Related papers: PFA(S)[S] and the Arhangel'skii-Tall problem
We lay some mathematically rigorous foundations for the resolution of differential equations with respect to semi-classical bases and topologies, namely Freud-Sobolev polynomials and spaces. In this quest, we uncover an elegant theory…
This paper makes significant progress towards resolving a conjecture relating strong forcing axioms like $PFA$ and the derived model at a limit of Woodin cardinals $\kappa$. In particular, using a concept called Covering Matrices, we show…
Analytical solutions to two axisymmetric problems of a penny-shaped crack when an annulus-shaped (model 1) or a disc-shaped (model 2) rigid inclusion of arbitrary profile are embedded into the crack are derived. The problems are governed by…
New integral representations for form factors in the two parametric SS model are proposed. Some form factors in the parafermionic sine-Gordon model and in an integrable perturbation of SU(2) coset conformal field theories are…
In this article, we extend Siegel's cross-ratio identity for $2\times2$ determinants over the truncated polynomial ring $F[\varepsilon]_\nu:=F[\varepsilon]/\varepsilon^\nu$. We compute cross-ratios and Goncharov's triple-ratios in…
Evolutionary models of languages are usually considered to take the form of trees. With the development of so-called tree constraints the plausibility of the tree model assumptions can be addressed by checking whether the moments of…
In this article we study the fractional Hankel transform and its inverse on certain Gel'fand-Shilov spaces of type S. The continuous fractional wavelet transform is defined involving the fractional Hankel transform. The continuity of…
The semantics of trivalent truth tables for the paraconsistent logic system P1, is characterized by a visual inference tool called trivalent semantic forcing trees. Given a formula, with this tool the nodes of the corresponding tree are…
We establish explicit formulas for Bell numbers and graphical Stirling numbers of complete multipartite graphs, complete bipartite graphs with removed perfect matchings, and Mycielskian trees. For complete multipartite graphs…
We investigate the iterative methods proposed by Maz'ya and Kozlov (see [3], [4]) for solving ill-posed reconstruction problems modeled by PDE's. We consider linear time dependent problems of elliptic, hyperbolic and parabolic types. Each…
We consider general Gaussian latent tree models in which the observed variables are not restricted to be leaves of the tree. Extending related recent work, we give a full semi-algebraic description of the set of covariance matrices of any…
This paper deals with the long time behavior of solutions to a "fractional Fokker-Planck" equation of the form $\partial_t f = I[f] + \text{div}(xf)$ where the operator $I$ stands for a fractional Laplacian. We prove an exponential in time…
The displayed tree phylogenetic network model is shown to sit as a natural submodel of the graphical model associated to a directed acyclic graph (DAG). This representation allows to derive a number of results about the displayed tree…
Let $T$ be a tree with induced partial order $\preceq$. We investigate centered Gaussian processes $X=(X_t)_{t\in T}$ represented as $$ X_t=\sigma(t)\sum_{v \preceq t}\alpha(v)\xi_v $$ for given weight functions $\alpha$ and $\sigma$ on $T$…
Let $p$ be a prime and let $G$ be a subgroup of a Sylow pro-$p$ subgroup of the group of automorphisms of the $p$-adic tree. We prove that if $G$ is fractal and $|G':\mathrm{st}_G(1)'|=\infty$, then the set $L(G)$ of left Engel elements of…
We examine the Petviashvilli method for solving the equation $ \phi - \Delta \phi = |\phi|^{p-1} \phi$ on a bounded domain $\Omega \subset \mathbb{R}^d$ with Dirichlet boundary conditions. We prove a local convergence result, using spectral…
We present a sufficient condition for irreducibility of forcing algebras and study the (non)-reducedness phenomenon. Furthermore, we prove a criterion for normality for forcing algebras over a polynomial base ring with coefficients in a…
We establish an Arakelov-type inequality for a morphism $f \colon (X,\Delta) \to S$, where $(X,\Delta)$ is a simple normal crossing semi-log canonical pair and $S$ is a smooth projective variety. As a consequence, we derive a bound on the…
It is an open problem whether definability in Propositional Dynamic Logic (PDL) on forests is decidable. Based on an algebraic characterization by Boja\'nczyk, et. al.,(2012) in terms of forest algebras, Straubing (2013) described an…
Let $r$ be a point in the first quadrant $Q_1$ of the plane $\mathbb{R}^2$ and let $P \subset Q_1$ be a set of points such that for any $p \in P$, its $x$- and $y$-coordinate is at least as that of $r$. A rectilinear Steiner arborescence…