Search Results: 'Nonlinear Numbers'

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16 results for "Nonlinear Numbers"
Nonlinearity in Life and Biomedical Sciences By Ralph W Lai
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New nonlinear concepts for data analysis in life and biomedical sciences are introduced. Biological science is loaded with data with various curves: C-curves, S-curves, and symmetric and asymmetric... More > bell curves, etc,; these curves are nonlinear curves. Different types of cuves are outcome of different nonlinear physical phenomena that can have different degree of nonlinearity and different ways of meauring nonlinearity. All these nonlinear phenomena can be assembled into groups and described by simple nonlinear equations. A nonlinear phenomenon needs to be described by multiple graphs in association with nonlinear equations. The book discusses the fundamentals of nonlinearity followed by describing the methodoogy for analyzing the nonlinear data. The book is based on two mathematical axioms and two universal standards for linear and nonlinear measurements. A series of Proportionality laws along wth the GVP (graph based, true value compared, and proportionality oriented) math system are discussed.< Less
Nonlinearity and Proportionality in Science, Medicine, and Engineering By Ralph Lai
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This book introduces a new αβ math for describing physical laws in science, medicine, and engineering. The αβ math is an extension to the traditional XY math to address the... More > nonlinearity of the continuous numbers. The book starts with introducing the fundamentals of nonlinearity followed by describing the methodology for analyzing the nonlinear phenomena.In the αβ math, the fundamentals of nonlinearity are based on two mathematical axioms and two universal standards for linear and nonlinear measurements. A series of proportionality laws, in conjunction with a Graph-based, true-Value compared, and Proportionality-oriented (GVP) math system, are introduced for assisting in data analyses. The new αβ math is built on the classification of continuous numbers into linear and nonlinear numbers. The linear numbers are defined as the continuous numbers that have no association with any asymptotes; and the nonlinear numbers are the continuous numbers that have association with one or two asymptotes.< Less
Time Force Non-Linear Handbook By Micheal Frantz
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Explore the future of a mankind where a large number of planets and moons are now colonized. Time Travelers, such as your character, explore the past to record history and prevent Renegade time... More > travelers from changing time.< Less
Azimuthal Modulational Instability of Vortex Solutions to the Two Dimensional Nonlinear Schrödinger Equation By Ronald Meyer Caplan
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We study the azimuthal modulational instability (MI) of vortices with different topological charges, in the focusing two-dimensional nonlinear Schrödinger (NLS) equation. The method of studying... More > the stability relies on freezing the radial direction in the Lagrangian functional of the NLS in order to form a quasi-one-dimensional azimuthal equation of motion, and then applying a stability analysis in Fourier space of the azimuthal modes. We formulate predictions of growth rates of individual modes and find that vortices are unstable below a critical azimuthal wave number. Steady state vortex solutions are found by first using a variational approach to obtain an asymptotic analytical ansatz, and then using it as an initial condition to a nonlinear equation numerical optimization routine. The stability analysis predictions are corroborated by direct numerical simulations of the NLS performed on a polar coordinate finite-difference scheme.< Less
Azimuthal Modulational Instability of Vortex Solutions to the Two Dimensional Nonlinear Schrödinger Equation By Ronald Meyer Caplan
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We study the azimuthal modulational instability (MI) of vortices with different topological charges, in the focusing two-dimensional nonlinear Schrödinger (NLS) equation. The method of studying... More > the stability relies on freezing the radial direction in the Lagrangian functional of the NLS in order to form a quasi-one-dimensional azimuthal equation of motion, and then applying a stability analysis in Fourier space of the azimuthal modes. We formulate predictions of growth rates of individual modes and find that vortices are unstable below a critical azimuthal wave number. Steady state vortex solutions are found by first using a variational approach to obtain an asymptotic analytical ansatz, and then using it as an initial condition to a nonlinear equation numerical optimization routine. The stability analysis predictions are corroborated by direct numerical simulations of the NLS performed on a polar coordinate finite-difference scheme.< Less
Hidden Structure of the System of Natural Numbers Decodes As Missing Link the Distribution of the Primes and the Riemann Hypothesis. By G.B. Engelen
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Hidden within the system of natural numbers exists a fundamental, static, deterministic, hybrid linear and nonlinear tree structure. It is founded on symmetry principles and forms the key to... More > understanding the enigma of the primes. This enables the full decoding and easy, forward, errorless calculation of the distribution of the primes. The discovery of the hidden structure of the system of natural numbers also decodes and clarifies the enigmatic aspects of the Riemann hypothesis.< Less
TSP 5.1 Reference Manual By Bronwyn Hall, Clint Cummins
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The TSP Reference Manual contains a detailed description of every TSP command (over 150) including the method(s) used, all the options, a description of the output generated, examples of use, and a... More > short list of references to the literature where relevant. The TSP software is a general-purpose computer language for econometric and statistical data processing, estimation, and model simulation. It can be used for any of the following tasks: applied econometrics, including teaching, macroeconomic research and forecasting, microeconometric research, analysis of panel data, sales forecasting, financial analysis. cost analysis and forecasting, Monte Carlo simulation, and estimation and simulation of economic models. Powerful nonlinear methods and extended language facilities such as symbolic differentiation, matrix algebra, and random number generation enable advanced users to experiment with their own estimation methods using a high level easy-to-program language.< Less
College Algebra By A. A. Frempong
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This book covers college algebra. The topics include the following: Polynomial, Nonlinear, and Radical Equations; Sets, Relations, Functions; Absolute Value Equations and Inequalities; Linear... More > Programming; Graphs of Functions; Asymptotes; Logarithms; Exponential and Logarithmic Equations; Graphs of Exponential and Logarithmic Functions; Matrix and Matrix Methods; Determinants; Complex Numbers and Operations; Polar Form of Complex Numbers; Roots of Complex Numbers; Graphing Polar Coordinates and Equations; Conic sections;; Remainder and Factor Theorems; Rational Roots; Partial Fractions; Sequences and Series; Binomial Theorem; Permutations and Combinations; and Mathematical Induction;< Less
The Sacred Numerology of Thoth By Tenzin Gyurme
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Where is it written that this Universe operates on a base 10 number system? So what number system best categorizes a Universal View? Base 10 or base 12? It is pretty obvious that it is base 12, at... More > least for those non-linear thinkers who can get their heads out of their Ass-ets, that is. This book is an tool for those Be-ings who are ready to awaken to their multi-dimensional selves and release the strangle hold that the 3 dimensional illusion has on their lives.< Less
The Sacred Numerology of ThoTh By tenzin gyurme
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Where is it written that this Universe operates on a base 10 number system? So what number system best categorizes a Universal View? Base 10 or base 12? It is pretty obvious that it is base 12, at... More > least for those non-linear thinkers who can get their heads out of their Ass-ets, that is. This book is an tool for those Be-ings who are ready to awaken to their multi-dimensional selves and release the strangle hold that the 3 dimensional illusion has on their lives.< Less