Статті в журналах: "Argument de point fixe"

1

XAVIER, JULIANA. "Handel’s fixed point theorem revisited." Ergodic Theory and Dynamical Systems 33, no. 5 (August 6, 2012): 1584–610. http://dx.doi.org/10.1017/s0143385712000338.

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AbstractMichael Handel proved in [A fixed-point theorem for planar homeomorphisms. Topology38 (1999), 235–264] the existence of a fixed point for an orientation-preserving homeomorphism of the open unit disk that can be extended to the closed disk, provided that it has points whose orbits form an oriented cycle of links at infinity. Later, Patrice Le Calvez gave a different proof of this theorem based only on Brouwer theory and plane topology arguments in [Une nouvelle preuve du théorème de point fixe de Handel. Geom. Topol.10(2006), 2299–2349]. These methods improved the result by proving the existence of a simple closed curve of index 1. We give a new, simpler proof of this improved version of the theorem and generalize it to non-oriented cycles of links at infinity.

2

Gretz, Shai, Roni Friedman, Edo Cohen-Karlik, Assaf Toledo, Dan Lahav, Ranit Aharonov, and Noam Slonim. "A Large-Scale Dataset for Argument Quality Ranking: Construction and Analysis." Proceedings of the AAAI Conference on Artificial Intelligence 34, no. 05 (April 3, 2020): 7805–13. http://dx.doi.org/10.1609/aaai.v34i05.6285.

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Identifying the quality of free-text arguments has become an important task in the rapidly expanding field of computational argumentation. In this work, we explore the challenging task of argument quality ranking. To this end, we created a corpus of 30,497 arguments carefully annotated for point-wise quality, released as part of this work. To the best of our knowledge, this is the largest dataset annotated for point-wise argument quality, larger by a factor of five than previously released datasets. Moreover, we address the core issue of inducing a labeled score from crowd annotations by performing a comprehensive evaluation of different approaches to this problem. In addition, we analyze the quality dimensions that characterize this dataset. Finally, we present a neural method for argument quality ranking, which outperforms several baselines on our own dataset, as well as previous methods published for another dataset.

3

Wreen, Michael J. "The Standing is Slippery." Philosophy 79, no. 4 (October 2004): 553–72. http://dx.doi.org/10.1017/s0031819104000440.

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This paper is a critical examination of the so-called slippery slope argument for the conservative position on abortion. The argument was discussed in the philosophic literature some time back, but has since fallen into disfavor.The argument is first exposed and a general objection to it is advanced, then rebutted. Rosalind Hursthouse's more detailed and stronger objection is next aired, but also found less than convincing. In the course of discussing her objection, the correct form of the argument is identified, and it's noted that rejection of the argument requires finding fault with its inductive premise. That, in turn, requires either (a) identifying and defending a cutoff point other than conception, or (b) not identifying a cutoff point but directly attacking the argument's conclusion. As far as (a) is concerned, all except one alternative cutoff point have severe problems that have been well discussed in the literature. The one that doesn't, the appearance of the ‘primitive streak’, is examined in detailed, but ultimately rejected. As for (b), five different grounds for rejecting the conclusion are identified and discussed, but none is found plausible.Variations on the slippery slope argument, concerning different conclusions that it may have, are then distinguished, related to each other, and critically discussed, and the paper ends with some cautionary remarks about the defense of the argument tendered.

4

Khan, Abdul Qadeer. "Global Dynamics, Bifurcation Analysis, and Chaos in a Discrete Kolmogorov Model with Piecewise-Constant Argument." Mathematical Problems in Engineering 2021 (November 5, 2021): 1–14. http://dx.doi.org/10.1155/2021/5259226.

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The local behavior with topological classifications, bifurcation analysis, chaos control, boundedness, and global attractivity of the discrete-time Kolmogorov model with piecewise-constant argument are investigated. It is explored that Kolmogorov model has trivial and two semitrival fixed points for all involved parameters, but it has an interior fixed point under definite parametric condition. Then, by linear stability theory, local dynamics with different topological classifications are investigated around trivial, semitrival, and interior fixed points. Further for the discrete Kolmogorov model, existence of periodic points is also investigated. It is also investigated the occurrence of bifurcations at interior fixed point and proved that at interior fixed point, there exists no bifurcation, except flip bifurcation by bifurcation theory. Next, feedback control method is utilized to stabilize chaos existing in discrete Kolmogorov model. Boundedness and global attractivity of the discrete Kolmogorov model are also investigated. Finally, obtained results are numerically verified.

5

Došlá, Zuzana, Mauro Marini, and Serena Matucci. "A fixed-point approach for decaying solutions of difference equations." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 379, no. 2191 (January 4, 2021): 20190374. http://dx.doi.org/10.1098/rsta.2019.0374.

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A boundary value problem associated with the difference equation with advanced argument * Δ ( a n Φ ( Δ x n ) ) + b n Φ ( x n + p ) = 0 , n ≥ 1 is presented, where Φ ( u ) = | u | α sgn u , α > 0, p is a positive integer and the sequences a , b , are positive. We deal with a particular type of decaying solution of (*), that is the so-called intermediate solution (see below for the definition). In particular, we prove the existence of this type of solution for (*) by reducing it to a suitable boundary value problem associated with a difference equation without deviating argument. Our approach is based on a fixed-point result for difference equations, which originates from existing ones stated in the continuous case. Some examples and suggestions for future research complete the paper. This article is part of the theme issue ‘Topological degree and fixed point theories in differential and difference equations’.

6

Jachymski, Jacek. "Another proof of the Browder–Göhde–Kirk theorem via ordering argument." Bulletin of the Australian Mathematical Society 65, no. 1 (February 2002): 105–7. http://dx.doi.org/10.1017/s0004972700020104.

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Using the Zermelo Principle, we establish a common fixed point theorem for two progressive mappings on a partially ordered set. This result yields the Browder–Göhde–Kirk fixed point theorem for nonexpansive mappings.

7

Aronowicz, Annette. "On Michael Fagenblat's A Covenant of Creatures." AJS Review 35, no. 1 (April 2011): 105–14. http://dx.doi.org/10.1017/s0364009411000092.

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Michael Fagenblat's A Covenant of Creatures is a bold and powerful book. Given the nuanced nature of its arguments, no sooner did I think I captured his thought than I discovered that Fagenblat might also have made the opposite point. Nonetheless, a central line of argument does run through the book. My task will be to present it and also to challenge it. The best tribute to this fine work is to engage in vigorous debate about its claims.

8

O'Regan, Donal. "Existence results for differential equations with reflection of the argument." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 57, no. 2 (October 1994): 237–60. http://dx.doi.org/10.1017/s1446788700037538.

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AbstractExistence principles are given for systems of differential equations with reflection of the argument. These are derived using fixed point analysis, specifically the Nonlinear Alternative. Then existence results are deduced for certain classes of first and second order equations with reflection of the argument.

9

Premoselli, Bruno. "A pointwise finite-dimensional reduction method for a fully coupled system of Einstein–Lichnerowicz type." Communications in Contemporary Mathematics 20, no. 06 (August 27, 2018): 1750076. http://dx.doi.org/10.1142/s0219199717500766.

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We construct non-compactness examples for the fully coupled Einstein–Lichnerowicz constraint system in the focusing case. The construction is obtained by combining pointwise a priori asymptotic analysis techniques, finite-dimensional reductions and a fixed-point argument. More precisely, we perform a fixed-point procedure on the remainders of the expected blow-up decomposition. The argument consists of an involved finite-dimensional reduction coupled with a ping-pong method. To overcome the non-variational structure of the system, we work with remainders which belong to strong function spaces and not merely to energy spaces. Performing both the ping-pong argument and the finite-dimensional reduction therefore heavily relies on the a priori pointwise asymptotic techniques of the [Formula: see text] theory.

10

Zhang, Xuemei, and Meiqiang Feng. "Green’s Function and Positive Solutions for a Second-Order Singular Boundary Value Problem with Integral Boundary Conditions and a Delayed Argument." Abstract and Applied Analysis 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/393187.

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This paper investigates the expression and properties of Green’s function for a second-order singular boundary value problem with integral boundary conditions and delayed argument-x′′t-atx′t+btxt=ωtft, xαt, t∈0, 1; x′0=0, x1-∫01htxtdt=0, wherea∈0, 1, 0, +∞, b∈C0, 1, 0, +∞and,ωmay be singular att=0or/and att=1. Furthermore, several new and more general results are obtained for the existence of positive solutions for the above problem by using Krasnosel’skii’s fixed point theorem. We discuss our problems with a delayed argument, which may concern optimization issues of some technical problems. Moreover, the approach to express the integral equation of the above problem is different from earlier approaches. Our results cover a second-order boundary value problem without deviating arguments and are compared with some recent results.

11

Guezane-Lakoud, A., and R. Khaldi. "Multiple Positive Solutions for a Fractional Boundary Value Problem with Fractional Integral Deviating Argument." International Journal of Mathematics and Mathematical Sciences 2012 (2012): 1–13. http://dx.doi.org/10.1155/2012/651508.

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This work is devoted to the existence of positive solutions for a fractional boundary value problem with fractional integral deviating argument. The proofs of the main results are based on Guo-Krasnoselskii fixed point theorem and Avery and Peterson fixed point theorem. Two examples are given to illustrate the obtained results, ending the paper.

12

Wu, Li, and Chuanzhi Bai. "Application of Fixed-Point Index Theory for a Nonlinear Fractional Boundary Value Problem with an Advanced Argument." Discrete Dynamics in Nature and Society 2021 (September 23, 2021): 1–7. http://dx.doi.org/10.1155/2021/6781541.

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In this paper, we investigate the existence of positive solutions of a class of fractional three-point boundary value problem with an advanced argument by using fixed-point index theory. Our results improve and extend some known results in the literature. Two examples are given to demonstrate the effectiveness of our results.

13

Peña Cervel, María Sandra. "Argument structure and implicational constructions at the crossroads." Review of Cognitive Linguistics 14, no. 2 (December 23, 2016): 474–97. http://dx.doi.org/10.1075/rcl.14.2.08pen.

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On the basis of corpus data and in consonance with cognitively-oriented constructionist approaches to language, mainly the work by Goldberg (1995, 2006) and the developments in Ruiz de Mendoza and Mairal (2008, 2011), we offer a fine-grained analysis of some specific instantiations of the resultative pattern based on the prepositional phrase to death. The analysis starts off from the classification of verb classes made by Levin (1993). The verbs in some of these classes are readily available for fusion into the resultative configuration. Others call for reconstrual in terms of high-level metaphor and/or metonymy before they can conform to the requirements of the pattern mentioned above. Thus, we focus on the way in which the resultative pattern overwrites the properties of some lexical groups of verbs through the licensing activity of such cognitive mechanisms as high-level metaphor and metonymy. Additionally, the prepositional phrase to death is shown to perform two key communicative functions from among those put forward by Boas (2003): placing emphasis on an end point or rendering a vague point clear. Finally, the paper examines the hyperbolic load of the PP to death in some contexts where this PP is seen as converting an argument-structure construction into an implicational one conveying the speaker’s (usually negative) reaction to a given state of affairs.

14

Jaradat, Mohammed M. M., Babak Mohammadi, Vahid Parvaneh, Hassen Aydi та Zead Mustafa. "PPF-Dependent Fixed Point Results for Multi-Valued ϕ-F-Contractions in Banach Spaces and Applications". Symmetry 11, № 11 (6 листопада 2019): 1375. http://dx.doi.org/10.3390/sym11111375.

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The solutions for many real life problems is obtained by interpreting the given problem mathematically in the form of f ( x ) = x . One of such examples is that of the famous Borsuk–Ulam theorem, in which using some fixed point argument, it can be guaranteed that at any given time we can find two diametrically opposite places in a planet with same temperature. Thus, the correlation of symmetry is inherent in the study of fixed point theory. In this paper, we initiate ϕ − F -contractions and study the existence of PPF-dependent fixed points (fixed points for mappings having variant domains and ranges) for these related mappings in the Razumikhin class. Our theorems extend and improve the results of Hammad and De La Sen [Mathematics, 2019, 7, 52]. As applications of our PPF dependent fixed point results, we study the existence of solutions for delay differential equations (DDEs) which have numerous applications in population dynamics, bioscience problems and control engineering.

15

Nakamura, Takuya. "Sur les arguments sémantiques du verbe expliquer et leur réalisation syntaxique." Actes du «27e colloque international sur le lexique et la grammaire» (L'Aquila, 10-13 septembre 2008). Première partie 32, no. 2 (December 15, 2009): 187–99. http://dx.doi.org/10.1075/li.32.2.03nak.

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In this preliminary descriptive research, taking one French verb (expliquer), we explore syntactic possibilities of argument realization. For this verb, at least four types of syntactic constructions are specified for a fixed set of semantic arguments. When the direct object is realized as a NP (and not as a bare Que P) assuming the role of “object” of explanation, it is observed that the subject can vary between the “agent” and “explanation” roles, in correlation with the change of the origin of “explanation”. This type of difference is to be considered a change of diathesis of the same verb. An agentive construction with a complement clause object happens to be a marginal one from the point of view of argument realization, functioning accidentally as a variant of a sentence with verbs of saying. This type of complement clause is a bare Que P in the sense that it does not manifest an alternation with a Que P headed by le fait.

16

Davidson, Barbara, and Robert Pargetter. "In Defence of the Dutch Book Argument." Canadian Journal of Philosophy 15, no. 3 (September 1985): 405–23. http://dx.doi.org/10.1080/00455091.1985.10716426.

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A starting point for this paper is that there is at least one concept of probability, call it epistemic probability, which can be identified with belief or some sort of idealised belief (e.g., rational belief). If this identification is to be of any significance, then it needs to be shown that epistemic probability is a ‘true’ probability concept and is subject to those restrictions and requirements which relate and govern probabilities, which we call the probability calculus.The most rehearsed argument to establish the probability calculus for epistemic probabilities is the Dutch Book Argument (DBA). There are two intuitions behind the DBA. The first is that if we can find some fine-grained behavioural measure of epistemic probability, then we may be able to show that epistemic probabilities obey the probability calculus by showing that the behaviour is of a kind which is, as a matter of necessity, subject to certain limitations and restrictions.

17

CHARKI, Z. "THE INITIAL VALUE PROBLEM FOR THE DEEP BÉNARD CONVECTION EQUATIONS WITH DATA IN Lq." Mathematical Models and Methods in Applied Sciences 06, no. 02 (March 1996): 269–77. http://dx.doi.org/10.1142/s0218202596000584.

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18

Ait Dads, Elhadi, Samir Fatajou, and Lahcen Khachimi. "Pseudo Almost Automorphic Solutions for Differential Equations Involving Reflection of the Argument." ISRN Mathematical Analysis 2012 (September 20, 2012): 1–20. http://dx.doi.org/10.5402/2012/626490.

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By means of the fixed point methods and the properties of the pseudo almost automorphic functions, the existence and uniqueness of pseudo almost automorphic solutions are obtained for differential equations involving reflection of the argument. For the nonscalar, case we use the exponential dichotomy properties.

19

Brattka, Vasco, Stéphane Le Roux, Joseph S. Miller, and Arno Pauly. "Connected choice and the Brouwer fixed point theorem." Journal of Mathematical Logic 19, no. 01 (June 2019): 1950004. http://dx.doi.org/10.1142/s0219061319500041.

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We study the computational content of the Brouwer Fixed Point Theorem in the Weihrauch lattice. Connected choice is the operation that finds a point in a non-empty connected closed set given by negative information. One of our main results is that for any fixed dimension the Brouwer Fixed Point Theorem of that dimension is computably equivalent to connected choice of the Euclidean unit cube of the same dimension. Another main result is that connected choice is complete for dimension greater than or equal to two in the sense that it is computably equivalent to Weak Kőnig’s Lemma. While we can present two independent proofs for dimension three and upward that are either based on a simple geometric construction or a combinatorial argument, the proof for dimension two is based on a more involved inverse limit construction. The connected choice operation in dimension one is known to be equivalent to the Intermediate Value Theorem; we prove that this problem is not idempotent in contrast to the case of dimension two and upward. We also prove that Lipschitz continuity with Lipschitz constants strictly larger than one does not simplify finding fixed points. Finally, we prove that finding a connectedness component of a closed subset of the Euclidean unit cube of any dimension greater than or equal to one is equivalent to Weak Kőnig’s Lemma. In order to describe these results, we introduce a representation of closed subsets of the unit cube by trees of rational complexes.

20

Muglia, Luigi, and Paolamaria Pietramala. "Second-Order Impulsive Differential Equations with Functional Initial Conditions on Unbounded Intervals." Journal of Function Spaces and Applications 2013 (2013): 1–9. http://dx.doi.org/10.1155/2013/479049.

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We present some results on the existence of solutions for second-order impulsive differential equations with deviating argument subject to functional initial conditions. Our results are based on Schaefer's fixed point theorem for completely continuous operators.

21

Garcia, Roberta Veloso, Juliana Marques Cianni dos Santos, and Estaner Claro Romão. "The use of Wittgenstein's language games to promote argumentation in children at the beginning of scientific literacy." International Journal for Innovation Education and Research 9, no. 7 (July 1, 2021): 84–99. http://dx.doi.org/10.31686/ijier.vol9.iss7.3222.

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The insertion of the individual in the scientific culture goes through scientific literacy and this, through teaching that privileges research and argumentation in the school scenario, mainly in Science classes. Based on indicators found in the literature that point to scientific literacy and models proposed by Lawson to define the structure of the argument, a table was elaborated to relate the argumentation of children in the second year of elementary school, leveling it in five levels that point to the logical reasoning and the dominion of content, taking into account Wittgenstein's linguistic games. To analyze what level the children were at, a didactic sequence was elaborated that allowed the observation and study of the arguments used by them. Considering such activities and the children's age group, it was observed that they tend not to complete the argumentative sequence, but they already have strong traces of scientific literacy.

22

Chiu, Kuo-Shou. "Existence and Global Exponential Stability of Equilibrium for Impulsive Cellular Neural Network Models with Piecewise Alternately Advanced and Retarded Argument." Abstract and Applied Analysis 2013 (2013): 1–13. http://dx.doi.org/10.1155/2013/196139.

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We introduce impulsive cellular neural network models with piecewise alternately advanced and retarded argument (in short IDEPCA). The model with the advanced argument is system with strong anticipation. Some sufficient conditions are established for the existence and global exponential stability of a unique equilibrium. The approaches are based on employing Banach’s fixed point theorem and a new IDEPCA integral inequality of Gronwall type. The criteria given are easily verifiable, possess many adjustable parameters, and depend on impulses and piecewise constant argument deviations, which provides exibility for the design and analysis of cellular neural network models. Several numerical examples and simulations are also given to show the feasibility and effectiveness of our results.

23

Recchia, Stefano. "Authorising humanitarian intervention: a five-point defence of existing multilateral procedures." Review of International Studies 43, no. 1 (August 31, 2016): 50–72. http://dx.doi.org/10.1017/s0260210516000279.

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AbstractEven scholars who support multilateralism in principle frequently question the value of securing approval from existing multilateral bodies for humanitarian intervention. The United Nations (UN) and regional organisations such as NATO, the argument goes, are far from democratic; furthermore, multilateralism is often a recipe for doing nothing; therefore, unauthorised intervention should be permissible in circumstances of ‘humanitarian necessity’. This article maintains that although today’s multilateral organisations and related procedures for authorising armed intervention may be suboptimal, they have significant output legitimacy. First, existing authorisation procedures reduce the risk of destabilising conflict spirals among powerful states. Second, they diminish the likelihood that humanitarianism will be used as a pretext. Third, they reduce epistemic problems concerning the identification of a just cause for intervention and thus the risk of accidental abuse. Fourth, they minimise the ‘moral hazard’ of humanitarian intervention. Finally, compliance with multilateral procedures is increasingly required for successful peacebuilding. This leads me to conclude that humanitarian warfare should always be authorised by the UN or regional multilateral organisations.

24

WU, CHUFEN, and PEIXUAN WENG. "STABILITY OF STEADY STATES AND EXISTENCE OF TRAVELING WAVES FOR A HOST-VECTOR EPIDEMIC." International Journal of Bifurcation and Chaos 21, no. 06 (June 2011): 1667–87. http://dx.doi.org/10.1142/s0218127411029355.

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We study the stability of steady states and establish the existence of traveling waves for a diffusive host-vector epidemic with a nonlocal spatiotemporal interaction. We develop the techniques of contracting-convex-sets, limit argument, singular perturbation and fixed point theorems.

25

Zhu, Shanliang, Shufang Zhang, Xinli Zhang, and Qingling Li. "Response Solutions for a Singularly Perturbed System Involving Reflection of the Argument." Advances in Mathematical Physics 2020 (March 21, 2020): 1–9. http://dx.doi.org/10.1155/2020/6738247.

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In this paper, the existence and uniqueness of response solutions, which has the same frequency ω with the nonlinear terms, are investigated for a quasiperiodic singularly perturbed system involving reflection of the argument. Firstly, we prove that all quasiperiodic functions with the frequency ω form a Banach space. Then, we obtain the existence and uniqueness of quasiperiodic solutions by means of the fixed-point methods and the B-property of quasiperiodic functions.

26

Moberg, Dennis J. "The Big Five and Organizational Virtue." Business Ethics Quarterly 9, no. 2 (April 1999): 245–72. http://dx.doi.org/10.2307/3857474.

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Abstract:Recent developments in personality research point to an alchemy of character composed of five elements: extroversion, agreeableness, conscientiousness, neuroticism, and openness to experience. This paper surveys this research for its implications to the study of the virtues in organizational ethics. After subjecting each of these five character traits to several tests as to what constitutes a virtue, the empirical evidence supports an organizational virtue of agreeableness and an organizational virtue of conscientiousness. Although the empirical evidence falls short, an argument is mobilized on behalf of an additional organizational virtue of openness to experience.

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Scarpa, Luca, and Ulisse Stefanelli. "An order approach to SPDEs with antimonotone terms." Stochastics and Partial Differential Equations: Analysis and Computations 8, no. 4 (January 3, 2020): 819–32. http://dx.doi.org/10.1007/s40072-019-00161-7.

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AbstractWe consider a class of parabolic stochastic partial differential equations featuring an antimonotone nonlinearity. The existence of unique maximal and minimal variational solutions is proved via a fixed-point argument for nondecreasing mappings in ordered spaces. This relies on the validity of a comparison principle.

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Md Asaduzzamana and Md Zulfikar Ali. "Existence of Positive Solution for a Nonlinear Weighted Bi-Harmonic System of Elliptic Partial Differential Equations via Fixed-Point Argument." GANIT: Journal of Bangladesh Mathematical Society 40, no. 1 (July 14, 2020): 54–70. http://dx.doi.org/10.3329/ganit.v40i1.48195.

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In this paper, we establish an existence criterion of positive solution for a nonlinear weighted bi-harmonic system of elliptic partial differential equations in the unit ball in Nn ( dimensionaleuclideanspace) The analysis of this paper is based on a topological method (a fixed-point argument). Initially, we establish a priori solution estimates, and then use a fixed-point theorem for deducing the existence of positive solutions. Finally, we prove a non-existence criterion as the complement of existence criterion. GANIT J. Bangladesh Math. Soc.Vol. 40 (2020) 54-70

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LI, YONGKUN, and ERLIANG XU. "THREE POSITIVE PERIODIC SOLUTIONS FOR DYNAMIC EQUATIONS WITH PIECEWISE CONSTANT ARGUMENT AND IMPULSE ON TIME SCALES." Glasgow Mathematical Journal 53, no. 2 (December 8, 2010): 369–77. http://dx.doi.org/10.1017/s0017089510000790.

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AbstractIn this paper, by using the Leggett–Williams fixed point theorem, the existence of three positive periodic solutions for differential equations with piecewise constant argument and impulse on time scales is investigated. Some easily verifiable sufficient criteria are established. Finally, an example is given to illustrate the results.

30

Raheem, A., and M. Kumar. "On controllability for a nondensely defined fractional differential equation with a deviated argument." Mathematical Sciences 13, no. 4 (October 26, 2019): 407–13. http://dx.doi.org/10.1007/s40096-019-00309-5.

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Abstract This article deals with a fractional differential equation with a deviated argument defined on a nondense set. A fixed-point theorem and the concept of measure of noncompactness are used to prove the existence of a mild solution. Furthermore, by using the compactness of associated cosine family, we proved that system is approximately controllable and obtains an optimal control which minimizes the performance index. To illustrate the abstract result, we included an example.

31

Feng, Jianfeng, and David Brown. "Fixed-Point Attractor Analysis for a Class of Neurodynamics." Neural Computation 10, no. 1 (January 1, 1998): 189–213. http://dx.doi.org/10.1162/089976698300017944.

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Nearly all models in neural networks start from the assumption that the input-output characteristic is a sigmoidal function. On parameter space, we present a systematic and feasible method for analyzing the whole spectrum of attractors—all-saturated, all-but-one-saturated, all-but-twosaturated, and so on—of a neurodynamical system with a saturated sigmoidal function as its input-output characteristic. We present an argument that claims, under a mild condition, that only all-saturated or all but-one-saturated attractors are observable for the neurodynamics. For any given all-saturated configuration [Formula: see text] (all-but-one-saturated configuration [Formula: see text]) the article shows how to construct an exact parameter region R([Formula: see text])([Formula: see text]([Formula: see text])) such that if and only if the parameters fall within R([Formula: see text])([Formula: see text]([Formula: see text])), then [Formula: see text]([Formula: see text]) is an attractor (a fixed point) of the dynamics. The parameter region for an all-saturated fixed-point attractor is independent of the specific choice of a saturated sigmoidal function, whereas for an all-but-one-saturated fixed point, it is sensitive to the input-output characteristic. Based on a similar idea, the role of weight normalization realized by a saturated sigmoidal function in competitive learning is discussed. A necessary and sufficient condition is provided to distinguish two kinds of competitive learning: stable competitive learning with the weight vectors representing extremes of input space and being fixed-point attractors, and unstable competitive learning. We apply our results to Linsker's model and (using extreme value theory in statistics) the Hopfield model and obtain some novel results on these two models.

32

Curien, Nicolas, and Adrien Joseph. "Partial match queries in two-dimensional quadtrees: a probabilistic approach." Advances in Applied Probability 43, no. 01 (March 2011): 178–94. http://dx.doi.org/10.1017/s0001867800004742.

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We analyze the mean cost of the partial match queries in random two-dimensional quadtrees. The method is based on fragmentation theory. The convergence is guaranteed by a coupling argument of Markov chains, whereas the value of the limit is computed as the fixed point of an integral equation.

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Curien, Nicolas, and Adrien Joseph. "Partial match queries in two-dimensional quadtrees: a probabilistic approach." Advances in Applied Probability 43, no. 1 (March 2011): 178–94. http://dx.doi.org/10.1239/aap/1300198518.

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We analyze the mean cost of the partial match queries in random two-dimensional quadtrees. The method is based on fragmentation theory. The convergence is guaranteed by a coupling argument of Markov chains, whereas the value of the limit is computed as the fixed point of an integral equation.

34

CLAPP, MÓNICA, and TOBIAS WETH. "TWO SOLUTIONS OF THE BAHRI–CORON PROBLEM IN PUNCTURED DOMAINS VIA THE FIXED POINT TRANSFER." Communications in Contemporary Mathematics 10, no. 01 (February 2008): 81–101. http://dx.doi.org/10.1142/s0219199708002715.

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We consider the problem [Formula: see text] where Ω is a bounded smooth domain in ℝN, N ≥ 3, and [Formula: see text] is the critical Sobolev exponent. We assume that Ω is annular shaped, i.e. there are constants R2 > R1 > 0 such that {x ∈ ℝN : R1 < |x| < R2} ⊂ Ω and {x ∈ ℝN : |x| < R1}\Ω ≠ ∅. Coron [7] showed that there is one positive solution to this problem if R2/R1 is large enough. We establish the existence of at least two pairs of nontrivial solutions in this case. The proof combines a deformation argument on the Nehari manifold with cohomological information derived from Dold's fixed point transfer. To deal with the lack of compactness, an energy estimate recently proved by one of the authors is used.

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DHAGE, BAPURAO C., JANHAVI B. DHAGE, and JAVID ALI. ""Monotone iteration method for general nonlinear two point boundary value problems with deviating arguments"." Carpathian Journal of Mathematics 38, no. 2 (February 28, 2022): 405–15. http://dx.doi.org/10.37193/cjm.2022.02.11.

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"In this paper we shall study the existence and approximation results for a nonlinear two point boundary value problem of a second order ordinary differential equation with general form of Dirichlet/Neumann type boundary conditions. The nonlinearity present on right hand side of the differential equation is assumed to be Caratho´eodory containing a deviating argument. The proofs of the main results are based on a monotone iteration method contained in the hybrid fixed point principles of Dhage (2014) in an ordered Banach space. Finally, some remarks concerning the merits of our monotone iteration method over other frequently used iteration methods in the theory of nonlinear differential equations are given in the conclusion."

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Karthikeyan, Shanmugasundaram, and Krishnan Balachandran. "Constrained controllability of nonlinear stochastic impulsive systems." International Journal of Applied Mathematics and Computer Science 21, no. 2 (June 1, 2011): 307–16. http://dx.doi.org/10.2478/v10006-011-0023-0.

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Constrained controllability of nonlinear stochastic impulsive systemsThis paper is concerned with complete controllability of a class of nonlinear stochastic systems involving impulsive effects in a finite time interval by means of controls whose initial and final values can be assigned in advance. The result is achieved by using a fixed-point argument.

37

Chiu, Kuo-Shou. "Periodic Solutions for Nonlinear Integro-Differential Systems with Piecewise Constant Argument." Scientific World Journal 2014 (2014): 1–14. http://dx.doi.org/10.1155/2014/514854.

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We investigate the existence of the periodic solutions of a nonlinear integro-differential system with piecewise alternately advanced and retarded argument of generalized type, in short DEPCAG; that is, the argument is a general step function. We consider the critical case, when associated linear homogeneous system admits nontrivial periodic solutions. Criteria of existence of periodic solutions of such equations are obtained. In the process we use Green’s function for periodic solutions and convert the given DEPCAG into an equivalent integral equation. Then we construct appropriate mappings and employ Krasnoselskii’s fixed point theorem to show the existence of a periodic solution of this type of nonlinear differential equations. We also use the contraction mapping principle to show the existence of a unique periodic solution. Appropriate examples are given to show the feasibility of our results.

38

Watkins, Will. "Modified Wiener equations." International Journal of Mathematics and Mathematical Sciences 27, no. 6 (2001): 347–56. http://dx.doi.org/10.1155/s0161171201006561.

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This paper is concerned with a class of functional differential equations whose argument transforms are involutions. In contrast to the earlier works in this area, which have used only involutions with a fixed point, we also admit involutions without a fixed point. In the first case, an initial value problem for a differential equation with involution is reduced to an initial value problem for a higher order ordinary differential equation. In our case, either two initial conditions or two boundary conditions are necessary for a solution; the equation is then reduced to a boundary value problem for a higher order ODE.

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BEN-EL-MECHAIEKH, HICHEM, and ROBERT W. DIMAND. "VON NEUMANN, VILLE, AND THE MINIMAX THEOREM." International Game Theory Review 12, no. 02 (June 2010): 115–37. http://dx.doi.org/10.1142/s0219198910002556.

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Von Neumann proved the minimax theorem (existence of a saddle-point solution to 2 person, zero sum games) in 1928. While his second article on the minimax theorem, stating the proof, has long been translated from German, his first announcement of his result (communicated in French to the Academy of Sciences in Paris by Borel, who had posed the problem settled by Von Neumann's proof) is translated here for the first time. The proof presented by Von Neumann and Morgenstern (1944) is not Von Neumann's rather involved proof of 1928, but is based on what they called "The Theorem of the Alternative for Matrices" which is in essence a reformulation of an elegant and elementary result by Borel's student Jean Ville in 1938. Ville's argument was the first to bring to light the simplifying role of convexity and to highlight the connection between the existence of minimax and the solvability of systems of linear inequalities. It by-passes nontrivial topological fixed point arguments and allows the treatment of minimax by simpler geometric methods. This approach has inspired a number of seminal contributions in convex analysis including fixed point and coincidence theory for set-valued mappings. Ville's contributions are discussed briefly and von Neuman's original communication, Ville's note, and Borel's commentary on it are translated here for the first time.

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Dobriţoiu, Maria. "The Existence and Uniqueness of the Solution of a Nonlinear Fredholm–Volterra Integral Equation with Modified Argument via Geraghty Contractions." Mathematics 9, no. 1 (December 24, 2020): 29. http://dx.doi.org/10.3390/math9010029.

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Using some of the extended fixed point results for Geraghty contractions in b-metric spaces given by Faraji, Savić and Radenović and their idea to apply these results to nonlinear integral equations, in this paper we present some existence and uniqueness conditions for the solution of a nonlinear Fredholm–Volterra integral equation with a modified argument.

41

Benevich, Fedor. "FIRE AND HEAT: YAḤYĀ B. ʿADĪ AND AVICENNA ON THE ESSENTIALITY OF BEING SUBSTANCE OR ACCIDENT". Arabic Sciences and Philosophy 27, № 2 (17 серпня 2017): 237–67. http://dx.doi.org/10.1017/s0957423917000030.

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AbstractAvicenna's analysis of the definition of substance and accident repeatedly emphasizes two points: one and the same essence cannot be substance in one instance and accident in another; whetherxis extrinsic or intrinsic for an underlying subject,ydoes not tell us anything as to whetherxis substance or not. Both points are development in an argument against certain unnamed people who claimed the opposite. In this article I will show that Avicenna's opponents are to be identified with the mainstream Baghdad Peripatetic School (Ibn Suwār, Ibn al-Ṭayyib) which based itself on the Late Antique rule that “parts of substances are substances”. As for Avicenna's own position, it was developed on the basis of the heterodox position of Yaḥyā b. ʿAdī, who anticipated Avicenna's first point. This is a further piece of evidence for something that has only recently begun to be appreciated: the influence of Ibn ʿAdī on Avicenna.

42

Neog, Murchana, Mohammed M. M. Jaradat та Pradip Debnath. "Common Fixed Point Results of Set Valued Maps for Aφ-Contraction and Generalized ϕ-Type Weak Contraction". Symmetry 11, № 7 (8 липня 2019): 894. http://dx.doi.org/10.3390/sym11070894.

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The solutions for many real life problems may be obtained by interpreting the given problem mathematically in the form f ( x ) = x . One such example is that of the famous Borsuk–Ulam theorem in which, using some fixed point argument, it can be guaranteed that at any given time we can find two diametrically opposite places in a planet with same temperature. Thus, the correlation of symmetry is inherent in the study of fixed point theory. In this article, some new results concerning coincidence and a common fixed point for an A φ -contraction and a generalized ϕ -type weak contraction are established. We prove our results for set valued maps without using continuity of the corresponding maps and completeness of the relevant space. Our results generalize and extend several existing results. Some new examples are given to demonstrate the generality and non-triviality of our results.

43

Jakobsen, Tor Georg, Joachim Vogt Isaksen, Gunn Kari O. Skavhaug, and Hilde Anderssen Bakkan. "The Turning Point of Tolerance: Ethnic Attitudes in a Global Perspective." International Journal on Minority and Group Rights 23, no. 1 (January 30, 2016): 80–104. http://dx.doi.org/10.1163/15718115-02301001.

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Is diversity associated with ethnic aversion? To address this issue we employ a theoretical perspective to explain global patterns in individual ethnic attitudes. We suggest that there is a turning point of tolerance, and this could be why earlier studies differ in their conclusions. In short, we argue that up until a certain point more intergroup contact will lead to increased tolerance. However, when this threshold is reached, any further diversity will lead to less tolerance. This study applies data from all five waves of the World Values Survey, combined with the updated ethnolinguistical fractionalisation index and relevant controls. Our models reveal a threshold effect in non-Western societies, and that ethnically polarised societies are most tolerant. This finding supports the argument that conflicts taking place along ethnic lines are not caused primarily by ethnic hatred, indicating that ethnicity might be used as an instrument to create violent conflict.

44

Dond, Asha K., and Amiya K. Pani. "A Priori and A Posteriori Estimates of Conforming and Mixed FEM for a Kirchhoff Equation of Elliptic Type." Computational Methods in Applied Mathematics 17, no. 2 (April 1, 2017): 217–36. http://dx.doi.org/10.1515/cmam-2016-0041.

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AbstractIn this article, a priori and a posteriori estimates of conforming and expanded mixed finite element methods for a Kirchhoff equation of elliptic type are derived. For the expanded mixed finite element method, a variant of Brouwer’s fixed point argument combined with a monotonicity argument yields the well-posedness of the discrete nonlinear system. Further, a use of both Helmholtz decomposition of $L^{2}$-vector valued functions and the discrete Helmholtz decomposition of the Raviart–Thomas finite elements helps in a crucial way to achieve optimal a priori as well as a posteriori error bounds. For both conforming and expanded mixed form, reliable and efficient a posteriori estimators are established. Finally, the numerical experiments are performed to validate the theoretical convergence rates.

45

Wang, Yi, Wei-dong Song, Dan Fang, and Qing-wei Guo. "Guidance and Control Design for a Class of Spin-Stabilized Projectiles with a Two-Dimensional Trajectory Correction Fuze." International Journal of Aerospace Engineering 2015 (2015): 1–15. http://dx.doi.org/10.1155/2015/908304.

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A guidance and control strategy for a class of 2D trajectory correction fuze with fixed canards is developed in this paper. Firstly, correction control mechanism is researched through studying the deviation motion, the key point of which is the dynamic equilibrium angle. Phase lag of swerve response is the dominating factor for correction control, and formula is deduced with the Mach number as argument. Secondly, impact point deviation prediction based on perturbation theory is proposed, and the numerical solution and application method are introduced. Finally, guidance and control strategy is developed, and simulations to validate the strategy are conducted.

46

BENKHALTI, RACHID, ABDELHAI ELAZZOUZI, and KHALIL EZZINBI. "PERIODIC SOLUTIONS FOR SOME NONLINEAR PARTIAL NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS." International Journal of Bifurcation and Chaos 20, no. 02 (February 2010): 545–55. http://dx.doi.org/10.1142/s0218127410025600.

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In this work, we study the existence of periodic solutions for some nonlinear partial functional differential equation of neutral type. We assume that the linear part is nondensely defined and satisfies the Hille–Yosida condition. The delayed part is assumed to be ω-periodic with respect to the first argument. Using a fixed point theorem for multivalued mapping, some sufficient conditions are given to prove the existence of periodic solutions.

47

Munteanu, Ionuţ. "Feedback exponential stabilization of the semilinear heat equation with nonlocal initial conditions." Nonlinear Analysis: Modelling and Control 26, no. 6 (November 1, 2021): 1106–22. http://dx.doi.org/10.15388/namc.2021.26.24809.

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The present paper is devoted to the problem of stabilization of the one-dimensional semilinear heat equation with nonlocal initial conditions. The control is with boundary actuation. It is linear, of finite-dimensional structure, given in an explicit form. It allows to write the corresponding solution of the closed-loop equation in a mild formulation via a kernel, then to apply a fixed point argument in a convenient space.

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Blömker, Dirk, Giuseppe Cannizzaro, and Marco Romito. "Random initial conditions for semi-linear PDEs." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 150, no. 3 (January 29, 2019): 1533–65. http://dx.doi.org/10.1017/prm.2018.157.

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AbstractWe analyse the effect of random initial conditions on the local well-posedness of semi-linear PDEs, to investigate to what extent recent ideas on singular stochastic PDEs can prove useful in this framework.In particular, in some cases, stochastic initial conditions extend the validity of the fixed-point argument to larger spaces than deterministic initial conditions would allow, but in general, it is never possible to go beyond the threshold that is predicted by critical scaling, as in our general class of equations we are not exploiting any special structure present in the equation.We also give a specific example where the level of regularity for the fixed-point argument reached by random initial conditions is not yet critical, but it is already sharp in the sense that we find infinitely many random initial conditions of slightly lower regularity, where there is no solution at all. Thus criticality cannot be reached even by random initial conditions.The existence and uniqueness in a critical space is always delicate, but we can consider the Burgers equation in logarithmically sub-critical spaces, where existence and uniqueness hold, and again random initial conditions allow to extend the validity to spaces of lower regularity which are still logarithmically sub-critical.

49

Bach, Tobias, Jan Boon, Stefan Boye, Heidi Houlberg Salomonsen, Koen Verhoest, and Kai Wegrich. "In the Line of Fire: European Financial Regulators before, during, and after the Crisis." der moderne staat – Zeitschrift für Public Policy, Recht und Management 12, no. 1-2019 (June 24, 2019): 5–29. http://dx.doi.org/10.3224/dms.v12i1.03.

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A key argument in recent theorizing on the drivers of bureaucratic behaviour is that agencies seek to establish and maintain a unique reputation. While recent years have witnessed substantial empirical support for this claim, the field lacks comparative examinations of the dynamics of reputation and its management throughout crisis periods. This article draws on a systematic media content analysis to explore the exposure and communication responses of the German, Belgian and Danish financial regulators to reputational threats before, during, and after the financial crisis. Our results point at the dynamic and context-sensitive nature of reputation management.

50

Li, Haiyan, and Jianguo Gao. "Qualitative analysis of a parabolic–elliptic attraction–repulsion chemotaxis model with logistic source." International Journal of Biomathematics 09, no. 04 (April 22, 2016): 1650051. http://dx.doi.org/10.1142/s1793524516500510.

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In this paper, we focus on the qualitative analysis of a parabolic–elliptic attraction–repulsion chemotaxis model with logistic source. Applying a fixed point argument, [Formula: see text]-estimate technique and Moser’s iteration, we derive that the model admits a unique global solution provided the initial cell mass satisfying [Formula: see text] for [Formula: see text] While for [Formula: see text], there are no restrictions on the initial cell mass and the result still holds.

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