Complete Integrability of a Nonlinear Elliptic System, Generating Bi-umbilical Foliated Semi-symmetric Hypersurfaces in R^4

Николай Кутев, Величка Милушева - Намираме експлицитно всичките би-омбилични фолирани полусиметрични повърхнини в четиримерното евклидово пространство R^4

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.

Lp Microlocal Properties for Multi-Quasi-Elliptic Pseudodifferential Operators

2010 Mathematics Subject Classification: Primary 35S05; Secondary 35A17.

On the Holomorphic Extension of Solutions of Elliptic Pseudodifferential Equations

2010 Mathematics Subject Classification: 35B65, 35S05, 35A20.

Interior Boundaries for Degenerate Elliptic Equations of Second Order Some Theory and Numerical Observations

2010 Mathematics Subject Classification: Primary 35J70; Secondary 35J15, 35D05.

On Modified Method of Simplest Equation for Obtaining Exact Solutions of Nonlinear PDEs: Case of Elliptic Simplest Equation

2010 Mathematics Subject Classification: 74J30, 34L30.

Existence Theorems for Non-Cooperative Elliptic Systems

2010 Mathematics Subject Classification: 35J65, 35K60, 35B05, 35R05.

On Principle Eigenvalue for Linear Second Order Elliptic Equations in Divergence Form

2002 Mathematics Subject Classification: 35J15, 35J25, 35B05, 35B50

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.

The Asymptotic Behaviour of the First Eigenvalue of Linear Second-Order Elliptic Equations in Divergente Form

2000 Mathematics Subject Classification: 35J70, 35P15.

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.