Convergence of the largest eigenvalue of normalized sample covariance matrices when p and n both tend to infinity with their ratio converging to zero

Let $\mathbf{X}_p=(\mathbf{s}_1,...,\mathbf{s}_n)=(X_{ij})_{p \times n}$ where $X_{ij}$'s are independent and identically distributed (i.i.d.) random variables with $EX_{11}=0,EX_{11}^2=1$ and $EX_{11}^4<\infty$. It is showed that the largest eigenvalue of the random matrix $\mathbf{A}_p=\frac{1}{2\sqrt{np}}(\mathbf{X}_p\mathbf{X}_p^{\prime}-n\mathbf{I}_p)$ tends to 1 almost surely as $p\rightarrow\infty,n\rightarrow\infty$ with $p/n\rightarrow0$.Comment: Published in at http://dx.doi.org/10.3150/11-BEJ381 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Design procedure for low-drag subsonic airfoils

Airfoil has least amount of drag under given restrictions of boundary layer transition position, lift coefficient, thickness ratio, and Reynolds number based on airfoil chord. It is suitable for use as wing and propeller aircraft sections operating at subsonic speeds and for hydrofoil sections and blades for fans, compressors, turbines, and windmills

Sustainability analysis of Chinese transport policy

Whilst the world economy is developed, the life and development of human beings have been threatened by the imbalance among environmental and ecological aspects. Thus sustainability is becoming increasingly the focus of various social fields. For most developing countries, a strategy with good sustainability for social development is of long-term significance to keep the economy in expansion. This paper first reviews the conceptual framework and up-to-date development of sustainability. Second, it reviews the current transport situation of China and its future demands. Third, the paper analyses transport policy from the viewpoints of energy consumption and environment pollution caused by transportation. It finally summarises suggestions for transport policy that China should consider in the future

Marginally Trapped Surfaces in the Nonsymmetric Gravitational Theory

We consider a simple, physical approach to the problem of marginally trapped surfaces in the Nonsymmetric Gravitational Theory (NGT). We apply this approach to a particular spherically symmetric, Wyman sector gravitational field, consisting of a pulse in the antisymmetric field variable. We demonstrate that marginally trapped surfaces do exist for this choice of initial data.Comment: REVTeX 3.0 with epsf macros and AMS symbols, 3 pages, 1 figur

Strain Stiffening Induced by Molecular Motors in Active Crosslinked Biopolymer Networks

We have studied the elastic response of actin networks with both compliant and rigid crosslinks by modeling molecular motors as force dipoles. Our finite element simulations show that for compliant crosslinkers such as filamin A, the network can be stiffened by two orders of magnitude while stiffening achieved with incompliant linkers such as scruin is significantly smaller, typically a factor of two, in excellent agreement with recent experiments. We show that the differences arise from the fact that the motors are able to stretch the compliant crosslinks to the fullest possible extent, which in turn causes to the deformation of the filaments. With increasing applied strain, the filaments further deform leading to a stiffened elastic response. When the crosslinks are incompliant, the contractile forces due to motors do not alter the network morphology in a significant manner and hence only small stiffening is observed.Comment: 4 pages, 5 figure