Rational Realization Research Articles

Von der res cogitans zum Relationengeflecht?

The concepts of autonomy and subjectivity are crucial not only for modern philosophy of law but also for its practice. Nevertheless, postmodern philosophy and postmodern theory of law claim to suspend these concepts, interpreting them as hypostatized narratives. The article argues that contrary to the postmodern reading, already the early modern concept of subjectivity is very fragile: It has no reality outside of a historical process in which the principle of subjectivity is connected to its external objective conditions of existence. These conditions are both theoretical and practical; the former are acquired by science, the latter by social, political, and legal history. This history has not been the pure realization of rationality. The development of the state of law from the state of nature, including the original appropriation and legalization of private property, has been a history of violence. This violence has not simply been overcome but is preserved in modern legal systems, too. It takes a materialistic social theory to tell this story in opposition to the narrative of modern law as a pure triumph of human freedom. This also entails that the subjectivity that stands at the end of this story is not only fragile but also fragmented.

A decomposition theorem for Herman maps

In 1980s, Thurston established a topological characterization theorem for postcritically finite rational maps. In this paper, a decomposition theorem for a class of postcritically infinite branched covering termed Herman map is developed. It's shown that every Herman map can be decomposed along a stable multicurve into finitely many Siegel maps and Thurston maps, such that the combinations and rational realizations of these resulting maps essentially dominate the original one. This result is motivated by a non-expanding version of McMullen's problem, and Thurston's theory on characterization of rational maps. It enables us to prove a Thurston-type theorem for rational maps with Herman rings.

Theory and Experimental Study of Two-stage Auto-cascade Low Temperature Refrigerator

It is increased gradually in scientific research and daily life of two-stage auto-cascade low temperature refrigerator. Study and improve the refrigeration system performance plays an important role; characteristics of energy saving and environmental protection research also has important significance. Single-stage compression two-stage auto-cascade refrigeration system using non-azeotropic mixture refrigerant, the low temperature environment could be realized according to the pressure and temperature changes of refrigerant in the low temperature refrigerator and the relationship of vapor-liquid equilibrium. Three dimensional pressure-enthalpy diagram and enthalpy-composition diagram of two-stage auto-cascade cycle are analyzed using refrigerant properties analysis software NIST Refprop 8.0. The mixed refrigerant R600a and R23 is discussed and selected suitable for –60 ℃low temperature refrigerator, and the operation temperature and pressure of system are analyzed. The temperature and pressure and the refrigerant substances at the conjunction changes with time of two-stage auto-cascade low temperature refrigerator are studied through experimental methods. A relatively complete concept of two-stage auto-cascade refrigeration system for low temperature refrigerator is established; a rational realization of the temperature and pressure changes and vapor-liquid equilibrium is recognized. It is important to improve the performance of this kind of refrigerator and the products popularization.

Trust and ecological rationality in a computing context

In this paper, I examine a key issue affecting trust in the context of a computing environment, as it affects human agents and artificial agents. Specifically, the paper focuses on the role that "resource conservation" plays in an analysis of moral trust and epistemic trust involving agents. I will argue that resource conservation is a necessary condition in the definition of a moral trust relation, that there is a conceptual relationship between a moral trust relation and epistemic trust---that epistemic trust is a necessary condition for moral trust---, and that a moral trust relation might provide a basic mechanism for the realization of ecological rationality in human agents.

Anthropology an Intellectual Tradition and Contemporary Relevance

The notion of invariable human nature has been an important subject of enquiry and continues even in the modern times. The relative malleability has been argued in recent centuries by the early mechanists Thomas Hobbes and Jean Jaques Rousseau. As Rousseau stated “We do not know what our nature permits us to be” thinkers like Hegel and Marx argued against invariable human nature. Still more recent scientific perspective such as behaviorism, modern psychology claims to be neutral in this regard. To them human’s origin posses underlying mechanism, having capacities for change and diversity, which ultimately is a violation of the classical philosophical anthropology. The resulting fragmentation, as a consequence, has impacted intellectual enquiry. It is pertinent to say that the new dialectics of change fail to comprehend ethics and moral values, which are associated with higher aim, realization of good life, politics implied to reach agreements on better conditions, and realization of rationality (which engages in enquiry to realize the common good), thereby jeopardizing place of humanity in the cosmos. The new global forces have made people powerless, reduced them to a cog in the environment of uncertainty, ultimately leading to a looming war of all against all that is inexorably destroying the conditions for life. The policies and characteristics of the modern state and their bureaucracies rather accelerate these sequences which may lead to eradication of humanity. In this paper we try to resolve issues of legacy, along with the new dialectical patterns of globalization.

Realization Theory for Rational Systems: Minimal Rational Realizations

The study of realizations of response maps is a topic of control and system theory. Realization theory is used in system identification and control synthesis.

Realization Theory for Rational Systems: The Existence of Rational Realizations

In this paper we solve the problem of the existence of rational realizations of response maps. Sufficient and necessary conditions for a response map to be realizable by a rational system are presented. We provide also the characterization of the existence of rationally observable and canonical rational realizations for a given response map.

Minimum Rank of Matrices Described by a Graph or Pattern over the Rational, Real and Complex Numbers

We use a technique based on matroids to construct two nonzero patterns $Z_1$ and $Z_2$ such that the minimum rank of matrices described by $Z_1$ is less over the complex numbers than over the real numbers, and the minimum rank of matrices described by $Z_2$ is less over the real numbers than over the rational numbers. The latter example provides a counterexample to a conjecture by Arav, Hall, Koyucu, Li and Rao about rational realization of minimum rank of sign patterns. Using $Z_1$ and $Z_2$, we construct symmetric patterns, equivalent to graphs $G_1$ and $G_2$, with the analogous minimum rank properties. We also discuss issues of computational complexity related to minimum rank.

Rational realization of maximum eigenvalue multiplicity of symmetric tree sign patterns

A sign pattern is a matrix whose entries are elements of {+, −, 0}; it describes the set of real matrices whose entries have the signs in the pattern. A graph (that allows loops but not multiple edges) describes the set of symmetric matrices having a zero-nonzero pattern of entries determined by the absence or presence of edges in the graph. DeAlba et al. [L.M. DeAlba, T.L. Hardy, I.R. Hentzel, L. Hogben, A. Wangsness, Minimum rank and maximum eigenvalue multiplicity of symmetric tree sign patterns, Linear Algebra Appl., in press, doi:10.1016/j.laa.2006.02.018.] gave algorithms for the computation of maximum multiplicity and minimum rank of matrices associated with a tree sign pattern or tree, and an algorithm to obtain an integer matrix realizing minimum rank. We extend these results by giving algorithms to obtain a symmetric rational matrix realizing the maximum multiplicity of a rational eigenvalue among symmetric matrices associated with a symmetric tree sign pattern or tree.

Rational realizations of the minimum rank of a sign pattern matrix

A sign pattern matrix is a matrix whose entries are from the set {+, −, 0}. The minimum rank of a sign pattern matrix A is the minimum of the ranks of the real matrices whose entries have signs equal to the corresponding entries of A. It is conjectured that the minimum rank of every sign pattern matrix can be realized by a rational matrix. The equivalence of this conjecture to several seemingly unrelated statements are established. For some special cases, such as when A is entrywise nonzero, or the minimum rank of A is at most 2, or the minimum rank of A is at least n − 1 (where A is m × n), the conjecture is shown to hold. Connections between this conjecture and the existence of positive rational solutions of certain systems of homogeneous quadratic polynomial equations with each coefficient equal to either −1 or 1 are investigated.

Reason, Society and Religion

I have two main objectives in this essay: (1) to situate the events of 11 September within the context of the impact of modernization on religious consciousness and institutions; and (2) to suggest, albeit without adequate empirical support, that militant Islamic opposition to the West in general and the United States in particular is itself an effect of the peculiar path of modernization that has unfolded in the Gulf region of the Middle East over the last 200 years. To develop my argument, I draw upon Habermas's theory of social evolution. Since this strategy requires explaining the key components of that theory, I devote a good part of the article to this task. The paper has five parts. In parts one and two, I criticize competing explanations of the events of 11 September from left, right and center. All these positions fail in one way or another to take seriously the religious significance of those events. In part three, I explain the six central dimensions of Habermas's theory of social evolution: (1) communicative rationality; (2) communicative action; (3) life-world; (4) system; (5) social typology; and (6) the systemic colonization of the life-world. In part four, I examine the relation between religion and modernity. In part five, I examine the modernization processes in the Gulf region of the Middle East. Empirical evidence tentatively suggests that such a process has been one-dimensional, focusing on systemic complexity to the detriment of the communicative rationalization of the life-world. Such evidence also indicates the existence of widespread systemic colonization of the life-world. If the empirical data are correct, then we can explain the emergence of extreme militant Islamic fundamentalism as an effect of a retarded development of those socio-political structures necessary for the realization of communicative rationality.

Playing Language Games and Performing Rituals: Religious Studies as Ideological State Apparatus

AbstractThe Wittgensteinian philosophy of language games in the service of "religion" is circular and closed from criticism, and this generates the illusion that "religion" is compellingly universal. Also some historians, while attempting to uncover the specific and localized origins of the modern category "religion" in early modern Europe, simultaneously and unwittingly reconstruct the assumed universality of the category by uncritically using the problematized word in a description of societies in which the modern category, according to their own research findings, did not yet exist. These techniques suggest an unacknowledged ideological field lying behind the usages of the category. I argue that "religion" is one of a pair, the other half being "non-religion" or "the secular". The formation of the modern notion of religion needs to be seen initially in relation to privatized Protestant piety and the separation of church and state, whereby an apparently demystified human nature and fully rational modern civil society was made possible. But the application of the religion-secular distinction to an increasing number of colonies has resulted in "religion" becoming a catch-all container for indigenous institutions and practices that impede progress (i.e., impede realization of secular rationality by the natives). Debates about the logic of the religion-secular category can only become fruitful when we analyze the way in which they each construct their other half. However, the way "religion" is institutionalized and investigated in the academy elides its function in the invention and legitimation of the modern Euro-American secular, for it is treated as though it stands alone, either as a category in its own right or as a natural reality corresponding to that category.

ROBUST CONTROL OF CHAOTIC VIBRATIONS FOR IMPACTING HEAT EXCHANGER TUBES IN CROSSFLOW

A robust feedback controller design to suppress flutter-type chaotic vibrations in baffled heat exchanger tubes is presented. The vibrations are the result of the fluid dynamic forces on the tube which behave as a negative damping element. A consequence of these vibrations is that the heat exchanger tubes impact with the baffle plates thereby reducing the service life of the heat exchanger. To eliminate the resulting tube impacts, a feedback control strategy is proposed. The heat exchanger tube and the fluid dynamic forces acting on the tube are modeled with linear delayed differential equations. Due to the presence of the delay, these equations do not have a rational realization. The feedback controller is realized using a frequency domain loop shaping approach which is well suited for systems with transcendental transfer functions. The control effector is a magnetic force transducer that acts on the heat exchanger tube. The design strategy is based upon the premise that stabilizing the linear instability about the undeformed tube position will preclude the formation of the nonlinear chaotic vibrations that arise from impacting. The feedback controller is shown to provide robust stability and performance over a large flow velocity regime

Tilings by related zonotopes

We study periodic tilings of d-dimensional space by clusters of related zonotopes. For such tilings, the fundamental region relative to a fully-dimensional translation group is the finite union of zonotopes constructed as Minkowski sums of subsets of a given set of generating vectors. For any rationally-realizable zonotope Z, the rational realization itself determines a unique periodic tiling in which one of the cells is the zonotope Z. In an effort to find analogous tilings using nonrational zonotopes, we conjecture a characterization in terms of a new family oriented matroid structures, for which we provide axioms.

Third-order rational function realization with one operational amplifier

Simulation of third-order rational functions with constant coefficients by a single operational amplifier is discussed in this paper. The design procedure and the design equations for four different circuits are also given.

To Improve the System of Production Training

The shortening of the second stage of instruction in the secondary general education school creates the need for a discussion of how we can achieve the further, more rational realization of the Leninist principle of combining instruction with productive labor, of linking the school and life.