when 0 < k ≤ p. We will say that a smooth projective variety X has Bott vanishing if for every ample line bundle L, i > 0 and j H(X,ΩjX ⊗ L) = 0 The purpose of this paper is to show that Bott vanishing is a simple consequence of a very specific condition on the Frobenius morphism in prime characteristic p. Recall that the absolute Frobenius morphism F : X → X on X, where X is a variety over Z/p...

This paper describes a method of interpreting three dimensional motion of an object by making use of r i g i d i t y assumption and orientation of i t s edge. We employ a vanishing point to determine the orientat ion. We propose a new idea of using cross ra t i o , i .e . one of the most fundamental concepts in projective geometry to f ind a vanishing point of a l ine . This allows to calculate...

The idea in this paper is to show how a generalized “log” version of the Kodaira vanishing theorem can be employed to improve the results of Theorem 1 (which was also proved by Kodaira vanishing) when we have more knowledge about the equations for Y . The idea is to find a hypersurface F ⊂ P which has high multiplicity along Y , is “log canonical” near Y , and has relatively small degree, then ...

We revisit a classical scenario in communication theory: a source is generating a waveform which we sample at regular intervals; we wish to transform the signal in such a way as to minimize distortion in its reconstruction, despite noise. The transformation must be online (also called causal), in order to enable real-time signaling. The noise model we consider is adversarial `1-bounded; this is...

In this paper, we give explicit construction of multiwavelets on polygonal region in R 2 that is associated with a nested triangular tessellation. Two di erent constructions will be presented. The rst construction is very similar to Alpert's construction in [3], but unlike the latter 1-D construction, in which case symmetry of basis functions comes in almost automatically, the multiwavelets fro...

The introduction of vanishing moment recovery (VMR) functions in our recent work (also called “fundamental functions” in an independent paper by Daubechies, Han, Ron, and Shen) modifies the so-called “unitary extension principle” to allow the construction of compactly supported affine frames with any desirable order of vanishing moments up to the order of polynomial reproduction of the given as...

It is generally known that the orbital diamagnetism of a classical system of charged particles in thermal equilibrium is identically zero – the Bohr-van Leeuwen theorem. Physically, this null result derives from the exact cancellation of the orbital diamagnetic moment associated with the complete cyclotron orbits of the charged particles by the paramagnetic moment subtended by the incomplete or...

The common belief that the CMB is Gaussian distributed can be directly traced back to the generic assumption that the quantum fluctuations of the inflaton field are placed in the vacuum state 1. Relaxing this assumption might lead to detectable signatures in various astrophysical tests, most interestingly in future CMB and large-scale structure observations. In this note, we study CMB non-Gauss...

We initially discuss a new and simple method of parameterization of compactly supported biorthogonal wavelet systems with more than one vanishing moment. To this end we express both primal and dual scaling function filters (low pass) as products of two Laurent polynomials. The first factor ensures required vanishing moments and the second factor is parameterized and adjusted to provide required...

The purpose of the current paper is to introduce some new methods for studying the p-adic Banach spaces introduced by Emerton [9]. We first relate these spaces to more familiar sheaf cohomology groups. As an application, we obtain a more general version of Emerton’s spectral sequence. We also calculate the spaces in some easy cases. As a consequence, we obtain a number of vanishing theorems.