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Journal articles on the topic 'Weakly decomposition'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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1

Hernandez, Bryan, Deza Amistas, Ralph John De la Cruz, Lauro Fontanil, Aurelio de los Reyes, and Eduardo Mendoza. "Independent, Incidence Independent and Weakly Reversible Decompositions of Chemical Reaction Networks." MATCH Communications in Mathematical and in Computer Chemistry 87, no. 2 (2021): 367–96. http://dx.doi.org/10.46793/match.87-2.367h.

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Chemical reaction networks (CRNs) are directed graphs with reactant or product complexes as vertices, and reactions as arcs. A CRN is weakly reversible if each of its connected components is strongly connected. Weakly reversible networks can be considered as the most important class of reaction networks. Now, the stoichiometric subspace of a network is the linear span of the reaction vectors (i.e., difference between the product and the reactant complexes). A decomposition of a CRN is independent (incidence independent) if the direct sum of the stoichiometric subspaces (incidence maps) of the

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2

Cariello, Daniel. "Separability for weakly irreducible matrices." Quantum Information and Computation 14, no. 15&16 (2014): 1308–37. http://dx.doi.org/10.26421/qic14.15-16-4.

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This paper is devoted to the study of the separability problem in the field of Quantum information theory. We focus on the bipartite finite dimensional case and on two types of matrices: SPC and PPT matrices (see definitions 32 and 33). We prove that many results hold for both types. If these matrices have specific Hermitian Schmidt decompositions then they are separable in a very strong sense (see theorem 38 and corollary 39). We prove that both types have what we call \textbf{split decompositions} (see theorems 41 and 42). We also define the notion of weakly irreducible matrix (see definitio

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3

Jain, S. K., and S. R. López-Permouth. "Weakly-injective modules over hereditary noetherian prime rings." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 58, no. 3 (1995): 287–97. http://dx.doi.org/10.1017/s1446788700038325.

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AbstractA module M is said to be wealdy-injective if and only if for every finitely generated submodule N of the injective hull E(M) of M there exists a submodule X of E(M), isomorphic to M such that N ⊂ X. In this paper we investigate weakly-injective modules over bounded hereditary noetherian prime rings. In particular we show that torsion-free modules over bounded hnp rings are always wealdy-injective, while torsion modules with finite Goldie dimension are weakly-injective only if they are injective.As an application, we show that weakly-injective modules over bounded Dedekind prime rings h

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4

Caldas, Miguel, and Saeid Jafari. "A decomposition of $\boldsymbol{\delta}$-open functions." Sarajevo Journal of Mathematics 11, no. 2 (2024): 267–71. http://dx.doi.org/10.5644/sjm.11.2.12.

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In 2008, M. Caldas and G. Navalagi introduced a new class of generalized open functions called weakly $\delta$-open functions. By introducing a new type of open functions called relatively weakly $\delta$-open together with weakly $\delta$-open functions, we establish a new decomposition of $\delta$-open functions. 2010 Mathematics Subject Classification. 54A40, 54C10, 54D10; Secondary: 54C08

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Khare, Mona, and Bhawna Singh. "Weakly tight functions and their decomposition." International Journal of Mathematics and Mathematical Sciences 2005, no. 18 (2005): 2991–98. http://dx.doi.org/10.1155/ijmms.2005.2991.

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The present paper deals with the study of a weakly tight function and its relation to tight functions. We obtain a Jordan-decomposition-type theorem for a locally bounded weakly tight real-valued function defined on a sublattice ofIX, followed by the notion of a total variation.

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6

Mihai, Talmaciu, and Nechita Elena. "BRAIN Journal - Optimization Problems on Threshold Graphs." Brain Journal 1, SPECIAL ISSUE ON COMPLEXITY IN SCIENCES AND ARTIFICIAL INTELLIGENCE (2010): 61–68. https://doi.org/10.5281/zenodo.1036727.

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ABSTRACT During the last three decades, different types of decompositions have been processed in the field of graph theory. Among these we mention: decompositions based on the additivity of some characteristics of the graph, decompositions where the adjacency law between the subsets of the partition is known, decompositions where the subgraph induced by every subset of the partition must have predeterminate properties, as well as combinations of such decompositions. In this paper we characterize threshold graphs using the weakly decomposition, determine: density and stability number, Wiener in

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Chen, Bang-Yen, Uday de, and Fatemah Mofarreh. "Study of weakly Ricci-symmetric spacetimes under gray’s decomposition and f (R,T)-gravity." Filomat 36, no. 7 (2022): 2391–401. http://dx.doi.org/10.2298/fil2207391c.

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In this paper we characterize weakly Ricci-symmetric spacetimes (WRS)n endowed with the Gray?s Decomposition. We provide, several interesting results of (WRS)n in Gray?s Decomposition. In addition we discuss some results based on weakly Ricci-symmetric Generalized Robertson Walker (GRW) spacetimes. Moreover, we study (WRS)n spacetimes which satisfy the f (R, T)-gravity equation.

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8

Talmaciu, Mihai, and Elena Nechita. "On Polar, Trivially Perfect Graphs." International Journal of Computers Communications & Control 5, no. 5 (2010): 939. http://dx.doi.org/10.15837/ijccc.2010.5.2257.

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<p>During the last decades, different types of decompositions have been processed in the field of graph theory. In various problems, for example in the construction of recognition algorithms, frequently appears the so-called weakly decomposition of graphs.<br />Polar graphs are a natural extension of some classes of graphs like bipartite graphs, split graphs and complements of bipartite graphs. Recognizing a polar graph is known to be NP-complete. For this class of graphs, polynomial algorithms for the maximum stable set problem are unknown and algorithms for the dominating set pro

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Singh Khurana, Surjit. "A decomposition of bounded, weakly measurable functions." Tatra Mountains Mathematical Publications 49, no. 1 (2011): 67–70. http://dx.doi.org/10.2478/v10127-011-0025-1.

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ABSTRACT Let (X,A,μ) be a complete probability space, ρ a lifting, Tρ the associated Hausdorff lifting topology on X and E a Banach space. Suppose F: (X,Tρ)-> E”σ be a bounded continuous mapping. It is proved that there is an A ∈ A such that FXA has range in a closed separable subspace of E (so FXA:X → E is strongly measurable) and for any B ∈ A with μ(B) > 0 and B ∩ A = ø, FXB cannot be weakly equivalent to a E-valued strongly measurable function. Some known results are obtained as corollaries.

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10

Michel, Joachim, and Mei-Chi Shaw. "A decomposition problem on weakly pseudoconvex domains." Mathematische Zeitschrift 230, no. 1 (1999): 1–19. http://dx.doi.org/10.1007/pl00004685.

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11

Bandelt, Hans-Jürgen, and Victor Chepoi. "Decomposition andl1-Embedding of Weakly Median Graphs." European Journal of Combinatorics 21, no. 6 (2000): 701–14. http://dx.doi.org/10.1006/eujc.1999.0377.

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12

R. Rajeswari and A. Muhaseen Fathima. "STRUCTURE OF WEAKLY SEMI-I-OPEN SETS VIA SEMI LOCAL FUNCTIONS." jnanabha 53, no. 01 (2023): 55–61. http://dx.doi.org/10.58250/jnanabha.2023.53106.

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We introduce, study and investigate the concepts of weakly semi -Is - open sets and some properties of the set. We introduce weakly semi -Is- open functions and weakly semi -Is- closed functions. Also, we introduced notion of weakly semi -Is- open sets and weakly semi -Is- closed sets. We discussed its properties and its relationship between other sets in topological spaces as said in below introduction. We also furnish decomposition of continuity in this paper.

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Kubrusly, C. S., and P. C. M. Vieira. "Boundedly Spaced Subsequences and Weak Dynamics." Journal of Function Spaces 2018 (September 5, 2018): 1–5. http://dx.doi.org/10.1155/2018/4732836.

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Weak supercyclicity is related to weak stability, which leads to the question that asks whether every weakly supercyclic power bounded operator is weakly stable. This is approached here by investigating weak l-sequential supercyclicity for Hilbert-space contractions through Nagy–Foliaş–Langer decomposition, thus reducing the problem to the quest of conditions for a weakly l-sequentially supercyclic unitary operator to be weakly stable, and this is done in light of boundedly spaced subsequences.

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14

Krishna, Kumar Srivastava. "Central SS-Elements of a Ring." MATHEMATICS EDUCATION LV, no. 3, September 2021 (2021): 35–40. https://doi.org/10.5281/zenodo.7418690.

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         <em> The notions of Central SS-elements, weakly idempotent SS-element of a ring are initiated and some results are obtained. Further, it is shown that every element ‘a’ of ring has a decomposition a=e+f, where e is an idempotent element and f is weakly idempotent SS-element satisfying the condition ef=0.          </em>

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15

Ebert, Udo. "The decomposition of inequality reconsidered: Weakly decomposable measures." Mathematical Social Sciences 60, no. 2 (2010): 94–103. http://dx.doi.org/10.1016/j.mathsocsci.2010.05.001.

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16

Talmaciu, Mihai, Elena Nechita, and Laszlo Barna Iantovics. "Recognition and Combinatorial Optimization Algorithms for Bipartite Chain Graphs." Computing and Informatics 32, no. 2 (2013): 313–29. https://doi.org/10.5281/zenodo.10436224.

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In this paper we give a recognition algorithm in O(n(n+m)) time for bipartite chain graphs, and directly calculate the density of such graphs. For their stability number and domination number, we give algorithms comparable to the existing ones. We point out some applications of bipartite chain graphs in chemistry and approach the Minimum Chain Completion problem.

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17

Hatir, Esref, and Saeid Jafari. "On Weakly Semi-I-Open Sets and Another Decomposition of Continuity via Ideals." Sarajevo Journal of Mathematics 2, no. 1 (2024): 107–14. http://dx.doi.org/10.5644/sjm.02.1.11.

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In this paper, we introduce the notions of weakly semi-I-open set and weakly semi-I-continuous functions to obtain a decomposition of continuity. We also investigated the fundamental properties of such functions. 1991 Mathematics Subject Classification. Primary: 54C10, 54A05; Secondary: 54D25, 54D30

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18

Piazza, Luisa Di, and Kazimierz Musiał. "Decompositions of Weakly Compact Valued Integrable Multifunctions." Mathematics 8, no. 6 (2020): 863. http://dx.doi.org/10.3390/math8060863.

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We give a short overview on the decomposition property for integrable multifunctions, i.e., when an “integrable in a certain sense” multifunction can be represented as a sum of one of its integrable selections and a multifunction integrable in a narrower sense. The decomposition theorems are important tools of the theory of multivalued integration since they allow us to see an integrable multifunction as a translation of a multifunction with better properties. Consequently, they provide better characterization of integrable multifunctions under consideration. There is a large literature on it

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19

Devi, V. Renuka, and D. Sivaraj. "On Weakly Semi-$\mathcal{I}$-Open Sets." Sarajevo Journal of Mathematics 3, no. 2 (2024): 267–76. http://dx.doi.org/10.5644/sjm.03.2.13.

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A decomposition of continuity via ideals is given. Characterizations of completely codense ideals are given in terms of weakly semi-$\mathcal{I}$-open sets. Also, properties of weakly semi-$\mathcal{I}$-open sets and their relation with other sets are discussed. 2000 Mathematics Subject Classification. 54A05, 54A10

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20

Ortu, Fulvio, Federico Severino, Andrea Tamoni, and Claudio Tebaldi. "A persistence‐based Wold‐type decomposition for stationary time series." Quantitative Economics 11, no. 1 (2020): 203–30. http://dx.doi.org/10.3982/qe994.

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This paper shows how to decompose weakly stationary time series into the sum, across time scales, of uncorrelated components associated with different degrees of persistence. In particular, we provide an Extended Wold Decomposition based on an isometric scaling operator that makes averages of process innovations. Thanks to the uncorrelatedness of components, our representation of a time series naturally induces a persistence‐based variance decomposition of any weakly stationary process. We provide two applications to show how the tools developed in this paper can shed new light on the determin

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21

Xu, Xiyun, and Ming Xu. "Geodesic orbit and weakly symmetric spray manifolds." Comptes Rendus. Mathématique 363, G4 (2025): 337–44. https://doi.org/10.5802/crmath.673.

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In this paper, we introduce the geodesic orbit and weakly symmetric properties in homogeneous spray geometry. When a homogeneous spray manifold is endowed with a reductive decomposition, we use the spray vector field to describe these properties, and prove that a weakly symmetric spray manifold must be geodesic orbit, which generalizes its analog in homogeneous Riemannian and Finsler geometries.

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Singh, Sumit, та Manoj Kumar Rana. "On βκ-normal spaces". Proyecciones (Antofagasta) 42, № 3 (2023): 695–712. http://dx.doi.org/10.22199/issn.0717-6279-4277.

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A topological space X is called βκ-normal if for every pair of disjoint regularly closed sets A and B, there exist disjoint open sets U and V of X such that = A, = B and ∩ = ∅. In this paper, we investigated a weaker form of normality called βκ-normality which is simultaneous generalization of normality, κ-normality and almost β-normality. Some new decomposition of normality is obtained in terms weakly β-normal spaces.

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23

Breaz, Simion, Peter Danchev, and Yiqiang Zhou. "Rings in which every element is either a sum or a difference of a nilpotent and an idempotent." Journal of Algebra and Its Applications 15, no. 08 (2016): 1650148. http://dx.doi.org/10.1142/s0219498816501486.

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Generalizing the notion of nil-cleanness from [A. J. Diesl, Nil clean rings, J. Algebra 383 (2013) 197–211], in parallel to [P. V. Danchev and W. Wm. McGovern, Commutative weakly nil clean unital rings, J. Algebra 425 (2015) 410–422], we define the concept of weak nil-cleanness for an arbitrary ring. Its comprehensive study in different ways is provided as well. A decomposition theorem of a weakly nil-clean ring is obtained. It is completely characterized when an abelian ring is weakly nil-clean. It is also completely determined when a matrix ring over a division ring is weakly nil-clean.

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24

Su, Wu Chung, and Zoran Gajic. "Decomposition method for solving weakly coupled algebraic Riccati equation." Journal of Guidance, Control, and Dynamics 15, no. 2 (1992): 536–38. http://dx.doi.org/10.2514/3.20871.

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25

Hatir, E., and T. Noiri. "Weakly pre-I-open sets and decomposition of continuity." Acta Mathematica Hungarica 106, no. 3 (2005): 227–38. http://dx.doi.org/10.1007/s10474-005-0015-3.

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26

Cassak, Paul A., M. Hasan Barbhuiya, and H. Arthur Weldon. "Pressure–strain interaction. II. Decomposition in magnetic field-aligned coordinates." Physics of Plasmas 29, no. 12 (2022): 122307. http://dx.doi.org/10.1063/5.0125252.

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In weakly collisional and collisionless magnetized plasmas, the pressure–strain interaction describes the rate of conversion between bulk flow and thermal energy density. In this study, we derive an analytical expression for the pressure–strain interaction in a coordinate system with an axis aligned with the local magnetic field. The result is eight groups of terms corresponding to different physical mechanisms that can contribute to the pressure–strain interaction. We provide a physical description of each term. The results are immediately of interest to weakly collisional and collisionless m

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27

Bader, Uri, Christian Rosendal, and Roman Sauer. "On the cohomology of weakly almost periodic group representations." Journal of Topology and Analysis 06, no. 02 (2014): 153–65. http://dx.doi.org/10.1142/s1793525314500125.

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We initiate a study of cohomological aspects of weakly almost periodic group representations on Banach spaces, in particular, isometric representations on reflexive Banach spaces. Using the Ryll–Nardzewski fixed point theorem, we prove a vanishing result for the restriction map (with respect to a subgroup) in the reduced cohomology of weakly periodic representations. Combined with the Alaoglu–Birkhoff decomposition theorem, this generalizes and complements theorems on continuous group cohomology by several authors.

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Eivazloo, Jafar S., and Somayyeh Tari. "SCE-Cell Decomposition and OCP in Weakly O-Minimal Structures." Notre Dame Journal of Formal Logic 57, no. 3 (2016): 399–410. http://dx.doi.org/10.1215/00294527-3507270.

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29

Hideaki, Kaneko. "A schauder decomposition and weakly singular integral equations in Lp." Numerical Functional Analysis and Optimization 7, no. 2-3 (1985): 221–34. http://dx.doi.org/10.1080/01630568508816190.

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30

Bochev, Pavel, and Denis Ridzal. "Optimization-based additive decomposition of weakly coercive problems with applications." Computers & Mathematics with Applications 71, no. 11 (2016): 2140–54. http://dx.doi.org/10.1016/j.camwa.2015.12.032.

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31

Rüttimann, Gottfried T. "Weakly Purely Finitely Additive Measures." Canadian Journal of Mathematics 46, no. 4 (1994): 872–85. http://dx.doi.org/10.4153/cjm-1994-049-1.

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AbstractLet L be an orthomodular poset. A positive measure ξ on L is said to be weakly purely finitely additive if the zero measure is the only completely additive measure majorized by ξ. It was shown in [15] that, in an arbitrary orthomodular poset L, every positive measures μ is the sum v + ξ of a positive completely additive measure v and a weakly purely finitely additive measure ξ. We give sufficient conditions for this Yosida-Hewitt-type decomposition to be unique.A positive measure λ on L is said to be filtering if every non-zero element p in L majorizes a non-zero element q on which λ v

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STRAUBING, HOWARD, PASCAL TESSON, and DENIS THÉRIEN. "WEAKLY ITERATED BLOCK PRODUCTS AND APPLICATIONS TO LOGIC AND COMPLEXITY." International Journal of Algebra and Computation 20, no. 02 (2010): 319–41. http://dx.doi.org/10.1142/s0218196710005686.

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Unlike the wreath product, the block product is not associative at the level of varieties. All decomposition theorems involving block products, such as the bilateral version of Krohn–Rhodes' theorem, have always assumed a right-to-left bracketing of the operands. We consider here the left-to-right bracketing, which is generally weaker. More precisely, we are interested in characterizing for any pseudovarieties of monoids U, V the smallest pseudovariety W that contains U and such that W □ V = W. This allows us to obtain new decomposition results for a number of important varieties such as DA, D

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Stamenkovic, Aleksandar, Stefan Stanimirovic, and Vesa Halava. "Certain linear and weakly linear systems of matrix equations over semirings. Applications in a state reduction of weighted automata." Filomat 36, no. 8 (2022): 2775–93. http://dx.doi.org/10.2298/fil2208775s.

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In this paper we study particular linear and weakly linear systems of matrix equations over semirings, with the aim of describing and computing functions as solutions to those systems. Our special attention is devoted to solutions whose ranks are as small as possible. We prove the existence of solutions with the smallest ranks, give their characterizations, and present a method for their computations. Regarding weakly linear systems, the method is based on the well known partition refinement algorithm by Kanellakis and Smolka, adapted to work with weighted labeled transition systems. Moreover,

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Alban, David H., and John Pastor. "Decomposition of aspen, spruce, and pine boles on two sites in Minnesota." Canadian Journal of Forest Research 23, no. 9 (1993): 1744–49. http://dx.doi.org/10.1139/x93-220.

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Boles of quaking aspen (Populustremuloides Michx.), white spruce (Piceaglauca (Moench) Voss), red pine (Pinusresinosa Ait.), and jack pine (Pinusbanksiana Lamb.) were sampled after decomposing for 11–17 years. Mass loss and changes in chemical composition were determined. Density decreased by 40–73%, and the decomposition constant (k) decreased in the order aspen > spruce > red pine > jack pine. Although the decomposition rate was strongly species dependent, it did not differ between the two sites. The decomposition constant was weakly related to lignin and phosphorus concentration in

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Girardi, Maria, and William B. Johnson. "The Complete Continuity Property and Finite Dimensional Decompositions." Canadian Mathematical Bulletin 38, no. 2 (1995): 207–14. http://dx.doi.org/10.4153/cmb-1995-029-6.

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AbstractA Banach space has the complete continuity property (CCP) if each bounded linear operator from L1 into is completely continuous (i.e., maps weakly convergent sequences to norm convergent sequences). The main theorem shows that a Banach space failing the CCP has a subspace with a finite dimensional decomposition which fails the CCP. If furthermore the space has some nice local structure (such as fails cotype or is a lattice), then the decomposition may be strengthened to a basis.

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Li, Ziyue, Nurettin Dorukhan Sergin, Hao Yan, Chen Zhang, and Fugee Tsung. "Tensor Completion for Weakly-Dependent Data on Graph for Metro Passenger Flow Prediction." Proceedings of the AAAI Conference on Artificial Intelligence 34, no. 04 (2020): 4804–10. http://dx.doi.org/10.1609/aaai.v34i04.5915.

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Low-rank tensor decomposition and completion have attracted significant interest from academia given the ubiquity of tensor data. However, low-rank structure is a global property, which will not be fulfilled when the data presents complex and weak dependencies given specific graph structures. One particular application that motivates this study is the spatiotemporal data analysis. As shown in the preliminary study, weakly dependencies can worsen the low-rank tensor completion performance. In this paper, we propose a novel low-rank CANDECOMP / PARAFAC (CP) tensor decomposition and completion fr

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Tan, Qiang, and Haifeng Xu. "Lefschetz decomposition for de Rham cohomology on weakly Lefschetz symplectic manifolds." Frontiers of Mathematics in China 10, no. 5 (2015): 1169–78. http://dx.doi.org/10.1007/s11464-015-0483-x.

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Naghipour, R., and M. Sedghi. "Weakly associated primes and primary decomposition of modules over commutative rings." Acta Mathematica Hungarica 110, no. 1-2 (2006): 1–12. http://dx.doi.org/10.1007/s10474-006-0002-3.

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Wencel, Roman. "On the strong cell decomposition property for weakly o-minimal structures." Mathematical Logic Quarterly 59, no. 6 (2013): 452–70. http://dx.doi.org/10.1002/malq.201200016.

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Anan?ev, A. V., M. Yu Boltoeva, N. L. Sukhov, G. L. Bykov, and B. G. Ershov. "Catalytic decomposition of hydrazine in weakly alkaline solutions on platinum nanoparticles." Radiochemistry 46, no. 6 (2004): 578–82. http://dx.doi.org/10.1007/s11137-005-0031-8.

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Hempel, Tim, Mauricio J. del Razo, Christopher T. Lee, Bryn C. Taylor, Rommie E. Amaro, and Frank Noé. "Independent Markov decomposition: Toward modeling kinetics of biomolecular complexes." Proceedings of the National Academy of Sciences 118, no. 31 (2021): e2105230118. http://dx.doi.org/10.1073/pnas.2105230118.

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To advance the mission of in silico cell biology, modeling the interactions of large and complex biological systems becomes increasingly relevant. The combination of molecular dynamics (MD) simulations and Markov state models (MSMs) has enabled the construction of simplified models of molecular kinetics on long timescales. Despite its success, this approach is inherently limited by the size of the molecular system. With increasing size of macromolecular complexes, the number of independent or weakly coupled subsystems increases, and the number of global system states increases exponentially, m

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Chuiko, Sergey, Olga Nesmelova, and Mykyta Popov. "Adomian decomposition method in the theory of weakly nonlinear boundary value problems." Proceedings of the Institute of Applied Mathematics and Mechanics NAS of Ukraine 37 (June 27, 2023): 61–73. http://dx.doi.org/10.37069/1683-4720-2023-37-6.

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The problem of solvability of nonlinear boundary value problems originates from the classical theory of periodic boundary value problems for systems of ordinary differential equations, developed in the works of A. Poincare, O.M. Lyapunov, I.G. Malkin, Yu.O. Mitropolsky, A.M. Samoilenko, O.A. Boichuk and others. In the classical works of R. Bellman, J. Hale, Y.O. Mitropolsky, A.M. Samoilenko and O.A.~Boichuk, the conditions for solvability of nonlinear boundary value problems for systems of differential equations in critical cases were obtained. To find solutions to nonlinear boundary value pro

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V, Beulah. "Notions of Decomposition of β^* _G -Continuity Via Grills". ECS Transactions 107, № 1 (2022): 1235–43. http://dx.doi.org/10.1149/10701.1235ecst.

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In this paper, we have introduced β* G-local function as where the family of semi-preopen sets in the grill topological space (X,τ,G ). Also we have investigated the decomposition of β* G-continuous map in the grill topological space. Furthermore, the weakly β* G-continuous map is defined and examined.

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Iriye, Kouyemon, Daisuke Kishimoto, and Ran Levi. "Characterisation of polyhedral products with finite generalised Postnikov decomposition." Forum Mathematicum 32, no. 5 (2020): 1253–69. http://dx.doi.org/10.1515/forum-2020-0059.

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AbstractA generalised Postnikov tower for a space X is a tower of principal fibrations with fibres generalised Eilenberg–MacLane spaces, whose inverse limit is weakly homotopy equivalent to X. In this paper we give a characterisation of a polyhedral product {Z_{K}(X,A)} whose universal cover either admits a generalised Postnikov tower of finite length, or is a homotopy retract of a space admitting such a tower. We also include p-local and rational versions of the theorem. We end with a group theoretic application.

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Dzade, N. Y., A. Roldan, and N. H. de Leeuw. "The surface chemistry of NOx on mackinawite (FeS) surfaces: a DFT-D2 study." Phys. Chem. Chem. Phys. 16, no. 29 (2014): 15444–56. http://dx.doi.org/10.1039/c4cp01138d.

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The potential catalytic properties of iron sulfide mackinawite are explored for the adsorption, activation and decomposition of environmentally important NO<sub>x</sub> molecules. The NO<sub>x</sub> species interact weakly with the energetically most (001) surface, but adsorb strongly onto the (011), (100) and (111) surfaces, preferentially at Fe sites via charge donation.

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FELDMAN, JOEL, HORST KNÖRRER, and EUGENE TRUBOWITZ. "SINGLE SCALE ANALYSIS OF MANY FERMION SYSTEMS PART 2: THE FIRST SCALE." Reviews in Mathematical Physics 15, no. 09 (2003): 995–1037. http://dx.doi.org/10.1142/s0129055x03001783.

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Abstract:

The first renormalization group map arising from the momentum space decomposition of a weakly coupled system of fermions at temperature zero differs from all subsequent maps. Namely, the component of momentum dual to temperature may be arbitrarily large — there is no ultraviolet cutoff. The methods of Part 1 are supplemented to control this special case.

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Lipatov, I. I., and A. D. Polyanin. "Decomposition and exact solutions of equations of a weakly compressible barotropic fluid." Doklady Physics 58, no. 3 (2013): 116–20. http://dx.doi.org/10.1134/s1028335813030099.

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Nakkar, H. M., and D. D. Anderson. "Associated and weakly associated prime elements and primary decomposition in lattice modules." Algebra Universalis 25, no. 1 (1988): 196–209. http://dx.doi.org/10.1007/bf01229970.

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Chastand, Marc, and Norbert Polat. "On geodesic structures of weakly median graphs I. Decomposition and octahedral graphs." Discrete Mathematics 306, no. 13 (2006): 1272–84. http://dx.doi.org/10.1016/j.disc.2005.10.034.

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Corona, Dario, and Andrea Cristofaro. "Optimality principles and decomposition of tracking controllers for weakly dual redundant systems." Optimal Control Applications and Methods 39, no. 4 (2018): 1451–66. http://dx.doi.org/10.1002/oca.2420.

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