Search results for "Theorem"

An equivalent formulation of 0-closed sesquilinear forms

2022

AbstractIn 1970, McIntosh introduced the so-called 0-closed sesquilinear forms and proved a corresponding representation theorem. In this paper, we give a simple equivalent formulation of 0-closed sesquilinear forms. The main underlying idea is to consider minimal pairs of non-negative dominating forms.

MR3136895 Reviewed Ray, S.; Garai, A. The Laplace derivative. Math. Student 81 (2012), no. 1-4, 171–175. (Reviewer: Pasquale Vetro) 26A24

2014

In this paper the authors consider the Laplace derivative of a real function of a real variable introduced by R. E. Svetic [Comment. Math. Univ. Carolin. 42 (2001), no. 2, 331–343; MR1832151 (2002d:26008)]. The aim of this paper is to study the properties of the first-order Laplace derivative. They also prove Rolle's theorem, Darboux's theorem and other such theorems for the Laplace derivative.

MR3085505 Reviewed Boonpogkrong, Varayu Stokes' theorem on manifolds: a Kurzweil-Henstock approach. Taiwanese J. Math. 17 (2013), no. 4, 1183–1196

2013

Relaxation result for differential inclusions with Stieltjes derivative

2023

The aim of this paper is to provide a Filippov-Wa\.{z}ewski Relaxation Theorem for the very general setting of Stieltjes differential inclusions. New relaxation results can be deduced for generalized differential problems, for impulsive differential inclusions with multivalued impulsive maps and possibly countable impulsive moments and also for dynamic inclusions on time scales.

MR2944786 Reviewed Turzański, Marian The Bolzano-Poincaré-Miranda theorem—discrete version. Topology Appl. 159 (2012), no. 13, 3130–3135. (Reviewer: …

2014

The author gives a discrete version of the Bolzano-Poincaré-Miranda theorem. Further, the author uses the main result to prove the Bolzano-Poincaré-Miranda theorem and a theorem on partitions.

Iterated Conditionals, Trivalent Logics, and Conditional Random Quantities

2022

We consider some notions of iterated conditionals by checking the validity of some desirable basic logical and probabilistic properties, which are valid for simple conditionals. We consider de Finetti’s notion of conditional as a three-valued object and as a conditional random quantity in the betting framework. We recall the notions of conjunction and disjunction among conditionals in selected trivalent logics. Then, we analyze the two notions of iterated conditional introduced by Calabrese and de Finetti, respectively. We show that the compound probability theorem and other basic properties are not preserved by these objects, by also computing some probability propagation rules. Then, for …

On general conditional random quantities

2009

In the first part of this paper, recalling a general discussion on iterated conditioning given by de Finetti in the appendix of his book, vol. 2, we give a representation of a conditional random quantity $X|HK$ as $(X|H)|K$. In this way, we obtain the classical formula $\pr{(XH|K)} =\pr{(X|HK)P(H|K)}$, by simply using linearity of prevision. Then, we consider the notion of general conditional prevision $\pr(X|Y)$, where $X$ and $Y$ are two random quantities, introduced in 1990 in a paper by Lad and Dickey. After recalling the case where $Y$ is an event, we consider the case of discrete finite random quantities and we make some critical comments and examples. We give a notion of coherence fo…

Disentangling conditional effects of multiple regime shifts on Atlantic cod productivity

2020

AbstractRegime shifts are increasingly prevalent in the ecological literature. However, definitions vary, and many detection methods are subjective. Here, we employ an operationally objective means of identifying regime shifts, using a Bayesian online change-point detection algorithm able to simultaneously identify shifts in the mean and(or) variance of time series data. We detected multiple regime shifts in long-term (59-154 years) patterns of coastal Norwegian Atlantic cod (>70% decline) and putative drivers of cod productivity: North Atlantic Oscillation (NAO); sea-surface temperature; zooplankton abundance; fishing mortality (F). The consequences of an environmental or climate-relate…

The Oort conjecture on Shimura curves in the Torelli locus of hyperelliptic curves

2017

Abstract Oort has conjectured that there do not exist Shimura varieties of dimension >0 contained generically in the Torelli locus of genus-g curves when g is sufficiently large. In this paper we prove the analogue of this conjecture for Shimura curves with respect to the hyperelliptic Torelli locus of genus g > 7 .

Cosmological shock waves: clues to the formation history of haloes

2012

Shock waves developed during the formation and evolution of cosmic structures encode crucial information on the hierarchical formation of the Universe. We analyze an Eulerian AMR hydro + N-body simulation in a $\Lambda$CDM cosmology focused on the study of cosmological shock waves. The combination of a shock-capturing algorithm together with the use of a halo finder allows us to study the morphological structures of the shock patterns, the statistical properties of shocked cells, and the correlations between the cosmological shock waves appearing at different scales and the properties of the haloes harbouring them. The shocks in the simulation can be split into two broad classes: internal w…