球面稳定同伦群中的一族新元素及h_0b_1~2在π_*V(1)中的收敛性

对连通有限型谱x,y,存在着Adams谱序列(ASS){Es,tr,dr}满足(1)dr:Es,tr→Es r,t r-1r 是谱序列的微分,(2)Es,t2≌Exts,tA(H*(X),H*(Y)),(3)并且收敛到[∑t-sY,X]p.当X是球谱S, Moore谱M,Toda-Smith谱V(1)时,(πt-sX)p分别为S,M,v(1)的稳定同伦群.本文通过Adams 谱序列,发现了球谱S的稳定同伦群中的一族非零元素γth0b21及Toda-Smith谱V(1)的稳定同伦群中的非零元素h0b21.在利用Adams谱序列求解同伦群的过程中,需要计算有关Exts,tA(H*X,H*Y) 的结果.利用谱的上纤维序列导出的Ext群的正合序列和May谱序列,得出Exts,tA(H*X,H*Y)的某些结果.本文令p≥7为奇素数,q=2(p-1).     

非局部初值问题解的存在性定理

近来非局部问题的研究日见增多,但涉及带非线性边界条件的初值问题文献 较少.本文目的在于证明一个半线性方程的齐次边值问题和一个非线性边界条件问题 解的存在性.主要使用半群,分数次幂函数空间,广义Poincare算子等工具.     

权为任意正实数的Poincare级数（II）解析的情形

设ｒ为一个正实数，１＜ｒ＜２，是一个Ｈ－群，υ：Γ→Ｃ是一个乘子系（定义见文［８］）．本文在［８］的基础上讨论了Ｐｏｉｎｃａｒｅ级数的存在性．令Ｐ＿（ｎｒ）（ｚ，υ，Ａ＿ｊ，Γ，ｋ＿ｊ）＝Ｐ＿（ｎｒ）（ｚ，０，υ，Γ，ｋ＿ｊ）．这里Ｐ＿（ｎｒ）（ｚ，ｓ，Ａ＿ｊ，Γ，ｋ＿ｊ）如文［８］中定义．我们有：定理｛Ｐ＿（ｎｒ）（ｚ，υ，Ａ＿ｊ，Γ，ｋ＿ｊ）｝ｎ＋ｋ＿Ｋ＞０是群Γ的，权为ｒ的具有乘子系υ的全纯歧点型模形式，且它们张成歧点型模形式所成的空间．应用这个结果，我们证明了一些模形式的性质并推导出一个重要的恒等式．该恒等式在半整权模形式的Ｆｏｕｒｉｅｒ系数估计中有极重要的地位．     

ZERO SET OF SOBOLEV FUNCTIONS WITH NEGATIVE POWER OF INTEGRABILITY

§1. Introduction Let ? ? Rn (n ≥1) be an open set, p ≥1. We consider functions u ∈W1 (?), such ,pthat, for some α> 0, |u|? < ∞. α (1.1) ?When p = 1, it is also natural to consider u ∈BV (?) which satis?es (1.1). For any u ∈W1 (?), p ≥1 or u ∈BV (?), we de?ne its zero set by …     

POINCAR BIFURCATION FOR QUADRATIC SYSTEMS WITH A CENTER REGION AND AN UNBOUNDED TRIANGULAR REGION

In this paper, we discuss the Poincare bifurcation for a class of quadratic systems with an unbounded triangular region and a center region. It is proved, by Poincare bifurcation, that inside the center region quadratic system perturbed by quadratic polynomial perturbation may generate three limit cycles.     

Optimized Dropping and Rolling (ODR) method for packing of poly-disperse spheres

Powder-based microstructures are traditionally modelled using densely packed spherical particles. In this letter, a new dropping and rolling packing algorithm is employed by means of analytical equations, to investigate the random packing of spherical particles. The three-dimensional randomly packed microstructures are quantified in terms of packing density and computational time.     

On the Performance of Video Resolution,Motion and Dynamism in Transmission Using Near-Capacity Transceiver for Wireless Communication

This article investigates the performance of various sophisticated channel coding and transmission schemes for achieving reliable transmission of a highly compressed video stream. Novel error protection schemes including Non-Convergent Coding (NCC) scheme, Non-Convergent Coding assisted with Differential Space Time Spreading (DSTS) and Sphere Packing (SP) modulation (NCDSTS-SP) scheme and Convergent Coding assisted with DSTS and SP modulation (CDSTS-SP) are analyzed using Bit Error Ratio (BER) and Peak Signal to Noise Ratio (PSNR) performance metrics. Furthermore, error reduction is achieved using sophisticated transceiver comprising SP modulation technique assisted by Differential Space Time Spreading. The performance of the iterative Soft Bit Source Decoding (SBSD) in combination with channel codes is analyzed using various error protection setups by allocating consistent overall bit-rate budget. Additionally, the iterative behavior of SBSD assisted RSC decoder is analyzed with the aid of Extrinsic Information Transfer (EXIT) Chart in order to analyze the achievable turbo cliff of the iterative decoding process. The subjective and objective video quality performance of the proposed error protection schemes is analyzed while employing H.264 advanced video coding and H.265 high efficient video coding standards, while utilizing diverse video sequences having different resolution, motion and dynamism. It was observed that in the presence of noisy channel the low resolution videos outperforms its high resolution counterparts. Furthermore, it was observed that the performance of video sequence with low motion contents and dynamism outperforms relative to video sequence with high motion contents and dynamism. More specifically, it is observed that while utilizing H.265 video coding standard, the Non-Convergent Coding assisted with DSTS and SP modulation scheme with enhanced transmission mechanism results in Eb/N0 gain of 20 dB with reference to the Non-Convergent Coding and transmission mechanism at the objective PSNR value of 42 dB. It is important to mention that both the schemes have employed identical code rate. Furthermore, the Convergent Coding assisted with DSTS and SP modulation mechanism achieved superior performance with reference to the equivalent rate Non-Convergent Coding assisted with DSTS and SP modulation counterpart mechanism, with a performance gain of 16 dB at the objective PSNR grade of 42 dB. Moreover, it is observed that the maximum achievable PSNR gain through H.265 video coding standard is 45 dB, with a PSNR gain of 3 dB with reference to the identical code rate H.264 coding scheme.     

Boundary integral equations on the sphere with radial basis functions: error analysis

Radial basis functions are used to define approximate solutions to boundary integral equations on the unit sphere. These equations arise from the integral reformulation of the Laplace equation in the exterior of the sphere, with given Dirichlet or Neumann data, and a vanishing condition at infinity. Error estimates are proved. Numerical results supporting the theoretical results are presented.     

Brownian Motion and Ornstein–Uhlenbeck Processes in Planar Shape Space

We discuss Brownian motion and Ornstein–Uhlenbeck processes specified directly in planar shape space. In particular, we obtain the drift and diffusion coefficients of Brownian motion in terms of Kendall shape variables and Goodall–Mardia polar shape variables. Stochastic differential equations are given and the stationary distributions are obtained. By adding in extra drift to a reference figure, Ornstein–Uhlenbeck processes can be studied, for example with stationary distribution given by the complex Watson distribution. The triangle case is studied in particular detail, and some simulations given. Connections with existing work are made, in particular with the diffusion of Euclidean shape. We explore statistical inference for the parameters in the model with an application to cell shape modelling.      

A non-uniform discretization of stochastic heat equations with multiplicative noise on the unit sphere

We investigate a discretization of a class of stochastic heat equations on the unit sphere with multiplicative noise. A spectral method is used for the spatial discretization and the truncation of the Wiener process, while an implicit Euler scheme with non-uniform steps is used for the temporal discretization. Some numerical experiments inspired by Earth’s surface temperature data analysis GISTEMP provided by NASA are given.