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The Schroder-Bernstein property for a-saturated models
Schroder-Bernstein property a-saturated models Logic
2012/3/1
A first-order theory T has the Schr\"oder-Bernstein (SB) property if any pair of elementarily bi-embeddable models are isomorphic. We prove that T has an expansion by constants that has the SB propert...
Examples of the Generalized Quantum Permanent Compromise Attack to the Blum-Micali Construction
Examples of the Generalized Quantum Permanent Compromise Blum-Micali Construction
2011/1/19
This file contains examples of the generalized quantum permanent compromise attack to the Blum-
Micali construction. The examples presented here illustrate the attack described in the paper published...
Product update is an operation on models introduced into epistemic logic in order to represent a broad class of informational events. If adding modalities representing product update to a language do...
Conley Conjecture for Negative Monotone Symplectic Manifolds
Conley Conjecture Negative Monotone Symplectic Manifolds
2010/11/24
We prove the Conley conjecture for negative monotone, closed symplectic manifolds, i.e., the existence of infinitely many periodic orbits for Hamiltonian diffeomorphisms of such manifolds.
A quantum stochastic Lie-Trotter product formula
quantum stochastic Lie-Trotter product formula
2010/11/24
A Trotter product formula is established for unitary quantum stochastic processes governed by quantum stochastic differential equations with constant bounded coefficients.
Jets, Lifts and Dynamics
Jets Lifts Dynamics
2010/11/9
We show that complete cotangent lifts of vector fields, their decomposition into vertical representative and holonomic part provide a geometrical framework underlying Eulerian equations of continuum ...
We give an elementary proof of the Kontsevich conjecture that asserts that the iterations of the noncommutative rational map K_r:(x,y)-->(xyx^{-1},(1+y^r)x^{-1}) are given by noncommutative Laurent po...
On cohomology of Witt vectors of algebraic integers and a conjecture of Hesselholt
Witt vectors algebraic integers conjecture of Hesselholt
2010/11/19
Let $K$ be a complete discrete valued field of characteristic zero with residue field $k_K$ of characteristic $p > 0$. Let $L/K$ be a finite Galois extension with the Galois group $G$ and suppose tha...
An improved bound for the Manickam-Miklós-Singhi conjecture
the Manickam-Miklós-Singhi conjecture math
2010/11/18
We show that for $n>k(4e\log k)^k$ every set $\{x_1,..., x_n\}$ of $n$ real numbers with $\sum_{i=0}^{n}x_i \geq 0$ has at least $\binom{n-1}{k-1}$ $k$-element subsets of a non-negative sum. This is ...
Separation of time-scales and model reduction for stochastic reaction networks
Separation time-scales stochastic reaction networks
2010/11/12
A stochastic model for a chemical reaction network is embedded in a one-parameter family of models with species numbers and rate constants scaled by powers of the parameter. A systematic approach is ...
Models for $(\infty, n)$-categories and the cobordism hypothesis
the cobordism hypothesis math
2010/11/8
In this paper we introduce the models for $(\infty, n)$-categories which have been developed to date, as well as the comparisons between them that are known and conjectured. We review the role of $(\i...
Nonparametric tests of the Markov hypothesis in continuous-time models
Nonparametric tests Markov hypothesis continuous-time models
2010/11/18
We propose several statistics to test the Markov hypothesis for $\beta$-mixing stationary processes sampled at discrete time intervals. Our tests are based on the Chapman--Kolmogorov equation. We est...
The number of Goldbach representations of an integer
Goldbach representations of an integer math
2010/11/19
We prove the following result: Let $N \geq 2$ and assume the Riemann Hypothesis (RH) holds. Then \[ \sum_{n=1}^{N} R(n) =\frac{N^{2}}{2} -2 \sum_{\rho} \frac{N^{\rho + 1}}{\rho (\rho + 1)} + O(N \log...
Let $\pi, \pi'$ be tempered representations of an affine Hecke algebra with positive parameters. We study their Euler--Poincar\'e pairing $EP (\pi,\pi')$, the alternating sum of the dimensions of the...
On a Conjecture of a Bound for the Exponent of the Schur Multiplier of a Finite $p$-Group
Conjecture Exponent Schur Multiplier Finite $p$-Group
2010/11/18
Let $G$ be a $p$-group of nilpotency class $k$ with finite exponent $\exp(G)$ and let $m=\lfloor\log_pk\rfloor$. We show that $\exp(M^{(c)}(G))$ divides $\exp(G)p^{m(k-1)}$, for all $c\geq1$, where $...