相关论文: Generic sets in spaces of measures and generic sin…

We derive for generally covariant theories the generic dependency of observables on the original fields, corresponding to coordinate-dependent gauge fixings. This gauge choice is equivalent to a choice of intrinsically defined coordinates…

We study a wide class of metrics in a Lebesgue space with a standard measure, the class of so-called admissible metrics. We consider the cone of admissible metrics, introduce a special norm in it, prove compactness criteria, define the…

Let $\mathbb F=\mathbb R$ or $\mathbb C$ and $n\in\b N$. Let $(S_k)_{k\ge0}$ be a time-homogeneous random walk on $GL_n(\b F)$ associated with an $U_n(\b F)$-biinvariant measure $\nu\in M^1(GL_n(\b F))$. We derive a central limit theorem…

We make a detailed investigation of the generic properties that polynomial mappings possess. An important starting point is the work by Farnik, Jelonek and Ruas in 2019, where they prove some of those properties in the context of…

In quantum theory, observables with a continuous spectrum are known to be fundamentally different from those with a discrete and finite spectrum. While some fundamental tests and applications of quantum mechanics originally formulated for…

We consider scenarios where the dynamics of a quantum system are partially determined by prior local measurements of some interacting environmental degrees of freedom. The resulting effective system dynamics are described by a disordered…

We introduce boundary special generic maps, a class of submersions from manifolds with boundary to Euclidean spaces whose restriction to the boundary has only boundary definite fold points as its singular points. We derive the…

We introduce a parametrized notion of genericity for Delaunay triangulations which, in particular, implies that the Delaunay simplices of $\delta$-generic point sets are thick. Equipped with this notion, we study the stability of Delaunay…

We introduce a universality theorem for functionals of measures on partitions which "behave like" the Ewens measure. Various limit theorems for the Ewens measure, most notably the Poisson-Dirichlet limit for the longest parts, the…

Universal representation of geometric patterns of disordered matters is investigated with the aid of general topology. By utilizing the result obtained in the previous study (S. Ohmori, et.al., Phys. Scr. 94, 105213 (2019)) that any…

We define a general framework that includes objects such as tilings, Delone sets, functions and measures. We define local derivability and mutual local derivability (MLD) between any two of these objects in order to describe their…

We prove the uniqueness of solutions to Dirichlet problem for p-harmonic maps with images in a small geodesic ball of the target manifold. As a consequence, we show that such maps have Hoelder continuous derivatives. This gives an extension…

We study generic holomorphic families of dynamical systems presenting problems of small divisors with fixed arithmetic. We prove that we have convergence for all parameter values or divergence everywhere except for an exceptional set in the…

We report on some advances made in the problem of singularities in general relativity. First is introduced the singular semi-Riemannian geometry for metrics which can change their signature (in particular be degenerate). The standard…

If $\Lambda $ is a measure space, $u:\Lambda ^{m}\rightarrow \Bbb{R}$ is a given function and $N\geq m,$ the function $U(x_{1},...,x_{N})=\left( \begin{array}{l} N \\ m \end{array} \right) ^{-1}\sum_{1\leq i_{1}<\cdots <i_{m}\leq…

Measure homology is a variation of singular homology designed by Thurston in his discussion of simplicial volume. Zastrow and Hansen showed independently that singular homology (with real coefficients) and measure homology coincide…

Persistent homology is a popular and useful tool for analysing finite metric spaces, revealing features that can be used to distinguish sets of unlabeled points and as input into machine learning pipelines. The famous stability theorem of…

Two series of integrable theories are constructed which have soliton solutions and can be thought of as generalizations of the sine-Gordon theory. They exhibit internal symmetries and can be described as gauged WZW theories with a potential…

We use a construction which we call generalized cylinders to give a new proof of the fundamental theorem of hypersurface theory. It has the advantage of being very simple and the result directly extends to semi-Riemannian manifolds and to…

Glasses are known to exhibit quantitative universalities at low temperatures, the most striking of which is the ultrasonic attenuation coefficient 1/Q. In this work we develop a theory of coupled generic blocks with a certain randomness…