On Typical Compact Convex Sets in Hilbert Spaces

Let E be an infinite dimensional separable space and for e ∈ E and X a nonempty compact convex subset of E, let qX(e) be the metric antiprojection of e on X. Let n ≥ 2 be an arbitrary integer. It is shown that for a typical (in the sence of the Baire category) compact convex set X ⊂ E the metric antiprojection qX(e) has cardinality at least n for every e in a dense subset of E.

Compact sensors based on cascaded single-mode-multimode-single-mode fiber structures

Concatenated single-mode-multimode-single-mode (SMS) structures are demonstrated as functional sensing platforms. The devices are fabricated by periodically inserting micrometric sections of multimode optical fiber (MMF) in a single-mode fiber (SMF). The periodic change of the core diameter produces a single strong resonant transmission notch, tunable in the wavelength range from 1200 to 1600 nm. It was found that the position of the notch changed with temperature and refractive index. The devices introduced here are highly compact (length less than 5 mm), simple to fabricate and robust; hence, they are adequate for diverse sensing applications. © 2013 The Japan Society of Applied Physics.

A compact, portable and low cost generic interrogation strain sensor system using an embedded VCSEL, detector and fibre Bragg grating

We present a compact, portable and low cost generic interrogation strain sensor system using a fibre Bragg grating configured in transmission mode with a vertical-cavity surface-emitting laser (VCSEL) light source and a GaAs photodetector embedded in a polymer skin. The photocurrent value is read and stored by a microcontroller. In addition, the photocurrent data is sent via Bluetooth to a computer or tablet device that can present the live data in a real time graph. With a matched grating and VCSEL, the system is able to automatically scan and lock the VCSEL to the most sensitive edge of the grating. Commercially available VCSEL and photodetector chips are thinned down to 20 µm and integrated in an ultra-thin flexible optical foil using several thin film deposition steps. A dedicated micro mirror plug is fabricated to couple the driving optoelectronics to the fibre sensors. The resulting optoelectronic package can be embedded in a thin, planar sensing sheet and the host material for this sheet is a flexible and stretchable polymer. The result is a fully embedded fibre sensing system - a photonic skin. Further investigations are currently being carried out to determine the stability and robustness of the embedded optoelectronic components. © 2012 Copyright Society of Photo-Optical Instrumentation Engineers (SPIE).

Regular Averaging and Regular Extension Operators in Weakly Compact Subsets of Hilbert Spaces

2000 Mathematics Subject Classification: Primary 46E15, 54C55; Secondary 28B20.

Pseudo-Compact Semi-Topological Groups

Митрофан М. Чобан, Петър Ст. Кендеров, Уорън Б. Муурс - Полу-топологична група (съответно, топологична група) е група, снабдена с топология, относно която груповата оперция произведение е частично непрекъсната по всяка от променливите (съответно, непрекъсната по съвкупност от променливите и обратната операция е също непрекъсната). В настоящата работа ние даваме условия, от топологичен характер, една полу-топологична група да е всъщност топологична група. Например, ние показваме, че всяка сепарабелна псевдокомпактна полу-топологична група е топологична група. Показваме също, че всяка локално псевдокомпактна полу-топологична група, чиято групова операция е непрекъсната по съвкупност от променливите е топологична група.

Multipliers on Spaces of Functions on a Locally Compact Abelian Group with Values in a Hilbert Space

2000 Mathematics Subject Classification: Primary 43A22, 43A25.

Weakly Compact Generating and Shrinking Markusevic Bases

2000 Mathematics Subject Classification: 46B30, 46B03.

Grewia gum 1:some mechanical and swelling properties of compact and film

Purpose: To study the mechanical and dynamic swelling properties of grewia gum, evaluate its compression behaviour and determine the effect of drying methods on its properties. Methods: Compacts (500 mg) of both freeze-dried and air-dried grewia gum were separately prepared by compression on a potassium bromide (KBr) press at different pressures and subjected to Heckel analysis. Swelling studies were performed using 200 mg compacts of the gum (freeze-dried or air-dried) compressed on a KBr press. The mechanical properties of the films of the gum prepared by casting 1 % dispersions of the gum were evaluated using Hounsfield tensiometer. The mechanical properties of grewia gum films were compared with films of pullulan and guar gum which were similarly prepared. The effect of temperature on the water uptake of the compacts was studied and the data subjected to Schott's analysis. Results: Drying conditions had no effect on the yield pressure of the gum compacts as both air-dried and freeze-dried fractions had a yield pressure of 322.6 MPa. The plots based on Schott's equation for the grewia gum samples showed that both samples (freeze-dried and air-dried) exhibited long swelling times. Grewia gum film had a tensile strength of 19.22±3.61 MPa which was similar to that of pullulan films (p > 0.05). It had an elastic modulus of 2.13±0.12 N/mm2 which was significantly lower (p < 0.05) than those of pullulan and guar gum with elastic moduli of 3.33±0.00 and 2.86±0.00 N/mm2, respectively. Conclusion: The type of drying method used does not have any effect on the degree of plasticity of grewia gum compacts. Grewia gum obtained by either drying method exhibited extended swelling duration. Matrix tablet formulations of the gum will likely swell slowly and promote sustained release of drug. © Pharmacotherapy Group, Faculty of Pharmacy, University of Benin, Benin City.

A compact polymer optical fibre ultrasound detector

Polymer optical fibre (POF) is a relatively new and novel technology that presents an innovative approach for ultrasonic endoscopic applications. Currently, piezo electric transducers are the typical detectors of choice, albeit possessing a limited bandwidth due to their resonant nature and a sensitivity that decreases proportionally to their size. Optical fibres provide immunity from electromagnetic interference and POF in particular boasts more suitable physical characteristics than silica optical fibre. The most important of these are lower acoustic impedance, a reduced Young's Modulus and a higher acoustic sensitivity than single-mode silica fibre at both 1 MHz and 10 MHz. POF therefore offers an interesting alternative to existing technology. Intrinsic fibre structures such as Bragg gratings and Fabry-Perot cavities may be inscribed into the fibre core using UV lasers. These gratings are a modulation of the refractive index of the fibre core and provide the advantages of high reflectivity, customisable bandwidth and point detection. We present a compact in fibre ultrasonic point detector based upon a POF Bragg grating (POFBG) sensor. We demonstrate that the detector is capable of leaving a laboratory environment by using connectorised fibre sensors and make a case for endoscopic ultrasonic detection through use of a mounting structure that better mimics the environment of an endoscopic probe. We measure the effects of water immersion upon POFBGs and analyse the ultrasonic response for 1, 5 and 10 MHz.

Angular distribution of prompt photons using the compact muon solenoid detector at a square root of S = 7 TeV

The study of the angular distribution of photon plus jet events in pp collisions at [special characters omitted] = 7 TeV with the Compact Muon Solenoid (CMS) detector is presented. The photon is restricted to the central region of the detector (:η: <1.4442) while the jet is allowed to be present in both central and forward regions of CMS (:η: < 2.4). Dominant backgrounds due to jets fragmenting into neutral mesons are accounted for through the use of a template method that discriminates between signal and background. The angular distribution, :η*:, is defined as the absolute value of the difference in η between the leading photon and leading jet in an event divided by two. The angular distribution ranging from 0–1.4 was examined and compared with next-to-leading order QCD predictions and was found to be in good agreement.

The H I chronicles of LITTLE THINGS blue compact dwarf galaxies

Star formation occurs when the gas (mostly atomic hydrogen; H I) in a galaxy becomes disturbed, forming regions of high density gas, which then collapses to form stars. In dwarf galaxies it is still uncertain which processes contribute to star formation and how much they contribute to star formation. Blue compact dwarf (BCD) galaxies are low mass, low shear, gas rich galaxies that have high star formation rates when compared to other dwarf galaxies. What triggers the dense burst of star formation in BCDs but not other dwarfs is not well understood. It is often suggested that BCDs may have their starburst triggered by gravitational interactions with other galaxies, dwarf-dwarf galaxy mergers, or consumption of intergalactic gas. However, there are BCDs that appear isolated with respect to other galaxies, making an external disturbance unlikely.^ Here, I study six apparently isolated BCDs from the LITTLE THINGS sample in an attempt to understand what has triggered their burst of star formation. LITTLE THINGS is an H I survey of 41 dwarf galaxies. Each galaxy has high angular and velocity resolution H I data from the Very Large Array (VLA) telescope and ancillary stellar data. I use these data to study the detailed morphology and kinematics of each galaxy, looking for signatures of starburst triggers. In addition to the VLA data, I have collected Green Bank Telescope data for the six BCDs. These high sensitivity, low resolution data are used to search the surrounding area of each galaxy for extended emission and possible nearby companion galaxies.^ The VLA data show evidence that each BCD has likely experienced some form of external disturbance despite their apparent isolation. These external disturbances potentially seen in the sample include: ongoing/advanced dwarf-dwarf mergers, an interaction with an unknown external object, and external gas consumption. The GBT data result in no nearby, separate H I companions at the sensitivity of the data. These data therefore suggest that even though these BCDs appear isolated, they have not been evolving in isolation. It is possible that these external disturbances may have triggered the starbursts that defines them as BCDs.^

Groups of unstable Adams operations on p-local compact groups

Peer reviewed

Automorphisms of p-local compact groups

Peer reviewed

Groups of unstable Adams operations on p-local compact groups

Peer reviewed