A Müntz space having no complement in

in . In the present paper, we prove that there is a Müntz space not complemented in .

     

Two-Equation Turbulence Modelling of a Transitional Separation Bubble

Calculations of the Reynolds averaged equations using two different turbulence models have been compared with direct numerical simulation of a transitional separation bubble. Three methods of transition modelling were investigated. The first had no transition adjustment, the second involved fixing the transition point at the location observed in the simulation and the third was a direct transformation of a method proposed by Wilcox [1] which involved sensitising the eddy viscosity and transport equations to the local turbulent Reynolds number. The models captured the general features of the flow but were unable to show the recovery behaviour of the flow behind the bubble. Reasons for the failure are discussed using apriori analysis of terms in the model equations. This revised version was published online in July 2006 with corrections to the Cover Date.     

PRESSURE-VELOCITY EQUILIBRIUM HYDRODYNAMIC MODELS

This article describes mathematical models for phase separated mixtures of materials that are in pressure and velocity equilibrium but not necessarily temperature equilibrium. General conditions for constitutive models for such mixtures that exhibit a single mixture sound speed are discussed and specific examples are described.     

Constructive and Destructive Two-Pulse Excitation Investigated with a White-Light Michelson Interferometer

Linear propagation of two pulses through methanol solution of aluminum phthalocyanine chloride is investigated using a modified white-light Michelson interferometer. The observed coherence time of the white light is 6 fs, and the separation between the two-excitation pulses is set to about 10 fs. The excitation is dependent on the phase-relation between the two pulses. We have observed an enhancement of the excitation when the two pulses are in-phase and strong suppression of the excitation when the two pulses are out of phase by π.     

Search for scalar bottom quark pair production with the ATLAS detector in pp collisions at sqrt[s]=7 TeV

The results of a search for pair production of the scalar partners of bottom quarks in 2.05 fb(-1) of pp collisions at sqrt[s]=7 TeV using the ATLAS experiment are reported. Scalar bottom quarks are searched for in events with large missing transverse momentum and two jets in the final state, where both jets are identified as originating from a bottom quark. In an R-parity conserving minimal supersymmetric scenario, assuming that the scalar bottom quark decays exclusively into a bottom quark and a neutralino, 95% confidence-level upper limits are obtained in the b(1) - χ(1)(0) mass plane such that for neutralino masses below 60 GeV scalar bottom masses up to 390 GeV are excluded.     

Search for the standard model Higgs boson in the diphoton decay channel with 4.9 fb(-1) of pp collision data at √s=7 TeV with ATLAS

A search for the standard model Higgs boson is performed in the diphoton decay channel. The data used correspond to an integrated luminosity of 4.9 fb(-1) collected with the ATLAS detector at the Large Hadron Collider in proton-proton collisions at a center-of-mass energy of √s=7 TeV. In the diphoton mass range 110-150 GeV, the largest excess with respect to the background-only hypothesis is observed at 126.5 GeV, with a local significance of 2.8 standard deviations. Taking the look-elsewhere effect into account in the range 110-150 GeV, this significance becomes 1.5 standard deviations. The standard model Higgs boson is excluded at 95% confidence level in the mass ranges of 113-115 GeV and 134.5-136 GeV.     

Quantum Phase Properties of Photon Added and Subtracted Displaced Fock States

Quantum phase properties of photon added and subtracted displaced Fock states (and their limiting cases) are investigated from a number of perspectives, and it is shown that the quantum phase properties are dependent on the quantum state engineering operations performed. Specifically, the analytic expressions for quantum phase distributions and angular Q distribution as well as measures of quantum phase fluctuation and phase dispersion are obtained. The uniform phase distribution of the initial Fock states is observed to be transformed by the unitary operation (i.e., displacement operator) into non‐Gaussian shape, except for the initial vacuum state. It is observed that the phase distribution is symmetric with respect to the phase of the displacement parameter and becomes progressively narrower as its amplitude increases. The non‐unitary (photon addition/subtraction) operations make it even narrower in contrast to the Fock parameter, which leads to broadness. The photon subtraction is observed to be a more powerful quantum state engineering tool in comparison to the photon addition. Further, one of the quantum phase fluctuation parameters is found to reveal the existence of antibunching in both the engineered quantum states under consideration. Finally, the relevance of the engineered quantum states in the quantum phase estimation is also discussed.     

Scale invariant amplitude modulated phase-only filtering

A new synthetic discriminant-function-based amplitude modulated phase-only filtering technique is proposed for scale invariant pattern recognition. This technique has been found to yield improved correlation output when compared with the alternate techniques. The proposed technique is inherently suitable for optical implementation using the currently available spatial light modulators. Simulation results confirm the effectiveness of the proposed technique.