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The gain in the number of iterations is typically factors of 2 and 4 for the two implementations made of the Gauss--Seidel algorithm. ... The Gauss--Seidel algorithm is then described and, by analogy to the plan--parallel case, we see how to introduce it in spherical geometry. ... Léger for the help provided concerning the Gauss-Seidel algorithm. We also thank J. R. Pardo for his useful revision of the present manuscript. ...doi:10.1051/0004-6361:200810103 fatcat:bzoxopxmezdujbg7zib4hfdjiu
This eases the extraction of Seidel sum coefficients from Eq. (7) . ... Seidel coefficients, on the other hand, are derived from an expansion series. ...doi:10.1364/ao.50.00h220 pmid:22193012 fatcat:le2misn6znh2pbpggoirogl2nm
to the sparse link matrix of the web and avoiding the strict sequential update of the Gauss-Seidel method. ... Initial results suggest that using an asynchronous version of the Gauss-Seidel method can yield a faster convergence than using the traditional power method while maintaining the communications according ... Fig. 4 . 4 Sequential Gauss-Seidel against Asynchronous Gauss-Seidel errors. Fig. 5 . 5 Sequential Gauss-Seidel against Randomized Gauss-Seidel errors. ...doi:10.23919/acc.2018.8431212 dblp:conf/amcc/SilvestreHS18 fatcat:rrluqhgtmfgyxnf5kom2yjm4qm
■ AUTHOR INFORMATION Corresponding Author *E-mail: firstname.lastname@example.org. Notes The authors declare no competing financial interest. ...doi:10.1021/ol501365j pmid:24857691 pmcid:PMC4059224 fatcat:rns7te6kkvanbjepvds7mvuzfi
An alternate approach to ring-substituted propargylic amines was developed independently by the Li 5 and Seidel 6 groups. 7, 8 These researchers showed that amino acids such as proline and pipecolic ... alternate route appears to be viable based on the reversibility of certain iminium alkynylations, as recently demonstrated by Nakamura and coworkers. 18 The first redox-A 3 reaction was reported by the Seidel ...doi:10.1039/c4qo00022f pmid:24955245 pmcid:PMC4061755 fatcat:carjr3pj6zfzdkfgepimt3ckb4
Supporting Information General Information: All reagents and solvents were purchased from commercial sources. Toluene was distilled prior to use. Microwave reactions were carried out in a CEM Discover reactor. Silicon carbide (SiC) passive heating elements were purchased from Anton Paar. Purification of reaction products was carried out by flash chromatography using Sorbent Technologies Standard Grade silica gel (60 Å, 230-400 mesh). Analytical thin layer chromatography was performed on EMdoi:10.1039/c1cc11560j pmid:21556391 fatcat:mzmetpbtejac7m7ekem6qxmo2e
more »... nt 0.25 mm silica gel 60 F 254 plates. Visualization was accomplished with UV light, and DMP and PMA stains, followed by heating. Melting points were recorded on a Thomas Hoover capillary melting point apparatus and are uncorrected. Infrared spectra were recorded on an ATI Mattson Genesis Series FT-Infrared spectrophotometer. Proton nuclear magnetic resonance spectra ( 1 H-NMR) were recorded on a Varian VNMRS-500 MHz and a Varian VNMRS-400 MHZ and were reported in ppm using the solvent as an internal standard (CDCl 3 at 7.26 ppm). Data are reported as app = apparent, s = singlet, d = doublet, t = triplet, q = quartet, sex = sextet, m = multiplet, comp = complex, br = broad; coupling constant(s) in Hz. Proton-decoupled carbon nuclear magnetic resonance ( 13 C-NMR) spectra were recorded on a Varian VNMRS-500 MHz and a Varian VNMRS-400 MHz and are reported in ppm using the solvent as an internal standard (CDCl 3 at 77.0 ppm). Mass spectra were recorded on a Finnigan LCQ-DUO mass spectrometer. trans-4-Hydroxy-L-proline and (S)-(-)-indoline-2-carboxylic acid were purchased from commercial sources and used as received. The aldehydes were purified either by distillation or by recrystallization prior to use. Products 2a 2 , 2b 3 , 2c 3 , 2e 2 , 2j 2 , 2l 1 , 2m 5 , 2p 6 , 2q 4 , 8a 4 were previously reported and their published characterization data matched ours in all respects. General Procedure: A 10 mL microwave reaction tube was charged with aldehyde (1.0 mmol, 1.0 equiv), trans-4-hydroxy-L-proline (0.157 g, 1.2 mmol, 1.2 equiv), toluene (0.5 M, 2.0 mL), and benzoic acid (0.024 g, 0.2 mmol, 0.2 equiv). A 10 x 8 mm SiC passive cylindrical heating element was carefully added on its side to the reaction tube. The reaction tube was sealed with a Teflon-lined snap cap, and heated in the microwave reactor at 240 ºC (200 W, 50-170 psi) for the appropriate time. After cooling with compressed air flow, the crude reaction mixture was diluted with EtOAc (5 mL) and washed with saturated aqueous NaHCO 3 (3 x 5 mL). The aqueous layers were extracted with EtOAc (3 x 5 mL) and the combined organic layers dried over anhydrous Na 2 SO 4 . The solvent was removed in vacuo and the product was purified by flash silica gel column chromatography. Electronic Supplementary Material (ESI) for Chemical Communications This journal is
. :2 • Rhaleb Zayer, Daniel Mlakar, Markus Steinberger, Hans-Peter Seidel We drop the assumption that tessellation cells need to be separated by lines. ...arXiv:1804.09152v1 fatcat:mepiayw76ngzznozeoxdduiyhy
Type-based reasoning is popular in functional programming. In particular, parametric polymorphism constrains functions in such a way that statements about their behavior can be derived without consulting function definitions. Is the same possible in a strongly, and polymorphically, typed functional logic language? This is the question we study in this paper. Logical features like nondeterminism and free variables cause interesting effects, which we examine based on examples and address bydoi:10.1145/1816027.1816035 fatcat:4q5jwn3g4fdkhlqiafuo2es56q
more »... fying appropriate conditions that guarantee standard free theorems or inequational versions thereof to hold. We see this case study as a stepping stone for a general theory, not provided here, involving the definition of a logical relation and other machinery required for parametricity arguments appropriate to functional logic languages.
The direct α-arylation/N-alkylation of cyclic amines was achieved in a redox-neutral fashion under mild conditions. Transformations occur in the absence of any additives or are promoted by simple carboxylic acids. Redox-neutral 1 approaches to the α-functionalization of amines offer attractive alternatives to the more prevalent oxidative variants. 2 With regard to the mechanism of these reactions, the majority of redox-neutral amine α-functionalizations involve hydride-shifts or sigmatropicdoi:10.1021/ol403431u pmid:24328366 pmcid:PMC3946350 fatcat:ketfialgkzedrmrx5fnsrra3rm
more »... ansfer steps. 3 As part of a broader effort, our group has developed a number of reactions in which amine α-functionalization is accomplished via a different approach that features azomethine ylides as reactive intermediates (Scheme 1). 4,5,6 Here we report a strategy that enables the redox-neutral α-arylation of simple cyclic amines. Our approach to the redox-neutral α-functionalization of amines involves the condensation of a secondary amine (e.g., pyrrolidine) with an aldehyde to give intermediates 1/1′ (Scheme 1). These species undergo redox-isomerization via azomethine ylide 3 to provide intermediates 4/4′ which are ultimately captured with a nucleophile HNu to yield αfunctionalized amine 5. The difficulty in realizing such transformations lies in the wellestablished propensity of species 1/1′ to undergo classic organic reactions (e.g., Strecker, Mannich, Kabachnik-Fields reaction, Friedel-Crafts alkylation, alkynylation, etc.). In previous work, we have successfully averted the classic reaction pathway by employing appropriate catalysts such as carboxylic acids or copper carboxylates in combination with sterically demanding aldehydes (e.g., 2,6-dichlorobenzaldehyde, mesitaldehyde). In favorable cases (α-cyanation 4f and α-phosphine oxide formation 4j ) compounds 2 can undergo equilibration to the apparently thermodynamically more stable regioisomers 5. This finding enabled the use of simple aromatic aldehydes as reaction partners. We commenced our efforts toward the development of a redox-neutral amine αarylation 7, 8, 9, 10, 11 by exposing a mixture of pyrrolidine, 2,6-dichlorobenzaldehyde, βnaphthol and benzoic acid (20 mol %) to reflux in toluene (Scheme 2). Remarkably, the
Acknowledgment We are grateful to the current and former members of the Seidel research group who have contributed to the development of this field. ... Commun. (28d) Seidel, Org. ... Classic condensation-based transformations (29a) Seidel, J. Am. Chem. Soc. 2012, 134, 15305. Reviews (29p) Seidel, Org. Chem. Front. 2014, 1, 426. (29q) Seidel, Acc. Chem. ...doi:10.1055/s-0040-1706051 pmid:34825124 pmcid:PMC8612105 fatcat:h65vbaizhjgerils5cfkol4jza
Lecture Notes in Computer Science
Disproof can be as important as proof in studying programs and programming languages. In particular, side conditions in a statement about program behavior are sometimes best understood and explored by trying to exhibit a falsifying example in the absence of a condition in question. Automation is as desirable for such falsification as it is for verification. We develop formal and implemented tools for counterexample generation in the context of free theorems, i.e., statements derived fromdoi:10.1007/978-3-642-12251-4_14 fatcat:wmhuq4abb5f2zojybk54vr6yk4
more »... phic typesà la relational parametricity. The machinery we use is rooted in constraining the type system and in intuitionistic proof search.
Experimental procedures and characterization data (PDF) ■ AUTHOR INFORMATION Corresponding Author *E-mail: email@example.com. Notes The authors declare no competing financial interest. ...doi:10.1021/acs.orglett.6b00151 pmid:26895555 pmcid:PMC4782176 fatcat:iciwqz57gzhutpyg5gomkfu35i
This is similar to an approach developed by Daniels et al. (21) , which only recently became available. ... Seidel, unpublished) . Subsequently the DNA fragment was ligated as described above to labeled attachment handles cut with BsrGI and PspOMI. ...doi:10.1016/j.bpj.2009.12.4292 pmid:20371326 pmcid:PMC2849096 fatcat:dhio4h4flrfdbchbezwma4key4
Again this conjecture was proved by Seidel in  , and it means that we are able to give a complete, and fairly explicit, classification in terms of the possible values of O(G). ...doi:10.1016/j.ejc.2011.04.004 fatcat:o6tyiyvfmbfdlfp7dzv5rwoeiq
Seidel 1 . 1 ...doi:10.1016/j.bpj.2012.11.1475 fatcat:x4onyzkasrgo3dchj7kxu3cv7a
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