DOUBLING HOMOTOPY K3 SURFACES

Abstract We define solitons for the generalized Ricci flow on an exact Courant algebroid. We then define a family of flows for left-invariant Dorfman brackets on an exact Courant algebroid over a simply connected nilpotent Lie group, generalizing the bracket flows for nilpotent Lie brackets in a way that might make this new family of flows useful for the study of generalized geometric flows such as the generalized Ricci flow. We provide explicit examples of both constructions on the Heisenberg group. We also discuss solutions to the generalized Ricci flow on the Heisenberg group.

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Every algebraic Kummer surface is the K3-cover of an Enriques surface

Nagoya Mathematical Journal ◽

10.1017/s0027763000003019 ◽

1990 ◽

Vol 118 ◽

pp. 99-110 ◽

Cited By ~ 11

Author(s):

Jong Hae Keum

Keyword(s):

Crucial Role ◽

K3 Surfaces ◽

Abelian Surface ◽

Enriques Surface ◽

Kummer Surface ◽

3 Dimensional ◽

Complex Torus ◽

Kummer Surfaces ◽

Dimension 2 ◽

Simply Connected

A Kummer surface is the minimal desingularization of the surface T/i, where T is a complex torus of dimension 2 and i the involution automorphism on T. T is an abelian surface if and only if its associated Kummer surface is algebraic. Kummer surfaces are among classical examples of K3-surfaces (which are simply-connected smooth surfaces with a nowhere-vanishing holomorphic 2-form), and play a crucial role in the theory of K3-surfaces. In a sense, all Kummer surfaces (resp. algebraic Kummer surfaces) form a 4 (resp. 3)-dimensional subset in the 20 (resp. 19)-dimensional family of K3-surfaces (resp. algebraic K3 surfaces).

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Serre–Tate theory for Calabi–Yau varieties

Journal für die reine und angewandte Mathematik (Crelles Journal) ◽

10.1515/crelle-2021-0041 ◽

2021 ◽

Vol 0 (0) ◽

Author(s):

Piotr Achinger ◽

Maciej Zdanowicz

Keyword(s):

Weak Sense ◽

Higher Dimensions ◽

Explicit Construction ◽

K3 Surfaces ◽

Canonical Coordinates ◽

Canonical Class ◽

Witt Vectors ◽

Hodge Filtration ◽

Relative Version ◽

Simply Connected

Abstract Classical Serre–Tate theory describes deformations of ordinary abelian varieties. It implies that every such variety has a canonical lift to characteristic zero and equips the base of its universal deformation with a Frobenius lifting and canonical multiplicative coordinates. A variant of this theory has been obtained for ordinary K3 surfaces by Nygaard and Ogus. In this paper, we construct canonical liftings modulo p 2 {p^{2}} of varieties with trivial canonical class which are ordinary in the weak sense that the Frobenius acts bijectively on the top cohomology of the structure sheaf. Consequently, we obtain a Frobenius lifting on the moduli space of such varieties. The quite explicit construction uses Frobenius splittings and a relative version of Witt vectors of length two. If the variety has unobstructed deformations and bijective first higher Hasse–Witt operation, the Frobenius lifting gives rise to canonical coordinates. One of the key features of our liftings is that the crystalline Frobenius preserves the Hodge filtration. We also extend Nygaard’s approach from K3 surfaces to higher dimensions, and show that no non-trivial families of such varieties exist over simply connected bases with no global one-forms.

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Microstructure and crystal symmetry of Pb2Sr2(Y/Ca)Cu3O9−δ

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100173455 ◽

1990 ◽

Vol 48 (4) ◽

pp. 64-65

Author(s):

Y. P. Lin ◽

J. S. Xue ◽

J. E. Greedan

Keyword(s):

Electron Diffraction ◽

High Temperature Superconductors ◽

Carbon Film ◽

Basic Structure ◽

Crystal Symmetry ◽

X Ray Diffraction ◽

X Ray ◽

Space Groups ◽

New Family ◽

Convergent Beam

A new family of high temperature superconductors based on Pb2Sr2YCu3O9−δ has recently been reported. One method of improving Tc has been to replace Y partially with Ca. Although the basic structure of this type of superconductors is known, the detailed structure is still unclear, and various space groups has been proposed. In our work, crystals of Pb2Sr2YCu3O9−δ with dimensions up to 1 × 1 × 0.25.mm and with Tc of 84 K have been grown and their superconducting properties described. The defects and crystal symmetry have been investigated using electron microscopy performed on crushed crystals supported on a holey carbon film.Electron diffraction confirmed x-ray diffraction results which showed that the crystals are primitive orthorhombic with a=0.5383, b=0.5423 and c=1.5765 nm. Convergent Beam Electron Diffraction (CBED) patterns for the and axes are shown in Figs. 1 and 2 respectively.

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A new family of fluorescent calcium indicators designed to resist leakage or for measuring calcium near membranes

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100168578 ◽

1994 ◽

Vol 52 ◽

pp. 168-169

Author(s):

Martin Poenie ◽

Akwasi Minta ◽

Charles Vorndran

Keyword(s):

Metal Binding ◽

Acetoxymethyl Ester ◽

Binding Properties ◽

Fura 2 ◽

New Family ◽

Anion Transporter ◽

Calcium Indicator ◽

Calcium Indicators ◽

High Calcium ◽

Intracellular Compartmentalization

The use of fura-2 as an intracellular calcium indicator is complicated by problems of rapid dye leakage and intracellular compartmentalization which is due to a probenecid sensitive anion transporter. In addition there is increasing evidence for localized microdomains of high calcium signals which may not be faithfully reported by fura-2.We have developed a new family of fura-2 analogs aimed at addressing some of these problems. These new indicators are based on a modified bapta which can be readily derivatized to produce fura-2 analogs with a variety of new properties. The modifications do not affect the chromophore and have little impact on the spectral and metal binding properties of the indicator. One of these new derivatives known as FPE3 is a zwitterionic analog of fura-2 that can be loaded into cells as an acetoxymethyl ester and whose retention in cells is much improved. The improved retention of FPE3 is important for both cuvettebased measurements of cell suspensions and for calcium imaging.

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Scanning tunneling microscopy and atomic force microscopy: New tools for biology

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100155864 ◽

1989 ◽

Vol 47 ◽

pp. 778-779

Author(s):

CE Bracker ◽

P. K. Hansma

Keyword(s):

Physical Property ◽

Scanning Probe ◽

Scanning Tunneling ◽

Small Scale ◽

Tunneling Microscopy ◽

Force Microscopy ◽

New Family ◽

Small Probe ◽

Atomic Force ◽

Transmission Electron

A new family of scanning probe microscopes has emerged that is opening new horizons for investigating the fine structure of matter. The earliest and best known of these instruments is the scanning tunneling microscope (STM). First published in 1982, the STM earned the 1986 Nobel Prize in Physics for two of its inventors, G. Binnig and H. Rohrer. They shared the prize with E. Ruska for his work that had led to the development of the transmission electron microscope half a century earlier. It seems appropriate that the award embodied this particular blend of the old and the new because it demonstrated to the world a long overdue respect for the enormous contributions electron microscopy has made to the understanding of matter, and at the same time it signalled the dawn of a new age in microscopy. What we are seeing is a revolution in microscopy and a redefinition of the concept of a microscope.Several kinds of scanning probe microscopes now exist, and the number is increasing. What they share in common is a small probe that is scanned over the surface of a specimen and measures a physical property on a very small scale, at or near the surface. Scanning probes can measure temperature, magnetic fields, tunneling currents, voltage, force, and ion currents, among others.

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Porphyrin-functionalized coordination star polymers and their potential applications in photodynamic therapy

Polymer Chemistry ◽

10.1039/c9py01391a ◽

2019 ◽

Vol 10 (45) ◽

pp. 6116-6121 ◽

Cited By ~ 3

Author(s):

Tan Ji ◽

Lei Xia ◽

Wei Zheng ◽

Guang-Qiang Yin ◽

Tao Yue ◽

...

Keyword(s):

Photodynamic Therapy ◽

Self Assembly ◽

Star Polymers ◽

New Family ◽

Potential Applications

We present a new family of porphyrin-functionalized coordination star polymers prepared through combination of coordination-driven self-assembly and post-assembly polymerization. Their self-assembly behaviour in water and potential for photodynamic therapy were demonstrated.

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