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The moduli space must not only be Kähler, but also the Kähler form must lift to integral cohomology. Such manifolds are called Hodge manifolds . The first example appeared in the 1979 article "Spontaneous Symmetry Breaking and Higgs Effect in Supergravity Without Cosmological Constant" [ 4 ] and the general statement appeared 3 years later in ...
When the bundles have rank 1 and degree zero, the study of coarse moduli space is the study of the Jacobian variety. In applications to physics, the number of moduli of vector bundles and the closely related problem of the number of moduli of principal G-bundles has been found to be significant in gauge theory. [citation needed]
FORM was started in 1984 as a successor to Schoonschip, an algebra engine developed by M. Veltman. It was initially coded in FORTRAN 77, but rewritten in C before the release of version 1.0 in 1989. Version 2.0 was released in 1991. The version 3.0 of FORM has been publicized in 2000.
A modular form f that vanishes at q = 0 (equivalently, a 0 = 0, also paraphrased as z = i∞) is called a cusp form (Spitzenform in German). The smallest n such that a n ≠ 0 is the order of the zero of f at i∞. A modular unit is a modular function whose poles and zeroes are confined to the cusps. [5]
"High school physics textbooks" (PDF). Reports on high school physics. American Institute of Physics; Zitzewitz, Paul W. (2005). Physics: principles and problems. New York: Glencoe/McGraw-Hill. ISBN 978-0078458132
Illustration of uniform compression. The bulk modulus (or or ) of a substance is a measure of the resistance of a substance to bulk compression.It is defined as the ratio of the infinitesimal pressure increase to the resulting relative decrease of the volume.
The current version is a revised version of the original 1960 textbook Physics for Students of Science and Engineering by Halliday and Resnick, which was published in two parts (Part I containing Chapters 1-25 and covering mechanics and thermodynamics; Part II containing Chapters 26-48 and covering electromagnetism, optics, and introducing ...
For the ring R = Z[√−5], both the module R and its submodule M generated by 2 and 1 + √−5 are indecomposable. While R is not isomorphic to M, R ⊕ R is isomorphic to M ⊕ M; thus the images of the M summands give indecomposable submodules L 1, L 2 < R ⊕ R which give a different decomposition of R ⊕ R.