A Note on twin primes and the modular ring Z 6

The modular ring ?₆ defines integers via (6r _i + (i ? 3)) where i is the class and r _i the row when tabulated in an array. Since only Classes 2₆ and 4₆ contain odd primes, this modular ring is ideally suited to the analysis of twin primes. The calculations are facilitated by the use of the right-end digit (RED) technique.     

Signal modeling using the gradient search

This letter presents a new method for continuous signal modeling. Firstly, the continuous signal can be represented as a function of the trigonometric functional extension (Fourier series). Fourier series of the signal are parameterized by the fundamental frequency and unknown parameters. Then, the gradient-based iterative identification algorithm is derived, for estimating parameters of the signal model with known and unknown frequencies, separately. Finally, the simulation results indicate that the proposed algorithm is effective.     

Krull property of generalized power series rings

Let D be an integral domain and let $(S,\le )$ be a torsion-free, ≤-cancellative, subtotally ordered monoid. We show that the generalized power series ring $?D^{S,\le }?$ is a Krull domain if and only if D is a Krull domain and S is a Krull monoid.     

On the estimation of nonlinear time series models

In the present paper, a framework for parametric estimation in nonlinear time series is developed. Strong consistency and asymptotic normality of minimum Hellinger distance estimates for a determined class of nonlinear models are investigated. The main Interest for these estimates is motivated by their robustness under perturbations as it has been emphazized in Beran [2]. The first part of the paper is devoted to the study of some probabilistic properties which ensure the existence and the optimal properties of the estimates     

Tuning the mesogenic properties of 5-alkoxy-2-(4-alkoxyphenyl)pyrimidine liquid crystals: the effect of a phenoxy end-group in two sterically equivalent series

Two sterically equivalent series of phenoxy-terminated 5-alkoxy-2-(4-alkoxyphenyl)pyrimidine liquid crystals were synthesised, and their mesogenic properties were characterised by polarised optical microscopy and differential scanning calorimetry (DSC). The phenoxy end-group causes a significant increase in melting point and inhibits – at least partially – the mesomorphism of these materials relative to the parent isomers; in most cases, the broad enantiotropic SmC phase formed by the parent isomers is suppressed by the addition of the phenoxy end-group. However, detailed analyses by small-angle X-ray scattering and monodomain 2D X-ray scattering suggest that these compounds form a SmA phase with a partially intercalated bilayer structure in which the phenoxy end-groups are nanosegregated. Such an intercalated bilayer structure might enable the tuning of smectogenic properties by appropriate substitution of the phenoxy end-groups.     

On the free vibration response of rectangular plates,partially supported on elastic foundation

Rectangular plates on distributed elastic foundations are widely employed in footings and raft foundations of variety of structures. In particular, mounted columns and single footings may partially occupy the rectangular plate of any kind.     

基于RBM的神经网络时间序列预测

为了克服神经网络依赖初始化结果,泛化能力不强的缺点,提出一种基于受限玻尔兹曼机(RBM)的神经网络模型.利用无监督学习方法优化神经网络的初始权值和阈值,将RBM与神经网络融合起来,模型与时间序列神经网络做实验对比,结果表明,基于受限的玻尔兹曼机的神经网络模型优于神经网络预测模型,模型可以提高预测的精准度,具有一定的应用意义.     

n阶不等距常系数线性差分方程的解

利用Mikusinski的算符演算理论和移动算符的幂级数表示,给出了n阶不等距常系数线性差分方程的解法.     

Measurement of viscoelastic properties for polymers by nanoindentation

A new method has been proposed and verified to measure the viscoelastic properties of polymers by nanoindentation tests. With the mechanical response of load–displacement curves at different loading rates, the parameters of creep compliance and relaxation modulus are calculated through the viscoelastic contact model. Dynamic thermomechanical analysis (DMA) tests are conducted to compare the results by the proposed technique. The results show that the correlation coefficients between DMA tests and the new method are above 0.9 in the entire range, which verified the feasibility of the method. The loading curves fitted by the model are identical to the experimental curves within the discrete points and so it shows that this technique is more suitable for general linear viscoelastic materials. Numerical creep tests are carried out to examine the effectiveness of the proposed method by input the Prony series calculated by the three-element Maxwell model and the viscoelastic contact model. The good agreement shows that the proposed technique can be applied in practice.