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Nonreflexive quantum mechanics is a formulation of quantum theory based on a non-classical logic termed \ita{nonreflexive logic} (a.k.a. `non-reflexive'). In these logics, the standard notion of identity, as encapsulated in classical logic and set theories, does not hold in full. The basic aim of this kind of approach to quantum mechanics is to take seriously the claim made by some authors according to whom quantum particles are \ita{non-individuals} in some sense, and also to take into account the fact that they may be absolutely indistinguishable (or indiscernible). The nonreflexive formulation of quantum theory assumes these features of the objects already at the level of the underlying logic, so that no use is required of symmetrization postulates or other mathematical devices that serve to pretend that the objects are indiscernible (when they are not: all objects that obey classical logic are \ita{individuals} in a sense). Here, we present the ideas of the development of nonreflexive quantum mechanics and discuss some philosophical (mainly metaphysical) motivations and consequences of it., Comment: 22 pages, no figures, accepted paper

In this paper we consider the phenomenon of superpositions in quantum mechanics and suggest a way to deal with the idea in a logical setting from a syntactical point of view, that is, as subsumed in the language of the formalism, and not semantically. We restrict the discussion to the propositional level only. Then, after presenting the motivations and a possible world semantics, the formalism is outlined and we also consider within this schema the claim that superpositions may involve contradictions, as in the case of the Schr\"odinger's cat, which (it is usually said) is both alive and dead. We argue that this claim is a misreading of the quantum case. Finally, we sketch a new form of quantum logic that involves three kinds of negations and present the relationships among them. The paper is a first approach to the subject, introducing some main guidelines to be developed by a `syntactical' logical approach to quantum superpositions., Comment: 17 pages, forthcoming in Probing the Meaning and Structure of Quantum Mechanics: Superpositions, Semantics, Dynamics and Identity, D. Aerts, C. de Ronde, H. Freytes and R. Giuntini (Eds.), World Scientific, Singapore, 2015

In this paper we study the integrability of a class of nonlinear non autonomous quad graph equations compatible around the cube introduced by Boll. We show that all these equations possess three point generalized symmetries which are subcases of either the Yamilov discretization of the Krichever--Novikov equation or of its non autonomous extension. We also prove that all those symmetries are integrable as pass the algebraic entropy test.

Context: Co-orbital systems are bodies that share the same mean orbit. They can be divided into different families according to the relative mass of the co-orbital partners and the particularities of their movement. Janus and Epimetheus are unique in that they are the only known co-orbital pair of comparable masses and thus the only known system in mutual horseshoe orbit. Aims: We aim to establish whether the Janus-Epimetheus system might have formed by disruption of an object in the current orbit of Epimetheus. Methods: We assumed that four large main fragments were formed and neglected smaller fragments. We used numerical integration of the full N-body problem to study the evolution of different fragment arrangements. Collisions were assumed to result in perfectly inelastic merging of bodies. We statistically analysed the outcome of these simulations to infer whether co-orbital systems might have formed from the chosen initial conditions. Results: Depending on the range of initial conditions, up to 9% of the simulations evolve into co-orbital systems. Initial velocities around the escape velocity of Janus yield the highest formation probability. Analysis of the evolution shows that all co-orbital systems are produced via secondary collisions. The velocity of these collisions needs to be low enough that the fragments can merge and not be destroyed. Generally, collisions are found to be faster than an approximate cut-off velocity threshold. However, given a sufficiently low initial velocity, up to 15% of collisions is expected to result in merging. Hence, the results of this study show that the considered formation scenario is viable., Comment: 9 Pages, 8 Figures

The Prime Focus Spectrograph (PFS) is an optical/near-infrared multifiber spectrograph with 2394 science fibers distributed across a 1.3-deg diameter field of view at the Subaru 8.2-m telescope. The wide wavelength coverage from 0.38 {\mu}m to 1.26 {\mu}m, with a resolving power of 3000, simultaneously strengthens its ability to target three main survey programs: cosmology, galactic archaeology and galaxy/AGN evolution. A medium resolution mode with a resolving power of 5000 for 0.71 {\mu}m to 0.89 {\mu}m will also be available by simply exchanging dispersers. We highlight some of the technological aspects of the design. To transform the telescope focal ratio, a broad-band coated microlens is glued to each fiber tip. A higher transmission fiber is selected for the longest part of the cable system, optimizing overall throughput; a fiber with low focal ratio degradation is selected for the fiber-positioner and fiber-slit components, minimizing the effects of fiber movements and fiber bending. Fiber positioning will be performed by a positioner consisting of two stages of piezo-electric rotary motors. The positions of these motors are measured by taking an image of artificially back-illuminated fibers with the metrology camera located in the Cassegrain container; the fibers are placed in the proper location by iteratively measuring and then adjusting the positions of the motors. Target light reaches one of the four identical fast-Schmidt spectrograph modules, each with three arms. The PFS project has passed several project-wide design reviews and is now in the construction phase., Comment: 19 pages, 11 figures

The main purpose of this article is to show how symmetry structures in partial differential equations can be preserved in a discrete world and reflected in difference schemes. Three different structure preserving discretizations of the Liouville equation are presented and then used to solve specific boundary value problems. The results are compared with exact solutions satisfying the same boundary conditions. All three discretizations are on four point lattices. One preserves linearizability of the equation, another the infinite-dimensional symmetry group as higher symmetries, the third one preserves the maximal finite-dimensional subgroup of the symmetry group as point symmetries. A 9-point invariant scheme that gives a better approximation of the equation, but significantly worse numerical results for solutions is presented and discussed.

FOCCoS, Fiber Optical Cable and Connector System, has the main function of capturing the direct light from the focal plane of Subaru Telescope using optical fibers, each one with a microlens in its tip, and conducting this light through a route containing connectors to a set of four spectrographs. The optical fiber cable is divided in 3 different segments called Cable A, Cable B and Cable C. Multi-fibers connectors assure precise connection among all optical fibers of the segments, providing flexibility for instrument changes. To assure strong and accurate connection, these sets are arranged inside two types of assemblies: the Tower Connector, for connection between Cable C and Cable B; and the Gang Connector, for connection between Cable B and Cable A. Throughput tests were made to evaluate the efficiency of the connections. A lifetime test connection is in progress. Cable C is installed inside the PFI, Prime Focus Instrument, where each fiber tip with a microlens is bonded to the end of the shaft of a 2-stage piezo-electric rotatory motor positioner; this assembly allows each fiber to be placed anywhere within its patrol region, which is 9.5mm diameter.. Each positioner uses a fiber arm to support the ferrule, the microlens, and the optical fiber. 2400 of these assemblies are arranged on a motor bench plate in a hexagonal-closed-packed disposition., Comment: 11 pages, 20 figures

The Fiber Optical Cable and Connector System (FOCCoS), provides optical connection between 2400 positioners and a set of spectrographs through optical fibers cables as part of PFS instrument for Subaru telescope. The optical fiber cable will be segmented in 3 parts along the route, cable A, cable B and cable C, connected by a set of multi-fiber connectors. The company USCONEC produces the multi-fiber connector under study. The USCONEC 32F model can connect 32 optical fibers in a 4 x 8 matrix arrangement. The ferrules are made of a durable composite, Polyphenylene Sulfide (PPS) based thermoplastic. The connections are held in place by a push-on/pull-off latch, and the connector can also be distinguished by a pair of metal guide pins that protrude from the front of the connector. Two fibers per connector will be used for monitoring the connection procedure. It was found to be easy to polish and it is small enough to be mounted in groups. Highly multiplexed instruments like PFS require a fiber connector system that can deliver excellent optical performance and reliability. PFS requires two different types of structures to organize the connectors. The Tower Connector system, with 80 multi-fiber connectors, will be a group of connectors for connecting cable B (Telescope Structure) with cable C (Positioners Plate). The Gang Connector system is a group of 8 gang connectors, each one with 12 multi-fibers connectors, for connecting cable B (Telescope Structure) with cable A (Spectrograph). The bench tests with these connector systems and the chosen fibers should measure the throughput of light and the stability after many connections and disconnections. In this paper we describe tests and procedures to evaluate the throughput and FRD increment. The lifetime of the ferrules is also in evaluation.

The Fiber Optical Cable and Connector System, FOCCoS, for the Prime Focus Spectrograph, PFS, is responsible for transporting light from the Subaru Telescope focal plane to a set of four spectrographs. Each spectrograph will be fed by a convex curved slit with 616 optical fibers organized in a linear arrangement. The slit frontal surface is covered with a special dark composite, made with refractory oxide, which is able to sustain its properties with minimum quantities of abrasives during the polishing process; this stability is obtained This stability is obtained by the detachment of the refractory oxide nanoparticles, which then gently reinforce gently the polishing process and increase its the efficiency. The surface roughness measured in several samples after high performance polishing was about 0.01 microns. Furthermore, the time for obtaining a polished surface with this quality is about 10 times less than the time required for polishing a brass, glass or ceramic surface of the same size. In this paper, we describe the procedure developed for high quality polishing of this type of slit. The cylindrical polishing described here, uses cylindrical concave metal bases on which glass paper is based. The polishing process consists to use grid sequences of 30 microns, 12 microns, 9 microns, 5 microns, 3 microns, 1 micron and, finally, a colloidal silica on a chemical cloth. To obtain the maximum throughput, the surface of the fibers should be polished in such a way that they are optically flat and free from scratches. The optical fibers are inspected with a microscope at all stages of the polishing process to ensure high quality. The efficiency of the process may be improved by using a cylindrical concave composite base as a substrate suitable for diamond liquid solutions. Despite this process being completely by hand, the final result shows a very high quality.

The Fiber Optical Cable and Connector System, FOCCoS, subsystem of the Prime Focus Spectrograph, PFS, for Subaru telescope, is responsible to feed four spectrographs with a set of optical fibers cables. The light injection for each spectrograph is assured by a convex curved slit with a linear array of 616 optical fibers. In this paper we present a design of a slit that ensures the right direction of the fibers by using masks of micro holes. This kind of mask is made by a technique called electroforming, which is able to produce a nickel plate with holes in a linear sequence. The precision error is around 1micron in the diameter and 1 micron in the positions of the holes. This nickel plate may be produced with a thickness between 50 and 200 microns, so it may be very flexible. This flexibility allows the mask to be bent into the shape necessary for a curved slit. The concept requires two masks, which we call Front Mask, and Rear Mask, separated by a gap that defines the thickness of the slit. The pitch and the diameter of the holes define the linear geometry of the slit; the curvature of each mask defines the angular geometry of the slit. Obviously, this assembly must be mounted inside a structure rigid and strong enough to be supported inside the spectrograph. This structure must have a CTE optimized to avoid displacement of the fibers or increased FRD of the fibers when the device is submitted to temperatures around 3 degrees Celsius, the temperature of operation of the spectrograph. We have produced two models. Both are mounted inside a very compact Invar case, and both have their front surfaces covered by a dark composite, to reduce stray light. Furthermore, we have conducted experiments with two different internal structures to minimize effects caused by temperature gradients.

The Prime Focus Spectrograph (PFS) is an optical/near-infrared multi-fiber spectrograph with 2394 science fibers, which are distributed in 1.3 degree diameter field of view at Subaru 8.2-meter telescope. The simultaneous wide wavelength coverage from 0.38 um to 1.26 um, with the resolving power of 3000, strengthens its ability to target three main survey programs: cosmology, Galactic archaeology, and galaxy/AGN evolution. A medium resolution mode with resolving power of 5000 for 0.71 um to 0.89 um also will be available by simply exchanging dispersers. PFS takes the role for the spectroscopic part of the Subaru Measurement of Images and Redshifts project, while Hyper Suprime-Cam works on the imaging part. To transform the telescope plus WFC focal ratio, a 3-mm thick broad-band coated glass-molded microlens is glued to each fiber tip. A higher transmission fiber is selected for the longest part of cable system, while one with a better FRD performance is selected for the fiber-positioner and fiber-slit components, given the more frequent fiber movements and tightly curved structure. Each Fiber positioner consists of two stages of piezo-electric rotary motors. Its engineering model has been produced and tested. Fiber positioning will be performed iteratively by taking an image of artificially back-illuminated fibers with the Metrology camera located in the Cassegrain container. The camera is carefully designed so that fiber position measurements are unaffected by small amounts of high special-frequency inaccuracies in WFC lens surface shapes. Target light carried through the fiber system reaches one of four identical fast-Schmidt spectrograph modules, each with three arms. Prototype VPH gratings have been optically tested. CCD production is complete, with standard fully-depleted CCDs for red arms and more-challenging thinner fully-depleted CCDs with blue-optimized coating for blue arms., Comment: 14 pages, 12 figures, submitted to "Ground-based and Airborne Instrumentation for Astronomy V, Suzanne K. Ramsay, Ian S. McLean, Hideki Takami, Editors, Proc. SPIE 9147 (2014)"

The Liouville equation is well known to be linearizable by a point transformation. It has an infinite dimensional Lie point symmetry algebra isomorphic to a direct sum of two Virasoro algebras. We show that it is not possible to discretize the equation keeping the entire symmetry algebra as point symmetries. We do however construct a difference system approximating the Liouville equation that is invariant under the maximal finite subalgebra $ SL_x \lf 2 , \mathbb{R} \rg \otimes SL_y \lf 2 , \mathbb{R} \rg $. The invariant scheme is an explicit one and provides a much better approximation of exact solutions than comparable standard (non invariant) schemes.

In the process of constructing invariant difference schemes which approximate partial differential equations we write down a procedure for discretizing an arbitrary partial differential equation on an arbitrary lattice. An open problem is the meaning of a lattice which does not satisfy the Clairaut--Schwarz--Young theorem. To analyze it we apply the procedure on a simple example, the potential Burgers equation with two different lattices, an orthogonal lattice which is invariant under the symmetries of the equation and satisfies the commutativity of the partial difference operators and an exponential lattice which is not invariant and does not satisfy the Clairaut--Schwarz--Young theorem. A discussion on the numerical results is also presented showing the different behavior of both schemes for two different exact solutions and their numerical approximations., Comment: 14 pages, 4 figures

Following J.-Y.B\'eziau in his pioneer work on non-standard interpretations of the traditional square of opposition, we have applied the abstract structure of the square to study the relation of opposition between states in superposition in orthodox quantum mechanics in \cite{are14}. Our conclusion was that such states are \ita{contraries} (\ita{i.e.} both can be false, but both cannot be true), contradicting previous analyzes that have led to different results, such as those claiming that those states represent \ita{contradictory} properties (\ita{i. e.} they must have opposite truth values). In this chapter we bring the issue once again into the center of the stage, but now discussing the metaphysical presuppositions which underlie each kind of analysis and which lead to each kind of result, discussing in particular the idea that superpositions represent potential contradictions. We shall argue that the analysis according to which states in superposition are contrary rather than contradictory is still more plausible.

We discuss the idea that superpositions in quantum mechanics may involve contradictions or contradictory properties. A state of superposition such as the one comprised in the famous Schr\"odinger's cat, for instance, is sometimes said to attribute contradictory properties to the cat: being dead and alive at the same time. If that were the case, we would be facing a revolution in logic and science, since we would have one of our greatest scientific achievements showing that real contradictions exist. We analyze that claim by employing the traditional square of opposition. We suggest that it is difficult to make sense of the idea of contradiction in the case of quantum superpositions. From a metaphysical point of view the suggestion also faces obstacles, and we present some of them.

The symmetry algebra of the differential--difference equation $$\dot u_n = [P(u_n)u_{n+1}u_{n-1} + Q(u_n)(u_{n+1}+u_{n-1})+ R(u_n)]/(u_{n+1}-u_{n-1}),$$ where $P$, $Q$ and $R$ are arbitrary analytic functions is shown to have the dimension $1 \le \mbox{dim}L \le 5$. When $P$, $Q$ and $R$ are specific second order polynomials in $u_n$ (depending on 6 constants) this is the integrable discretization of the Krichever--Novikov equation. We find 3 cases when the arbitrary functions are not polynomials and the symmetry algebra satisfies $\mbox{dim}L=2$. These cases are shown not to be integrable. The symmetry algebras are used to reduce the equations to purely difference ones. The symmetry group is also used to impose periodicity $u_{n+N}=u_n$ and thus to reduce the differential--difference equation to a system of $N$ coupled ordinary three points difference equations.