Canonical and D-transformations in theories with constraints

We describe a class of transformations in a super phase space (we call them D-transformations) which play the role of ordinary canonical transformations in theories with second-class constraints. Namely, in such theories they preserve the form invariance of equations of motion, their quantum analogs are unitary transformations, and the measure of integration in the corresponding Hamiltonian path integral is invariant under these transformations.     

Virtual hydrocarbon and combinatorial databases for use with CAVEAT

Three new virtual databases have been developed for use with the bond-orientation-based database searching program CAVEAT. These consist of a database of trisubstituted monocyclic hydrocarbons having ethyl, vinyl, and phenyl substituents; a database of unsubstituted bicyclic hydrocarbons; and a database of core structures from established combinatorial synthetic methods having hydrogen, ethyl, vinyl, and phenyl substituents at the readily varied positions. Each collection of molecules was subjected to a batch conformational search, minimization, and conversion to a vector database for use with CAVEAT.     

Counting statistics and detector properties of quantum point contacts

Quantum detector properties of the quantum point contact (QPC) are analyzed for an arbitrary electron transparency and coupling strength to the measured system and are shown to be determined by the electron counting statistics. Conditions of the quantum-limited operation of the QPC detector, which prevent information loss through the scattering time and scattering phases, are found for arbitrary coupling. We show that the phase information can be restored and used for the quantum-limited detection by inclusion of the QPC detector in the electronic Mach-Zehnder interferometer.     

A new ac electrospray mechanism by Maxwell-Wagner polarization and capillary resonance

We report a new high-frequency (>10 kHz) ac electrospray that is capable of generating micron-sized electroneutral drops. Unlike its dc counterpart, the drops are not ejected continuously from a sharp Taylor cone but intermittently from a resonating meniscus at the orifice. We attribute the resonant frequency to the capillary-inertia vibration time of the meniscus and the drop ejection to the Maxwell-Wagner electric stress at the drop tip, which is observed to reverse its direction across a crossover frequency. Above this frequency, the oppositely directed Maxwell-Wagner force causes the liquid to recede up the microneedle as an apparent electrowetting effect.     

Weight Multiplicity Free Representations, g-Endomorphism Algebras, and Dynkin Polynomials

Throughout this paper, G is a connected semisimple algebraicgroup defined over an algebraically closed field k of characteristiczero, and g is its Lie algebra.     

Anomalous absorption of bulk shear sagittal acoustic waves in a layered structure with viscous fluid

It is demonstrated theoretically that the absorptivity of bulk shear sagittal waves by an ultra-thin layer of viscous fluid between two different elastic media has a strong maximum (in some cases as good as 100%) at an optimal layer thickness. This thickness is usually much smaller than the penetration depths and lengths of transverse and longitudinal waves in the fluid. The angular dependencies of the absorptivity are demonstrated to have significant and unusual structure near critical angles of incidence. The effect of non-Newtonian properties and non-uniformities of the fluid layer on the absorptivity is also investigated. In particular, it is shown that the absorption in a thin layer of viscous fluid is much more sensitive to non-zero relaxation time(s) in the fluid layer than the absorption at an isolated solid-fluid interface.     

An Inverse Problem for an Harmonic Oscillator Perturbed by Potential: Uniqueness

Consider the perturbed harmonic oscillator Ty = -y" + x²y + q(x)y on L²(R) where the real potential q satisfy some assumption on infinity (the case q L²(R), (t+1)^-rdt), r < 1 is covered).     

Formation,structure, and structural properties of a new filamentary tubular form: hollow conical-helix of graphitic boron nitride

A novel tubular form of graphitic boron nitride (BN) displaying a hollow conical-helix was discovered. It was generated via wrapping a single beltlike filament according to the geometry of an Archimedes spiral. Cone apex angles of helical-conical nanotubes (HCNTs) were found to exhibit specific values, each of which refers to a certain coincidence site lattice. A unique structural property of HCNTs was observed, displaying the transformation of apex angles during the annealing process. The observed apex angles were reduced with decreasing annealing temperature, which is in accordance with an estimated HCNT strain energy decrease for a given tubular radius. It is suggested that the curvature and apex angle of a HCNT are determined by a sole dynamic element, that is, enthalpy (DeltaH), whereas the HCNT disclination configuration changes through helical sliding of the filament.     

Isotropy Representations, Eigenvalues of a Casimir Element, and Commutative Lie Subalgebras

Let h be a reductive subalgebra of a semisimple Lie algebrag and C_h U(h) be the Casimir element determined by the restrictionof the Killing form on g to h. The paper studies eigenvaluesof C_h on the isotropy representation mg/h. Some general estimatesconnecting the eigenvalues and the Dynkin indices of m are given.If h is a symmetric subalgebra, it is shown that describingthe maximal eigenvalue of C_h on exterior powers of m is connectedwith possible dimensions of commutative Lie subalgebras in m,thereby extending a result of Kostant. In this situation, aformula is also given for the maximal eigenvalue of C_h on m.More generally, a similar picture arises if h = g, where isan automorphism of finite order m and m is replaced by the eigenspaceof corresponding to a primitive mth root of unity.