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Journal articles on the topic 'SMALED'

Author: Grafiati

Published: 7 December 2024

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1

Sharkova, I. V., P. A. Shatalov, and E. L. Dadali. "VARIETY OF CLINICAL MANIFESTATIONS IN MUTATIONS IN THE DYNC1H1 GENE." Russian neurological Journal, no. 3 (September 3, 2019): 31–36. http://dx.doi.org/10.30629/2658-7947-2019-24-3-31-36.

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Introduction. To date, DYNC1H1 gene mutations are known for large number of hereditary diseases. It is believed that different mutations have variable effects to protein function and, accordingly, to various clinical manifestations. Results. There are a clinical and genetic characteristics of two Russian patients with two types of diseases: spinal muscular atrophy with predominant lesion of the lower extremities (SMALED) and non-syndromic mental retardation type 13 (MR13) in combination with a brain malformations and epilepsy due to newly identified mutations in the DYNC1H1 gene. Conclusion There is some evidence in support of the hypothesis that the amino acid sequence changing in the tail domain of dynein lead to the appearance of SMALED, and in the motor domain lead to MR13. Exome or genome sequencing are required as the main method for their diagnosis due to the high genetic heterogeneity of non-syndromic MR and SMALED, the lack of specific clinical markers and hotspot mutations in the DYNC1H1 gene.

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2

Ribeiro-Mourão, Francisco, Ana Vilan, Sara Passos-Silva, Fernando Silveira, Miguel Leão, and Mafalda Sampaio. "Intrafamilial Variability of the R694C Variant in BICD2 Presenting with Lethal Severe Arthrogryposis." Journal of Neonatology 36, no. 1 (January 11, 2022): 63–68. http://dx.doi.org/10.1177/09732179211068815.

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Arthrogryposis multiplex congenita (AMC) is a heterogeneous condition comprising congenital multiple joint contractures, and it is secondary to decreased fetal mobility following environmental/genetic abnormalities. BICD2 pathogenic variants have been associated with autosomal dominant spinal muscular atrophy with lower extremity predominance (SMALED2). We report the case of a newborn with decreased fetal movements and ventriculomegaly diagnosed in utero, born with severe AMC, multiple bone fractures, congenital hip dislocation, and respiratory insufficiency that led to neonatal death. His mother had AMC diagnosis without established etiology. Her phenotype characterization was key to guide the genetic investigation. A BICD 2 heterozygous variant (NM_001003800.1; c.2080C > T; p. [Arg694Cys]) was detected both in the mother and the newborn. This variant had previously been reported in 3 cases, all having de novo severe SMALED-type 2B (MIM#618291) phenotype. This is the first report of this variant (p. [Arg694Cys]) presenting with an inherited, severe, and lethal phenotype associated to intrafamilial variability, suggesting a more complex phenotype-genotype correlation than previously stated.

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3

Aziz, Iqra, Mark Davis, and Christina Liang. "Late adult-onset spinal muscular atrophy with lower extremity predominance (SMALED)." BMJ Case Reports 15, no. 3 (March 2022): e248297. http://dx.doi.org/10.1136/bcr-2021-248297.

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An elderly man in his early 80s presented with a 6-month history of worsening lower limb weakness on a background of a longer-standing waddling gait. Examination revealed bilateral scapular winging, and weakness in his proximal and distal lower limbs. Electromyography showed widespread chronic partial denervation changes, while sensory and motor nerve conduction parameters were preserved. After little progression over the course of 18 months, motor neuron disease was deemed less likely. Genetic testing revealed BICD2-related spinal muscular atrophy with lower extremity dominance (SMALED2), a disease that is usually of earlier onset. He is the oldest patient in the literature to be diagnosed with SMALED2 while maintaining ambulation, suggesting the milder spectrum of BICD2-related disease.

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4

Trimouille, Aurélien, Émilie Obre, Guillaume Banneau, Alexandra Durr, Giovanni Stevanin, Fabienne Clot, Perrine Pennamen, et al. "An in-frame deletion in BICD2 associated with a non-progressive form of SMALED." Clinical Neurology and Neurosurgery 166 (March 2018): 1–3. http://dx.doi.org/10.1016/j.clineuro.2018.01.013.

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5

Hemerková, Pavlína, Hana Matulová, Pavel Kunc, Lenka Pospíšlová, and Jiří Jandura. "Spinal muscular atrophy affecting the lower limbs, dominantly inherited (SMALED), an example of a non-5q form of the disease." Neurologie pro praxi 24, no. 1 (March 3, 2023): 65–69. http://dx.doi.org/10.36290/neu.2022.051.

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6

WIELER, SUSANA. "Smale spaces via inverse limits." Ergodic Theory and Dynamical Systems 34, no. 6 (June 28, 2013): 2066–92. http://dx.doi.org/10.1017/etds.2013.19.

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AbstractA Smale space is a chaotic dynamical system with canonical coordinates of contracting and expanding directions. The basic sets for Smale’s Axiom $A$ systems are a key class of examples. We consider the special case of irreducible Smale spaces with zero-dimensional contracting directions, and characterize these as stationary inverse limits satisfying certain conditions.

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7

Barinova, M. K., E. Y. Gogulina, and O. V. Pochinka. "Omega-classification of Surface Diffeomorphisms Realizing Smale Diagrams." Nelineinaya Dinamika 17, no. 3 (2021): 321–34. http://dx.doi.org/10.20537/nd210306.

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The present paper gives a partial answer to Smale’s question which diagrams can correspond to $(A,B)$-diffeomorphisms. Model diffeomorphisms of the two-dimensional torus derived by “Smale surgery” are considered, and necessary and sufficient conditions for their topological conjugacy are found. Also, a class $G$ of $(A,B)$-diffeomorphisms on surfaces which are the connected sum of the model diffeomorphisms is introduced. Diffeomorphisms of the class $G$ realize any connected Hasse diagrams (abstract Smale graph). Examples of diffeomorphisms from $G$ with isomorphic labeled Smale diagrams which are not ambiently $\Omega$-conjugated are constructed. Moreover, a subset $G_{*}\subset G$ of diffeomorphisms for which the isomorphism class of labeled Smale diagrams is a complete invariant of the ambient $\Omega$-conjugacy is singled out.

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8

Becker, Lena-Luise, Hormos Salimi Dafsari, Jens Schallner, Dalia Abdin, Michael Seifert, Florence Petit, Thomas Smol, et al. "The clinical-phenotype continuum in DYNC1H1-related disorders—genomic profiling and proposal for a novel classification." Journal of Human Genetics 65, no. 11 (August 12, 2020): 1003–17. http://dx.doi.org/10.1038/s10038-020-0803-1.

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AbstractMutations in the cytoplasmic dynein 1 heavy chain gene (DYNC1H1) have been identified in rare neuromuscular (NMD) and neurodevelopmental (NDD) disorders such as spinal muscular atrophy with lower extremity dominance (SMALED) and autosomal dominant mental retardation syndrome 13 (MRD13). Phenotypes and genotypes of ten pediatric patients with pathogenic DYNC1H1 variants were analyzed in a multi-center study. Data mining of large-scale genomic variant databases was used to investigate domain-specific vulnerability and conservation of DYNC1H1. We identified ten patients with nine novel mutations in the DYNC1H1 gene. These patients exhibit a broad spectrum of clinical findings, suggesting an overlapping disease manifestation with intermixed phenotypes ranging from neuropathy (peripheral nervous system, PNS) to severe intellectual disability (central nervous system, CNS). Genomic profiling of healthy and patient variant datasets underlines the domain-specific effects of genetic variation in DYNC1H1, specifically on toleration towards missense variants in the linker domain. A retrospective analysis of all published mutations revealed domain-specific genotype–phenotype correlations, i.e., mutations in the dimerization domain with reductions in lower limb strength in DYNC1H1–NMD and motor domain with cerebral malformations in DYNC1H1–NDD. We highlight that the current classification into distinct disease entities does not sufficiently reflect the clinical disease manifestation that clinicians face in the diagnostic work-up of DYNC1H1-related disorders. We propose a novel clinical classification for DYNC1H1-related disorders encompassing a spectrum from DYNC1H1–NMD with an exclusive PNS phenotype to DYNC1H1–NDD with concomitant CNS involvement.

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9

Hoang, Ha Thi, Max A. Schlager, Andrew P. Carter, and Simon L. Bullock. "DYNC1H1 mutations associated with neurological diseases compromise processivity of dynein–dynactin–cargo adaptor complexes." Proceedings of the National Academy of Sciences 114, no. 9 (February 14, 2017): E1597—E1606. http://dx.doi.org/10.1073/pnas.1620141114.

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Mutations in the human DYNC1H1 gene are associated with neurological diseases. DYNC1H1 encodes the heavy chain of cytoplasmic dynein-1, a 1.4-MDa motor complex that traffics organelles, vesicles, and macromolecules toward microtubule minus ends. The effects of the DYNC1H1 mutations on dynein motility, and consequently their links to neuropathology, are not understood. Here, we address this issue using a recombinant expression system for human dynein coupled to single-molecule resolution in vitro motility assays. We functionally characterize 14 DYNC1H1 mutations identified in humans diagnosed with malformations in cortical development (MCD) or spinal muscular atrophy with lower extremity predominance (SMALED), as well as three mutations that cause motor and sensory defects in mice. Two of the human mutations, R1962C and H3822P, strongly interfere with dynein’s core mechanochemical properties. The remaining mutations selectively compromise the processive mode of dynein movement that is activated by binding to the accessory complex dynactin and the cargo adaptor Bicaudal-D2 (BICD2). Mutations with the strongest effects on dynein motility in vitro are associated with MCD. The vast majority of mutations do not affect binding of dynein to dynactin and BICD2 and are therefore expected to result in linkage of cargos to dynein–dynactin complexes that have defective long-range motility. This observation offers an explanation for the dominant effects of DYNC1H1 mutations in vivo. Collectively, our results suggest that compromised processivity of cargo–motor assemblies contributes to human neurological disease and provide insight into the influence of different regions of the heavy chain on dynein motility.

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10

Amini, Massoud, Ian F. Putnam, and Sarah Saeidi Gholikandi. "Homology for one-dimensional solenoids." MATHEMATICA SCANDINAVICA 121, no. 2 (October 22, 2017): 219. http://dx.doi.org/10.7146/math.scand.a-26265.

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Smale spaces are a particular class of hyperbolic topological dynamical systems, defined by David Ruelle. The definition was introduced to give an axiomatic description of the dynamical properties of Smale's Axiom A systems when restricted to a basic set. They include Anosov diffeomeorphisms, shifts of finite type and various solenoids constructed by R. F. Williams. The second author constructed a homology theory for Smale spaces which is based on (and extends) Krieger's dimension group invariant for shifts of finite type. In this paper, we compute this homology for the one-dimensional generalized solenoids of R. F. Williams.

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11

Li, Qingdu, Lina Zhang, and Fangyan Yang. "An Algorithm to Automatically Detect the Smale Horseshoes." Discrete Dynamics in Nature and Society 2012 (2012): 1–9. http://dx.doi.org/10.1155/2012/283179.

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Smale horseshoes, curvilinear rectangles and their U-shaped images patterned on Smale's famous example, provide a rigorous way to study chaos in dynamical systems. The paper is devoted to constructing them in two-dimensional diffeomorphisms with the existence of transversal homoclinic saddles. We first propose an algorithm to automatically construct “horizontal” and “vertical” sides of the curvilinear rectangle near to segments of the stable and of the unstable manifolds, respectively, and then apply it to four classical chaotic maps (the Duffing map, the Hénon map, the Ikeda map, and the Lozi map) to verify its effectiveness.

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12

YU, BIN. "Smale solenoid attractors and affine Hirsch foliations." Ergodic Theory and Dynamical Systems 39, no. 2 (May 4, 2017): 531–53. http://dx.doi.org/10.1017/etds.2017.30.

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The main purpose of this paper is to study north–south Smale solenoid diffeomorphisms on$3$-manifolds by using affine Hirsch foliations. A north–south Smale solenoid diffeomorphism$f$on a closed$3$-manifold$M$is a diffeomorphism whose non-wandering set is composed of a Smale solenoid attractor$\unicode[STIX]{x1D6EC}_{a}$and a Smale solenoid repeller$\unicode[STIX]{x1D6EC}_{r}$. The key observation is that a north–south Smale solenoid diffeomorphism$f$automatically induces two non-isotopically leaf-conjugate affine Hirsch foliations${\mathcal{H}}^{s}$and${\mathcal{H}}^{u}$on the orbit space of the wandering set of$f$(abbreviated to thewandering orbit spaceof$f$) by the stable and unstable manifolds of$\unicode[STIX]{x1D6EC}_{a}$and$\unicode[STIX]{x1D6EC}_{r}$, respectively. Under this viewpoint, we build some close relationships between north–south Smale solenoid diffeomorphisms and Hirsch manifolds (the closed$3$-manifolds admitting two non-isotopically leaf-conjugate affine Hirsch foliations).∙On the one hand, the union of the wandering orbit spaces is nearly in one-to-one correspondence with the union of Hirsch manifolds.∙On the other hand, surprisingly, the topology of the wandering orbit space (Hirsch manifold) is nearly a complete invariant of north–south Smale solenoid diffeomorphisms up to semi-global conjugacy.Moreover, as applications, we consider several more concrete questions. For instance, we prove that every diffeomorphism in many semi-global conjugacy classes of north–south Smale solenoid diffeomorphisms are not structurally stable.

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13

Hem, Erlend, and Steinar Madsen. "Smale legemidler." Tidsskrift for Den norske legeforening 136, no. 3 (2016): 241. http://dx.doi.org/10.4045/tidsskr.15.1247.

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14

Smale, Steve, and Michael Shub. "Smale horseshoe." Scholarpedia 2, no. 11 (2007): 3012. http://dx.doi.org/10.4249/scholarpedia.3012.

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15

Cheng, Xuhua, and Zhikun She. "A Note on the Existence of a Smale Horseshoe in the Planar Circular Restricted Three-Body Problem." Abstract and Applied Analysis 2015 (2015): 1–8. http://dx.doi.org/10.1155/2015/965829.

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It has been proved that, in the classical planar circular restricted three-body problem, the degenerate saddle point processes transverse homoclinic orbits. Since the standard Smale-Birkhoff theorem cannot be directly applied to indicate the chaotic dynamics of the Smale horseshoe type, we in this note alternatively apply the Conley-Moser conditions to analytically prove the existence of a Smale horseshoe in this classical restricted three-body problem.

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16

Ahn, Hyunjin, and Myeongju Kang. "Emergent dynamics of various Cucker–Smale type models with a fractional derivative." Mathematical Biosciences and Engineering 20, no. 10 (2023): 17949–85. http://dx.doi.org/10.3934/mbe.2023798.

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<abstract><p>In this paper, we demonstrate emergent dynamics of various Cucker–Smale type models, especially standard Cucker–Smale (CS), thermodynamic Cucker–Smale (TCS), and relativistic Cucker–Smale (RCS) with a fractional derivative in time variable. For this, we adopt the Caputo fractional derivative as a widely used standard fractional derivative. We first introduce basic concepts and previous properties based on fractional calculus to explain its unusual aspects compared to standard calculus. Thereafter, for each proposed fractional model, we provide several sufficient frameworks for the asymptotic flocking of the proposed systems. Unlike the flocking dynamics which occurs exponentially fast in the original models, we focus on the flocking dynamics that occur slowly at an algebraic rate in the fractional systems.</p></abstract>

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17

ZHAO, XUEZHI. "Non-singular Smale flows on three-dimensional manifolds and Whitehead torsion." Ergodic Theory and Dynamical Systems 31, no. 1 (November 24, 2009): 301–15. http://dx.doi.org/10.1017/s0143385709000935.

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AbstractThis paper deals with non-singular Smale flows on oriented 3-manifolds. We shall show a relation between the properties of invariant sets of a Smale flow and a kind of Whitehead torsion of the underlying manifold.

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18

Gerber, Samuel, Oliver Rübel, Peer-Timo Bremer, Valerio Pascucci, and Ross T. Whitaker. "Morse–Smale Regression." Journal of Computational and Graphical Statistics 22, no. 1 (January 19, 2012): 193–214. http://dx.doi.org/10.1080/10618600.2012.657132.

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19

DE REZENDE, KETTY A., GUIDO G. E. LEDESMA, and OZIRIDE MANZOLI NETO. "Smale flows on." Ergodic Theory and Dynamical Systems 35, no. 5 (April 13, 2015): 1546–81. http://dx.doi.org/10.1017/etds.2015.2.

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In this paper, we use abstract Lyapunov graphs as a combinatorial tool to obtain a complete classification of Smale flows on$\mathbb{S}^{2}\times \mathbb{S}^{1}$. This classification gives necessary and sufficient conditions that must be satisfied by an (abstract) Lyapunov graph in order for it to be associated to a Smale flow on$\mathbb{S}^{2}\times \mathbb{S}^{1}$.

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20

Frich, Jan. "Re: Smale legemidler." Tidsskrift for Den norske legeforening 136, no. 6 (2016): 508. http://dx.doi.org/10.4045/tidsskr.16.0212.

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21

Wekre, Lena Lande, and Stein Are Aksnes. "Re: Smale legemidler." Tidsskrift for Den norske legeforening 136, no. 6 (2016): 508. http://dx.doi.org/10.4045/tidsskr.16.0213.

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Hem, Erlend, and Steinar Madsen. "Re: Smale legemidler." Tidsskrift for Den norske legeforening 136, no. 10 (2016): 894. http://dx.doi.org/10.4045/tidsskr.16.0441.

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23

Shub, Michael. "Morse-Smale systems." Scholarpedia 2, no. 3 (2007): 1785. http://dx.doi.org/10.4249/scholarpedia.1785.

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24

Hou, Chengjun, and Xiamoman Chen. "A note on the ideals of groupoid C*-algebras from Smale spaces." Bulletin of the Australian Mathematical Society 64, no. 2 (October 2001): 271–79. http://dx.doi.org/10.1017/s0004972700039939.

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In this note, we characterise completely the ideals of the groupoid C*-algebra arising from the asymptotic equivalence relation on the points of a Smale space and show that the related Ruelle algebra is simple when the Smale space is topologically transitive.

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25

Galewski, Marek. "On variational nonlinear equations with monotone operators." Advances in Nonlinear Analysis 10, no. 1 (August 2, 2020): 289–300. http://dx.doi.org/10.1515/anona-2020-0102.

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Abstract Using monotonicity methods and some variational argument we consider nonlinear problems which involve monotone potential mappings satisfying condition (S) and their strongly continuous perturbations. We investigate when functional whose minimum is obtained by a direct method of the calculus of variations satisfies the Palais-Smale condition, relate minimizing sequence and Galerkin approximaitons when both exist, then provide structure conditions on the derivative of the action functional under which bounded Palais-Smale sequences are convergent. Finally, we make some comment concerning the convergence of Palais-Smale sequence obtained in the mountain pass theorem due to Rabier.

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26

YU, BIN. "The templates of non-singular Smale flows on three manifolds." Ergodic Theory and Dynamical Systems 32, no. 3 (May 24, 2011): 1137–55. http://dx.doi.org/10.1017/s0143385711000150.

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AbstractIn this paper, we first discuss some connections between template theory and the description of basic sets of Smale flows on 3-manifolds due to F. Béguin and C. Bonatti. The main tools we use are symbolic dynamics, template moves and some combinatorial surgeries. Secondly, we obtain some relationship between the surgeries and the number of S1×S2 factors of M for a non-singular Smale flow on a given closed orientable 3-manifold M. We also prove that any template T can model a basic set Λ of a non-singular Smale flow on nS1×S2 for some positive integer n.

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27

Cho, Cheol-Hyun, and Hansol Hong. "Orbifold Morse–Smale–Witten complexes." International Journal of Mathematics 25, no. 05 (May 2014): 1450040. http://dx.doi.org/10.1142/s0129167x14500402.

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Given a Morse–Smale function on an effective orientable orbifold, we construct its Morse–Smale–Witten complex. We show that critical points of a certain type have to be discarded to build a complex properly, and that gradient flows should be counted with suitable weights. Its homology is proven to be isomorphic to the singular homology of the quotient space under the self-indexing assumption. For a global quotient orbifold [M/G], such a complex can be understood as the G-invariant part of the Morse complex of M, where the G-action on generators of the Morse complex has to be defined including orientation spaces of unstable manifolds at the critical points. Alternatively in the case of global quotients, we introduce the notion of weak group actions on Morse–Smale–Witten complexes for non-invariant Morse–Smale functions on M, which give rise to genuine group actions on the level of homology.

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Yang, Xiao Fang, and Jian Lu. "Nanostructured 316 Stainless Steel Prepared under Traction by Surface Mechanical Attrition Treatment." Materials Science Forum 614 (March 2009): 201–6. http://dx.doi.org/10.4028/www.scientific.net/msf.614.201.

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A nanostructured 316 austenitic stainless steel sample was prepared under traction using a new surface mechanical attrition treatment (SMAT) system. The microstructure of the surface layer of the SMATed sample was characterized using an optical microscope and transmission electron microscope (TEM). Microhardness on the cross-section was investigated by nanoindentation measurement. Results showed that a deeper nanostructured layer was obtained in comparison with that of the sample SMATed without traction.

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CHUA, LEON O. "LOCAL ACTIVITY IS THE ORIGIN OF COMPLEXITY." International Journal of Bifurcation and Chaos 15, no. 11 (November 2005): 3435–56. http://dx.doi.org/10.1142/s0218127405014337.

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Many scientists have struggled to uncover the elusive origin of "complexity", and its many equivalent jargons, such as emergence, self-organization, synergetics, collective behaviors, nonequilibrium phenomena, etc. They have provided some qualitative, but not quantitative, characterizations of numerous fascinating examples from many disciplines. For example, Schrödinger had identified "the exchange of energy" from open systems as a necessary condition for complexity. Prigogine has argued for the need to introduce a new principle of nature which he dubbed "the instability of the homogeneous". Turing had proposed "symmetry breaking" as an origin of morphogenesis. Smale had asked what "axiomatic" properties must a reaction–diffusion system possess to make the Turing interacting system oscillate. The purpose of this paper is to show that all the jargons and issues cited above are mere manifestations of a new fundamental principle called local activity, which is mathematically precise and testable. The local activity theorem provides the quantitative characterization of Prigogine's "instability of the homogeneous" and Smale's quest for an axiomatic principle on Turing instability. Among other things, a mathematical proof is given which shows none of the complexity-related jargons cited above is possible without local activity. Explicit mathematical criteria are given to identify a relatively small subset of the locally-active parameter region, called the edge of chaos, where most complex phenomena emerge.

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THOMSEN, KLAUS. "The homoclinic and heteroclinic C*-algebras of a generalized one-dimensional solenoid." Ergodic Theory and Dynamical Systems 30, no. 1 (June 29, 2009): 263–308. http://dx.doi.org/10.1017/s0143385709000042.

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AbstractD. Ruelle and I. Putnam have constructed three C*-algebras from the homoclinic and heteroclinic structure of a Smale space. This paper gives gives a complete description of these algebras when the Smale space is one of the generalized one-dimensional solenoids studied by R. Williams and I. Yi.

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Li, Qingdu, and Xiao-Song Yang. "A 3D Smale Horseshoe in a Hyperchaotic Discrete-Time System." Discrete Dynamics in Nature and Society 2007 (2007): 1–9. http://dx.doi.org/10.1155/2007/16239.

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This paper presents a three-dimensional topological horseshoe in the hyperchaotic generalized Hénon map. It looks like a planar Smale horseshoe with an additional vertical expansion, so we call it 3D Smale horseshoe. In this way, a computer assisted verification of existence of hyperchaos is provided by means of interval analysis.

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32

Grines, V. Z., E. Ya Gurevich, and O. V. Pochinka. "On Embedding of the Morse-Smale Diffeomorphisms in a Topological Flow." Contemporary Mathematics. Fundamental Directions 66, no. 2 (December 15, 2020): 160–81. http://dx.doi.org/10.22363/2413-3639-2020-66-2-160-181.

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This review presents the results of recent years on solving of the Palis problem on finding necessary and sufficient conditions for the embedding of Morse-Smale cascades in topological flows. To date, the problem has been solved by Palis for Morse-Smale diffeomorphisms given on manifolds of dimension two. The result for the circle is a trivial exercise. In dimensions three and higher new effects arise related to the possibility of wild embeddings of closures of invariant manifolds of saddle periodic points that leads to additional obstacles for Morse-Smale diffeomorphisms to embed in topological flows. The progress achieved in solving of Paliss problem in dimension three is associated with the recently obtained complete topological classification of Morse-Smale diffeomorphisms on three-dimensional manifolds and the introduction of new invariants describing the embedding of separatrices of saddle periodic points in a supporting manifold. The transition to a higher dimension requires the latest results from the topology of manifolds. The necessary topological information, which plays key roles in the proofs, is also presented in the survey.

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Ha, Seung-Yeal, Moon-Jin Kang, and Bongsuk Kwon. "A hydrodynamic model for the interaction of Cucker–Smale particles and incompressible fluid." Mathematical Models and Methods in Applied Sciences 24, no. 11 (August 6, 2014): 2311–59. http://dx.doi.org/10.1142/s0218202514500225.

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We present a new hydrodynamic model for the interactions between collision-free Cucker–Smale flocking particles and a viscous incompressible fluid. Our proposed model consists of two hydrodynamic models. For the Cucker–Smale flocking particles, we employ the pressureless Euler system with a non-local flocking dissipation, whereas for the fluid, we use the incompressible Navier–Stokes equations. These two hydrodynamic models are coupled through a drag force, which is the main flocking mechanism between the particles and the fluid. The flocking mechanism between particles is regulated by the Cucker–Smale model, which accelerates global flocking between the particles and the fluid. We show that this model admits the global-in-time classical solutions, and exhibits time-asymptotic flocking, provided that the initial data is appropriately small. In the course of our analysis for the proposed system, we first consider the hydrodynamic Cucker–Smale equations (the pressureless Euler system with a non-local flocking dissipation), for which the global existence and the time-asymptotic behavior of the classical solutions are also investigated.

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Gatey, Atul M., Santosh S. Hosmani, Rajkumar Singh, and Satyam Suwas. "Surface Engineering of Stainless Steels: Role of Surface Mechanical Attrition Treatment (SMAT)." Advanced Materials Research 794 (September 2013): 238–47. http://dx.doi.org/10.4028/www.scientific.net/amr.794.238.

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Surface mechanical attrition treatment (SMAT) technique has became popular to develop a nanostructured surface layer on metallic materials for upgrading their overall properties and performance. In this paper, we have presented the SMATing behavior of low stacking fault energy material like AISI 304 using optical microscopy, SEM, microhardness measurement and XRD analysis. SMATing was performed for 15, 30, 45, 60, 75, 90 min by using hardened bearing-steel balls (size: 5.7 mm diameter, hardness: 500HV0.1) at 50 Hz vibrating frequency. XRD analysis indicated the lowest grain-size of about 8.6 nm in the surface region of specimen SMATed for 60 min. In comparison with the non-SMATed specimen, 17 times increase in the dislocation density and 4 times increase in the micro-strain were observed in this SMATed specimen. Improvement in the surface-hardness due to the SMAT was almost two times hardness before SMAT was 190 HV0.1 and after SMAT it was 400 HV0.1. There is a gradual decrease in the hardness value across the cross-section of the specimen, and core-hardness value was reached after 300 μm depth below the surface. XRD results indicated the possibility of martensitic phase transformation at the surface during SMATing of AISI 304 steel. SMATed AISI 304 specimens showed good thermal stability at 550°C for 6 h which was confirmed by microhardness measurement

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Cheng, Xuhua, and Zhikun She. "Study on Chaotic Behavior of the Restricted Four-Body Problem with an Equilateral Triangle Configuration." International Journal of Bifurcation and Chaos 27, no. 02 (February 2017): 1750026. http://dx.doi.org/10.1142/s0218127417500262.

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In this paper, the chaotic behavior of a planar restricted four-body problem with an equilateral triangle configuration is analytically studied. Firstly, according to the perturbation method of Melnikov, the planar restricted four-body problem is regarded as a perturbation of the two-body model. Then, we show that the Melnikov integral function has a simple zero, arriving at the existence of transversal homoclinic orbits. Afterwards, since the standard Smale–Birkhoff homoclinic theorem cannot be directly applied to the case of a degenerate saddle, we alternatively construct an invertible map [Formula: see text] and check that [Formula: see text] is a Smale horseshoe map, showing that our restricted four-body problem possesses chaotic behavior of the Smale horseshoe type.

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36

Gutierrez, C., X. Jarque, J. Llibre, and M. A. Teixeira. "Global Injectivity ofC1Maps of the Real Plane, Inseparable Leaves and the Palais–Smale Condition." Canadian Mathematical Bulletin 50, no. 3 (September 1, 2007): 377–89. http://dx.doi.org/10.4153/cmb-2007-036-0.

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AbstractWe study two sufficient conditions that imply global injectivity for aC1mapX: ℝ2→ ℝ2such that its Jacobian at any point of ℝ2is not zero. One is based on the notion of half-Reeb component and the other on the Palais–Smale condition. We improve the first condition using the notion of inseparable leaves. We provide a new proof of the sufficiency of the second condition. We prove that both conditions are not equivalent, more precisely we show that the Palais–Smale condition implies the nonexistence of inseparable leaves, but the converse is not true. Finally, we show that the Palais–Smale condition it is not a necessary condition for the global injectivity of the mapX.

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DEELEY, ROBIN J., and KAREN R. STRUNG. "Group actions on Smale space -algebras." Ergodic Theory and Dynamical Systems 40, no. 9 (April 10, 2019): 2368–98. http://dx.doi.org/10.1017/etds.2019.11.

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Group actions on a Smale space and the actions induced on the $\text{C}^{\ast }$-algebras associated to such a dynamical system are studied. We show that an effective action of a discrete group on a mixing Smale space produces a strongly outer action on the homoclinic algebra. We then show that for irreducible Smale spaces, the property of finite Rokhlin dimension passes from the induced action on the homoclinic algebra to the induced actions on the stable and unstable $\text{C}^{\ast }$-algebras. In each of these cases, we discuss the preservation of properties (such as finite nuclear dimension, ${\mathcal{Z}}$-stability, and classification by Elliott invariants) in the resulting crossed products.

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DEELEY, ROBIN J., D. BRADY KILLOUGH, and MICHAEL F. WHITTAKER. "Functorial properties of Putnam’s homology theory for Smale spaces." Ergodic Theory and Dynamical Systems 36, no. 5 (March 19, 2015): 1411–40. http://dx.doi.org/10.1017/etds.2014.134.

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We investigate functorial properties of Putnam’s homology theory for Smale spaces. Our analysis shows that the addition of a conjugacy condition is necessary to ensure functoriality. Several examples are discussed that elucidate the need for our additional hypotheses. Our second main result is a natural generalization of Putnam’s Pullback Lemma from shifts of finite type to non-wandering Smale spaces.

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39

Elena Ya., Elena Ya, and Elena K. Rodionova. "Bicolor Graph of Morse-Smale Cascades on Manifolds of Dimension Three." Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva 25, no. 2 (June 30, 2023): 37–52. http://dx.doi.org/10.15507/2079-6900.25.202302.37-52.

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The purpose of this study is to single out a class of Morse-Smale cascades (diffeomorphisms) with a three-dimensional phase space that allow topological classification using combinatorial invariants. In the general case, an obstacle to such a classification is the possibility of wild embedding of separatrix closures in the ambient manifold, which leads to a countable set of topologically nonequivalent systems. To solve the problem, we study the orbit space of a cascade. The ambient manifold of a diffeomorphism can be represented as a union of three pairwise disjoint sets: a connected attractor and a repeller whose dimension does not exceed one, and their complement consisting of wandering points of a cascade called the characteristic set. It is known that the topology of the orbit space of the restriction of the Morse-Smale diffeomorphism to the characteristic set and the embedding of the projections of two-dimensional separatrices into it is a complete topological invariant for Morse-Smale cascades on three-dimensional manifolds. Moreover, a criterion for the inclusion of Morse-Smale cascades in the topological flow was obtained earlier.These results are used in this paper to show that the topological conjugacy classes of Morse-Smale cascades that are included in a topological flow and do not have heteroclinic curves admit a combinatorial description. More exactly, the class of Morse-Smale diffeomorphisms without heteroclinic intersections, defined on closed three-dimensional manifolds included in topological flows and not having heteroclinic curves, is considered. Each cascade from this class is associated with a two-color graph describing the mutual arrangement of two-dimensional separatrices of saddle periodic points. It is proved that the existence of an isomorphism of two-color graphs that preserves the color of edges is a necessary and sufficient condition for the topological conjugacy of cascades. It is shown that the speed of the algorithm that distinguishes two-color graphs depends polynomially on the number of its vertices. An algorithm for constructing a representative of each topological conjugacy class is described.

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40

Trivizoli, Lucieli M. "Cartas de Matemáticos Estrangeiros sobre o Contexto Brasileiro no Início da Década de 1970." Bolema: Boletim de Educação Matemática 33, no. 63 (April 2019): 290–308. http://dx.doi.org/10.1590/1980-4415v33n63a14.

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Resumo Em 1971, foi realizado o Simpósio Internacional de Sistemas Dinâmicos, em Salvador, com a participação de importantes matemáticos brasileiros e estrangeiros. Steve Smale, renomado matemático e ganhador da Medalha Fields, foi um dos palestrantes destacado no evento. Neste artigo, serão apresentadas a carta que Paul Koosis escreveu a Steve Smale criticando sua ida ao Brasil naquele momento político, a carta de Smale com sua resposta justificando a sua participação no evento e a carta em que Mike Shub descreve suas impressões sobre a atmosfera no Brasil durante o regime militar. Todas as cartas foram divulgadas no boletim informativo Mother Functor, no Departamento de Matemática da Universidade da Califórnia, em Berkeley. A partir das cartas, pretende-se levantar aspectos do contexto do desenvolvimento científico matemático no Brasil em meados das décadas de 1960 e 1970.

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MENDOZA JIMENEZ, Joel. "CONSTRUCCIÓN DE UNA HERRADURA CON MEDIDA DE LEBESGUE POSITIVA." Scientia 22, no. 22 (January 1, 2021): 187–208. http://dx.doi.org/10.31381/scientia.v22i22.3577.

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En este artículo, se estudia la construcción de una herradura con medida de Lebesgue positiva, esta herradura es edificada de manera análoga a la herradura de Smale. La diferencia es que la herradura de Smale tiene medida de Lebesgue cero presentando caos, que desde el punto de vista probabilístico podría ser despreciable, sin embargo al construir la herradura con medida positiva vemos que no lo es.

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NEKRASHEVYCH, VOLODYMYR. "SELF-SIMILAR INVERSE SEMIGROUPS AND SMALE SPACES." International Journal of Algebra and Computation 16, no. 05 (October 2006): 849–74. http://dx.doi.org/10.1142/s0218196706003153.

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Self-similar inverse semigroups are defined using automata theory. Adjacency semigroups of s-resolved Markov partitions of Smale spaces are introduced. It is proved that a Smale space can be reconstructed from the adjacency semigroup of its Markov partition, using the notion of the limit solenoid of a contracting self-similar semigroup. The notions of the limit solenoid and a contracting semigroup is described.

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43

Larson, Bill. "The Smale Collection II." Journal of Gemmology 37, no. 7 (2021): 745. http://dx.doi.org/10.15506/jog.2021.37.7.745.

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Gyulassy, Attila, David Gunther, Joshua A. Levine, Julien Tierny, and Valerio Pascucci. "Conforming Morse-Smale Complexes." IEEE Transactions on Visualization and Computer Graphics 20, no. 12 (December 31, 2014): 2595–603. http://dx.doi.org/10.1109/tvcg.2014.2346434.

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45

Lee, Manseob. "KUPKA-SMALE DIFFERENTIABLE MAPS." Journal of the Chungcheong Mathematical Society 28, no. 2 (May 15, 2015): 201–5. http://dx.doi.org/10.14403/jcms.2015.28.2.201.

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46

Burkin, I. M., and D. V. Soboleva. "On a Smale problem." Differential Equations 47, no. 1 (January 2011): 1–9. http://dx.doi.org/10.1134/s0012266111010010.

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47

Gao, Ping, and Bo-ling Guo. "Smale horseshoes and chaos in discretized perturbed NLS systems (II)—Smale horseshoes." Applied Mathematics and Mechanics 26, no. 11 (November 2005): 1402–8. http://dx.doi.org/10.1007/bf03246245.

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48

Fernando, Luiz, and C. Da Rocha. "Characterization of MorseSmale isotopy classes on surfaces." Ergodic Theory and Dynamical Systems 5, no. 1 (March 1985): 107–22. http://dx.doi.org/10.1017/s0143385700002789.

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AbstractIn this paper we use Thurston's work on the dynamics of diffeomorphisms on surfaces to show that a diffeomorphism ƒ on a surface is isotopic to a Morse- Smale one if and only if the growth rate of the length of the words representing elements of the fundamental group under iteration by ƒ is one. Morse-Smale isotopy classes are also shown to be the same as Nielsen's algebraically finite type.

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Yang, Ming Jin, Xi Wen Li, and Tie Lin Shi. "Fluid Flowing of Cohesive Mixing in the Tank of a Planetary Mixer." Applied Mechanics and Materials 109 (October 2011): 75–78. http://dx.doi.org/10.4028/www.scientific.net/amm.109.75.

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Fluid flowing of mixing is mathematically expressed as mapping. The Smale horseshoe map is a typical model for cohesive mixing, and has a tremendously positive influence on mixing. Based on Smale Horseshoe Mapping Model, a method of defining move parameters of the mixing system of a planetary mixer was presented in this paper. The fluid flowing of the mixing system obtained shows good performance of ergodicity and mixing.

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MA, JIMING, and BIN YU. "GENUS TWO SMALE–WILLIAMS SOLENOID ATTRACTORS IN 3-MANIFOLDS." Journal of Knot Theory and Its Ramifications 20, no. 06 (June 2011): 909–26. http://dx.doi.org/10.1142/s0218216511009108.

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Using alternating Heegaard diagrams, we construct some 3-manifolds which admit diffeomorphisms such that the non-wandering sets of the diffeomorphisms are composed of Smale–Williams solenoid attractors and repellers. An interesting example is the truncated-cube space. In addition, we prove that if the nonwandering set of the diffeomorphism consists of genus two Smale–Williams solenoids, then the Heegaard genus of the closed manifold is at most two.

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