Infinite Versions Research Articles

Use of Feminist Literary Theory in Developing a Critical Language for Hypertext

The Writing 2000 Conference highlighted an urgency for discussion of the role that contemporary critical theory will play in the acceptance of hypertext narratives. The modernist view of the importance of the permanence of fixed recording in black and white and the predominance of an heroic narrative structure conflicts with the concept of hypertext as a text that is never fixed with the possibility of infinite versions. The question that needs to be addressed is, whether this infinite flexibility is a problem for the writer/reader of hyperfiction or if it could offer possibilities that recorded, fixed, linear print cannot.

Infinite Nests of Reguli

In this article, infinite versions of t-nests for t=q,(q-1), (q+1),2(q-1) and mixed nests of reguli are constructed. Furthermore, a classification of all group replaceable spreads is given.

Growth, Death, and Taxes

A number of recent studies suggest that flat rate taxes may have important effects on long-run growth in the neoclassical growth model with human capital. In contrast to the traditional human capital literature, these studies assume that agents are infinitely lived and face constant returns in training. This paper shows that abstracting from life-cycle features and diminishing returns distorts growth effects in important ways. Analytical solutions for the growth effects of wage taxes are compared for finite and infinite horizon versions of the neoclassical growth model. The notion that growth effects with long but finite horizons are well approximated by infinite horizons is shown to be invalid, except in special cases. Generically, the assumptions made in the literature lead to a systematic overstatement of growth effects. Illustrative numerical results suggest that the discrepancies may be large.

Functional Integral Representation of a Model in Quantum Electrodynamics

This paper presents functional integral representations for heat semigroups with infinitesimal generators given by self-adjoint Hamiltonians (Pauli–Fierz Hamiltonians) describing an interaction of a non-relativistic charged particle and a quantized radiation field in the Coulomb gauge without the dipole approximation. By the functional integral representations, some inequalities are derived, which are infinite degree versions of those known for finite dimensional Schrödinger operators with classical vector potentials.

Infinite Versions of Some Problems from Finite Complexity Theory

Recently, several authors have explored the connections between NP-complete problems for finite objects and the complexity of their analogs for infinite objects. In this paper, we will categorize infinite versions of several problems arising from finite complexity theory in terms of their recursion theoretic complexity and proof theoretic strength. These infinite analogs can behave in a variety of unexpected ways. Startling parallels exist between the computational complexity of certain graph theoretic problems and the recursion theoretic complexity and proof theoretic strength of their infi- nite analogs. For example, the problem of deciding which finite graphs have an Euler path is known to be P-time computable (9), and Beigel and Gasarch (4) have shown that the problem of deciding which infinite recursive graphs have an Euler path is arithmetical. By contrast, the problem of deciding which finite graphs have Hamilton paths is NP-complete (8), and Harel (6) has shown that the problem of deciding which infinite recursive graphs have a Hamilton graph is � 1 complete. Thus, the possibly greater computational complex- ity is paralleled by a demonstrable increase in recursion theoretic complexity. This pattern can also be seen through an application of the techniques of reverse mathematics. The

Taking It to the Limit: On Infinite Variants of NP-Complete Problems

We define infinite, recursive versions of NP optimization problems. For example,Max Cliquebecomes the question of whether a recursive graph contains an infinite clique. The present paper was motivated by trying to understand what makes some NP problems highly undecidable in the infinite case, while others remain on low levels of the arithmetical hierarchy. We prove two results; one enables using knowledge about the infinite case to yield implications to the finite case, and the other enables implications in the other direction. Moreover, taken together, the two results provide a method for proving (finitary) problems to be outside the syntactic classMaxNP, and, hence, outsideMaxSNP too, by showing that their infinite versions areΣ11-complete. We illustrate the technique with many examples, resulting ?in a large number of newΣ11-complete problems.

Bounded sample path control of discrete time jump linear systems

A bounded sample path control strategy, based on the idea of minimizing an upper bound of the possible costs to go, is formulated. The finite and infinite versions of the JLQBSP (jump linear quadratic bounded sample path) problem are solved. A set of sufficient conditions for the existence and uniqueness of steady-state solutions that stabilize the controlled system with certainty (i.e. on any sample path) is also presented. The resulting costs are finite. The sufficient conditions are based on concepts of absolute controllability and observability of the jump linear system. This JLQBSP controller requires less precise information about form transition probabilities (only the directed interaction matrix is needed) and provides reliable control in all circumstances. Consequently, sometimes it is more appropriate for potential applications than JLQ control algorithms that are optimal in only an average sense. >

Minimal non-two-colorable hypergraphs and minimal unsatisfiable formulas

Seymour ( Quart. J. Math. Oxford 25 (1974) , 303–312) proved that a minimal non 2-colorable hypergraph on n vertices has at least n edges. A related fact is that a minimal unsatisfiable CNF formula in n variables has at least n + 1 clauses (an unpublished result of M. Tarsi.) The link between the two results is shown; both are given infinite versions and proved using transversal theory (Seymour's original proof used linear algebra). For the proof of the first fact we give a strengthening of König's duality theorem, both in the finite and infinite cases. The structure of minimal unsatisfiable CNF formulas in n variables containing precisely n + 1 clauses is characterised, and this characterization is given a geometric interpretation.

The Existence of Perfect Equilibria in a Model of Growth with Altruism between Generations

An intertemporal model of consumption and bequest behaviour is specified and analysed as a game between generations. The main feature of this game is that no a priori restrictions (like linearity) are placed on the strategy choice of generations. The paper gives an existence proof for perfect (Nash) equilibria in finite and infinite horizon versions of the model and determines characteristic properties of equilibrium strategies. The main result is to demonstrate existence of stationary perfect equilibrium if the time horizon is infinite.

Stochastic Production Planning with Production Constraints

This paper considers an infinite horizon stochastic production planning problem with the constraint that production rate must be nonnegative. It is shown that an optimal feedback solution exists for the problem. Moreover, this solution is characterized and is then compared with the solution of the unconstrained problem. Also obtained, by using a policy iteration procedure, are computational solutions to the related problems with upper bounds on the production rate. which determines production rates over time to minimize an integral representing a discounted quadratic loss function. The loss function is defined in terms of the deviations of production and inventory levels from their rated or factory-optimal values. The model is solved both with and without nonnegative production constraints. A stochastic extension of this paper involving a white noise process (1) is analyzed by Sethi and Thompson (9), (10). Closed-form solutions for optimal feedback production policy for both finite and infinite horizon versions of the model without production constraints are obtained. In particular, the model must allow negative production rates or disposals. In this paper, we consider the stochastic production planning problem with the constraint that production rates must be nonnegative. Only the infinite horizon problem is treated. It is shown that an optimal feedback solution exists for the problem. This solution is characterized. Also obtained, by using a policy iteration procedure, are computational solutions to the related problems with upper bounds on the production rate.

Critical Phenomena for Spitzer's Reversible Nearest Particle Systems

Motivated by several results and open problems concerning Harris' basic contact process, we consider the relationship between the critical behavior of the finite and infinite versions of Spitzer's reversible nearest particle systems. We show that the critical values for the finite and infinite systems agree, but that the behavior of the two systems at the common critical value can differ. The Nash-Williams recurrence criterion for reversible Markov chains is an important tool used in the proofs of the main results, and we give a new treatment of that theory. Finally, we compute several critical exponents for the nearest particle systems.

Linear optimal stochastic control using instantaneous output feedback‡

Abstract The problem of determining the linear feedback control of the instantaneous system output which minimizes a quadratic performance measure for a linear system with state and control-dependent noise is solved in this paper. Both the finite and infinite terminal time versions of this problem are treated. For the latter case, a sufficient condition for the existence of an optimal control is obtained. For the finite terminal time problem, it is shown that a two-point boundary value problem must be solved to realize the optimal control. For the infinite terminal time case, two non-linear matrix equations must be solved to realize the optimal control. Some discussion on the numerical methods used by the author to solve these equations is included in the paper.

The Optimal Regulator Problem for a Stationary Linear System With State-Dependent Noise

The problem of minimizing a quadratic functional of the system outputs and control for a stationary linear system with state-dependent noise is solved in this paper. Both the finite final time and infinite final time versions of the problem are treated. For the latter case existence conditions are obtained using the second method of Lyapunov. The optimal controls for both problems are obtained using Bellman’s continuous dynamic programming. In light of this, the system dynamics are assumed to determine a diffusion process. For the infinite final time version of the problem noted above, sufficient conditions are obtained for the stability of the optimal system and uniqueness of the optimal control law. In addition, for this problem, an example is treated. The computational results for this example illustrate some of the qualitative features of regulators for linear, stationary systems with state-dependent disturbances.