This monograph proves that any finite random number sequence is represented by the multiplicative congruential (MC) way. It also shows that an MC random number generator (d, z) formed by the modulus d and the multiplier z should be selected by new regular simplex criteria to give random numbers an excellent disguise of independence. The new criteria prove further that excellent subgenerators (d1,z1) and (d2,z2) with coprime odd submoduli d1 and d2 form an excellent combined generator (d = d1d2,z) with high probability by Sunzi’s theorem of the 5th-6th centuries (China), contrasting the fact that such combinations could never be found with MC subgenerators selected in the 20th-century criteria. Further, a combined MC generator (d = d1d2,z) of new criteria readily realizes periods of 252 or larger, requiring only fast double-precision arithmetic by powerful Sunzi’s theorem. We also obtain MC random numbers distributed on spatial lattices, say two-dimensional 4000 by 4000 lattices which may be tori, with little pair correlations of random numbers across the nearest neighbors. Thus, we evade the problems raised by Ferrenberg, Landau, and Wong.

This monograph proves that any finite random number sequence is represented by the multiplicative congruential (MC) way. It also shows that an MC random number generator (d, z) formed by the modulus d and the multiplier z should be selected by new regular simplex criteria to give random numbers an excellent disguise of independence. The new criteria prove further that excellent subgenerators (d1,z1) and (d2,z2) with coprime odd submoduli d1 and d2 form an excellent combined generator (d = d1d2,z) with high probability by Sunzi’s theorem of the 5th-6th centuries (China), contrasting the fact that such combinations could never be found with MC subgenerators selected in the 20th-century criteria. Further, a combined MC generator (d = d1d2,z) of new criteria readily realizes periods of 252 or larger, requiring only fast double-precision arithmetic by powerful Sunzi’s theorem. We also obtain MC random numbers distributed on spatial lattices, say two-dimensional 4000 by 4000 lattices which may be tori, with little pair correlations of random numbers across the nearest neighbors. Thus, we evade the problems raised by Ferrenberg, Landau, and Wong.

Designed for teaching, this English translation of the tried and tested Organometallic Chemistry 2/e textbook from the Japan Society of Coordination Chemistry can be used as an introductory text for chemistry undergraduates and also provide a bridge to more advanced courses. The book is split into two parts, the first acts as a concise introduction to the field, explaining fundamental organometallic chemistry. The latter covers cutting edge theories and applications, suitable for further study.

Beginning with fundamental reaction patterns concerning bonds between transition metals and carbon atoms, the authors show how these may be combined to achieve a desired reaction and/or construct a catalytic cycle. To understand the basics and make effective use of the knowledge, numerous practice questions and model answers to encourage the reader’s deeper understanding are included.

The advanced section covers the chemistry relating to bonds between transition metals and main group elements, such as Si, N, P, O and S, is described. This chemistry has some similarities to transition metal-carbon chemistry, but also many differences and unique aspects, which the book explains clearly.

Organometallic complexes are now well known and widely used. In addition, transition metal complexes with main group element other than carbon as a ligating atom are becoming more important. It is thus important to have a bird’s-eye view of transition metal complexes, regardless of the ligand type. This book acts as solid introduction for chemistry students and newcomers in various fields who need to deal with transition metal complexes.

Designed for teaching, this English translation of the tried and tested Organometallic Chemistry 2/e textbook from the Japan Society of Coordination Chemistry can be used as an introductory text for chemistry undergraduates and also provide a bridge to more advanced courses. The book is split into two parts, the first acts as a concise introduction to the field, explaining fundamental organometallic chemistry. The latter covers cutting edge theories and applications, suitable for further study.

Beginning with fundamental reaction patterns concerning bonds between transition metals and carbon atoms, the authors show how these may be combined to achieve a desired reaction and/or construct a catalytic cycle. To understand the basics and make effective use of the knowledge, numerous practice questions and model answers to encourage the reader’s deeper understanding are included.

The advanced section covers the chemistry relating to bonds between transition metals and main group elements, such as Si, N, P, O and S, is described. This chemistry has some similarities to transition metal-carbon chemistry, but also many differences and unique aspects, which the book explains clearly.

Organometallic complexes are now well known and widely used. In addition, transition metal complexes with main group element other than carbon as a ligating atom are becoming more important. It is thus important to have a bird’s-eye view of transition metal complexes, regardless of the ligand type. This book acts as solid introduction for chemistry students and newcomers in various fields who need to deal with transition metal complexes.

This monograph proves that any finite random number sequence is represented by the multiplicative congruential (MC) way. It also shows that an MC random number generator (d, z) formed by the modulus d and the multiplier z should be selected by new regular simplex criteria to give random numbers an excellent disguise of independence. The new criteria prove further that excellent subgenerators (d1,z1) and (d2,z2) with coprime odd submoduli d1 and d2 form an excellent combined generator (d = d1d2,z) with high probability by Sunzi’s theorem of the 5th-6th centuries (China), contrasting the fact that such combinations could never be found with MC subgenerators selected in the 20th-century criteria. Further, a combined MC generator (d = d1d2,z) of new criteria readily realizes periods of 252 or larger, requiring only fast double-precision arithmetic by powerful Sunzi’s theorem. We also obtain MC random numbers distributed on spatial lattices, say two-dimensional 4000 by 4000 lattices which may be tori, with little pair correlations of random numbers across the nearest neighbors. Thus, we evade the problems raised by Ferrenberg, Landau, and Wong.

This monograph proves that any finite random number sequence is represented by the multiplicative congruential (MC) way. It also shows that an MC random number generator (d, z) formed by the modulus d and the multiplier z should be selected by new regular simplex criteria to give random numbers an excellent disguise of independence. The new criteria prove further that excellent subgenerators (d1,z1) and (d2,z2) with coprime odd submoduli d1 and d2 form an excellent combined generator (d = d1d2,z) with high probability by Sunzi’s theorem of the 5th-6th centuries (China), contrasting the fact that such combinations could never be found with MC subgenerators selected in the 20th-century criteria. Further, a combined MC generator (d = d1d2,z) of new criteria readily realizes periods of 252 or larger, requiring only fast double-precision arithmetic by powerful Sunzi’s theorem. We also obtain MC random numbers distributed on spatial lattices, say two-dimensional 4000 by 4000 lattices which may be tori, with little pair correlations of random numbers across the nearest neighbors. Thus, we evade the problems raised by Ferrenberg, Landau, and Wong.

Designed for teaching, this English translation of the tried and tested Organometallic Chemistry 2/e textbook from the Japan Society of Coordination Chemistry can be used as an introductory text for chemistry undergraduates and also provide a bridge to more advanced courses. The book is split into two parts, the first acts as a concise introduction to the field, explaining fundamental organometallic chemistry. The latter covers cutting edge theories and applications, suitable for further study.

Beginning with fundamental reaction patterns concerning bonds between transition metals and carbon atoms, the authors show how these may be combined to achieve a desired reaction and/or construct a catalytic cycle. To understand the basics and make effective use of the knowledge, numerous practice questions and model answers to encourage the reader’s deeper understanding are included.

The advanced section covers the chemistry relating to bonds between transition metals and main group elements, such as Si, N, P, O and S, is described. This chemistry has some similarities to transition metal-carbon chemistry, but also many differences and unique aspects, which the book explains clearly.

Organometallic complexes are now well known and widely used. In addition, transition metal complexes with main group element other than carbon as a ligating atom are becoming more important. It is thus important to have a bird’s-eye view of transition metal complexes, regardless of the ligand type. This book acts as solid introduction for chemistry students and newcomers in various fields who need to deal with transition metal complexes.

Designed for teaching, this English translation of the tried and tested Organometallic Chemistry 2/e textbook from the Japan Society of Coordination Chemistry can be used as an introductory text for chemistry undergraduates and also provide a bridge to more advanced courses. The book is split into two parts, the first acts as a concise introduction to the field, explaining fundamental organometallic chemistry. The latter covers cutting edge theories and applications, suitable for further study.

Beginning with fundamental reaction patterns concerning bonds between transition metals and carbon atoms, the authors show how these may be combined to achieve a desired reaction and/or construct a catalytic cycle. To understand the basics and make effective use of the knowledge, numerous practice questions and model answers to encourage the reader’s deeper understanding are included.

The advanced section covers the chemistry relating to bonds between transition metals and main group elements, such as Si, N, P, O and S, is described. This chemistry has some similarities to transition metal-carbon chemistry, but also many differences and unique aspects, which the book explains clearly.

Organometallic complexes are now well known and widely used. In addition, transition metal complexes with main group element other than carbon as a ligating atom are becoming more important. It is thus important to have a bird’s-eye view of transition metal complexes, regardless of the ligand type. This book acts as solid introduction for chemistry students and newcomers in various fields who need to deal with transition metal complexes.