Comprehensive Organic Name Reactions and Reagents Vol.2 書角輕微擠壓
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【簡介】
With over 850 listings, Comprehensive Organic Name Reactions and Reagents is the most comprehensive collection of name reactions and reagents available today. Information provided on each reaction includes a description of the reaction, the reaction scheme, a brief bio of the person(s) for which the reaction is named, proposed mechanisms, modifications (if applicable), applications, related reactions (if applicable), experimental examples, and references to primary literature. With several indices, this is the definitive reference that helps bench chemists and students navigate the growing number of name reactions and reagents.
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Comprehensive Organic Name Reactions and Reagents Vol:1 書角輕微擠壓
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【簡介】
With over 850 listings, Comprehensive Organic Name Reactions and Reagents is the most comprehensive collection of name reactions and reagents available today. Information provided on each reaction includes a description of the reaction, the reaction scheme, a brief bio of the person(s) for which the reaction is named, proposed mechanisms, modifications (if applicable), applications, related reactions (if applicable), experimental examples, and references to primary literature. With several indices, this is the definitive reference that helps bench chemists and students navigate the growing number of name reactions and reagents.
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COMPREHENSIVE SUMMARY OF THE BENFORD\'S LAW PHENOME
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Numbers are written in our digital language system by conveniently and efficiently utilizing the ten digits 0 to 9 in much the same way as sentences and books are written in the English language system by conveniently utilizing the 26 letters A to Z. Surprisingly, and against all common sense or intuition, the spread of these ten digits within numbers of random data is not uniform, but rather highly uneven. Benford's Law predicts that the first digit on the left-most side of numbers is proportioned between all possible digits 1 to 9 approximately according to LOG(1 + 1/digit), so that occurrences of low digits such as {1, 2, 3} in the first position are much more frequent than occurrences of high digits such as {7, 8, 9}. Remarkably, Benford's Law is found to be valid in almost all real life statistics, from data relating to physics, astronomy, chemistry, geology, and biology to data relating to economics, accounting, finance, engineering, and governmental census information. Therefore, Benford's Law stands as the only common thread running through and uniting all scientific disciplines!
This book represents an intense and concentrated effort by the author to narrate this digital, numerical, and quantitative story of the Benford's Law phenomenon as briefly and as concisely as possible, while still ensuring a comprehensive coverage of all its aspects, results, causes, explanations, and perspectives. The most recent research results and discoveries in this field are included within this book in such a way as to be comprehensible and engaging to readers of all proficiencies.
Errata(s)
Errata (177 KB)
Sample Chapter(s)
Sample of Section I: The Digits Phenomenon
Contents:
About the Author
Introduction
The Digits Phenomenon:
The First Digit on the Left Side of Numbers
Benford's Law and the Predominance of Low Digits
Second-Digits and Third-Digits Distributions
The Quantitative Origin of the Digital-Numerical Phenomenon
The Scale Invariance Principle
The Base Invariance Principle
Physical Order of Magnitude of Data
Robust Measure of Physical Order of Magnitude
Two Essential Requirements for Benford Behavior
Sum of Squared Deviations Measure
The Mistaken Use of the Chi-Square Test in Benford's Law
Causes and Explanations:
Multiplication Processes Lead to Positive Skewness and Often to Benford
Addition Processes Lead to the Symmetrical Normal away from Benford
The Multiplicative Central Limit Theorem and Lognormal Distribution
Multiplications are More Prevalent than Additions in Real-Life Data
Tugs of War between Addition and Multiplication
Partitions Typically Lead to Positive Skewness and Often to Benford
One-Dimensional Random Staged Partition
One-Dimensional Chaotic Repeated Partition
One-Dimensional Random Real Partition
Two-Dimensional Random Partition
The General Requirements for Partitions to Converge to Benford
Benford Model for Planet and Star Formations
Consolidation and Fragmentation Processes
Random Exponential Growth Leads to Positive Skewness and Benford
Data Aggregation Leads to Positive Skewness and Often to Benford
Chains of Statistical Distributions and Benford's Law
Meta-Explanation or the Explanation of all Explanations
The Logarithmic Perspective:
Benford's Law as Uniformity of Mantissa
Rising or Falling Mantissa Distributions
Uniqueness of k/x Distribution and Its Central Role in Benford's Law
Related Log Conjecture
The Random and Deterministic Flavors in Benford's Law
The Great Prevalence of the Digital Development Pattern in Data
The Absence of the Digital Development Pattern in k/x Distribution
Benford's Law in Its Purest Form
Constant Base Raised to a Random Power
General Results:
General Results in Benford's Law
First Two Digits versus Last Two Digits
The Law of Relative Quantities:
The Relating Concepts of Digits, Numbers, and Quantities
The Arbitrariness of our Positional Number System
Two Radically Different Interpretations of the Benford Phenomenon
The Quest for a Universal and Number-System-Invariant Measure
The Shape and Nature of Histograms are Number-System Invariant
Constructing a Three-Bin Histogram Signifying Small, Medium, and Big
Constructing a Set of Infinitely Expanding Histograms
Numerical Consistency in Bin Schemes for 15 Real-Life Data Sets
The Postulate on Relative Quantities
Application of the Postulate via Generic Bin Scheme on k/x
The Infinite Sequence Result for the Bin Scheme on k/x
The General Law of Relative Quantities
Benford's Law as a Special Case and Direct Consequence of GLORQ
The Universal Law of Relative Quantities
Benford Second-Order Digits Interpreted as an Irregular Bin Scheme
Concluding Historical and Conceptual Perspectives
Appendices:
Infinite Sequence Reduction
Data Sets
Glossary of Frequently Used Abbreviations
First Two Digits versus Last Two Digits
Index
Readership: This book is suitable for expert mathematicians, statisticians, and scientists, as well as university students of these disciplines. This book is also suitable for the layman, the non-expert, and the educated general public, who are not necessarily proficient in mathematics, statistics, and the sciences, but who have enough interest to still be able to understand the topic on the whole.
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