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  • 1
    Keywords: Mathematical physics--Data processing. ; Electronic books.
    Type of Medium: Online Resource
    Pages: 1 online resource (174 pages)
    Edition: 1st ed.
    ISBN: 9781483138305
    Language: English
    Note: Front Cover -- Arithmetic Applied Mathematics -- Copyright Page -- Table of Contents -- Preface -- Chapter 1. Gravity -- 1.1 INTRODUCTION -- 1.2 GRAVITY -- Chapter 2. Long and Short Range Forces: Gravitation and Molecular Attraction and Repulsion -- 2.1 INTRODUCTION -- 2.2 GRAVITATION -- 2.3 BASIC PLANAR CONCEPTS -- 2.4 DISCRETE GRAVITATION AND PLANETARY MOTION -- 2.5 THE GENERALIZED NEWTON'S METHOD -- 2.6 AN ORBIT EXAMPLE -- 2.7 GRAVITY REVISITED -- 2.8 CLASSICAL MOLECULAR FORCES -- 2.9 REMARK -- Chapter 3. The N-body Problem -- 3.1 INTRODUCTION -- 3.2 THE THREE-BODY PROBLEM -- 3.3 CONSERVATION OF ENERGY -- 3.4 SOLUTION OF THE DISCRETE THREE-BODY PROBLEM -- 3.5 CENTER OF GRAVITY -- 3.6 CONSERVATION OF LINEAR MOMENTUM -- 3.7 CONSERVATION OF ANGULAR MOMENTUM -- 3.8 THE N-BODY PROBLEM -- 3.9 REMARK -- Chapter 4. Conservative Models -- 4.1 INTRODUCTION -- 4.2 THE SOLID STATE BUILDING BLOCK -- 4.3 FLOW OF HEAT IN A BAR -- 4.4 OSCILLATION OF AN ELASTIC BAR -- 4.5 LAMINAR AND TURBULENT FLUID FLOWS -- Chapter 5. Nonconservative Models -- 5.1 INTRODUCTION -- 5.2 SHOCK WAVES -- 5.3 THE LEAP-FROG FORMULAS -- 5.4 THE STEFAN PROBLEM -- 5.5 EVOLUTION OF PLANETARY TYPE BODIES -- 5.6 FREE SURFACE FLUID FLOW -- 5.7 POROUS FLOW -- Chapter 6. Foundational Concepts of Special Relativity -- 6.1 INTRODUCTION -- 6.2 BASIC CONCEPTS -- 6.3 EVENTS AND A SPECIAL LORENTZ TRANSFORMATION -- 6.4 A GENERAL LORENTZ TRANSFORMATION -- Chapter 7. Arithmetic Special Relativistic Mechanics in One Space Dimension -- 7.1 INTRODUCTION -- 7.2 PROPER TIME -- 7.3 VELOCITY AND ACCELERATION -- 7.4 REST MASS AND MOMENTUM -- 7.5 THE DYNAMICAL DIFFERENCE EQUATION -- 7.7 THE MOMENTUM-ENERGY VECTOR -- 7.8 REMARKS -- Chapter 8. Arithmetic Special Relativistic Mechanics in Three Space Dimensions -- 8.1 INTRODUCTION -- 8.2 VELOCITY, ACCELERATION, AND PROPER TIME -- 8.3 MINKOWSKI SPACE. , 8.4 4-VELOCITY AND 4-ACCELERATION -- 8.5 MOMENTUM AND ENERGY -- 8.6 THE MOMENTUM-ENERGY 4-VECTOR -- 8.7 DYNAMICS -- Chapter 9. Lorentz Invariant Computations -- 9.1 INTRODUCTION -- 9.2 INVARIANT COMPUTATIONS -- 9.3 AN ARITHMETIC, NEWTONIAN HARMONIC OSCILLATOR -- 9.4 AN ARITHMETIC, RELATIVISTIC HARMONIC OSCILLATOR -- 9.5 MOTION OF AN ELECTRIC CHARGE IN A MAGNETIC FIELD -- Appendix 1: Fortran Program for General N-body Interaction -- Appendix 2: Fortran Program for Planetary-type Evolution -- References and Sources for Further Reading -- Index.
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  • 2
    Online Resource
    Online Resource
    San Diego :Elsevier Science & Technology,
    Keywords: Mathematical physics-Data processing. ; Electronic books.
    Type of Medium: Online Resource
    Pages: 1 online resource (174 pages)
    Edition: 1st ed.
    ISBN: 9781483279855
    DDC: 530.1502854
    Language: English
    Note: Front Cover -- Arithmetic Applied Mathematics -- Copyright Page -- Table of Contents -- Preface -- Chapter 1. Gravity -- 1.1 INTRODUCTION -- 1.2 GRAVITY -- Chapter 2. Long and Short Range Forces: Gravitation and Molecular Attraction and Repulsion -- 2.1 INTRODUCTION -- 2.2 GRAVITATION -- 2.3 BASIC PLANAR CONCEPTS -- 2.4 DISCRETE GRAVITATION AND PLANETARY MOTION -- 2.5 THE GENERALIZED NEWTON'S METHOD -- 2.6 AN ORBIT EXAMPLE -- 2.7 GRAVITY REVISITED -- 2.8 CLASSICAL MOLECULAR FORCES -- 2.9 REMARK -- Chapter 3. The N-body Problem -- 3.1 INTRODUCTION -- 3.2 THE THREE-BODY PROBLEM -- 3.3 CONSERVATION OF ENERGY -- 3.4 SOLUTION OF THE DISCRETE THREE-BODY PROBLEM -- 3.5 CENTER OF GRAVITY -- 3.6 CONSERVATION OF LINEAR MOMENTUM -- 3.7 CONSERVATION OF ANGULAR MOMENTUM -- 3.8 THE N-BODY PROBLEM -- 3.9 REMARK -- Chapter 4. Conservative Models -- 4.1 INTRODUCTION -- 4.2 THE SOLID STATE BUILDING BLOCK -- 4.3 FLOW OF HEAT IN A BAR -- 4.4 OSCILLATION OF AN ELASTIC BAR -- 4.5 LAMINAR AND TURBULENT FLUID FLOWS -- Chapter 5. Nonconservative Models -- 5.1 INTRODUCTION -- 5.2 SHOCK WAVES -- 5.3 THE LEAP-FROG FORMULAS -- 5.4 THE STEFAN PROBLEM -- 5.5 EVOLUTION OF PLANETARY TYPE BODIES -- 5.6 FREE SURFACE FLUID FLOW -- 5.7 POROUS FLOW -- Chapter 6. Foundational Concepts of Special Relativity -- 6.1 INTRODUCTION -- 6.2 BASIC CONCEPTS -- 6.3 EVENTS AND A SPECIAL LORENTZ TRANSFORMATION -- 6.4 A GENERAL LORENTZ TRANSFORMATION -- Chapter 7. Arithmetic Special Relativistic Mechanics in One Space Dimension -- 7.1 INTRODUCTION -- 7.2 PROPER TIME -- 7.3 VELOCITY AND ACCELERATION -- 7.4 REST MASS AND MOMENTUM -- 7.5 THE DYNAMICAL DIFFERENCE EQUATION -- 7.6 ENERGY -- 7.7 THE MOMENTUM-ENERGY VECTOR -- 7.8 REMARKS -- Chapter 8. Arithmetic Special Relativistic Mechanics in Three Space Dimensions -- 8.1 INTRODUCTION -- 8.2 VELOCITY, ACCELERATION, AND PROPER TIME -- 8.3 MINKOWSKI SPACE. , 8.4 4-VELOCITY AND 4-ACCELERATION -- 8.5 MOMENTUM AND ENERGY -- 8.6 THE MOMENTUM-ENERGY 4-VECTOR -- 8.7 DYNAMICS -- Chapter 9. Lorentz Invariant Computations -- 9.1 INTRODUCTION -- 9.2 INVARIANT COMPUTATIONS -- 9.3 AN ARITHMETIC, NEWTONIAN HARMONIC OSCILLATOR -- 9.4 AN ARITHMETIC, RELATIVISTIC HARMONIC OSCILLATOR -- 9.5 MOTION OF AN ELECTRIC CHARGE IN A MAGNETIC FIELD -- Appendix 1: Fortran Program for General N-body Interaction -- Appendix 2: Fortran Program for Planetary-type Evolution -- References and Sources for Further Reading -- Index.
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Annali di matematica pura ed applicata 110 (1976), S. 211-222 
    ISSN: 1618-1891
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary The aim of the present paper is to study a nonlinear stochastic integral equation of the form $$x(t; \omega ) = h(t, x(t; \omega )) + \mathop \smallint \limits_0^t k_1 (t, \tau ; \omega )f_1 (\tau , x(\tau ; \omega ))d\tau + \mathop \smallint \limits_0^t k_2 (t, \tau ; \omega )f_2 (\tau , x(\tau ; \omega ))d\beta (\tau ; \omega )$$ . Sufficient conditions are given for the existence and uniqueness of a random solution, a second order stochastic process. Special cases of the above mixed Lebesgue-Ito-Doob type of integral equation are given which are useful in applications. In addition, an example of a stochastic control system illustrates the usefulness of the theoretical findings.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Journal of optimization theory and applications 30 (1980), S. 89-98 
    ISSN: 1573-2878
    Keywords: Command, control, and communication ; integral equations ; optimal decision functions ; minimum expected cost
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A formidable problem in the mathematical studies of C3 (command, control, and communication) is the determination of the optimal decision rules for force commitments to be employed by headquarters. Recursive equations are derived for an amphibious campaign with time-invariant linear dynamics and quadratic costs. Air and ground commanders are assumed to have perfect intelligence with degraded communication between them.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Journal of optimization theory and applications 30 (1980), S. 309-318 
    ISSN: 1573-2878
    Keywords: Command ; control ; and communications ; military cybernetics ; optimal decision functions ; minimum expected cost
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A new generation ofC 3 (command, control, and communication) models for military cybernetics is developed. Recursive equations for the solution of theC 3 problem are derived for an amphibious campaign with linear, time-varying dynamics. Air and ground commanders are assumed to have perfect intelligence and perfect communications. Numerical results are given for the optimal decision rules.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Springer
    Acta mathematica hungarica 29 (1977), S. 283-288 
    ISSN: 1588-2632
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
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  • 7
    Publication Date: 2011-01-19
    Description: Spatial asymmetry is crucial to development. One mechanism for generating asymmetry involves the localized synthesis of a key regulatory protein that diffuses away from its source, forming a spatial gradient. Although gradients are prevalent in eukaryotes, at both the tissue and intracellular levels, it is unclear whether gradients of freely diffusible proteins can form within bacterial cells given their small size and the speed of diffusion. Here, we show that the bacterium Caulobacter crescentus generates a gradient of the active, phosphorylated form of the master regulator CtrA, which directly regulates DNA replication. Using a combination of mathematical modeling, single-cell microscopy, and genetic manipulation, we demonstrate that this gradient is produced by the polarly localized phosphorylation and dephosphorylation of CtrA. Our data indicate that cells robustly establish the asymmetric fates of daughter cells before cell division causes physical compartmentalization. More generally, our results demonstrate that uniform protein abundance may belie gradients and other sophisticated spatial patterns of protein activity in bacterial cells.
    Print ISSN: 0027-8424
    Electronic ISSN: 1091-6490
    Topics: Biology , Medicine , Natural Sciences in General
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