Hom-quantum groups I: quasi-triangular Hom-bialgebras

We introduce a Hom-type generalization of quantum groups, called quasi-triangular Hom-bialgebras. They are non-associative and non-coassociative analogues of Drinfel'd's quasi-triangular bialgebras, in which the non-(co)associativity is controlled by a twisting map. A family of quasi-triangular Hom-bialgebras can be constructed from any quasi-triangular bialgebra, such as Drinfel'd's quantum enveloping algebras. Each quasi-triangular Hom-bialgebra comes with a solution of the quantum Hom-Yang-Baxter equation, which is a non-associative version of the quantum Yang-Baxter equation. Solutions of the Hom-Yang-Baxter equation can be obtained from modules of suitable quasi-triangular Hom-bialgebras.Comment: 21 page

Quantum rings as electron spin beam splitters

Quantum interference and spin-orbit interaction in a one-dimensional mesoscopic semiconductor ring with one input and two output leads can act as a spin beam splitter. Different polarization can be achieved in the two output channels from an originally totally unpolarized incoming spin state, very much like in a Stern-Gerlach apparatus. We determine the relevant parameters such that the device has unit efficiency.Comment: 4 pages, 3 figures; minor change

A comparative investigation of the efficacy of CO2 and high power diode lasers for the forming of EN3 mild steel sheets

A comparative investigation of the effectiveness of a high power diode laser (HPDL) and a CO2 laser for the forming of thin section EN3 mild steel sheet has been conducted. The buckling mechanism was identified as the laser forming mechanism responsible for the induced bending. For both lasers it was found that the induced bending angles increased with an increasing number of irradiations and high laser powers, whilst decreasing as the traverse speed was increased. Also, it was apparent from the experimental results that the laser bending angle was only linearly proportional to the number of irradiations when the latter was small due to local material thickening along the bend edge with a high number of irradiations. Owing to the mild steel’s greater beam absorption at the HPDL wavelength, larger bending angles were induced when using the HPDL. However, under certain conditions the performance of the CO2 laser in terms of induced bending angle was seen to approach that of the HPDL. Nevertheless, similar results between the two lasers were only achieved with increasing irradiations, thus it was concluded that the efficacy of the HPDL was higher than that of the CO2 laser insofar as it was more efficient. From graphical results and the employment of an analytical procedure, the laser line energy range in which accurate control of the HPDL bending of the mild steel sheets could be exercised efficiently was found to be 53 J mm-1 < P/v < 78 J mm-1, whilst for the CO2 laser the range was 61 J mm-1 < P/v < 85 J mm-1

Domain Walls in MQCD and Monge-Ampere Equation

We study Witten's proposal that a domain wall exists in M-theory fivebrane version of QCD (MQCD) and that it can be represented as a supersymmetric three-cycle in G_2 holonomy manifold. It is shown that equations defining the U(1) invariant domain wall for SU(2) group can be reduced to the Monge-Ampere equation. A proof of an algebraic formula of Kaplunovsky, Sonnenschein and Yankielowicz is presented. The formal solution of equations for domain wall is constructed.Comment: Latex, 18 pages, section 4.2 modified, typos correcte

Distribution of Flux Vacua around Singular Points in Calabi-Yau Moduli Space

We study the distribution of type IIB flux vacua in the moduli space near various singular loci, e.g. conifolds, ADE singularities on P1, Argyres-Douglas point etc, using the Ashok- Douglas density det(R + omega). We find that the vacuum density is integrable around each of them, irrespective of the type of the singularities. We study in detail an explicit example of an Argyres-Douglas point embedded in a compact Calabi-Yau manifold.Comment: 27 pages, 1 figure; v2: minor change, references added ; v3: references added, published versio

Founding quantum theory on the basis of consciousness

In the present work, quantum theory is founded on the framework of consciousness, in contrast to earlier suggestions that consciousness might be understood starting from quantum theory. The notion of streams of consciousness, usually restricted to conscious beings, is extended to the notion of a Universal/Global stream of conscious flow of ordered events. The streams of conscious events which we experience constitute sub-streams of the Universal stream. Our postulated ontological character of consciousness also consists of an operator which acts on a state of potential consciousness to create or modify the likelihoods for later events to occur and become part of the Universal conscious flow. A generalized process of measurement-perception is introduced, where the operation of consciousness brings into existence, from a state of potentiality, the event in consciousness. This is mathematically represented by (a) an operator acting on the state of potential-consciousness before an actual event arises in consciousness and (b) the reflecting of the result of this operation back onto the state of potential-consciousness for comparison in order for the event to arise in consciousness. Beginning from our postulated ontology that consciousness is primary and from the most elementary conscious contents, such as perception of periodic change and motion, quantum theory follows naturally as the description of the conscious experience.Comment: 41 pages, 3 figures. To be published in Foundations of Physics, Vol 36 (6) (June 2006), published online at http://dx.doi.org/10.1007/s10701-006-9049-

Special Lagrangian cones with higher genus links

For every odd natural number g=2d+1 we prove the existence of a countably infinite family of special Lagrangian cones in C^3 over a closed Riemann surface of genus g, using a geometric PDE gluing method.Comment: 48 page

Anti-self-dual Riemannian metrics without Killing vectors, can they be realized on K3?

Explicit Riemannian metrics with Euclidean signature and anti-self dual curvature that do not admit any Killing vectors are presented. The metric and the Riemann curvature scalars are homogenous functions of degree zero in a single real potential and its derivatives. The solution for the potential is a sum of exponential functions which suggests that for the choice of a suitable domain of coordinates and parameters it can be the metric on a compact manifold. Then, by the theorem of Hitchin, it could be a class of metrics on $K3$, or on surfaces whose universal covering is $K3$.Comment: Misprints in eqs.(9-11) corrected. Submitted to Classical and Quantum Gravit

IMECE2002-33981 VIBRATION ANALYSIS AND CONTROL OF A ROTATING FLEXIBLE ARM WITH ACLD TREATMENT

ABSTRACT In this paper, the vibration behavior and control of a clamped-free rotating flexible cantilever arm with fully covered Active Constrained Layer Damping (ACLD) treatment is investigated. The arm is rotating in a horizontal plane in which the gravitational effect and rotary inertia are neglected. The stress-strain relationship for the viscoelastic material (VEM) is described by a complex shear modulus while the shear deformations in the two piezoelectric layers are neglected. Hamilton&apos;s principle in conjunction with finite element method (FEM) is used to derive the nonlinear coupled differential equations of motion and the associated boundary conditions that describe the rigid hub angle rotation, the arm transverse displacement and the axial deformations of the three-layer composite. This refined model takes into account the effects of centrifugal stiffening due to the rotation of the beam and the potential energies of the VEM due to extension and bending. Active controllers are designed with PD for the piezo-sensor and actuator. The vibration frequencies and damping factors of the closed-loop beam/ACLD system are obtained after solving the characteristic complex eigenvalue problem numerically. The effects of different rotating speed, thickness ratio and loss factor of the VEM as well as different controller gain on the damped frequency and damping ratio are presented. The results of this study will be useful in the design of adaptive and smart structures for vibration suppression and control in rotating structures such as rotorcraft blades or robotic arms

Period Integrals of CY and General Type Complete Intersections

We develop a global Poincar\'e residue formula to study period integrals of families of complex manifolds. For any compact complex manifold $X$ equipped with a linear system $V^*$ of generically smooth CY hypersurfaces, the formula expresses period integrals in terms of a canonical global meromorphic top form on $X$. Two important ingredients of our construction are the notion of a CY principal bundle, and a classification of such rank one bundles. We also generalize our construction to CY and general type complete intersections. When $X$ is an algebraic manifold having a sufficiently large automorphism group $G$ and $V^*$ is a linear representation of $G$, we construct a holonomic D-module that governs the period integrals. The construction is based in part on the theory of tautological systems we have developed in the paper \cite{LSY1}, joint with R. Song. The approach allows us to explicitly describe a Picard-Fuchs type system for complete intersection varieties of general types, as well as CY, in any Fano variety, and in a homogeneous space in particular. In addition, the approach provides a new perspective of old examples such as CY complete intersections in a toric variety or partial flag variety.Comment: An erratum is included to correct Theorem 3.12 (Uniqueness of CY structure