Possible competitive modes of decarboxylation in the annulation reactions of ortho-substituted anilines and arylglyoxylates

Annulation reactions of ortho-substituted anilines and arylglyoxylates to the tandem synthesis of nitrogen heterocycles in the presence of K2S2O8 have been investigated, which occur via decarboxylation before or after the reaction with anilines.

A Chaotic Chemical Reactor With and Without Delay: Bifurcations, Competitive Modes, and Amplitude Death

Bifurcations in Huang’s chaotic chemical reactor leading from simple dynamics into chaotic regimes are considered. Following the linear stability analysis, the periodic orbit resulting from a Hopf bifurcation of any of the six fixed points is constructed analytically by the method of multiple scales, and its stability is determined from the resulting normal form and verified by numerical simulations. The dynamically rich range of parameters past the Hopf bifurcation is next explored. In order to bring some order to the search for parameter regimes with more complex dynamics, we employ the recent conjecture of Competitive Modes to find chaotic parameter sets in the large multiparameter space for this system. In addition, it is demonstrated that, by changing the point of view, one may tightly localize the chaotic attractor in shape and location in the phase space by mapping the Competitive Modes surfaces geometrically. Finally, we consider the effect of delay on the system, leading to the suppression of the Hopf bifurcation in some regimes, and also all of the subsequent complex dynamics. In modern terminology, this is an example of Amplitude Death, rather than Oscillation Death, as the complex system dynamics is quenched, with all the variables additionally settling to a fixed point of the original system.

After the Solidarity and Consensus Debates: Habermas, Rorty and Fraser as Pragmatist Sources for Activist Dialogical Art

This paper poses a relationship between pragmatist understandings of intersubjective communication and long-term “dialogical art” practices promoting social change. Art historian Grant Kester contends that two dialogical art projects by Suzanne Lacy and Austrian Art collective WochenKlausur reflect Habermas’ theory of communicative action through which the “better argument” is universally validated. Kester simultaneously acknowledges such projects inculcate non-competitive modes of intersubjective exchange that appear contrary to Habermas. I look at the “philosophical narrative” debates between Richard Rorty and Habermas to suggest that Rorty’s eschewal of Habermasian rationalization in favor of affective modes of contingent solidarity, taken with Nancy Fraser’s understanding of enmeshed public/private discourse in the context of feminist counterpublics, draws out the political-ethical orientation of activist dialogical art practices.

On the Inverse Problem of Competitive Modes and the Search for Chaotic Dynamics

Generalized competitive modes (GCM) have been used as a diagnostic tool in order to analytically identify parameter regimes which may lead to chaotic trajectories in a given first order nonlinear dynamical system. The approach involves recasting the first order system as a second order nonlinear oscillator system, and then checking to see if certain conditions on the modes of these oscillators are satisfied. In the present paper, we will consider the inverse problem of GCM: If a system of second order oscillator equations satisfy the GCM conditions, can we then construct a first order dynamical system from it which admits chaotic trajectories? Solving the direct inverse problem is equivalent to finding solutions to an inhomogeneous form of the Euler equations. As there are no general solutions to this PDE system, we instead consider the problem for restricted classes of functions for autonomous systems which, upon obtaining the nonlinear oscillatory representation, we are able to extract at least two of the modes explicitly. We find that these methods often make finding chaotic regimes a much simpler task; many classes of parameter-function regimes that lead to nonchaos are excluded by the competitive mode conditions, and classical knowledge of dynamical systems then allows us to tune the free parameters or functions appropriately in order to obtain chaos. To find new hyperchaotic systems, a similar approach is used, but more effort and additional considerations are needed. These results demonstrate one method for constructing new chaotic or hyperchaotic systems.

Competitive Modes for the Detection of Chaotic Parameter Regimes in the General Chaotic Bilinear System of Lorenz Type

We study chaotic behavior of solutions to the bilinear system of Lorenz type developed by Celikovsky and Vanecek [1994] through an application of competitive modes. This bilinear system of Lorenz type is one possible canonical form holding the Lorenz equation as a special case. Using a competitive modes analysis, which is a completely analytical method allowing one to identify parameter regimes for which chaos may occur, we are able to demonstrate a number of parameter regimes which admit a variety of distinct chaotic behaviors. Indeed, we are able to draw some interesting conclusions which relate the behavior of the mode frequencies arising from writing the state variables for the Celikovsky–Vanecek model as coupled oscillators, and the types of emergent chaotic behaviors observed. The competitive modes analysis is particularly useful if all but one of the model parameters are fixed, and the remaining free parameter is used to modify the chaos observed, in a manner analogous to a bifurcation parameter. Through a thorough application of the method, we are able to identify several parameter regimes which give new dynamics (such as specific forms of chaos) which were not observed or studied previously in the Celikovsky–Vanecek model. Therefore, the results demonstrate the advantage of the competitive modes approach for detecting new parameter regimes leading to chaos in third-order dynamical systems.

Kasdienė refleksija ir filosofo refleksijos radikalumas

The object of the investigation is the specificity of philosophical and everyday reflections, their interrelations. The author makes an attempt to reveal the invariant constitutive characteristics of the structure of the reflective space of philosophy, to define the sense of specific radicalism of philosophical reflection. The radicalism as effort and way to extend presence of us in one's own experience and as self-aware transformation of own experience which presuppose the unity of the factual and the due as possible (and necessary) for man is revealed. The variant of the “metaphysics of presence” of man in the objects and relations of his experience as the way of historical and logical identification of philosophical reflection is developed. The “metaphysics of presence” is introduced as common dimension of the intelligibility, which permits the author to compare competitive modes of reflection of human experience (reductive and nonreductive, deterministic and transcendental) and to interpret them as irreplaceable and mutually supplementary ways of broadening the limits of self-consciousness of human experience.