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We give deterministic polynomial-time algorithms that, given an order, compute the primitive idempotents and determine a set of generators for the group of roots of unity in the order. Also, we show that the discrete logarithm problem in the group of roots of unity can be solved in polynomial time. As an auxiliary result, we solve the discrete logarithm problem for certain unit groups in finite rings. Our techniques, which are taken from commutative algebra, may have further potential in the context of cryptology and computer algebra. 相似文献
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Lee J. Silverberg Tapas K. Mal Carlos N. Pacheco Megan L. Povelones Madeline F. Malfara Anthony F. Lagalante Mark A. Olsen Hemant P. Yennawar Hany F. Sobhi Kayla R. Baney Robin L. Bozeman Craig S. Eroh Michael J. Fleming Tracy L. Garcia Casey L. Gregory Julia E. Hahn Alyssa M. Hatter Lexi L. Johns Tianna L. Klinger Jennie J. Li Andrew J. Menig Grace C. Muench Melissa E. Ramirez Jordyn Reilly Nicole Sacco Alexandra M. Sheidy Marla M. Stoner Eric N. Thompson Soroush F. Yazdani 《Molecules (Basel, Switzerland)》2021,26(20)
A series of fourteen 2-aryl-3-phenyl-2,3-dihydro-4H-pyrido[3,2-e][1,3]thiazin-4-ones was prepared at room temperature by T3P-mediated cyclization of N-phenyl-C-aryl imines with thionicotinic acid, two difficult substrates. The reactions were operationally simple, did not require specialized equipment or anhydrous solvents, could be performed as either two or three component reactions, and gave moderate–good yields as high as 63%. This provides ready access to N-phenyl compounds in this family, which have been generally difficult to prepare. As part of the study, the first crystal structure of neutral thionicotinic acid is also reported, and showed the molecule to be in the form of the thione tautomer. Additionally, the synthesized compounds were tested against T. brucei, the causative agent of Human African Sleeping Sickness. Screening at 50 µM concentration showed that five of the compounds strongly inhibited growth and killed parasites. 相似文献
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This paper considers Fourier series approximations of one- and two-dimensional functions over the half-range, that is, over the sub-interval [0, L] of the interval [−L, L] in one-dimensional problems and over the sub-domain [0, Lx] × [0, Ly] of the domain [−Lx, Lx] × [−Ly, Ly] in two-dimensional problems. It is shown how to represent these functions using a Fourier series that employs a smooth extension. The purpose of the smooth extension is to improve the convergence characteristics otherwise obtained using the even and odd extensions. Significantly improved convergence characteristics are illustrated in one-dimensional and two-dimensional problems. 相似文献
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Lee J. Silverberg Carlos Pacheco Debashish Sahu Peter Scholl Hany F. Sobhi Joshua T. Bachert Kaitlyn Bandholz Ryan V. Bendinsky Heather G. Bradley Baylee K. Colburn David J. Coyle Jonathon R. Dahl Megan Felty Ryan F. Fox Kyanna M. Gonzalez Jasra M. Islam Stacy E. Koperna Quentin J. Moyer Duncan J. Noble Melissa E. Ramirez Ziwei Yang 《Journal of heterocyclic chemistry》2020,57(4):1797-1805
A series of 11 novel 3-aryl-2-phenyl-2,3-dihydro-4H-1,3-benzothiazin-4-ones was prepared at room temperature by T3P-mediated cyclization of N-aryl-C-phenyl imines with thiosalicylic acid. This provides simple and ready access to N-aryl compounds in this family, which have been generally difficult to prepare. 相似文献
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Foundations of Chemistry - No exact definition of an “organic” substance has been agreed upon by the chemical community and textbook definitions vary substantially. The question of what... 相似文献
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The effects of lateral interactions on the two-dimensional distribution of adspecies on solid surfaces and their consequences for reaction kinetics are demonstrated for the bimolecular reactive systemA+BAB. The discussion concentrates on systems where one reactant,A, is stationary while the other,B, is freely diffusing and instantaneously relaxing. A modified Bethe-Peierls-type lattice gas approximation is formulated in order to account for the rapidly-equilibrating distribution ofB atoms. The approximation takes into account all nearest and next nearest neighbor interactions between the adspecies and the nonuniformity of the lattice available toB implied by the presence of immobileA's on the surface. This model is combined with a Monte Carlo simulation of the reactive events in order to calculate reaction rates, e.g., in temperature-programmed processes. The rates are compared with full Monte Carlo simulations (for all kinetic processes), showing good agreement between the two schemes, except at very high coverages, where very long range correlations in the system which are ignored in the lattice gas approximation must be taken into account.This paper is dedicated to Howard Reiss in celebration of his 66th birthday. 相似文献