Topology synthesis of three-legged spherical parallel manipulators employing Lie group theory

Driven by the requirements of the bionic joint or tracking equipment for the spherical parallel manipulators (SPMs) with three rotational degrees-of-freedom (DoFs), this paper carries out the topology synthesis of a class of three-legged SPMs employing Lie group theory. In order to achieve the intersection of the displacement subgroups, the subgroup characteristics and operation principles are defined in this paper. Mainly drawing on the Lie group theory, the topology synthesis procedure of three-legged SPMs including four stages and two functional blocks is proposed, in which the assembly principles of three legs are defined. By introducing the circular track, a novel class of three-legged SPMs is synthesized, which is the important complement to the existing SPMs. Finally, four typical examples are given to demonstrate the finite displacements of the synthesized three-legged SPMs.

The solvable Lie group N_{6, 28}: an example of an almost C_0(\mathcal{K})-C*-algebra

Motivated by the description of the C*-algebra of the affine automorphism group N6,28 of the Siegel upper half-plane of degree 2 as an algebra of operator fields defined over the unitary dual View the MathML source of the group, we introduce a family of C*-algebras, which we call almost C0(K), and we show that the C*-algebra of the group N6,28 belongs to this class.

Universal elements for non-linear operators and their applications

We prove that under certain topological conditions on the set of universal elements of a continuous map T acting on a topological space X, that the direct sum T and M_g is universal, where M_g is multiplication by a generating element of a compact topological group. We use this result to characterize R_+-supercyclic operators and to show that whenever T is a supercyclic operator and z_1,...,z_n are pairwise different non-zero complex numbers, then the operator z_1T\oplus ... \oplus z_n T is cyclic. The latter answers affirmatively a question of Bayart and Matheron.

Closable multipliers

Let $(X,\mu)$ and $(Y,\nu)$ be standard measure spaces. A function $\nph\in L^\infty(X\times Y,\mu\times\nu)$ is called a (measurable) Schur multiplier if the map $S_\nph$, defined on the space of Hilbert-Schmidt operators from $L_2(X,\mu)$ to $L_2(Y,\nu)$ by multiplying their integral kernels by $\nph$, is bound-ed in the operator norm. The paper studies measurable functions $\nph$ for which $S_\nph$ is closable in the norm topology or in the weak* topology. We obtain a characterisation of w*-closable multipliers and relate the question about norm closability to the theory of operator synthesis. We also study multipliers of two special types: if $\nph$ is of Toeplitz type, that is, if $\nph(x,y)=f(x-y)$, $x,y\in G$, where $G$ is a locally compact abelian group, then the closability of $\nph$ is related to the local inclusion of $f$ in the Fourier algebra $A(G)$ of $G$. If $\nph$ is a divided difference, that is, a function of the form $(f(x)-f(y))/(x-y)$, then its closability is related to the ``operator smoothness'' of the function $f$. A number of examples of non closable, norm closable and w*-closable multipliers are presented.

Decay measures on locally compact abelian topological groups

Source: PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS Volume: 131 Pages: 1257-1273 Part: Part 6 Published: 2001 Times Cited: 5 References: 23 Citation MapCitation Map beta Abstract: We show that the Banach space M of regular sigma-additive finite Borel complex-valued measures on a non-discrete locally compact Hausdorff topological Abelian group is the direct sum of two linear closed subspaces M-D and M-ND, where M-D is the set of measures mu is an element of M whose Fourier transform vanishes at infinity and M-ND is the set of measures mu is an element of M such that nu is not an element of MD for any nu is an element of M \ {0} absolutely continuous with respect to the variation \mu\. For any corresponding decomposition mu = mu(D) + mu(ND) (mu(D) is an element of M-D and mu(ND) is an element of M-ND) there exist a Borel set A = A(mu) such that mu(D) is the restriction of mu to A, therefore the measures mu(D) and mu(ND) are singular with respect to each other. The measures mu(D) and mu(ND) are real if mu is real and positive if mu is positive. In the case of singular continuous measures we have a refinement of Jordan's decomposition theorem. We provide series of examples of different behaviour of convolutions of measures from M-D and M-ND.

The rotational broadening of V395 Carinae. Implications on the compact object's mass

Context: The masses previously obtained for the X-ray binary 2S 0921-630 inferred a compact object that was either a high-mass neutron star or low-mass black-hole, but used a previously published value for the rotational broadening (v sin i) with large uncertainties. Aims: We aim to determine an accurate mass for the compact object through an improved measurement of the secondary star's projected equatorial rotational velocity. Methods: We have used UVES echelle spectroscopy to determine the v sin i of the secondary star (V395 Car) in the low-mass X-ray binary 2S 0921-630 by comparison to an artificially broadened spectral-type template star. In addition, we have also measured v sin i from a single high signal-to-noise ratio absorption line profile calculated using the method of Least-Squares Deconvolution (LSD). Results: We determine v sin i to lie between 31.3±0.5 km s-1 to 34.7±0.5 km s-1 (assuming zero and continuum limb darkening, respectively) in disagreement with previous results based on intermediate resolution spectroscopy obtained with the 3.6 m NTT. Using our revised v sin i value in combination with the secondary star's radial velocity gives a binary mass ratio of 0.281±0.034. Furthermore, assuming a binary inclination angle of 75° gives a compact object mass of 1.37±0.13 M_?. Conclusions: We find that using relatively low-resolution spectroscopy can result in systemic uncertainties in the measured v sin i values obtained using standard methods. We suggest the use of LSD as a secondary, reliable check of the results as LSD allows one to directly discern the shape of the absorption line profile. In the light of the new v sin i measurement, we have revised down the compact object's mass, such that it is now compatible with a canonical neutron star mass.

VLT FORS spectra of blue supergiants in the Local Group galaxy NGC 6822

Half hour exposures using the ESO VLT/FORS1 combination at Paranal in Chile have allowed us to obtain spectra for three B supergiants in the dwarf irregular galaxy NGC 6822. The spectra have been analysed using non-LTE techniques and temperatures, gravities, helium content and abundances have been obtained. Overall the metallicity of NGC 6822 is found to lie between that of the LMC and of the SMC, in agreement with previous observations of H II regions and in contrast to the earlier findings of Massey et al. (1995). The analysis of H-alpha yields estimates of the mass-loss rates and wind momenta. These results demonstrate that significantly longer exposures with the same instruments will allow us to perform quantitative spectroscopy of blue supergiants in galaxies far beyond the Local Group.

An isomorphism between group C*-algebras of ax + b-like groups

We give a necessary and sufficient condition for two ax+b-like groups to have isomorphic C*-algebras. In particular, we show that there are many non-isomorphic ax+b -like Lie groups having isomorphic group C*-algebras.

Thermolyzable polymer networks and star polymers containing a novel, compact, degradable acylal-based dimethacrylate cross-linker: Synthesis, characterization, and thermolysis

A compact, cleavable acylal dimethacrylate cross-linker, 1,1-ethylenediol dimethacrylate (EDDMA), was synthesized from the anhydrous iron(III) chloride-catalyzed reaction between methacrylic anhydride and acetaldehyde. The ability of EDDMA to act as cross-linker was demonstrated by using it for the preparation of one neat cross-linker network, four star polymers of methyl methacrylate (MMA), and four randomly cross-linked MMA polymer networks using group transfer polymerization (GTP). For comparison, the corresponding polymer structures based on the commercially available ethylene glycol dimethacrylate (EGDMA) cross-linker (isomer of EDDMA) were also prepared via GTR The number of arms of the EDDMA-based star polymers was lower than that of the corresponding EGDMA polymers, whereas the degrees of swelling in tetrahydrofuran of the EDDMA-based MMA networks were higher than those of their EGDMA-based counterparts. Although none of the EDDMA-containing polymers could be cleanly hydrolyzed under basic or acidic conditions, they could be thermolyzed at 200 degrees C within 1 day giving lower molecular weight products.

Sets of multiplicity and closable multipliers on group algebras

We undertake a detailed study of the sets of multiplicity in a second countable locally compact group G and their operator versions. We establish a symbolic calculus for normal completely bounded maps from the space B(L-2(G)) of bounded linear operators on L-2 (G) into the von Neumann algebra VN(G) of G and use it to show that a closed subset E subset of G is a set of multiplicity if and only if the set E* = {(s,t) is an element of G x G : ts(-1) is an element of E} is a set of operator multiplicity. Analogous results are established for M-1-sets and M-0-sets. We show that the property of being a set of multiplicity is preserved under various operations, including taking direct products, and establish an Inverse Image Theorem for such sets. We characterise the sets of finite width that are also sets of operator multiplicity, and show that every compact operator supported on a set of finite width can be approximated by sums of rank one operators supported on the same set. We show that, if G satisfies a mild approximation condition, pointwise multiplication by a given measurable function psi : G -> C defines a closable multiplier on the reduced C*-algebra G(r)*(G) of G if and only if Schur multiplication by the function N(psi): G x G -> C, given by N(psi)(s, t) = psi(ts(-1)), is a closable operator when viewed as a densely defined linear map on the space of compact operators on L-2(G). Similar results are obtained for multipliers on VN(C).

Sets of p-multiplicity in locally compact groups

We initiate the study of sets of p-multiplicity in locally compact groups and their operator versions. We show that a closed subset E of a second countable locally compact group G is a set of p-multiplicity if and only if E∗={(s,t):ts−1∈E} is a set of operator p-multiplicity. We exhibit examples of sets of p-multiplicity, establish preservation properties for unions and direct products, and prove a p-version of the Stone–von Neumann Theorem.

A comparison of different pre-lysis methods and extraction kits for recovery of Stretococcus agalacticae (Lancefield group B Streptococcus) DNA from whole blood

Sub-optimal recovery of bacterial DNA from whole blood samples can limit the sensitivity of molecular assays to detect pathogenic bacteria. We compared 3 different pre-lysis protocols (none, mechanical pre-lysis and achromopeptidasepre-lysis) and 5 commercially available DNA extraction platforms for direct detection of Group B Streptococcus (GBS) in spiked whole blood samples, without enrichment culture. DNA was extracted using the QIAamp Blood Mini kit (Qiagen), UCP Pathogen Mini kit (Qiagen), QuickGene DNA Whole Blood kit S (Fuji), Speed Xtract Nucleic Acid Kit 200 (Qiagen) and MagNA Pure Compact Nucleic Acid Isolation Kit I (Roche Diagnostics Corp). Mechanical pre-lysis increased yields of bacterial genomic DNA by 51.3 fold (95% confidence interval; 31.6–85.1, p < 0.001) and pre-lysis with achromopeptidase by 6.1 fold (95% CI; 4.2–8.9, p < 0.001), compared with no pre-lysis. Differences in yield dueto pre-lysis were 2–3 fold larger than differences in yield between extraction methods. Including a pre-lysis step can improve the limits of detection of GBS using PCR or other molecular methods without need for culture.