On the Arithmetic of Endomorphism Ring End$$({Z_p} \times {Z_{{p^m}}})$$

For a prime p, let \({E_{P,{P^m}}} = \left\{ {\left( {\begin{array}{*{20}{c}}aamp;b \\ {{p^{m – 1}}c}amp;d \end{array}} \right)\left| {a,b,c \in {Z_p},d} \right. \in {Z_{{p^m}}}} \right\}\). We first establish a ring isomorphism from \({Z_{p,{p^m}}}\)onto \({E_{p,{p^m}}}\). Then we provide a way to compute -d and d^–1 by using arithmetic in Z_p and \({Z_{{p^m}}}\), and characterize the invertible elements of \({E_{p,{p^m}}}\). Moreover, we introduce the minimal polynomial for each element in \({E_{p,{p^m}}}\)and give its applications.     

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.     

Further results on generalized LCM matrices

Let S={x_1,x_2,...,x_n } be a set of n distinct positive integers and f be an arithmetic function.By(f[S])(resp.( f[S])),we denote the n*n matrix whose i,j entry is Σ[x_i,x_j]|l l∈S f(l) (resp.Σx∈Sf(x)-Σ x_i,|l l∈S f(l)-Σ x_j,|l l∈S f(l)+Σ[x_i,x_j]|l l∈S f(l)).In this paper,we first investigate the structures of the matrices ( f[S]) and( f[S]),then we give the formulae for the determinants of these matrices.These extend the results obtained by Bege in 2011.Finally,we give two examples to demonstrate the validity of our main results.     

Critical Chords of Convex Bodies of Constant Width

In this paper, we show that when Minkowski measure of asymmetry of convex body K of constant width is bigger than α (n-1), K has at least n+1 critical chords, where \(\alpha (n) = \frac{{n + \sqrt {2n(n + 1)} }}{{n + 2}}\).     

Global existence and bounded estimate of solutions of the BBM-Burgers equation

By the construction of a Cauchy sequence in a Banach space and the global bounded estimate of solution,we obtain the global existence and the bounded estimate of solution of BBM-Burgers equation without the viscous term u_t +∑ n j=1 f_j(u)_xj-γ_1△u_t+γ_3△~2u=0with large initial date in 4-dimension space.     

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.     

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.     

Relative contribution of the anthropogenic forcing and natural variability to the interdecadal shift of climate during the late 1970s and 1990s

Global warming accelerated after the late 1970s and slowed down after the late 1990s, accompanying the significant interdecadal changes in the regional climate. We hypothesized that the interdecadal changes linearly consisted of two independent components, anthropogenic forcing and natural decadal variability, which can be represented simply by the radiative forcing effect of carbon dioxide \((\text{RF}_{\text {CO}_2})\) and the Pacific Decadal Oscillation (PDO), respectively. The combined effect of the \(\text{RF}_{\text {CO}_2}\) and PDO could explain the majority of the surface temperature changes during the late 1970s and 1990s, but the magnitudes of the relative contribution of the \(\text{RF}_{\text {CO}_2}\) and the PDO are inconsistent in different regions. For both the surface temperature and geopotential height, the \(\text{RF}_{\text {CO}_2}\) could induce significantly positive anomalies over almost the entire globe for these two shifts, exhibiting a larger magnitude in the mid–high latitudes and in the late 1990s shift. The PDO could induce opposite anomalies for the two interdecadal shifts due to its phase transitions (negative-positive–negative). Furthermore, for the shift in the late 1970s, both the \(\text{RF}_{\text {CO}_2}\) (53.7 %–66.7 %) and the PDO (33.3 %–46.3 %) were important in regulating the tropical geopotential height, whereas the \(\text{RF}_{\text {CO}_2}\) dominated the changes in the mid-latitudes. For the western Pacific subtropical high, the \(\text{RF}_{\text {CO}_2}\) (PDO) could explain 52.3 %–62.1 % (37.9 %–47.7 %) of the change. The negative effect of the PDO counteracted most of the \(\text{RF}_{\text {CO}_2}\) effects for the late 1990s shift.     

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.     

Gas-based reduction of vanadium titano-magnetite concentrate: behavior and mechanisms

The reduction of vanadium titano-magnetite pellets by H₂-CO at temperatures from 850 to 1050℃ was investigated in this paper. The influences of pre-oxidation treatment, reduction temperature, and V_H2/(V_H2 + V_CO) on the metallization degree were studied. The results showed that pre-oxidation played a substantial role in the reduction of vanadium titano-magnetite pellets. During the reduction process, the metallization degree increased with increasing temperature and increasing V_H2/(V_H2 + V_CO). The phase transformation of pre-oxidized vanadium titano-magnetite pellets during the reduction process under an H₂ atmosphere and a CO atmosphere was discussed, and the reduced samples were analyzed by scanning electron microscopy (SEM) in conjunction with back scatter electron (BSE) imaging. The results show that the difference in thermodynamic reducing ability between H₂ and CO is not the only factor that leads to differences in the reduction results obtained using different atmospheres. Some of Fe_3-xTi_xO₄ cannot be reduced under a CO atmosphere because of the densification of particles' structure and because of the enrichment of Mg in unreacted cores. By contrast, a loose structure of particles was obtained when the pellets were reduced under an H₂ atmosphere and this structure decreased the resistance to gas diffusion. Moreover, the phenomenon of Mg enrichment in unreacted cores disappeared during H₂ reduction. Both the lower resistance to gas diffusion and the lack of Mg enrichment facilitated the reduction of vanadium titano-magnetite.     

Super-Edge-Connectivity of G(k,d,s)(s≥k/2)

A graph G is super-edge-connected,for short super-λ,if every minimum edge-cut consists of edges adjacent to a vertex of minimum degree.Alphabet overlap graph G(k,d,s)is undirected,simple graph with vertex set V={v|v=1()kv…v;vi∈{1,2,…,d},i=1,…,k}.Two vertices u=(u1…uk)and v=(v1…vk)are adjacent if and only if us+i=vi or vs+i=ui(i=1,…,k-s).In particular G(k,d,1)is just an undirected de Bruijn graph.In this paper,we show that the diameter of G(k,d,s)is k s,the girth is 3.Finally,we prove that G(k,d,s)(s≥k/2)is super-λ.     

The semileptonic decays of B/B s meson in the perturbative QCD approach: a short review

In this short review, we present the current status about the theoretical and experimental studies for some important semileptonic decays of \(B/B_s\) mesons. We firstly gave a brief introduction for the experimental measurements for \(B/B_s \rightarrow P (l^+l^-, l^-\bar{\nu }_l, \nu \bar{\nu })\) decays, the BaBar’s \(R(D)\) and \(R(D^*)\) anomaly, the \(P_5^\prime \) deviation for \(B^0 \rightarrow K^{*0} \mu ^+ \mu ^-\) decay. We then made a careful discussion about the evaluations for the relevant form factors in the light-cone QCD sum rule, the heavy quark effective theory, and the perturbative QCD factorization approach. By using the form factors calculated in the perturbative (pQCD) approach, we then calculate and show the pQCD predictions for the decay rates of many semileptonic decays of \(B/B_s\) mesons. We also made careful phenomenological analysis for these pQCD predictions and found, in general, the following points: (a) For all the considered \(B/B_s\) semileptonic decays, the next-to-leading order pQCD predictions for their decay rates agree well with the data and those from other different theoretical methods; (b) For \(R(D)\) and \(R(D^*)\) , the pQCD predictions agree very well with the data, the BaBar’s anomaly of \(R(D^{(*)})\) are therefore explained successfully in the standard model by employing the pQCD approach; and (c) We defined several new ratios \(R_D^{l,\tau }\) and \(R_{D_s}^{l,\tau }\) , they may be more sensitive to the QCD dynamics which controls the \(B/B_s \rightarrow (D^{(*)},D_s^{(*)} )\) transitions than the old ratios, we therefore strongly suggest LHCb and the forthcoming Super- \(B\) experiments to measure these new ratios.     

Texture evolution of commercial pure Ti during cold rolling and recrystallization annealing

X-ray diffraction (XRD) was employed to analyze the texture evolution of commercial pure (CP) Ti during cold rolling and recrystallization annealing. The texture components were measured by electron backscattered diffraction (EBSD) after recrystallization annealing. The CP Ti tends to form a texture with the basal pole tilted 30°-40° away from the normal direction toward the transverse direction. The texture of the initial hot-rolled plate can be classified into three kinds, i.e., the pyramid texture (1013)[5230] and (2021)[1015], the basal plane texture (0001)[2110], and the stronger prism texture (1120)[0001]. After cold rolling and annealing (700℃, 60 min), the main texture components are the cold-rolled texture (1125)[1123] and the recrystallized texture (1013)[5230]. The texture (2021)[1015] is inherited from the texture of the initial hot-rolled plate with the decrease of orientation density gradually. The volume contents of the cold-rolled texture {2115} <0110> and the recrystallized texture {1013} <1210> are calculated by EBSD. After recrystallization annealing, the specimen is rich in the recrystallized texture and inherits some of texture components from the cold-rolled texture. When the annealing time is prolonged, the anisotropic value decreases.     

The loop effects on the chargino decays ～χ±1→～χ0 1ff ′in the MSSM

The lighter chargino three body decays ～χ±1→～χ0 1ff ′ via the W^± boson and the charged Higgs boson H^± were studied in the R-parity conserved Minimal Supersymmetric Standard Model （MSSM）. We treat ～χ±1 decays as production and decay of W^± and H^± i.e.,～χ±1→～χ01W^±（H^±） → χ0 1ff ′. Both higgsino- like and wino-like ～χ±1 decays were well investigated. These decays are calculated at 1-loop level and the loop corrections are found to be less than three percent. The signal of the charged Higgs H^± production from ～χ±1 decays is discussed. It will offer important information about the chargino and neutralino sector, as well as the charged Higgs sector in the MSSM.     

Higgs precision measurements and flavor physics: a supersymmetric example

Rare decays in flavor physics often suffer from Helicity suppress and Loop suppress. Helicity flip is a direct consequence of chiral \(U(3)\) symmetry breaking and electroweak symmetry breaking. The identical feature is also shared by the mass generation of SM fermions. In this review, we use the Minimal Supersymmetric Standard Model (MSSM) as an example to illustrate an explicit connection between bottom Yukawa coupling and rare decay process of \(b\rightarrow s\gamma \) . We take a symmetry approach to study the common symmetry breaking in supersymmetric correction to bottom quark mass generation and \(b\rightarrow s\gamma \) . We show that Large Peccei-Quinn symmetry breaking effect and \(R\) -symmetry breaking effect required by \(b\rightarrow s\gamma \) inevitably lead to significant reduction of bottom Yukawa \({y}_{b}\) . To compromise the reduction in \(b\bar{b}\) , a new decay is also needed to keep the Higgs total width as the SM value.     

The bubble leakage mechanism for vertical upflows by the phase separation concept

Recently,our research group proposed the phase separation condenser tube,in which a mesh cylinder was inserted to form the flow structure of‘‘gas near the tube wall and liquid in the tube core’’,significantly enhance the condensation heat transfer.But the bubble leakage towards the core region may worsen the heat transfer enhancement.In order to prevent the bubble leakage,the critical criterion was proposed based on the Young–Laplace equation,considering the inertia force,viscous force and pulsating flow.It was found that the critical criterion depends on the dimensionless parameter G*,the We number and a coefficient C.The numerical model was developed in terms of the volume of fluid method to predict the two-phase laminar flow in the phase separation condenser tube.The results show that the bubble leakage takes place at the bubble tip,which is agreed with the experimental observations.The critical curve distinguishing the non-bubble-breaking and bubble-breaking was obtained by comparing the bubble dynamics at different G*and We.The coefficient C was determined.The critical criterion for the bubble leakage is given as G We0:22We0:99349 G4:7 103 We0:00651t196:39We0:006514cosa DHW,providing the design and operation guidance for the phase separation condenser tube.     

On convergence of singular integral operators with respect to path of integration

Givenf being Hölder continuous in a regionG?C. For the Cauchy principal integral $$I(\Gamma ,f) = \frac{1}{{\pi i}} \int_\Gamma {\frac{{f(\zeta )}}{{\zeta - \zeta _0 }}d\zeta , \zeta _0 \in \Gamma } $$ where Γ?G is a smooth closed contour, it is established that, if a sequence of smooth closed contours Γn?G(n∈N) smoothly convergent to Γ, then the corresponding sequenceI(Γ _n, f)is convergent to I(Γ, f). Furthermore, when Γ is approximated by a sequence of complex cubic splines $S_{\Delta _n } (\Gamma )$ interpolatory to Γ, the error $|I(\Gamma ,f)--I(S_{\Delta _n } (\Gamma ,f)|$ is estimated.     

On the scalability of PSRS algorithm

In this paper, using the metric of iso-efficiency function [1]. we analyze the scalability of PSRS (Parallel Sorting by Regular Sample) algorithm [2] on two popular architectures (Mesh and Hypercube). The isoefficiency function of PSRS on 2-dimensional mesh withp processors reaches the lower bound $\Omega \left( {\sqrt p \cdot 2^{c\sqrt F } } \right)$ for that of sorting algorithms on this architecture. In this sense, we say, the scalability of PSRS is optimal on 2-dimensional mesh. The iso-efficiency function of PSRS on hypercube is equal to that of PSRS on 2-dimensional mesh. After changing the data exchanging scheme of PSRS, we get a new iso-efficiency functionO(log² p·p ^Ciogp), which is better than that of PSRS on 2-dimensional mesh So we say that hypercube is more suitable for PSRS than 2-dimensional mesh.     

Form factors for B meson weak decays in QCD light cone sum rules with a chiral current correlator

We report some applications of QCD light cone sum rules (LCSR) to \(B\) meson weak decays. Special emphasis is on estimates of the form factors for \(B\) decays into a pseudoscalar ( \(P\) )/vector ( \(V\) ) meson, with a certain chiral current correlator. The main new ingredient, as compared with the case of the standard correlators, is that in the operator product expansion calculations, the contributions due to the twist-3 distribution amplitudes of the related light mesons, which are less known and would bring a larger uncertainty to the calculations with the standard correlators, cancel out fully in the \(B\rightarrow P\) case and do out partially in the \(B\rightarrow V\) one. An important observation, which is similar to that in soft collinear effective theory, is made in twist-3 approximation: whereas only one independent form factor is needed for parameterizing the hadronic matrix elements for a \(B\rightarrow P\) transition induced by all the relevant heavy-light quark currents, there exist two independent form factors under the condition of neglecting the terms suppressed by a factor of \(m_V^2\) , for the \(B\rightarrow V\) transition. Therefore, the improved LCSR approach could be of stronger predictive power for the weak form factors. Also, this approach is employed to understand the \(B\rightarrow D\) transitions by introducing a leading twist-2 DA for an energetic \(D\) meson, combined with some of other QCD-based approaches. A detailed QCD next-to-leading order calculation of the \(B\rightarrow \pi \) form factors is presented for an illustrative purpose, and the sum rule results are used to extract the Cabibbo–Kobayashi–Maskawa matrix element \(|V_{ub}|\) from the latest BaBar data.