General Problem Fundamental Sciences System

by

© Ph. D. & Dr. Sc. Lev Gelimson

 

 

 

General Problem Fundamental Sciences System (Essential)

 

 

Fundamental Science on General Problem Essence

 

General Problem Theory (Essential)

 

General Problem Type and Setting Theory

Fundamental Science of General Problem Pseudosolution

 

General Problem Pseudosolution Theory

Fundamental Science on General Problem Solving Strategy

 

General Problem Solving Strategy Theory

Fundamental Science of General Problem Transformation

 

General Problem Transformation Theory

 

Unit Factor Theory

 

Physical Unit Removal Theory

 

Distance Transformation Theory

 

Power Distance Transformation Theories

 

Unknown Balance Theory

 

Fundamental Science of General Problem Analysis

 

General Problem Analysis Theory

Fundamental Science of General Problem Synthesis

 

General Problem Synthesis Theory

Fundamental Science of General Problem Testing

 

Directed Test System Theory

 

Distribution Theory

 

General Center Theory

 

Triangle Theory

 

Fundamental Science of General Problem Estimation

 

Power Theory

 

Power Product Theory

 

General Subproblem Estimation Theory

 

General Problem Estimation Theory

Fundamental Science on General Problem Iteration

 

Single-Source Iteration Theory

 

Multiple-Sources Iteration Theory

 

Intelligent Iteration Theory

 

Fundamental Science on General Problem Bisectors

Adjacent Sides Bisectors Theory

Adjacent Corners Bisectors Theory

Adjacent Sides and Corners Bisectors Theories in Universal Problem Solving Science

Opposite Sides Bisectors Theory

Opposite Corners Bisectors Theory

Opposite Sides and Corners Bisectors Theories in Universal Problem Solving Science

Equidistance Theory

Equidistance and Subjoining Equations Theories in Universal Problem Solving Science

Fundamental Science of Solving General Problems

 

Unit Factor Power Theories

Subjoining Equations Theory

Biquadrat Theory


Power Theories

Direct Theories

Fundamental Science on General Problem Distance

Distance Quadrat Theory

Distance Biquadrat Theory


Distance Power Theories

Fundamental Science on General Problem Reserve

Distance and Unierror Power Theories in Universal Problem Solving Science

Unierror Quadrat Theories

Unierror Biquadrat Theories

 

Fundamental Science on General Problem Approximation

 

Correction and Generalization of the Least Square Method

General Problem Theory Fundamentals (Correction and Generalization of the Absolute and Relative Errors and the Least Square Method)

Fundamental Methods of Solving General Problems via Unierrors (former Autoerrors, Hypererrors), Reserves, Reliabilities, and Risks (former General Estimation and Approximation Theory: Methods of the Least Normed Powers, Autoerror and Reserve Equalization Methods, and Direct-Solution Method)

 

Additional Special Monographs and Articles

 

Synergistic System of Fundamental Analytic Methods

General Analytic Methods

Linear Combination Method in Three-Dimensional Elasticity

Generalized Methods for Solving Functional Equations and Their Sets

Methods of Least Normalized Powers and Equalizing Errors for Solving Functional Equations

Providing Helicopter Fatigue Strength: Flight Conditions [Overmathematics and Other Fundamental Mathematical Sciences]

 

Fundamental Sciences of Solving General Problems

Quintessence

Main Monographs

 

Necessity and Usefulness of Fundamental Science of Solving General Problems, or Principal Shortcomings and Domains (Ranges) of Applicability and Adequacy of Known 

Objects (Numbers, Sets, and Systems), At Most Countable Operations, Relations, Quantities (Cardinality, Measures), Estimations (Absolute Error, Relative Error, Mean Square Error, Probability), Problem Concepts (Solution, Particular Solution, Quasisolution, Their Sets), and Methods of Solving Problems (Method of Particular Solutions, Least Square Method, Finite Element Method, Finite Point Method,  Artificial Randomization Methods) 

 

General Problem Object Theory: Uninumbers incl. Numbers, Quantisets incl. Sets, and Quantisystems incl. Systems

 

General Problem Operation Theory: Known Operations with Uninumbers, Quantisets, and Quantisystems, as well as Quantifying, Quantity Definition and Determination, also Uncountable Quantioperations (with Quantities)

 

General Problem Relation Theory: Known Relations with Uninumbers, Quantisets, and Quantisystems, as well as Quantirelations (with Quantities)

 

General Problem Uniquantity Theory

 

General Problem Estimation Theory: Deviation, Distance, Mean Power Errors, Unierrors, Reserves, Uninumber Probabilities, Reliabilities, and Risks

 

General Problem Form Theory: Quantisystem of Quantirelations; Pseudosolutions, Solutions, Quasisolutions, Antisolutions, Their Quantisets

 

General Problem Coordinate System Theory: Homogeneous and Nonhomogeneous Coordinate Systems

 

General Problem Invariance Theory: No Invariance (Fixed Origin), Linear Translation Invariance, Parallel Translation Invariance, Fixed-Center Rotation Invariance, Rotation Invariance, Proportional Transformation Invariance

 

General Problem Symmetry Theory: Central Symmetry, Axial Rotational Symmetry, Axial Mirror Symmetry in a Plane, Planar Mirror Symmetry in a Space

 

Fundamental Theory and Methods of General Linear Combinations

 

Fundamental Theory and Methods of Exhaustive Solutions

 

Fundamental Theory and Methods of General Problem Restructuring

 

Fundamental Theory and Methods of Partitioning General Problems

 

Fundamental Theory and Methods of Iteration Acceleration

 

Fundamental Theory and Methods of Error Minimization

 

Fundamental Theory and Methods of Reserve Maximization

 

Fundamental Theory and Methods of Error Equalization

 

Fundamental Theory and Methods of Reserve Equalization

 

Fundamental Theory and Methods of Power Increase

 

Fundamental Theory and Methods of Direct Solution

 

Fundamental Theory and Methods of Directed Numeric Tests

 

Applications of Fundamental Science of Solving General Problems