Local Energy Decay in Even Dimensions for the Wave Equation with a Time-Periodic Non-Trapping Metric and Applications to Strichartz Estimates

2000 Mathematics Subject Classification: 35B40, 35L15.

Directional Geodesic Active Contours

We present a non-conformal metric that generalizes the geodesic active contours approach for image segmentation. The new metric is obtained by adding to the Euclidean metric an additional term that penalizes the misalignment of the curve with the image gradient and multiplying the resulting metric by a conformal factor that depends on the edge intensity. In this way, a closer fitting to the edge direction results. The provided experimental results address the computation of the geodesics of the new metric by applying a gradient descent to externally provided curves. The good performance of the proposed techniques is demonstrated in comparison with other active contours methods.

Combining non-dominance, objective-order and spread metric to extend firefly algorithm to multi-objective optimization

In this paper, we propose an extension of the firefly algorithm (FA) to multi-objective optimization. FA is a swarm intelligence optimization algorithm inspired by the flashing behavior of fireflies at night that is capable of computing global solutions to continuous optimization problems. Our proposal relies on a fitness assignment scheme that gives lower fitness values to the positions of fireflies that correspond to non-dominated points with smaller aggregation of objective function distances to the minimum values. Furthermore, FA randomness is based on the spread metric to reduce the gaps between consecutive non-dominated solutions. The obtained results from the preliminary computational experiments show that our proposal gives a dense and well distributed approximated Pareto front with a large number of points.

On the boundedness on inhomogeneous Lipschitz spaces of fractional integrals, singular integrals and hypersingular integrals associated to non-doubling measures on metric spaces

In this paper we prove T1 type necessary and sufficient conditions for the boundedness on inhomogeneous Lipschitz spaces of fractional integrals and singular integrals defined on a measure metric space whose measure satisfies a n-dimensional growth. We also show that hypersingular integrals are bounded on these spaces.

Metric-scalar gravity with torsion and the measurability of the non-minimal coupling

The measurability of the non-minimal coupling is discussed by considering the correction to the Newtonian static potential in the semiclassical approach. The coefficient of the gravitational Darwin term (GDT) gets redefined by the non-minimal torsion scalar couplings. Based on a similar analysis of the GDT in the effective field theory approach to non-minimal scalar, we conclude that for reasonable values of the couplings the correction is very small.

Non-Hermitian multichannel theory of ultracold collisions modified by intense light fields tuned to the red of the trapping transition

We develop a systematic scheme to treat binary collisions between ultracold atoms in the presence of a strong laser field, tuned to the red of the trapping transition. We assume that the Rabi frequency is much less than the spacing between adjacent bound-state resonances, In this approach we neglect fine and hyperfine structures, but consider fully the three-dimensional aspects of the scattering process, up to the partial d wave. We apply the scheme to calculate the S matrix elements up to the second order in the ratio between the Rabi frequency and the laser detuning, We also obtain, fur this simplified multichannel model, the asymmetric line shapes of photoassociation spectroscopy, and the modification of the scattering length due to the light field at low, but finite, entrance kinetic energy. We emphasize that the present calculations can be generalized to treat more realistic models, and suggest how to carry out a thorough numerical comparison to this semianalytic theory. [S1050-2947(98)04902-6].

Some Para-Hermitian Related Complex Structures and Non-existence of Semi-Riemannian Metric on Some Spheres

It is shown that the spheres S^(2n) (resp: S^k with k ≡ 1 mod 4) can be given neither an indefinite metric of any signature (resp: of signature (r, k − r) with 2 ≤ r ≤ k − 2) nor an almost paracomplex structure. Further for every given Riemannian metric on an almost para-Hermitian manifold with the associated 2-form φ one can construct an almost Hermitian structure (under certain conditions, two different almost Hermitian structures) whose associated 2-form(s) is φ.

Evaluation of contact and non-contact trapping efficiencies of human scent chemical profiles and their stabilities under different environmental conditions

Establishing an association between the scent a perpetrator left at a crime scene to the odor of the suspect of that crime is the basis for the use of human scent identification evidence in a court of law. Law enforcement agencies gather evidence through the collection of scent from the objects that a perpetrator may have handled during the execution of the criminal act. The collected scent evidence is consequently presented to the canines for identification line-up procedures with the apprehended suspects. Presently, canine scent identification is admitted as expert witness testimony, however, the accurate behavior of the dogs and the scent collection methods used are often challenged by the court system. The primary focus of this research project entailed an evaluation of contact and non-contact scent collection techniques with an emphasis on the optimization of collection materials of different fiber chemistries to evaluate the chemical odor profiles obtained using varying environment conditions to provide a better scientific understanding of human scent as a discriminative tool in the identification of suspects. The collection of hand odor from female and male subjects through both contact and non-contact sampling approaches yielded new insights into the types of VOCs collected when different materials are utilized, which had never been instrumentally performed. Furthermore, the collected scent mass was shown to be obtained in the highest amounts for both gender hand odor samples on cotton sorbent materials. Compared to non-contact sampling, the contact sampling methods yielded a higher number of volatiles, an enhancement of up to 3 times, as well as a higher scent mass than non-contact methods by more than an order of magnitude. The evaluation of the STU-100 as a non-contact methodology highlighted strong instrumental drawbacks that need to be targeted for enhanced scientific validation of current field practices. These results demonstrated that an individual's human scent components vary considerably depending on the method used to collect scent from the same body region. This study demonstrated the importance of collection medium selection as well as the collection method employed in providing a reproducible human scent sample that can be used to differentiate individuals.

Linear non-local diffusion problems in metric measure spaces

The aim of this paper is to provide a comprehensive study of some linear non-local diffusion problems in metric measure spaces. These include, for example, open subsets in ℝN, graphs, manifolds, multi-structures and some fractal sets. For this, we study regularity, compactness, positivity and the spectrum of the stationary non-local operator. We then study the solutions of linear evolution non-local diffusion problems, with emphasis on similarities and differences with the standard heat equation in smooth domains. In particular, we prove weak and strong maximum principles and describe the asymptotic behaviour using spectral methods.

Nonexistence of regular stationary solution in a metric nonsymmetric theory of gravitation

It is proven that the field equations of a previously studied metric nonsymmetric theory of gravitation do not admit any non-singular stationary solution which represents a field of non-vanishing total mass and non-vanishing total fermionic charge.

Pure two-atom squeezed state in spontaneous emission from two non-identical atoms

We calculate the stationary state of the system of two non-identical two-level atoms driven by a finite-bandwidth two-mode squeezed vacuum. It is well known that two identical two-level atoms driven by a broadband squeezed vacuum may decay to a pure state, called the pure two-atom squeezed state, and that the presence of the antisymmetric state can change its purity. Here, we show that for small interatomic separations the stationary state of two non-identical atoms is not sensitive to the presence of the antisymmetric state and is the pure two-atom squeezed state. This effect is a consequence of the fact that in the system of two non-identical atoms the antisymmetric state is no longer the trapping state. We also calculate the squeezing properties of the emitted field and find that the squeezing spectrum of the output field may exhibit larger squeezing than that in the input squeezed vacuum. Moreover, we show that squeezing in the total field attains the optimum value which can ever be achieved in the field emitted by two atoms.

Local non-negative initial data scalar characterization of the Kerr solution

For any vacuum initial data set, we define a local, non-negative scalar quantity which vanishes at every point of the data hypersurface if and only if the data are Kerr initial data. Our scalar quantity only depends on the quantities used to construct the vacuum initial data set which are the Riemannian metric defined on the initial data hypersurface and a symmetric tensor which plays the role of the second fundamental form of the embedded initial data hypersurface. The dependency is algorithmic in the sense that given the initial data one can compute the scalar quantity by algebraic and differential manipulations, being thus suitable for an implementation in a numerical code. The scalar could also be useful in studies of the non-linear stability of the Kerr solution because it serves to measure the deviation of a vacuum initial data set from the Kerr initial data in a local and algorithmic way.

In situ evaluation of single-cell lysis by cytosol extraction observation through fluorescence decay and dielectrophoretic trapping time

We present a new method for lysis of single cells in continuous flow, where cells are sequentially trapped, lysed and released in an automatic process. Using optimized frequencies, dielectrophoretic trapping allows exposing cells in a reproducible way to high electrical fields for long durations, thereby giving good control on the lysis parameters. In situ evaluation of cytosol extraction on single cells has been studied for Chinese hamster ovary (CHO) cells through out-diffusion of fluorescent molecules for different voltage amplitudes. A diffusion model is proposed to correlate this out-diffusion to the total area of the created pores, which is dependent on the potential drop across the cell membrane and enables evaluation of the total pore area in the membrane. The dielectrophoretic trapping is no longer effective after lysis because of the reduced conductivity inside the cells, leading to cell release. The trapping time is linked to the time required for cytosol extraction and can thus provide additional validation of the effective cytosol extraction for non-fluorescent cells. Furthermore, the application of one single voltage for both trapping and lysis provides a fully automatic process including cell trapping, lysis, and release, allowing operating the device in continuous flow without human intervention.