We will give an elementary proof of a result of R. Hamilton for Ricci flow on compact surfaces. Let M be a compact surface. We will prove the global existence of solution of the Ricci flow ∂gij/∂t = (r − R)gij on M where R is the scalar curvature and r = R

We show here that the spectrum of the family of noncommutative harmonic oscillators Qw(α,β)(x,D) for α, β ∈ R+ in the range αβ = 1, is [0,+∞) and is entirely essential spectrum. The previous existing results concern the case αβ > 1 (case in which Qw(α,β)(x,D) is globally elliptic with a discrete spectrum whose qualitative properties are being extensively studied), and ours therefore extends the...

Sufficient conditions are given for the existence of oscillatory proper solutions of a differential equation with quasiderivatives Lny = f(t, L0y, . . . , Ln−1y) under the validity of the sign condition f(t, x1, . . . , xn)x1 ≤ 0, f(t, 0, x2, . . . , xn) = 0 on R+ × Rn.

This paper analyzes the likely impacts of the major policy reforms unveiled by the Government of India for revamping the country’s power sector. The provisions of the new enactment have recently come into force and seek a paradigm policy shift in the form of the Electricity Act 2003. The paper details out the key features of the Act and the likely power industry changes being brought about in t...

Here R+ denotes the upper half-plane and BMO(R 2 +×R 2 +) is defined to be the dual of the realvariable Hardy space H on the product domain R+×R 2 +. There are several equivalent ways to define this latter space and the reader is referred to [5] for the various characterizations. We will be more interested in the biholomorphic analogue of H, which can be defined in terms of the boundary values ...

Magnetic resonance imaging (MRI) is a biomedical imaging modality that provides high resolution images and excellent soft tissue contrast [1]. This makes MRI a preferable imaging modality for many applications. One limitation of MRI is slow data acquisition. MRI acquires data in the Fourier domain one point at a time, usually until enough data has been collected to approximately satisfy Nyquist...

We prove several Tauberian theorems for regularizing transforms of vector-valued distributions. The regularizing transform of f is given by the integral transform M φ(x, y) = (f ∗ φy)(x), (x, y) ∈ R n × R+, with kernel φy(t) = yφ(t/y). We apply our results to the analysis of asymptotic stability for a class of Cauchy problems, Tauberian theorems for the Laplace transform, the comparison of quas...

We consider scalar equation ut(t, x) = uxx(t, x)− u(t, x) + Z R K(x− y)g(u(t − h, y))dy, (∗) where g : R+ → R+ has exactly two fixed points: x1 = 0, x2 = κ > 0, and K is non-negative and such that R