Generalized Fock Spaces and the Stirling Numbers

The Bargmann-Fock-Segal space plays an important role in mathematical physics and has been extended into a number of directions. In the present paper, we imbed this space into a Gelfand triple. The spaces forming the Fréchet part (i.e., the space of test functions) of the triple are characterized both in a geometric way and in terms of the adjoint of multiplication by the complex variable, using the Stirling numbers of the second kind. The dual of the space of test functions has a topological algebra structure, of the kind introduced and studied by the first named author and Salomon

White Noise Space Analysis and Multiplicative Change of Measures

In this paper, we display a family of Gaussian processes, with explicit formulas and transforms. This is presented with the use of duality tools in such a way that the corresponding path-space measures are mutually singular. We make use of a corresponding family of representations of the canonical commutation relations (CCR) in an infinite number of degrees of freedom. A key feature of our construction is explicit formulas for associated transforms; these are infinite-dimensional analogs of Fourier transforms. Our framework is that of Gaussian Hilbert spaces, reproducing kernel Hilbert spaces and Fock spaces. The latter forms the setting for our CCR representations. We further show, with the use of representation theory and infinite-dimensional analysis, that our pairwise inequivalent probability spaces (for the Gaussian processes) correspond in an explicit manner to pairwise disjoint CCR representations

White Noise Space Analysis and Multiplicative Change of Measures

In this paper we display a family of Gaussian processes, with explicit formulas and transforms. This is presented with the use of duality tools in such a way that the corresponding path-space measures are mutually singular. We make use of a corresponding family of representations of the canonical commutation relations (CCR) in an infinite number of degrees of freedom. A key feature of our construction is explicit formulas for associated transforms; these are infinite-dimensional analogues of Fourier transforms. Our framework is that of Gaussian Hilbert spaces, reproducing kernel Hilbert spaces, and Fock spaces. The latter forms the setting for our CCR representations. We further show, with the use of representation theory, and infinite-dimensional analysis, that our pairwise inequivalent probability spaces (for the Gaussian processes) correspond in an explicit manner to pairwise disjoint CCR representations

Fast Moment Estimation in Data Streams in Optimal Space

We give a space-optimal streaming algorithm with update time $O(log^2(1/\epsilon)loglog(1/\epsilon))$ for approximating the pth frequency moment, 0 < p < 2, of a length-n vector updated in a data stream up to a factor of $1 \pm \epsilon$. This provides a nearly exponential improvement over the previous space optimal algorithm of [Kane-Nelson-Woodruff, SODA 2010], which had update time $\Omega(1/\epsilon^2)$. When combined with the work of [Harvey-Nelson-Onak, FOCS 2008], we also obtain the first algorithm for entropy estimation in turnstile streams which simultaneously achieves near-optimal space and fast update time.Engineering and Applied Science

Uranium-series ages of fossil corals from Mallorca, Spain: The “Neotyrrhenian” high stand of the Mediterranean Sea revisited

The emergent marine deposits of the Mediterranean basin have been recognized as an important record of Quaternary sea level history for more than a century. Previous workers identified what have been interpreted to be two separate high stands of sea in the late Quaternary, namely the “Eutyrrhenian” (thought to be ~120 ka) and the “Neotyrrhenian” (thought to be either ~100 ka or ~80 ka). On Mallorca, Spain, both of these named deposits lie close to present sea level, implying paleo-sea levels slightly above present during both marine isotope stages (MIS) 5.5/5e and either 5.3/5c or 5.1/5a. If these interpretations are correct, they conflict, at least in part, with sea level records from far-field localities. Weanalyzed corals fromtheNeotyrrhenian beds onMallorca,which gave U-series ages from~126 ka to ~118 ka. These ages are consistent with previously published amino acid data that show that the Neotyrrhenian and Eutyrrhenian deposits are not significantly different in age. A fossil molluscan fauna from the Neotyrrhenian deposits onMallorca has a warm-water paleozoogeographic aspect, with nine southward-ranging species and four extralimital southern species. When compared with sea surface temperatures obtained from planktonic foraminifera and alkenones from ODP core 977 in the nearby Alboran Sea, the only time period that shows comparable warmth is MIS 5.5/5e, consistent with the U-series ages of corals from the Neotyrrhenian deposits. We propose that the Neotyrrhenian deposits are a beachrock facies of the same age as the Eutyrrhenian deposits. This interpretation is consistent with the differences in physical sedimentology of the two deposits, explains the U-series and amino acid data indicating the same age, is consistent with the very slight elevation difference of the Neotyrrhenian and Eutyrrhenian beds, and explains the similar, though not identical paleozoogeographic aspects of their fossil faunas

Uranium-series ages of fossil corals from Mallorca, Spain: The “Neotyrrhenian” high stand of the Mediterranean Sea revisited

The emergent marine deposits of the Mediterranean basin have been recognized as an important record of Quaternary sea level history for more than a century. Previous workers identified what have been interpreted to be two separate high stands of sea in the late Quaternary, namely the “Eutyrrhenian” (thought to be ~120 ka) and the “Neotyrrhenian” (thought to be either ~100 ka or ~80 ka). On Mallorca, Spain, both of these named deposits lie close to present sea level, implying paleo-sea levels slightly above present during both marine isotope stages (MIS) 5.5/5e and either 5.3/5c or 5.1/5a. If these interpretations are correct, they conflict, at least in part, with sea level records from far-field localities. Weanalyzed corals fromtheNeotyrrhenian beds onMallorca,which gave U-series ages from~126 ka to ~118 ka. These ages are consistent with previously published amino acid data that show that the Neotyrrhenian and Eutyrrhenian deposits are not significantly different in age. A fossil molluscan fauna from the Neotyrrhenian deposits onMallorca has a warm-water paleozoogeographic aspect, with nine southward-ranging species and four extralimital southern species. When compared with sea surface temperatures obtained from planktonic foraminifera and alkenones from ODP core 977 in the nearby Alboran Sea, the only time period that shows comparable warmth is MIS 5.5/5e, consistent with the U-series ages of corals from the Neotyrrhenian deposits. We propose that the Neotyrrhenian deposits are a beachrock facies of the same age as the Eutyrrhenian deposits. This interpretation is consistent with the differences in physical sedimentology of the two deposits, explains the U-series and amino acid data indicating the same age, is consistent with the very slight elevation difference of the Neotyrrhenian and Eutyrrhenian beds, and explains the similar, though not identical paleozoogeographic aspects of their fossil faunas

Super-orbital re-entry in Australia - laboratory measurement, simulation and flight observation

There are large uncertainties in the aerothermodynamic modelling of super-orbital re-entry which impact the design of spacecraft thermal protection systems (TPS). Aspects of the thermal environment of super-orbital re-entry flows can be simulated in the laboratory using arc- and plasma jet facilities and these devices are regularly used for TPS certification work [5]. Another laboratory device which is capable of simulating certain critical features of both the aero and thermal environment of super-orbital re-entry is the expansion tube, and three such facilities have been operating at the University of Queensland in recent years[10]. Despite some success, wind tunnel tests do not achieve full simulation, however, a virtually complete physical simulation of particular re-entry conditions can be obtained from dedicated flight testing, and the Apollo era FIRE II flight experiment [2] is the premier example which still forms an important benchmark for modern simulations. Dedicated super-orbital flight testing is generally considered too expensive today, and there is a reluctance to incorporate substantial instrumentation for aerothermal diagnostics into existing missions since it may compromise primary mission objectives. An alternative approach to on-board flight measurements, with demonstrated success particularly in the ‘Stardust’ sample return mission, is remote observation of spectral emissions from the capsule and shock layer [8]. JAXA’s ‘Hayabusa’ sample return capsule provides a recent super-orbital reentry example through which we illustrate contributions in three areas: (1) physical simulation of super-orbital re-entry conditions in the laboratory; (2) computational simulation of such flows; and (3) remote acquisition of optical emissions from a super-orbital re entry event

The Complexity of Bariatric Patient’s Pharmacotherapy: Sildenafil Biopharmaceutics and Pharmacokinetics before vs. after Gastric Sleeve/Bypass

Postbariatric altered gastrointestinal (GI) anatomy/physiology may significantly harm oral drug absorption and overall bioavailability. In this work, sildenafil, the first phosphodiesterase-5 (PDE5) inhibitor, was investigated for impaired postbariatric solubility/dissolution and absorption; this research question is of particular relevance since erectile dysfunction (ED) is associated with higher body mass index (BMI). Sildenafil solubility was determined both in vitro and ex vivo, using pre- vs. postsurgery gastric contents aspirated from patients. Dissolution tests were done in conditions mimicking the stomach before surgery, after sleeve gastrectomy (post-SG, pH 5), and after one anastomosis gastric bypass (post-OAGB, pH 7). Finally, these data were included in physiologically based pharmacokinetic (PBPK) modelling (GastroPlus®) to simulate sildenafil PK before vs. after surgery. pH-dependent solubility was demonstrated with low solubility (0.3 mg/mL) at pH 7 vs. high solubility at pH 1–5, which was also confirmed ex vivo with much lower solubility values in postbariatric gastric samples. Hampered dissolution of all sildenafil doses was obtained under post-OAGB conditions compared with complete (100%) dissolution under both presurgery and post-SG conditions. PBPK simulations revealed delayed sildenafil absorption in postbariatric patients (increased tmax) and reduced Cmax, especially in post-OAGB patients, relative to a presurgery state. Hence, the effect of bariatric surgery on sildenafil PK is unpredictable and may depend on the specific bariatric procedure. This mechanistically based analysis suggests a potentially undesirable delayed onset of action of sildenafil following gastric bypass surgery

Generalized Fock spaces and the Stirling numbers

The Bargmann-Fock-Segal space plays an important role in mathematical physics, and has been extended into a number of directions. In the present paper we imbed this space into a Gelfand triple. The spaces forming the Fr\'echet part (i.e. the space of test functions) of the triple are characterized both in a geometric way and in terms of the adjoint of multiplication by the complex variable, using the Stirling numbers of the second kind. The dual of the space of test functions has a topological algebra structure, of the kind introduced and studied by the first named author and G. Salomon.Comment: revised versio

Origin of the Sinai-Negev erg, Egypt and Israel: mineralogical and geochemical evidence for the importance of the Nile and sea level history

The Sinai-Negev erg occupies an area of 13,000 km2 in the deserts of Egypt and Israel. Aeolian sand of this erg has been proposed to be derived from the Nile Delta, but empirical data supporting this view are lacking. An alternative source sediment is sand from the large Wadi El Arish drainage system in central and northern Sinai. Mineralogy of the Negev and Sinai dunes shows that they are high in quartz, with much smaller amounts of K-feldspar and plagioclase. Both Nile Delta sands and Sinai wadi sands, upstream of the dunes, also have high amounts of quartz relative to K-feldspar and plagioclase. However, Sinai wadi sands have abundant calcite, whereas Nile Delta sands have little or no calcite. Overall, the mineralogical data suggest that the dunes are derived dominantly from the Nile Delta, with Sinai wadi sands being a minor contributor. Geochemical data that proxy for both the light mineral fraction (SiO2/10-Al2O3 + Na2O + K2O-CaO) and heavy mineral fraction (Fe2O3-MgO-TiO2) also indicate a dominant Nile Delta source for the dunes. Thus, we report here the first empirical evidence that the Sinai-Negev dunes are derived dominantly from the Nile Delta. Linkage of the Sinai-Negev erg to the Nile Delta as a source is consistent with the distribution of OSL ages of Negev dunes in recent studies. Stratigraphic studies show that during the Last Glacial period, when dune incursions in the Sinai-Negev erg began, what is now the Nile Delta area was characterized by a broad, sandy, minimally vegetated plain, with seasonally dry anastomosing channels. Such conditions were ideal for providing a ready source of sand for aeolian transport under what were probably much stronger glacial-age winds. With the post-glacial rise in sea level, the Nile River began to aggrade. Post-glacial sedimentation has been dominated by fine-grained silts and clays. Thus, sea level, along with favorable climatic conditions, emerges as a major influence on the timing of dune activity in the Sinai-Negev erg, through its control on the supply of sand from the Nile Delta. The mineralogy of the Sinai-Negev dunes is also consistent with a proposed hypothesis that these sediments are an important source of loess in Israel