Time operators for one parameter semigroups

We develop two simple approaches to the construction of time operators for semigroups of continuous linear operators in Hilbert spaces provided that the generators of these semigroups are normal operators. The first approach enables us to give explicit formulas (in the spectral representations) both for the time operators and for their eigenfunctions. The other approach provides no explicit formula. However, it enables us to find necessary and sufficient conditions for the existence of time operators for semigroups of continuous linear operators in separable Hilbert spaces with normal generators. Time superoperators corresponding to unitary groups are also discussed.

Future development of gastrointestinal cancer incidence and mortality rates in Switzerland: a tumour registry- and population-based projection up to 2030.

QUESTIONS UNDER STUDY: Since tumour burden consumes substantial healthcare resources, precise cancer incidence estimations are pivotal to define future needs of national healthcare. This study aimed to estimate incidence and mortality rates of oesophageal, gastric, pancreatic, hepatic and colorectal cancers up to 2030 in Switzerland. METHODS: Swiss Statistics provides national incidences and mortality rates of various cancers, and models of future developments of the Swiss population. Cancer incidences and mortality rates from 1985 to 2009 were analysed to estimate trends and to predict incidence and mortality rates up to 2029. Linear regressions and Joinpoint analyses were performed to estimate the future trends of incidences and mortality rates. RESULTS: Crude incidences of oesophageal, pancreas, liver and colorectal cancers have steadily increased since 1985, and will continue to increase. Gastric cancer incidence and mortality rates reveal an ongoing decrease. Pancreatic and liver cancer crude mortality rates will keep increasing, whereas colorectal cancer mortality on the contrary will fall. Mortality from oesophageal cancer will plateau or minimally increase. If we consider European population-standardised incidence rates, oesophageal, pancreatic and colorectal cancer incidences are steady. Gastric cancers are diminishing and liver cancers will follow an increasing trend. Standardised mortality rates show a diminution for all but liver cancer. CONCLUSIONS: The oncological burden of gastrointestinal cancer will significantly increase in Switzerland during the next two decades. The crude mortality rates globally show an ongoing increase except for gastric and colorectal cancers. Enlarged healthcare resources to take care of these complex patient groups properly will be needed.

Studies on magnetic monopole solutions of non-abelian gauge theories and related problems

In 1931 Dirac studied the motion of an electron in the field of a magnetic monopole and found that the quantization of electric charge can be explained by postulating the mere existence of a magnetic monopole. Since 1974 there has been a resurgence of interest in magnetic monopole due to the work of ‘t’ Hooft and Polyakov who independently observed that monopoles can exist as finite energy topologically stable solutions to certain spontaneously broken gauge theories. The thesis, “Studies on Magnetic Monopole Solutions of Non-abelian Gauge Theories and Related Problems”, reports a systematic investigation of classical solutions of non-abelian gauge theories with special emphasis on magnetic monopoles and dyons which possess both electric and magnetic charges. The formation of bound states of a dyon with fermions and bosons is also studied in detail. The thesis opens with an account of a new derivation of a relationship between the magnetic charge of a dyon and the topology of the gauge fields associated with it. Although this formula has been reported earlier in the literature, the present method has two distinct advantages. In the first place, it does not depend either on the mechanism of symmetry breaking or on the nature of the residual symmetry group. Secondly, the results can be generalized to finite temperature monopoles.

SIGMA THEORY AND TWISTED CONJUGACY CLASSES

Using Sigma theory we show that for large classes of groups G there is a subgroup H of finite index in Aut(G) such that for phi is an element of H the Reidemeister number R(phi) is infinite. This includes all finitely generated nonpolycyclic groups G that fall into one of the following classes: nilpotent-by-abelian groups of type FP(infinity); groups G/G `` of finite Prufer rank; groups G of type FP(2) without free nonabelian subgroups and with nonpolycyclic maximal metabelian quotient; some direct products of groups; or the pure symmetric automorphism group. Using a different argument we show that the result also holds for 1-ended nonabelian nonsurface limit groups. In some cases, such as with the generalized Thompson`s groups F(n,0) and their finite direct products, H = Aut(G).

Novos registros na distribuição geográfica de anuros na floresta com araucária e considerações sobre suas vocalizações

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A dimension formula for reduced plethysms

The boson calculus formalism is used to construct realizations of basis states of irreducible representations of unitary groups taking as a paradigm the interacting boson models of atomic nuclei. These realizations, together with a theorem on plethysms for obtaining branching rules, allowed us to obtain a dimension formula for reduced plethysms. © 2005 IOP Publishing Ltd.

Estrutura cromossômica e caracterização cariotípica no complexo de espécies Synbranchus marmoratus (Teleostei, Synbranchiformes, Synbranchidae)

Pós-graduação em Ciências Biológicas (Genética) - IBB

Phylogenetic relationships of Malassezia species based on multilocus sequence analysis

Members of the genus Malassezia are lipophilic basidiomycetous yeasts, which are part of the normal cutaneous microbiota of humans and other warm-blooded animals. Currently, this genus consists of 14 species that have been characterized by phenetic and molecular methods. Although several molecular methods have been used to identify and/or differentiate Malassezia species, the sequencing of the rRNA genes and the chitin synthase-2 gene (CHS2) are the most widely employed. There is little information about the beta-tubulin gene in the genus Malassezia, a gene has been used for the analysis of complex species groups. The aim of the present study was to sequence a fragment of the beta-tubulin gene of Malassezia species and analyze their phylogenetic relationship using a multilocus sequence approach based on two rRNA genes (ITS including 5.8S rRNA and D1/D2 region of 26S rRNA) together with two protein encoding genes (CHS2 and beta-tubulin). The phylogenetic study of the partial beta-tubulin gene sequences indicated that this molecular marker can be used to assess diversity and identify new species. The multilocus sequence analysis of the four loci provides robust support to delineate species at the terminal nodes and could help to estimate divergence times for the origin and diversification of Malassezia species.

The M-theory origin of global properties of gauge theories

We show that global properties of gauge groups can be understood as geometric properties in M-theory. Different wrappings of a system of N M5-branes on a torus reduce to four-dimensional theories with AN−1 gauge algebra and different unitary groups. The classical properties of the wrappings determine the global properties of the gauge theories without the need to impose any quantum conditions. We count the inequivalent wrappings as they fall into orbits of the modular group of the torus, which correspond to the S-duality orbits of the gauge theories.

Classical Invariants for Principal Series and Isomorphisms of Root Data

We develop some new techniques to calculate the Schur indicator for self-dual irreducible Langlands quotients of the principal series representations. Using these techniques we derive some new formulas for the Schur indicator and the real-quaternionic indicator. We make progress towards developing an algorithm to decide whether or not two root data are isomorphic. When the derived group has cyclic center, we solve the isomorphism problem completely. An immediate consequence is a clean and precise classification theorem for connected complex reductive groups whose derived groups have cyclic center.

Domains in complex surfaces with non-compact automorphism groups

Let X be an arbitrary complex surface and D a domain in X that has a non-compact group of holomorphic automorphisms. A characterization of those domains D that admit a smooth, weakly pseudoconvex, finite type boundary orbit accumulation point is obtained.

3-MANIFOLD GROUPS, KÄHLER GROUPS AND COMPLEX SURFACES

Let G be a Kahler group admitting a short exact sequence 1 -> N -> G -> Q -> 1 where N is finitely generated. (i) Then Q cannot be non-nilpotent solvable. (ii) Suppose in addition that Q satisfies one of the following: (a) Q admits a discrete faithful non-elementary action on H-n for some n >= 2. (b) Q admits a discrete faithful non-elementary minimal action on a simplicial tree with more than two ends. (c) Q admits a (strong-stable) cut R such that the intersection of all conjugates of R is trivial. Then G is virtually a surface group. It follows that if Q is infinite, not virtually cyclic, and is the fundamental group of some closed 3-manifold, then Q contains as a finite index subgroup either a finite index subgroup of the three-dimensional Heisenberg group or the fundamental group of the Cartesian product of a closed oriented surface of positive genus and the circle. As a corollary, we obtain a new proof of a theorem of Dimca and Suciu in Which 3-manifold groups are Kahler groups? J. Eur. Math. Soc. 11 (2009) 521-528] by taking N to be the trivial group. If instead, G is the fundamental group of a compact complex surface, and N is finitely presented, then we show that Q must contain the fundamental group of a Seifert-fibered 3-manifold as a finite index subgroup, and G contains as a finite index subgroup the fundamental group of an elliptic fibration. We also give an example showing that the relation of quasi-isometry does not preserve Kahler groups. This gives a negative answer to a question of Gromov which asks whether Kahler groups can be characterized by their asymptotic geometry.

Damage diagnosis for complex steel truss bridges using multi-layer genetic algorithm

Considerate amount of research has proposed optimization-based approaches employing various vibration parameters for structural damage diagnosis. The damage detection by these methods is in fact a result of updating the analytical structural model in line with the current physical model. The feasibility of these approaches has been proven. But most of the verification has been done on simple structures, such as beams or plates. In the application on a complex structure, like steel truss bridges, a traditional optimization process will cost massive computational resources and lengthy convergence. This study presents a multi-layer genetic algorithm (ML-GA) to overcome the problem. Unlike the tedious convergence process in a conventional damage optimization process, in each layer, the proposed algorithm divides the GA’s population into groups with a less number of damage candidates; then, the converged population in each group evolves as an initial population of the next layer, where the groups merge to larger groups. In a damage detection process featuring ML-GA, as parallel computation can be implemented, the optimization performance and computational efficiency can be enhanced. In order to assess the proposed algorithm, the modal strain energy correlation (MSEC) has been considered as the objective function. Several damage scenarios of a complex steel truss bridge’s finite element model have been employed to evaluate the effectiveness and performance of ML-GA, against a conventional GA. In both single- and multiple damage scenarios, the analytical and experimental study shows that the MSEC index has achieved excellent damage indication and efficiency using the proposed ML-GA, whereas the conventional GA only converges at a local solution.

Four group decodable differential scaled unitary linear space-time codes

Differential Unitary Space-Time Block codes (STBCs) offer a means to communicate on the Multiple Input Multiple Output (MIMO) channel without the need for channel knowledge at both the transmitter and the receiver. Recently Yuen-Guan-Tjhung have proposed Single-Symbol-Decodable Differential Space-Time Modulation based on Quasi-Orthogonal Designs (QODs) by replacing the original unitary criterion by a scaled unitary criterion. These codes were also shown to perform better than differential unitary STBCs from Orthogonal Designs (ODs). However the rate (as measured in complex symbols per channel use) of the codes of Yuen-Guan-Tjhung decay as the number of transmit antennas increase. In this paper, a new class of differential scaled unitary STBCs for all even number of transmit antennas is proposed. These codes have a rate of 1 complex symbols per channel use, achieve full diversity and moreover they are four-group decodable, i.e., the set of real symbols can be partitioned into four groups and decoding can be done for the symbols in each group separately. Explicit construction of multidimensional signal sets that yield full diversity for this new class of codes is also given.