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871.
H. L. Stalford 《Journal of Optimization Theory and Applications》1995,86(3):685-718
Using a class of linear static controllers, we stabilize the Petersen open-loop two-dimensional linear system (Ref. 1), which consists of one time-varying uncertainty in the state matrixA and one timevarying uncertainty in the input matrixB. We show that the worst-case uncertainty strategy for the closed-loop system is a piecewise constant strategy of the angular state with three switches on the half-turn, –/2/2; it is unique with respect to a set of measure zero. Formulas are derived for the worst-case half-turn radius gainr
HT
as a function of the parameters of the class of stabilizing linear static controllers. Using the class of scalar-quadratic Lyapunov functions, we show that a necessary and sufficient condition for the closed-loop system to be robustly stable against all time-varying admissible uncertainties is thatr
HT
be less than unity. The bound on the time-varying real parameter uncertainties for the closed-loop system to be robustly stable is derived for the class of linear static feedback controllers. We obtain stabilizing linear static controllers such that the bound is as close to infinity as desired. The derived results are compared with numerical results obtained using commerical robust-control software. 相似文献
872.
Theendomorphism spectrum of an ordered setP, spec(P)={|f(P)|:f End(P)} andspectrum number, sp(P)=max(spec(P)\{|P|}) are introduced. It is shown that |P|>(1/2)n(n – 1)
n – 1 implies spec(P) = {1, 2, ...,n} and that if a projective plane of ordern exists, then there is an ordered setP of size 2n
2+2n+2 with spec(P)={1, 2, ..., 2n+2, 2n+4}. Lettingh(n)=max{|P|: sp(P)n}, it follows thatc
1
n
2h(n)c
2
n
n+1 for somec
1 andc
2. The lower bound disproves the conjecture thath(n)2n. It is shown that if |P| – 1 spec(P) thenP has a retract of size |P| – 1 but that for all there is a bipartite ordered set with spec(P) = {|P| – 2, |P| – 4, ...} which has no proper retract of size|P| – . The case of reflexive graphs is also treated.Partially supported by a grant from the NSERC.Partially supported by a grant from the NSERC. 相似文献
873.
Walter M. Miller 《Set-Valued Analysis》1995,3(2):181-194
A set-valued dynamical systemF on a Borel spaceX induces a set-valued operatorF onM(X) — the set of probability measures onX. We define arepresentation ofF, each of which induces an explicitly defined selection ofF; and use this to extend the notions of invariant measure and Frobenius-Perron operators to set-valued maps. We also extend a method ofS. Ulam to Markov finite approximations of invariant measures to the set-valued case and show how this leads to the approximation ofT-invariant measures for transformations , whereT corresponds to the closure of the graph of . 相似文献
874.
Self-avoiding random walks (SAWs) are studied on several hierarchical lattices in a randomly disordered environment. An analytical method to determine whether their fractal dimensionD
saw is affected by disorder is introduced. Using this method, it is found that for some lattices,D
saw is unaffected by weak disorder; while for othersD
saw changes even for infinitestimal disorder. A weak disorder exponent is defined and calculated analytically [ measures the dependence of the variance in the partition function (or in the effective fugacity per step)vL
on the end-to-end distance of the SAW,L]. For lattices which are stable against weak disorder (<0) a phase transition exists at a critical valuev=v
* which separates weak- and strong-disorder phases. The geometrical properties which contribute to the value of are discussed. 相似文献
875.
Titanium Tetrafluoride – a Surprising Simple Column Structure For the first time single crystals of TiF4 have been obtained by solvothermal decomposition of (O2)2Ti7F30 in anhydrous HF. The colourless, transparent needles crystallize orthorhombic in spacegroup Pnma–D (No. 62) with a = 2 281.1, b = 384.8, c = 956.8 pm, Z = 12. The new type of structure is dominated by isolated columns of corner-linked TiF6-octahedra. 相似文献
876.
Aminobenzoic acids in dioxane have been investigated by dipole moment and Kerr effect methods.m-Aminobenzoic acid exists in a solution mainly (60 %) in thesyn-form. Inp-aminobenzoic acid, conjugation flattens the pyramidal configuration of the nitrogen atom, which is even more flattened ino-aminobenzoic acid owing to an intramolecular hydrogen bond.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 5, pp. 859–861, May, 1994. 相似文献
877.
L. I. Zakharkin I. M. Churilova G. N. Antonova P. V. Petrovskii N. S. Ikonnikov 《Russian Chemical Bulletin》1994,43(8):1360-1362
Alkylation of cyclododecanone with ,-dibromoalkanes Br(CH)
n
Br (n=3, 4, 5) under conditions of phase-transfer catalysis in the presence of KOH results in the formation of either bicyclic ketones forn=3 and 5 or a mixture of bicyclic and spirocyclic ketones forn=4.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 8, pp. 1436–1438, August, 1994. 相似文献
878.
Jeffrey Axten Jennifer Troy Peter Jiang Mendel Trachtman Charles W. Bock 《Structural chemistry》1994,5(2):99-108
Ab initio molecular orbital calculations are used to study the modified Schlenk equilibrium: 2RMgCl (RMgCl)2 MgR2 + MgCl2 Mg(Cl2)MgR2 with R=H and CH3. In the absence of any solvents, calculations indicate that the formation of the various possible bridged dimers (RMgCl)2 is substantially exothermic. However, using dimethylether as a model solvent, we show that the formation of the dimer (Me2O)(CH3)Mg(Cl2)Mg(CH3)(OMe2) is exothermic only when entropic effects are included. 相似文献
879.
Summary The concept of hull convexity (midpoint hull convexity) for set-valued functions in vector spaces is examined. This concept, introduced by A. V. Fiacco and J. Kyparisis (Journal of Optimization Theory and Applications,43 (1986), 95–126), is weaker than one of convexity (midpoint convexity).The main result is a sufficient condition for a midpoint hull convex set-valued function to be continuous. This theorem improves a result obtained by K. Nikodem (Bulletin of the Polish Academy of Sciences, Mathematics,34 (1986), 393–399). 相似文献
880.
J. D. Fanning 《Aequationes Mathematicae》1994,47(2-3):143-149
Summary We prove the following two non-existence theorems for symmetric balanced ternary designs. If 1 = 1 and 0 (mod 4) then eitherV = + 1 or 42 – + 1 is a square and (42 – + 1) divides 2 – 1. If 1 = 2 thenV = ((m + 1)/2)
2 + 2,K = (m
2 + 7)/4 and = ((m – 1)/2)2 + 1 wherem 3 (mod 4). An example belonging to the latter series withV = 18 is constructed. 相似文献