On special rational curves in Grassmannians

Numerical and geometric characterizations, among all morphisms , of those which are -equivalent to the canonical morphism induced by the Morita equivalence –, are presented. The author was partially supported by KBN grants 1P03A 036 26 and 115/E-343/SPB/6.PR UE/DIE 50/2005-2008. Received: 10 September 2005     

Dual pairs and Kostant-Sekiguchi correspondence. II. Classification of nilpotent elements

We classify the homogeneous nilpotent orbits in certain Lie color algebras and specialize the results to the setting of a real reductive dual pair. For any member of a dual pair, we prove the bijectivity of the two Kostant-Sekiguchi maps by straightforward argument. For a dual pair we determine the correspondence of the real orbits, the correspondence of the complex orbits and explain how these two relations behave under the Kostant-Sekiguchi maps. In particular we prove that for a dual pair in the stable range there is a Kostant-Sekiguchi map such that the conjecture formulated in [6] holds. We also show that the conjecture cannot be true in general.     

Total linearization of probability density evolution equations

Total linearization of the Boltzmann and Vlasov equations is used to present a technique applicable to equations which have polynomial-type nonlinearities and describe the evolution of probability density functions or distributions. It is an extension of an earlier result, where a method yielding a linear equation with a nonlinear constraint was presented.     

Turán numbers for odd wheels

The Turán number $\text{ex}(n,G)$ is the maximum number of edges in any $n$-vertex graph that does not contain a subgraph isomorphic to $G$. A wheel$W_n$ is a graph on $n$ vertices obtained from a $C_{n?1}$ by adding one vertex $w$ and making $w$ adjacent to all vertices of the $C_{n?1}$. We obtain two exact values for small wheels:

$\text{ex}(n,W_5)=?\frac{n^2}{4}+\frac{n}{2}?,$

$\text{ex}(n,W_7)=?\frac{n^2}{4}+\frac{n}{2}+1?.$

Given that $\text{ex}(n,W_6)$ is already known, this paper completes the spectrum for all wheels up to 7 vertices. In addition, we present the construction which gives us the lower bound $\text{ex}(n,W_{2k+1})>?\frac{n^2}{4}?+?\frac{n}{2}?$ in general case.     

Ergodic properties of Poisson processes with almost periodic intensity

Summary We discuss in this paper a non-homogeneous Poisson process A driven by an almost periodic intensity function. We give the stationary version A ^* and the Palm version A ⁰ corresponding to A ^*. Let (T _i ,i) be the inter-point distance sequence in A and (T _i ⁰ ,i) in A ⁰. We prove that forj, the sequence (T _i+j,i) converges in distribution to (T _i ⁰ ,i). If the intensity function is periodic then the convergence is in variation.     

Background removal procedure for rapid scan EPR

In rapid scan EPR the changing magnetic field creates a background signal with components at the scan frequency and its harmonics. The amplitude of the background signal increases with scan width and is more significant for weak EPR signals such as are obtained in the presence of magnetic field gradients. A procedure for distinguishing this background from the EPR signal is proposed, mathematically described, and tested for various experimental conditions.     

On constraining the speed of gravitational waves following GW150914

We point out that the observed time delay between the detection of the signal at the Hanford and Livingston LIGO sites from the gravitational wave event GW150914 places an upper bound on the speed of propagation of gravitational waves, c_gw ? 1.7 in the units of speed of light. Combined with the lower bound from the absence of gravitational Cherenkov losses by cosmic rays that rules out most of subluminal velocities, this gives a model-independent double-sided constraint 1 ? c_gw ? 1.7. We compare this result to model-specific constraints from pulsar timing and cosmology.