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

Combined SIRT3 and SIRT5 deletion is associated with inner retinal dysfunction in a mouse model of type 1 diabetes

Abstract Diabetic retinopathy (DR) is a major cause of blindness in working adults in the industrialized world. In addition to vision loss caused by macular edema and pathological angiogenesis, DR patients often exhibit neuronal dysfunction on electrophysiological testing, suggesting that there may be an independent neuronal phase of disease that precedes vascular disease. Given the tremendous metabolic requirements of the retina and photoreceptors in particular, we hypothesized that derangements in metabolic regulation may accelerate retinal dysfunction in diabetes. As such, we induced hyperglycemia with streptozotocin in mice with monoallelic Nampt deletion from rod photoreceptors, mice lacking SIRT3, and mice lacking SIRT5 and tested multiple components of retinal function with electroretinography. None of these mice exhibited accelerated retinal dysfunction after induction of hyperglycemia, consistent with normal-appearing retinal morphology in hyperglycemic Sirt3 −/− or Sirt5 −/− mice. However, mice lacking both SIRT3 and SIRT5 (Sirt3 −/− Sirt5 −/− mice) exhibited significant evidence of inner retinal dysfunction after induction of hyperglycemia compared to hyperglycemic littermate controls, although this dysfunction was not accompanied by gross morphological changes in the retina. These results suggest that SIRT3 and SIRT5 may be involved in regulating neuronal dysfunction in DR and provide a foundation for future studies investigating sirtuin-based therapies