相关论文: Carlson's <_1-relation on the class of epsilon num…

This paper grew out of the observation that the possibilities of proof by induction and definition by recursion are often confused. The paper reviews the distinctions. The von Neumann construction of the ordinal numbers includes a…

Using effective field theory techniques we compute the next to leading order Spin(1)Spin(1) terms in the potential of spinning compact objects at third Post-Newtonian order, including sub-leading self-induced finite size effects. This…

A system of uniform families on an infinite subset $M$ of $\nn$ is a collection $(\cca_{\xi})_{\xi<\omega_1}$ of families of finite subsets of $\nn$ (where, $\cca_k$ consists of all $k$--element subset of $M$, for $k\in \nn$) with the…

Let $K_{exp+}$ be the class of all structures $A$ such that the automorphism group of $A$ has at most $c n^{d n}$ orbits in its componentwise action on the set of $n$-tuples with pairwise distinct entries, for some constants $c,d$ with $d <…

Classical principal component analysis (PCA) may suffer from the sensitivity to outliers and noise. Therefore PCA based on $\ell_1$-norm and $\ell_p$-norm ($0 < p < 1$) have been studied. Among them, the ones based on $\ell_p$-norm seem to…

Let p$\ge$2 be a given prime number. We prove, for any number field kappa and any integer e$\ge$1, the p-rank $\epsilon$-conjecture, on the p-class groups Cl\_F, for the family F\_kappa^p^e of towers F/kappa built as successive degree p…

Shannon entropies of one- and two-electron atomic structure factors in the position and momentum representations are used to examine the behavior of the off-diagonal elements of density matrices with respect to the uncertainty principle and…

The Pascal matrix, $P$, is an upper diagonal matrix whose entries are the binomial coefficients. In 1993 Call and Velleman demonstrated that it satisfies the beautiful relation $P=\exp(H)$ in which $H$ has the numbers 1, 2, 3, etc. on its…

Let $\ell$ be a prime divisor of the order of a finite unitary reflection group. We classify up to conjugacy the parabolic and reflection subgroups that are minimal with respect to inclusion, subject to containing an $\ell$-Sylow subgroup.…

If $\lambda <\kappa$ are infinite cardinals, a linear order $L$ is isomorphic to a maximal chain in $[\kappa ]^{\kappa |\kappa }$ (resp. $[\kappa ]^{\lambda |\kappa }$; $[\kappa ]^{\kappa |\lambda }$) iff $L$ is weakly Boolean, the weight…

In the short note, we describe a sampling construction that yields a sequence of graphons converging to a prescribed limit graphon in 1-norm. This convergence is stronger than the convergence in the cut norm, usually used to study graphon…

We show that it is consistent relative to a weakly compact cardinal that strong homology is additive and compactly supported within the class of locally compact separable metric spaces. This complements work of Marde\v{s}i\'{c} and Prasolov…

Let p>3 be a prime number and let r be an integer with 1<r<p-1. For each r, let moreover G_r denote the unique quotient of the maximal class pro-p group of size p^{r+1}. We show that the mod-p cohomology ring of G_r has depth one and that,…

This paper continues math.LO/0009087. We present a rank function for NSOP_1 theories and give an example of a theory which is NSOP_1 but not simple. We also investigate the connection between maximality in the ordering <^* among complete…

Let kappa a regular uncountable cardinal and lambda a cardinal >kappa, and suppose lambda^{<kappa} is less than the covering number for category cov(M_{kappa,kappa}). Then (a) I_{kappa,lambda}^+ -->^kappa (I_{kappa, lambda}^+,omega +1)^2,…

We continue the investigations in the author's book on cardinal arithmetic, assuming some knowledge of it. We deal with the cofinality of (S_{<= aleph_0}(kappa), subseteq) for kappa real valued measurable (Section 3), densities of box…

In this paper we investigate more characterizations and applications of $\delta$-strongly compact cardinals. We show that, for a cardinal $\kappa$ the following are equivalent: (1) $\kappa$ is $\delta$-strongly compact, (2) For every…

We prove that it is not possible to classify separable von Neumann factors of types $\II_1$, $\II_\infty$ or $\III_\lambda$, $0\leq \lambda\leq1$, up to isomorphism by a Borel measurable assignment of "countable structures" as invariants.…

Given an uncountable cardinal $\kappa$, we consider the question of whether subsets of the power set of $\kappa$ that are usually constructed with the help of the Axiom of Choice are definable by $\Sigma_1$-formulas that only use the…

In the course of many mathematical developments involving 'number systems' like $\mathbb{N}, \mathbb{Z}, \mathbb{Q}, \mathbb{R}, \mathbb {C}$ etc., it sometimes becomes necessary to abstract away and study certain properties of the number…