Generalized iterated wreath products of symmetric groups and generalized rooted trees correspondence

Consider the generalized iterated wreath product $S_{r_1}\wr \ldots \wr S_{r_k}$ of symmetric groups. We give a complete description of the traversal for the generalized iterated wreath product. We also prove an existence of a bijection between the equivalence classes of ordinary irreducible representations of the generalized iterated wreath product and orbits of labels on certain rooted trees. We find a recursion for the number of these labels and the degrees of irreducible representations of the generalized iterated wreath product. Finally, we give rough upper bound estimates for fast Fourier transforms.Comment: 18 pages, to appear in Advances in the Mathematical Sciences. arXiv admin note: text overlap with arXiv:1409.060

Generalized iterated wreath products of cyclic groups and rooted trees correspondence

Consider the generalized iterated wreath product $\mathbb{Z}_{r_1}\wr \mathbb{Z}_{r_2}\wr \ldots \wr \mathbb{Z}_{r_k}$ where $r_i \in \mathbb{N}$. We prove that the irreducible representations for this class of groups are indexed by a certain type of rooted trees. This provides a Bratteli diagram for the generalized iterated wreath product, a simple recursion formula for the number of irreducible representations, and a strategy to calculate the dimension of each irreducible representation. We calculate explicitly fast Fourier transforms (FFT) for this class of groups, giving literature's fastest FFT upper bound estimate.Comment: 15 pages, to appear in Advances in the Mathematical Science

Arsenite sorption and co-precipitation with calcite

Sorption of As(III) by calcite was investigated as a function of As(III) concentration, time and pH. The sorption isotherm, i.e. the log As(III) vs. log [As(OH)3 degrees / Assat] plot is S-shaped and has been modelled on an extended version of the surface precipitation model. At low concentrations, As(OH)3 degrees is adsorbed by complexation to surface Ca surface sites, as previously described by the X-ray standing wave technique. The inflexion point of the isotherm, where As(OH)3 degrees is limited by the amount of surface sites (ST), yields 6 sites nm-2 in good agreement with crystallographic data. Beyond this value, the amount of sorbed arsenic increases linearly with solution concentration, up to the saturation of arsenic with respect to the precipitation of CaHAsO3(s). The solid solutions formed in this concentration range were examined by X-ray and neutron diffraction. The doped calcite lattice parameters increase with arsenic content while c/a ratio remains constant. Our results made on bulk calcite on the atomic displacement of As atoms along [0001] direction extend those published by Cheng et al., (1999) on calcite surface. This study provides a molecular-level explanation for why As(III) is trapped by calcite in industrial treatments.Comment: 9 page

Note on the thermodynamic Bethe Ansatz approach to the quantum phase diagram of the strong coupling ladder compounds

We investigate the low-temperature phase diagram of the exactly solved su(4) two-leg spin ladder as a function of the rung coupling $J_{\perp}$ and magnetic field $H$ by means of the thermodynamic Bethe Ansatz (TBA). In the absence of a magnetic field the model exhibits three quantum phases, while in the presence of a strong magnetic field there is no singlet ground state for ferromagnetic rung coupling. For antiferromagnetic rung coupling, there is a gapped phase in the regime H H_{c2} and a Luttinger liquid magnetic phase in the regime H_{c1} < H < H_{c2}. The critical behaviour derived using the TBA is consistent with the existing experimental, numerical and perturbative results for the strong coupling ladder compounds. This includes the spin excitation gap and the critical fields H_{c1} and H_{c2}, which are in excellent agreement with the experimental values for the known strong coupling ladder compounds (5IAP)_2CuBr_4 2H_2 O, Cu_2(C_5 H_{12} N_2)_2 Cl_4 and (C_5 H_{12} N)_2 CuBr_4. In addition we predict the spin gap $\Delta \approx J_{\perp}-{1/2}J_{\parallel}$ for the weak coupling compounds with $J_{\perp} \sim J_{\parallel}$, such as (VO)_2 P_2 O_7, and also show that the gap opens for arbitrary $J_{\perp}/ J_{\parallel}$.Comment: 10 pages, 3 figure

Phase diagram of the su(8) quantum spin tube

We calculate the phase diagram of an integrable anisotropic 3-leg quantum spin tube connected to the su(8) algebra. We find several quantum phase transitions for antiferromagnetic rung couplings. Their locations are calculated exactly from the Bethe Ansatz solution and we discuss the nature of each of the different phases.Comment: 10 pages, RevTeX, 1 postscript figur

A new method of measuring the impedance of the human respiratory system at moderate frequencies

The stability of aircrew breathing equipment depends not only on the stability of the oxygen regulator, but also on the impedance of the system it feeds, which includes the user's respiratory system. A method of measuring the human respiratory impedance, in the range 5-90 c/s, by comparing oscillating pressures at two points in an external reference system, is described; and results are given for nose and mouth, heavy and light, breathing. The effect of altitude, and of increased external resistance to breathing are briefly discussed. The importance of correct representation of man's impedance in dynamic testing of oxygen equipment is illustrated by reference to the characteristics of a present-day simulator and system, and an improved type of simulator is suggested

Celebrating Cercignani's conjecture for the Boltzmann equation

Cercignani's conjecture assumes a linear inequality between the entropy and entropy production functionals for Boltzmann's nonlinear integral operator in rarefied gas dynamics. Related to the field of logarithmic Sobolev inequalities and spectral gap inequalities, this issue has been at the core of the renewal of the mathematical theory of convergence to thermodynamical equilibrium for rarefied gases over the past decade. In this review paper, we survey the various positive and negative results which were obtained since the conjecture was proposed in the 1980s.Comment: This paper is dedicated to the memory of the late Carlo Cercignani, powerful mind and great scientist, one of the founders of the modern theory of the Boltzmann equation. 24 pages. V2: correction of some typos and one ref. adde

Application of phage display to high throughput antibody generation and characterization.

We have created a high quality phage display library containing over 1010 human antibodies and describe its use in the generation of antibodies on an unprecedented scale. We have selected, screened and sequenced over 38,000 recombinant antibodies to 292 antigens, yielding over 7,200 unique clones. 4,400 antibodies were characterized by specificity testing and detailed sequence analysis and the data/clones are available online. Sensitive detection was demonstrated in a bead based flow cytometry assay. Furthermore, positive staining by immunohistochemistry on tissue microarrays was found for 37% (143/381) of antibodies. Thus, we have demonstrated the potential of and illuminated the issues associated with genome-wide monoclonal antibody generation.RIGHTS : This article is licensed under the BioMed Central licence at http://www.biomedcentral.com/about/license which is similar to the 'Creative Commons Attribution Licence'. In brief you may : copy, distribute, and display the work; make derivative works; or make commercial use of the work - under the following conditions: the original author must be given credit; for any reuse or distribution, it must be made clear to others what the license terms of this work are

Ensembl Genomes 2013: scaling up access to genome-wide data

Ensembl Genomes (http://www.ensemblgenomes.org) is an integrating resource for genome-scale data from non-vertebrate species. The project exploits and extends technologies for genome annotation, analysis and dissemination, developed in the context of the vertebrate-focused Ensembl project, and provides a complementary set of resources for non-vertebrate species through a consistent set of programmatic and interactive interfaces. These provide access to data including reference sequence, gene models, transcriptional data, polymorphisms and comparative analysis. This article provides an update to the previous publications about the resource, with a focus on recent developments. These include the addition of important new genomes (and related data sets) including crop plants, vectors of human disease and eukaryotic pathogens. In addition, the resource has scaled up its representation of bacterial genomes, and now includes the genomes of over 9000 bacteria. Specific extensions to the web and programmatic interfaces have been developed to support users in navigating these large data sets. Looking forward, analytic tools to allow targeted selection of data for visualization and download are likely to become increasingly important in future as the number of available genomes increases within all domains of life, and some of the challenges faced in representing bacterial data are likely to become commonplace for eukaryotes in future

A mathematical and computational review of Hartree-Fock SCF methods in Quantum Chemistry

We present here a review of the fundamental topics of Hartree-Fock theory in Quantum Chemistry. From the molecular Hamiltonian, using and discussing the Born-Oppenheimer approximation, we arrive to the Hartree and Hartree-Fock equations for the electronic problem. Special emphasis is placed in the most relevant mathematical aspects of the theoretical derivation of the final equations, as well as in the results regarding the existence and uniqueness of their solutions. All Hartree-Fock versions with different spin restrictions are systematically extracted from the general case, thus providing a unifying framework. Then, the discretization of the one-electron orbitals space is reviewed and the Roothaan-Hall formalism introduced. This leads to a exposition of the basic underlying concepts related to the construction and selection of Gaussian basis sets, focusing in algorithmic efficiency issues. Finally, we close the review with a section in which the most relevant modern developments (specially those related to the design of linear-scaling methods) are commented and linked to the issues discussed. The whole work is intentionally introductory and rather self-contained, so that it may be useful for non experts that aim to use quantum chemical methods in interdisciplinary applications. Moreover, much material that is found scattered in the literature has been put together here to facilitate comprehension and to serve as a handy reference.Comment: 64 pages, 3 figures, tMPH2e.cls style file, doublesp, mathbbol and subeqn package