Vertex disjoint cycles in intersection graphs of bases of matroids

The intersection graph of bases of a matroid M=(E, B) is a graph G=G~I(M) with vertex set V(G) and edge set E(G) such that V(G)=B(M) and E(G)={BB′:|B∩B′|≠0, B, B′∈B(M), where the same notation is used for the vertices of G and the bases of M. Suppose that|V(G~I(M))| =n and k_1+k_2+…+k_p=n, where k_i is an integer, i=1, 2,…, p. In this paper, we prove that there is a partition of V(G~I(M)) into p parts V_1 , V_2,…, V_p such that |V_i| =k_i and the subgraph H_i induced by V_i contains a k_i-cycle when k_i ≥3, H_i is isomorphic to K_2 when k_i =2 and H_i is a single point when k_i =1.     

Enhancement of magnetoelectric properties in a surface-mount magnetoelectric device

The fabrication and properties of a novel double layered surface-mount magnetoelectric(ME) device are investigated and reported. This ME device is made up of two opposite polarized piezoelectric PZT slices bonded on the same side of a magnetostrictive material Metglas, forming a novel two PZT in-series device. ME voltage obtained from the two PZT in-series is obviously higher than that of single PZT in a magnetic field with certain value. The ME voltage coefficient(αV) of the surface-mount ME device is significantly enhanced by adjusting the thickness of Metglas: 1) At a frequency of 1 k Hz, αV of this device increases with the layer number of Metglas increased, and the maximum value of αV is about 4.25 times than the minimum; 2) At a frequency of 5 k Hz, the maximum value of αV is 458 mV /Oe, which derives from the ME device with three layers Metglas. This novel design provides an effective way to manufacture miniature and high sensitive ME devices, which makes it possible to apply ME device into integrated circuit(IC).     

Binding number,minimum degree and bipancyclism in bipartite graphs

Let G =(V_1,V_2,E) be a balanced bipartite graph with2 n vertices.The bipartite binding number of G,denoted by B(G),is defined to be n if G =K_n and min i∈{1,2}|N(S)|n min |N(S)|/|S|otherwise.We call G bipancyclic if it contains a cycle of every even length m for 4 ≤ m ≤ 2n.A theorem showed that if G is a balanced bipartite graph with 2n vertices,B(G) 3 / 2 and n 139,then G is bipancyclic.This paper generalizes the conclusion as follows:Let 0 c 3 / 2 and G be a 2-colmected balanced bipartite graph with 2n(n is large enough) vertices such that B(G) c and δ(G)(2-c)n/(3-c)+2/3.Then G is bipancyclic.     

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.     

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.     

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.     

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.     

<Emphasis Type="Italic">a</Emphasis>-Wythoff’s game with <Emphasis Type="Italic">n</Emphasis> players

Letting a = 1 in a- Wythoff’s game introduced by Fraenkel yields Wythoff’s game which is a well-known 2-player impartial combinatorial game introduced by Wythoff in 1907. A method of solving n-player impartial games was presented by Krawec in 2012. In this paper, we employ Krawec’s function to analyze n > 2 players a-Wythoff’s game and obtain game values for all a 1. The results obtained cover n-player Wythoff’s game, a special case 1-Wythoff’s game.     

The periodic solution for a kind odd order delay differential equation

In this paper, we use the coincidence degree theory to research the odd order delay differential equation a(t)χ(2n+1)(t)+b(t)χ(t)+g(t,-τ(t)))=p(t), and we obtain the sufficient conditions for the existence of periodic solutions, which improves and generalizes some related results in the literatures.     

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.     

Research on a Class of Equations over Finite Fields

Let F_q stand for the finite field of odd characteristic p with q elements(q=p~n,n∈N)and F_q~* denote the set of all the nonzero elements of F_q.In this paper,by using the augmented degree matrix and the result given by Cao,we obtain a formula for the number of rational points of the following equation over F_q:f(x _1,x _2,...,x _n)=(a_1 x_1 x_2~d+a_2 x_2 x_3~d...+a_(n-1)x_(n-1)x_n~d+a_n x_n x_1~d)~λ-bx_1~(d1)x_2~d2...x_n~(dn),with a_i,b∈F_q~*,n≥2,λ0 being positive integers,and d,d_i being nonnegative integers for 1≤i n.This technique can be applied to the polynomials of the form h_1~λ=h_2 with λ being positive integer and h_1,h_2∈F_q[x _1,x _2,...,x _n].It extends the results of the Markoff-Hurwitz-type equations.     

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.     

Influence of growth conditions on the electrochemical synthesis of SnS thin films and their optical properties

Tin sulfide (SnS) thin films were prepared by electrodeposition onto fluorine-doped tin oxide (FTO) glass substrates using an aqueous solution containing SnCl₂ and Na₂S₂O₃ at various deposition potentials (E) and bath concentrations. The pH value and temperature of the solution were kept constant. The deposited films were characterized using X-ray diffraction (XRD), field-emission scanning electron microscopy (FESEM), photoluminescence (PL), and ultraviolet–visible (UV–Vis) spectroscopy. The FESEM images demonstrated that changes in the deposition potential (E) and solution concentration led to marked changes in the morphology of the deposited SnS films. Energy-dispersive X-ray analysis (EDXA) results showed that the Sn/S atomic ratio strongly depended on both the solution concentration and the deposition potential. To obtain an Sn/S atomic ratio approximately equal to 1, the optimal Sn2+/S₂O₃2- molar ratio and E parameter were 1/8 and -1.0 V, respectively. The XRD patterns showed that the synthesized SnS was obviously polycrystalline, with an orthorhombic structure. The effects of the variations of bath concentration and deposition potential on the band-gap energy (E_g) were studied using PL and UV–Vis experiments. The PL spectra of all the SnS films contained two peaks in the visible region and one peak in the infrared (IR) region. The UV–Vis spectra showed that the optical band-gap energy varies from 1.21 to 1.44 eV.     

Influences of the shape of magnetic material on the magnetoelectric properties of the PZT/Metglas composite

In this paper, the influences of the shape of magnetic material on the magnetoelectric(ME) properties of PZT/Metglas magnetoelectric(ME) composites have been investigated. The results indicate that, with the decrease of the waist length(L_w) of the dumbbell-shaped Metglas, the magnetic flux density in the center region and ME coefficients(α_(ME)) of the composites increase, while the optimal bias magnetic field Hdc decreases on the contrary. In an AC magnetic field of 1 kHz, the maximum αME(α_(Max)) of the composite with L_w= 20 mm exhibits 1.3 times larger than that of the one with L_w=50 mm, and the optimal Hdc deceases by 15%. At the resonant frequencies of each composites, α_(Max) is enhanced by 1.3 times as L_w decreases from 50 to 20 mm. The simulation made by Comsol Multiphysics and the theoretical analysis based on an equivalent magnetic circuit confirm the experimental results.     

Stress corrosion cracking of X80 pipeline steel exposed to high pH solutions with different concentrations of bicarbonate

Susceptibilities to stress corrosion cracking (SCC) of X80 pipeline steel in high pH solutions with various concentrations of HCO₃? at a passive potential of ?0.2 V vs. SCE were investigated by slow strain rate tensile (SSRT) test. The SCC mechanism and the effect of HCO₃? were discussed with the aid of electrochemical techniques. It is indicated that X80 steel shows enhanced susceptibility to SCC with the concentration of HCO₃? increasing from 0.15 to 1.00 mol/L, and the susceptibility can be evaluated in terms of current density at ?0.2 V vs. SCE. The SCC behavior is controlled by the dissolution-based mechanism in these circumstances. Increasing the concentration of HCO₃? not only increases the risk of rupture of passive films but also promotes the anodic dissolution of crack tips. Besides, little susceptibility to SCC is found in dilute solution containing 0.05 mol/L HCO₃? for X80 steel. This can be attributed to the inhibited repassivation of passive films, manifesting as a more intensive dissolution in the non-crack tip areas than at the crack tips.     

The Reverse Hoelder Classes in Martingale Setting

In martingale setting, it has been shown that Ap weights can be factorized in terms of A1 weights. This factorization benefits many problems very much. ]n this paper, the new class of RH~ plays the same role for RHs, which makes the reverse HOlder inequalities hold with exponent s＞1, that the class A1 does for Ap class. Therefore, the Jones‘ factorization theorem for Ap weights was extended to include some information about the reverse HOlder classes. And it is the most convenient obiect in weight theory indeed.     

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.     

Reduction in secondary dendrite arm spacing in cast eutectic Al-Si piston alloys by cerium addition

The effects of Ce on the secondary dendrite arm spacing (SDAS) and mechanical behavior of Al-Si-Cu-Mg alloys were investigated. The reduction of SDAS at different Ce concentrations was evaluated in a directional solidification experiment via computer-aided cooling curve thermal analysis (CA CCTA). -The results showed that 0.1wt%-1.0wt% Ce addition resulted in a rapid solidification time, △T_S, and low solidification temperature, △T_S, whereas 0.1wt% Ce resulted in a fast solidification time, △ta-Al, of the α-Al phase. Furthermore, Ce addition refined the SDAS, which was reduced to approximately 36%. The mechanical properties of the alloys with and without Ce were investigated using tensile and hardness tests. The quality index (Q) and ultimate tensile strength of (UTS) Al-Si-Cu-Mg alloys significantly improved with the addition of 0.1wt% Ce. Moreover, the base alloy hardness was improved with increasing Ce concentration.     

Generalized Intersection Bodies with Parameter

AIn 2005, the classical intersection bodies and L_p intersection bodies were extended. Afterwards, the concept of general L_p intersection bodies and the generalized intersection bodies was introduced. In this paper, we define the generalized bodies with parameter. Besides, we establish the extremal values for volume, Brunn-Minkowski type inequality for radial combination and L_p harmonic Blaschke combination of this notion.     

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.