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Applications of Groups and Isomorphic Groups to Topics in the Standard Curriculum, Grades 9-11: Part II

The Mathematics Teacher, 1975
It is possible to form a set in an infinite additive group by beginning with any nonzero real a and adding it to itself over and over again, then including zero and the opposites of all numbers in the set. We call such a set the set of integral multiples of a. If a = 3, then here is such a set.
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Type fuzzy quantifiers determined by fuzzy measures defined on residuated lattices. Part II. Permutation and isomorphism invariances

Fuzzy Sets and Systems, 2014
Abstract We study the properties of permutation invariance and isomorphism invariance of fuzzy quantifiers of type 〈 1 , 1 〉 defined using fuzzy measures and integrals. These properties hold if fuzzy quantifiers are invariant with respect to permutations (bijective mappings) on the universe of discourse (permutation invariance) and with ...
Antonín Dvorák, Michal Holcapek
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ChemInform Abstract: Liquid‐Crystalline Alicyclic Compounds. Part 3. Synthesis and Isomorphism of Ethers and Esters Containing the Phenylcyclohexane Fragment.

ChemInform, 1993
AbstractChemInform is a weekly Abstracting Service, delivering concise information at a glance that was extracted from about 100 leading journals. To access a ChemInform Abstract of an article which was published elsewhere, please select a “Full Text” option. The original article is trackable via the “References” option.
L. A. KARAMYSHEVA   +5 more
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Some Implications of the Pitch Class/Order Number Isomorphism Inherent in the Twelve-Tone System: Part One

Perspectives of New Music, 1988
TN "TWELVE-TONE INVARIANTS as Compositional Determinants" Milton Babbitt described the twelve-tone system in terms of operations upon pairings of the twelve pitch classes with twelve order numbers.1 In doing so he provided a basis for studying the twelve-tone system that has far-reaching implications.2 Viewing the twelve-tone system from the basis of ...
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Isomorphous Substitution of Si in Zeolite Single Crystals. Part II. On The Boron Distribution and Coordination In [B]-ZSM-5

1989
FTIR microscope measurements in the transmission mode on single crystal sheets of [B]-ZSM-5 have been used to study the lattice boron distribution and coordination in the crystals. The infrared scans indicate that a homogeneous boron distribution is present in the [B]-ZSM-5 crystals, which contained 0–4 B/uc.
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