REIDEMEISTER TORSION AND ANALYTIC TORSION OF SPHERES

We provide a simple topological derivation of a formula for the Reidemeister and the analytic torsion of spheres.

THE IMPLICIT FUNCTION THEOREM FOR CONTINUOUS FUNCTIONS

In the present paper we obtain a new homological version of the implicit function theorem and some versions of the Darboux theorem. Such results are proved for continuous maps on topological manifolds. As a consequence. some versions of these classic theorems are proved when we consider differenciable (not necessarily C-1) maps.

Discontinuous local semiflows for Kurzweil equations leading to LaSalle`s invariance principle for differential systems with impulses at variable times

In this paper, we consider an initial value problem for a class of generalized ODEs, also known as Kurzweil equations, and we prove the existence of a local semidynamical system there. Under certain perturbation conditions, we also show that this class of generalized ODEs admits a discontinuous semiflow which we shall refer to as an impulsive semidynamical system. As a consequence, we obtain LaSalle`s invariance principle for such a class of generalized ODEs. Due to the importance of LaSalle`s invariance principle in studying stability of differential systems, we include an application to autonomous ordinary differential systems with impulse action at variable times. (C) 2011 Elsevier Inc. All rights reserved.

The doodle of a finitely determined map germ from R(2) to R(3)

Let f : U subset of R(2) -> R(3) be a representative of a finitely determined map germ f : (R(2), 0) -> (R(3), 0). Consider the curve obtained as the intersection of the image of the mapping f with a sufficiently small sphere s(epsilon)(2) centered at the origin in R(3), call this curve the associated doodle of the map germ f. For a large class of map germs the associated doodle has many transversal self-intersections. The topological classification of such map germs is considered from the point of view of the associated doodles. (C) 2009 Elsevier Inc. All rights reserved.

A Productivity-Based Approach to LAN Topology Design

Over the useful life of a LAN, network downtimes will have a negative impact on organizational productivity not included in current Network Topological Design (NTD) problems. We propose a new approach to LAN topological design that includes the impact of these productivity losses into the network design, minimizing not only the CAPEX but also the expected cost of unproductiveness attributable to network downtimes over a certain period of network operation.

Liquid crystalline cellulosic elastomers: free standing anisotropic films under stretching

The structure and local ordering of 1,6-hexamethylenediisocyanate-(acetoxypropy1) cellulose (HDI-APC) liquid crystalline elastomer thin films are investigated by using X-ray diffraction and scattering techniques. Optical microscopy and mechanical essays are performed to complement the investigation. The study is performed in films subjected or not to an uniaxial stress. Our results indicate that the film is constituted by a bundle of helicoidal fiber-like structure, where the cellobiose block spins around the axis of the fiber, like a string-structure in a smectic-like packing, with the pitch defined by a smectic-like layer. The fibers are in average perpendicular to the smectic-like planes. Without the stretch, these bundles are warped, only with a residual orientation along the casting direction. The stretch orients the bundles along it, increasing the smectic-like and the nematic-like ordering of the fibers. Under stress, the network of molecules which connects the cellobiose blocs and forms the cellulosic matrix tends to organize their links in a hexagonal-like structure with lattice parameter commensurate to the smectic-like structure.

Experimental identification of chaotic fibers

In a 2D parameter space, by using nine experimental time series of a Clitia`s circuit, we characterized three codimension-1 chaotic fibers parallel to a period-3 window. To show the local preservation of the properties of the chaotic attractors in each fiber, we applied the closed return technique and two distinct topological methods. With the first topological method we calculated the linking, numbers in the sets of unstable periodic orbits, and with the second one we obtained the symbolic planes and the topological entropies by applying symbolic dynamic analysis. (C) 2007 Elsevier Ltd. All rights reserved.

Pulsating strings in Lunin-Maldacena backgrounds

We consider pulsating strings in Lunin-Maldacena backgrounds, specifically in deformed Minkowski spacetime and deformed AdS(5) x S(5). We find the relation between the energy and the oscillation number of the pulsating string when the deformation is small. Since the oscillation number is an adiabatic invariant it can be used to explore the regime of highly excited string states. We then quantize the string and look for such a sector. For the deformed Minkowski background we find a precise match with the classical results if the oscillation number is quantized as an even number. For the deformed AdS(5) x S(5) we find a contribution which depends on the deformation parameter.

Notes on beta-deformations of the pure spinor superstring in AdS(5) x S(5)

We study the properties of the vertex operator for the beta-deformation of the superstring in AdS(5) x S(5) in the pure spinor formalism. We discuss the action of supersymmetry on the infinitesimal beta-deformation, the application of the homological perturbation theory, and the relation between the worldsheet description and the spacetime supergravity description. (C) 2011 Elsevier B.V. All rights reserved.

Magnetic hysteresis loop shift in NiFe(2)O(4) nanocrystalline powder with large grain boundary fraction

Magnetic properties of nanocrystalline NiFe(2)O(4) spinel mechanically processed for 350 h have been studied using temperature dependent from both zero-field and in-field (57)Fe Mossbauer spectrometry and magnetization measurements. The hyperfine structure allows us to distinguish two main magnetic contributions: one attributed to the crystalline grain core, which has magnetic properties similar to the NiFe(2)O(4) spinel-like structure (n-NiFe(2)O(4)) and the other one due to the disordered grain boundary region, which presents topological and chemical disorder features(d-NiFe(2)O(4)). Mossbauer spectrometry determines a large fraction for the d-NiFe(2)O(4) region(62% of total area) and also suggests a speromagnet-like structure for it. Under applied magnetic field, the n-NiFe(2)O(4) spins are canted with angle dependent on the applied field magnitude. Mossbauer data also show that even under 120 kOe no magnetic saturation is observed for the two magnetic phases. In addition, the hysteresis loops, recorded for scan field of 50 kOe, are shifted in both field and magnetization axes, for temperatures below about 50 K. The hysteresis loop shifts may be due to two main contributions: the exchange bias field at the d-NiFe(2)O(4)/n-NiFe(2)O(4) interfaces and the minor loop effect caused by a high magnetic anisotropy of the d-NiFe(2)O(4) phase. It has also been shown that the spin configuration of the spin-glass like phase is modified by the consecutive field cycles, consequently the n-NiFe(2)O(4)/d-NiFe(2)O(4) magnetic interaction is also affected in this process. (C) 2010 Elsevier B.V. All rights reserved.

Coherent and semiclassical states in a magnetic field in the presence of the Aharonov-Bohm solenoid

A new approach to constructing coherent states (CS) and semiclassical states (SS) in a magnetic-solenoid field is proposed. The main idea is based on the fact that the AB solenoid breaks the translational symmetry in the xy-plane; this has a topological effect such that there appear two types of trajectories which embrace and do not embrace the solenoid. Due to this fact, one has to construct two different kinds of CS/SS which correspond to such trajectories in the semiclassical limit. Following this idea, we construct CS in two steps, first the instantaneous CS (ICS) and then the time-dependent CS/SS as an evolution of the ICS. The construction is realized for nonrelativistic and relativistic spinning particles both in (2 + 1) and (3 + 1) dimensions and gives a non-trivial example of SS/CS for systems with a nonquadratic Hamiltonian. It is stressed that CS depending on their parameters (quantum numbers) describe both pure quantum and semiclassical states. An analysis is represented that classifies parameters of the CS in such respect. Such a classification is used for the semiclassical decompositions of various physical quantities.

Quantum current algebra for the AdS(5) x S(5) superstring

The sigma model describing the dynamics of the superstring in the AdS(5) x S(5) background can be constructed using the coset PSU(2, 2 vertical bar 4)/SO(4, 1) x SO(5). A basic set of operators in this two dimensional conformal field theory is composed by the left invariant currents. Since these currents are not (anti) holomorphic, their OPE`s is not determined by symmetry principles and its computation should be performed perturbatively. Using the pure spinor sigma model for this background, we compute the one-loop correction to these OPE`s. We also compute the OPE`s of the left invariant currents with the energy momentum tensor at tree level and one loop.

Landau analog levels for dipoles in non-commutative space and phase space - Landau analog levels for dipoles

We investigate the analog of Landau quantization, for a neutral polarized particle in the presence of homogeneous electric and magnetic external fields, in the context of non-commutative quantum mechanics. This particle, possessing electric and magnetic dipole moments, interacts with the fields via the Aharonov-Casher and He-McKellar-Wilkens effects. For this model we obtain the Landau energy spectrum and the radial eigenfunctions of the non-commutative space coordinates and non-commutative phase space coordinates. Also we show that the case of non-commutative phase space can be treated as a special case of the usual non-commutative space coordinates.

Conservation laws and tachyon potentials in the sliver frame

Conservation laws have provided an elegant and efficient tool to evaluate the open string field theory interaction vertex, they have been originally implemented in the case where the string field is expanded in the Virasoro basis. In this work we derive conservation laws in the case where the string field is expanded in the so-called sliver L(0)-basis. As an application of this new set of conservation laws, we compute the open string field action relevant to the tachyon condensation and in order to present not only an illustration but also an additional information, we evaluate the action without imposing a gauge choice.

MODELING THE EVOLUTION OF COMPLEX NETWORKS THROUGH THE PATH-STAR TRANSFORMATION AND OPTIMAL MULTIVARIATE METHODS

The topology of real-world complex networks, such as in transportation and communication, is always changing with time. Such changes can arise not only as a natural consequence of their growth, but also due to major modi. cations in their intrinsic organization. For instance, the network of transportation routes between cities and towns ( hence locations) of a given country undergo a major change with the progressive implementation of commercial air transportation. While the locations could be originally interconnected through highways ( paths, giving rise to geographical networks), transportation between those sites progressively shifted or was complemented by air transportation, with scale free characteristics. In the present work we introduce the path-star transformation ( in its uniform and preferential versions) as a means to model such network transformations where paths give rise to stars of connectivity. It is also shown, through optimal multivariate statistical methods (i.e. canonical projections and maximum likelihood classification) that while the US highways network adheres closely to a geographical network model, its path-star transformation yields a network whose topological properties closely resembles those of the respective airport transportation network.