Related papers: The distributivity numbers of of P(om) /fin and it…

We provide examples of multiplicative functions $f$ supported on the squarefree integers, such that on primes $f(p)=\pm1$ and such that $M_f(x):=\sum_{n\leq x} f(n)=o(\sqrt{x})$. Further, by assuming the Riemann hypothesis (RH) we can go…

We consider a pair of one-parameter (alpha) families of generalized two-qubit determinantal Hilbert-Schmidt probability distributions, p_{alpha}(|rho^{PT}|) and q_{alpha}(|rho|), where rho is a 4 x 4 density matrix, rho^{PT}, its partial…

We consider a linear diffusion equation on $\Omega:=\mathbb{R}^2\setminus\bar{\Omega_\mathcal{O}}$, where $\Omega_\mathcal{O}$ is a bounded domain. The time-dependent flux on the boundary $\Gamma:=\partial\Omega_\mathcal{O}$ is prescribed.…

Let $f\colon\mathbb{N}\rightarrow\mathbb{N}_0$ be a multiplicative arithmetic function such that for all primes $p$ and positive integers $\alpha$, $f(p^{\alpha})<p^{\alpha}$ and $f(p)\vert f(p^{\alpha})$. Suppose also that any prime that…

Associated to the problem of rolling one surface along another there is a five-manifold M with a rank two distribution. If the two surfaces are spheres then M is the product of the rotation group SO_3 with the two-sphere and its…

We consider several formalizations in the language of second-order arithmetic of "The formula $\phi$ is a theorem of $\omega$-logic", including some which have been studied in the literature and a new variant defined via a least fixed…

We show that in the aleph_2-stage countable support iteration of Mathias forcing over a model of CH the complete Boolean algebra generated by absolutely divergent series under eventual dominance is not isomorphic to the completion of…

We give a forcing construction of the square principle on omega_1 using forcing with conditions whose domain is finite.

We have developed an alternative formulation based on ${\bf F} = M {\bf a}$ rather than ${\bf F} = d{\bf P}/dt$ for studying variable mass systems. It is shown that ${\bf F} = M {\bf a}$ can be particularly useful in this context, as…

We analyse the balls in bins process with feedback with primary focus on the power law feedback function $f(\omega)=\eta \omega^{\gamma}\,$, $\eta>0\,$ $\gamma \geq0\,$. Using the recursive solution to the master equation we find for power…

We prove the formula for the second order "thick" distributional derivative of 1/r in 3 dimensional Euclidean space. This formula generalizes the well known Frahm formulas for the distributional derivatives of 1/r.

The colour dipole multiplicity distribution is analysed for the wave function of a heavy onium state at small $x$. Numerical results for the average multiplicity and the effect of cutoffs on its power growth are presented. Then, the full…

In proofs of L_2-differentiability, Lebesgue densities of a central distribution are often assumed right from the beginning. Generalizing Theorem 4.2 of Huber[81], we show that in the class of smooth parametric group models these densities…

A central problem in computational statistics is to convert a procedure for sampling combinatorial from an objects into a procedure for counting those objects, and vice versa. Weconsider sampling problems coming from *Gibbs distributions*,…

Let $\mathbb{F}$ be a filtration and $\tau$ be a random time. Let $\mathbb{G}$ be the progressive enlargement of $\mathbb{F}$ with $\tau$. We study the validity of the following formula, called optional splitting formula : For any…

We consider very general "random integers" and (attempt to) prove that many multiplicative and additive functions of such integers have limiting distributions. These integers include, for instance, the curvatures of Apollonian circle…

We prove that any countable support iteration formed with posets with $\omega_2$-p.i.c.\ has $\omega_2$-c.c., assuming CH in the ground model and assuming also that $\omega_1$ is not collapsed. This improves earlier results of Shelah by…

We obtained the probabilities for the values of the M\"obius function for arbitrary numbers and found that the asymptotic densities of the squarefree integers among the odd and even numbers are $8/\pi^2$ and $4/\pi^2$, respectively. It is…

The space-time foliation Sigma compatible with the gravitational field g on a 4-manifold M determines a fibration pi of M, pi : M -> N is a surjective submersion over the 1-dimensional leaves space N. M is then written as a disjoint union…

We consider shape functionals obtained as minima on Sobolev spaces of classical integrals having smooth and convex densities, under mixed Dirichlet-Neumann boundary conditions. We propose a new approach for the computation of the second…