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 \({F_{{2^m}}}\).     

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.     

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.     

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 \(\alpha (n) = \frac{{n + \sqrt {2n(n + 1)} }}{{n + 2}}\).     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

A quantum algorithm that deletes marked states from an arbitrary database

We present a general quantum deletion algorithm that deletes M marked states from an N-item quantum database with arbitrary initial distribution. The general behavior of this algorithm is analyzed, and analytic result is given. When the number of marked states is no more than 3N/4 , this algorithm requires just a single query, and this achieves exponential speedup over classical algorithm.     

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 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.     

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.     

Retrieval of column-averaged volume mixing ratio of CO2 with ground-based high spectral resolution solar absorption

The total column-averaged volume mixing ratio of atmospheric carbon dioxide （Xco2） has been retrieved with high spectral resolution solar absorption data obtained from ground-based Fourier transform spectrometer （FTS） measurements at Xichong, a coastal site in the district of Shenzhen in southern China. Based on differential optical absorption spectroscopy （DOAS） theory, the Xco2 was retrieved by finding the best match of observed high spectral resolution solar absorption data and monochromatic radia- tion transfer model calculations. The averaged Xco2 in the whole observation period was about 394.9 ppm. The uncertainty of the retrieval was estimated to be 2.0 ppm （0.51%） by comparing retrievals at two bands. The preliminary results show that Xc% retrieved by this method can be used to validate satellite remote sensing of Xco2.     

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.     

Molecular dynamics simulation of nanoscale contact and sliding processes for probes with different tip radius of curvature

Three-dimensional simulations were carried out molecular dynamics （MD） to study the contact and sliding processes between diamond points with different tip radius of curvature and surfaces of single crystal copper. The material deformation, abrasion mechanism, lattice defects, the force of contact process, and the sliding friction process were investigated. The simulation results show that the contact force, dislocations, and stacking fault defects, increase during the contact process with increasing contact depth or tip radius of curvature. The dislocations emit along the [10i-] and [i-01] direction and then a glide band is formed. It was also found that a greater tip radius of cur- vature results in a larger groove and more material defor- mation. The normal force and friction increase with increasing tip radius of curvature, but the coefficient of friction decreases. The stacking faults spread along the sliding direction and increase with increasing tip radius of curvature. In addition, the number of upheaval atoms increases as the radius of tip curvature or sliding distance increases.     

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.