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Journal articles on the topic 'Lifting property'

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Published: 4 June 2021

Last updated: 31 January 2023

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1

Macheras, N. D., and W. Strauss. "On products of almost strong liftings." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 60, no. 3 (June 1996): 311–33. http://dx.doi.org/10.1017/s1446788700037836.

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AbstractDealing with a problem posed by Kupka we give results concerning the permanence of the almost strong lifting property (respectively of the universal strong lifting property) under finite and countable products of topological probability spaces. As a basis we prove a theorem on the existence of liftings compatible with products for general probability spaces, and in addition we use this theorem for discussing finite products of lifting topologies.

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2

Giraldo, Antonio. "Shape Fibrations, Multivalued Maps and Shape Groups." Canadian Journal of Mathematics 50, no. 2 (April 1, 1998): 342–55. http://dx.doi.org/10.4153/cjm-1998-018-7.

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AbstractThe notion of shape fibration with the near lifting of near multivalued paths property is studied. The relation of thesemaps–which agreewith shape fibrations having totally disconnected fibers–with Hurewicz fibrations with the unique path lifting property is completely settled. Some results concerning homotopy and shape groups are presented for shape fibrations with the near lifting of near multivalued paths property. It is shown that for this class of shape fibrations the existence of liftings of a fine multivalued map is equivalent to an algebraic problem relative to the homotopy, shape or strong shape groups associated.

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3

Georgescu, George, and Claudia Mureşan. "Factor Congruence Lifting Property." Studia Logica 105, no. 1 (October 15, 2016): 179–216. http://dx.doi.org/10.1007/s11225-016-9687-7.

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4

Nagel, Uwe. "Lifting the k-Buchsbaum property." Journal of Pure and Applied Algebra 152, no. 1-3 (September 2000): 267–73. http://dx.doi.org/10.1016/s0022-4049(99)00130-9.

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5

Cheptea, Daniela, and George Georgescu. "Boolean lifting property in quantales." Soft Computing 24, no. 8 (February 15, 2020): 6169–81. http://dx.doi.org/10.1007/s00500-020-04752-8.

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6

Han, Sang-Eon. "Unique pseudolifting property in digital topology." Filomat 26, no. 4 (2012): 739–46. http://dx.doi.org/10.2298/fil1204739h.

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The generalized universal lifting property plays an important role in classical topology. In digital topology we also have its digital version [5, 6, 14]. More precisely, the paper [6] established the concept of a digital covering (see also [11, 17]). It has substantially contributed to the calculation of digital fundamental groups of some digital spaces, the classification of digital spaces and so forth. The paper [6] also established the unique lifting property of a digital covering which plays an important role in studying both digital covering and digital homotopy theory. Motivated by the unique lifting property, the paper develops a pseudocovering which is weaker than a digital covering and investigates its various properties. Furthermore, the paper proves that a pseudocovering with some hypothesis has the unique pseudolifting property which is weaker than the unique lifting property in digital covering theory.

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7

Majid, Mohammed, and Ghafur Abd. "Principally supplemented module and lifting property." International Journal of Physical Sciences 8, no. 19 (May 23, 2013): 967–72. http://dx.doi.org/10.5897/ijps2013.3856.

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8

Georgescu, George, and Claudia Mureşan. "Boolean lifting property for residuated lattices." Soft Computing 18, no. 11 (July 16, 2014): 2075–89. http://dx.doi.org/10.1007/s00500-014-1318-5.

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9

Kermani, Neda Arjomand, Esfandiar Eslami, and Arsham Borumand Saeid. "Central lifting property for orthomodular lattices." Mathematica Slovaca 70, no. 6 (December 16, 2020): 1307–16. http://dx.doi.org/10.1515/ms-2017-0433.

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AbstractWe introduce and investigate central lifting property (CLP) for orthomodular lattices as a property whereby all central elements can be lifted modulo every p-ideal. It is shown that prime ideals, maximal ideals and finite p-ideals have CLP. Also Boolean algebras, simple chain finite orthomodular lattices, subalgebras of an orthomodular lattices generated by two elements and finite orthomodular lattices have CLP. The main results of the present paper include the investigation of CLP for principal p-ideals and finite direct products of orthomodular lattices.

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10

Chinburg, T., R. Guralnick, and D. Harbater. "Oort groups and lifting problems." Compositio Mathematica 144, no. 4 (July 2008): 849–66. http://dx.doi.org/10.1112/s0010437x08003515.

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AbstractLet k be an algebraically closed field of positive characteristic p. We consider which finite groups G have the property that every faithful action of G on a connected smooth projective curve over k lifts to characteristic zero. Oort conjectured that cyclic groups have this property. We show that if a cyclic-by-p group G has this property, then G must be either cyclic or dihedral, with the exception of A4 in characteristic two. This proves one direction of a strong form of the Oort conjecture.

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11

Crivei, Septimiu. "Relatively Lifting Modules." Algebra Colloquium 17, spec01 (December 2010): 789–98. http://dx.doi.org/10.1142/s1005386710000738.

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We consider a generalization of lifting modules relative to a class [Formula: see text] of modules and a proper class 𝔼 of short exact sequences of modules. These modules will be called 𝔼-[Formula: see text]-lifting. We establish characterizations of modules with the property that every direct sum of copies of them is 𝔼-[Formula: see text]-lifting.

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12

Georgescu, G. "New results on Congruence Boolean Lifting Property." Journal of Algebraic Hyperstructures and Logical Algebras 3, no. 1 (February 1, 2022): 15–34. http://dx.doi.org/10.52547/hatef.jahla.3.1.3.

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13

Charatonik, Janusz J. "The lifting property for classes of mappings." International Journal of Mathematics and Mathematical Sciences 23, no. 10 (2000): 717–22. http://dx.doi.org/10.1155/s0161171200002763.

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The lifting property of continua for classes of mappings is defined. It is shown that the property is preserved under the inverse limit operation. The results, when applied to the class of confluent mappings, exhibit conditions under which the induced mapping between hyperspaces is confluent. This generalizes previous results in this topic.

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14

Caselli, Fabrizio, and Paolo Sentinelli. "The generalized lifting property of Bruhat intervals." Journal of Algebraic Combinatorics 45, no. 3 (October 14, 2016): 687–700. http://dx.doi.org/10.1007/s10801-016-0721-7.

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15

Courtney, Kristin E. "Universal $C^∗$-algebras with the local lifting property." MATHEMATICA SCANDINAVICA 127, no. 2 (August 31, 2021): 361–81. http://dx.doi.org/10.7146/math.scand.a-126018.

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The Local Lifting Property (LLP) is a localized version of projectivity for completely positive maps between $\mathrm{C}^*$-algebras. Outside of the nuclear case, very few $\mathrm{C}^*$-algebras are known to have the LLP\@. In this article, we show that the LLP holds for the algebraic contraction $\mathrm{C}^*$-algebras introduced by Hadwin and further studied by Loring and Shulman. We also show that the universal Pythagorean $\mathrm{C}^*$-algebras introduced by Brothier and Jones have the Lifting Property.

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16

Black, Elena V. "On Semidirect Products and the Arithmetic Lifting Property." Journal of the London Mathematical Society 60, no. 3 (December 1999): 677–88. http://dx.doi.org/10.1112/s002461079900784x.

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17

Grekas, S. "Remarks on the strong lifting property for products." Israel Journal of Mathematics 58, no. 2 (June 1987): 198–204. http://dx.doi.org/10.1007/bf02785677.

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18

Johnson, William B., and Timur Oikhberg. "Separable lifting property and extensions of local reflexivity." Illinois Journal of Mathematics 45, no. 1 (January 2001): 123–37. http://dx.doi.org/10.1215/ijm/1258138258.

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19

Vanaja, N. "Lifting Property of Direct Sums of Hollow Modules." Communications in Algebra 35, no. 10 (September 21, 2007): 3110–27. http://dx.doi.org/10.1080/00927870701405157.

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20

Hager, Anthony W., and Robert Raphael. "The countable lifting property for Riesz space surjections." Indagationes Mathematicae 27, no. 1 (January 2016): 75–84. http://dx.doi.org/10.1016/j.indag.2015.07.005.

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21

Kye, Seung-Hyeok, and Zhong-Jin Ruan. "On the Local Lifting Property for Operator Spaces." Journal of Functional Analysis 168, no. 2 (November 1999): 355–79. http://dx.doi.org/10.1006/jfan.1999.3475.

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22

Hadwin, Don. "A Lifting Characterization of Rfd C*-Algebras." MATHEMATICA SCANDINAVICA 115, no. 1 (August 12, 2014): 85. http://dx.doi.org/10.7146/math.scand.a-18004.

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We prove a conjecture of Terry Loring that characterizes separable RFD C*-algebras in terms of a lifting property. In addition we introduce and study generalizations of RFD algebras. If $k$ is an infinite cardinal, we say a C*-algebra is residually less than $k$ dimensional, if the family of representations on Hilbert spaces of dimension less than $k$ separates the points of the algebra. We give characterizations of this property and prove that this class is closed under free products in the nonunital category. For free products in the unital category, the results depend on the cardinal $k$.

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23

Dawood, Suliman. "OnCℵ-Fibrations in Bitopological Semigroups." Scientific World Journal 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/675761.

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We extend the path lifting property in homotopy theory for topological spaces to bitopological semigroups and we show and prove its role in theCℵ-fibration property. We give and prove the relationship between theCℵ-fibration property and an approximate fibration property. Furthermore, we study the pullback maps forCℵ-fibrations.

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24

Juárez-Anguiano, H., F. Marmolejo, and C. Oldair-Renteria. "A characterization of proper morphisms by the lifting property." Topology and its Applications 312 (May 2022): 108087. http://dx.doi.org/10.1016/j.topol.2022.108087.

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25

Dong, Zhe. "On the approximating local lifting property for operator spaces." Journal of Mathematical Analysis and Applications 336, no. 2 (December 2007): 1054–60. http://dx.doi.org/10.1016/j.jmaa.2007.03.056.

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26

Dong, Z. "On the Local Lifting Properties of Operator Spaces." Canadian Journal of Mathematics 61, no. 6 (December 1, 2009): 1262–78. http://dx.doi.org/10.4153/cjm-2009-059-7.

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Abstract In this paper, we mainly study operator spaces which have the locally lifting property (LLP). The dual of any ternary ring of operators is shown to satisfy the strongly local reflexivity, and this is used to prove that strongly local reflexivity holds also for operator spaces which have the LLP. Several homological characterizations of the LLP and weak expectation property are given. We also prove that for any operator space V, V** has the LLP if and only if V has the LLP and V* is exact.

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27

Brazas, Jeremy, and Hanspeter Fischer. "Test map characterizations of local properties of fundamental groups." Journal of Topology and Analysis 12, no. 01 (September 4, 2018): 37–85. http://dx.doi.org/10.1142/s1793525319500390.

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Local properties of the fundamental group of a path-connected topological space can pose obstructions to the applicability of covering space theory. A generalized covering map is a generalization of the classical notion of covering map defined in terms of unique lifting properties. The existence of generalized covering maps depends entirely on the verification of the unique path lifting property for a standard covering construction. Given any path-connected metric space [Formula: see text], and a subgroup [Formula: see text], we characterize the unique path lifting property relative to [Formula: see text] in terms of a new closure operator on the [Formula: see text]-subgroup lattice that is induced by maps from a fixed “test” domain into [Formula: see text]. Using this test map framework, we develop a unified approach to comparing the existence of generalized coverings with a number of related properties.

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28

Bosi, Gianni, and Magalì Zuanon. "Lifting Theorems for Continuous Order-Preserving Functions and Continuous Multi-Utility." Axioms 12, no. 2 (January 27, 2023): 123. http://dx.doi.org/10.3390/axioms12020123.

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We present some lifting theorems for continuous order-preserving functions on locally and σ-compact Hausdorff preordered topological spaces. In particular, we show that a preorder on a locally and σ-compact Hausdorff topological space has a continuous multi-utility representation if, and only if, for every compact subspace, every continuous order-preserving function can be lifted to the entire space. Such a characterization is also presented by introducing a lifting property of ≾-C-compatible continuous order-preserving functions on closed subspaces. The assumption of paracompactness is also used in connection to lifting conditions.

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29

ORHAN, NIL, and DERYA KESKIN TÜTÜNCÜ. "CHARACTERIZATIONS OF LIFTING MODULES IN TERMS OF COJECTIVE MODULES AND THE CLASS OF ℬ(M,X)." International Journal of Mathematics 16, no. 06 (July 2005): 647–60. http://dx.doi.org/10.1142/s0129167x05003041.

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In this note, we introduce the (small, pseudo-)ℬ(M,X)-cojective modules and we generalize (small, pseudo-)cojective modules via the class ℬ(M,X). Let M = M1 ⊕ M2 be an X-amply supplemented module with the finite internal exchange property. Then for every decomposition of M = Mi ⊕ Mj, Mi is ℬ(Mj,X)-cojective for i ≠ j, M1 and M2 are X-lifting if and only if M is X-lifting. We also prove that for an X-amply supplemented module M = M1 ⊕ M2 such that M1 and M2 are indecomposable X-lifting modules, if M2 is ℬ(M1,X)-cojective and M1 is small-ℬ(M2,X)-cojective then M is X-lifting.

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30

Bondarko, M. V., and V. A. Sosnilo. "On the Weight Lifting Property for Localizations of Triangulated Categories." Lobachevskii Journal of Mathematics 39, no. 7 (September 2018): 970–84. http://dx.doi.org/10.1134/s1995080218070077.

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31

Kuratomi, Yosuke. "On Direct Sums of Lifting Modules and Internal Exchange Property." Communications in Algebra 33, no. 6 (May 2005): 1795–804. http://dx.doi.org/10.1081/agb-200063365.

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32

Basu, Amitabh, and Joseph Paat. "Operations that Preserve the Covering Property of the Lifting Region." SIAM Journal on Optimization 25, no. 4 (January 2015): 2313–33. http://dx.doi.org/10.1137/140990413.

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33

Barani nia, B., and A. Borumand Saeid. "Classes of pseudo BL-algebras with right Boolean lifting property." Transactions of A. Razmadze Mathematical Institute 172, no. 2 (August 2018): 146–63. http://dx.doi.org/10.1016/j.trmi.2017.09.003.

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34

Pisier, Gilles. "A non-nuclear $$C^*$$-algebra with the weak expectation property and the local lifting property." Inventiones mathematicae 222, no. 2 (June 17, 2020): 513–44. http://dx.doi.org/10.1007/s00222-020-00977-4.

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35

Enochs, Edgar E., and Ivo Herzog. "A Homotopy of Quiver Morphisms with Applications to Representations." Canadian Journal of Mathematics 51, no. 2 (April 1, 1999): 294–308. http://dx.doi.org/10.4153/cjm-1999-015-0.

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AbstractIt is shown that a morphism of quivers having a certain path lifting property has a decomposition that mimics the decomposition of maps of topological spaces into homotopy equivalences composed with fibrations. Such a decomposition enables one to describe the right adjoint of the restriction of the representation functor along a morphism of quivers having this path lifting property. These right adjoint functors are used to construct injective representations of quivers. As an application, the injective representations of the cyclic quivers are classified when the base ring is left noetherian. In particular, the indecomposable injective representations are described in terms of the injective indecomposable R-modules and the injective indecomposable R[x; x−1]-modules.

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36

Liao, Fanghui, and Zongguang Liu. "Some Properties of Triebel–Lizorkin and Besov Spaces Associated with Zygmund Dilations." Canadian Mathematical Bulletin 59, no. 4 (December 1, 2016): 834–48. http://dx.doi.org/10.4153/cmb-2016-030-9.

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AbstractIn this paper, using Calderón’s reproducing formula and almost orthogonality estimates, we prove the lifting property and the embedding theorem of the Triebel–Lizorkin and Besov spaces associated with Zygmund dilations.

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37

Hsu, Yu-Ping. "The Lifting of the UKK Property from E to C E." Proceedings of the American Mathematical Society 123, no. 9 (September 1995): 2695. http://dx.doi.org/10.2307/2160563.

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38

Giraldo, Antonio, and Jose M. R. Sanjurjo. "Multifibrations. A Class of Shape Fibrations with the Path Lifting Property." Czechoslovak Mathematical Journal 51, no. 1 (March 2001): 29–38. http://dx.doi.org/10.1023/a:1013793418931.

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39

Eder, S. "SOME ASPECTS OF THE LIFTING PROPERTY OF THE SPACE £∞(μ,X)." Quaestiones Mathematicae 21, no. 3-4 (November 1998): 269–88. http://dx.doi.org/10.1080/16073606.1998.9632046.

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40

Wang, Chengyun, Feng Tian, Shanjie Zhao, Guansiwei Shang, Yuteng Ma, and Dawei Chen. "Design of Monitoring PTZ with High Scalability." Frontiers of Mechatronical Engineering 2, no. 1 (May 28, 2020): 13. http://dx.doi.org/10.18282/fme.v2i1.839.

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<p>Provided a design scheme of a lifting PTZ with high-scalability for detecting search and rescue robots based on the analysis and reference o f various lifting mechanisms at home and abroad. It proposed a rigid-flexible dual-property automatic lifting mechanism transmission scheme which adopt s a roll-up spring as a supporting mechanism, a gear and a sprocket as a transmission mechanism, and a telescopic rod as an auxiliary supporting mechanism, which provides a new solution for the disadvantages of the traditional lifting mechanisms with large original volume and poor telescopic performance. Through the actual test, the mechanism can raise to the target stroke of 2 meters in 60s smoothly and widen the field of view of the image capturing device effectively based on the detection and rescue robot, which improves the ability of passing the narrow space and rescuing obviously.</p>

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41

Zhao, Rui Dong, Chun Ming Xiong, Zhen Tao, Jian Jun Zhang, Lei Su, Chun Qing Lin, and Hua Yong Liu. "A New Nodal Analysis Method of Artificial Lifting System." Advanced Materials Research 402 (November 2011): 812–15. http://dx.doi.org/10.4028/www.scientific.net/amr.402.812.

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Nodal analysis, defined as a systems approach to the optimization of oil and gas wells, is used to evaluate thoroughly a complete producing system. For the systematicness easily ignored during the design of artificial lifting system, based on coordination principle of reservoir, wellbore and lifting equipment, the concept of well performance curves are proposed. With the well performance curves, a new nodal analysis method of artificial lifting system is obtained, which is more efficient. Upstream and downstream pressure of pump and pressure difference provided by pump are displayed in well performance curve, which reflects the property of the well itself. Through further research of well performance curve, the energy of well itself will be fully developed, system effectiveness will be raised, and energy consumption will be reduced.

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42

Diesl, Alexander J., Samuel J. Dittmer, and Pace P. Nielsen. "Idempotent lifting and ring extensions." Journal of Algebra and Its Applications 15, no. 06 (March 30, 2016): 1650112. http://dx.doi.org/10.1142/s0219498816501127.

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We answer multiple open questions concerning lifting of idempotents that appear in the literature. Most of the results are obtained by constructing explicit counter-examples. For instance, we provide a ring [Formula: see text] for which idempotents lift modulo the Jacobson radical [Formula: see text], but idempotents do not lift modulo [Formula: see text]. Thus, the property “idempotents lift modulo the Jacobson radical” is not a Morita invariant. We also prove that if [Formula: see text] and [Formula: see text] are ideals of [Formula: see text] for which idempotents lift (even strongly), then it can be the case that idempotents do not lift over [Formula: see text]. On the positive side, if [Formula: see text] and [Formula: see text] are enabling ideals in [Formula: see text], then [Formula: see text] is also an enabling ideal. We show that if [Formula: see text] is (weakly) enabling in [Formula: see text], then [Formula: see text] is not necessarily (weakly) enabling in [Formula: see text] while [Formula: see text] is (weakly) enabling in [Formula: see text]. The latter result is a special case of a more general theorem about completions. Finally, we give examples showing that conjugate idempotents are not necessarily related by a string of perspectivities.

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43

PESIN, YA B., S. SENTI, and K. ZHANG. "Lifting measures to inducing schemes." Ergodic Theory and Dynamical Systems 28, no. 2 (April 2008): 553–74. http://dx.doi.org/10.1017/s0143385707000806.

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AbstractIn this paper we study the liftability property for piecewise continuous maps of compact metric spaces, which admit inducing schemes in the sense of Pesin and Senti [Y. Pesin and S. Senti. Thermodynamical formalism associated with inducing schemes for one-dimensional maps. Mosc. Math. J.5(3) (2005), 669–678; Y. Pesin and S. Senti. Equilibrium measures for maps with inducing schemes. Preprint, 2007]. We show that under some natural assumptions on the inducing schemes—which hold for many known examples—any invariant ergodic Borel probability measure of sufficiently large entropy can be lifted to the tower associated with the inducing scheme. The argument uses the construction of connected Markov extensions due to Buzzi [J. Buzzi. Markov extensions for multi-dimensional dynamical systems. Israel J. Math.112 (1999), 357–380], his results on the liftability of measures of large entropy, and a generalization of some results by Bruin [H. Bruin. Induced maps, Markov extensions and invariant measures in one-dimensional dynamics. Comm. Math. Phys.168(3) (1995), 571–580] on relations between inducing schemes and Markov extensions. We apply our results to study the liftability problem for one-dimensional cusp maps (in particular, unimodal and multi-modal maps) and for some multi-dimensional maps.

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44

Shibata, Yoshiharu. "On lifting and extending properties on direct sums of hollow uniform modules." Algebra and Discrete Mathematics 33, no. 1 (2022): 156–64. http://dx.doi.org/10.12958/adm1643.

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A module M is said to belifting if, for anysubmodule N of M, there exists a direct summand X of M contained in N such that N/X is small in M/X. A module M is said to satisfy the finite internal exchange propertyif, for any direct summand X of M and any finite direct sum decomposition M=Lni=1Mi, there exists a direct summand M′i of Mi (i= 1,2, . . . , n) such that M=X⊕(Lni=1M′i). In this paper, we first give characterizations forthe square of a hollow and uniform module to be lifting (extending). In addition, we solve negatively the question "Does any lifting module satisfy the finite internal exchange property?" as an application of this result.

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45

Gonzalez, M., and V. M. Onieva. "Lifting results for sequences in Banach spaces." Mathematical Proceedings of the Cambridge Philosophical Society 105, no. 1 (January 1989): 117–21. http://dx.doi.org/10.1017/s0305004100001419.

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Several important classes of Banach spaces are characterized by means of convergence properties of sequences. For example, if X is a Banach space, then X belongs to the class Nl1 of spaces without copies of l1, the class R of reflexive spaces or the class F of finite-dimensional spaces if and only if each bounded sequence has respectively a weakly Cauchy (w-Cauchy), weakly convergent (w-convergent) or convergent subsequence. Similarly X is in the class WSC of weakly sequentially complete spaces, or the class SCH of spaces with the Schur property if and only if each w-Cauchy sequence is w-convergent, or convergent, respectively; note that X ∈ SCH if and only if each w-convergent sequence of X is convergent (see [12], p. 47).

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46

Puechmorel, Stéphane. "Lifting Dual Connections with the Riemann Extension." Mathematics 8, no. 11 (November 21, 2020): 2079. http://dx.doi.org/10.3390/math8112079.

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Let (M,g) be a Riemannian manifold equipped with a pair of dual connections (∇,∇*). Such a structure is known as a statistical manifold since it was defined in the context of information geometry. This paper aims at defining the complete lift of such a structure to the cotangent bundle T*M using the Riemannian extension of the Levi-Civita connection of M. In the first section, common tensors are associated with pairs of dual connections, emphasizing the cyclic symmetry property of the so-called skewness tensor. In a second section, the complete lift of this tensor is obtained, allowing the definition of dual connections on TT*M with respect to the Riemannian extension. This work was motivated by the general problem of finding the projective limit of a sequence of a finite-dimensional statistical manifold.

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47

Yassin Habeeb, Zahraa, and Daher Al Baydli. "MIXED SERRE FIBRATION." Wasit Journal of Pure sciences 1, no. 2 (September 1, 2022): 50–60. http://dx.doi.org/10.31185/wjps.37.

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-In this paper we introduce and study new concept the mixed Serre fibration (M-Serre fibration) on CW-complex space, and Mixed path lifting property (by short M-PLP). Most of theorems which are valid for Serre fibration be also valid for M-Serre fibration.

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48

Zhan, Wei Xia, Ji Wen Tan, and Yan Wen. "De-Noising of Damage Signal in Wire Rope Based on Adaptive Lifting Wavelet." Advanced Materials Research 139-141 (October 2010): 2556–60. http://dx.doi.org/10.4028/www.scientific.net/amr.139-141.2556.

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At the basis of the adaptive lifting wavelet transform, a method was proposed for solving the problem of noise suppression of the wire rope damage signals. A wavelet with damage property was constructed via lifting scheme, that is,the adaptive update-filter and the adaptive predict-filter were designed using the statistics information of the wire rope damage signals. And the compromise algorithm between software-threshold and hard-threshold was used in the threshold processing. The traditional wavelet and the above proposed transform are applied in de-noising of the practical acquisition of wire rope damage signal. The contrast experiments show that the noise elimination with the improved lifting scheme is better than that achieved by traditional wavelet transform. Moreover, this presented scheme retains the effective information in the break signals and greatly improves the design flexibility and the process speed.

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49

Hsu, Yu-Ping. "The lifting of the UKK property from $E$ to $C\sb E$." Proceedings of the American Mathematical Society 123, no. 9 (September 1, 1995): 2695. http://dx.doi.org/10.1090/s0002-9939-1995-1246527-2.

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50

Oja, Eve. "Lifting of the approximation property from Banach spaces to their dual spaces." Proceedings of the American Mathematical Society 135, no. 11 (November 1, 2007): 3581–88. http://dx.doi.org/10.1090/s0002-9939-07-08996-4.

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