The aim of this paper is to prove the following Theorem 1. Let G be a finite abelian group acting faithfully on a complex smooth project variety X of general type with numerically effective (nef) canonical divisor, of dimension n. Then |G| ≤ C(n)K n X , where C(n) depends only on n. We refer to the Introduction of [Ca-Sch] for a nice account of the history for the study of bounds of automorphis...

We prove that double exponentiation is an upper bound to Ramsey theorem for colouring of pairs when we want to predetermine the order of the differences of successive members of the homogeneous set. I thank Alice Leonhardt for excellent typing. Research supported by the United States-Israel Binational Science Foundation Publication number 515; Latest Revision 02/95 Done Erdős 80th birthday meet...

To quote Shannon from his paper A Mathematical theory of communication: “The fundamental problem of communication is that of reproducing at one point either exactly or approximately a message selected at another point.” The basic setup of the communication problem consists of a source that generates digital information which is to reliably communicated to a destination through a channel, prefer...

In this short paper we prove a quantitative version of the Khintchine–Groshev Theorem with congruence conditions. Our argument relies on classical Schmidt counting generic lattice points, which in turn certain variance bound space lattices.

to demonstrate more visibly the close relation between thecontinuity and integrability, a new proof for the banach-zareckitheorem is presented on the basis of the radon-nikodym theoremwhich emphasizes on measure-type properties of the lebesgueintegral. the banach-zarecki theorem says that a real-valuedfunction $f$ is absolutely continuous on a finite closed intervalif and only if it is continuo...

The Upper Bound Conjecture is verified for a class of odd-dimensional simplicial complexes that in particular includes all Eulerian simplicial complexes with isolated singularities. The proof relies on a new invariant of simplicial complexes—a short simplicial h-vector.

Strassen’s lower bound for polynomial evaluation and Bezout’s theorem Recall Strassen’s algorithm from the previous lecture: Given: (a0, . . . , an−1), (x1, . . . , xn) ∈ K, and polynomial p(x) = ∑n−1 i=0 aix i Task: find (z1, . . . , zn), zi = p(xi) How many steps do we need to accomplish this task? Using the Fast Fourier Transform (FFT) we need O(n log n) steps. Strassen was interested whethe...

For an absolutely continuous probability measure on Rd and a nonnegative integer k, let ~ sk( ;0) denote the probability that the convex hull of k + d + 1 random points which are i.i.d. according to contains the origin 0. For d and k given, we determine a tight upper bound on ~ sk( ;0), and we characterize the measures in Rd which attain this bound. As we will see, this result can be considered...

Given a weight vector [Formula: see text] with each bounded by certain constraints, we obtain lower bound for the Hausdorff dimension of set text], where is twice continuously differentiable manifold. From this produce general approximation function limits. The proof based on technique developed Beresnevich et al. in 2017, but use an alternative mass transference style theorem proven Wang, Wu a...

Let D(n) denote the cardinality of the largest subset of the set {1, 2, . . . , n} such that the difference of no pair of elements is a square. A well-known theorem of Furstenberg and Sárközy states that D(n) = o(n). In the other direction, Ruzsa has proven that D(n) & nγ for γ = 1 2 ( 1 + log 7 log 65 ) ≈ 0.733077. We improve this to γ = 1 2 ( 1 + log 12 log 205 ) ≈ 0.733412.