallic acid is analyzed with high performance liquid chromatography (HPLC) method. The results show that the increase of gallic acid concentration from 4.54% to 7.46% leads to enhancement of the antioxidant capacities in vivo of the E. fischeriana Steud processing T. chebula Retz. The significant antioxidant capacity in vivo (p<0.05) of the processed product possesses is better than the unprocessed herb. Its superoxide dismutase (SOD) and malondia-ldehyde (MDA) contents in serum, the MDA content in liver can match the effects of vitamine E when administered at high dosage.     

Fault-tolerant cycles embedding in folded hypercubes

The generalized conditional fault-tolerant embedding is investigated, in which the n-dimensional folded hypercube networks(denoted by FQ_n) acts as the host graph, and the longest fault-free cycle represents the guest graph. Under the conditions looser than that of previous works, it is shown that FQ_n has a cycle with length at least 2~n-2︱F_v︱ when the number of faulty vertices and non-critical edges is at most 2n-4; where ︱F_v︱ is the number of faulty vertices. It provides further theoretical evidence for the fact that FQ_n has excellent node-fault-tolerance and edge-fault-tolerance when used as a topology of large scale computer networks.     

<Emphasis Type="Italic">Lp</Emphasis>-dual mixed geominimal surface area

In this paper, a new Lp-dual mixed geominimal surface area is defined by Lp-dual mixed quermassintegrals, which extends the definition of Lp-dual geominimal surface area and generalizes some related inequalities established by Wan and Wang.