Tocochromanols composition in kernels recovered from different apricot varieties: RP-HPLC/FLD and RP-UPLC-ESI/MSn study

Composition of tocochromanols in kernels recovered from 16 different apricot varieties (Prunus armeniaca L.) was studied. Three tocopherol (T) homologues, namely α, γ and δ, were quantified in all tested samples by an RP-HPLC/FLD method. The γ-T was the main tocopherol homologue identified in apricot kernels and constituted approximately 93% of total detected tocopherols. The RP-UPLC-ESI/MSⁿ method detected trace amounts of two tocotrienol homologues α and γ in the apricot kernels. The concentration of individual tocopherol homologues in kernels of different apricots varieties, expressed in mg/100 g dwb, was in the following range: 1.38–4.41 (α-T), 42.48–73.27 (γ-T) and 0.77–2.09 (δ-T). Moreover, the ratio between individual tocopherol homologues α:γ:δ was nearly constant in all varieties and amounted to approximately 2:39:1.     

h-ADAPTIVITY ANALYSIS BASED ON MULTIPLE SCALE REPRODUCING KERNEL PARTICLE METHOD

IntroductionAs one of the meshfree methods, multiple scale reproducing kernel particle method(RKPM)[1,2]bears, besides the common features of all meshfree methods, a uniqueinherent feature of multiresolution analysis by which the structural response can b…     

Numerical solution of one‐dimensional Burgers' equation

In this article, an iterative method for the approximate solution of a class of Burgers' equation is obtained in reproducing kernel space . It is proved the approximation converges uniformly to the exact solution u(x, t) for any initial function under trivial conditions, the derivatives of are also convergent to the derivatives of u(x, t), and the approximate solution is the best approximation under the system © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1251–1264, 2015     

A new approach to pointwise heat kernel upper bounds on doubling metric measure spaces

On doubling metric measure spaces endowed with a strongly local regular Dirichlet form, we show some characterisations of pointwise upper bounds of the heat kernel in terms of global scale-invariant inequalities that correspond respectively to the Nash inequality and to a Gagliardo–Nirenberg type inequality when the volume growth is polynomial. This yields a new proof and a generalisation of the well-known equivalence between classical heat kernel upper bounds and relative Faber–Krahn inequalities or localised Sobolev or Nash inequalities. We are able to treat more general pointwise estimates, where the heat kernel rate of decay is not necessarily governed by the volume growth. A crucial role is played by the finite propagation speed property for the associated wave equation, and our main result holds for an abstract semigroup of operators satisfying the Davies–Gaffney estimates.     

求解Helmholtz方程基于核重构思想的最小二乘配点法

基于核重构思想构造近似函数，将配点法和最小二乘原理相结合对微分方程进行离散， 建立了Helmholtz方程的最小二乘配点格式，并分别研究了Helmholtz方程的波传播问题和 边界层问题. 通过数值算例可以发现，给出的数值计算结果非常接近于精确解，计算精度明显高于SPH 法的数值结果，且随着节点数目的增加，其精确度越来越高，具有良好的收敛性.     

Integral operators commuting with dilations and rotations in generalized Morrey-type spaces

We find conditions for the boundedness of integral operators $K$ commuting with dilations and rotations in a local generalized Morrey space. We also show that under the same conditions, these operators preserve the subspace of such Morrey space, known as vanishing Morrey space. We also give necessary conditions for the boundedness when the kernel is non-negative. In the case of classical Morrey spaces, the obtained sufficient and necessary conditions coincide with each other. In the one-dimensional case, we also obtain similar results for global Morrey spaces. In the case of radial kernels, we also obtain stronger estimates of $Kf$ via spherical means of $f$. We demonstrate the efficiency of the obtained conditions for a variety of examples such as weighted Hardy operators, weighted Hilbert operator, their multidimensional versions, and others.     

Kibble–Slepian formula and generating functions for 2D polynomials

We prove a generalization of the Kibble–Slepian formula (for Hermite polynomials) and its unitary analogue involving the 2D Hermite polynomials recently proved in [16]. We derive integral representations for the 2D Hermite polynomials which are of independent interest. Several new generating functions for 2D q-Hermite polynomials will also be given.     

Effects of physics change in Monte Carlo code on electron pencil beam dose distributions

Pencil beam algorithms used in computerized electron beam dose planning are usually described using the small angle multiple scattering theory. Alternatively, the pencil beams can be generated by Monte Carlo simulation of electron transport. In a previous work, the 4th version of the Electron Gamma Shower (EGS) Monte Carlo code was used to obtain dose distributions from monoenergetic electron pencil beam, with incident energy between 1 MeV and 50 MeV, interacting at the surface of a large cylindrical homogeneous water phantom. In 2000, a new version of this Monte Carlo code has been made available by the National Research Council of Canada (NRC), which includes various improvements in its electron-transport algorithms. In the present work, we were interested to see if the new physics in this version produces pencil beam dose distributions very different from those calculated with oldest one. The purpose of this study is to quantify as well as to understand these differences. We have compared a series of pencil beam dose distributions scored in cylindrical geometry, for electron energies between 1 MeV and 50 MeV calculated with two versions of the Electron Gamma Shower Monte Carlo Code. Data calculated and compared include isodose distributions, radial dose distributions and fractions of energy deposition. Our results for radial dose distributions show agreement within 10% between doses calculated by the two codes for voxels closer to the pencil beam central axis, while the differences are up to 30% for longer distances. For fractions of energy deposition, the results of the EGS4 are in good agreement (within 2%) with those calculated by EGSnrc at shallow depths for all energies, whereas a slightly worse agreement (15%) is observed at deeper distances. These differences may be mainly attributed to the different multiple scattering for electron transport adopted in these two codes and the inclusion of spin effect, which produces an increase of the effective range of electrons.