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Fundamental divisors on Fano varieties of index n-3
Fundamental divisors Fano varieties of index n-3
2010/11/30
Let X be a Fano manifold of dimension n and index n−3. Kawa-mata proved the non vanishing of the global sections of the fundamental divisor in the case n = 4. Moreover he proved that if Y is a g...
From logarithmic to subdiffusive polynomial fluctuations for internal DLA and related growth models
internal diffusion limited aggregation cluster growth
2010/12/6
We consider a family of cluster growth models on Zd, which generalize internal diffusion limited aggregation (internal DLA). The latter model is simplest to describe:random walks start at the origin, ...
Corrigendum --- Quadratic Class Numbers Divisible by 3
Corrigendum Quadratic Class Numbers Divisible by 3
2010/12/10
In attempting to handle N+(X) the paper states that the Scholz reflection principle “yields 3|h(k) for any positive integer for which 3|h(−3k)”. This is not correct, and one cannot establish a r...
We define a new sequence of positive integers, associated with Catalan numbers and Narayana polynomials.
In this note we present a description of wave front evolving from an algebraic hypersurface by means of a pull-back of the discriminantal loci of a tame polynomial via a polynomial mapping. As an appl...
From quasi-entropy
f-divergence quasi-entropy von Neumann entropy relative entropy monotonicity property
2010/12/15
The subject is the overview of the use of quasi-entropy in finite dimensional spaces. Matrix monotone functions and relative modular operators are used. The origin is the relative entropy and the f-di...
Power multiples in binary recurrence sequences: an approach by congruences
Power multiples binary recurrence sequences approach by congruences
2010/12/13
We introduce an elementary congruence-based procedure to look for q-th power multiples in arbitrary binary recurrence sequences (q 3). The procedure allows to prove that no such multiples exist in m...
Generalized Semimagic Squares for Digital Halftoning
Generalized Semimagic Squares Digital Halftoning
2010/12/15
Completing Aronov et al.’s study on zero-discrepancymatrices for digital halftoning, we determine all (m, n, k, l) for which it is possible to put mn consecutive integers on an m × n board (with wrap-...
DJKM algebras I: Their Universal Central Extension
Krichever-Novikov Algebras Landau-Lifshitz differential equation Date-Jimbo-Miwa-Kashiwara algebras universal central extension
2010/11/30
The purpose of this paper is to explicitly describe in terms of generators and relations the universal central extension of the infinite dimensional Lie algebra, g C[t, t−1, u|u2 = (t2 −...
Primitive Divisors of Certain Elliptic Divisibility Sequences
Elliptic curve Elliptic divisibility sequence Primitive diviso Canonical height
2010/11/30
We establish conditions necessary for the n-th element of any elliptic divisibility sequence generated by points on Ea : y2 = x3+ax to not have a primitive divisor. As a consequence of this, along wit...
On fractional parts of powers of real numbers close to 1
fractional parts of powers real numbers close to 1
2010/12/10
We prove that there exist arbitrarily small positive real num-bers " such that every integral power (1 + ")n is at a distance greater than 2−17"| log "|−1 to the set of rational integers. ...
On Extending the Langlands-Shahidi Method to Arithmetic Quotients of Loop Groups
automorphic L-functions Eisenstein series loop groups
2010/12/10
We discuss certain Eisenstein series on arithmetic quotients of loop groups, ˆG , which are associated to cusp forms on finite-dimensional groups associated with maximal parabolics of ˆG .
A new series for $\pi^3$ and related congruences
Series for 3 central binomial coefficients congruences modulo prime powers
2010/12/14
Let H(2)n denote the second-order harmonic numberP0
Almost regular involutory automorphisms of uniquely 2-divisible groups
almost regular involutory automorphism uniquely 2-divisible group
2010/11/29
We prove that a uniquely 2-divisible group that admits an almost regular involutory automorphism is solvable.
Thue-Morse at Multiples of an Integer
Thue-Morse sequence sum of digits congruences arithmetic progressions
2010/12/14
Let t = (tn)n0 be the classical Thue-Morse sequence defined
by tn = s2(n) mod 2, where s2 is the sum of the bits in the binary repre-sentation of n. It is well known that for any integer k ≥ 1 the f...