Related papers: A note on Leibniz rule for difference quotient
In this very short note we slightly generalize some relations for one-part double Hurwitz numbers from math.AG/0209282.
We derive a separability criterion for bipartite quantum systems which generalizes the already known criteria. It is based on observables having generic commutation relations. We then discuss in detail the relation among these criteria.
I expound here in a more detailed way a proof of an important Serini's theorem, which I have already sketched in a previous Note. Two related questions are briefly discussed.
This note considers the notion of divergence-preserving branching bisimilarity. It briefly surveys results pertaining to the notion that have been obtained in the past one-and-a-half decade, discusses its role in the study of expressiveness…
We conservatively extend classical elementary differential calculus to the Cartesian closed category of convergence spaces. By specializing results about the convergence space representation of directed graphs, we use Cayley graphs to…
We derive an inequality on the discrepancy of sequences on the ring of $p$-adic integers $\ZZ_p$ using techniques from Fourier analysis. The inequality is used to obtain an upper bound on the discrepancy of the sequence $\alpha_n = na +b$,…
This note contains a short and simple proof of Wormald's differential equation method (that yields slightly improved approximation guarantees and error probabilities). This powerful method uses differential equations to approximate the…
In this short note, we briefly discuss the Borel-Cantelli lemma and propose a new generalization of the first part of it.
A more detailed derivation of the Heisenberg uncertainty principle from the certainty principle is given.
We establish an analogue of the Goldbach conjecture for Laurent polynomials with positive integer coefficients.
In this paper we give a criterion of irreducibility for a complex power series in two variables, using the notion of jacobian Newton diagrams, defined with respect to any direction. Moreover we study the singularity at infinity of a plane…
We give a necessary and sufficient condition for the canonical divisor to vanish on a quasi-homogeneous affine algebraic variety.
An algebraic deformation theory of morphisms of dual Leibniz algebras is obtained.
In the paper we describe derivations of some classes of Leibniz algebras. It is shown that any derivation of a simple Leibniz algebra can be written as a combination of three derivations. Two of these ingredients are a Lie algebra…
I present a proof of the quantum probability rule from decision-theoretic assumptions, in the context of the Everett interpretation. The basic ideas behind the proof are those presented in Deutsch's recent proof of the probability rule, but…
In this note we prove an inequality involving primes and the product of consecutive primes.
Schleischitz [arXiv:1701.01129] determined exponents of best approximations to a strong Liouville number by integer polynomials and algebraic numbers of precribed degree. In this note, we show that we cannot extend his result to arbitrary…
We show that standard deviation $\s$ satisfies the Leibniz inequality $\s(fg) \leq \s(f)\|g\| + \|f\|\s(g)$ for bounded functions f, g on a probability space, where the norm is the supremum norm. A related inequality that we refer to as…
These notes deal with a few aspects of Lie algebras and Lie groups, including some matters related to exponentiation.
In this work, we construct the de Rham complex with differential operator d satisfying the Q-Leibniz rule, where Q is a complex number, and the condition $d^3=0$ on an associative unital algebra with quadratic relations. Therefore we…