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Статті в журналах з теми "Extensions compactes"

Автор: Grafiati

Опубліковано: 14 грудня 2024

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1

Casanovas, Enrique. "Compactly expandable models and stability." Journal of Symbolic Logic 60, no. 2 (June 1995): 673–83. http://dx.doi.org/10.2307/2275857.

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Анотація:

In analogy to ω-logic, one defines M-logic for an arbitrary structure M (see [5],[6]). In M-logic only those structures are considered in which a special part, determined by a fixed unary predicate, is isomorphic to M. Let L be the similarity type of M and T its complete theory. We say that M-logic is κ-compact if it satisfies the compactness theorem for sets of < κ sentences. In this paper we introduce the related notion of compactness for expandability: a model M is κ-compactly expandable if for every extension T′ ⊇ T of cardinality < κ, if every finite subset of T′ can be satisfied in an expansion of M, then T′ can also be satisfied in an expansion of M. Moreover, M is compactly expandable if it is ∥M∥+-compactly expandable. It turns out that M-logic is κ-compact iff M is κ-compactly expandable.Whereas for first-order logic consistency and finite satisfiability are the same, consistency with T and finite satisfiability in M are, in general, no longer the same thing. We call the model Mκ-expandable if every consistent extension T′ ⊇ T of cardinality < κ can be satisfied in an expansion of M. We say that M is expandable if it is ∥M∥+-expandable. Here we study the relationship between saturation, expandability and compactness for expandability. There is a close parallelism between our results about compactly expandable models and some theorems of S. Shelah about expandable models, which are in fact expressed in terms of categoricity of PC-classes (see [7, Th. VI.5.3, VI.5.4 and VI.5.5]). Our results could be obtained directly from these theorems of Shelah if expandability and compactness for expandability were the same notion.

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2

Caicedo, Xavier. "A simple solution to Friedman's fourth problem." Journal of Symbolic Logic 51, no. 3 (September 1986): 778–84. http://dx.doi.org/10.2307/2274031.

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AbstractIt is shown that Friedman's problem, whether there exists a proper extension of first order logic satisfying the compactness and interpolation theorems, has extremely simple positive solutions if one considers extensions by generalized (finitary) propositional connectives. This does not solve, however, the problem of whether such extensions exist which are also closed under relativization of formulas.

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3

Zhang, Zhihua. "Approximation of Bivariate Functions via Smooth Extensions." Scientific World Journal 2014 (2014): 1–16. http://dx.doi.org/10.1155/2014/102062.

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For a smooth bivariate function defined on a general domain with arbitrary shape, it is difficult to do Fourier approximation or wavelet approximation. In order to solve these problems, in this paper, we give an extension of the bivariate function on a general domain with arbitrary shape to a smooth, periodic function in the whole space or to a smooth, compactly supported function in the whole space. These smooth extensions have simple and clear representations which are determined by this bivariate function and some polynomials. After that, we expand the smooth, periodic function into a Fourier series or a periodic wavelet series or we expand the smooth, compactly supported function into a wavelet series. Since our extensions are smooth, the obtained Fourier coefficients or wavelet coefficients decay very fast. Since our extension tools are polynomials, the moment theorem shows that a lot of wavelet coefficients vanish. From this, with the help of well-known approximation theorems, using our extension methods, the Fourier approximation and the wavelet approximation of the bivariate function on the general domain with small error are obtained.

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4

van den Berg, Benno, and Ieke Moerdijk. "The axiom of multiple choice and models for constructive set theory." Journal of Mathematical Logic 14, no. 01 (June 2014): 1450005. http://dx.doi.org/10.1142/s0219061314500056.

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We propose an extension of Aczel's constructive set theory CZF by an axiom for inductive types and a choice principle, and show that this extension has the following properties: it is interpretable in Martin-Löf's type theory (hence acceptable from a constructive and generalized-predicative standpoint). In addition, it is strong enough to prove the Set Compactness theorem and the results in formal topology which make use of this theorem. Moreover, it is stable under the standard constructions from algebraic set theory, namely exact completion, realizability models, forcing as well as more general sheaf extensions. As a result, methods from our earlier work can be applied to show that this extension satisfies various derived rules, such as a derived compactness rule for Cantor space and a derived continuity rule for Baire space. Finally, we show that this extension is robust in the sense that it is also reflected by the model constructions from algebraic set theory just mentioned.

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5

Kim, Yong-Chan, and S. E. Abbas. "Some good extensions of compactness." Journal of Korean Institute of Intelligent Systems 13, no. 5 (October 1, 2003): 614–20. http://dx.doi.org/10.5391/jkiis.2003.13.5.614.

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6

Enayat, Ali. "Conservative extensions of models of set theory and generalizations." Journal of Symbolic Logic 51, no. 4 (December 1986): 1005–21. http://dx.doi.org/10.2307/2273912.

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Анотація:

An attempt to answer the following question gave rise to the results of the present paper. Let be an arbitrary model of set theory. Does there exist an elementary extension of satisfying the two requirements: (1) contains an ordinal exceeding all the ordinals of ; (2) does not enlarge any (hyper) integer of ? Note that a trivial application of the ordinary compactness theorem produces a model satisfying condition (1); and an internal ultrapower modulo an internal ultrafilter produces a model satisfying condition (2) (but not (1), because of the axiom of replacement). Also, such a satisfying both conditions (1) and (2) exists if the external cofinality of the ordinals of is countable, since by [KM], would then have an elementary end extension.Using a class of models constructed by M. Rubin using in [RS], and already employed in [E1], we prove that our question in general has a negative answer (see Theorem 2.3). This result generalizes the results of M. Kaufmann and the author (appearing respectively in [Ka] and [E1]) concerning models of set theory with no elementary end extensions.In the course of the proof it was necessary to establish that all conservative extensions (see Definition 2.1) of models of ZF must be cofinal. This is in direct contrast with the case of Peano arithmetic where all conservative extensions are end extensional (as observed by Phillips in [Ph1]). This led the author to introduce two useful weakenings of the notion of a conservative end extension which, as shown by the “completeness” theorems in §3, can exist.

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7

Paúl, Pedro J. "New applications of Pták's extension theorem to weak compactness." Czechoslovak Mathematical Journal 39, no. 3 (1989): 454–58. http://dx.doi.org/10.21136/cmj.1989.102316.

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8

Gasparis, I. "An extension of James's compactness theorem." Journal of Functional Analysis 268, no. 1 (January 2015): 194–209. http://dx.doi.org/10.1016/j.jfa.2014.10.021.

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9

Aygün, Halis, A. Arzu Bural, and S. R. T. Kudri. "Fuzzy Inverse Compactness." International Journal of Mathematics and Mathematical Sciences 2008 (2008): 1–9. http://dx.doi.org/10.1155/2008/436570.

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Анотація:

We introduce definitions of fuzzy inverse compactness, fuzzy inverse countable compactness, and fuzzy inverse Lindelöfness on arbitrary -fuzzy sets in -fuzzy topological spaces. We prove that the proposed definitions are good extensions of the corresponding concepts in ordinary topology and obtain different characterizations of fuzzy inverse compactness.

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10

Pal, Arupkumar. "Regularity of operators on essential extensions of the compacts." Proceedings of the American Mathematical Society 128, no. 9 (February 28, 2000): 2649–57. http://dx.doi.org/10.1090/s0002-9939-00-05611-2.

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11

Cencelj, M., and A. N. Dranishnikov. "Extension of Maps to Nilpotent Spaces." Canadian Mathematical Bulletin 44, no. 3 (September 1, 2001): 266–69. http://dx.doi.org/10.4153/cmb-2001-026-1.

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AbstractWe show that every compactum has cohomological dimension 1 with respect to a finitely generated nilpotent group G whenever it has cohomological dimension 1 with respect to the abelianization of G. This is applied to the extension theory to obtain a cohomological dimension theory condition for a finite-dimensional compactum X for extendability of every map from a closed subset of X into a nilpotent CW-complex M with finitely generated homotopy groups over all of X.

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12

Buhagiar, David, and Mirna Džamonja. "Square compactness and the filter extension property." Fundamenta Mathematicae 252, no. 3 (2021): 325–42. http://dx.doi.org/10.4064/fm787-4-2020.

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13

Noorany, Iraj, and Curt Scheyhing. "Lateral Extension of Compacted-Fill Slopes in Expansive Soils." Journal of Geotechnical and Geoenvironmental Engineering 141, no. 1 (January 2015): 04014083. http://dx.doi.org/10.1061/(asce)gt.1943-5606.0001190.

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14

Chamashev, Marat, and Guliza Namazova. "ON COMPACTNESS TYPE EXTENSIONS OF TOPOLOGYCAL AND UNIFORM SPACES." Вестник Ошского государственного университета. Математика. Физика. Техника, no. 1(4) (June 11, 2024): 247–50. http://dx.doi.org/10.52754/16948645_2024_1(4)_46.

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Анотація:

In this article extensions of real-complete Tychonoff and uniform spaces are considered, as well as locally compact paracompact and locally compact Lindelöff extensions of Tychonoff and uniform spaces.

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15

Rubin, Leonard R., and Philip J. Schapiro. "Resolutions for metrizable compacta in extension theory." Transactions of the American Mathematical Society 358, no. 6 (May 26, 2005): 2507–36. http://dx.doi.org/10.1090/s0002-9947-05-03747-5.

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16

Tian, Yuhang, Yanmin Shuai, Xianwei Ma, Congying Shao, Tao Liu, and Latipa Tuerhanjiang. "Improved Landscape Expansion Index and Its Application to Urban Growth in Urumqi." Remote Sensing 14, no. 20 (October 20, 2022): 5255. http://dx.doi.org/10.3390/rs14205255.

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Анотація:

Automatic determination of quantitative parameters describing the pattern of urban expansion is extremely important for urban planning, urban management and civic resource configuration. Though the widely adopted LEI (landscape expansion index) has exhibited the potential to capture the evolution of urban landscape patterns using multi-temporal remote sensing data, erroneous determination still exists, especially for patches with special shapes due to the limited consideration of spatial relationships among patches. In this paper, we improve the identification of urban landscape expansion patterns with an enhancement of the topological relationship. We propose MCI (Mean patch Compactness Index) and AWCI (Area-Weighted Compactness Index) in terms of the moment of inertia shape index. The effectiveness of the improved approach in identifying types of expansion patches is theoretically demonstrated with a series of designed experiments. Further, we apply the proposed approaches to the analysis of urban expansion features and dynamics of urban compactness over Urumqi at various 5-year stages using available SUBAD-China data from 1990–2015. The results achieved by the theoretical experiments and case application show our approach effectively suppressed the effects induced by shapes of patches and buffer or envelope box parameters for the accurate identification of patch type. Moreover, the modified MCI and AWCI exhibited an improved potential in capturing the landscape scale compactness of urban dynamics. The investigated 25-year urban expansion of Urumqi is dominated by edge-expansion patches and supplemented by outlying growth, with opposite trends of increasing and decreasing, with a gradual decrease in landscape fragmentation. Our examination using the proposed MCI and AWCI indicates Urumqi was growing more compact in latter 15-year period compared with the first 10 years studied, with the primary urban patches tending to be compacted earlier than the entire urban setting. The historical transformation trajectories based on remote sensing data show a significant construction land gain—from 1.06% in 1990 to 6.96% in 2015—due to 289.16 km2 of recently established construction, accompanied by fast expansion northward, less dynamic expansion southward, and earlier extension in the westward direction than eastward. This work provides a possible means to improve the identification of patch expansion type and further understand the compactness of urban dynamics.

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17

Kuijper, Josefien. "A descent principle for compactly supported extensions of functors." Annals of K-Theory 8, no. 3 (August 27, 2023): 489–529. http://dx.doi.org/10.2140/akt.2023.8.489.

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18

Levin, Michael. "Constructing Compacta of Different Extensional Dimensions." Canadian Mathematical Bulletin 44, no. 1 (March 1, 2001): 80–86. http://dx.doi.org/10.4153/cmb-2001-009-2.

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19

Tang, Van Lam, Boris Igorevich Bulgakov, and Olga Vladimirovna Aleksandrova. "DETERMINATION OF ADHESIVE STRENGTH LAYER’S ROLLER COMPACTED CONCRETE THE METHOD AXIAL EXTENSION." Vestnik MGSU, no. 6 (June 2017): 647–53. http://dx.doi.org/10.22227/1997-0935.2017.6.647-653.

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Roller compacted concrete for the construction of hydraulic and hydroelectric buildings is a composite material, which consists of a binder, fine aggregate (sand), coarse aggregate (gravel or crushed stone), water and special additives that provide the desired concrete workability and impart the required concrete performance properties. Concrete mixture is prepared at from concrete mixing plants strictly metered quantities of cement, water, additives and graded aggregates, whereupon they are delivered to the site laying Mixer Truck and sealing layers with each stack layer. The advantages of roller compaction technology should include the reduction of construction time, which allows fast commissioning construction projects, as well as reduce the amount of investment required. One of the main problems encountered in the process of roller compaction of the concrete mix is the need to provide the required adhesion strength between layers of concrete. This paper presents a method for determining the strength of adhesion between the concrete layers of different ages roller compacted concrete using axial tension. This method makes it possible to obtain objective and accurate results with a total thickness of layers of compacted concrete of up to 300…400 mm. Results from this method, studies have shown that the value of strength between the concrete layers in addition to the composition of the concrete and adhesion depends on the quality and the parallel end surfaces of the cylinder-models, which are mounted steel plates for axial tension, as well as the state of the contact surfaces of the concrete layer. The method can be used to determine the strength of interlayer adhesion in roller compacted concrete, which are used in the construction of dams and other hydraulic structures.

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20

MATHEW, SUNIL C., and Vivek S. "On the extensions of a double fuzzy topological space." Journal of Advanced Studies in Topology 9, no. 1 (July 6, 2018): 75–93. http://dx.doi.org/10.20454/jast.2018.1431.

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This paper introduces extensions of a double fuzzy topological space and investigates the link between the associated fuzzy topologies of a given space and its extensions. It is also explored whether the \((r, s)\)-connectedness and \((p, q)\)-compactness of a double fuzzy topological space are carried over to its extensions.

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21

Liu, Jun Xin, Zhong Fu Chen, and Wei Fang Xu. "Study on Character of Triaxial Extension Strength of Compacted Clay." Advanced Materials Research 243-249 (May 2011): 2183–87. http://dx.doi.org/10.4028/www.scientific.net/amr.243-249.2183.

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For soils, failure occurs with lower deviatoric stress under the same pressure (the first invariant of stress tensor) in TXE compared with the strength of the triaxial compression, which is indicated that the strength of soils strongly depends on the third invariant of stress deviator; Although in the traditional Mohr-Coulomb criterion it can be reflected in difference of strength between triaxial extension and compression under the same pressure, it’s nothing to do with the pressure for the strength ratio between triaxial extension and compression. By TXC and TXE, changes of deviatoric stress and the ratio with the pressure were studied

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22

Brodskii, N. B. "Extension of maps to the hyperspace ofUVn-compacta." Russian Mathematical Surveys 54, no. 6 (December 31, 1999): 1236–37. http://dx.doi.org/10.1070/rm1999v054n06abeh000233.

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23

Herrlich, Horst, Paul Howard, and Kyriakos Keremedis. "On extensions of countable filterbases to ultrafilters and ultrafilter compactness." Quaestiones Mathematicae 41, no. 2 (September 19, 2017): 213–25. http://dx.doi.org/10.2989/16073606.2017.1376229.

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24

Garncarek, Ł. "Property of rapid decay for extensions of compactly generated groups." Publicacions Matemàtiques 59 (July 1, 2015): 301–12. http://dx.doi.org/10.5565/publmat_59215_02.

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25

Balder, Erik J. "On compactness results for multi-scale convergence." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 129, no. 3 (1999): 467–76. http://dx.doi.org/10.1017/s0308210500021466.

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Two relative compactness results for two-scale convergence in homogenization, due to G. Nguetseng, were recently extended to the multi-scale case by G. Allaire and M. Briane. Whereas their extension of Nguetseng's first result, which is in L2, is straightforward, their extension of his second result, which takes place in the Sobolev space H1, is quite complicated, even though it follows Nguetseng by using the fact that the image of H1 under the gradient mapping is the orthogonal complement of the set of divergence-free functions. Here a much simpler proof is provided by deriving the H1-type result from combining the first extension result with the fact that the above-mentioned image space is also the space of all rotation-free fields. Moreover, this approach reveals that the two results can be seen as corollaries of a fundamental relative compactness result for Young measures.

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26

Ben-Neria, Omer. "Diamonds, compactness, and measure sequences." Journal of Mathematical Logic 19, no. 01 (June 2019): 1950002. http://dx.doi.org/10.1142/s0219061319500028.

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We establish the consistency of the failure of the diamond principle on a cardinal [Formula: see text] which satisfies a strong simultaneous reflection property. The result is based on an analysis of Radin forcing, and further leads to a characterization of weak compactness of [Formula: see text] in a Radin generic extension.

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27

BURNS, DAVID. "ON THE GALOIS STRUCTURE OF ARITHMETIC COHOMOLOGY I: COMPACTLY SUPPORTED -ADIC COHOMOLOGY." Nagoya Mathematical Journal 239 (November 16, 2018): 294–321. http://dx.doi.org/10.1017/nmj.2018.41.

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We investigate the Galois structures of $p$-adic cohomology groups of general $p$-adic representations over finite extensions of number fields. We show, in particular, that as the field extensions vary over natural families the Galois modules formed by these cohomology groups always decompose as the direct sum of a projective module and a complementary module of bounded $p$-rank. We use this result to derive new (upper and lower) bounds on the changes in ranks of Selmer groups over extensions of number fields and descriptions of the explicit Galois structures of natural arithmetic modules.

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28

Zabotin,, Vladislav I., and Pavel A. Chernyshevskij. "Extension of Strongins Global Optimization Algorithm to a Function Continuous on a Compact Interval." Computer Research and Modeling 11, no. 6 (December 2019): 1111–19. http://dx.doi.org/10.20537/2076-7633-2019-11-6-1111-1119.

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29

Bami, M. Lashkarizadeh, B. Mohammadzadeh, and R. Nasr-Isfahani. "Inner invariant extensions of Dirac measures on compactly cancellative topological semigroups." Bulletin of the Belgian Mathematical Society - Simon Stevin 14, no. 4 (November 2007): 699–708. http://dx.doi.org/10.36045/bbms/1195157138.

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30

Calabuig, J. M., E. Jiménez Fernández, M. A. Juan, and E. A. Sánchez Pérez. "Optimal extensions of compactness properties for operators on Banach function spaces." Topology and its Applications 203 (April 2016): 57–66. http://dx.doi.org/10.1016/j.topol.2015.12.075.

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31

Lu, Peirong, Yaxin Liu, Yujie Yang, Yu Zhu, and Zhonghua Jia. "Evaluating Soil Water–Salt Dynamics under Brackish Water Drip Irrigation in Greenhouses Subjected to Localized Topsoil Compaction." Agriculture 14, no. 3 (March 3, 2024): 412. http://dx.doi.org/10.3390/agriculture14030412.

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Анотація:

Localized soil compaction in greenhouses resulting from less frequent tillage operations and frequent trampling by farmers inevitably disturbs the continuity and homogeneity of soil’s hydraulic properties, which impacts the precision of greenhouse cultivation regarding water supply and salinity control. However, predicting water–salt dynamics under partly compacted topsoil is difficult because of the interactions between many factors related to soil properties, including irrigation method and water quality, which are especially subjected to varied compaction sizes and positions. Here, two field treatments were conducted in brackish water (3 g L−1) drip-irrigated plots, with the designed soil compaction region (40 cm width and 30 cm depth) adjacent to (T1) and below (T2) the drip lines. The calibrated and validated HYDRUS-2D model was applied to analyze salt exchanges across the vertical and horizontal interfaces between the compacted and non-compacted zones and the associated solute concentration variations within these two zones. The results indicated that the limited horizontal solute flux under T1 enhanced the subsequent downward flux below the drip lines, whereas, under T2, the restricted downward flux with relatively limited improved horizontal salt spreading resulted in more salt retention in the soil profile. Additional scenario simulations considering the vertical and horizontal extension of soil compaction sizes (ranging from 10 × 10 cm to 40 × 40 cm) were also conducted and revealed that, with the same increment in compaction size, the vertical extension of the compacted zone aggravated salt accumulation compared with that of horizontal extension, while the simulated cumulative water and salt downward fluxes were positive in relation to the compaction sizes in both vertical and horizontal directions under T1, but negative under T2. The findings of this study explore the effect of relative positions between drip lines and the soil compaction zone on salt transports under brackish water irrigation and reveal the potential soil salinization trend as extending compaction regions in the vertical or horizontal direction.

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32

Işık, Hüseyin, Shahram Banaei, Farhan Golkarmanesh, Vahid Parvaneh, Choonkil Park, and Maryam Khorshidi. "On New Extensions of Darbo’s Fixed Point Theorem with Applications." Symmetry 12, no. 3 (March 6, 2020): 424. http://dx.doi.org/10.3390/sym12030424.

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Анотація:

In this paper, we extend Darbo’s fixed point theorem via weak JS-contractions in a Banach space. Our results generalize and extend several well-known comparable results in the literature. The technique of measure of non-compactness is the main tool in carrying out our proof. As an application, we study the existence of solutions for a system of integral equations. Finally, we present a concrete example to support the effectiveness of our results.

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33

Fatehi, M. "On the Generalized Hardy Spaces." Abstract and Applied Analysis 2010 (2010): 1–14. http://dx.doi.org/10.1155/2010/803230.

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Анотація:

We introduce new spaces that are extensions of the Hardy spaces and we investigate the continuity of the point evaluations as well as the boundedness and the compactness of the composition operators on these spaces.

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34

Cen, Y. G., R. Z. Zhao, L. H. Cen, Z. J. Miao, and X. F. Chen. "Explicit construction of compactly supported biorthogonal multiwavelets via matrix extension." IMA Journal of Applied Mathematics 79, no. 3 (February 4, 2013): 502–34. http://dx.doi.org/10.1093/imamat/hxt001.

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35

Warner, M. W. "A theorem on sequentiality and compactness, with its fuzzy extension." Fuzzy Sets and Systems 30, no. 3 (May 1989): 321–27. http://dx.doi.org/10.1016/0165-0114(89)90023-7.

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36

Guerrero-García, Guillermo Iván, Enrique González-Tovar, Martín Chávez-Páez, Jacek Kłos, and Stanisław Lamperski. "Quantifying the thickness of the electrical double layer neutralizing a planar electrode: the capacitive compactness." Physical Chemistry Chemical Physics 20, no. 1 (2018): 262–75. http://dx.doi.org/10.1039/c7cp05433e.

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37

Karsli, Harun. "Extension of the generalized Bézier operators by wavelets." General Mathematics 30, no. 2 (December 1, 2022): 3–15. http://dx.doi.org/10.2478/gm-2022-0010.

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Анотація:

Abstract In this paper we introduce a novel extension of generalized Bézier operators by replacing the sample values f ( k n ) f\left({{k\overn}}\right) with the wavelet expansion of the function f. Using the compactly supported Daubechies wavelets, we construct a wavelet type extension of the generalized Bézier operators defined by Gupta [7]. Moreover, we investigate some properties of these operators in some function spaces.

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38

Dahia, Elhadj. "The extension of two-Lipschitz operators." Applied General Topology 25, no. 1 (April 2, 2024): 47–56. http://dx.doi.org/10.4995/agt.2024.20296.

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The paper deals with some further results concerning the class of two-Lipschitz operators. We prove first an isometric isomorphism identification of two-Lipschitz operators and Lipschitz operators. After defining and characterize the adjoint of two-Lipschitz operator, we prove a Schauder type theorem on the compactness of the adjoint. We study the extension of two-Lipschitz operators from cartesian product of two complemented subspaces of a Banach space to the cartesian product of whole spaces. Also, we show that every two-Lipschitz functional defined on cartesian product of two pointed metric spaces admits an extension with the same two-Lipschitz norm, under some requirements on domaine spaces.

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39

Chang, Shun-Cheng. "Compactness theorems for critical metrics of the Weyl functional on compact Kähler surfaces." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 62, no. 2 (April 1997): 217–28. http://dx.doi.org/10.1017/s144678870000077x.

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40

Sims, Brailey, and David Yost. "Linear Hahn–Banach extension operators." Proceedings of the Edinburgh Mathematical Society 32, no. 1 (February 1989): 53–57. http://dx.doi.org/10.1017/s0013091500006908.

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Given any subspace N of a Banach space X, there is a subspace M containing N and of the same density character as N, for which there exists a linear Hahn–Banach extension operator from M* to X*. This result was first proved by Heinrich and Mankiewicz [4, Proposition 3.4] using some of the deeper results of Model Theory. More precisely, they used the Banach space version of the Löwenheim–Skolem theorem due to Stern [11], which in turn relies on the Löwenheim–Skolem and Keisler–Shelah theorems from Model Theory. Previously Lindenstrauss [7], using a finite dimensional lemma and a compactness argument, obtained a version of this for reflexive spaces. We shall show that the same finite dimensional lemma leads directly to the general result, without any appeal to Model Theory.

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41

Смирнов, Сергей Николевич, and Sergey Smirnov. "A guaranteed deterministic approach to superhedging: mixed strategies and game equilibrium." Mathematical Game Theory and Applications 12, no. 1 (March 30, 2020): 60–90. http://dx.doi.org/10.17076/mgta_2020_1_11.

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For a discrete-time superreplication problem, a guaranteed deterministic formulation is considered: the problem is to ensure a cheapest coverage of the contingent claim on an option under all scenarios which are set using a priori defined compacts, depending on the price history: price increments at each moment of time must lie in the corresponding compacts. The market is considered with trading constraints and without transaction costs. The statement of the problem is game-theoretic in nature and leads directly to the Bellman - Isaacs equations. In this article, we introduce a mixed extension of the ``market'' pure strategies. Several results concerning game equilibrium are obtained.

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42

Tial, M. "Integral of an extension of the sine addition formula." Mathematical Modeling and Computing 10, no. 3 (2023): 833–40. http://dx.doi.org/10.23939/mmc2023.03.833.

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In this paper, we determine the continuous solutions of the integral functional equation of Stetkær's extension of the sine addition law ∫Gf(xyt)dμ(t)=f(x)χ1(y)+χ2(x)f(y), x,y∈G, where f:G→C, G is a locally compact Hausdorff group, μ is a regular, compactly supported, complex-valued Borel measure on G and χ1, χ2 are fixed characters on G.

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43

Danenko, V. F., L. M. Gurevich, E. Yu Kushkina, and E. B. Gladskikh. "EXTENSION OF THE SCOPE OF STEEL COMPACTED STRANDS AND ROPES MADE OF THEM." Izvestiya Visshikh Uchebnykh Zavedenii. Chernaya Metallurgiya = Izvestiya. Ferrous Metallurgy 59, no. 11 (January 1, 2016): 764–72. http://dx.doi.org/10.17073/0368-0797-2016-11-764-772.

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44

Arora, Pamma D., Yongqiang Wang, Anne Bresnick, Paul A. Janmey, and Christopher A. McCulloch. "Flightless I interacts with NMMIIA to promote cell extension formation, which enables collagen remodeling." Molecular Biology of the Cell 26, no. 12 (June 15, 2015): 2279–97. http://dx.doi.org/10.1091/mbc.e14-11-1536.

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We examined the role of the actin-capping protein flightless I (FliI) in collagen remodeling by mouse fibroblasts. FliI-overexpressing cells exhibited reduced spreading on collagen but formed elongated protrusions that stained for myosin10 and fascin and penetrated pores of collagen-coated membranes. Inhibition of Cdc42 blocked formation of cell protrusions. In FliI-knockdown cells, transfection with constitutively active Cdc42 did not enable protrusion formation. FliI-overexpressing cells displayed increased uptake and degradation of exogenous collagen and strongly compacted collagen fibrils, which was blocked by blebbistatin. Mass spectrometry analysis of FliI immunoprecipitates showed that FliI associated with nonmuscle myosin IIA (NMMIIA), which was confirmed by immunoprecipitation. GFP-FliI colocalized with NMMIIA at cell protrusions. Purified FliI containing gelsolin-like domains (GLDs) 1–6 capped actin filaments efficiently, whereas FliI GLD 2–6 did not. Binding assays showed strong interaction of purified FliI protein (GLD 1–6) with the rod domain of NMMIIA ( kD = 0.146 μM), whereas FliI GLD 2–6 showed lower binding affinity ( kD = 0.8584 μM). Cells expressing FliI GLD 2–6 exhibited fewer cell extensions, did not colocalize with NMMIIA, and showed reduced collagen uptake compared with cells expressing FliI GLD 1–6. We conclude that FliI interacts with NMMIIA to promote cell extension formation, which enables collagen remodeling in fibroblasts.

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45

Bankston, Paul. "A hierarchy of maps between compacta." Journal of Symbolic Logic 64, no. 4 (December 1999): 1628–44. http://dx.doi.org/10.2307/2586802.

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AbstractLet CH be the class of compacta (i.e., compact Hausdorff spaces), with BS the subclass of Boolean spaces. For each ordinal α and pair (K, L) of subclasses of CH, we define Lev≥α(K, L), the class of maps of level at least α from spaces in K to spaces in L, in such a way that, for finite α, Lev≥α(BS, BS) consists of the Stone duals of Boolean lattice embeddings that preserve all prenex first-order formulas of quantifier rank α. Maps of level ≥ 0 are just the continuous surjections, and the maps of level ≥ 1 are the co-existential maps introduced in [8]. Co-elementary maps are of level ≥ω a for all ordinals α: of course in the Boolean context, the co-elementary maps coincide with the maps of level ≥ ω. The results of this paper include:(i) every map of level ≥ ωis co-elementary;(ii) the limit maps of an co-indexed inverse system of maps of level ≥ α are also of level ≥ α; and(iii) if K is a co-elementary class, k > ω and Lev≥k(K,K) = Lev≥k+1(K,K), then Lev≥1(K,K) = Lev≥(K,K).A space X ∈ K is co-existentially closed inK if Lev≥0(K, X) = Lev≥1(K,X). Adapting the technique of “adding roots,” by which one builds algebraically closed extensions of fields (and, more generally, existentially closed extensions of models of universal-existential theories), we showed in [8] that every infinite member of a co-inductive co-elementary class (such as CH itself, BS, or the class CON of continua) is a continuous image of a space of the same weight that is co-existentially closed in that class. We show here that every compactum that is co-existentially closed in CON (a co-existentially closed continuum) is both indecomposable and of covering dimension one.

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46

Paúl, Pedro J. "A quantitative extension of a theorem of Valdivia on weak compactness." Journal of Mathematical Analysis and Applications 456, no. 2 (December 2017): 1517–20. http://dx.doi.org/10.1016/j.jmaa.2017.07.072.

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47

Enayat, Ali. "Weakly compact cardinals in models of set theory." Journal of Symbolic Logic 50, no. 2 (June 1985): 476–86. http://dx.doi.org/10.2307/2274236.

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The central notion of this paper is that of a κ-elementary end extension of a model of set theory. A model is said to be a κ-elementary end extension of a model of set theory if > and κ, which is a cardinal of , is end extended in the passage from to , i.e., enlarges κ without enlarging any of its members (see §0 for more detail). This notion was implicitly introduced by Scott in [Sco] and further studied by Keisler and Morley in [KM], Hutchinson in [H] and recently by the author in [E]. It is not hard to see that if has a κ-elementary end extension then κ must be regular in . Keisler and Morley [KM] noticed that this has a converse if is countable, i.e., if κ is a regular cardinal of a countable model then has a κ-elementary end extension. Later Hutchinson [H] refined this result by constructing κ-elementary end extensions 1 and 2 of an arbitrary countable model in which κ is a regular uncountable cardinal, such that 1 adds a least new element to κ while 2 adds no least new ordinal to κ. It is a folklore fact of model theory that the Keisler-Morley result gives soft and short proofs of countable compactness and abstract completeness (i.e. recursive enumera-bility of validities) of the logic L(Q), studied extensively in Keisler's [K2]; and Hutchinson's refinement does the same for stationary logic L(aa), studied by Barwise et al. in [BKM]. The proof of Keisler-Morley and that of Hutchinson make essential use of the countability of since they both rely on the Henkin-Orey omitting types theorem. As pointed out in [E, Theorem 2.12], one can prove these theorems using “generic” ultrapowers just utilizing the assumption of countability of the -power set of κ. The following result, appearing as Theorem 2.14 in [E], links the notion of κ-elementary end extension to that of measurability of κ. The proof using (b) is due to Matti Rubin.

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48

Kirk, W. A. "Transfinite methods in metric fixed-point theory." Abstract and Applied Analysis 2003, no. 5 (2003): 311–24. http://dx.doi.org/10.1155/s1085337503205029.

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This is a brief survey of the use of transfinite induction in metric fixed-point theory. Among the results discussed in some detail is the author's 1989 result on directionally nonexpansive mappings (which is somewhat sharpened), a result of Kulesza and Lim giving conditions when countable compactness implies compactness, a recent inwardness result for contractions due to Lim, and a recent extension of Caristi's theorem due to Saliga and the author. In each instance, transfinite methods seem necessary.

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49

Bezem, Marc. "Compact and majorizable functionals of finite type." Journal of Symbolic Logic 54, no. 1 (March 1989): 271–80. http://dx.doi.org/10.2307/2275030.

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The main result of this paper will be that various notions of majorizability and compactness coincide in the full typestructure over the natural numbers. Moreover we shall show that the extensional typestructure of strongly majorizable functionals can be obtained by applying Zucker's construction ( )E to any of these coinciding intensional typestructures. A different result is proved in the typestructure of effective operations, where not every majorizable functional is compact. Finally we shall introduce the concept of relative compactness in the full typestructure and prove that there are just two degrees of compactness.

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50

Helzerman, R. A., and M. P. Harper. "MUSE CSP: An Extension to the Constraint Satisfaction Problem." Journal of Artificial Intelligence Research 5 (November 1, 1996): 239–88. http://dx.doi.org/10.1613/jair.298.

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This paper describes an extension to the constraint satisfaction problem (CSP) called MUSE CSP (MUltiply SEgmented Constraint Satisfaction Problem). This extension is especially useful for those problems which segment into multiple sets of partially shared variables. Such problems arise naturally in signal processing applications including computer vision, speech processing, and handwriting recognition. For these applications, it is often difficult to segment the data in only one way given the low-level information utilized by the segmentation algorithms. MUSE CSP can be used to compactly represent several similar instances of the constraint satisfaction problem. If multiple instances of a CSP have some common variables which have the same domains and constraints, then they can be combined into a single instance of a MUSE CSP, reducing the work required to apply the constraints. We introduce the concepts of MUSE node consistency, MUSE arc consistency, and MUSE path consistency. We then demonstrate how MUSE CSP can be used to compactly represent lexically ambiguous sentences and the multiple sentence hypotheses that are often generated by speech recognition algorithms so that grammar constraints can be used to provide parses for all syntactically correct sentences. Algorithms for MUSE arc and path consistency are provided. Finally, we discuss how to create a MUSE CSP from a set of CSPs which are labeled to indicate when the same variable is shared by more than a single CSP.

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