The nature and function of the categories in the philosophy of Immanuel Kant, James Ward, S. Alexander

The aim of this investigation is to discuss the merits of the three radically divergent views as to the nature and function of the categories held by Kant, Ward and Alexander.The scope of the study is expressly limited to considerations and problems of a general nature with reference to the epistemo-logical categories. Consequently, if, as some maintain, there are categories unique to the several sciences, our discussion may be described as confined to the categories of Consciousness. It is, therefore, not directly concerned with such subsidiary problems as the number of the categories, or the status of unique categories in such special sciences as morality and aesthetics.These delimitations of the problem require no apology. They are justified on the methodological principle that the basic issues of a problem should be thoroughly investigated and clearly defined before embarking on subsidiary questions.This subject was suggested some years ago by the very cavalier treatment of a priori categories in most contemporary thought. The recent appearance of several works giving explicit attention to the nature of the categories is a gratifying assurance that the problem is not a dead issue.The somewhat lengthy discussion of Kant is due (i) to the sharing of Professor Alexander's conviction "that with or after Plato there is nothing comparable in importance upon this subject with what may be learned from him,"; (ii) Exposition of Kant must be supported by detailed and extensive evidence in view of the conflicts of doctrine in the master himself, and the divergencies of interpretation among his expositors.In tracing the growth and development of the Kantian theory of categories in the seventies, the dating of the Reflexionen by Adickes in the Berlin edition is assumed as authoritative

Fast-slow asymptotic for semi-analytical ignition criteria in FitzHugh-Nagumo system

We study the problem of initiation of excitation waves in the FitzHugh-Nagumo model. Our approach follows earlier works and is based on the idea of approximating the boundary between basins of attraction of propagating waves and of the resting state as the stable manifold of a critical solution. Here, we obtain analytical expressions for the essential ingredients of the theory by singular perturbation using two small parameters, the separation of time scales of the activator and inhibitor, and the threshold in the activator's kinetics. This results in a closed analytical expression for the strength-duration curve.Comment: 10 pages, 5 figures, as accepted to Chaos on 2017/06/2

Dynamic properties of the spin-1/2 XY chain with three-site interactions

We consider a spin-1/2 XY chain in a transverse (z) field with multi-site interactions. The additional terms introduced into the Hamiltonian involve products of spin components related to three adjacent sites. A Jordan-Wigner transformation leads to a simple bilinear Fermi form for the resulting Hamiltonian and hence the spin model admits a rigorous analysis. We point out the close relationships between several variants of the model which were discussed separately in previous studies. The ground-state phases (ferromagnet and two kinds of spin liquid) of the model are reflected in the dynamic structure factors of the spin chains, which are the main focus in this study. First we consider the zz dynamic structure factor reporting for this quantity a closed-form expression and analyzing the properties of the two-fermion (particle-hole) excitation continuum which governs the dynamics of transverse spin component fluctuations and of some other local operator fluctuations. Then we examine the xx dynamic structure factor which is governed by many-fermion excitations, reporting both analytical and numerical results. We discuss some easily recognized features of the dynamic structure factors which are signatures for the presence of the three-site interactions.Comment: 28 pages, 10 fugure

Quantum Fluctuations of a Coulomb potential

Long-range properties of the two-point correlation function of the electromagnetic field produced by an elementary particle are investigated. Using the Schwinger-Keldysh formalism it is shown that this function is finite in the coincidence limit outside the region of particle localization. In this limit, the leading term in the long-range expansion of the correlation function is calculated explicitly, and its gauge independence is proved. The leading contribution turns out to be of zero order in the Planck constant, and the relative value of the root mean square fluctuation of the Coulomb potential is found to be 1/\sqrt{2}, confirming the result obtained previously within the S-matrix approach. It is shown also that in the case of a macroscopic body, the \hbar^0 part of the correlation function is suppressed by a factor 1/N, where N is the number of particles in the body. Relation of the obtained results to the problem of measurability of the electromagnetic field is mentioned.Comment: 15 pages, 2 figure

The Quantum Mellin transform

We uncover a new type of unitary operation for quantum mechanics on the half-line which yields a transformation to ``Hyperbolic phase space''. We show that this new unitary change of basis from the position x on the half line to the Hyperbolic momentum $p_\eta$, transforms the wavefunction via a Mellin transform on to the critial line $s=1/2-ip_\eta$. We utilise this new transform to find quantum wavefunctions whose Hyperbolic momentum representation approximate a class of higher transcendental functions, and in particular, approximate the Riemann Zeta function. We finally give possible physical realisations to perform an indirect measurement of the Hyperbolic momentum of a quantum system on the half-line.Comment: 23 pages, 6 Figure

Universal low-energy properties of three two-dimensional particles

Universal low-energy properties are studied for three identical bosons confined in two dimensions. The short-range pair-wise interaction in the low-energy limit is described by means of the boundary condition model. The wave function is expanded in a set of eigenfunctions on the hypersphere and the system of hyper-radial equations is used to obtain analytical and numerical results. Within the framework of this method, exact analytical expressions are derived for the eigenpotentials and the coupling terms of hyper-radial equations. The derivation of the coupling terms is generally applicable to a variety of three-body problems provided the interaction is described by the boundary condition model. The asymptotic form of the total wave function at a small and a large hyper-radius $\rho$ is studied and the universal logarithmic dependence $\sim \ln^3 \rho$ in the vicinity of the triple-collision point is derived. Precise three-body binding energies and the $2 + 1$ scattering length are calculated.Comment: 30 pages with 13 figure

A dynamic magneto-optical trap for atom chips

We describe a dynamic magneto-optical trap (MOT) suitable for the use with vacuum systems in which optical access is limited to a single window. This technique facilitates the long-standing desire of producing integrated atom chips, many of which are likely to have severely restricted optical access compared with conventional vacuum chambers. This "switching-MOT" relies on the synchronized pulsing of optical and magnetic fields at audio frequencies. The trap's beam geometry is obtained using a planar mirror surface, and does not require a patterned substrate or bulky optics inside the vacuum chamber. Central to the design is a novel magnetic field geometry that requires no external quadrupole or bias coils which leads toward a very compact system. We have implemented the trap for 85Rb and shown that it is capable of capturing 2 million atoms and directly cooling below the Doppler temperature

A classification model of the lean barriers and enablers: a case from Brazilian healthcare

Lean is widely known as an approach to improve the process, reducing wastes and adding value to the customer. However, around 70% of the lean projects fail during its journey, this situation is related to barriers and enablers to implement lean projects. Thus, this paper aims to analyse and classify lean barriers and enablers into an organizational model. The methodology is based on systematic literature review as well as a case study. The paper presents a classification model into seven organizational aspects as well as propositions related to patient’s behaviour and the public healthcare system

Nonrelativistic Chern-Simons Vortices on the Torus

A classification of all periodic self-dual static vortex solutions of the Jackiw-Pi model is given. Physically acceptable solutions of the Liouville equation are related to a class of functions which we term Omega-quasi-elliptic. This class includes, in particular, the elliptic functions and also contains a function previously investigated by Olesen. Some examples of solutions are studied numerically and we point out a peculiar phenomenon of lost vortex charge in the limit where the period lengths tend to infinity, that is, in the planar limit.Comment: 25 pages, 2+3 figures; improved exposition, corrected typos, added one referenc