GC-MS分析大蒜中的挥发油和大蒜精油

采用气相色谱—质谱法,分析比较大蒜中的挥发油以及大蒜精油的化学成分,通过非负矩阵因子分解(NMF)方法解析色谱重叠峰,并用峰面积百分比法计算各化学成分的峰面积相对百分含量。确定了大蒜中37种化学成分,其中含硫化合物34种,大蒜精油中的32种化学成分,含硫化合物28种。     

Practical alternating least squares for tensor ring decomposition

Tensor ring (TR) decomposition has been widely applied as an effective approach in a variety of applications to discover the hidden low-rank patterns in multidimensional and higher-order data. A well-known method for TR decomposition is the alternating least squares (ALS). However, solving the ALS subproblems often suffers from high cost issue, especially for large-scale tensors. In this paper, we provide two strategies to tackle this issue and design three ALS-based algorithms. Specifically, the first strategy is used to simplify the calculation of the coefficient matrices of the normal equations for the ALS subproblems, which takes full advantage of the structure of the coefficient matrices of the subproblems and hence makes the corresponding algorithm perform much better than the regular ALS method in terms of computing time. The second strategy is to stabilize the ALS subproblems by QR factorizations on TR-cores, and hence the corresponding algorithms are more numerically stable compared with our first algorithm. Extensive numerical experiments on synthetic and real data are given to illustrate and confirm the above results. In addition, we also present the complexity analyses of the proposed algorithms.     

Next-to-leading-order calculation in kT factorization

We explain the framework for calculating next-to-leading-order (NLO) corrections to exclusive processes in the kT factorization theorem, taking πγ→γ T as an example. Partons off-shell by k2T are considered in both the quark diagrams from full QCD and the effective diagrams for the pion wave function. The gauge dependences in the above two sets of diagrams cancel, when deriving the kT-dependent hard kernel as their difference. The light-cone singularities in the kT-dependent pion wave function are regularized by rotating the Wilson lines away from the light cone. Both the large double logarithms In2 kT and ln2x, x being a parton momentum fraction, arise from the loop correction to the virtual photon vertex, the former being absorbed into the pion wave function, and the latter into a jet function.     

CP violation in B→φKs decay in R-parity violating supersymmetry

In the framework of R-parity violating supersymmetry, we investigate the time dependent CP asymmetry SφKs anomaly of B→φKs decay. When the values of the weak phase φ in the R-parity violating coupling fall into certain parameter spaces (246°<φ<263°) we find that this anomaly can be easily ex-plained; at the same time, the branching ratio of B →φKs decay can also be in agreement with experimental measurements.     

B → ρ（ω, φ）η（＇） Decays and NLO Contributions in pQCD Approach

By employing the perturbative QCD （pQCD） factorization approach, we calculate some important next- to-leading-order （NLO） contributions to the two-body charmless hadronic decays B^＋ →ρ^＋η（＇） and B^0 → ρ^0（ω, φ）η（＇）, induced by the vertex QCD corrections, the quark-loops as well as the chromo-magnetic penguins. From the numerical results and phenomenological analysis we find that （a） for B^± → ρ^±η（＇） （B^0 → ρ^0（ω, φ）η（＇）decays, the partial NLO contributions to branching ratios are small （large） in magnitude; and （b） the pQCD predictions for ACP^dir（B^± → ρ^±η（＇）） are consistent with the data, while the predicted .ACP（B^0 → ρ^0（ω）η（＇）） are generally large in magnitude and could be tested by the forthcoming LHCb experiments.     

Study on Bd → φKs Decay in EDQS Model

We study Bd → φKs decay in extra down-type quarks （EDQS） model with a non-universal Z boson associated with flavor changing neutral currents （FCNCs） at the tree level. With the up-to-date experimental data of Br（Bd → φKs）, SCKs, and ACKs, we derive the bounds on the Z-b-s coupling parameter ｜Ubs ｜ and the new weak phase φ, using the constrained parameter spaces, we finally give predictions for Bd → φφ decay, which could be tested at the Fermilab Tevatron and the LHC-b experiments.     

CP violation in B→φKs decay in R-parity violating supersymmetry

In the framework of R-parity violating supersymmetry, we investigate the time dependent CP asymmetry SφKs anomaly of B→φKs decay. When the values of the weak phase φ in the R-parity violating coupling fall into certain parameter spaces （246°〈 φ 〈 263°） we find that this anomaly can be easily explained; at the same time, the branching ratio of B→φKs decay can also be in agreement with experimental measurements.     

Preconditioning methods for discontinuous Galerkin solutions of the Navier–Stokes equations

A Newton–Krylov method is developed for the solution of the steady compressible Navier–Stokes equations using a discontinuous Galerkin (DG) discretization on unstructured meshes. Steady-state solutions are obtained using a Newton–Krylov approach where the linear system at each iteration is solved using a restarted GMRES algorithm. Several different preconditioners are examined to achieve fast convergence of the GMRES algorithm. An element Line-Jacobi preconditioner is presented which solves a block-tridiagonal system along lines of maximum coupling in the flow. An incomplete block-LU factorization (Block-ILU(0)) is also presented as a preconditioner, where the factorization is performed using a reordering of elements based upon the lines of maximum coupling. This reordering is shown to be superior to standard reordering techniques (Nested Dissection, One-way Dissection, Quotient Minimum Degree, Reverse Cuthill–Mckee) especially for viscous test cases. The Block-ILU(0) factorization is performed in-place and an algorithm is presented for the application of the linearization which reduces both the memory and CPU time over the traditional dual matrix storage format. Additionally, a linear p-multigrid preconditioner is also considered, where Block-Jacobi, Line-Jacobi and Block-ILU(0) are used as smoothers. The linear multigrid preconditioner is shown to significantly improve convergence in term of number of iterations and CPU time compared to a single-level Block-Jacobi or Line-Jacobi preconditioner. Similarly the linear multigrid preconditioner with Block-ILU smoothing is shown to reduce the number of linear iterations to achieve convergence over a single-level Block-ILU(0) preconditioner, though no appreciable improvement in CPU time is shown.     

Divisibity,iterated digit sums,primality tests

The divisibility of numbers is obtained by iteration of the weighted sum of their integer digits. Then evaluation of the related congruences yields information about the primality of numbers in certain recursive sequences. From the row elements in generalized Delannoy triangles, we can verify the primality of any constellation of numbers. When a number set is not a prime constellation, we can identify factors of their composite numbers. The constellation primality test is proven in all generality, and examples are given for twin primes, prime triplets, and Sophie Germain primes.      

On equivalence and explicit solutions of a class of matrix equations

It is shown in this paper that three types of matrix equations AX−XF=BY,AX−EXF=BY and which have wide applications in control systems theory, are equivalent to the matrix equation with their coefficient matrices satisfying some relations. Based on right coprime factorization to , explicit solutions to the equation are proposed and thus explicit solutions to the former three types of matrix equations can be immediately established. With the special structure of the proposed solutions, necessary conditions to the nonsingularity of matrix X are also obtained. The proposed solutions give an ultimate and unified formula for the explicit solutions to these four types of linear matrix equations.