2,908 research outputs found
On the genus of projective curves not contained in hypersurfaces of given degree
Fix integers r >= 4 and i >= 2 (for r = 4 assume i >= 3). Assume that the rational number s defined by the equation ((i + 1)(2))s + (i + 1) = ((r + i) )(i)is( ) an integer. Fix an integer d >= s. Divide d - 1 = ms + epsilon, 0 <= epsilon <= s - 1, and set G(r;d, i) := ((m)(2))s + m epsilon. As a number, 2 G(r; d, i) is nothing but the Castelnuovo's bound G(s + 1;d) for a curve of degree d in Ps+1. In the present paper we prove that G(r; d, i) is also an upper bound for the genus of a reduced and irreducible complex projective curve in P-r, of degree d >> max{ r,i}, not contained in hypersurfaces of degree <= i. We prove that the bound G(r; d, i) is sharp if and only if there exists an integral surface S subset of P-r of degree s, not contained in hypersurfaces of degree <= i. Such a surface, if existing, is necessarily the isomorphic projection of a rational normal scroll surface of degree s in Ps+1 The existence of such a surface S is known for r >= 5, and 2 <= i <= 3. It follows that, when r >= 5, and i = 2 or i = 3, the bound G(r; d, i) is sharp, and the extremal curves are isomorphic projection in P-r of Castelnuovo's curves of degree d in Ps+1. We do not know whether the bound G(r; d, i) is sharp for i > 3
Mode Confinement in Photonic Quasi-Crystal Point-Defect Cavities for Particle Accelerators
In this Letter, we present a study of the confinement properties of
point-defect resonators in finite-size photonic-bandgap structures composed of
aperiodic arrangements of dielectric rods, with special emphasis on their use
for the design of cavities for particle accelerators. Specifically, for
representative geometries, we study the properties of the fundamental mode (as
a function of the filling fraction, structure size, and losses) via 2-D and 3-D
full-wave numerical simulations, as well as microwave measurements at room
temperature. Results indicate that, for reduced-size structures, aperiodic
geometries exhibit superior confinement properties by comparison with periodic
ones.Comment: 4 pages, 4 figures, accepted for publication in Applied Physics
Letter
Inherently chiral calix[4]arenes with planar chirality: two new entries to the family
The synthesis of two new inherently chiral calix[4]arenes (ICCs, 1 and 2), endowed with electron-rich concave surfaces, has been achieved through the desymmetrization of a lower rim distal-bridged oxacyclophane (OCP) macrocycle. The new highly emissive ICCs were resolved by chiral HPLC, and the enantiomeric nature of the isolated antipodes proved by electronic circular dichroism (CD). Using time-dependent density functional calculations of CD spectra, their absolute configurations were established. NMR studies with (S)-Pirkle's alcohol unequivocally showed that the host-guest interactions occur in the chiral pocket comprehending the calix-OCP exo cavities and the carbazole moieties
Transport in strongly-coupled graphene-LaAlO3/SrTiO3 hybrid systems
We report on the transport properties of hybrid devices obtained by
depositing graphene on a LaAlO3/SrTiO3 oxide junction hosting a 4 nm-deep
two-dimensional electron system. At low graphene-oxide inter-layer bias the two
electron systems are electrically isolated, despite their small spatial
separation, and very efficient reciprocal gating is shown. A pronounced
rectifying behavior is observed for larger bias values and ascribed to the
interplay between electrostatic depletion and tunneling across the LaAlO3
barrier. The relevance of these results in the context of strongly-coupled
bilayer systems is discussed.Comment: 10 pages, 3 figure
Hybrid photonic-bandgap accelerating cavities
In a recent investigation, we studied two-dimensional point-defected photonic
bandgap cavities composed of dielectric rods arranged according to various
representative periodic and aperiodic lattices, with special emphasis on
possible applications to particle acceleration (along the longitudinal axis).
In this paper, we present a new study aimed at highlighting the possible
advantages of using hybrid structures based on the above dielectric
configurations, but featuring metallic rods in the outermost regions, for the
design of extremely-high quality factor, bandgap-based, accelerating
resonators. In this framework, we consider diverse configurations, with
different (periodic and aperiodic) lattice geometries, sizes, and
dielectric/metal fractions. Moreover, we also explore possible improvements
attainable via the use of superconducting plates to confine the electromagnetic
field in the longitudinal direction. Results from our comparative studies,
based on numerical full-wave simulations backed by experimental validations (at
room and cryogenic temperatures) in the microwave region, identify the
candidate parametric configurations capable of yielding the highest quality
factor.Comment: 13 pages, 5 figures, 3 tables. One figure and one reference added;
minor changes in the tex
On the Validity of Immersive Virtual Reality as tool for multisensory evaluation of urban spaces
The Europe2020 document indicates a new strategy to turn EU into a smart, sustainable and inclusive economy. At local level urban planning policies may help to reach these aims. Several research works proposed the Immersive Virtual Reality as tool to evaluate the effectiveness of these interventions. Nevertheless people's perception within virtual environments still needs to be verified. In this study, two groups of participants had to provide subjective measures related to the global, acoustic and visual quality of a real environment or of a multisensory reproduced version in Immersive Virtual Reality. Outcomes highlight the ecological effectiveness of this multisensory tool
Heat-kernel Coefficients and Spectra of the Vector Laplacians on Spherical Domains with Conical Singularities
The spherical domains with conical singularities are a convenient
arena for studying the properties of tensor Laplacians on arbitrary manifolds
with such a kind of singular points. In this paper the vector Laplacian on
is considered and its spectrum is calculated exactly for any
dimension . This enables one to find the Schwinger-DeWitt coefficients of
this operator by using the residues of the -function. In particular, the
second coefficient, defining the conformal anomaly, is explicitly calculated on
and its generalization to arbitrary manifolds is found. As an
application of this result, the standard renormalization of the one-loop
effective action of gauge fields is demonstrated to be sufficient to remove the
ultraviolet divergences up to the first order in the conical deficit angle.Comment: plain LaTeX, 23 pp., revised version, a misprint in expressions (1.8)
and (4.38) of the second heat coefficient for the vector Laplacian is
corrected. No other change
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