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This article concerns the question, Which subsets of ?m can be represented with linear matrix inequalities (LMIs)? This gives some perspective on the scope and limitations of one of the most powerful techniques commonly used in control theory. Also, before having much hope of representing engineering problems as LMIs by automatic methods, one needs a good idea of which problems can and cannot be represented by LMIs. Little is currently known about such problems. In this article we give a necessary condition that we call “rigid convexity,” which must hold for a set ?? ? ?m in order for ?? to have an LMI representation. Rigid convexity is proved to be necessary and sufficient when m = 2. This settles a question formally stated by Pablo Parrilo and Berndt Sturmfels in [15]. As shown by Lewis, Parillo, and Ramana [11], our main result also establishes (in the case of three variables) a 1958 conjecture by Peter Lax on hyperbolic polynomials. © 2006 Wiley Periodicals, Inc. 相似文献
23.
Blundell Tom L. Bolanos-Garcia Victor Chirgadze Dimitri Y. Harmer Nicholas J. Lo Thomas Pellegrini Luca Sibanda B. Lynn 《Structural chemistry》2002,13(3-4):405-412
Signaling in living systems needs to achieve high specificity, to be reversible, and to achieve high signal to noise. Signaling mediated by multiprotein systems has evolved that avoids the requirement for high-affinity binary complexes that would be difficult to reverse and which, in the overcrowded cell, would lead to excessive noise in the system. Symmetrical structures are only occasionally formed. When they are, it is principally to colocate components, for example, the tyrosyl kinases of growth factors, where dimers form. Symmetry is, however, often broken, presumably to create more sensitivity and specificity in the signaling system by assembling other components, into higher-order multiprotein systems. The binding of a single heparin to two 1:1 FGF:FGFR complexes is an example, as is the binding of a single ligase to the Xrcc4 dimer, perhaps so creating a further DNA-binding site. 相似文献
24.
Phil Diamond Peter Kloeden Victor Kozyakin Alexei Pokrovskii 《Mathematische Nachrichten》1998,191(1):59-81
The finiteness of computer arithmetic can lead to some dramatic differences between the behaviour of a continuous dynamical system and a computer simulation. A thorough rigorous theoretical analysis of what may or what does happen is usually extremely difficult and to date little has been done even in relatively simple contexts. The comparative behaviour of a rotation mapping in the plane and on a uniform lattice in the plane is one such example. Simulations show that the rounding operator applied to a planar rotation mapping more or less preserves the qualitative behaviour of the original mapping, whereas the application of the truncation operator to a planar rotation can lead to quite different dynamical features. In this paper a theoretical justification of the properties of the planar rotation mappings under truncation to a, uniform integer lattice is provided, in particular properties of boundedness and dissipativity are investigated. 相似文献
25.
Studies of breakdown threshold intensity for air at various pressures in the range of 24–760 torr using 0.355, 0.532 and 1.06
μm radiation are reported. We observep
−0.8 scaling ofI
th at 1.06 μm and a weak scaling ofp
−0.4 at 0.532 and 0.355 μm radiation. Strong dependence of breakdown spot size on laser power but weak dependence on air pressure
is observed. 相似文献
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We derive the action of 2D gravity from the two-cocycle of the Virasoro group by using a previously introduced method for constructing a dynamical system from a Lie group. A natural construction and explanation of the hidden SL(2,
)-Kac-Moody symmetry, of general applicability, is provided. We also show how the proper quantization goes beyond the ordinary co-adjoint orbit method, and the possible connection with the Poisson-Lie groups. 相似文献
29.
Victor Pambuccian 《Mathematical Logic Quarterly》1992,38(1):345-348
We proved in the first part [1] that plane geometry over Pythagorean fields is axiomatizable by quantifier-free axioms in a language with three individual constants, one binary and three ternary operation symbols. In this paper we prove that two of these operation symbols are superfluous. 相似文献
30.
A method is developed for performing a local reduction of the governing physics for fluid problems with domains that contain a combination of narrow and non‐narrow regions, and the computational accuracy and performance of the method are measured. In the narrow regions of the domain, where the fluid is assumed to have no inertia and the domain height and curvature are assumed small, lubrication, or Reynolds, theory is used locally to reduce the two‐dimensional Navier–Stokes equations to the one‐dimensional Reynolds equation while retaining a high degree of accuracy in the overall solution. The Reynolds equation is coupled to the governing momentum and mass equations of the non‐narrow region with boundary conditions on the mass and momentum flux. The localized reduction technique, termed ‘stitching,’ is demonstrated on Stokes flow for various geometries of the hydrodynamic journal bearing—a non‐trivial test problem for which a known analytical solution is available. The computational advantage of the coupled Stokes–Reynolds method is illustrated on an industrially applicable fully‐flooded deformable‐roll coating example. The examples in this paper are limited to two‐dimensional Stokes flow, but extension to three‐dimensional and Navier–Stokes flow is possible. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献