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This chapter focuses on the fact that in certain dialects of Dutch the polarity markers yes and no can be accompanied by subject clitics and/or agreement suffixes. Just as in the previous chapter, there are many empirical similarities between this construction and Short Do Replies. This chapter argues that the structure underlying conjugated instances of yes and no is in fact a Short Do Reply that has been PF-deleted. As such, this construction combines PF-deletion and pro. The chapter also provides an account for the absence of clitics and (complementizer) agreement endings under sluicing.

This chapter applies the group theoretic technique introduced in Chapter 6 to a number of chemically interesting problems. These problems include molecular orbital treatment of AH _n (n = 2-6) molecules and cyclic conjugated polyenes (with and without d-orbital participation), construction of hybrid orbitals, relationship between molecular orbital and hybridization theories, molecular vibrations, etc. A large number of worked examples have been selected to illustrate that group theory can be used to simplify the physical problem and yield solutions of chemical significance. The advantage of this method becomes more obvious when the symmetry of the chemical system increases. Indeed, for highly symmetric molecules, very complex problems can have simple and elegant solutions. Even for less symmetric systems, symmetry arguments can still lead to meaningful results and conclusions that cannot be easily obtained otherwise.

This chapter presents the basic concepts and tools that are useful for modelling and for Bayesian inference. It defines density kernels useful for simplifying notation and computations and explains the likelihood principle and its implications for the Bayesian treatment of nuisance parameters. It discusses the notion of natural conjugate inference, which is an important tool of Bayesian analysis in the case of the exponential family, and provides details on the natural conjugate framework.

This chapter examines prior densities applicable for the regression model. It addresses the question of how to specify precisely the shape and the contents of the prior density in an empirical application and defines the concept of non-informative prior. It explains the restrictive properties of the natural conjugate prior in the regression model and discusses issues concerning the treatment of exact restrictions and exchangeable prior densities.

Reduction of SU(n) tensors is described. Conjugate representations are identified. The dimension of the totally symmetric and totally antisymmetric tensors is obtained. All irreducible SU(n) tensors of rank r are described in detail for r equal to 2, 3 and 4. These results are specialized for n equal to 2 and 3. The most general irreducible representation of SU(n) corresponding to the partition (f ₁, f ₂, …, f_n ) can be specified by the n–1 integers p_k = f_k – f_{k +1}, 1 ≤ k ≤ n–1, and a formula is given for its dimension. The reduction of the Kronecker product of two irreducible representations of SU(n) is described. Biographical notes on Kronecker are given.

Reality properties of spinors are described by defining conjugate, self-conjugate and complex representations. Two types of self-conjugate representations are identified and named orthogonal and symplectic. It is shown that the semispinors of so(8k) and the spinors of so(8k±1) are orthogonal, the semispinors of so(8k±2) are complex, and the spinors of so(8k±3) and the semispinor of so(8k+4) are symplectic.

Every variable (function) on the phase space has a conjugate variable. If the action is independent of a variable, then its conjugate is a conserved quantity. Energy (Hamiltonian) is shown to be conserved. A digression applies this method to solve the problem for a minimal surface of revolution (catenary).

There are three main paradigms used to study memory in nonverbal (primarily human) organisms: visual habituation, mobile conjugate reinforcement paradigm, and deferred and elicited imitation. This chapter reviews the research in each of these three areas and what they tell us about the development of very early memory. Along the way, evidence about whether these tasks can be used to distinguish between implicit (not consciously accessible) and explicit (consciously accessible) memory is discussed.

Jaesook Yun of Sungkyunkwan University devised (J. Org. Chem. 2009, 74, 4232) a method, based on conjugate addition to a cyano alkyne, for the preparation of nitriles such as 1 with high geometric control. Enantioselective conjugate reduction then delivered the doubly arylated stereogenic center of 2 in high ee. Pher G. Andersson of Uppsala University described (J. Am. Chem. Soc. 2009, 131, 8855) a similar approach to diarylated ternary stereogenic centers. Motomu Kanai and Masakatsu Shibasaki of the University of Tokyo developed (J. Am. Chem. Soc. 2009, 131, 3858) a complementary approach to dialkylated stereogenic centers based on enantioselective conjugate cyanation of α-methylene N-acylpyrroles such as 3. Cathleen M. Crudden of Queen’s University established (J. Am. Chem. Soc. 2009, 131, 5024) that a benzylic organoborane, prepared by enantioselective hydroboration of styrene, coupled with an aryl iodide such as 6 in good yield and with > 90% retention of ee. Kwunmin Chen of National Taiwan Normal University devised ( Adv. Synth. Cat. 2009, 351, 1273) an organocatalyst for the enantioselective Michael addition of an α,α,-dialkyl aldehyde such as 9 to a nitroalkene. Wenhu Duan of the East China University of Science and Technology and Wei Wang of the University of New Mexico together developed (Organic Lett. 2009, 11, 2864) an organocatalyst for the enantioselective addition of nitromethane 12 to an unsaturated ketone such as 11. Xiaodong Shi of West Virginia University found (Angew. Chem. Int. Ed. 2009, 48, 1279) that commercial diphenyl prolinol effectively promoted enantioselective conjugate addition of 15 to 14. Enantioselective methods for the construction of alkylated quaternary centers have also been put forward. Kin-ichi Tadano of Keio University devised (Tetrahedron Lett. 2009, 50, 1139) a glucose-derived chiral auxiliary that effectively directed the absolute sense of the alkylation of 17. Li Deng of Brandeis University reported (Tetrahedron 2009, 65, 3139) further details of his elegant Cinchona -mediated conjugate addition of 19 to 20. Francesca Marini of the Università degli Studi di Perugia extended (Adv. Synth. Cat. 2009, 351, 103) this approach to selenones, effecting, over two steps, enantioselective vinylation.

The complex tetracyclic alkaloid (-)-acutumine 3, isolated from the Asian vine Menispermum dauricum, shows selective T-cell toxicity. The two adjacent cyclic all-carbon quaternary centers of 3 offered a particular challenge. Steven L. Castle of Brigham Young University solved (J. Am. Chem. Soc. 2009, 131, 6674) this problem by effecting net enantioselective conjugate allylation of the enantiomerically pure substrate 1 to give 2 with high diastereocontrol. The starting coupling partners ( Organic Lett . 2006, 8, 3757; Organic Lett. 2007, 9, 4033) for the synthesis were the Weinreb amide 4, prepared over several steps from 2,3- dimethoxyphenol, and the diastereomerically- and enantiomerically-pure cyclopentenyl iodide 5, prepared by singlet oxygenation of cyclopentadiene followed by enzymatic hydrolysis. Transmetalation of 5 by the Knochel protocol, addition of the resulting organometallic to 4 and enantioselective (and therefore diastereoselective) reduction of the resulting ketone delivered the alcohol 6. Methods for installing cyclic halogenated stereogenic centers are not well developed. Exposure of the allylic alcohol to mesyl chloride gave the chloride 7 with inversion of absolute configuration. Remarkably, this chlorinated center was carried through the rest of the synthesis without being disturbed. A central step in the synthesis of 3 was the spirocyclization of 7 to 8. Initially, iodine atom abstraction generated the aryl radical. The diastereoselectivity of the radical addition to the cyclopentene was set by the adjacent silyloxy group. The α-keto radical so generated reacted with the Et3Al to give a species that was oxidized by the oxaziridine to the α-keto alcohol, again with remarkable diastereocontrol. Conjugate addition to the cyclohexenone 1 failed, so an alternative strategy was developed, diastereoselective 1,2-allylation of the ketone followed by oxy-Cope rearrangement. The stereogenic centers of 1 are remote from the cyclohexenone carbonyl, so could not be used to control the facial selectivity of the addition. Fortunately, the stoichiometric enantiomerically-pure Nakamura reagent delivered the allyl group preferentially to one face of the ketone 1, to give 9. The subsequent sigmatropic rearrangement to establish the very congested second quaternary center of 2 then proceeded with remarkable facility, at 0°C for one hour.

Mohammad Navid Soltani Rad of Shiraz University of Technology has shown (Tetrahedron Lett. 2007, 48, 6779) that with tosylimidazole (TsIm) activation in the presence of NaCN, primary, secondary and tertiary alcohols are converted into the corresponding nitriles. Gregory C. Fu of MIT has devised (J. Am. Chem. Soc. 2007, 129, 9602) a Ni catalyst that mediated the coupling of sp3-hybridized halides such as 3 with sp3-hybridized organoboranes such as 4, to give 5. Usually, carbanions with good leaving groups in the beta position do not couple efficiently, but just eliminate. Scott D. Rychnovsky of the University of California, Irvine has found (Organic Lett . 2007, 9, 4757) that initial protection of 6 as the alkoxide allowed smooth reduction of the sulfide and addition of the derived alkyl lithium to the amide 7 to give 8. Doubly-activated Michael acceptors such as 11 are often too unstable to isolate. J. S. Yadav of the Indian Institute of Chemical Technology, Hyderabad has shown (Tetrahedron Lett. 2007, 48, 7546) that Baylis-Hillman adducts such as 9 can be oxidized in situ, with concomitant Sakurai addition to give 12. Rather than use the usual Li or Na or K enolate, Don M. Coltart of Duke University has found (Organic Lett. 2007, 9, 4139) that ketones such as 13 will condense with amides such as 14 to give the diketone 15 on exposure to MgBr2. OEt2 and i -Pr2 NEt. Simultaneously, Gérard Cahiez of the Université de Cergy (Organic Lett. 2007, 9, 3253) and Janine Cossy of ESPCI Paris (Angew. Chem. Int. Ed. 2007, 46, 6521) reported that Fe salts will catalyze the coupling of sp2 -hybridized Grignard reagents such as 17 with alkyl halides. John Montgomery of the University of Michigan has described (J. Am. Chem. Soc. 2007, 129, 9568) the Ni-mediated regio- and enantioselective addition of an alkynes 20 to an aldehyde 19 to give the allylic alcohol 21. In a third example of sp2 - sp3 coupling, Troels Skrydstrup of the University of Aarhus has established (J. Org. Chem. 2007, 72, 6464) that Negishi coupling with alkenyl phosponates such as 23 proceeded efficiently.

Second-order conditions for both parameter optimization problems and optimal control problems are analysed. A new conjugate point test procedure is discussed and illustrated. For an optimal control problem we will examine the second variation of the cost. The first variation subject to constraints provides first-order NC for a minimum of J. Second-order conditions provide SC a minimum.

Fiber spinning is one of the oldest polymer processing operations that have contributed significantly to our society, especially after the commercialization of polyamide (nylon) synthetic fibers in the 1940s by DuPont Company. Subsequent commercialization of poly(ethylene terephthalate) (PET) and polyacrylonitrile fibers in the 1950s made the synthetic fiber industry very prosperous. For a given fiber-forming polymer, different spinning techniques can produce fibers possessing markedly different physical and/or mechanical properties. Thus, the fiber industry made continuous efforts through the 1960s and 1970s to modify existing processes and develop new ones. One very important breakthrough from such efforts emerged in the late 1970s, enabling one to melt spin at exceedingly high take-up speeds, widely known today as “high-speed melt spinning.” While the fiber manufacturers carefully guarded their spinning techniques, the commercial developments were documented in numerous patents. Beginning in the early 1960s, some fundamental studies on fiber spinning were reported in the open literature, and they are summarized in the three-volume monograph edited by Mark et al. (1967). An understanding of fiber spinning requires knowledge of momentum, energy, and/or mass transport. In addition, knowledge of macromolecular behavior under deformation (i.e., stretching) is also necessary for understanding such complicated problems as molecular orientation under stretching, crystallization kinetics under cooling, and fiber morphology as affected by spinning conditions. In the late 1950s, and the early 1960s, Ziabicki and coworkers (Ziabicki 1959, 1961; Ziabicki and Kedzierska 1959, 1960a, 1960b, 1962a, 1962b) made seminal contributions to a fundamental understanding of fiber-spinning processes, and their efforts were summarized in Ziabicki’s monograph (1976a). In the 1970s, a new class of synthetic fibers, known as “high-modulus wholly aromatic fibers,” was developed (Bair and Morgan 1972; Daniels et al. 1971; Frazer 1972; Kwolek 1971; Logullo 1971; Morgan et al. 1974) and subsequently commercialized with the trade name of Kevlar by DuPont (Kwolek 1971). The chemical structure of such synthetic fibers consists of rigid rodlike molecules that orient easily along the stretching direction during spinning, giving rise to high modulus in the spun fibers. The chemical structure and mechanical properties of the wholly aromatic fibers are well documented in the monograph edited by Black and Preston (1973).

Akiya Ogawa of Osaka Prefecture University found (Tetrahedron Lett. 2010, 51, 6580) that the Sm-mediated reductive coupling of a halide 1 with CO2 to give the carboxylic acid 2 was strongly promoted by visible light. Gregory C. Fu of MIT designed (Angew. Chem. Int. Ed. 2010, 49, 6676) a Ni catalyst for the coupling of a primary borane 4 with a secondary alkyl halide 3. James P. Morken of Boston College devised (Org. Lett. 2010, 12, 3760) conditions for the carbonylative conjugate addition of a dialkyl zinc to an enone 6 to give the 1,4-dicarbonyl product 7. Louis Fensterbank of the Institut Parisien de Chimie Moléculaire developed (Angew. Chem. Int. Ed. 2010, 49, 8721; not illustrated) a protocol for the conjugate addition of alkyl boranes to enones. Hyunik Shin of LG Life Science, Daejeon, and Sang-gi Lee of Ewha Womans University showed (Tetrahedron Lett. 2010, 51, 6893) that the intermediate from Blaise homologation of a nitrile 8 was a powerful nucleophile, smoothly opening an epoxide 10 to deliver 11. Sébastien Reymond and Janine Cossy of ESPCI ParisTech found (J. Org. Chem. 2010, 75, 5151) that FeCl3 smoothly catalyzed the coupling of an alkenyl Grignard 13 with the primary iodide 12. The Ti-mediated coupling of an alkyne 16 with an allylic alkoxide 15 (J. Am. Chem. Soc. 2010, 132, 9576) developed by Glenn C. Micalizio of Scripps/Florida was the key step in the total synthesis (J. Am. Chem. Soc. 2010, 132, 11422) of lehualide B. Huanfeng Jiang of the South China University of Technology observed (Chem. Commun. 2010, 46, 8049) that KI added to a bromoalkyne 18 to give the dihalide 19 with high geometric control. Haruhiko Fuwa of Tohoku University improved (Org. Lett. 2010, 12, 5354) the selective hydroiodination of a methyl alkyne 20 to 21. Takuya Kurahashi and Seijiro Matsubara of Kyoto University devised (Chem. Commun. 2010, 46, 8055) the Ni-catalyzed three-component coupling of an alkyne 22, methyl acrylate 23, and phenyl isocyanate to give the doubly homologated lactam 24. Patrick H. Toy of the University of Hong Kong showed (Synlett 2010, 1997; Org. Lett. 2010, 12, 4996 for a polymer with covalently attached base) that resin-bound triphenylphosphine participated efficiently in the Wittig coupling of 26 with an aldehyde 25.

Arene diazonium salts are effective precursors for the Heck reaction. Sandro Cacchi of the Università degli Studi “La Sapienza,” Roma, observed (Synlett 2009, 1277) that the diazonium salt generated in situ from 1 coupled with 2 to deliver the butenolide 3. Daniel J. Canney of Temple University established (Tetrahedron Lett. 2009, 50, 5914) conditions for the homologation of an alkenyl ester such as 4 to the homologated lactone 5. Tsutomu Katsuki of Kyushu University established (J. Am. Chem. Soc. 2009, 131, 14218) that Ir-mediated C-H insertion converted 6 into 8 with high diastereo- and enantiocontrol. Thomas J. J. Müller of the Heinrich-Heine-Universität, Düsseldorf, optimized ( Adv. Synth. Cat. 2009, 351, 2921) the Rh-mediated enantioselective cycloisomerization of 9 to 10. Santosh J. Gharpure of the Indian Institute of Technology, Madras, showed (Organic Lett. 2009, 11, 5466) that the intramolecular cyclopropanation of 11 proceeded with high diasterocontrol. Reduction of the intermediate cyclopropane then delivered the cyclic ether 12. Brian L. Pagenkopf of the University of Western Ontario optimized (Organic Lett. 2009, 11, 5614) the diastereoselective Co-catalyzed oxidative cyclization of 13 to 14. Mark C. Bagley and Andrew E. Graham of Cardiff University found (Tetrahedron Lett. 2009, 50, 6823) that microwave heating promoted the selective BaMnO4 oxidation of 1,3-, 1,4-, and 1,5-diols such as 15 to the corresponding lactones. David W. Lupton of Monash University developed (J. Am. Chem. Soc. 2009, 131, 14176) the remarkable cyclization of 17 to 19, catalyzed by the carbene precursor 18. Hirokazu Urabe of the Tokyo Institute of Technology showed (J. Am. Chem. Soc. 2009, 131, 3166) that the unusual Rh-catalyzed cyclization of an alkynyl sulfone 20 proceeded with substantial diastereocontrol, delivering the cyclic ether 21 as the major product. Jeffrey S. Johnson of the University of North Carolina established (J. Am. Chem. Soc. 2009, 131, 14202) that Sc(OTf)3 was a particularly efficient catalyst for the opening of 22 with 23 and then reclosure, leading to 24. Steven D. R. Christie and Gareth J. Pritchard of Loughborough University (Chem. Commun. 2009, 7339) and Michael A. Kerr of the University of Western Ontario (J. Org. Chem. 2009, 74, 8414) investigated related condensations.