Unimathematical Data Processing Fundamental Sciences System

by

© Ph. D. & Dr. Sc. Lev Gelimson

Unimathematical Data Processing Fundamental Sciences System (Essential)

Fundamental Science of Unimathematical Data Processing Essence and Strategy

Main Monographs

Necessity and Usefulness of Fundamental Science of Data Processing, or Principal Shortcomings and Domains (Ranges) of Applicability and Adequacy of Known Data Processing Concepts and Methods: at Most Countable Operations, Relations, Quantities (Cardinality, Measures), Estimations (Absolute Error, Relative Error, Mean Square Error, Probability), and Least Square Method

Fundamental Theory of Data Operations: Known Operations with Uninumbers, Quantisets, and Quantisystems, as well as Quantifying, Quantity Definition and Determination, also Uncountable Quantioperations (with Quantities)

Fundamental Theory of Data Relations: Known Relations with Uninumbers, Quantisets, and Quantisystems, as well as Quantirelations (with Quantities)

Fundamental Theory of Data Estimations: Coordinate Difference, Absolute Error, Deviation, Distance, Mean Power Errors, Unierrors, Reserves, Uninumber Probabilities, Reliabilities, and Risks

Fundamental Theory of Approaches to Data Processing: Geometric vs. Analytic Approach; Single-Stage vs. Multiple-Stage Approach

Fundamental Theory and Methods of Data Partitioning: Simple (Longitudinal, Transversal) and Complex Data Partitioning

Fundamental Theory and Methods of Groupwise Centralizing the Data

Fundamental Theory and Methods of Linearly Approximating the Data

Fundamental Theory and Methods of Piecewise Linearly Approximating the Data

Fundamental Theory and Methods of Nonlinearly Approximating the Data

Fundamental Theory and Methods of Geometric Mean

Fundamental Theory and Methods of Least Powers

Fundamental Theory and Methods of Piecewise Linear Bounds Mean

Fundamental Theory and Methods of Curvilinear Bounds Mean

Fundamental Theory and Methods of Piecewise Linear Bounds Weighted Mean

Fundamental Theory and Methods of Curvilinear Bounds Weighted Mean

Fundamental Theory and Methods of Piecewise Linear Bounds Locally Weighted Mean

Fundamental Theory and Methods of Curvilinear Bounds Locally Weighted Mean

Fundamental Theory and Methods of Piecewise Linear Levels Mean

Fundamental Theory and Methods of Curvilinear Levels Mean

Fundamental Theory and Methods of Piecewise Linear Levels Weighted Mean

Fundamental Theory and Methods of Curvilinear Levels Weighted Mean

Fundamental Theory and Methods of Piecewise Linear Levels Locally Weighted Mean

Fundamental Theory and Methods of Curvilinear Levels Locally Weighted Mean

Fundamental Theory and Methods of Invariant Central Transformation

Fundamental Theory and Methods of Data Moments about Linear and Curvilinear Axes

Fundamental Theory and Methods of Data Continualization

Fundamental Theory and Methods of Data Clustering

Fundamental Theory and Methods of Homogeneous Data

Fundamental Theory and Methods of Nonhomogeneous Data

Fundamental Theory and Methods of Mean Square Distances

Fundamental Theory and Finite Methods of Linear Approximation

Fundamental Theory and Iterative Methods of Linear Approximation

Fundamental Theory and Methods of Iteration Acceleration

Fundamental Theory and Methods of Circular Approximation

Fundamental Theory and Methods of Least Normed Powers of Unierrors for Processing Data with a Fixed Origin

Fundamental Theory and Methods of Greatest Normed Reserves for Processing Data with a Fixed Origin

Fundamental Theory and Methods of Equalizing Unierrors for Processing Data with a Fixed Origin

Fundamental Theory and Methods of Equalizing Reserves for Processing Data with a Fixed Origin

Fundamental Theory and Methods of Recovering True Data

Applications of Fundamental Science of Data Processing