Search results for "Ordering"
showing 10 items of 55 documents
Rod-like ferrites obtained through thermal degradation of a molecular ferrimagnet
2010
This paper presents the characteristics of iron oxides obtained through thermal degradation of a molecular ferrimagnet, {N(n-C4H9)4[Fe II
Conditional convex orders and measurable martingale couplings
2014
Strassen's classical martingale coupling theorem states that two real-valued random variables are ordered in the convex (resp.\ increasing convex) stochastic order if and only if they admit a martingale (resp.\ submartingale) coupling. By analyzing topological properties of spaces of probability measures equipped with a Wasserstein metric and applying a measurable selection theorem, we prove a conditional version of this result for real-valued random variables conditioned on a random element taking values in a general measurable space. We also provide an analogue of the conditional martingale coupling theorem in the language of probability kernels and illustrate how this result can be appli…
A Unified Approach to Likelihood Inference on Stochastic Orderings in a Nonparametric Context
1998
Abstract For data in a two-way contingency table with ordered margins, we consider various hypotheses of stochastic orders among the conditional distributions considered by rows and show that each is equivalent to requiring that an invertible transformation of the vectors of conditional row probabilities satisfies an appropriate set of linear inequalities. This leads to the construction of a general algorithm for maximum likelihood estimation under multinomial sampling and provides a simple framework for deriving the asymptotic distribution of log-likelihood ratio tests. The usual stochastic ordering and the so called uniform and likelihood ratio orderings are considered as special cases. I…
Stochastic order characterization of uniform integrability and tightness
2013
We show that a family of random variables is uniformly integrable if and only if it is stochastically bounded in the increasing convex order by an integrable random variable. This result is complemented by proving analogous statements for the strong stochastic order and for power-integrable dominating random variables. Especially, we show that whenever a family of random variables is stochastically bounded by a p-integrable random variable for some p>1, there is no distinction between the strong order and the increasing convex order. These results also yield new characterizations of relative compactness in Wasserstein and Prohorov metrics.
Stochastic ordering of classical discrete distributions
2010
For several pairs $(P,Q)$ of classical distributions on $\N_0$, we show that their stochastic ordering $P\leq_{st} Q$ can be characterized by their extreme tail ordering equivalent to $ P(\{k_\ast \})/Q(\{k_\ast\}) \le 1 \le \lim_{k\to k^\ast} P(\{k\})/Q(\{k\})$, with $k_\ast$ and $k^\ast$ denoting the minimum and the supremum of the support of $P+Q$, and with the limit to be read as $P(\{k^\ast\})/Q(\{k^\ast\})$ for $k^\ast$ finite. This includes in particular all pairs where $P$ and $Q$ are both binomial ($b_{n_1,p_1} \leq_{st} b_{n_2,p_2}$ if and only if $n_1\le n_2$ and $(1-p_1)^{n_1}\ge(1-p_2)^{n_2}$, or $p_1=0$), both negative binomial ($b^-_{r_1,p_1}\leq_{st} b^-_{r_2,p_2}$ if and on…
Trace-element partitioning between amphibole and silicate melt.
2007
Knowledge of the partitioning behavior of trace elements between solid and liquid is a prerequisite for modern igneous and mantle petrology. Most of the mathematical models simulating melt generation, migration and evolution within the mantle and/or the crust require the availability of reliable solid/liquid partition coefficients for the mineral phases involved in the process. Calcic amphiboles are extremely important for the understanding of lithospheric processes because of both their common occurrence in a variety of igneous and metamorphic rocks types and their capability of hosting a large number of geochemically important trace elements. A series of studies on the partitioning behavi…
A simple algorithm for finding short sigma-definite representatives
2010
We describe a new algorithm which for each braid returns a quasi-geodesic sigma-definite word representative, defined as a braid word in which the generator sigma_i with maximal index i appears either only positively or only negatively.
Embedding mapping class groups of orientable surfaces with one boundary component
2012
We denote by $S_{g,b,p}$ an orientable surface of genus $g$ with $b$ boundary components and $p$ punctures. We construct homomorphisms from the mapping class groups of $S_{g,1,p}$ to the mapping class groups of $S_{g',1,(b-1)}$, where $b\geq 1$. These homomorphisms are constructed from branched or unbranched covers of $S_{g,1,0}$ with some properties. Our main result is that these homomorphisms are injective. For unbranched covers, this construction was introduced by McCarthy and Ivanov~\cite{IM}. They proved that the homomorphisms are injective. A particular cases of our embeddings is a theorem of Birman and Hilden that embeds the braid group on $p$ strands into the mapping class group of …
O możliwościach zastosowania kategorii granicy w analizie zjawiska korupcji
2016
Od lat 90. XX wieku obserwujemy istotny wzrost zainteresowania kwestią korupcji. To również czas ponownego odkrycia problemu granic i pogranicza jako zagadnień centralnych dla procesów towarzyszących człowiekowi pod koniec stulecia. Globalizacja, kolejna fala demokratyzacji oraz upadek ZSRR to zmiany, który stworzyły nowe, strukturalne warunki dla zjawisk korupcyjnych oraz dla przedefiniowania granic politycznych. Pomimo podobieństwa uwarunkowań inspirujących do systematycznej refleksji nad korupcją i granicami, zarówno badania nad korupcją, jak i badania nad granicami zazwyczaj traktowane są jako odrębne obszary badawcze. Możemy jednak wyodrębnić pewne płaszczyzny, na których badania te sp…
Contact formation in random networks of elongated objects
2014
The effect of steric hindrance is an important aspect of granular packings as it gives rise to, e.g., limitations on the densities of ordered and disordered packings, both of which are essentially defined by the geometry of the constituents. Here we focus on random packing of rods via deposition and their distributions of contact number and segment length. Such statistical properties are relevant for mechanical properties of the structures, but the (quite large) steric effects on them have not been addressed in previous studies. We therefore develop a theory that describes the statistical properties of rod packings, while taking into account that the deposited rods cannot overlap and thus i…