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This article describes several natural methods of constructing random probability measures with prescribed mean and variance, and focuses mainly on a technique which constructs a sequence of simple (purely discrete, finite number of atoms) distributions with the prescribed mean and with variances which increase to the desired variance. Basic properties of the construction are established, including conditions guaranteeing full support of the generated measures, and conditions guaranteeing that the final measure is discrete. Finally, applications of the construction method to optimization problems such as Plackett's Problem are mentioned, and to experimental determination of average-optimal solutions of certain control problems.  相似文献   
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Electron paramagnetic resonance is used to detect the formation of free radicals caused by exposure to ultraviolet radiation in chemically untreated rabbit skin. A fast jump in EPR signal level, occurring over a few seconds, is observed immediately after a skin sample is exposed to UV. This is followed by a slower increase toward an elevated steady-state signal over a period of hours as the skin is continuously exposed to a UV light source. Upon cessation of UV light exposure, EPR signal levels undergo an abrupt drop followed by a slower decay toward natural levels. Elevated free radical concentrations following UV exposure are found to persist for several hours in whole skin. These results are consistent with time-resolved EPR measurements of photoinduced radicals in various natural melanins.  相似文献   
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We introduce and study the complex of “stable forms” on supermanifolds. Stable forms on a supermanifold M are represented by Lagrangians of “copaths” (formal systems of equations, which may or may not specify actual surfaces) on M×ℝ D . Changes of D give rise to stability isomorphisms. The resulting (direct limit) {Cartan-de Rham} complex made of stable forms extends both in positive and negative degree. Its positive half is isomorphic to the complex of forms defined as Lagrangians of paths, studied earlier. Including the negative half is crucial, in particular, for homotopy invariance. For stable forms we introduce (non-obvious) analogs of exterior multiplication by covectors and contraction with vectors and find the anticommutation relations that they obey. Remarkably, the version of the Clifford algebra so obtained is based on the super anticommutators rather than the commutators and (before stabilization) it includes some central element σ. An analog of Cartan's homotopy identity is proved, which also contains this “stability operator”σ. Received: 3 January 2000 / Accepted: 15 September 2001  相似文献   
108.
Let \(\dot y\) =f(y,t) withy(t 0)=y 0 possess a solutiony(t) fortt 0. Sett n=t 0+nh, n=1, 2,.... Lety 0 denote the approximate solution ofy(t n) defined by the composite multistep method with \(\dot y_n \) =f(y n ,t n ) andN=1, 2,.... It is conjectured that the method is stiffly stable with orderp=l for alll≧1 and shown to be so forl=1,..., 25. The method is intrinsically efficient in thatl future approximate solution values are established simultaneously in an iterative solution process with only one function evaluation per iteration for each of thel future time points. Step and order control are easily implemented, in that the approximate solution at only one past point appears in each component multistep formula of the method and in that the local truncation error for the first component multistep formula of the method is easily evaluated as $$T^{[l]} = \frac{h}{{t_{Nl} - t_{(N - 1)l - 1} }}\{ y_{Nl}^{PRED} - y_{Nl} \} ,$$ wherey Nl PRED denotes the value att Nl of the Lagrange interpolating polynomial passing through the pointsy (N?1)l+j att (N?1)l+j withj=?1, 0,...,l ? 1.  相似文献   
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The interaction of Eu(fod)3 with organic salts is studied.  相似文献   
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