Universal Abelian topological groups

A topological group G is said to be universal in a class K of topological groups if G is an element of K and if for every group H is an element of K there is a subgroup K of G that is isomorphic to H as a topological group. A group is constructed that is universal in the class of separable metrizable topological Abelian groups.

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.

Dimension theory and nonstable K1 of quadratic modules

Employing Bak’s dimension theory, we investigate the nonstable quadratic K-group K1,2n(A, ) = G2n(A, )/E2n(A, ), n 3, where G2n(A, ) denotes the general quadratic group of rank n over a form ring (A, ) and E2n(A, ) its elementary subgroup. Considering form rings as a category with dimension in the sense of Bak, we obtain a dimension filtration G2n(A, ) G2n0(A, ) G2n1(A, ) E2n(A, ) of the general quadratic group G2n(A, ) such that G2n(A, )/G2n0(A, ) is Abelian, G2n0(A, ) G2n1(A, ) is a descending central series, and G2nd(A)(A, ) = E2n(A, ) whenever d(A) = (Bass–Serre dimension of A) is finite. In particular K1,2n(A, ) is solvable when d(A) <.

Effect of B-group vitamins and antioxidant vitamins on hyperhomocysteinemia:a double-blind, randomized, factorial-design, controlled trial

Mild hyperhomocysteinemia is accepted as a risk factor for premature cardiovascular disease. In a population with a high prevalence of cardiovascular disease, we screened a group of clinically healthy working men aged 30-49 y (n = 509) for plasma homocysteine and 5,10-methylene tetrahydrofolate reductase (MTHFR) genotype status. Those with mildly elevated homocysteine concentrations (> or = 8.34 micromol/L) were selected for intervention. In a randomized, factorial-design, controlled trial we assessed the effects of B-group vitamins and antioxidant vitamin supplementation on homocysteine concentrations. The 132 men were randomly assigned to one of four groups: supplementation with B-group vitamins alone (1 mg folic acid, 7.2 mg pyridoxine, and 0.02 mg cyanocobalamin), antioxidant vitamins alone (150 mg ascorbic acid, 67 mg RRR-alpha-tocopherol, and 9 mg beta-carotene), B-group vitamins with antioxidant vitamins, or placebo. Intervention was double-blind. A total of 101 men completed the 8-wk intervention. When homocysteine concentrations were analyzed by group, significant (P <0.001) decreases (32.0% and 30.0%, respectively) were observed in both groups receiving B-group vitamins either with or without antioxidants. The effect of B-group vitamins alone over 8 wk was a reduction in homocysteine concentrations of 27.9% (95% CI: 22.0%, 33.3%; P <0.001) whereas antioxidants alone produced a nonsignificant increase of 5.1% (95% CI: -2.8%, 13.6%; P = 0.21). There was no evidence of any interaction between the two groups of vitamins. The effect of B-group vitamin supplementation seemed to depend on MTHFR genotype. Supplementation with the B-group vitamins with or without antioxidants reduced homocysteine in the men with mildly elevated concentrations, and hence may be effective in reducing cardiovascular risk.

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.

Beyond managerial talent: ‘key group’ identification and differential compensation practices in multinational companies

With the maturation of strategic human resource management scholarship, there appears to be a greater call to move from monolithic workforce management to a more strategic and differentiated emphasis on employees with the greatest capacity to enhance competitive advantage. There has been little consideration in the literature as to whether organizations formally identify key groups of employees based on their impact on organizational learning and core competences. Using survey evidence from 260 multinational companies (MNCs), this paper explores the extent to which key groups of employees are formally recognized and whether they are subject to differential compensation practices. The results demonstrate that just in excess of half of these MNCs identify a key group. There was considerable differentiation in the compensation practices between these key groups, managers and the largest occupational group in the workforce. The results give rise to questions worthy of future investigation, namely whether the differentiated approaches used lead to improved performance outcomes.

Models of open populations with space-limited recruitment: extension of theory and application to the barnacle Chthamalus montagui.

1. Barnacles are a good model organism for the study of open populations with space-limited recruitment. These models are applicable to other species with open supply of new individuals and resource limitation. The inclusion of space in models leads to reductions in recruitment with increasing density, and thus predictions of population size and stability are possible. 2. Despite the potential generality of a demographic theory for open space-limited populations, the models currently have a narrow empirical base. In this study, a model for an open population with space-limited recruitment was extended to include size-specific survival and promotions to any size class. The assumptions of this model were tested using data from a pan-European study of the barnacle Chthamalus montagui Southward. Two models were constructed: a 6-month model and a periodic annual model. Predicted equilibria and their stabilities were compared between shores. 3. Tests of model assumptions supported the extension of the theory to include promotions to any size class. Mortality was found to be size-specific and density independent. Studied populations were open, with recruitment proportional to free space. 4. The 6-month model showed a significant interaction between time and location for equilibrium free space. This may have been due to contrasts in the timing of structuring processes (i.e. creating and filling space) between Mediterranean and Atlantic systems. Integration of the 6-month models into a periodic annual model removed the differences in equilibrium-free space between locations. 5. Model predictions show a remarkable similarity between shores at a European scale. Populations were persistent and all solutions were stable. This reflects the apparent absence of density-dependent mortality and a high adult survivorship in C. montagui. As populations are intrinsically stable, observations of fluctuations in density are directly attributable to variations in the environmental forcing of recruitment or mortality