A formalized general theory of syntax with bindings

We present the formalization of a theory of syntax with bindings that has been developed and refined over the last decade to support several large formalization efforts. Terms are defined for an arbitrary number of constructors of varying numbers of inputs, quotiented to alpha-equivalence and sorted according to a binding signature. The theory includes a rich collection of properties of the standard operators on terms, such as substitution and freshness. It also includes induction and recursion principles and support for semantic interpretation, all tailored for smooth interaction with the bindings and the standard operators

Gamow-Teller strength distributions in 64Co and 64Cu studied via the 64Ni(d,2He) and 64Ni(3He, t) reactions

Charge exchange reactions are important tools in the study of spin-isospin excitations in nuclei. For intermediate incident energies and very forward scattering angles, peaks corresponding to Gamow-Teller (GT) transitions are expected to dominate the measured spectra and their cross sections becomes proportional to the transition strength. We performed two different reactions on 64Ni for studying the GT transitions both in + and directions. For the investigation in + direction, the 64Ni(d,2He)64Co experiment was performed at the KVI, Groningen, by using a 171 MeV deuteron beam. The outgoing 2He particles were analyzed by the Big Bite Spectrometer and the EuroSuperNova detector. The complementary reaction, 64Ni(3He,t)64Cu, was performed at the RCNP, Osaka, by using a 420 MeV 3He beam. The outgoing tritium particles were analyzed by the Grand Raiden Spectrometer and the RCNP detector. By the simplicity of these transitions, the strengths determined in this experimental study are a good tool to check different theoretical models. The model independent Ikeda sum rule could also be checked. Only about 29% of the total predicted strength was found in our study suggesting the necessity of an investigation to higher excitation energies, up to about 50 MeV, that could bring more information. But, as the shape and magnitude of the continuum region is still a matter of study, the experimental estimation of the GT strength in this region and the extraction of the full strength remain a problem. Because the studied nuclei are in fp-shell region, the obtained GT strengths constitute an important input in astrophysics, being required for the theoretical calculations of the rates of electron captures processes taking place in the late stage of the supernovae explosion. Important spectroscopic information was also obtained both for 64Co and 64Cu due to the reaction selectivity and the excellent energy resolution achieved in the two experiments

Polarization-squeezed light formation in a medium with electronic Kerr nonlinearity

We analyze the formation of polarization-squeezed light in a medium with electronic Kerr nonlinearity. Quantum Stokes parameters are considered and the spectra of their quantum fluctuations are investigated. It is established that the frequency at which the suppression of quantum fluctuations is the greatest can be controlled by adjusting the linear phase difference between pulses. We shown that by varying the intensity or the nonlinear phase shift per photon for one pulse, one can effectively control the suppression of quantum fluctuations of the quantum Stokes parameters.Comment: final version, RevTeX, 10 pages, 5 eps figure

The Aesthetics of Paradoxism (Second Edition)

In the history of thought and creation, the decisive events, the great and significant moments, the strongly affirmative stages - then the imposition of the optimizing novelties - have depended on the name and prestige of a personality. Referring to those, we personalize further on. The examples are extremely numerous, even in our nearest past. When we mention a creation - in the largest sense of the term - with the name of the personality who illustrates it most extensively at a given time, we state precisely the specific importance of it; we give it, with other words, the identity to which we can refer continuously with full knowledge and without causing any confusion among the receivers. The facts are called with the name of the man who produced them, and in this way we can compose a parallel onomastic dictionary, in which the work is included in the person’s space, keeping its content. The consecrated proper names evolve through quickly imposed habits, a large range of increments that announce the essential outline of their peak production. No space for ambiguity remains when we address to readers or listeners who are somewhat acquainted with the subject and we use such terms as Aristotelianism, Platonism, Kantianism, Hegelianism, Proustianism, Eminescianism, Barbianism, etc. We have even the advantage of a centered communication when we suggest with a sole notion the work as well as its dominant features, linked with the renown of the concerned author. There is no doubt that this way of denomination, when practiced a long time, has become a reflex and now is part of the habits of a correct expression. And neither the semantic objectification of works by a person nor the inherent axiological sanction disturb anybody. Personification being inevitable in creation, the history of art can be superposed to the history of the authors or, at, least gets tangled very strongly with them. It is precisely the case with the recent literary movement of Paradoxism, conceived in Romania and affirmed in the United States, which is closely bound to the temperament, inclination, taste and creative disposition of its initiator and organizer, the poet-mathematician Florentin Smarandache (paradoxism = smarandachism, in an “internal” and already notorious interpretation)

CAUSALITY, MEMORY ERASING AND DELAYED CHOICE EXPERIMENTS

Comment on [R.L. Ingraham, Phys. Rev. A 50, 4502 (1994)]. Ingraham suggested ``a delayed-choice experiment with partial, controllable memory erasing''. It is shown that he cannot be right since his predictions contradict relativistic causality. A subtle quantum effect which was overlooked by Ingraham is explained.Comment: 4 pages, LaTe

A quantum delayed choice experiment

Quantum systems exhibit particle-like or wave-like behaviour depending on the experimental apparatus they are confronted by. This wave-particle duality is at the heart of quantum mechanics, and is fully captured in Wheeler's famous delayed choice gedanken experiment. In this variant of the double slit experiment, the observer chooses to test either the particle or wave nature of a photon after it has passed through the slits. Here we report on a quantum delayed choice experiment, based on a quantum controlled beam-splitter, in which both particle and wave behaviours can be investigated simultaneously. The genuinely quantum nature of the photon's behaviour is tested via a Bell inequality, which here replaces the delayed choice of the observer. We observe strong Bell inequality violations, thus showing that no model in which the photon knows in advance what type of experiment it will be confronted by, hence behaving either as a particle or as wave, can account for the experimental data

Scalar and tensorial topological matter coupled to (2+1)-dimensional gravity:A.Classical theory and global charges

We consider the coupling of scalar topological matter to (2+1)-dimensional gravity. The matter fields consist of a 0-form scalar field and a 2-form tensor field. We carry out a canonical analysis of the classical theory, investigating its sectors and solutions. We show that the model admits both BTZ-like black-hole solutions and homogeneous/inhomogeneous FRW cosmological solutions.We also investigate the global charges associated with the model and show that the algebra of charges is the extension of the Kac-Moody algebra for the field-rigid gauge charges, and the Virasoro algebrafor the diffeomorphism charges. Finally, we show that the model can be written as a generalized Chern-Simons theory, opening the perspective for its formulation as a generalized higher gauge theory.Comment: 40 page

Simulating quantum correlations as a distributed sampling problem

It is known that quantum correlations exhibited by a maximally entangled qubit pair can be simulated with the help of shared randomness, supplemented with additional resources, such as communication, post-selection or non-local boxes. For instance, in the case of projective measurements, it is possible to solve this problem with protocols using one bit of communication or making one use of a non-local box. We show that this problem reduces to a distributed sampling problem. We give a new method to obtain samples from a biased distribution, starting with shared random variables following a uniform distribution, and use it to build distributed sampling protocols. This approach allows us to derive, in a simpler and unified way, many existing protocols for projective measurements, and extend them to positive operator value measurements. Moreover, this approach naturally leads to a local hidden variable model for Werner states.Comment: 13 pages, 2 figure