2,094 research outputs found
The compact support property for measure-valued processes
No full textThe purpose of this article is to give a rather thorough understanding of the compact support property for measure-valued processes corresponding to semi-linear equations of the form u(t) = Lu + beta u - alpha u(p) in R-d x (0, infinity), p is an element of (1, 2]; u(x, 0) = f(x) in R-d; u (x, t) >= 0 in R-d x [0, infinity). In particular, we shall investigate how the interplay between the underlying motion (the diffusion process corresponding to L) and the branching affects the compact support property. In [J. Englander, R. Pinsky, On the construction and support properties of measure-valued diffusions on D subset of R-d with spatially dependent branching, Ann. Probab. 27 (1999) 684-730], the compact support property was shown to be equivalent to a certain analytic criterion concerning uniqueness of the Cauchy problem for the semi-linear parabolic equation related to the measured valued process. In a subsequent paper [J. Englander, R. Pinsky, Uniqueness/nonuniqueness for nonnegative solutions of second-order parabolic equations of the form u(t) = Lu + Vu - gamma u(p) in R-n, J. Differential Equations 192 (2003) 396-428], this analytic property was investigated purely from the point of view of partial differential equations. Some of the results obtained in this latter paper yield interesting results concerning the compact support property. In this paper, the results from [J. Englander, R. Pinsky, Uniqueness/nonuniqueness, for nonnegative solutions of second-order parabolic equations of the form u(t) = Lu + Vu - gamma u(p) in R-n, J. Differential Equations 192 (2003) 396-428] that are relevant to the compact support property are presented, sometimes with extensions. These results are interwoven with new results and some informal heuristics. Taken together, they yield a rather comprehensive picture of the compact support property. Inter alia, we show that the concept of a measure-valued process hitting a point can be investigated via the compact support property, and suggest an alternate proof of a result concerning the hitting of points by super-Brownian motion. (c) 2005 Elsevier SAS. All rights reserved
Strong law of large numbers and mixing for the invariant distributions of measure-valued diffusions
No full textAbstractLet M(Rd) denote the space of locally finite measures on Rd and let M1(M(Rd)) denote the space of probability measures on M(Rd). Define the mean measure πν of ν∈M1(M(Rd)) byπν(B)=∫M(Rd)η(B)dν(η),forB⊂Rd.For such a measure ν with locally finite mean measure πν, let f be a nonnegative, locally bounded test function satisfying 〈f,πν〉=∞. ν is said to satisfy the strong law of large numbers with respect to f if 〈fn,η〉/〈fn,πν〉 converges almost surely to 1 with respect to ν as n→∞, for any increasing sequence {fn} of compactly supported functions which converges to f. ν is said to be mixing with respect to two sequences of sets {An} and {Bn} if∫M(Rd)f(η(An))g(η(Bn))dν(η)−∫M(Rd)f(η(An))dν(η)∫M(Rd)g(η(Bn))dν(η)converges to 0 as n→∞ for every pair of functions f,g∈Cb1([0,∞)). It is known that certain classes of measure-valued diffusion processes possess a family of invariant distributions. These distributions belong to M1(M(Rd)) and have locally finite mean measures. We prove the strong law of large numbers and mixing for many such distributions
Ross syndrome: a case report
No full textRoss syndrome is a rare partial dysautonomic syndrome of unknown aetiology, characterized by segmental hypo/ anhidrosis associated with Holmes-Adie syndrome (tonic pupil and hypo/areflexia). The hypohydrosis or anhydrosis is patchy initially, later it becomes segmental or diffuse. This is due to affection of postganglionic cholinergic parasympathetic and sympathetic fibers involvement. There are a very few cases (approximately 50) have been reported in the literature since its original description. Author report a 22 years old male with classical features of Ross syndrome
Subsurface mapping of the Ross Island flexural basin, southwest Antarctica
No full text2016 Summer.Includes bibliographical references.Ross Island is a post-Miocene (< 4.6 Ma) volcanic island located in the Ross Sea region of southwest Antarctica. This region of Antarctica borders the western edge of the West Antarctic Rift System, along the Transantarctic Mountain front. Marine and over-ice multi-channel seismic reflection surveys and borehole studies targeting the Ross Sea region over the last 30+ years have been used in this study to develop a seismic stratigraphic model of the development and evolution of the Ross Island flexural basin. Four key stratigraphic horizons were identified and mapped to fully capture the basin-fill, as well as strata lying above and below the flexural basin. From oldest to youngest these horizons are named RIB-m, RIM-g, RIM-b and RIB-r. Time structure, isochron and isochore maps were created for the horizons and the stratigraphic intervals they bound. The seismic stratigraphic record shows the Ross Island flexural moat formation post-dates the main tectonic subsidence phase within the Victoria Land Basin. The maps presented here are the first to fully illustrate the evolution of the Ross Island flexural basin. The maps highlight depositional patterns of two distinct periods of flexural subsidence and basin-filling superimposed on the older N-S trending Victoria Land Basin depocenter. Two units of flexural basin fill, Unit FFI between horizons RIM-g and RIM-b (the oldest flexural basin fill), and Unit FFII between horizons RIM-b and RIB-r (the youngest flexural basin fill) are associated with the two periods of flexural subsidence. Flexural moat subsidence and subsequent filling occurred episodically during periods of active volcanism on the island. Unit FFI is estimated to range from ca. 4 to 2 Ma, corresponding with formation of the Mt. Bird volcanic edifice on Ross Island. Unit FFII ranges in age from ca. 2 to 1 Ma, and is related to Mt. Terror, Mt. Erebus, and Hut Point Peninsula volcanism. The isochore maps suggest the depocenter of the flexural basin during both time intervals was located north of the island, instead of directly beneath the Ross Island topographic load. Factors contributing to the northerly location of the depocenter include i) volcanic loading by McMurdo Volcanic Group subsea volcanic features north of the island, ii) partial compensation of the main Ross Island load by low-density, partially molten rock beneath the island, iii) extensional faulting within the Terror Rift, and iv) seaward-thickening shelf sediments transported from the Ross Ice Shelf. The seismic data show that the onset of filling of the flexural moat around Ross Island coincided with the end of ice grounding events in the area. We infer that this was caused by flexural subsidence of the seafloor to accommodate the Ross Island load
Timor-Leste human development report 2011 : managing natural resources for human development : developing the non-oil economy to achieve the MDGs
No full textPrincipal Author John G Taylor, Coordinator Rui Gomes, Authors, Technical Background Papers Tobias N. Rasmussen, Andrew Rosser, Martin Sandbu, Michael Ross, Tibor van Staveren, Ricardo F. Neupert, Rui A. Gomes, John G Taylor, Sonny Harmadi, Hafiz Pash
Web 2.0: Hypertext by Any Other Name?
No full textWeb 2.0 is the popular name of a new generation of Web applications, sites and companies that emphasis openness, community and interaction. Examples include technologies such as Blogs and Wikis, and sites such as Flickr. In this paper we compare these next generation tools to the aspirations of the early Hypertext pioneers to see if their aims have finally been realized
Spectral gap and rate of convergence to equilibrium for a class of conditioned Brownian motions
No full textAbstractIf a Brownian motion is physically constrained to the interval [0,γ] by reflecting it at the endpoints, one obtains an ergodic process whose exponential rate of convergence to equilibrium is π2/2γ2. On the other hand, if Brownian motion is conditioned to remain in (0,γ) up to time t, then in the limit as t→∞ one obtains an ergodic process whose exponential rate of convergence to equilibrium is 3π2/2γ2. A recent paper [Grigorescu and Kang, J. Theoret. Probab. 15 (2002) 817–844] considered a different kind of physical constraint—when the Brownian motion reaches an endpoint, it is catapulted to the point pγ, where p∈(0,12], and then continues until it again hits an endpoint at which time it is catapulted again to pγ, etc. The resulting process—Brownian motion physically returned to the point pγ—is ergodic and the exponential rate of convergence to equilibrium is independent of p and equals 2π2/γ2. In this paper we define a conditioning analog of the process physically returned to the point pγ and study its rate of convergence to equilibrium
Multiproxy quantitative paleoceanographic dataset from late Quaternary marine sediment archives in the western Ross Sea (Antarctica)
No full textThe past ice sheet dynamics and the timing of retreat events in the paleo-record in the Ross Sea is an issue still few understood. In order to contribute to this topic, we provide a multiproxy data from marine sediment archives (cores and box cores) collected in three sites in the Central Basin (Western Ross Sea, Antarctica). Each site recorded different environments, affected by different oceanographic conditions and sedimentary regime. This makes the three investigated sediment cores and box cores unique and useful for comparison with other studied cores collected in the same basin. The data set includes physical (paleomagnetism, grain size and petrography), chemical, micropaleontological (diatom, foraminifera and silicoflagellate assemblages) analyses and cryptotephra characterization increasing the information already reported in literature. The importance of this dataset is related to a multi-disciplinary approach in a site, the Central Basin, few investigated which represents a key area to connect the Southern Ocean and the Ross Sea. © 2024 The Author
The Behavior of the Life Span for Solutions tout=Δu+a(x)upinRd
No full textAbstractLetT*(λ,φ) denote the life span of the positive, bounded solutionu(x,t) to the equationut=Δu+a(u)upinRdandu(x,0)=λφ(x), where 0≨a(x)∈Cα(Rd), 0≨φ(x)∈Cb(Rd),p>1, andλ>0 is a parameter. Depending ona,φ,p, andd, it is possible thatT*(λ,φ)=∞, forλ>0 sufficiently small, or thatT*(λ,φ)<∞, for allλ>0, in which case limλ→0T*(λ,φ)=∞. It is always true that limλ→∞T*(λ,φ)=0. In this paper we investigate the asymptotic behavior ofT*(λ,φ) asλ→0 in the case thatT*(λ,φ)<∞, for allλ>0, and asλ→∞ in all cases. The asymptotic order depends heavily ona,φ,p, anddin the case thatλ→0, whereas in the case thatλ→∞, it depends only on whether there exists anx0witha(x0),φ(x0)≠0, or whether the supports ofaandφare separated by a positive distance
On comparing the solutions of linear diffusion equations with those of singular nonlinear “fast” diffusion equations
No full textAbstractWe bound the solution of the nonlinear fast diffusion equation, above and below, by solutions of corresponding linear equations run on fact clocks
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