112,277 research outputs found
A comparison of three recent selection theorems
No full textsummary:We compare a recent selection theorem given by Chistyakov using the notion of modulus of variation, with a selection theorem of Schrader based on bounded oscillation and with a selection theorem of Di Piazza-Maniscalco based on bounded -oscillation
Variants of a selection principle for sequences of regulated and non-regulated functions
No full textLet be a nonempty subset of \RB, a metric space with
metric and the set of all functions mapping into
. Given \vep>0 and , we denote by N(\vep,f,T) the
least upper bound of those n\in\NB, for which there exist
numbers from such that
and
d(f(s_i),f(t_i))>\vep for all (N(\vep,f,T)=0 if
there are no such 's). The following pointwise selection
principle is proved: {\em If a sequence of functions\/
is such that the closure in
of the sequence\/ is compact for each
and\/ \limsup_{j\to\infty}N(\vep,f_j,T)<\infty for all
\vep>0, then\/ contains a subsequence,
converging pointwise on to a function , such that
N(\vep,f,T)0}. We establish several
variants of this result for functions with values in a metric
semigroup and reflexive separable Banach space as well as for the
weak pointwise and almost everywhere convergence of extracted
subsequences, and comment on the necessity of conditions in the
selection principles. We show that many Helly-type pointwise
selection principles are consequences of our results, which can be
applied to sequences of non-regulated functions, and compare them
with recent results by Chistyakov [J. Math. Anal. Appl. 310
(2005) 609--625] and Chistyakov and Maniscalco [J. Math. Anal.
Appl. 341 (2008) 613--625]
A pointwise selection principle for metric semigoup valued functions
No full textLet \emptyset\neq T \subset \RB, \hspace{.1in} (X,d,+) be an additive commutative semigroup with metric satisfying for all and the set of
all functions from into . If n \in \NB and , we set , where the supremum is taken over
all numbers from such that We prove the following pointwise selection theorem: \textit{If a sequence of functions \{f_j\}_{j \in \NB} \subset X^T is such that the closure in of the set \{f_j(t)\}_{j \in \NB} is compact for each t \in T, and
then it contains a subsequence which converges pointwise on .} We show by examples that this result is sharp and present two of its variants
Off-resonant quantum Zeno and anti-Zeno effects on entanglement
No full textWe examine the appearance of Zeno and anti-Zeno effects (Misra and Sudarshan 1977 J. Math. Phys. 18 756; Kofman and Kurizki 2000 Nature 405 546; Kofman and Kurizki 1996 Phys. Rev. A 54 3750; Facchi et al 2001 Phys. Rev. Lett. 86 2699) in the entanglement dynamics of two qubits off-resonantly coupled to the same lossy cavity when the unitary evolution of the system is interrupted by repeated projective measurements. We describe in detail these quantum effects by comparing the measurement-induced coarse-grained dynamics to the entanglement evolution in the absence of measurements in several scenarios (Francica et al 2009 Phys. Rev. A 79 032310). In particular, we examine the strong and weak coupling regimes, the role of the relative coupling strengths between the two qubits and the reservoir and the effect of the detuning from the main cavity frequency. We show that the anti-Zeno effect can occur in the entanglement dynamics when the qubit frequencies are detuned from the main reservoir frequency. Furthermore, we find that Zeno and anti-Zeno effects can even appear sequentially many times as a function of the interval between the measurements. Finally, we show that, in the off-resonant regime, we can preserve the entanglement using the quantum Zeno effect more efficiently than in the resonant limit (Maniscalco et al 2008 Phys. Rev. Lett. 100 090503), even if, in this case, no sub-radiant state exists
Stay on target: compensation and causation in breach of trust claims AIB v Mark Redler [2014] UKSC 58; [2014] 3 W.L.R. 1367
No full textComments on the Supreme Court ruling in AIB Group (UK) Plc v Mark Redler & Co Solicitors, which clarified the personal rights a beneficiary may invoke against a trustee for misapplication of trust assets. Reviews the facts of AIB, the court's approach to the limits of trustee liability, the distinction between traditional and commercial trusts, and the remaining uncertainties over the causation rules applicable to equitable compensation claims
ONJ in osteometabolic patients: NO guilty verdict for teeth extraction
No full textThe aim of this study is to evaluate retrospectively the impact of some variables on the risk of oNJ onset in osteometabolic non-cancer patients by logistic regression analyses
Efficient Simulation of Orthogonal Multicarrier Transmission over Multipath Fading Channels
No full textFilterbank orthogonal multicarrier transmission schemes, such as OFDM/OQAM, are currently under intense study for their spectral efficiency and suitability for the physical layer of Cognitive Radio. Nonetheless, the mathematical description of the signal is cumbersome, and closed form expressions for performance figures are not available, so performance analysis on fading channels has to be performed by means of simulations. We propose an algorithm for simulating the received signal over multipath frequency selective fading channels, based on Taylor series expansion of the channel transfer function. The proposed method is compared to the state-of-the-art FFT-based method in terms of computational complexity
PROPRIETARY ESTOPPEL AND VENDOR PURCHASER CONSTRUCTIVE TRUSTS
No full textThe recent Supreme Court decision in Scott v Southern Pacific Mortgages [2014] UKSC 52; [2014] H.L.R. 48 considered whether a promise made by the buyer of a piece of land, before completion, could give rise to a proprietary estoppel claim. Obiter, the court also considered the width and applicability of the rule in Abbey National B.S. v Cann [1991] A.C. 56, which has traditionally been seen to provide that completion and the creation of a mortgage charge are to be considered as one transaction in cases of acquisition mortgages where the purchaser could not have purchased the property without the mortgage loan
The rule of the civil law was followed: l’uso del diritto romano nelle corti inglesi
No full textNel corso della sua storia, la common law inglese ha mantenuto un rapporto fertile ma ambiguo con il diritto romano. Dai trattati medievali ai riferimenti ispirati alla teoria del diritto naturale di Sir John Holt (1642-1710) e Lord Mansfield (1705-1793), la sua influenza si è presentata in vesti diverse. Se la complessa storia di questo rapporto è stata oggetto di numerosi studi, molta meno attenzione è stata invece dedicata al ricorso al diritto romano e comune nella giurisprudenza contemporanea delle corti inglesi. Questo studio affronta la questione prendendo in esame tre esempi: le decisioni della House of Lords in Foskett v McKeown [2000] UKHL 29, Fairchild v Glenhaven Funeral Services Ltd [2002] UKHL 22, e la recentissima decisione della corte d’appello in Borwick Development Solutions v Clear Water Fisheries [2020] EWCA Civ 578. Come risulterà evidente, il ruolo delle fonti romane nei tribunali di common law risulta problematico sotto due aspetti principali. Nei casi in cui è utilizzato come mero strumento di comparazione, alla stregua di altre giurisdizioni straniere, non è chiaro se e su quali basi i giudici debbano attribuirgli lo stesso peso persuasivo che viene attribuito alle altre fonti contemporanee. Quando la tradizione del diritto romano è invece chiamata in causa dai giudici in virtù del suo legame storico con un particolare istituto o sotto l’influenza di precedenti riferimenti ad essa nella giurisprudenza, l’incertezza è doppia, risultando oscurato sia il metodo da applicare nell’indagine delle fonti, sia il loro ruolo effettivo per la corretta applicazione ed interpretazione della legge
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