Bohmian Trajectories of Airy Packets

The discovery of Berry and Balazs in 1979 that the free-particle Schr\"odinger equation allows a non-dispersive and accelerating Airy-packet solution has taken the folklore of quantum mechanics by surprise. Over the years, this intriguing class of wave packets has sparked enormous theoretical and experimental activities in related areas of optics and atom physics. Within the Bohmian mechanics framework, we present new features of Airy wave packet solutions to Schr\"odinger equation with time-dependent quadratic potentials. In particular, we provide some insights to the problem by calculating the corresponding Bohmian trajectories. It is shown that by using general space-time transformations, these trajectories can display a unique variety of cases depending upon the initial position of the individual particle in the Airy wave packet. Further, we report here a myriad of nontrivial Bohmian trajectories associated to the Airy wave packet. These new features are worth introducing to the subject's theoretical folklore in light of the fact that the evolution of a quantum mechanical Airy wave packet governed by the Schr\"odinger equation is analogous to the propagation of a finite energy Airy beam satisfying the paraxial equation. Numerous experimental configurations of optics and atom physics have shown that the dynamics of Airy beams depends significantly on initial parameters and configurations of the experimental set-up.Comment: 8 page

Dividing Line between Quantum and Classical Trajectories: Bohmian Time Constant

This work proposes an answer to a challenge posed by Bell on the lack of clarity in regards to the line between the quantum and classical regimes in a measurement problem. To this end, a generalized logarithmic nonlinear Schr\"odinger equation is proposed to describe the time evolution of a quantum dissipative system under continuous measurement. Within the Bohmian mechanics framework, a solution to this equation reveals a novel result: it displays a time constant which should represent the dividing line between the quantum and classical trajectories. It is shown that continuous measurements and damping not only disturb the particle but compel the system to converge in time to a Newtonian regime. While the width of the wave packet may reach a stationary regime, its quantum trajectories converge exponentially in time to classical trajectories. In particular, it is shown that damping tends to suppress further quantum effects on a time scale shorter than the relaxation time of the system. If the initial wave packet width is taken to be equal to 2.8 10^{-15} m (the approximate size of an electron), the Bohmian time constant is found to have an upper limit, i. e., ${\tau_{B\max}} = {10^{- 26}}s$

Total variation denoising in l1l^1 anisotropy

We aim at constructing solutions to the minimizing problem for the variant of Rudin-Osher-Fatemi denoising model with rectilinear anisotropy and to the gradient flow of its underlying anisotropic total variation functional. We consider a naturally defined class of functions piecewise constant on rectangles (PCR). This class forms a strictly dense subset of the space of functions of bounded variation with an anisotropic norm. The main result shows that if the given noisy image is a PCR function, then solutions to both considered problems also have this property. For PCR data the problem of finding the solution is reduced to a finite algorithm. We discuss some implications of this result, for instance we use it to prove that continuity is preserved by both considered problems.Comment: 34 pages, 9 figure

Intellectual Property Protection in Philippine Agriculture: a Developmental Perspective

This paper is premised on the debate on whether intellectual property protection furthers economic development in developing countries. One view is that more is better, arguing that intellectual property rights trigger research and technological advancement. The other view is that more means not better, but worse. Advocates of this view claim that developing countries, being second comers in a world where developed countries got a head start in development are confronted with rules imposed by the first comers , intellectual property rules included, which are of course, designed by the latter to serve their interests This note suggests two general approaches so that intellectual property protection could best serve Philippine developmental objectives. One is reducing compliance with the TRIPS to the barest minimum possible. Another is the formulation and implementation of laws and policies that would strengthen farmers\u27 rights

Multi-sensor system using plastic optical fibers for intrinsically safe level measurements

A system for measuring liquid level in multiple tanks using optical fibe technology has been developed. Oil fiel service industry or any sector requiring liquid level measurements in flammabl atmospheres can be benefite from this intrinsically safe technology. The device used a single lens for the emitting and receiving fibe and it is based on amplitude variations as a function of the liquid distance and not in time of fligh or phase detection. Being the firs fiber-opti liquid level sensor with those characteristics for long ranges (>200 cm). A simple model to describe their behavior has been derived and tested on two prototypes. A Monte-Carlo method is used to fi the experimental data and obtain the model parameters. High accuracy between experimental data and fitte curve is obtained. The prototypes have a good linearity, better than 1.5% FS (full scale). Sensor heads are made of plastic optical fiber (POF) that are easy to handle, flexible and economical. They are excited by 650 nm lasers, housed in ST-connectors to obtain compact and rough prototypes. Optical multiplexing is used to increase the measuring safety area. Frequency division multiplexing is used to address each sensor head. A discussion about the influenc of tilts and aberrations is also included.Publicad

Untaxing Taxes: An Attempt to Compare Philippine and US Laws on Tax-Free Corporate Reorganizations

In comparing tax-free corporate reorganizations between Philippine and US law, the author wishes to learn how the US legal system would approach similar tax situations in the Philippines so he could apply it in the practice of law. Labyrinthine as they may be, US tax rules are so well-developed that they are excellent subjects for a comparative study. This paper validates the fact that Philippine and US tax laws on tax-free corporate exchanges have a lot in common. It also shows that in a lot of areas where Philippine law is silent, US tax laws have already devoted extensive treatment to such areas (i.e. spin-offs, triangular reorganizations, etc.). With respect to these areas, the issue is whether the principles developed therein are applicable to the Philippines. In his book De l\u27esprit des lois ( Spirit of the Laws ) , Montesquieu, the famous French political thinker, postulated that what makes a law effective is its spirit, referring to the correct fit thereof to the conditions of the locality in which it would be applied. Communing with such spirit is thus seen as the goal of any law. Viewed in this light, determining the spirit of the aforementioned areas of law is the next logical issue. That could be very taxing but is definitely challenging

Untaxing Taxes: An Attempt to Compare Philippine and US Laws on Tax-Free Corporate Reorganizations

In comparing tax-free corporate reorganizations between Philippine and US law, the author wishes to learn how the US legal system would approach similar tax situations in the Philippines so he could apply it in the practice of law. Labyrinthine as they may be, US tax rules are so well-developed that they are excellent subjects for a comparative study. This paper validates the fact that Philippine and US tax laws on tax-free corporate exchanges have a lot in common. It also shows that in a lot of areas where Philippine law is silent, US tax laws have already devoted extensive treatment to such areas (i.e. spin-offs, triangular reorganizations, etc.). With respect to these areas, the issue is whether the principles developed therein are applicable to the Philippines. In his book De l\u27esprit des lois ( Spirit of the Laws ) , Montesquieu, the famous French political thinker, postulated that what makes a law effective is its spirit, referring to the correct fit thereof to the conditions of the locality in which it would be applied. Communing with such spirit is thus seen as the goal of any law. Viewed in this light, determining the spirit of the aforementioned areas of law is the next logical issue. That could be very taxing but is definitely challenging