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Journal articles on the topic 'Stable isomorphism'

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Author: Grafiati

Published: 10 December 2022

Last updated: 28 January 2023

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1

Eleftherakis, G. K. "Morita Equivalence of Nest Algebras." MATHEMATICA SCANDINAVICA 113, no. 1 (September 1, 2013): 83. http://dx.doi.org/10.7146/math.scand.a-15483.

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Let $\mathscr{N}_1$ (resp. $\mathscr{N}_2$) be a nest, $A$ (resp. $B$) be the corresponding nest algebra, $A_0$ (resp. $B_0$) be the subalgebra of compact operators. We prove that the nests $\mathscr{N}_1, \mathscr{N}_2$ are isomorphic if and only if $A$ and $B$ are weakly-$*$ Morita equivalent if and only if $A_0$ and $ B_0$ are strongly Morita equivalent. We characterize the nest isomorphisms which implement stable isomorphism between the corresponding nest algebras.

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2

SØRENSEN, ADAM P. W. "Geometric classification of simple graph algebras." Ergodic Theory and Dynamical Systems 33, no. 4 (July 5, 2012): 1199–220. http://dx.doi.org/10.1017/s0143385712000260.

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AbstractInspired by Franks’ classification of irreducible shifts of finite type, we provide a short list of allowed moves on graphs that preserve the stable isomorphism class of the associated $C^*$-algebras. We show that if two graphs have stably isomorphic and simple unital algebras then we can use these moves to transform one into the other.

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3

Eleftherakis, G. K., V. I. Paulsen, and I. G. Todorov. "Stable isomorphism of dual operator spaces." Journal of Functional Analysis 258, no. 1 (January 2010): 260–78. http://dx.doi.org/10.1016/j.jfa.2009.06.034.

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4

Murray, Michael K., and Daniel Stevenson. "Bundle Gerbes: Stable Isomorphism and Local Theory." Journal of the London Mathematical Society 62, no. 3 (December 2000): 925–37. http://dx.doi.org/10.1112/s0024610700001551.

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5

Gupta, Sushmita, and Sanjukta Roy. "Stable Matching Games: Manipulation via Subgraph Isomorphism." Algorithmica 80, no. 9 (October 27, 2017): 2551–73. http://dx.doi.org/10.1007/s00453-017-0382-5.

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6

Friedman, Sy-David, Tapani Hyttinen, and Agatha C. Walczak-Typke. "Potential isomorphism of elementary substructures of a strictly stable homogeneous model." Journal of Symbolic Logic 76, no. 3 (September 2011): 987–1004. http://dx.doi.org/10.2178/jsl/1309952530.

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AbstractThe results herein form part of a larger project to characterize the classification properties of the class of submodels of a homogeneous stable diagram in terms of the solvability (in the sense of [1]) of the potential isomorphism problem for this class of submodels.We restrict ourselves to locally saturated submodels of the monster model , of some power π. We assume that in Gödel's constructive universe , π is a regular cardinal at least the successor of the first cardinal in which , is stable.We show that the collection of pairs of submodels in as above which are potentially isomorphic with respect to certain cardinal-preserving extensions of is equiconstructible with 0#. As 0# is highly “transcendental” over , this provides a very strong statement to the effect that potential isomorphism for this class of models not only fails to be set-theoretically absolute, but is of high (indeed of the highest possible) complexity.The proof uses a novel method that does away with the need for a linear order on the skeleton.

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7

Wei, Changguo. "Note on the Kasparov Product of C*-algebra Extensions." Canadian Mathematical Bulletin 56, no. 4 (December 1, 2013): 870–80. http://dx.doi.org/10.4153/cmb-2012-001-3.

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AbstractUsing the Dadarlat isomorphism, we give a characterization for the Kasparov product of C*-algebra extensions. A certain relation between KK(A;𝓠(B)) and KK(A;𝓠(KB)) is also considered when B is not stable, and it is proved that KK(A;𝓠(B)) and KK(A;𝓠(KB)) are not isomorphic in general.

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8

Carlsen, Toke Meier, Efren Ruiz, and Aidan Sims. "Equivalence and stable isomorphism of groupoids, and diagonal-preserving stable isomorphisms of graph $C^*$-algebras and Leavitt path algebras." Proceedings of the American Mathematical Society 145, no. 4 (October 27, 2016): 1581–92. http://dx.doi.org/10.1090/proc/13321.

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9

Wiegand, Roger, and Sylvia Wiegand. "Stable isomorphism of modules over one-dimensional rings." Journal of Algebra 107, no. 2 (May 1987): 425–35. http://dx.doi.org/10.1016/0021-8693(87)90097-4.

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10

Zhang, Shuang. "Stable Isomorphism of Hereditary C ∗ -Subalgebras and Stable Equivalence of Open Projections." Proceedings of the American Mathematical Society 105, no. 3 (March 1989): 677. http://dx.doi.org/10.2307/2046918.

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11

Zhang, Shuang. "Stable isomorphism of hereditary $C\sp *$-subalgebras and stable equivalence of open projections." Proceedings of the American Mathematical Society 105, no. 3 (March 1, 1989): 677. http://dx.doi.org/10.1090/s0002-9939-1989-0961418-7.

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12

Chirvasitu, Alexandru. "Rigidity results for automorphisms of Hardy--Toeplitz C∗-algebras." Journal of Operator Theory 87, no. 1 (March 15, 2022): 295–317. http://dx.doi.org/10.7900/jot.2020sep17.2307.

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We prove a number of results on the automorphisms and isomorphisms between Hardy--Toeplitz algebras T(D) associated to bounded symmetric domains D: that the stable isomorphism class of T(D) determines D (even when it is reducible), that for reducible domains D=D1×⋯×Ds the automorphisms of the Shilov boundary ˇS(D) induced by those of T(D) permute the Shilov boundaries ˇS(Di), and that by contrast to arbitrary solvable algebras, automorphisms of T(D) that are trivial on their character spaces ˇS(D) are trivial on the entire spectrum ˆT(D).

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13

Wilson, S. M. J. "The isomorphism class of a set of lattices." Mathematical Proceedings of the Cambridge Philosophical Society 105, no. 2 (March 1989): 197–210. http://dx.doi.org/10.1017/s0305004100067682.

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AbstractLet R be a Dedekind domain with field of quotients K. Let A be a finite-dimensional K-algebra. We consider isomorphism classes and genera in a category whose objects are indexed sets of full R-lattices in some ambient A-module and whose morphisms are the A-homomorphisms of the ambient A-modules which map each lattice into its corresponding lattice. We find conditions under which the stable A-isomorphism class of one particular lattice in an indexed set will determine the stable class of the indexed set within its genus. We apply our methods to show that if L/K is a tame Galois extension of algebraic number fields then the stable isomorphism class of the set of ambiguous ideals in L considered as Galois modules over K is determined by the class of the ring of integers in L together with the inertia subgroups and their standard representations over the respective residue fields of R.

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14

Rutherford, Daniel, and Michael Sullivan. "Cellular Legendrian contact homology for surfaces, part II." International Journal of Mathematics 30, no. 07 (June 2019): 1950036. http://dx.doi.org/10.1142/s0129167x19500368.

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This paper is a continuation of [Cellular computation of Legendrian contact homology for surfaces, preprint (2016)]. For Legendrian surfaces in [Formula: see text]-jet spaces, we prove that the Cellular DGA defined in [Cellular computation of Legendrian contact homology for surfaces, preprint (2016)] is stable tame isomorphic to the Legendrian contact homology DGA, modulo the explicit construction of a specific Legendrian surface. In [Cellular computation of Legendrian contact homology for surfaces, to appear in Internat. J. Math.], we construct this surface, thereby completing Theorem 5.1 and the proof of the isomorphism.

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15

Koerwien, Martin. "A complicated ω-stable depth 2 theory." Journal of Symbolic Logic 76, no. 1 (March 2011): 47–65. http://dx.doi.org/10.2178/jsl/1294170989.

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AbstractWe present a countable complete first order theory T which is model theoretically very well behaved: it eliminates quantifiers, is ω-stable, it has NDOP and is shallow of depth two. On the other hand, there is no countable bound on the Scott heights of its countable models, which implies that the isomorphism relation for countable models is not Borel.

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16

Zhang, Shuang, Ai Gao, and Lixun Zhu. "Research on Splitting Isomorphism of Leibniz Algebra and Non-Abelian expansion." Tobacco Regulatory Science 7, no. 5 (September 30, 2021): 2158–68. http://dx.doi.org/10.18001/trs.7.5.132.

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In this study, Leibniz algebras and the derivations and properties of Leibniz algebras were given, respectively. The stable automorphism group of explicit splitting extension was calculated via the stable automorphism group of Abelian extension of finite group splitting. Based on the stable automorphism group of the splitting extension studied, the non-Abelian extension and the second order non-Abelian co-homology group of Leibniz algebra were investigated in detail according to the stable automorphism group of the splitting extension.

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17

Bentmann, Rasmus. "Cuntz Splice invariance for purely infinite graph algebras." MATHEMATICA SCANDINAVICA 122, no. 1 (February 20, 2018): 91. http://dx.doi.org/10.7146/math.scand.a-96633.

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18

Ma, Nana, Qingjun Luo, and Geni Xu. "Characterization of extension map on fuzzy weakly cut-stable map." AIMS Mathematics 7, no. 5 (2022): 7507–18. http://dx.doi.org/10.3934/math.2022421.

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<abstract><p>In this paper, based on a complete residuated lattice, we propose the definition of fuzzy weakly cut-stable map and prove the extension property of the fuzzy weakly cut-stable map. Following this, it is explored the conditions under which the extension map to be fuzzy order isomorphism.</p></abstract>

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19

Kodaka, Kazunori. "Partial automorphisms of stable C*-algebras and Hilbert C*-bimodules." Journal of the Australian Mathematical Society 79, no. 3 (December 2005): 391–98. http://dx.doi.org/10.1017/s1446788700010971.

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AbstractLet A be a C*-algebra and K the C*-algebra of all compact operators on a countably infinite dimensional Hilbert space. In this note, we shall show that there is an isomorphism of a semigroup of equivalence classes of certain partial automorphisms of A ⊗ K onto a semigroup of equivalence classes of certain countably generated A-A-Hilbert bimodules.

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20

Bhatt, Bhargav, Wei Ho, Zsolt Patakfalvi, and Christian Schnell. "Moduli of products of stable varieties." Compositio Mathematica 149, no. 12 (September 6, 2013): 2036–70. http://dx.doi.org/10.1112/s0010437x13007288.

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AbstractWe study the moduli space of a product of stable varieties over the field of complex numbers, as defined via the minimal model program. Our main results are: (a) taking products gives a well-defined morphism from the product of moduli spaces of stable varieties to the moduli space of a product of stable varieties; (b) this map is always finite étale; and (c) this map very often is an isomorphism. Our results generalize and complete the work of Van Opstall in dimension$1$. The local results rely on a study of the cotangent complex using some derived algebro-geometric methods, while the global ones use some differential-geometric input.

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21

Balmer, Paul, Ivo Dell’Ambrogio, and Beren Sanders. "Grothendieck–Neeman duality and the Wirthmüller isomorphism." Compositio Mathematica 152, no. 8 (May 23, 2016): 1740–76. http://dx.doi.org/10.1112/s0010437x16007375.

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We clarify the relationship between Grothendieck duality à la Neeman and the Wirthmüller isomorphism à la Fausk–Hu–May. We exhibit an interesting pattern of symmetry in the existence of adjoint functors between compactly generated tensor-triangulated categories, which leads to a surprising trichotomy: there exist either exactly three adjoints, exactly five, or infinitely many. We highlight the importance of so-called relative dualizing objects and explain how they give rise to dualities on canonical subcategories. This yields a duality theory rich enough to capture the main features of Grothendieck duality in algebraic geometry, of generalized Pontryagin–Matlis duality à la Dwyer–Greenless–Iyengar in the theory of ring spectra, and of Brown–Comenetz duality à la Neeman in stable homotopy theory.

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22

Dean, Andrew J. "On Inductive Limit Type Actions of the Euclidean Motion Group on Stable UHF Algebras." Canadian Mathematical Bulletin 49, no. 2 (June 1, 2006): 213–25. http://dx.doi.org/10.4153/cmb-2006-022-x.

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AbstractAn invariant is presented which classifies, up to equivariant isomorphism, C*-dynamical systems arising as limits from inductive systems of elementary C*-algebras on which the Euclidean motion group acts by way of unitary representations that decompose into finite direct sums of irreducibles.

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23

Stavrova, Anastasia. "Non-stable K1-functors of Multiloop Groups." Canadian Journal of Mathematics 68, no. 1 (February 1, 2016): 150–78. http://dx.doi.org/10.4153/cjm-2015-035-2.

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AbstractLet k be a field of characteristic 0. Let G be a reductive group over the ring of Laurent polynomials . Assume that G contains amaximal R-torus, and that every semisimple normal subgroup of G contains a two-dimensional split torus G2m. We show that the natural map of non-stable K1-functors, also called Whitehead groups, KG1(R) → KG1 ( k((x1)) … ((xn))) is injective, and an isomorphism if G is semisimple. As an application, we provide a way to compute the difference between the full automorphism group of a Lie torus (in the sense of Yoshii–Neher) and the subgroup generated by exponential automorphisms.

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24

Matsumoto, Kengo. "State splitting, strong shift equivalence and stable isomorphism of Cuntz–Krieger algebras." Dynamical Systems 34, no. 1 (May 29, 2018): 93–112. http://dx.doi.org/10.1080/14689367.2018.1470227.

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25

Haget, Y., L. Bonpunt, F. Michaud, P. Negrier, M. A. Cuevas-Diarte, and H. A. J. Oonk. "Coefficients of molecular homeomorphism and crystalline isomorphism in the series of 2-R-naphthalene (R = H, F, Cl, CH3, SH, Br)." Journal of Applied Crystallography 23, no. 6 (December 1, 1990): 492–96. http://dx.doi.org/10.1107/s0021889890007051.

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Crystallographic data on the stable and metastable phases of the high-temperature forms of the substances of the series of substituted naphthalenes are given. The data are used to calculate for each pair of substances the coefficient ∊K of molecular homeomorphism as well as the coefficient ∊m of crystalline isomorphism, which allow a comparison of the (stable and/or metastable) crystal framework.

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26

Jiao, Runzhi, Qingsong Wang, Tao Lai, and Haifeng Huang. "Multi-Hypothesis Topological Isomorphism Matching Method for Synthetic Aperture Radar Images with Large Geometric Distortion." Remote Sensing 13, no. 22 (November 17, 2021): 4637. http://dx.doi.org/10.3390/rs13224637.

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The dramatic undulations of a mountainous terrain will introduce large geometric distortions in each Synthetic Aperture Radar (SAR) image with different look angles, resulting in a poor registration performance. To this end, this paper proposes a multi-hypothesis topological isomorphism matching method for SAR images with large geometric distortions. The method includes the Ridge-Line Keypoint Detection (RLKD) and Multi-Hypothesis Topological Isomorphism Matching (MHTIM). Firstly, based on the analysis of the ridge structure, a ridge keypoint detection module and a keypoint similarity description method are designed, which aim to quickly produce a small number of stable matching keypoint pairs under large look angle differences and large terrain undulations. The keypoint pairs are further fed into the MHTIM module. Subsequently, the MHTIM method is proposed, which uses the stability and isomorphism of the topological structure of the keypoint set under different perspectives to generate a variety of matching hypotheses, and iteratively achieves the keypoint matching. This method uses both local and global geometric relationships between two keypoints, hence it achieving better performance compared with traditional methods. We tested our approach on both simulated and real mountain SAR images with different look angles and different elevation ranges. The experimental results demonstrate the effectiveness and stable matching performance of our approach.

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27

DEICKE, KLAUS. "EXTERIOR EQUIVALENCE FOR POINTWISE UNITARY COACTIONS." International Journal of Mathematics 12, no. 01 (February 2001): 63–79. http://dx.doi.org/10.1142/s0129167x01000630.

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Let G be a second countable locally compact group and A a separable continuous trace C*-algebra. To each pointwise unitary coaction δ of G on A one can associate a proper G-bundle [Formula: see text], π × μ → π. We show that two pointwise unitary coactions δ and ∊ of G on A are exterior equivalent if and only if the proper G-bundles [Formula: see text] and [Formula: see text] are isomorphic. Thus, if A is stable, there exists a bijection between the isomorphism classes of proper G-bundles over [Formula: see text] and the exterior equivalence classes of pointwise unitary coactions of G on A. Moreover, when G is abelian we recover a theorem of Olesen and Raeburn.

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28

Sheu, Albert Jeu-Liang. "A Cancellation Theorem for Modules Over the Group C*-Algebras of Certain Nilpotent Lie Groups." Canadian Journal of Mathematics 39, no. 2 (April 1, 1987): 365–427. http://dx.doi.org/10.4153/cjm-1987-018-7.

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In recent years, there has been a rapid growth of the K-theory of C*-algebras. From a certain point of view, C*-algebras can be treated as “non-commutative topological spaces”, while finitely generated projective modules over them can be thought of as “non-commutative vector bundles”. The K-theory of C*-algebras [30] then generalizes the classical K-theory of topological spaces [1]. In particular, the K0-group of a unital C*-algebra A is the group “generated” by (or more precisely, the Grothendieck group of) the commutative semigroup of stable isomorphism classes of finitely generated projective modules over A with direct summation as the binary operation. The semigroup gives an order structure on K0(A) and is usually called the positive cone in K0(A).Around 1980, the work of Pimsner and Voiculescu [18] and of A. Connes [4] provided effective ways to compute the K-groups of C*-algebras. Then the classification of finitely generated projective modules over certain unital C*-algebras up to stable isomorphism could be done by computing their K0-groups as ordered groups. Later on, inspired by A. Connes's development of non-commutative differential geometry on finitely generated projective modules [2], the deeper question of classifying such modules up to isomorphism and hence the so-called cancellation question were raised (cf. [21] ).

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29

Kashina, M. A., and V. R. Popov. "Non-University Mass Student Public Associations: Institutional Isomorphism as a Factor of Stability." Administrative Consulting, no. 12 (January 12, 2022): 126–37. http://dx.doi.org/10.22394/1726-1139-2021-12-126-137.

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The relevance of this research is about the need to search for factors that increase the stability of youth associations, including student ones. Only stable youth associations can effectively socialize young people and form them as active actors in civil society. The project is a desk study and has a quality design.Object: non-university mass student public associations. They were created in Russia in the 60s of the twentieth century: student building brigades (SSO) and student nature protective brigades (DOP). Subject: institutional isomorphism of non-university student public associations. Purpose: to assess the impact of character and the degree of isomorphism of student public associations on their stability.Research results. It is shown that the main factor in the stability of student public associations is the level of their compliance with institutional requirements. It leads to forced isomorphism. The cause of this isomorphism is the monopoly of sources of support for the activities of these associations. In Russia, the state has such a monopoly. Student associations must take into account the institutional factors, in particular the requirements of higher-level systems and institutions. It gives them the necessary resources to continue their activities. Intra-organizational factors (level of social significance, charisma of leaders, mass character, and others) are less important for ensuring their sustainability.

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30

Yun, Zhiwei. "Langlands duality and global Springer theory." Compositio Mathematica 148, no. 3 (March 19, 2012): 835–67. http://dx.doi.org/10.1112/s0010437x11007433.

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AbstractWe compare the cohomology of (parabolic) Hitchin fibers for Langlands dual groups G and G∨. The comparison theorem fits in the framework of the global Springer theory developed by the author. We prove that the stable parts of the parabolic Hitchin complexes for Langlands dual group are naturally isomorphic after passing to the associated graded of the perverse filtration. Moreover, this isomorphism intertwines the global Springer action on one hand and Chern class action on the other. Our result is inspired by the mirror symmetric viewpoint of geometric Langlands duality. Compared to the pioneer work in this subject by T. Hausel and M. Thaddeus, R. Donagi and T. Pantev, and N. Hitchin, our result is valid for more general singular fibers. The proof relies on a variant of Ngô’s support theorem, which is a key point in the proof of the Fundamental Lemma.

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31

BRATTELI, OLA, PALLE E. T. JØRGENSEN, KI HANG KIM, and FRED ROUSH. "Non-stationarity of isomorphism between AF algebras defined by stationary Bratteli diagrams." Ergodic Theory and Dynamical Systems 20, no. 6 (December 2000): 1639–56. http://dx.doi.org/10.1017/s0143385700000912.

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We first study situations where the stable AF algebras defined by two square primitive non-singular incidence matrices with non-negative integer matrix elements are isomorphic, even though no powers of the associated automorphisms of thecorresponding dimension groups are isomorphic. More generally we consider necessary and sufficient conditions for two such matrices to determine isomorphic dimension groups.We give several examples.

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32

martin, maryanne, and gregory v. jones. "constraints from handedness on the evolution of brain lateralization." Behavioral and Brain Sciences 28, no. 4 (August 2005): 603–4. http://dx.doi.org/10.1017/s0140525x05370105.

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can we understand brain lateralization in humans by analysis in terms of an evolutionarily stable strategy? the attempt to demonstrate a link between lateralization in humans and that in, for example, fish appears to hinge critically on whether the isomorphism is viewed as a matter of homology or homoplasy. consideration of human handedness presents a number of challenges to the proposed framework.

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33

BISWAS, INDRANIL, and VICENTE MUÑOZ. "TORELLI THEOREM FOR MODULI SPACES OF SL(r,ℂ)-CONNECTIONS ON A COMPACT RIEMANN SURFACE." Communications in Contemporary Mathematics 11, no. 01 (February 2009): 1–26. http://dx.doi.org/10.1142/s0219199709003260.

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Let X be any compact connected Riemann surface of genus g, with g ≥ 3. For any r ≥ 2, let [Formula: see text] denote the moduli space of holomorphic SL (r,ℂ)-connections over X. It is known that the biholomorphism class of the complex variety [Formula: see text] is independent of the complex structure of X. If g = 3, then we assume that r ≥ 3. We prove that the isomorphism class of the variety [Formula: see text] determines the Riemann surface X uniquely up to an isomorphism. A similar result is proved for the moduli space of holomorphic GL (r,ℂ)-connections on X. We also show that the Torelli theorem remains valid for the moduli spaces of connections, as well as those of stable vector bundles, on geometrically irreducible smooth projective curves defined over the field of real numbers.

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34

FARNSTEINER, ROLF. "AUSLANDER–REITEN COMPONENTS FOR G1T-MODULES." Journal of Algebra and Its Applications 04, no. 06 (December 2005): 739–59. http://dx.doi.org/10.1142/s0219498805001502.

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In this paper we study the Auslander–Reiten quiver of the highest weight category of finite-dimensional G1T-modules, associated to a smooth reductive algebraic group G. By relating properties of stable Auslander–Reiten components to those of their rank varieties we show that there are at most three isomorphism types of these components. For the Frobenius kernels G1Tr the maximal ranks of tubes are determined.

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35

DROSTE, MANFRED, and RÜDIGER GÖBEL. "UNIVERSAL INFORMATION SYSTEMS." International Journal of Foundations of Computer Science 01, no. 04 (December 1990): 413–24. http://dx.doi.org/10.1142/s012905419000028x.

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In the theory of denotational semantics of programming languages, several authors proved the existence of particular kinds of universal domains. D. Scott constructed universal information systems, which are, however, not unique up to isomorphism. Here, we use a model-theoretic technique to establish the existence and uniqueness of a universal homogeneous information system. Similar results are also obtained for canonical and for stable information systems, respectively.

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36

Delcheva, Zlatka, Tsveta Stanimirova, and Nadia Petrova. "Order of osakaite–namuwite–lahnsteinite formation during alkalization of sulfate solutions." Review of the Bulgarian Geological Society 83, no. 2 (December 2022): 51–61. http://dx.doi.org/10.52215/rev.bgs.2022.83.2.51.

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Experiments with dropwise alkalization of a 0.1 M ZnSO4 solution with 1M NaOH were carried out to establish the formation order of Zn-hydroxy-sulfate minerals (osakaite, namuwite, and lahnsteinite). During the controlled alkalization with 1M NaOH of a 0.1M ZnSO4 solution, namuwite (osakaite), lahnsteinite and wulfingite are successively formed. The obtained precipitates were characterized by powder X-ray diffraction (XRD) and SEM-EDS methods. The formation conditions and regions of stability of osakaite and namuwite are at near circumneutral pH (6.5–7), while lahnsteinite is stable at high pH (11–12). This explains the wider distribution of namuwite and osakaite in nature. The isomorphic substitution of Zn2+ cation with Cu2+ in the hydroxide layer of the Zn-hydroxy-sulfate minerals during controlled alkalization was studied using mixed 0.1M ZnSO4 + CuSO4 solution (molar ratio Zn:Cu = 4:1 and 1:1). During controlled alkalization of mixed Zn-Cu sulfate solutions, 25% copper cations are isomorphic incorporated in the namuwite (osakaite) and lahnsteinite structures. It was determined that this Cu2+ content is the upper limit of the isomorphism and corresponds to the occupation of 1/3 of octahedral positions.

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37

Bellovin, Rebecca, and Otmar Venjakob. "Wach Modules, Regulator Maps, and $\varepsilon$-Isomorphisms in Families." International Mathematics Research Notices 2019, no. 16 (November 6, 2017): 5127–204. http://dx.doi.org/10.1093/imrn/rnx276.

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Abstract We prove the “local $\varepsilon$-isomorphism” conjecture of Fukaya and Kato [13] for certain crystalline families of $G_{{\mathbf{Q}_p}}$-representations. This conjecture can be regarded as a local analog of the Iwasawa main conjecture for families. Our work extends earlier work of Kato for rank-$1$ modules (cf. [33]), of Benois and Berger for crystalline $G_{{\mathbf{Q}_p}}$-representations with respect to the cyclotomic extension (cf. [1]), as well as of Loeffler et al. (cf. [21]) for crystalline $G_{{\mathbf{Q}_p}}$-representations with respect to abelian $p$-adic Lie extensions of ${\mathbf{Q}_p}$. Nakamura [24, 25] has also formulated a version of Kato’s $\varepsilon$-conjecture for affinoid families of $(\varphi,\Gamma)$-modules over the Robba ring, and proved his conjecture in the rank-$1$ case. He used this case to construct an $\varepsilon$-isomorphism for families of trianguline $(\varphi,\Gamma)$-modules, depending on a fixed triangulation. Our results imply that this $\varepsilon$-isomorphism is independent of the chosen triangulation for certain crystalline families. The main ingredient of our proof consists of the construction of families of Wach modules generalizing work of Wach and Berger [6] and following Kisin’s approach to the construction of potentially semi-stable deformation rings [18].

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38

Chukanov, Nikita V., Nadezhda V. Shchipalkina, Roman Yu Shendrik, Marina F. Vigasina, Vladimir L. Tauson, Sergey V. Lipko, Dmitry A. Varlamov, et al. "Isomorphism and Mutual Transformations of S-Bearing Components in Feldspathoids with Microporous Structures." Minerals 12, no. 11 (November 18, 2022): 1456. http://dx.doi.org/10.3390/min12111456.

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The isomorphism of S-bearing feldspathoids belonging to the cancrinite, sodalite, tugtupite, vladimirivanovite, bystrite, marinellite and scapolite structure types has been investigated using a multimethodical approach based on infrared, Raman and electron spin resonance (ESR), as well as ultraviolet, visible and near infrared (UV–Vis–near IR) absorption spectroscopy methods and involving chemical and X-ray diffraction data. Sapozhnikovite Na8(Al6Si6O24)(HS)2 and sulfite and thiosulfate analogues of cancrinite are synthesized hydrothermally and characterized by means of electron microprobe analyses, powder X-ray diffraction and Raman spectroscopy. The possibility of the incorporation of significant amounts of SO42−, S4 and SO32− in the crystal structures of cancrisilite, sulfhydrylbystrite and marinellite, respectively, has been established for the first time. Thermal conversions of S-bearing groups in the synthetic sulfite cancrinite and sapozhnikovite analogues as well as natural vladinirivanovite and S4-bearing haüyne under oxidizing and reducing conditions have been studied using the multimethodical approach. The SO42− and S2− anions and the S3•– radical anion are the most stable S-bearing species under high-temperature conditions (in the range of 700–800 °C); their ratio in the heated samples is determined by the redox conditions and charge-balance requirement. The HS− and S52− anions are stable only under highly reducing conditions.

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Bulois, Michael, Christian Lehn, Manfred Lehn, and Ronan Terpereau. "Towards a symplectic version of the Chevalley restriction theorem." Compositio Mathematica 153, no. 3 (March 2017): 647–66. http://dx.doi.org/10.1112/s0010437x16008277.

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If $(G,V)$ is a polar representation with Cartan subspace $\mathfrak{c}$ and Weyl group $W$, it is shown that there is a natural morphism of Poisson schemes $\mathfrak{c}\oplus \mathfrak{c}^{\ast }/W\rightarrow V\oplus V^{\ast }/\!\!/\!\!/G$. This morphism is conjectured to be an isomorphism of the underlying reduced varieties if$(G,V)$ is visible. The conjecture is proved for visible stable locally free polar representations and some other examples.

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40

Roushon, S. K. "The Farrell-Jones isomorphism conjecture for 3-manifold groups." Journal of K-Theory 1, no. 1 (November 30, 2007): 49–82. http://dx.doi.org/10.1017/is007011012jkt005.

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AbstractWe show that the Fibered Isomorphism Conjecture (FIC) of Farrell and Jones corresponding to the stable topological pseudoisotopy functor is true for fundamental groups of a large class of 3-manifolds. We also prove that if the FIC is true for irreducible 3-manifold groups then it is true for all 3-manifold groups. In fact, this follows from a more general result we prove, namely we show that if the FIC is true for each vertex group of a graph of groups with trivial edge groups then the FIC is true for the fundamental group of the graph of groups. This result is part of a program to prove the FIC for the fundamental group of a graph of groups where all the vertex and edge groups satisfy the FIC. A consequence of the first result gives a partial solution to a problem in the problem list of R. Kirby. We also deduce that the FIC is true for a class of virtually P D3-groups.Another main aspect of this article is to prove the FIC for all Haken 3-manifold groups assuming that the FIC is true for B-groups. By definition a B-group contains a finite index subgroup isomorphic to the fundamental group of a compact irreducible 3-manifold with incompressible nonempty boundary so that each boundary component is of genus ≥ 2. We also prove the FIC for a large class of B-groups and moreover, using a recent result of L.E. Jones we show that the surjective part of the FIC is true for any B-group.

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Galetto, Federico, Anthony Vito Geramita, and David Louis Wehlau. "Degrees of Regular Sequences With a Symmetric Group Action." Canadian Journal of Mathematics 71, no. 03 (January 7, 2019): 557–78. http://dx.doi.org/10.4153/cjm-2017-035-3.

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AbstractWe consider ideals in a polynomial ring that are generated by regular sequences of homogeneous polynomials and are stable under the action of the symmetric group permuting the variables. In previous work, we determined the possible isomorphism types for these ideals. Following up on that work, we now analyze the possible degrees of the elements in such regular sequences. For each case of our classification, we provide some criteria guaranteeing the existence of regular sequences in certain degrees.

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Bai, Jinrong, Qibin Shi, and Shiguang Mu. "A Malware and Variant Detection Method Using Function Call Graph Isomorphism." Security and Communication Networks 2019 (September 22, 2019): 1–12. http://dx.doi.org/10.1155/2019/1043794.

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The huge influx of malware variants are generated using packing and obfuscating techniques. Current antivirus software use byte signature to identify known malware, and this method is easy to be deceived and generally ineffective for identifying malware variants. Antivirus experts use hash signature to verify if captured sample is one of the malware databases, and this method cannot recognize malware variants whose hash signatures have changed completely. Function call graph is a high-level abstraction representation of a program and more stable and resilient than byte or hash signature. In this paper, function call graph is used as signature of a program, and two kinds of graph isomorphism algorithms are employed to identify known malware and its variants. Four experiments are designed to evaluate the performance of the proposed method. Experimental results indicate that the proposed method is effective and efficient for identifying known malware and a portion of their variants. The proposed method can also be used to index and locate a large-scale malware database and group malware to the corresponding family.

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Farjoun, Emmanuel Dror, and Claude L. Schochet. "Spaces of sections of Banach algebra bundles." Journal of K-Theory 10, no. 2 (April 4, 2012): 279–98. http://dx.doi.org/10.1017/is012002001jkt183.

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AbstractSuppose thatBis a G-Banach algebra over= ℝ or ℂXis a finite dimensional compact metric space, ζ :P → Xis a standard principalG-bundle, andAζ= Γ(X,P×GB) is the associated algebra of sections. We produce a spectral sequence which converges to π*(GLoAζ) withA related spectral sequence converging toK*+1(Aζ) (the real or complex topologicalK-theory) allows us to conclude that ifBis Bott-stable, (i.e., if π*(GLoB) →K*+1(B) is an isomorphism for all * > 0) then so isAζ.

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Caruso, Xavier, and David Lubicz. "Linear algebra over and related rings." LMS Journal of Computation and Mathematics 17, no. 1 (2014): 302–44. http://dx.doi.org/10.1112/s146115701300034x.

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AbstractLet $\mathfrak{R}$ be a complete discrete valuation ring, $S=\mathfrak{R}[[u]]$ and $d$ a positive integer. The aim of this paper is to explain how to efficiently compute usual operations such as sum and intersection of sub-$S$-modules of $S^d$. As $S$ is not principal, it is not possible to have a uniform bound on the number of generators of the modules resulting from these operations. We explain how to mitigate this problem, following an idea of Iwasawa, by computing an approximation of the result of these operations up to a quasi-isomorphism. In the course of the analysis of the $p$-adic and $u$-adic precisions of the computations, we have to introduce more general coefficient rings that may be interesting for their own sake. Being able to perform linear algebra operations modulo quasi-isomorphism with $S$-modules has applications in Iwasawa theory and $p$-adic Hodge theory. It is used in particular in Caruso and Lubicz (Preprint, 2013, arXiv:1309.4194) to compute the semi-simplified modulo $p$ of a semi-stable representation.

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Packer, Judith A. "Moore Cohomology and Central Twisted Crossed Product C*-Algebras." Canadian Journal of Mathematics 48, no. 1 (February 1, 1996): 159–74. http://dx.doi.org/10.4153/cjm-1996-007-6.

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AbstractLet G be a locally compact second countable group, let X be a locally compact second countable Hausdorff space, and view C(X, T) as a trivial G-module. For G countable discrete abelian, we construct an isomorphism between the Moore cohomology group Hn(G, C(X, T)) and the direct sum Ext(Hn-1(G), Ȟl(βX, Ζ)) ⊕ C(X, Hn(G, T)); here Ȟ1 (βX, Ζ) denotes the first Čech cohomology group of the Stone-Čech compactification of X, βX, with integer coefficients. For more general locally compact second countable groups G, we discuss the relationship between the Moore group H2(G, C(X, T)), the set of exterior equivalence classes of element-wise inner actions of G on the stable continuous trace C*-algebra C0(X) ⊗ 𝒦, and the equivariant Brauer group BrG(X) of Crocker, Kumjian, Raeburn, and Williams. For countable discrete abelian G acting trivially on X, we construct an isomorphism is the group of equivalence classes of principal Ĝ bundles over X first considered by Raeburn and Williams.

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Pillay, Anand. "On types of CB-rank 1 in simple theories." Journal of the Institute of Mathematics of Jussieu 7, no. 4 (October 2008): 895–99. http://dx.doi.org/10.1017/s147474800800025x.

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AbstractWe prove that if M0 is a model of a simple theory, and p(x) is a complete type of Cantor–Bendixon rank 1 over M0, then p is stationary and regular. As a consequence we obtain another proof that any countable model M0 of a countable complete simple theory T has infinitely many countable elementary extensions up to M0-isomorphism. The latter extends earlier results of the author in the stable case, and is a special case of a recent result of Tanovic.

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Aprodu, Marian, and Vasile Brînzănescu. "Moduli spaces of vector bundles over ruled surfaces." Nagoya Mathematical Journal 154 (1999): 111–22. http://dx.doi.org/10.1017/s0027763000025332.

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AbstractWe study moduli spaces M(c1, c2, d, r) of isomorphism classes of algebraic 2-vector bundles with fixed numerical invariants c1, c2, d, r over a ruled surface. These moduli spaces are independent of any ample line bundle on the surface. The main result gives necessary and sufficient conditions for the non-emptiness of the space M(c1, c2, d, r) and we apply this result to the moduli spaces ML(c1, c2) of stable bundles, where L is an ample line bundle on the ruled surface.

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48

Meesschaert, Niels, Sven Raum, and Stefaan Vaes. "Stable orbit equivalence of Bernoulli actions of free groups and isomorphism of some of their factor actions." Expositiones Mathematicae 31, no. 3 (2013): 274–94. http://dx.doi.org/10.1016/j.exmath.2012.08.012.

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MATSUMOTO, KENGO. "-ALGEBRAS ASSOCIATED WITH LAMBDA-SYNCHRONIZING SUBSHIFTS AND FLOW EQUIVALENCE." Journal of the Australian Mathematical Society 95, no. 2 (August 7, 2013): 241–65. http://dx.doi.org/10.1017/s1446788713000219.

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AbstractThe class of $\lambda $-synchronizing subshifts generalizes the class of irreducible sofic shifts. A $\lambda $-synchronizing subshift can be presented by a certain $\lambda $-graph system, called the $\lambda $-synchronizing $\lambda $-graph system. The $\lambda $-synchronizing $\lambda $-graph system of a $\lambda $-synchronizing subshift can be regarded as an analogue of the Fischer cover of an irreducible sofic shift. We will study algebraic structure of the ${C}^{\ast } $-algebra associated with a $\lambda $-synchronizing $\lambda $-graph system and prove that the stable isomorphism class of the ${C}^{\ast } $-algebra with its Cartan subalgebra is invariant under flow equivalence of $\lambda $-synchronizing subshifts.

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50

Muafi and Rizqi Adhyka Kusumawati. "Strategic consensus on organizational performance: A contingency approach of organizational culture and isomorphic pressure." Journal of Industrial Engineering and Management 13, no. 2 (July 1, 2020): 352. http://dx.doi.org/10.3926/jiem.2480.

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Purpose: This research aims to test and analyze the consensus of organizational strategy with the contingency of organizational culture and isomorphism pressure which have an impact on organizational performance moderated by human capital. The survey is conducted to the owners/managers of Batik Micro Small Medium Entreprises (MSMEs) in 18 villages in Pekalongan, Indonesia.Design/methodology/approach: The data collecting is using questionnaire and interview to some owner/managers and leader of the Batik group. Pekalongan is a city of Batik that has Batik MSMEs spread in every area of the villages. Therefore, the sampling technique used in this research includes two stages: proportional area random sampling and purposive sampling. 17 MSMEs were taken as samples in each village. Furthermore, after selecting 17 MSMEs, the study used purposive sampling technique with a sample size of 170 MSMEs. This research uses three variables: isomorphism, organizational culture, and organizational strategy measured by semantic scale and use two bipolar typologies. As for organizational performance, it is measured using Likert scale. The data analysis technique is using Euclidience Distance Simple Regression with contingency approach and moderation of Euclidience Distance Simple Regression.Findings: These results provide are; (1) The higher the alignment degree between imitation strategy and hierarchy culture, the higher the organizational performance will be; (2) The higher the alignment degree between innovation strategy and adhocracy culture, the higher the organizational performance will be; (3) Human capital strengthens the consensus of imitation strategy with the contingency of hierarchy culture and benign isomorphism, so that the organizational performance is higher; (4) Human capital does not strengthen the consensus of innovation strategy with the contingency of adhocracy culture and hostile isomorphism, so that the organizational performance is higher.Research limitations/implications: The sampling technique of this research is done using purposive sampling, so it is feared that it cannot generalize to the existing population. The data collection also uses primary data with measurement approach based on the owner/manager perceptions, which sometimes still requires assistance and good understanding for the respondents. Organizational performance will be increase if the condition of hierarchy culture, benign isomorphism, and imitation strategy are supported by the moderation role of human capital that can strengthen the relationship with organizational performance.Practical implications: The higher the alignment degree between imitation strategy and hierarchy culture, the higher the organizational performance will be. If the organization tend to choose imitation strategy, it is more emphasizes on low market pressure, support from government regulation, low public and media pressure, and stable politic and safety, and vice versa.Originality/value: This research wants to fill the research gap by examining the importance of having an alignment of organization strategy (Imitation vs Innovation) related with the contingency of organizational culture (Hierarchy vs Adhocracy) and isomorphism pressure (Benign vs Hostile) so that Batik MSMEs entrepreneurs can further improve their organizational performance (operational performance and environmental performance).

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