Isoparametric functions and exotic spheres

The first part of the paper is to improve the fundamental theory of isoparametric functions on general Riemannian manifolds. Next we focus our attention on exotic spheres, especially on "exotic" 4-spheres (if exist) and the Gromoll-Meyer sphere. In particular, as one of main results we prove: there exists no properly transnormal function on any exotic 4-sphere if it exists. Furthermore, by projecting an $S^3$-invariant isoparametric function on $Sp(2)$, we construct a properly transnormal but not an isoparametric function on the Gromoll-Meyer sphere with two points as the focal varieties.Comment: 21 pages, to appear in Journal f\"ur die reine und angewandte Mathematik (Crelles Journal

Boston University Tuba Quartet, April 10, 1986

This is the concert program of the Boston University Tuba Quartet performance on Thursday, April 10, 1986 at 6:00 p.m., at Concert Hall, 855 Commonwealth Avenue. Works performed were Ronde and Salterelle by Tielman Susato, Fugue in G minor by Johann Sebastian Bach, The Colors Churn Within the Thunderstorm by Franz Schubert, The Two Ways of Virtue by F. Schubert, In Majesty Upon the Sublime Throne by F. Schubert, Kierkegaard by Meyer Kupferman, Brass Tacks by Lennie Niehaus, Wonderland Duets by Raymond Luedeke, Music 4 Tubas by John Stevens, and El Capitan by John Philip Sousa. Digitization for Boston University Concert Programs was supported by the Boston University Humanities Library Endowed Fund

Theoretical spectroscopy: Full quantum dynamical study of the vibrational structure of hydrated hydroxide

In many processes, the impact of nuclear quantum phenomena cannot be neglected if a physically correct simulation is aimed for [1]. This quantum description of the nuclear motion is usually obtained by mapping the system onto a grid, thus implying a discretisation of the configuration space. As a consequence, all quantities take the form of high-order tensors. Unfortunately, multidimensional representations imply an exponential scaling of data and the concomitant number of operations with system size as well as the difficulty of computing multidimensional integrals [2]. Solutions to these issues, in particular when considering the representation of the potential energy surface, exist in the form of tensor-decomposition schemes. We present the recently developed the Multigrid POTFIT (MGPF) algorithm [3] which alleviates the exponential scaling by avoiding the calculations on the full grid. Moreover, we introduceour latest improvements to the algorithm which provide numerical stability and higher accuracy through the use of non-product grids for combined modes [4]. We illustrate the power of the MGPF algorithm in conjunction with the Multiconfiguration Time-Dependent Hartree (MCTDH) method in the case of the full-dimensional (9D) study of the vibrational structure [5] and the computation of the infrared spectrum [6] of the hydrated hydroxide complex (H3O2-). [1] Fabien Gatti (Ed.) in Molecular Quantum Dynamics From Theory to Applications. Springer (2014). [2] H.-D. Meyer, F. Gatti, G. A. Worth (Eds.) Multidimensional Quantum Dynamics: MCTDH Theory and Applications, Wiley (2009). [3] D. Peláez, H.D. Meyer, The multigrid POTFIT (MGPF) method: Grid representations of potentials for quantum dynamics of large systems, J. Chem. Phys., 138, 014108 (2013). [4] D. Peláez, H.D. Meyer (in preparation) [5] D. Peláez, K. Sadri, H.-D. Meyer, Full-dimensional MCTDH/MGPF study of the ground and lowest lying vibrational states of the bihydroxide complex, Spectrochimica Acta Part A,119, 42 (2014). [6] D. Peláez, H.D. Meyer, On the infrared absorption spectrum of the hydrated hydroxide (H3O2-) cluster anion, Chem. Phys., (in press) (2016).Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Микроэлементный состав круглогодично вегетирующих макро-водорослей каменистой литорали оз. Байкал (Россия)

Приведены результаты исследования микроэлементного состава вегетирующих круглый год водорослей литорали Южного Байкала. Установлено, что в минеральном составе Cladophora compacta (C. Meyer) C. Meyer, Chaetocladiella pumila (C. Meyer) C. Meyer et Skabitsch. преобладают Mn, Sr, Ti; в Tolypothrix distorta (Fl. Dan) Kütz. f. distorta, Schizothrix sp. – Ti и Sr, а в Stratonostoc verrucosum (Vauch.) Elenk. f. verrucosum – Sr и Zn. Для исследуемых видов характерно групповое концентрирование микроэлементов. По сравнению с водой, изучаемые виды аккумулируют Ti>La>Ce>Mn,Y. C. compacta, Ch. pumila и Schizothrix sp. выделяются из общего ряда способностью аккумулировать Rb, Schizothrix sp. – Cd и Cu. По сравнению с донными отложениями, водоросли накапливают Mo. Кроме того, для Ch. pumila, T. distorta, S. verrucosum характерно концентрирование Zn, для Ch. pumila и Schizothrix sp. – Cd, для Schizothrix sp. – Cu. По степени накопления микроэлементов относительно воды водоросли образуют следующий ряд: T. distorta > Schizothrix sp.> Ch. pumila > C. compacta > S. verrucosum; относительно донных отложений – Ch. pumila > C. compacta > Schizothrix sp.> T. distorta > S. verrucosum.The results of examination of trace element composition of all-the-year-round vegetating algae on the stony littoral of Lake Baikal are presented. It has been found out that the mineral composition of Cladophora compacta (C. Meyer) C. Meyer, Chaetocladella pumila (C. Meyer) C. Meyer et Skabitsch. is dominated by Mn, Sr, Ti; Tolypothrix distorta (Fl. Dan) Kütz. f. distorta, Schizothrix sp. by Ti and Sr, Stratonostoc verrucosum (Vauch.) Elenk. f. verrucosum by Sr and Zn. In these species trace elements concentrate in groups. With respect to water, the species under study concentrate Ti>La>Ce>Mn,Y. C. compacta, Ch. pumila and Schizothrix sp. stand out by their ability to accumulate Rb, Schizothrix sp. - Cd and Cu. In comparison to bottom sediments, algae accumulate Mo, and moreover, Ch. pumila, T. distorta, S. verrucosum concentrate Zn, Ch. pumila, Schizothrix sp. Cd and Schizothrix sp. - Cu. According to the intensity of concentrating trace elements with respect to water, the algae may be presented in the following sequence: T. distorta > Schizothrix sp. > Ch. pumila > C compacta > S. verrucosum; with respect to bottom sediments Ch. pumila > C. compacta > Schizothrix sp. > T. distorta > S. verrucosum

Representation Theorems for Quadratic F{\cal F}-Consistent Nonlinear Expectations

In this paper we extend the notion of ``filtration-consistent nonlinear expectation" (or "${\cal F}$-consistent nonlinear expectation") to the case when it is allowed to be dominated by a $g$-expectation that may have a quadratic growth. We show that for such a nonlinear expectation many fundamental properties of a martingale can still make sense, including the Doob-Meyer type decomposition theorem and the optional sampling theorem. More importantly, we show that any quadratic ${\cal F}$-consistent nonlinear expectation with a certain domination property must be a quadratic $g$-expectation. The main contribution of this paper is the finding of the domination condition to replace the one used in all the previous works, which is no longer valid in the quadratic case. We also show that the representation generator must be deterministic, continuous, and actually must be of the simple form

AMBER: Assessment of Metagenome BinnERs

Meyer F, Hofmann P, Belmann P, et al. AMBER: Assessment of Metagenome BinnERs. GigaScience. 2018;7(6): giy069