Related papers: Gap Theorem for Separated Sequences without Pain
The subject of this paper is the problem of arrangement of real algebraic curves on real algebraic surfaces. In this paper we extend Rokhlin, Kharlamov-Gudkov-Krakhnov and Kharlamov-Marin congruences for curves on surfaces and give some…
We introduce a notion of curvature on finite, combinatorial graphs. It can be easily computed by solving a linear system of equations. We show that graphs with curvature bounded below by $K>0$ have diameter bounded by $\mbox{diam}(G) \leq…
We offer a new perspective on the closed graph theorem and the open mapping theorem for separated barrelled spaces and fully complete spaces.
We provide some explicit algebraic criteria in terms of the Goldman bracket to decide whether two free homotopy classes of loops on an oriented surface admit disjoint representatives. We extend Kabiraj's method using the hyperbolic geometry…
The paper concerns the Gelfand-Kirillov dimension and the generating series of nonsymmetric operads. An analogue of Bergman's gap theorem is proved, namely, no finitely generated locally finite nonsymmetric operad has Gelfand-Kirillov…
The Three Gap Theorem, also known as the Steinhaus Conjecture, is a classical result on the combinatorics of the fractional part function, and has since been generalized in many ways. In this paper, we pose a new problem related to these…
We show a smoothed version of Goldston-Pintz-Yildirim's sifting argument to detect small gaps between primes, which has a higly flexible error term. Our argument is applicable to high dimensional Selberg sieve situations as well, although…
The Endpoint Theorem links the existence of a sequence (curve), without accumulation points, in a manifold to the existence of an open embedding of that manifold so that the image of the given sequence (curve) has a unique endpoint. It…
The transverse-traceless gauge condition is an important concept in the theory of gravitational wave. It is well known that vacuum is one of the key conditions to guarantee the existence of the transverse-traceless gauge. Although it is…
We give a proof of the Gap Labeling Conjecture formulated by J. Bellissard. This gives information about the spectrum of a Schrodinger operator associated to a quasicrystal. The proof makes use of a version of Connes' Index Theorem for…
In this paper, we give a new proof of an arithmetic analogue of the Riemann-Roch Theorem, due originally to Serge Lang. Lang's result was first proved using the lattice point geometry of Minkowski. By contrast, our proof is completely…
The paper established sufficient conditions of predictability with degeneracy for the spectrum at $M$-periodically located isolated points on the unit circle. It is also shown that $m$-periodic subsequences of these sequences are also…
In a recent work Friedlander studied the problem of how large consecutive prime gaps should be in order that the sum of the reciprocals should be divergent. Supposing a very deep Hypothesis, a generalization of the Hardy--Littlewood prime…
The detour between two points u and v (on edges or vertices) of an embedded planar graph whose edges are curves is the ratio between the shortest path in in the graph between u and v and their Euclidean distance. The maximum detour over all…
In this work we prove the undecidability (and $\Sigma^0_1$-completeness) of several theories of semirings with fixed points. The generality of our results stems from recursion theoretic methods, namely the technique of effective…
This work extends the discrete compactness results of Walkington (SIAM J. Numer. Anal., 47(6):4680--4710, 2010) for high-order discontinuous Galerkin time discretizations of parabolic problems to more general function space settings. In…
By Gromov's compactness theorem for metric spaces, every uniformly compact sequence of metric spaces admits an isometric embedding into a common compact metric space in which a subsequence converges with respect to the Hausdorff distance.…
The accumulated quadrature weights of Gaussian quadrature formulae constitute bounds on the integral over the intervals between the quadrature nodes. Classical results in this concern date back to works of Chebyshev, Markov and Stieltjes…
In this paper, we prove a version of the arithmetic Bertini theorem asserting that there exists a strictly small and generically smooth section of a given arithmetically free graded arithmetic linear series.
The cutoff phenomenon describes the case when an abrupt transition occurs in the convergence of a Markov chain to its equilibrium measure. There are various metrics which can be used to measure the distance to equilibrium, each of which…