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1.
Azepane rings have been constructed diastereoselectively upon a carbohydrate derivative utilising reductive amination and RCM. The stereochemistry of the ring junctions was confirmed by X-ray crystallography and NMR. Diastereoselective dihydroxylation has also been employed to afford a tetrahydroxylated azepane carbohydrate derivative with potential biological activity. 相似文献
2.
3.
L. Erbe A. Peterson S.H. Saker 《Journal of Mathematical Analysis and Applications》2007,329(1):112-131
In this paper, we extend the oscillation criteria that have been established by Hille [E. Hille, Non-oscillation theorems, Trans. Amer. Math. Soc. 64 (1948) 234-252] and Nehari [Z. Nehari, Oscillation criteria for second-order linear differential equations, Trans. Amer. Math. Soc. 85 (1957) 428-445] for second-order differential equations to third-order dynamic equations on an arbitrary time scale T, which is unbounded above. Our results are essentially new even for third-order differential and difference equations, i.e., when T=R and T=N. We consider several examples to illustrate our results. 相似文献
4.
Louis Block James Keesling Shihai Li Kevin Peterson 《Journal of statistical physics》1989,55(5-6):929-939
A new algorithm is presented for computing the topological entropy of a unimodal map of the interval. The accuracy of the algorithm is discussed and some graphs of the topological entropy which are obtained using the algorithm are displayed. 相似文献
5.
The Sommerfeld diffraction theory is extended to the case of extremely short pulses. It is shown that a simple qualitative
analysis and a quantitative solution of a wide class of diffraction problems are possible for pulses with durations of the
order of the period of the light oscillations and an arbitrary initial distribution of the light field.
Pis’ma Zh. éksp. Teor. Fiz. 66, No. 5, 323–326 (10 September 1997)
Deceased 相似文献
6.
Gary L. Peterson 《Monatshefte für Mathematik》1996,121(3):275-290
AnI-E group is a group in which the endomorphism near-ring generated by the group's inner automorphisms equals the endomorphism near-ring generated by its endomorphisms. In this paper we shall completely determine the finite groups that are semidirect products of cyclic groups and areI-E groups. 相似文献
7.
Dominic G. B. Edelen 《International Journal of Theoretical Physics》1990,29(7):687-737
Families of horizontal ideals of contact manifolds of finite order are studied. Each horizontal ideal is shown to admit ann-dimensional module of Cauchy characteristic vectors that is also a module of annihilators (in the sense of Cartan) of the contact ideal. Since horizontal ideals are generated by 1-forms, any completely integrable horizontal ideal in the family leads to a foliation of the contact manifold by submanifolds of dimensionn on which the horizontal ideal vanishes. Explicit conditions are obtained under which an open subset of a leaf of this foliation is the graph of a solution map of the fundamental ideal that characterizes a given system of partial differential equations of finite order withn independent variables. The solution maps are obtained by sequential integration of systems of autonomous ordinary differential equations that are determined by the Cauchy characteristic vector fields for the problem. We show that every smooth solution map can be obtained in this manner. Let {Vi¦1in} be a basis for the module of Cauchy characteristic vector fields that are in Jacobi normal form. If a subsidiary balance ideal admits each of then vector fieldsV
i as a smooth isovector field, then certain leaves of the foliation generated by the corresponding closed horizontal ideal are shown to be graphs of solution maps of the fundamental ideal. A subclass of these constructions agree with those of the Cartan-Kähler theorem. Conditions are also obtained under which every leaf of the foliation is the graph of a solution map. Solving a given system ofr partial differential equations withn independent variables on a first-order contact manifold is shown to be equivalent to the problem of constructing a complete system of independent first integrals. Properties of systems of first integrals are analyzed by studying the collection ISO[A
ij
] of all isovectors of the horizontal ideal. We show that ISO[A
ij
] admits the direct sum decomposition *[A
ij
]W[A
ij
] as a vector space, where *[A
ij
] is the module of Cauchy characteristics of the horizontal ideal. ISO[A
ij
] also forms a Lie algebra under the standard Lie product,*[A
ij
] andW[A
ij
] are Lie subalgebras of ISO[A
ij
], and [A
ij
] is an ideal. A change of coordinates that resolves (straightens out) the canonical basis for *[A
ij
] is constructed. This change of coordinates is used to reduce the problem of solving the given system of PDE to the problem of root extraction of a system ofr functions ofn variables, and to establish the existence of solutions to a second-order system of overdetermined PDE that generate the subspaceW[A
ij
]. Similar results are obtained for second-order contact manifolds. Extended canonical transformations are studied. They are shown to provide algorithms for calculating large classes of closed horizontal ideals and a partial analog of classical Hamilton-Jacobi theory. 相似文献
8.
Kochocki JA Allison WW Alner GJ Ambats I Ayres DS Balka LJ Barr GD Barrett WL Benjamin D Border P Brooks CB Cobb JH Cockerill DJ Coover K Courant H Dahlin B DasGupta U Dawson JW Edwards VW Fields TH Kirby-Gallagher LM Garcia-Garcia C Giles RH Goodman MC Heller K Heppelman S Hill N Hoftiezer JH Jankowski DJ Johns K Joyce T Kafka T Litchfield PJ Lopez FV Lowe M Mann WA Marshak ML May EN McMaster L Milburn RH Miller W Napier A Oliver WP Pearce GF Perkins DH Peterson EA Price LE Roback D Rosen DB 《Physical review D: Particles and fields》1990,42(9):2967-2973
9.
John R. Peterson Tamara J. Winter Hoang D. Do Robin D. Rogers 《Journal of chemical crystallography》1989,19(1):135-145
Structural and conformational information obtained from the crystal structure and solution1H nmr investigations of the title compound are compared. The 4-aryltetralone, C24H24O10, crystallizes as a chloroform solvate in the monoclinic space group, P21/n, witha=12.519(4),b=17.938(6),c=12.534(9)Å,=111.90(5)°, and Dcalc=1.51 g cm–3 forZ=4. The data for this compound were collected at –150°C. Least-squares refinement of 2796 observed [F
o5(F
o)] reflections led to the final agreement index ofR=0.062. A threefold static disorder was observed for one of the carboxyl groups. The second carboxyl group participates in an intramolecular hydrogen bond and is thus ordered. The1H nmr spectrum revealed the title compound to exist as a keto-enol tautomeric mixture in solution. Vicinal hydrogen coupling constant analysis proved reliable in ascertaining B-ring stereochemistry of 2,3-disubstituted-4-aryltetralones. 相似文献
10.