Braided Matrix Structure of the Sklyanin Algebra and of the Quantum Lorentz Group

Braided groups and braided matrices are novel algebraic structures living in braided or quasitensor categories. As such they are a generalization of super-groups and super-matrices to the case of braid statistics. Here we construct braided group versions of the standard quantum groups $U_q(g)$. They have the same FRT generators $l^\pm$ but a matrix braided-coproduct \und\Delta L=L\und\tens L where $L=l^+Sl^-$, and are self-dual. As an application, the degenerate Sklyanin algebra is shown to be isomorphic to the braided matrices $BM_q(2)$; it is a braided-commutative bialgebra in a braided category. As a second application, we show that the quantum double D(\usl) (also known as the `quantum Lorentz group') is the semidirect product as an algebra of two copies of \usl, and also a semidirect product as a coalgebra if we use braid statistics. We find various results of this type for the doubles of general quantum groups and their semi-classical limits as doubles of the Lie algebras of Poisson Lie groups.Comment: 45 pages. Revised (= much expanded introduction

The Braided Heisenberg Group

We compute the braided groups and braided matrices $B(R)$ for the solution $R$ of the Yang-Baxter equation associated to the quantum Heisenberg group. We also show that a particular extension of the quantum Heisenberg group is dual to the Heisenberg universal enveloping algebra $U_{q}(h)$, and use this result to derive an action of $U_{q}(h)$ on the braided groups. We then demonstrate the various covariance properties using the braided Heisenberg group as an explicit example. In addition, the braided Heisenberg group is found to be self-dual. Finally, we discuss a physical application to a system of n braided harmonic oscillators. An isomorphism is found between the n-fold braided and unbraided tensor products, and the usual `free' time evolution is shown to be equivalent to an action of a primitive generator of $U_{q}(h)$ on the braided tensor product.Comment: 33 page

Towards Spinfoam Cosmology

We compute the transition amplitude between coherent quantum-states of geometry peaked on homogeneous isotropic metrics. We use the holomorphic representations of loop quantum gravity and the Kaminski-Kisielowski-Lewandowski generalization of the new vertex, and work at first order in the vertex expansion, second order in the graph (multipole) expansion, and first order in 1/volume. We show that the resulting amplitude is in the kernel of a differential operator whose classical limit is the canonical hamiltonian of a Friedmann-Robertson-Walker cosmology. This result is an indication that the dynamics of loop quantum gravity defined by the new vertex yields the Friedmann equation in the appropriate limit.Comment: 8 page

High pressure water jet cutting and stripping

High pressure water cutting techniques have a wide range of applications to the American space effort. Hydroblasting techniques are commonly used during the refurbishment of the reusable solid rocket motors. The process can be controlled to strip a thermal protective ablator without incurring any damage to the painted surface underneath by using a variation of possible parameters. Hydroblasting is a technique which is easily automated. Automation removes personnel from the hostile environment of the high pressure water. Computer controlled robots can perform the same task in a fraction of the time that would be required by manual operation

Force-induced rupture of a DNA duplex

The rupture of double-stranded DNA under stress is a key process in biophysics and nanotechnology. In this article we consider the shear-induced rupture of short DNA duplexes, a system that has been given new importance by recently designed force sensors and nanotechnological devices. We argue that rupture must be understood as an activated process, where the duplex state is metastable and the strands will separate in a finite time that depends on the duplex length and the force applied. Thus, the critical shearing force required to rupture a duplex within a given experiment depends strongly on the time scale of observation. We use simple models of DNA to demonstrate that this approach naturally captures the experimentally observed dependence of the critical force on duplex length for a given observation time. In particular, the critical force is zero for the shortest duplexes, before rising sharply and then plateauing in the long length limit. The prevailing approach, based on identifying when the presence of each additional base pair within the duplex is thermodynamically unfavorable rather than allowing for metastability, does not predict a time-scale-dependent critical force and does not naturally incorporate a critical force of zero for the shortest duplexes. Additionally, motivated by a recently proposed force sensor, we investigate application of stress to a duplex in a mixed mode that interpolates between shearing and unzipping. As with pure shearing, the critical force depends on the time scale of observation; at a fixed time scale and duplex length, the critical force exhibits a sigmoidal dependence on the fraction of the duplex that is subject to shearing.Comment: 10 pages, 6 figure

Pelarasan ukur lanjutan

Buku ini mengandungi beberapa bab iaitu kandungan bab 1 teknik iterasi dalam pelarasan, model persamaan cerapan, model persamaan syarat, bab 2 pelarasan kaedah jujukan dengan persamaan, cerapan, penambahan cerapan baru keatas persamaan normal, pelarasan kaedah jujukan, kesan keatas X*, kesan keatas SX*, useful matrix equalities (ume), bab 3 gabungan persamaan cerapan dan persamaan syarat, tiori, contoh, bab 4 pra-analisa jaringan, pengenalan, jenis-jenis rekabentuk 44 4.3 contoh, bab 5 penyelesaian persamaan normal dengan, kaedah cholesky, penyelesaian sistem persamaan linear, penyelesaian untuk songsangan matriks normal, kelebihan kaedah cholesky, lampiran a : persamaan cerapan jarak dan sudut, lampiran b : bacaan tambahan

Folk theories of objects in motion

There are three main strands of research which have investigated people’s intuitive knowledge of objects in motion. (1) Knowledge of the trajectories of objects in motion; (2) knowledge of the causes of motion; and (3) the categorisation of motion as to whether it has been produced by something animate or inanimate. We provide a brief introduction to each of these areas. We then point to some linguistic and cultural differences which may have consequences for people’s knowledge of objects in motion. Finally, we describe two experimental tasks and an ethnographic task that will allow us to collect data in order to establish whether, indeed, there are interesting cross-linguistic/cross-cultural differences in lay theories of objects in motion

Synthesis of Hydrogels by Free Radical Copolymerization of Sago Starch or Chitosan and Hydrophilic Vinyl Monomers and Their Characterizations

Sago starch was incorporated in the synthesis of polymer gel networks by free radical crosslinking copolymerization in an aqueous solution using potassium persulfate as an initiator. Three different monomers (2-acrylamido-2- methylpropanesulfonic acid (AMPS), acrylic acid and methyl-2-acrylamido-2- methoxyacetate (MAMOA)) with a common crosslinking agent (N,N'- methylenebisacrylamide (NMBA)) were used to synthesize these gel networks. A series of studies was carried out to evaluate and optimize the effect of the reaction parameters such as the amount of the monomer, the cross linking agent and sago starch as well as liquor volume on the polymer gel networks yield. It was found that the percentages of gelation fraction and total conversion were dependent on these parameters. The swelling behaviors of these polymeric gel networks from the dry state In distilled water and NaCl solutions of different concentration were also investigated. The maximum saturated water absorbency of 440 g H₂O/g dry gel was obtained for the gel network prepared from 1 g sago starch, 38.16 x l0⁻³ mol AMPS and 1.29 x l0⁻³ mol NMBA in the presence of 45 mL liquor volume. The absorbency of the hydrogel networks in the salt solutions was affected by the salt concentrations and the charge number of cations and anions