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Статті в журналах з теми "Flat functors"

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Автор: Grafiati

Опубліковано: 10 грудня 2022

Оновлено: 28 січня 2023

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1

Crivei, Septimiu. "On Flat Objects of Finitely Accessible Categories." Scientific World Journal 2013 (2013): 1–4. http://dx.doi.org/10.1155/2013/451091.

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Flat objects of a finitely accessible additive category are described in terms of some objects of the associated functor category of , called strongly flat functors. We study closure properties of the class of strongly flat functors, and we use them to deduce the known result that every object of a finitely accessible abelian category has a flat cover.

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2

Hu, Hongde. "Flat functors and free exact categories." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 60, no. 2 (April 1996): 143–56. http://dx.doi.org/10.1017/s1446788700037575.

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AbstractLet C be a small category with weak finite limits, and let Flat(C) be the category of flat functors from C to the category of small sets. We prove that the free exact completion of C is the category of set-valued functors of Flat (C) which preserve small products and filtered colimits. In case C has finite limits, this gives A. Carboni and R. C. Magno's result on the free exact completion of a small category with finite limits.

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3

Hu, Jiangsheng, Huanhuan Li, Yuxian Geng, and Dongdong Zhang. "Frobenius functors and Gorenstein flat dimensions." Communications in Algebra 48, no. 3 (October 24, 2019): 1257–65. http://dx.doi.org/10.1080/00927872.2019.1677699.

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4

Crivei, Septimiu. "Flat Weakly FP-Injective and FP-Injective Weakly Flat Functors." Results in Mathematics 71, no. 3-4 (September 1, 2016): 1031–45. http://dx.doi.org/10.1007/s00025-016-0598-8.

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5

Farjoun, Emmanuel Dror, and Jérôme Scherer. "Conditionally flat functors on spaces and groups." Collectanea Mathematica 66, no. 1 (February 13, 2014): 149–60. http://dx.doi.org/10.1007/s13348-013-0102-7.

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6

Mao, Lixin. "Strongly FP-injective and strongly flat functors." Rendiconti del Seminario Matematico della Università di Padova 135 (2016): 133–49. http://dx.doi.org/10.4171/rsmup/135-7.

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7

Nicholson, W. K., and J. F. Watters. "Morita context functors." Mathematical Proceedings of the Cambridge Philosophical Society 103, no. 3 (May 1988): 399–408. http://dx.doi.org/10.1017/s0305004100065014.

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AbstractGiven a Morita context (R, V, W, S), there are functors W⊗() and hom (V, ) from R-mod to; S-mod and a natural transformation λ from the first to the second. This has an epi-mono factorization and the intermediate functor we denote by ()° with natural transformations and . The tensor functor is exact if and only if WR is flat, whilst the hom functor is exact if and only if RV is projective. We begin by determining conditions under which ()° is exact; this is Theorem 1.

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8

Aldrich, Stephen T., Edgar E. Enochs, and Juan A. Lopez Ramos. "Derived Functors of Hom Relative to Flat Covers." Mathematische Nachrichten 242, no. 1 (July 2002): 17–26. http://dx.doi.org/10.1002/1522-2616(200207)242:1<17::aid-mana17>3.0.co;2-f.

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9

Akatsa, Victor K. "Flat resolvents, minimal injective resolutions and negative torsion functors." Communications in Algebra 20, no. 11 (January 1992): 3105–18. http://dx.doi.org/10.1080/00927879208824508.

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10

Selvaraj, C., and R. Udhayakumar. "Derived Functors of Hom Relative to n-Flat Covers." Vietnam Journal of Mathematics 43, no. 3 (September 17, 2014): 571–82. http://dx.doi.org/10.1007/s10013-014-0097-8.

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11

Estrada, Sergio, Marco A. Pérez, and Haiyan Zhu. "Balanced pairs, cotorsion triplets and quiver representations." Proceedings of the Edinburgh Mathematical Society 63, no. 1 (August 13, 2019): 67–90. http://dx.doi.org/10.1017/s0013091519000270.

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Анотація:

AbstractBalanced pairs appear naturally in the realm of relative homological algebra associated with the balance of right-derived functors of the Hom functor. Cotorsion triplets are a natural source of such pairs. In this paper, we study the connection between balanced pairs and cotorsion triplets by using recent quiver representation techniques. In doing so, we find a new characterization of abelian categories that have enough projectives and injectives in terms of the existence of complete hereditary cotorsion triplets. We also provide a short proof of the lack of balance for derived functors of Hom computed using flat resolutions, which extends the one given by Enochs in the commutative case.

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12

Zhou, Borong. "A note on Morita context functors." Mathematical Proceedings of the Cambridge Philosophical Society 107, no. 2 (March 1990): 273–74. http://dx.doi.org/10.1017/s0305004100068547.

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It is claimed in [3], proposition 4 that if a Morita context (R, V, W, S) is such that WVW = W and S/WV is flat as a right S-module, then Vω = 0, ω ∈ W, implies ω = 0. The proof given for this uses proposition 5 of Azumaya[l] in which rings have unity and so is only applicable when the ring S has a unity. Thus proposition 4 in [3] should be amended so that the additional hypothesis that S has a unity is imposed for statement (4) to be equivalent to the first three statements. It is the purpose of this note to give an example to show that the claim in [3] is false in general.

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13

Mao, Lixin. "Notes on several orthogonal classes of flat and FP-injective functors." Mathematical Notes 95, no. 1-2 (January 2014): 78–90. http://dx.doi.org/10.1134/s0001434614010088.

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14

Fernández-Alonso, Rogelio, and Janeth Magaña. "Galois connections between lattices of preradicals induced by ring epimorphisms." Journal of Algebra and Its Applications 19, no. 03 (February 27, 2019): 2050045. http://dx.doi.org/10.1142/s0219498820500450.

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We continue the study of Galois connections between the lattices of preradicals of two rings [Formula: see text] and [Formula: see text] induced by an adjoint pair of functors between the categories [Formula: see text]-Mod and [Formula: see text]-Mod. In this paper, we focus on the functor triple induced by any ring homomorphism [Formula: see text], and particularly when it is a ring epimorphism. We give additional results when the epimorphism is flat and when it is projective.

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15

Fu, Xianhui, and Meiyuan Ni. "The Cotorsion Pair Cogenerated by the Subcategory of Stable Functors in ((R-mod)op, Ab)." Algebra Colloquium 26, no. 02 (May 7, 2019): 259–70. http://dx.doi.org/10.1142/s1005386719000208.

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Let R be an associative ring with identity. Denote by ((R-mod)op, Ab) the category consisting of contravariant functors from the category of finitely presented left R-modules R-mod to the category of abelian groups Ab. An object in ((R-mod)op, Ab) is said to be a stable functor if it vanishes on the regular module R. Let [Formula: see text] be the subcategory of stable functors. There are two torsion pairs [Formula: see text] and [Formula: see text], where ℱ1 is the subcategory of ((R-mod)op, Ab) consisting of functors with flat dimension at most 1. In this article, let R be a ring of weakly global dimension at most 1, and assume R satisfies that for any exact sequence 0 → M → N → K → 0, if M and N are pure injective, then K is also pure injective. We calculate the cotorsion pair [Formula: see text] cogenerated by [Formula: see text] clearly. It is shown that [Formula: see text] if and only if G/t1(G) is a projective object in [Formula: see text], i.e., G/t1(G) = (−,M) for some R-module M; and [Formula: see text] if and only if G/t2(G) is of the form (−, E), where E is an injective R-module.

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16

Ishida, Kazuhisa, Yasunari Shidama, and Adam Grabowski. "Definition of Flat Poset and Existence Theorems for Recursive Call." Formalized Mathematics 22, no. 1 (March 30, 2014): 1–10. http://dx.doi.org/10.2478/forma-2014-0001.

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Summary This text includes the definition and basic notions of product of posets, chain-complete and flat posets, flattening operation, and the existence theorems of recursive call using the flattening operator. First part of the article, devoted to product and flat posets has a purely mathematical quality. Definition 3 allows to construct a flat poset from arbitrary non-empty set [12] in order to provide formal apparatus which eanbles to work with recursive calls within the Mizar langauge. To achieve this we extensively use technical Mizar functors like BaseFunc or RecFunc. The remaining part builds the background for information engineering approach for lists, namely recursive call for posets [21].We formalized some facts from Chapter 8 of this book as an introduction to the next two sections where we concentrate on binary product of posets rather than on a more general case.

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17

Iyengar, Srikanth B., Joseph Lipman, and Amnon Neeman. "Relation between two twisted inverse image pseudofunctors in duality theory." Compositio Mathematica 151, no. 4 (November 19, 2014): 735–64. http://dx.doi.org/10.1112/s0010437x14007672.

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Grothendieck duality theory assigns to essentially finite-type maps $f$ of noetherian schemes a pseudofunctor $f^{\times }$ right-adjoint to $\mathsf{R}f_{\ast }$, and a pseudofunctor $f^{!}$ agreeing with $f^{\times }$ when $f$ is proper, but equal to the usual inverse image $f^{\ast }$ when $f$ is étale. We define and study a canonical map from the first pseudofunctor to the second. This map behaves well with respect to flat base change, and is taken to an isomorphism by ‘compactly supported’ versions of standard derived functors. Concrete realizations are described, for instance for maps of affine schemes. Applications include proofs of reduction theorems for Hochschild homology and cohomology, and of a remarkable formula for the fundamental class of a flat map of affine schemes.

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18

Yang, Xiaoyan, and Li Wang. "Homological invariants over non-positive DG-rings." Journal of Algebra and Its Applications 19, no. 08 (August 15, 2019): 2050153. http://dx.doi.org/10.1142/s0219498820501534.

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This paper explores various notions of projective, injective and flat dimensions, and the different versions of each dimension are compared to each other. Homological characterizations of these dimensions are provided in terms of bounded resolutions and vanishing of appropriate derived functors over a non-positive DG-ring. Some homological identities related to these homological invariants, such as Auslander–Buchsbaum formula, Bass formula and derived depth formula, are proved over a commutative Noetherian DG-ring.

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19

ZHANG, DONGDONG, and BAIYU OUYANG. "SEMIDUALIZING MODULES AND RELATED MODULES." Journal of Algebra and Its Applications 10, no. 06 (December 2011): 1261–82. http://dx.doi.org/10.1142/s0219498811005695.

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In this paper, we prove that the Bass class [Formula: see text] with respect to a semidualizing bimodule C contains all FP-injective S-modules. We introduce the definition of C-FP-injective modules, and give some characterizations of right coherent rings in terms of the C-flat S-modules and C-FP-injective S op -modules. We discuss when every S-module has an C-flat preenvelope which is epic (or monic). In addition, we investigate the left and right [Formula: see text]-resolutions of R-modules by left derived functors Ext n(-, -) over a left Noetherian ring S. As applications, some new characterizations of left perfect rings are induced by these modules associated with C. A few classical results of these rings are obtained as corollaries.

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20

Abellán García, Fernando. "Marked colimits and higher cofinality." Journal of Homotopy and Related Structures 17, no. 1 (December 16, 2021): 1–22. http://dx.doi.org/10.1007/s40062-021-00296-2.

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AbstractGiven a marked $$\infty $$ ∞ -category $$\mathcal {D}^{\dagger }$$ D † (i.e. an $$\infty $$ ∞ -category equipped with a specified collection of morphisms) and a functor $$F: \mathcal {D}\rightarrow {\mathbb {B}}$$ F : D → B with values in an $$\infty $$ ∞ -bicategory, we define "Equation missing", the marked colimit of F. We provide a definition of weighted colimits in $$\infty $$ ∞ -bicategories when the indexing diagram is an $$\infty $$ ∞ -category and show that they can be computed in terms of marked colimits. In the maximally marked case $$\mathcal {D}^{\sharp }$$ D ♯ , our construction retrieves the $$\infty $$ ∞ -categorical colimit of F in the underlying $$\infty $$ ∞ -category $$\mathcal {B}\subseteq {\mathbb {B}}$$ B ⊆ B . In the specific case when "Equation missing", the $$\infty $$ ∞ -bicategory of $$\infty $$ ∞ -categories and $$\mathcal {D}^{\flat }$$ D ♭ is minimally marked, we recover the definition of lax colimit of Gepner–Haugseng–Nikolaus. We show that a suitable $$\infty $$ ∞ -localization of the associated coCartesian fibration $${\text {Un}}_{\mathcal {D}}(F)$$ Un D ( F ) computes "Equation missing". Our main theorem is a characterization of those functors of marked $$\infty $$ ∞ -categories $${f:\mathcal {C}^{\dagger } \rightarrow \mathcal {D}^{\dagger }}$$ f : C † → D † which are marked cofinal. More precisely, we provide sufficient and necessary criteria for the restriction of diagrams along f to preserve marked colimits

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21

Asadollahi, Javad, and Shokrollah Salarian. "Complete Cohomologies and Some Homological Invariants." Algebra Colloquium 14, no. 01 (March 2007): 155–66. http://dx.doi.org/10.1142/s1005386707000156.

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There is a complete cohomology theory developed over a commutative noetherian ring in which injectives take the role of projectives in Vogel's construction of complete cohomology theory. We study the interaction between this complete cohomology, that is referred to as [Formula: see text]-complete cohomology, and Vogel's one and give some sufficient conditions for their equivalence. Using [Formula: see text]-complete functors, we assign a new homological invariant to any finitely generated module over an arbitrary commutative noetherian local ring, that would generalize Auslander's delta invariant. We generalize the results about the δ-invariant to arbitrary rings and give a sufficient condition for the vanishing of this new invariant. We also introduce an analogue of the notion of the index of a Gorenstein local ring, introduced by Auslander, for arbitrary local rings and study its behavior under flat extensions of local rings. Finally, we study the connection between the index and Loewy length of a local ring and generalize the main result of [11] to arbitrary rings.

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22

Zhang, Dongdong, and Baiyu Ouyang. "On n-Coherent Rings and (n,d)-Injective Modules." Algebra Colloquium 22, no. 02 (April 15, 2015): 349–60. http://dx.doi.org/10.1142/s1005386715000309.

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Let R be a ring, n, d be fixed non-negative integers, [Formula: see text] the class of (n,d)-injective left R-modules, and [Formula: see text] the class of (n,d)-flat right R-modules. In this paper, we prove that if R is a left n-coherent ring and m ≥ 2, then [Formula: see text] if and only if [Formula: see text], if and only if Ext m+k(M,N) = 0 for all left R-modules M, N and all k ≥ -1, if and only if Ext m-1(M,N) = 0 for all left R-modules M, N. Meanwhile, we prove that if R is a left n-coherent ring, then − ⊗ − is right balanced on [Formula: see text] by [Formula: see text], and investigate the global right [Formula: see text]-dimension of [Formula: see text] and the global right [Formula: see text]-dimension of [Formula: see text] by right derived functors of − ⊗ −. Some known results are obtained as corollaries.

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23

Belas, Robert, Eiko Horikawa, Shin-Ichi Aizawa, and Rooge Suvanasuthi. "Genetic Determinants of Silicibacter sp. TM1040 Motility." Journal of Bacteriology 191, no. 14 (May 29, 2009): 4502–12. http://dx.doi.org/10.1128/jb.00429-09.

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ABSTRACT Silicibacter sp. TM1040 is a member of the marine Roseobacter clade of Alphaproteobacteria that forms symbioses with unicellular eukaryotic phytoplankton, such as dinoflagellates. The symbiosis is complex and involves a series of steps that physiologically change highly motile bacteria into cells that readily form biofilms on the surface of the host. The initial phases of symbiosis require bacterial motility and chemotaxis that drive the swimming bacteria toward their planktonic host. Cells lacking wild-type motility fail to establish biofilms on host cells and do not produce effective symbioses, emphasizing the importance of understanding the molecular mechanisms controlling flagellar biosynthesis and the biphasic “swim-or-stick” switch. In the present study, we used a combination of bioinformatic and genetic approaches to identify the genes critical for swimming of Silicibacter sp. TM1040. More than 40 open reading frames with homology to known flagellar structural and regulatory genes were identified, most of which are organized into approximately eight operons comprising a 35.4-kb locus, with surprising similarity to the fla2 locus of Rhodobacter sphaeroides. The genome has homologs of CckA, CtrA, FlbT, and FlaF, proteins that in Caulobacter crescentus regulate flagellum biosynthesis. In addition, we uncovered three novel genes, flaB, flaC, and flaD, which encode flagellar regulatory proteins whose functions are likely to involve regulation of motor function (FlaD) and modulation of the swim-or-stick switch (FlaC). The data support the conclusion that Silicibacter sp. TM1040 uses components found in other Alphaproteobacteria, as well as novel molecular mechanisms, to regulate the expression of the genes required for motility and biofilm formation. These unique molecular mechanisms may enhance the symbiosis and survival of Roseobacter clade bacteria in the marine environment.

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24

Hug, Daniel, Günter Last, and Wolfgang Weil. "Distance measurements on processes of flats." Advances in Applied Probability 35, no. 1 (March 2003): 70–95. http://dx.doi.org/10.1239/aap/1046366100.

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Distance measurements are useful tools in stochastic geometry. For a Boolean modelZin ℝd, the classical contact distribution functions allow the estimation of important geometric parameters ofZ. In two previous papers, several types of generalized contact distributions have been investigated and applied to stationary and nonstationary Boolean models. Here, we consider random setsZwhich are generated as the union sets of Poisson processesXofk-flats,k∈ {0, …,d-1}, and study distances from a fixed point or a fixed convex body toZ. In addition, we also consider the distances from a given flat or a flag consisting of flats to the individual members ofXand investigate the associated process of nearest points in the flats ofX. In particular, we discuss to which extent the directional distribution ofXis determined by this point process. Some of our results are presented for more general stationary processes of flats.

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25

Hug, Daniel, Günter Last, and Wolfgang Weil. "Distance measurements on processes of flats." Advances in Applied Probability 35, no. 01 (March 2003): 70–95. http://dx.doi.org/10.1017/s000186780001209x.

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Анотація:

Distance measurements are useful tools in stochastic geometry. For a Boolean modelZin ℝd, the classical contact distribution functions allow the estimation of important geometric parameters ofZ. In two previous papers, several types of generalized contact distributions have been investigated and applied to stationary and nonstationary Boolean models. Here, we consider random setsZwhich are generated as the union sets of Poisson processesXofk-flats,k∈ {0, …,d-1}, and study distances from a fixed point or a fixed convex body toZ. In addition, we also consider the distances from a given flat or a flag consisting of flats to the individual members ofXand investigate the associated process of nearest points in the flats ofX. In particular, we discuss to which extent the directional distribution ofXis determined by this point process. Some of our results are presented for more general stationary processes of flats.

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26

Kalmokoff, Martin, Patricia Lanthier, Tammy-Lynn Tremblay, Mary Foss, Peter C. Lau, Greg Sanders, John Austin, John Kelly, and Christine M. Szymanski. "Proteomic Analysis of Campylobacter jejuni 11168 Biofilms Reveals a Role for the Motility Complex in Biofilm Formation." Journal of Bacteriology 188, no. 12 (June 15, 2006): 4312–20. http://dx.doi.org/10.1128/jb.01975-05.

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ABSTRACT Campylobacter jejuni remains the leading cause of bacterial gastroenteritis in developed countries, and yet little is known concerning the mechanisms by which this fastidious organism survives within its environment. We have demonstrated that C. jejuni 11168 can form biofilms on a variety of surfaces. Proteomic analyses of planktonic and biofilm-grown cells demonstrated differences in protein expression profiles between the two growth modes. Proteins involved in the motility complex, including the flagellins (FlaA, FlaB), the filament cap (FliD), the basal body (FlgG, FlgG2), and the chemotactic protein (CheA), all exhibited higher levels of expression in biofilms than found in stationary-phase planktonic cells. Additional proteins with enhanced expression included those involved in the general (GroEL, GroES) and oxidative (Tpx, Ahp) stress responses, two known adhesins (Peb1, FlaC), and proteins involved in biosynthesis, energy generation, and catabolic functions. An aflagellate flhA mutant not only lost the ability to attach to a solid matrix and form a biofilm but could no longer form a pellicle at the air-liquid interface of a liquid culture. Insertional inactivation of genes that affect the flagellar filament (fliA, flaA, flaB, flaG) or the expression of the cell adhesin (flaC) also resulted in a delay in pellicle formation. These findings demonstrate that the flagellar motility complex plays a crucial role in the initial attachment of C. jejuni 11168 to solid surfaces during biofilm formation as well as in the cell-to-cell interactions required for pellicle formation. Continued expression of the motility complex in mature biofilms is unusual and suggests a role for the flagellar apparatus in the biofilm phenotype.

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27

Adela Purba and Nelson Siahaan. "Design of Flat With Neighborhood Space With Urban Farming Function In Medan." International Journal of Architecture and Urbanism 5, no. 3 (November 30, 2021): 387–97. http://dx.doi.org/10.32734/ijau.v5i3.7720.

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Анотація:

In Medan, flats do not utilize neighborhood space as an urban farming area. In general, flats have a high density of occupants, inflexible designs, and the relationship between one door to another door is relatively close so that communal space is needed. Communal space is a space that functions as a place for social interaction activities for its residents. This flat design has green open spaces such as neighborhood space that can be used as communal spaces both socially and economically productively (urban farming) because flats require both functions. The design approach process used in this design is primary data collection through a field study process and physical data collection that supports scientific and factual data processing. The design analysis was carried out based on the results of literature review and data collection to identify the character of the design area, problems that arise, limitations and potentials, functional requirements, then conduct a review of the regional development plan. This flat is designed using an Ecological Architecture approach to reduce environmental problems in urban areas. The design creates a flat that considers the needs of communal space, green open space, and recreation areas to meet the needs of users. This design can create facilities for the community and become a tourist attraction.

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28

Kozłowski, Wojciech. "∇-flat functions on manifolds." Annales Polonici Mathematici 84, no. 2 (2004): 177–80. http://dx.doi.org/10.4064/ap84-2-7.

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29

BUCATARU, IOAN, and ZOLTÁN MUZSNAY. "FINSLER METRIZABLE ISOTROPIC SPRAYS AND HILBERT’S FOURTH PROBLEM." Journal of the Australian Mathematical Society 97, no. 1 (May 20, 2014): 27–47. http://dx.doi.org/10.1017/s1446788714000111.

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AbstractIt is well known that a system of homogeneous second-order ordinary differential equations (spray) is necessarily isotropic in order to be metrizable by a Finsler function of scalar flag curvature. In our main result we show that the isotropy condition, together with three other conditions on the Jacobi endomorphism, characterize sprays that are metrizable by Finsler functions of scalar flag curvature. We call these conditions the scalar flag curvature (SFC) test. The proof of the main result provides an algorithm to construct the Finsler function of scalar flag curvature, in the case when a given spray is metrizable. Hilbert’s fourth problem asks to determine the Finsler functions with rectilinear geodesics. A Finsler function that is a solution to Hilbert’s fourth problem is necessarily of constant or scalar flag curvature. Therefore, we can use the constant flag curvature (CFC) test, which we developed in our previous paper, Bucataru and Muzsnay [‘Sprays metrizable by Finsler functions of constant flag curvature’, Differential Geom. Appl.31 (3)(2013), 405–415] as well as the SFC test to decide whether or not the projective deformations of a flat spray, which are isotropic, are metrizable by Finsler functions of constant or scalar flag curvature. We show how to use the algorithms provided by the CFC and SFC tests to construct solutions to Hilbert’s fourth problem.

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30

Bulman-Fleming, Sydney. "Pullback-Flat Acts are Strongly Flat." Canadian Mathematical Bulletin 34, no. 4 (December 1, 1991): 456–61. http://dx.doi.org/10.4153/cmb-1991-073-2.

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AbstractLet 5 be a monoid. A right S-system A is called strongly flat if the functor A ⊗ — (from the category of left S-systems into the category of sets) preserves pullbacksand equalizers. (This concept arises in B. Stenström, Math. Nachr. 48(1971), 315-334 under the name weak flatness). The main result of the present paper is a proof that for A to be strongly flat it is in fact sufficient that A ⊗ — preserve only pullbacks. The approach taken is to develop an "interpolation" condition for pullback-preservation, and then to show its equivalence to Stenström's conditions for strong flatness.

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31

Gołębiowska, Anna, and Dariusz Prokopowicz. "NATIONAL HOUSING PROGRAM OF THE MAIN STRATEGIC AND PROGRAM DOCUMENT FOR THE CURRENT STATE RESIDENTIAL POLICY OF THE STATE." International Journal of New Economics and Social Sciences 6, no. 2 (December 22, 2017): 0. http://dx.doi.org/10.5604/01.3001.0010.7644.

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Launched in April 2016, the Family 500 Plus program significantly reduces the scale of poverty in large families, contributes to the growth of consumption and perhaps also to the increase in fertility in Poland. The second key program of social family policy in Poland launched in December 2016 is the Flat Plus program. This program, through the improvement of the housing situation, should fulfill important functions of housing policy in the scope of reducing the social stratification of families in Poland. The main objective of the Flat Plus program is to significantly increase the availability of flats, especially low-cost rental apartments, with the option of purchasing property after 20-30 years of use. The consequence of developing this program on a larger scale in the coming years will be offering such housing primarily for families who have not been able to rent and buy flats on the open market due to low incomes and lack of creditworthiness. If the plan adopted by the government to develop the Flat Plus program in the coming years will be implemented by 2030, the level of housing availability for citizens in Poland will reach a level close to the average in the European Union.

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32

Yen, Jiun Y., Katherine M. Broadway, and Birgit E. Scharf. "Minimum Requirements of Flagellation and Motility for Infection of Agrobacterium sp. Strain H13-3 by Flagellotropic Bacteriophage 7-7-1." Applied and Environmental Microbiology 78, no. 20 (August 3, 2012): 7216–22. http://dx.doi.org/10.1128/aem.01082-12.

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ABSTRACTThe flagellotropic phage 7-7-1 specifically adsorbs toAgrobacteriumsp. strain H13-3 (formerlyRhizobium lupiniH13-3) flagella for efficient host infection. TheAgrobacteriumsp. H13-3 flagellum is complex and consists of three flagellin proteins: the primary flagellin FlaA, which is essential for motility, and the secondary flagellins FlaB and FlaD, which have minor functions in motility. Using quantitative infectivity assays, we showed that absence of FlaD had no effect on phage infection, while absence of FlaB resulted in a 2.5-fold increase in infectivity. AflaAdeletion strain, which produces straight and severely truncated flagella, experienced a significantly reduced infectivity, similar to that of aflaB flaDstrain, which produces a low number of straight flagella. A strain lacking all three flagellin genes is phage resistant. In addition to flagellation, flagellar rotation is required for infection. A strain that is nonmotile due to an in-frame deletion in the gene encoding the motor component MotA is resistant to phage infection. We also generated two strains with point mutations in themotAgene resulting in replacement of the conserved charged residue Glu98, which is important for modulation of rotary speed. A change to the neutral Gln caused the flagellar motor to rotate at a constant high speed, allowing a 2.2-fold-enhanced infectivity. A change to the positively charged Lys caused a jiggly motility phenotype with very slow flagellar rotation, which significantly reduced the efficiency of infection. In conclusion, flagellar number and length, as well as speed of flagellar rotation, are important determinants for infection by phage 7-7-1.

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33

Bulman-Fleming, Sydney, and Kenneth McDowell. "Monoids over which all weakly flat acts are flat." Proceedings of the Edinburgh Mathematical Society 33, no. 2 (June 1990): 287–98. http://dx.doi.org/10.1017/s0013091500018198.

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If R is a ring with identity and M is a left R-module then it is well known that the following statements are equivalent:(1) M is flat.(2) The functor −⊗M preserves embeddings of right ideals into R.This paper investigates situations in which the analogous statements are equivalent in the context of S-sets over a monoid S.

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34

Oldknow, Adrian. "On Twin Peaks and Flat Functions." Mathematical Gazette 79, no. 484 (March 1995): 47. http://dx.doi.org/10.2307/3619988.

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35

Kozłowski, Wojciech. "A remark on semi-∇-flat functions." Annales Polonici Mathematici 89, no. 2 (2006): 147–49. http://dx.doi.org/10.4064/ap89-2-4.

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36

Pan, Hong, Yonghong Jia, Dawei Zhao, Tianyu Xiu, and Fuzhi Duan. "A Tidal Flat Wetlands Delineation and Classification Method for High-Resolution Imagery." ISPRS International Journal of Geo-Information 10, no. 7 (July 1, 2021): 451. http://dx.doi.org/10.3390/ijgi10070451.

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As an important part of coastal wetlands, tidal flat wetlands provide various significant ecological functions. Due to offshore pollution and unreasonable utilization, tidal flats have been increasingly threatened and degraded. Therefore, it is necessary to protect and restore this important wetland by monitoring its distribution. Considering the multiple sizes of research objects, remote sensing images with high resolutions have unique resolution advantages to support the extraction of tidal flat wetlands for subsequent monitoring. The purpose of this study is to propose and evaluate a tidal flat wetland delineation and classification method from high-resolution images. First, remote sensing features and geographical buffers are used to establish a decision tree for initial classification. Next, a natural shoreline prediction algorithm is designed to refine the range of the tidal flat wetland. Then, a range and standard deviation descriptor is constructed to extract the rock marine shore, a category of tidal flat wetlands. A geographical analysis method is considered to distinguish the other two categories of tidal flat wetlands. Finally, a tidal correction strategy is introduced to regulate the borderline of tidal flat wetlands to conform to the actual situation. The performance of each step was evaluated, and the results of the proposed method were compared with existing available methods. The results show that the overall accuracy of the proposed method mostly exceeded 92% (all higher than 88%). Due to the integration and the performance superiority compared to existing available methods, the proposed method is applicable in practice and has already been applied during the construction project of Hengqin Island in China.

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37

Anagnostopoulou, V., K. Díaz-Ordaz, O. Jenkinson, and C. Richard. "Entrance time functions for flat spot maps." Nonlinearity 23, no. 6 (May 13, 2010): 1477–94. http://dx.doi.org/10.1088/0951-7715/23/6/011.

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38

PELED, RON, WOJCIECH SAMOTIJ, and AMIR YEHUDAYOFF. "Lipschitz Functions on Expanders are Typically Flat." Combinatorics, Probability and Computing 22, no. 4 (June 11, 2013): 566–91. http://dx.doi.org/10.1017/s0963548313000163.

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This work studies the typical behaviour of random integer-valued Lipschitz functions on expander graphs with sufficiently good expansion. We consider two families of functions: M-Lipschitz functions (functions which change by at most M along edges) and integer-homomorphisms (functions which change by exactly 1 along edges). We prove that such functions typically exhibit very small fluctuations. For instance, we show that a uniformly chosen M-Lipschitz function takes only M+1 values on most of the graph, with a double exponential decay for the probability of taking other values.

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39

Gardner, Robert B., Marcus Kriele, and Udo Simon. "Generalized spherical functions on projectively flat manifolds." Results in Mathematics 27, no. 1-2 (March 1995): 41–50. http://dx.doi.org/10.1007/bf03322268.

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40

Peled, Ron. "High-dimensional Lipschitz functions are typically flat." Annals of Probability 45, no. 3 (May 2017): 1351–447. http://dx.doi.org/10.1214/16-aop1089.

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41

Rim, Kyung Soo. "Maximal Functions over Hypersurfaces with Flat Points." Journal of Mathematical Analysis and Applications 260, no. 1 (August 2001): 70–82. http://dx.doi.org/10.1006/jmaa.2001.7436.

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42

Wu, Gaofei, and Matthew Geoffrey Parker. "On Boolean functions with several flat spectra." Cryptography and Communications 11, no. 5 (May 10, 2018): 853–80. http://dx.doi.org/10.1007/s12095-018-0309-2.

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43

Hochreiter, Sepp, and Jürgen Schmidhuber. "Flat Minima." Neural Computation 9, no. 1 (January 1, 1997): 1–42. http://dx.doi.org/10.1162/neco.1997.9.1.1.

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We present a new algorithm for finding low-complexity neural networks with high generalization capability. The algorithm searches for a “flat” minimum of the error function. A flat minimum is a large connected region in weight space where the error remains approximately constant. An MDL-based, Bayesian argument suggests that flat minima correspond to “simple” networks and low expected overfitting. The argument is based on a Gibbs algorithm variant and a novel way of splitting generalization error into underfitting and overfitting error. Unlike many previous approaches, ours does not require gaussian assumptions and does not depend on a “good” weight prior. Instead we have a prior over input output functions, thus taking into account net architecture and training set. Although our algorithm requires the computation of second-order derivatives, it has backpropagation's order of complexity. Automatically, it effectively prunes units, weights, and input lines. Various experiments with feedforward and recurrent nets are described. In an application to stock market prediction, flat minimum search outperforms conventional backprop, weight decay, and “optimal brain surgeon/optimal brain damage.”

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44

Juhas, Anamarija, and Ladislav A. Novak. "Maximally Flat Waveforms with Finite Number of Harmonics in Class-FPower Amplifiers." Mathematical Problems in Engineering 2013 (2013): 1–9. http://dx.doi.org/10.1155/2013/169590.

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In this paper general solution to the problem of finding maximally flat waveforms with finite number of harmonics (maximally flat trigonometric polynomials) is provided. Waveform coefficients are expressed in closed form as functions of harmonic orders. Two special cases of maximally flat waveforms (so-called maximally flat even harmonic and maximally flat odd harmonic waveforms), which proved to play an important role in class-Fand inverse class-Fpower amplifier (PA) operations, are also considered. For these two special types of waveforms, coefficients are expressed as functions of two parameters only. Closed form expressions for efficiency and power output capability of class-Fand inverse class-FPA operations with maximally flat waveforms are also provided as explicit functions of number of a harmonics.

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45

Sazeedeh, Reza. "Gorenstein injective, Gorenstein flat modules and the section functor." Journal of Pure and Applied Algebra 211, no. 3 (December 2007): 773–83. http://dx.doi.org/10.1016/j.jpaa.2007.04.013.

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46

Lundström, Niklas L. P. "Estimates for -harmonic functions vanishing on a flat." Nonlinear Analysis: Theory, Methods & Applications 74, no. 18 (December 2011): 6852–60. http://dx.doi.org/10.1016/j.na.2011.06.041.

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47

Thilliez, Vincent. "Division by Flat Ultradifferentiable Functions and Sectorial Extensions." Results in Mathematics 44, no. 1-2 (August 2003): 169–88. http://dx.doi.org/10.1007/bf03322923.

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48

Pirozhenko, I. G. "Spectral functions for the flat plasma sheet model." Journal of Physics A: Mathematical and General 39, no. 21 (May 10, 2006): 6657–64. http://dx.doi.org/10.1088/0305-4470/39/21/s66.

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49

Fu, Siqi, and Mei-Chi Shaw. "Bounded Plurisubharmonic Exhaustion Functions and Levi-flat Hypersurfaces." Acta Mathematica Sinica, English Series 34, no. 8 (April 20, 2018): 1269–77. http://dx.doi.org/10.1007/s10114-018-7411-4.

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50

Hsieh, Long Chang, and Tzu Hsia Chen. "Optimal Design of Polishing Trace for Link-Type Optical Fiber Polisher." Advanced Materials Research 328-330 (September 2011): 900–905. http://dx.doi.org/10.4028/www.scientific.net/amr.328-330.900.

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Mike Buzzetti proposes an optical fiber polisher which is a link-type mechanism with double flats in 1999. Buzzetti’s optical fiber polisher produce 8-shaped grinding traces to polish the end face of optical fiber connector. The purpose of this paper is to design the optimal polishing traces of single-plate optical fiber polisher to avoid the patent of Buzzetti’s mechanism. First, a link-type single-plate optical fiber polisher, which is consist 7 links and 8 joints, is proposed. Then, analyze the polishing trace, velocity, and acceleration of Buzzetti’s mechanism and new mechanism. Finally, we take the curvature scope percentage (sp) and the velocity deviation percentage (Vdp) as the objective functions, and use global search to achieve optimized design so that the double- crank single-plate optical fiber polisher will produce the optimum polishing trace which is like the digit “8”. The results of this paper are: (1) The velocity deviation percentage of double-crank single-flat optical fiber polisher (Vdp= 61.8241%) is lower then the original mechanism (Vdp= 76.8652%). And, (2) The maximum acceleration of double-crank single-flat optical fiber polisher (amax = 1231 cm/s2) is lower then the original mechanism (amax= 2323.0 cm/sec2). The result indicates that the polishing effect of the double-crank single-flat optical fiber polisher is better then original mechanism.

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