TAILIEUCHUNG - THE AMERICAN MATHEMATICAL MONTHLY VOLUME 107

In the third century of the Common Era (CE), when Rome dominated not only Europe, but also North Africa and the Near East, it was able to deploy fifty legions throughout the empire. In this forward defense strategy even the furthermost areas of the empire were secured by the on-site presence of an adequate number of legions of the Roman army. However, the empire had lost much of its muscle by the fourth century CE and the forces of Rome had diminished to only about twenty-five legions. It had thus become impossible to station legions in sufficient strength at all of the forward positions of the empire without. | Mo AMERICAN MATHEMATICAL NT HLY Volume 107 Number 7 August-September 2000 Charles s. ReVelle Kenneth E. Rosing Defenders Imperium Romanum A Classical Problem in Military strategy 585 Bruce c. Berndt Robert A. Rankin The Books studied by Ramanujan in India 595 Rajendra Bhatia Pinching Trimming Truncating and Averaging of Matrices 602 Gerald Beer When Is a Family of Sets a Family of Bounded Sets 609 David s. Moore George w. Cobb Statistics and Mathematics Tension and Cooperation 615 NOTES Jonathan Pakianathan Krishnan Shankar Nilpotent Numbers 631 Tom Jenkyns Eric Muller Triangular Triples from Ceilings to Floors 634 Rodney Nillsen Normal Numbers Without Measure Theory 639 THE EVOLUTION OF. M. M. Postnikov The Problem of Squarable Lunes 645 PROBLEMS AND SOLUTIONS 652 REVIEWS CoIm Mulcahy Jerrold w. Grossman Life by the Numbers. By Keith Devlin Small Worlds The Dynamics of Networks between Order and Randomness. By Duncan J. Watts 661 664 TELEGRAPHIC REVIEWS 669 Lester R. Ford Awards for 1999 672 AN OFFICIAL PUBLICATION OF THE MATHEMATICAL ASSOCIATION OF AMERICA NOTICE TO AUTHORS The MONTHLY publishes articles as well as notes and Other features about mathematics and the profession. Its readers span a broad spectrum of mathematical interests and include professional mathematicians as well as students of mathematics at all collegiate levels. Authors are invited to submit articles and notes that bring interesting mathematical ideas to a wide audience of MONTHLY readers. The Monthly s readers expect a high standard of exposition they expect articles to inform stimulate challenge enlighten and even entertain. MONTHLY articles are meant to be read enjoyed and discussed rather than just archived. Articles may be expositions of old or new results historical or biographical essays speculations or definitive treatments broad developments or explorations of a single application. Novelty and generality are far less important than clarity of exposition and broad appeal. .

• Toán học
• Defendens Imperium
• Military Strategy
• Averaging of Matrices
• Nilpotent Numbers
• Triangular Triples
• Measure Theory
• probability
• theory
• measure
• lectures
• Fundamental
• Capacity
• Harmonic measure
• Elementary theory
• The Schiffer variation
• Extremal length
• Loewners method
• Markov chain
• Maximum likelihood principle
• Measure of entropy
• Redundancy test
• Shannon‟s information theory
• Transitional probabilities
• BMC Cancer
• Gastric cancer
• Patient reported outcome
• Classical test theory
• Item response theory
• Minimal clinically important difference
• Risk measure
• Investment portfolio
• Value at Risk
• Expected shortfall
• Spectral risk measures
• Distortion theory
• báo cáo của tạp chí Journal of Operator Theory
• tài liệu báo cáo nghiện cứu khoa học
• cách trình bày báo cáo
• kiến thức toán học
• báo cáo toán học
• tài liệu báo cáo nghiên cứu khoa học
• Manuals for thesaurus construction
• Guidelines for thesaurus construction
• Aristotelian model of classification
• The classification of knowledge
• Software evaluation theory models
• Validity and reliability testing
• WC–Banach algebra
• Fixed point theorems
• Weak topology
• Measure of weak noncompactness
• Banach’s contraction principle
• Lecture Software engineering
• Software engineering
• Software metrics
• Why measure software
• Fundamentals of measurement theory
• Use case points
• Control theory
• Approximate reasoning
• Measure of fuzziness
• Earthquake engineering
• Hedge algebra
• Adolescent psychiatry
• Mental health
• Ecological systems theory
• Voluntary random sampling method
• Measure psychological well being
• BMC Bioinformatics
• DNA methylation
• Genomic feature analysis
• Information theory
• Mutual Information
• Gene ranking
• Methylation analysis
• Genome Biology
• Random matrix theory
• Cell phenotypes
• Single cell transcriptomes
• Non random substructure
• Medical and Scientific
• Scientific Applications
• Bioengineered Skin
• Skin Biopsy
• Environmental Research
• measure Fish Coloration