2.1.8. Michael Reaction 2245 2.1.9. Others 2247 2.2. Cyclization Reactions 2248 2.2.1. Carbon Diels−Alder Reactions 2248 2.2.2. Aza-Diels−Alder Reactions 2252 2.2.3. Other Hetero-Diels−Alder Reactions 2255 2.2.4. Ionic Diels−Alder Reaction 2256 2.2.5. 1,3-Dipolar Cycloadditions 2256 2.2.6. Other Cycloaddition Reactions 2258 2.2.7. Prins-type Cyclization 2259 2.3. Friedel−Crafts Acylation and Alkylation 2259 2.4. Baylis−Hillman Reaction 2263 2.5. Radical Addition 2264 2.6. Heterocycle Synthesis 2267 2.7. Diazocarbonyl Insertion 2270 3. C−X (X ) N, O, P, Etc.) Bond Formation 2271 3.1. Aromatic Nitration and Sulfonylation 2271 3.2. Michael Reaction 2272 3.3. Glycosylation 2273 3.4. Aziridination 2275 3.5. Diazocarbonyl Insertion 2276 3.6. Ring-Opening Reactions 2277 3.7. Other C−X Bond Formations 2280 4. Oxidation and Reduction 2280 4.1. Oxidation 2280 4.2. Reduction 2281 5. Rearrangement 2283 6. Protection and Deprotection 2285 6.1. Protection 2285 6.2. Deprotection 2288 7. Polymerization 2291 8. Miscellaneous Reactions 2291 9. Lanthanide(II) Triflates in Organic Synthesis 2295 10. Conclusion 2295 11. Acknowledgment 2295 12. References 2295

Rare-earth metal triflates in organic synthesis

Serine palmitoyltransferase, a key enzyme of sphingolipid metabolism.

6.1. Oxadiazoles 4154 6.2. Diazaphospholes 4154 7. Six-Membered Heterocycles with One Heteroatom 4155 7.1. Pyridines 4155 7.2. Pyridinones 4155 7.3. Quinolines 4156 7.4. Quinolinones 4157 7.5. Isoquinolines 4157 7.6. Acridines 4158 7.7. Pyranones 4158 7.8. Flavones 4159 8. Six-Membered Heterocycles with Two Heteroatoms 4159 8.1. Pyridazinones 4159 8.2. Pyrimidines 4159 8.3. Pyrimidinones 4160 8.4. Quinazolines 4162 8.5. Quinazolinones 4162 8.6. Quinoxalines 4164 8.7. Quinoxalinediones 4165 8.8. Oxazines 4165 8.9. Oxazinones 4166 8.10. Thiazines 4166 9. Six-Membered Heterocycles with Three Heteroatoms 4166

Solvent-free heterocyclic synthesis.

2.1.5. Electrophilic Attack on CdC 3994 2.1.6. NH Insertions in Diazo Compounds 3994 2.1.7. Pd Catalyzed Cyclizations 3994 2.2. Cyclizations by C-C Bond formation 3995 2.2.1. Nucleophilic Displacement of Halides 3995 2.2.2. Cyclizations Involving CdO Group 3995 2.3. Cycloadditions 3996 2.4. Ring Rearrangements 3997 2.4.1. Rearrangements of Four-Membered Rings 3997 2.4.2. Rearrangements of Larger Rings 3998 2.5. Reduction of Azetidin-2-ones 3998 2.6. Miscellaneous Syntheses 3999 2.7. Important Classes of Compounds 4000 2.7.1. Natural Products 4000 2.7.2. Azetidine Carboxylic Acids 4001 2.7.3. Exomethylene Azetidines 4002 2.7.4. Ligands for Metal-Catalyzed Reactions and Chiral Auxiliaries 4003

Novel syntheses of azetidines and azetidinones.

Preface 1. Quantum measurement theory 2. Useful concepts from information theory 3. Continuous measurement 4. Statistical mechanics, open systems, and measurement 5. Quantum feedback control 6. Metrology 7. Quantum mesoscopic systems I: circuits and measurements 8. Quantum mesoscopic systems II: measurement and control Appendices References Index.

Quantum Measurement Theory and its Applications

In Chapter 1 a very brief and rapid review of some basic topics in Jensen's inequality for positive linear maps and Kantorovich inequality for several types are given. Some basic ideas and the viewpoints of the Mond-Peceric method are given. In Chapter 2 general converses of Jensen's inequality are considered. The Mond-Peceric method is used to obtain the bounds. Many interesting inequalities are particularly considered. In Chapter 3 a generalization of a theorem of Li-Mathias for the normalized positive linear maps as an application of the Mond-Peceric method is considered. Lower and upper bounds in converses of Jensen's type inequalities are given. The cases of the sharp inequalities are investigated. The conversions of Jensen's inequality and other inequalities are particularly considered. In Chapter 4 the previous results and the same methods are applied to obtain the inequalities for the means. Reverse inequalities of power operator means on positive linear maps are studied. Several properties of power operator means under the chaotic order are considered. New bounds in inequalities for power operator means are given. In chapter 5 the theory of operator means established by Kubo and Ando assocaiated with the operator monotone functions is introduced. Based on complementary inequalities to Jensen's inequalities on positive linear maps, complementary inequalities to Ando's inequalities assocaiated with operator means are studied. In Chapter 6 the results and the same methods in the chapter 2 are applied to obtain the inequalities for the Hadamard product. Then the reverses inequalities on the Hadamard product of operators and operator means are considered. General inequalities for the Hadamard product of operators are observed. In chapter 7 a brief survey of several applications of both Furuta inequality and generalized Furuta inequality is given. In Chapter 8 the claims preserving the operator order and the chaotic order are considered as an application of the Mond-Peceric method. The overall results on the functions which preserve the operator order and the chaotic order are particularly considered.

Mond-Pecaric Method in Operator Inequalities

Extension of the furuta inequality and Ando-Hiai log-majorization

Operator inequalities associated with Hölder–McCarthy and Kantorovich inequalities

Furuta's inequality and its application to Ando's theorem

A ≥ B ≥ 0 assures (B r A p B r )1/q ≥ B(p+2r)/q for r ≥ 0, p ≥ 0, q ≥ 1 with (1 + 2r)q ≥ (p + 2r). This is Furuta’s inequality. In this paper, we show that Furuta’s inequality can be applied to estimate the value of the relative operator entropy and also this inequality can be applied to extend Ando’s result.

Takayuki Furuta

Papers

Mond-Pecaric Method in Operator Inequalities

Extension of the furuta inequality and Ando-Hiai log-majorization

Operator inequalities associated with Hölder–McCarthy and Kantorovich inequalities

Furuta's inequality and its application to Ando's theorem

Applications of Order Preserving Operator Inequalities