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91.
We present a simple method for determining the shape of fundamental domains of generalized modular groups related to Weyl groups of hyperbolic Kac?CMoody algebras. These domains are given as subsets of certain generalized upper half planes, on which the Weyl groups act via generalized modular transformations. Our construction only requires the Cartan matrix of the underlying finite-dimensional Lie algebra and the associated Coxeter labels as input information. We present a simple formula for determining the volume of these fundamental domains. This allows us to re-produce in a simple manner the known values for these volumes previously obtained by other methods. 相似文献
92.
Hermann Singer 《The Journal of mathematical sociology》2013,37(1):39-49
In a recent paper it was shown that the aliasing phenomenon, which leads to a severe identification problem in the estimation of stochastic differential equations, can be overcome by using a polygonal (or higher) approximation for the time paths of the exogenous variables. This work attempts to visualize the problem and presents several simulated trajectories of a continuous time AR(2)‐process (Ornstein‐Uhlenbeck‐process) together with the observationally equivalent structures. Furthermore it is shown that aliasing can even change the analytical properties of the time paths of the system: whereas the first component of the Ornstein‐Uhlenbeck‐process is differentiable, the trajectories of the aliasing structures are continuous, but not differentiable any more. 相似文献
93.
94.
An important aspect in the solution process of constraint satisfaction problems is to identify exclusion boxes which are boxes that do not contain feasible points. This paper presents a certificate of infeasibility for finding such boxes by solving a linearly constrained nonsmooth optimization problem. Furthermore, the constructed certificate can be used to enlarge an exclusion box by solving a nonlinearly constrained nonsmooth optimization problem. 相似文献
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97.
A cheap synthesis of the so‐called ‘decalin‐1,8‐diones’ started with the conjugate (1,4‐) addition of cyclohex‐2‐en‐1‐one derivatives to the γ‐position of the dilithium derivative (buta‐1,3‐diene‐1,1‐bis(olate)) of crotonic acid. Hydrogenation of these ‘1,4‐γ’ adducts and final cyclization afforded the enol tautomers of decalin‐1,8‐diones. Nucleophilic substitutions at these 3‐oxoenols by NH3 or primary amines created only monoamino products (namely, 3‐oxoenamines) whose reactions with OPCl3 yielded dihydro(1,3,2)oxazaphosphinin‐2‐one derivatives. The two regioisomers of a trimethyl‐3‐oxoenamine served as models for the constitutional assignments of the two rapidly interconverting (hence, individually NMR‐invisible), tautomeric trimethyl‐3‐oxoenols. Such methyl substitutions served to break the ‘pretended’ symmetry of ‘decalin‐1,8‐dione’. Hydrazine and 3‐oxoenols furnished oxygen‐free indazole derivatives whose N?H bonds exchanged with t1/2=ca. 0.00035 s at ca. ?58(9) °C. 相似文献
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99.
Daniel S. Covita Dimitrios F. Anagnostopoulos Hermann Fuhrmann Hubert Gorke Detlev Gotta Alexander Gruber Albert Hirtl Tomoichi Ishiwatari Paul Indelicato Thomas S. Jensen Eric-Olivier Le Bigot Valeri E. Markushin Michael Nekipelov Vladimir N. Pomerantsev Vladimir P. Popov Joaquim M. F. dos Santos Philipp Schmid Leopold M. Simons Marian Theisen Martino Trassinelli Joao F. C. A. Veloso Johann Zmeskal 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2018,72(4):72
100.
Hansurudolf Meier Hanspeter Kuenzi Hermann Fuhrer Günher Rist 《Phosphorus, sulfur, and silicon and the related elements》2013,188(1-4):537-538
Abstract The 2.4-bisfunctionalized phenol 1, a commercial antioxidant, is dehydrogenated regioselectively with potassium ferricyanide. affording the corresponding p-quinone methide 2. 1,6-Addition of nucleophiles e.g. thiols to 2 gives rise to the corresponding addition products e.g. the dithioacetals 4 of the corresponding substituted benzaldehyde. On the other hand, treatment of 2 with αα′-azoisobutyronitrile at 90°C leads to compounds 5a-b and 6, addition products of the cyanopropyl radical to the quinone methide 2. The structures of all products are confirmed mainly by 1H-NMR-and 13C-NMR-spectroscopy and the mode of their formation is discussed. 相似文献