Academic literature on the topic 'Fixed point argument'
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Journal articles on the topic "Fixed point argument"
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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.
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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.
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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’.
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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.
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Jaradat, Mohammed M. M., Babak Mohammadi, Vahid Parvaneh, Hassen Aydi, and Zead Mustafa. "PPF-Dependent Fixed Point Results for Multi-Valued ϕ-F-Contractions in Banach Spaces and Applications." Symmetry 11, no. 11 (November 6, 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.
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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.
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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.
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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.
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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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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.
Dissertations / Theses on the topic "Fixed point argument"
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Vážanová, Gabriela. "Existence a vlastnosti globálních řešení funkcionálních diferenciálních rovnic smíšeného typu." Doctoral thesis, Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií, 2020. http://www.nusl.cz/ntk/nusl-433560.
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Dizertační práce se věnuje funkcionálním diferenciálním rovnicím smíšeného typu. Poskytuje kritéria pro existenci globálních a semi-globálních řešení diferenciálních systémů smíšeného typu. Metody použité v teto práci spočívají v sestavení vhodných operátorů pro diferenciální rovnice a prokázání existence jejich pevných bodů. Tyto pevné body jsou potom použity ke konstrukci řešení rovnic s předcházením a zpožděním. V důkazech tvrzení jsou použity monotónní iterační metoda a Schauderovy-Tychonovovy věty o existenci pevného bodu. V obou případech jsou uvedeny také odhady řešení. Pokud je použita iterační metoda, lze tyto odhady zlepšit iterováním. Kromě toho jsou odvozena kritéria pro lineární rovnice a systémy a je uvedena řada přikladů. Dosažené výsledky lze aplikovat také pro obyčejné diferenciální rovnice nebo diferenciální rovnice se zpožděním či s předcházením argumentu.
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Oussaily, Aya. "Étude théorique et numérique des systèmes modélisant la dynamique des densités des dislocations." Thesis, Compiègne, 2021. https://bibliotheque.utc.fr/Default/doc/SYRACUSE/2021COMP2634.
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Dans cette thèse, nous nous intéressons à l’analyse théorique et numérique de la dynamique des densités des dislocations. Les dislocations sont des défauts linéaires qui se déplacent dans les cristaux lorsque ceux-ci sont soumis à des contraintes extérieures. D’une manière générale, la dynamique des densités des dislocations est décrite par un système d’équations de transport, où les champs de vitesse dépendent de manière non-locale des densités des dislocations. Au départ, notre travail se focalise sur l’étude d’un système unidimensionnel (2 × 2) de type Hamilton-Jacobi dérivé d’un système bidimensionnel proposé par Groma et Balogh en 1999. Pour ce modèle, nous montrons un résultat d’existence globale et d’unicité. En addition, nous nous intéressons à l’étude numérique de ce problème, complété par des conditions initiales croissantes, en proposant un schéma aux différences finies implicite dont on prouve la convergence. Ensuite, en s’inspirant du travail effectué pour la résolution de la dynamique des densités des dislocations, nous mettons en œuvre une théorie plus générale permettant d’obtenir un résultat similaire d’existence et d’unicité d’une solution dans le cas des systèmes de type eikonal unidimensionnels. En considérant des conditions initiales croissantes, nous faisons une étude numérique pour ce système. Sous certaines conditions de monotonies sur la vitesse, nous proposons un schéma aux différences finies implicite permettant de calculer la solution discrète et simuler ainsi la dynamique des dislocations à travers ce modèleIn this thesis, we are interested in the theoretical and numerical studies of dislocations densities. Dislocations are linear defects that move in crystals when those are subjected to exterior stress. More generally, the dynamics of dislocations densities are described by a system of transport equations where the velocity field depends non locally on the dislocations densities. First, we are interested in the study of a one dimensional submodel of a (2 × 2) Hamilton-Jacobi system introduced by Groma and Balogh in 1999, proposed in the two dimensional case. For this system, we prove global existence and uniqueness results. Adding to that, considering nondecreasing initial data, we study this problem numerically by proposing a finite difference implicit scheme for which we show the convergence. Then, inspired by the first work, we show a more general theory which allows us to get similar results of existence and uniqueness of solution in the case of one dimensional eikonal systems. By considering nondecreasing initial data, we study this problem numerically. Under certain conditions on the velocity, we propose a finite difference implicit scheme allowing us to calculate the discrete solution and simulate then the dislocations dynamics via this model
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Salloum, Zaynab. "Étude mathématique d’écoulements de fluides viscoélastiques dans des domaines singuliers." Thesis, Paris Est, 2008. http://www.theses.fr/2008PEST0017/document.
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Cette thèse est consacrée à l’analyse mathématique de trois problèmes d’écoulements de fluides viscoélastiques de type Oldroyd. Tout d’abord, nous étudions des écoulements stationnaires faiblement compressibles dans un domaine borné avec des conditions au bord de type "rentrante-sortante". Nous étudions aussi le problème d’écoulements stationnaires faiblement compressibles dans un coin convexe. En utilisant une méthode de point fixe (premier et deuxième problèmes) et une décomposition de Helmoltz (deuxième problème), nous montrons des résultats d’existence et d’unicité des solutions. Nous étudions également le cas d’un écoulement non stationnaire. Nous montrons un résultat d’existence locale et un résultat d’existence globale, avec des conditions initiales suffisamment petites, pour des fluides compressibles. Nous démontrons aussi la convergence du modèle d’écoulement viscoélastique compressible à faible nombre de Mach vers le modèle incompressible lorsque les données initiales sont "bien préparées"In this PHD thesis, we study three problems for viscoelastic flows of Oldroyd type. First, we study steady flows of slightly compressible in a bounded domain with non-zero velocities on the boundary ; the pressure and the extra-stress tensor are prescribed on the part of the boundary corresponding to entering velocity. This causes a weak singularity in the solution at the junction of incoming and outgoing flows. We also study the problem of steady flows of slightly compressible fluids with zero boundary conditions in a domain with an isolated corner point. Using a method of fixed point (first and second problems) and a Helmoltz decomposition (second problem), we show some results of existence and uniqueness of solutions. In the last part, we study the case of a non-steady flow : we show some results of local and of global existence, with sufficiently small initial data, for compressible flows. The zero-Mach number limit is also established
Books on the topic "Fixed point argument"
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Cappelen, Herman. Conceptual Engineering without Bedrock and without Fixed Points. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198814719.003.0018.
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This chapter considers whether there are any limits to conceptual engineering, developing the idea that there are no safe spaces from conceptual change. First, it considers Chalmers’s argument for bedrock concepts. It argues that Chalmers’s claim that there is an asymmetric structure in the space of disputes is an (implausible) empirical claim. Second, it considers Eklund’s claim to the effect that our thinnest normative concepts are irreplaceable, and this is a limit to conceptual engineering, and shows that Eklund doesn’t establish this. It ends by revisiting some old worries, defending the choice of the term ‘conceptual engineering’, and responding to the claim that by making conceptual engineering inscrutable and out of control, it has been debunked rather than defended. However, conceptual engineering is very hard for us to do, but so is (almost) everything that is important to us.
Book chapters on the topic "Fixed point argument"
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Titelbaum, Michael G. "Return to Reason." In Higher-Order Evidence, 226–45. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780198829775.003.0011.
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This chapter discusses responses to the author’s “Rationality’s Fixed Point (or: In Defense of Right Reason).” Among other things, the chapter: explains how the author understands rationality; explains why akrasia is irrational; intuitively overviews the argument from the Akratic Principle to the Fixed Point Thesis; explains why you can’t avoid this argument by distinguishing the rational from the reasonable, ideal rationality from everyday rationality, or substantive from structural norms; responds to the suggestion that misleading higher-order evidence creates rational dilemmas; explains why the Fixed Point Thesis doesn’t assume objectivist or externalist notions of rationality; dismisses complaints about agents who aren’t able to “figure out” what’s rational; then responds to an objection that peer disagreement undermines doxastic justification. Finally, the chapter modifies the author’s steadfast position on peer disagreement to take into account cases in which peer disagreement rationally affects an agent’s first-order opinions without affecting higher-order ones.
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"Fixed-Point Arguments." In Recursive Methods in Economic Dynamics, 501–41. Harvard University Press, 1989. http://dx.doi.org/10.2307/j.ctvjnrt76.21.
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"17 Fixed-Point Arguments." In Solutions Manual for Recursive Methods in Economic Dynamics, 270–83. Harvard University Press, 2002. http://dx.doi.org/10.4159/9780674038967-018.
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Wels, Jacques, and John Macnicol. "Is the ‘lump of labour’ a self-evident fallacy? The case of Great Britain." In Social Policy Review 31, edited by Elke Heins, Catherine Needham, and James Rees, 221–42. Policy Press, 2019. http://dx.doi.org/10.1332/policypress/9781447343981.003.0010.
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This article discusses the notion of a ‘lump of labour fallacy’ used since the end of the nineteenth century and more strongly over the recent period in order to criticise the idea that the number of jobs in an economy is fixed. Examining the recent literature using this notion, the article shows that the lump of labour fallacy is more often used as an assumption rather than examined in-depth. Despite a lack of empirical evidence, it became a key argument in the British debate, used, for instance, to justify an increase in the retirement age. From a critical point of view, the article concludes that an in-depth evaluation of the way the number of jobs varies still needs to be done, looking particularly at the evolution of working time.
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Cardaliaguet, Pierre, François Delarue, Jean-Michel Lasry, and Pierre-Louis Lions. "Mean Field Game System with a Common Noise." In The Master Equation and the Convergence Problem in Mean Field Games, 85–127. Princeton University Press, 2019. http://dx.doi.org/10.23943/princeton/9780691190716.003.0004.
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This chapter talks about the unique solvability of the mean field games (MFGs) system with common noise. In terms of a game with a finite number of players, the common noise describes some noise that affects all the players in the same way, so that the dynamics of one given particle reads a certain master equation. It explains the use of the standard convention from the theory of stochastic processes that consists in indicating the time parameter as an index in random functions. Using a continuation like argument instead of the classical strategy based on the Schauder fixed-point theorem, this chapter investigates the existence and uniqueness of a solution. It discusses the effect of the common noise in randomizing the MFG equilibria so that it becomes a random flow of measures.
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Todd, Patrick. "Grounding the Open Future." In The Open Future, 8–20. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780192897916.003.0002.
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In this chapter, Patrick Todd considers how presentists can argue that the future is open, holding fixed that they maintain that the past is not. He argues that any such presentist argument is doomed to failure, if it proceeds by appeal to a general thesis about truth (such as that “truth supervenes on being”). Thus, he contends, presentist open futurists should not argue for the open future from an intuition about truth in general, but from an intuition about the future in particular. The result, however, is that presentist open futurists cannot make their case by appeal to anything like a metaphysically neutral starting point. Nevertheless, due to certain asymmetries between facts about the past and facts about the future, a presentist open future view remains substantially theoretically motivated.
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"Infoeconomics." In Examining the Informing View of Organization, 256–75. IGI Global, 2014. http://dx.doi.org/10.4018/978-1-4666-5986-5.ch008.
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The chapter discusses economics of informing or infoeconomics, which refers to costs and benefits of informing agents and to their contribution to organizational performance. Controversies questioning contributions of IT/IS to productivity (IT productivity paradox) and to competitiveness (IT commodification argument) are discussed. It is argued that new infoeconomic measurement and better management may assist in leveraging productivity gains from the microeconomic to the macroeconomic level. Several methods of assessing costs and benefits of informing agents are proposed. It is further argued that the commodification argument points correctly that IT is no longer scarce but fails to account for a management factor and still prohibitive direct costs. Assessing benefits from IT/IS is quite challenging since these usually have support roles in organizations. The assessment of benefits of data, knowledge, and information is even more challenging since it depends on familiarity and hindsight. Valuing of professional knowledge is particularly important because it mediates in creation of business information. The challenges have become more pressing with the data analytics and big data trends. However, research lags behind. It is further argued that matching costs and benefits of informing agents is usually applied to a particular IS and calculated in some form of financial returns compared with fixed and variable lump costs of IT/IS. The chapter recalls several research cases to demonstrate relationships between IVO aspects and infoeconomics. The infoprocess perspective is characterized as a reliable guide for study and management of infoeconomics. The balanced scorecard methodology suits such an analysis. The point is made on Cloud computing, framing it as a new rental methods of IS services with certain benefits and still partly opaque costs.
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Maynard Smith, John, and Eors Szathmary. "The evolution of templates." In The Major Transitions in Evolution. Oxford University Press, 1997. http://dx.doi.org/10.1093/oso/9780198502944.003.0008.
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In this chapter, we discuss the origin and early evolution of genetic replication. The argument is complex, so we start with a brief outline. Section 4.2 discusses the nature of replication. We draw a distinction between simple replicators, limited hereditary replicators and indefinite hereditary replicators. Continued evolution requires indefinite hereditary replicators: it seems that such replicators depend on some form of template reproduction. In section 4.3, we point out that there is an error threshold for the accuracy of replication: for a given total quantity of genetic information—for example, for a fixed number of bases—there is an upper limit on the error rate of replication. If the error rate rises above this limit, natural selection cannot maintain the information. This leads to what we have called Eigen's paradox. In the absence of specific enzymes, replication accuracy is low. Hence the total genome size must be small—almost certainly, less than 100 nucleotides. The genome is therefore too small to code for accurate replication machinery. There is a catch-22 situation: no enzymes without a large genome, and no large genome without enzymes. The next three sections discuss possible solutions to the paradox. Section 4.4 considers populations of replicating RNA molecules. We point out that the dynamics of replication are such as to lead to the stable coexistence of a diverse population, but we do not think that this constitutes a solution to the paradox. Section 4.5 discusses the hypercycle, a particular relationship between replicators that makes it possible for a greater total quantity of information to be maintained with a given accuracy of replication. We argue that the further evolution of hypercycles requires that they be enclosed within compartments, because otherwise they are sensitive to parasitic replicators. We also discuss, rather inconclusively, the possibility that, even in the absence of compartments, cooperation might evolve, by a processes analogous to kin selection, if the components of the hypercycle were confined to a surface. Finally, we discuss an alternative model, the stochastic corrector model. This also depends on the existence of compartments, but emphasizes the importance of stochastic effects arising if there are small numbers of each kind of molecule in a compartment. Essentially, small numbers serve to generate variation upon which selection can act.
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Zinn-Justin, Jean. "Large-momentum behaviour in quantum field theory (QFT)." In Quantum Field Theory and Critical Phenomena, 593–606. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780198834625.003.0024.
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Renormalization group (RG) equations are used to characterize the large momentum behaviour of renormalized quantum field theories (QFT), assuming implicitly that such a universal large momentum physics can be defined, something which, beyond perturbation theory is not obvious. Since the initial effective QFT is valid only up to an energy-momentum scale much smaller than some cut-off, large momentum means much larger than the renormalization scale, but still much smaller than the cut-off scale. The existence of this large momentum physics implies the existence of a crossover scale between low and large momentum physics. One theoretic reason for discussing the large momentum behaviour is the apparent connection between the existence of consistent interacting renormalized QFTs and the presence of ultraviolet (UV) fixed points. The absence of identified UV fixed points in infrared-free QFTs, like the φ4 field theory or quantum electrodynamics (QED), leads to the triviality issue. The physics reason is that in collisions it is observed that quarks, fundamental particles of the Standard Model (SM) of particle physics, behave like free particles at the shortest distances presently accessible (the property of asymptotic freedom). This property can be explained by RG arguments if the free theory is an attractive UV fixed point. Therefore, the identification of QFTs where the free theory is an UV fixed point is important, and this has led to examine the large momentum behaviour of all QFTs renormalizable in four dimensions. It is shown that only theories having a non-Abelian gauge symmetry can be asymptotically free. As an application, the total cross section of electron–positron annihilation into hadrons at large momentum is calculated.
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Salman, Sanaa Moussa, and Ahmed M. A. El-Sayed. "Dynamics of Some Discretized Fractional-Order Differential Equations." In Advanced Applications of Fractional Differential Operators to Science and Technology, 58–114. IGI Global, 2020. http://dx.doi.org/10.4018/978-1-7998-3122-8.ch004.
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This chapter deals with fractional-order differential equations and their discretization. First of all, a discretization process for discretizing ordinary differential equations with piecewise constant arguments is presented. Secondly, a discretization method is proposed for discretizing fractional-order differential equations. Stability of fixed points of the discretized equations are investigated. Numerical simulations are carried out to show the dynamic behavior of the resulting difference equations such as bifurcation and chaos.
Conference papers on the topic "Fixed point argument"
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Ding, Qinghua, Kaiwen Zhou, and James Cheng. "Tight Convergence Rate of Gradient Descent for Eigenvalue Computation." In Twenty-Ninth International Joint Conference on Artificial Intelligence and Seventeenth Pacific Rim International Conference on Artificial Intelligence {IJCAI-PRICAI-20}. California: International Joint Conferences on Artificial Intelligence Organization, 2020. http://dx.doi.org/10.24963/ijcai.2020/453.
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Riemannian gradient descent (RGD) is a simple, popular and efficient algorithm for leading eigenvector computation [AMS08]. However, the existing analysis of RGD for eigenproblem is still not tight, which is O(log(n/epsilon)/Delta^2) due to [Xu et al., 2018]. In this paper, we show that RGD in fact converges at rate O(log(n/epsilon)/Delta), and give instances to shows the tightness of our result. This improves the best prior analysis by a quadratic factor. Besides, we also give tight convergence analysis of a deterministic variant of Oja's rule due to [Oja, 1982]. We show that it also enjoys fast convergence rate of O(log(n/epsilon)/Delta). Previous papers only gave asymptotic characterizations [Oja, 1982; Oja, 1989; Yi et al., 2005]. Our tools for proving convergence results include an innovative reduction and chaining technique, and a noisy fixed point iteration argument. Besides, we also give empirical justifications of our convergence rates over synthetic and real data.
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DeGiorgi, Virginia G., and M. A. Siddiq Qidwai. "An Analysis of Composite Piezoelectric Actuators Incorporating Nonlinear Material Behavior." In ASME 2010 Conference on Smart Materials, Adaptive Structures and Intelligent Systems. ASMEDC, 2010. http://dx.doi.org/10.1115/smasis2010-3628.
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Piezoelectric actuators of various composite designs have been proposed during the last few years including extension and shear bimorphs, tubular composites and multilayered actuators. These designs exploit the ability to define the actuation direction by varying the alignment between poling direction and applied electric field. Considerable research effort has been put to accurately model these actuators in order to attain predictive capability. The common factor in almost all of these studies is the assumption that the poled material behaves linearly under applied electric field. However, this assumption may only be accurate for the limited case of a homogenous actuator under relatively unconstrained environment, such as that of simply supported boundary conditions. In the case of composite structures, the actuation can potentially be restricted by non-actuating constituents resulting in multi-dimensional loading states, which may cause domain switching. The same argument can be made for most boundary conditions that are imposed in practical applications, such as when the actuator is clamped or fixed. Another point of concern is the presence of discontinuities and minor defects in the actuator. Both of these would promote non-uniform electric field causing domain switching, and hence, unexpected actuator output. Unless proven otherwise, these concerns directly affect the credibility of life cycle estimates based upon linear models. In this paper linear and nonlinear material models will be used to determine actuator performance using an established constitutive model in a commercial finite element code. Actuator performance for both material cases will be calculated and compared with existing analytical predictions under the same set of boundary conditions.
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Gutierrez, Juan Pablo, Terry B. Sullivan, and Gerald J. Feller. "Turning NGCC Into IGCC: Cycle Retrofitting Issues." In ASME 2006 Power Conference. ASMEDC, 2006. http://dx.doi.org/10.1115/power2006-88112.
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The increase in price of natural gas and the need for a cleaner technology to generate electricity has motivated the power industry to move towards Integrated Gasification Combined Cycle (IGCC) plants. The system uses a low heating value fuel such as coal or biomass that is gasified to produce a mixture of hydrogen and carbon monoxide. The potential for efficiency improvement and the decrease in emissions resulting from this process compared to coal-fired power plants are strong evidence to the argument that IGCC technology will be a key player in the future of power generation. In addition to new IGCC plants, and as a result of new emissions regulations, industry is looking at possibilities for retrofitting existing natural gas plants. This paper studies the feasibility of retrofitting existing gas turbines of Natural Gas Combined Cycle (NGCC) power plants to burn syngas, with a focus on the water/steam cycle design limitations and necessary changes. It shows how the gasification island processes can be treated independently and then integrated with the power block to make retrofitting possible. This paper provides a starting point to incorporate the gasification technology to current natural gas plants with minor redesigns.
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Schuknecht, Nathan H., Pamela A. Kulbeik, and Deven M. O’Rourke. "The Economic Potential and Technical Feasibility of Hybridizing Coal Power Plants With Molten Salt Parabolic Troughs." In ASME 2017 11th International Conference on Energy Sustainability collocated with the ASME 2017 Power Conference Joint With ICOPE-17, the ASME 2017 15th International Conference on Fuel Cell Science, Engineering and Technology, and the ASME 2017 Nuclear Forum. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/es2017-3140.
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When a coal-fired power plant is considered for closure, arguments are commonly made about the loss of jobs and unrealized investments. Facing this pressure, governments are reluctant to enact enforceable emission standards, and these plants continue to emit pollutants into the atmosphere. As the equipment ages, the plants may retire, but in their lifetime they will cause irreversible environmental damage. This report presents a method to mediate this damage, create jobs, maintain the efficiency of the turbine, and maintain or increase the capacity factor of the plant. Solar parabolic troughs using molten salt technology are scalable and can meet the steam conditions of a standard Rankine cycle coal-fired power plant. A marriage of these technologies allows the parabolic trough field to be installed without new power generation equipment. The turbine, generator, and transmission equipment are already in place, and when compared to a standalone concentrated solar power (CSP) plant, can be amortized over a greater number of operational hours without the use of very large amounts of thermal storage. That allows for a reduction in capital investment compared to a greenfield CSP plant, and reduces the levelized cost of energy (LCOE) from the solar contribution to well below current US Department of Energy SunShot targets. Coal-fired plant operators note that they typically cannot operate at partial power output without reducing the efficiency of their turbine accordingly. So, while a photovoltaic hybridization can take advantage of existing transmission infrastructure, it will require that the coal-fired system reduces its output and will consequently reduce the efficiency of the coal cycle. If we have to burn coal, we should do it in the most efficient way possible. Hybridizing with a molten salt parabolic trough installation makes use of the same turbine as the coal-fired system, which maintains the overall efficiency of the turbine at its design point and optimal load. With this model, the coal plant can operate at full power, reduce overall usage of coal while maintaining or even increasing employment opportunities, and reduce CO2 emissions.
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"Ethos, Pathos and Logos: Rhetorical Fixes for an Old Problem: Fake News." In InSITE 2019: Informing Science + IT Education Conferences: Jerusalem. Informing Science Institute, 2019. http://dx.doi.org/10.28945/4154.
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Aim/Purpose: The proliferation of fake news through social media threatens to undercut the possibility of ascertaining facts and truth. This paper explores the use of ancient rhetorical tools to identify fake news generally and to see through the misinformation juggernaut of President Donald Trump. Background: The ancient rhetorical appeals described in Aristotle’s Rhetoric—ethos (character of the speaker), pathos (nature of the audience) and logos (message itself)—might be a simple, yet profound fix for the era of fake news. Also known as the rhetorical triangle and used as an aid for effective public speaking by the ancient Greeks, the three appeals can also be utilized for analyzing the main components of discourse. Methodology: Discourse analysis utilizes insights from rhetoric, linguistics, philosophy and anthropology in in order to interpret written and spoken texts. Contribution This paper analyzes Donald Trump’s effective use of Twitter and campaign rallies to create and sustain fake news. Findings: At the point of the writing of this paper, the Washington Post Trump Fact Checker has identified over 10,000 untruths uttered by the president in his first two years of office, for an average of eight untruths per day. In addition, analysis demonstrates that Trump leans heavily on ethos and pathos, almost to the exclusion of logos in his tweets and campaign rallies, making spectacular claims, which seem calculated to arouse emotions and move his base to action. Further, Trump relies heavily on epideictic rhetoric (praising and blaming), excluding forensic (legal) and deliberative rhetoric, which the ancients used for sustained arguments about the past or deliberations about the future of the state. In short, the analysis uncovers how and ostensibly why Trump creates and sustains fake news while claiming that other traditional news outlets, except for FOX news, are the actual purveyors of fake news. Recommendations for Practitioners: Information systems and communication practitioners need to be aware of the ways in which the systems they create and monitor are vulnerable to targeted attacks of the purveyors of fake news. Recommendation for Researchers: Further research on the identification and proliferation of fake news from a variety of disciplines is needed, in order to stem the flow of misinformation and untruths through social media. Impact on Society: The impact of fake news is largely unknown and needs to be better understood, especially during election cycles. Some researchers believe that social media constitute a fifth estate in the United States, challenging the authority of the three branches of government and the traditional press. Future Research: As noted above, further research on the identification and proliferation of fake news from a variety of disciplines is needed, in order to stem the flow of misinformation and untruths through social media.
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Galgoul, Nelson Szilard, Andre´ Luiz Lupinacci Massa, and Cla´udia Albergaria Claro. "A Discussion on How Internal Pressure is Treated in Offshore Pipeline Design." In 2004 International Pipeline Conference. ASMEDC, 2004. http://dx.doi.org/10.1115/ipc2004-0337.
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The design of rigid submarine pipelines has been the object of extensive research work over the last few years, where the most relevant issues include upheaval and lateral buckling problems. Both of these problems systematically associate temperature and pressure loads, where the treatment of the first is obvious, while the latter have always been a matter of discussion. In 1974 Palmer and Baldry [1] presented a theoretical-experimental contribution, in which they have set a pattern that has been followed ever since. Another similar and well known paper was published by Sparks in 1983 [7], who only present a physical interpretation of this same theory. Most of the present day industry codes define an effective axial force, according to which, fixed end pipelines will be under compression due to internal pressure. The starting point of the discussion presented in [1] was that internal pressure produces a lateral force, which is numerically equal to the pressure times internal cross-sectional area times the pipeline curvature: q=p.Ai.d2y/dx2(1) This equation is demonstrated further ahead in this paper. Palmer and Baldry then based their arguments on the traditional equation of the pinned column buckling problem, studied by Euler [2]: EId4y/dx4+Pd2y/dx2=0(2) for which the well known solution is: P=π2EI/L2(3) and on the associated problem studied by Timoshenko [3], which adds a distributed lateral load q to the same problem: EId4y/dx4+Pd2y/dx2=q(4) Replacing q with the lateral pressure given above, they were able to have their own problem fall back onto the Euler solution: EId4y/dx4+Pd2y/dx2=p.Ai.d2y/dx2P-pAi=π2EI/L2(5) After correcting for the Poisson effect they were able to determine the new critical axial force caused by the pressure. Unfortunately, however, the arguments set forth in [1] have been misunderstood. The fact that both axial force and lateral force multiply curvature does not make them forces of the same nature. Being able to add them has solved a mathematical equation, but still hasn’t converted the lateral force to axial. The authors wish to prove that [1] presents no more than a tool, which can be used in the analysis of global buckling problems of pipelines subject to both temperature and pressure. It will be shown, however, that this pressure will not produce an axial force, as now-a-days prescribed conservatively in many pipeline codes, which is even used for stress checking.