Researches of DC—Problem Under the Model S in which the Numbers of Defective Coins are not Fixed

In this paper,we research general Defective Cion Problem under the model S,i.e,the number d of Defective cions is not fixed. For d=O,1,or 2. we get some good results.     

具有非光滑边界层函数的线性变系数抛物型方程初边值问题的差分格式

本文利用非均匀网格和指数型拟合差分方法给出了具有非光滑边界层函数的线性抛物型方程关于小参数ε一致收敛的差分格式.文章还给出了误差估计和数值结果.     

非牛顿流体内流传热研究

在本文中,研究了注入轴对称模腔非牛顿流体非定常流动.本文的第二部份研究了上随体Maxwell流体管内热流动.对于注入模腔流动.其本构方程采用幂律流体模型方程.为了避免在表现粘度中温度关系引起的非线性.引进了一特征粘度的概念.描述本力学过程的基本方程是,本构方程、定常状态的运动方程、非定常能量方程及连续方程.该方程组在空间是二维问题,在数学上是三维问题.采用分裂差分格式求得本方程组的数值解答.分裂法曾成功应用于求解牛顿流体问题.在本文中,首次将分裂法成功地应用解决非牛顿流体流动问题.对于圆管内热流,给出了差分格式,使基本方程组化为一个三对角方程组.其结果,给出了不同时刻的模腔内二维温度分布.     

对流扩散方程的一种新型差分格式

对流扩散方程可以描述众多的物理化学现象，因而对其寻求稳定的，实用的数值解法有着重要的现实意义。本文针对形式较一般的一维非定常对流扩散方程，构造了对角元严格占优的Crank-Nicholson差分格式，然后对其分别用分离变量的方法以及能量估计的方法作了稳定性的分析，最后给出了数值试验的结果，数值结果表明本文构造的格式能够较好的处理经典的Crank-Nicholson格式所不能处理的对流项系数较大的对流扩散方程，并具有较好的精度。     

二维抛物型方程的高精度多重网格解法

提出了数值求解二维抛物型方程的一种新的高精度加权平均紧隐格式，利用Fourier分析方法证明了该格式是无条件稳定的，为了克服传统迭代法在求解隐格式是收敛速度慢的缺陷，利用了多重网格加速技术，大大加快了迭代收敛速度，提高了求解效率，数值实验结果验证了方法的精确性和可靠性。     

BV estimates of Lax-Friedrichs' scheme for a class of nonlinear hyperbolic conservation laws

We give uniform BV estimates and -stability of Lax-Friedrichs' scheme for a class of systems of strictly hyperbolic conservation laws whose integral curves of the eigenvector fields are straight lines, i.e., Temple class, under the assumption of small total variation. This implies that the approximate solutions generated via the Lax-Friedrichs' scheme converge to the solution given by the method of vanishing viscosity or the Godunov scheme, and then the Glimm scheme or the wave front tracking method.

     

A numerical study of the motion of a wave running up a beach

The main difficulty for the numerical calculation of the wave running up a beach is the treatment of its moving water boundary. In this paper a scheme of turning the free boundary problem into a fixed boundary problem is designed. The calculated run-up height is consistent with the experiments. Some interesting wave phenomena are also found.     

Tracking an Auto-Regressive Process with Limited Communication per Unit Time

Samples from a high-dimensional first-order auto-regressive process generated by an independently and identically distributed random innovation sequence are observed by a sender which can communicate only finitely many bits per unit time to a receiver. The receiver seeks to form an estimate of the process value at every time instant in real-time. We consider a time-slotted communication model in a slow-sampling regime where multiple communication slots occur between two sampling instants. We propose a successive update scheme which uses communication between sampling instants to refine estimates of the latest sample and study the following question: Is it better to collect communication of multiple slots to send better refined estimates, making the receiver wait more for every refinement, or to be fast but loose and send new information in every communication opportunity? We show that the fast but loose successive update scheme with ideal spherical codes is universally optimal asymptotically for a large dimension. However, most practical quantization codes for fixed dimensions do not meet the ideal performance required for this optimality, and they typically will have a bias in the form of a fixed additive error. Interestingly, our analysis shows that the fast but loose scheme is not an optimal choice in the presence of such errors, and a judiciously chosen frequency of updates outperforms it.     

Multiple Observations for Secret-Key Binding with SRAM PUFs

We present a new Multiple-Observations (MO) helper data scheme for secret-key binding to an SRAM-PUF. This MO scheme binds a single key to multiple enrollment observations of the SRAM-PUF. Performance is improved in comparison to classic schemes which generate helper data based on a single enrollment observation. The performance increase can be explained by the fact that the reliabilities of the different SRAM cells are modeled (implicitly) in the helper data. We prove that the scheme achieves secret-key capacity for any number of enrollment observations, and, therefore, it is optimal. We evaluate performance of the scheme using Monte Carlo simulations, where an off-the-shelf LDPC code is used to implement the linear error-correcting code. Another scheme that models the reliabilities of the SRAM cells is the so-called Soft-Decision (SD) helper data scheme. The SD scheme considers the one-probabilities of the SRAM cells as an input, which in practice are not observable. We present a new strategy for the SD scheme that considers the binary SRAM-PUF observations as an input instead and show that the new strategy is optimal and achieves the same reconstruction performance as the MO scheme. Finally, we present a variation on the MO helper data scheme that updates the helper data sequentially after each successful reconstruction of the key. As a result, the error-correcting performance of the scheme is improved over time.     

The fine structure levels and spin-singlet contributions to zero-field-splitting parameters of Cr2+ ion in CdGa2S4

A theoretical investigation is reported of the fine structure levels and the spin-singlet contributions to zero-field-splitting (ZFS) parameters for Cr²⁺ ion in CdGa₂S₄ crystals. Firstly, the complete energy matrix including all spin states for a 3d ⁴ ion in tetrahedral D _2d symmetry is constructed according the double-group chain in the strong-field scheme. Then, by diagonalizing the complete energy of electron–electron interactions, the crystal field and the spin–orbit coupling for the Cr²⁺ (3d ⁴) ion in CdGa₂S₄ crystal, the fine structure levels and the spin-singlet contributions to ZFS parameters a, D and F are calculated. The results show that the spin-singlet contribution to D is negligible, but the contributions to a and F are very important. So, to obtain more accurate ZFS parameters for 3d ⁴ ions in the tetrahedral crystals, all spin states should be considered.