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...

In the present paper, we study several qualitative properties of a class of nonlinear switched systems under certain switching laws. First, we show that if all the subsystems are linear time-invariant and the system matrices are commutative componentwise and stable, then the entire switched system is globally exponentially stable under arbitrary switching laws. Next, we study the above linear s...

One way to analyze complicated non-autonomous flows is through trying to understand their transport behavior. In a quantitative, set-oriented approach to transport, finite time coherent sets play an important role. These are time-parametrized families of sets with unlikely transport to and from their surroundings under small or vanishing random perturbations of the dynamics. Here we propose, as...

We study the asymptotic behavior of viscosity solutions uGλ Hamilton-Jacobi (HJ) equation λu(x)+G(x,u′)=c(G) in Ras positive discount factor λ tends to 0, where G(x,p):=H(x,p)−V(x) is perturbation a Hamiltonian H∈ C(R×R), Z–periodic space variable and convex coercive momentum, by compactly supported potential V∈Cc(R). The constant c(G) appearing above defined as infimum values a∈R for which HJ ...

In this article, continuous and discontinuous integral controllers for multiple-input multiple-output (MIMO) systems are designed a large class of nonlinear systems, which (partially) feedback linearizable. These arbitrary positive or negative degree homogeneity derived by combining Lyapunov function obtained from the implicit (ILF) method with some extra explicit terms. Discontinuous able to s...

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 planar polynomial vector fields with a center at the origin can be written as an scalar differential equation, for example Abel equation. If the coefficients of an Abel equation satisfy the composition condition, then the Abel equation has a center at the origin. Also the composition condition is sufficient for vanishing the first order moments of the coefficients. The composition conjectur...

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 ...

Minimally modified gravity is a class of models with only the two tensor degrees freedom as in general relativity. Using framework auxiliary constraints these can maintain dynamical cosmological background. The form thereby restricted by requirement dark energy and avoidance breakdown perturbation theory. Studying linear perturbations around FLRW background results are, however, quite insensiti...