Unimetrology Fundamental Sciences Systems as a System of Revolutions in Metrology
by
© Ph. D. & Dr. Sc. Lev Gelimson
Academic Institute for Creating Fundamental Sciences (Munich, Germany)
Physical Monograph
The “Collegium” All World Academy of Sciences Publishers
Munich (Germany)
12th Edition (2012)
11th Edition (2010)
10th Edition (2004)
9th Edition (2003)
8th Edition (2001)
7th Edition (2000)
6th Edition (1995)
5th Edition (1994)
4th Edition (1993)
3nd Edition (1992)
2nd Edition (1987)
1st Edition (1977)
Abstract
Conventional metrology is based on the real numbers with gaps and on the usual nonuniversal low-sensitive measures with absorption and violations of conservation laws even in the finite, nothing to say about the overinfinite, the infinite, the infinitesimal, and the overinfinitesimal. Further, data processing in conventional metrology is based on the noninvariant absolute error, on the rarely applicable, and, moreover, acceptable relative error, as well as on the least square method. Its many defects are largely due to using the absolute error as the basis, to limiting with the analytically simplest second power usually quite inadequate, to rotational noninvariance (via utilizing ordinate differences by the two-dimensionality), and to no approximation quality estimability and improvability. Conventional metrology considers dimensional physical quantities such as ion implantation doses and mechanical stresses which depend on the choice of the measurement unit system and, therefore, are noninvariant and nonuniversal. In addition, measuring highly inhomogeneous distributions such as mechanical stresses in the zones of their concentration, as well as high-speed processes, leads to very significant averaging errors. They are due to the finiteness of the actual size and inertia of the measuring devices sensors, which makes it impossible to provide exact namely instantaneous and pointwise measurement. Therefore, it is necessary to determine the true values of measured quantities. The same holds for body decomposition (partition) errors with averaging the calculated parameters. But there are no known simple analytical solutions to such nontrivial problems of metrology.
Universal metrology, or unimetrology, is based on using the unimathematical uninumbers and perfectly sensitive uniquantities as universal measures without any absorption and violations of conservation laws in the overinfinite, the infinite, the finite, the infinitesimal, and the overinfinitesimal. In unimetrology, data processing is based on the invariant unierror, as well as the universal theories of unigrouping, uniboundaries, unilevels, unibisectors, distance powers, unierrors, and unireserves with approximation quality estimability and improvability. Unimetrology introduces invariant and universal dimensionless physical quantities such as ion implantation unidoses and mechanical unistresses that do not depend on the choice of the measurement unit system. In addition, for the first time, it becomes possible to adequately set and analytically solve nontrivial general and specific metrology problems. Their solutions provide precisely determining the true values of measured quantities. This is especially important for highly nonuniform distributions, such as mechanical stresses in the zones of their concentration, as well as for high-speed processes, and leads to the identification and subsequent elimination of very great averaging errors. The same holds for body decomposition (partition) errors with averaging the calculated parameters. As a result, unimetrology creates fundamentally new opportunities to obtain reliable measurement data and even to discover new phenomena and laws of nature.
Uniphilosophy (Exclusively Constructive Creative Philosophy) Principles as a System of Revolutions in Philosophy
Fundamental principles of uniphilosophy (exclusively constructive creative philosophy) build a fundamental system of revolutions in philosophy, in particular, the following subsystems.
1. Fundamental Principles of Uniphilosophy as a Fundamental Subsystem of Revolutions in Philosophy
The fundamental subsystem of revolutions in philosophy includes the following fundamental principles of uniphilosophy:
1. Exceptional natural constructivism (with the complete absence of artificial destructiveness).
2. Free efficient creativity (exclusively practically purposeful, verified, and efficient unlimitedly free creativity, intuition, and phantasy flight).
3. Scientific optimism and duty (each urgent problem can and must be solved adequately and efficiently enough).
4. Complication utilization (creating, considering, and efficiently utilizing only necessary and useful also contradictory objects and models, as well as difficulties, problems, and other complications).
5. Symbolic feasibility (at least symbolic existence of all the necessary and useful even contradictory objects and models).
2. Advanced Principles of Uniphilosophy as an Advanced Subsystem of Revolutions in Philosophy
The advanced subsystem of revolutions in philosophy includes the following advanced principles of uniphilosophy:
1. Exclusively efficient intuitive evidence and provability (reasonable fuzziness, intuitive ideas without axiomatic rigor if necessary and useful).
2. Unrestrictedly flexible constructivism (if necessary even creating new knowledge (concepts, approaches, methods, theories, doctrines, and even sciences) to adequately set, consider, and solve urgent problems).
3. Tolerable simplicity (choosing the best in the not evidently unacceptable simplest).
4. Perfect sensitivity, or conservation laws universality (no uncompensated change in a general object conserves its universal measures).
5. Exact discrimination of noncoinciding objects and models (possibly infinitely or overinfinitely large with infinitesimal or overinfinitesimal distinctions and differences).
6. Separate similar (proportional) limiting universalizability (the reduction of objects, systems, and their models to their own similar (proportional) limits as units).
7. Collective coherent reflectivity, definability, modelablity, expressibility, evaluability, determinability, estimability, approximability, comparability, solvability, and decisionability (in particular, in truly multidimensional and multicriterial systems of the expert definition, modeling, expression, evaluation, determination, estimation, approximation, and comparison of objects, systems, and models qualities which are disproportionate and hence incommensurable and not directly comparable, as well as in truly multidimensional and multicriterial decision-making systems).
3. Some Other Principles of Uniphilosophy
Among other principles of uniphilosophy are the following:
1. Truth priority (primacy of practically verified purely scientific truths and criteria prior to commonly accepted dogmas, views, agreements, and authority, with all due respect to them).
2. Peaceful pluralism (with peaceful development of scientific and life diversity).
3. Efficient creative inheritance (efficiently using, analyzing, estimating, and developing already available knowledge and information).
4. Efficient constructive freedom (unrestrictedly free exclusively constructive and useful self-determination and activity, in particular, in knowledge and information research, creation, and development).
5. Fundamentality priority (primacy of conceptual and methodological fundamentals).
6. Knowledge efficiency (only useful quality (acceptability, adequacy, depth, accuracy, etc.) and amount (volume, completeness, etc.) of knowledge, information, data, as well as creation, analysis, synthesis, verification, testing, structuring, systematization, hierarchization, generalization, universalization, modeling, measurement, evaluation, estimation, utilization, improvement, and development of objects, models, knowledge, information, and data along with intelligent management and self-management of activity).
7. Mutual definability and generalizability (relating successive generalization of concepts in definitions with optional linear sequence in knowledge construction).
8. Efficient unificability of opposites only conditionally distinguished (such as real/potential, real/ideal, specific/abstract, exact/inexact, definitively/possibly, pure/applied, theory/experiment/practice, nature/life/science, for example, the generally inaccurate includes the accurate as the limiting particular case with the zero error).
9. Partial laws sufficiency (if there are no known more general laws).
10. Focus on discoveries and inventions (dualistic unity and harmony of academic quality and originality, discovering phenomena of essence, inventive climbing, helpful knowledge bridges, creative multilingualism, scientific art, anti-envy, learnability, teachability, and terminology development).
The Principles of Uniphysics as the System of Revolutions in the Principles of Physics
The principles of uniphysics constitute the system of scientific revolutions in the principles of physics including the following subsystems.
The Fundamental Principles of Uniphysics as the Fundamental Subsystem of Revolutions in the Principles of Physics
The fundamental subsystem of revolutions in the principles of physics includes the following fundamental principles of uniphysics:
1. Urgent problems priority, exclusiveness, and typificability (adequately setting, exhaustively solving, and efficiently using urgent problems types only (with completely avoiding unnecessary considerations) as the unique criterion of the necessity and usefulness of creating and developing new knowledge).
2. Intuitive conceptual and methodological fundamentality priority (creating and efficiently using unified knowledge foundation due to fundamental general systems including objects, models, and intuitive fuzzy principles, concepts, and methodology).
3. Philosophical, mathematical, physical, and engineering meaningfulness, synergy, and intelligence primacy (with intuitive clarity, learnability, teachability, and efficient beauty as the united duality and harmony of quality and quantity, as well as of applicability and acceptability).
4. Controllability (the step-by-step testability, verifiability, estimability, invariance, immutability, strength, stability, and reliability of data, intermediate and final results, information, and general knowledge including concepts, approaches, methods, theories, doctrines, and sciences with the possibility of their correction, comprehensive improvement, generalization, universalization, structuring, systematization, and hierarchization).
5. Creating, inventing, and discovering directionality (the focus on creating and inventing new knowledge and the know-how, as well as on reasonably discovering new phenomena and laws of nature, along with the possibility of the generalization, universalization, systematization, and hierarchization of discoveries and inventions and with the united duality of scientific and technical architecture).
The Universalizability Principles of Uniphysics as the Universalizability Subsystem of Revolutions in the Principles of Physics
The universalizability subsystem of revolutions in the principles of physics includes the following universality principles of uniphysics:
1. Free efficient physical controlability (the expressibility, universalizability, invariance, measurability, estimability, and improvability of physical quantities, models, transformations, criteria, and knowledge).
2. Free efficient quality controlability (modelability, expressibility, universalizability, invariance, measurability, estimability, and improvability including providing and efficiently using the unity of variety and diversity, multicriteriality, polymethodicity, and multivariability in universally invariantly modeling, expressing, evaluating, measuring, and estimating data processing and approximation quality (via unierrors) along with accuracy and/or acceptability certainty via unireserves, unireliabilities, and unirisks without artificial randomization in deterministic problems).
3. Conservation laws universalizability (in the overinfinitesimal, the infinitesimal, the finite, the infinite, and the overinfinite).
4. The universalizability of laws of nature.
The General Noncriticality Principles of Uniphysics as the General Noncriticality Subsystem of Revolutions in the Principles of Physics
The general noncriticality subsystem of revolutions in the principles of physics includes the following general noncriticality principles of uniphysics:
1. Critical and limiting relations efficiency (the efficiency of the critical and limiting relations between the determining initial parameters of a problem).
2. General noncriticality (the joint definability and determinacy of subcritical, critical, and supercritical states, processes, and phenomena in a general structured system via joint generally noncritical relations).
3. General nonlimitability (the joint definability and determinacy of underlimiting, limiting, and overlimiting states, processes, and phenomena in a general structured system via joint generally nonlimiting relations).
4. Parameters reserves separability (the separability of the proper own reserves of the independent determining initial parameters in a problem).
The Unimathematical Principles of Uniphysics as the Unimathematical Subsystem of Revolutions in the Principles of Physics
The unimathematical subsystem of revolutions in the principles of physics includes the following unimathematical principles of uniphysics:
1. Tolerable simplicity (including the necessity and possibility of the tolerably simplest acceptable analytical solutions).
2. Unimodelability, uniexpressibility, unievaluability, and unimeasurability (using the unimathematical uninumbers, perfectly sensitive uniquantities as universal measures without any absorption and violations of conservation laws in the overinfinite, the infinite, the finite, the infinitesimal, and the overinfinitesimal, as well as unioperations, unisets, uniaggregates (unicontents), and unisystems).
3. Uniestimability, uniapproximability, and uniproblem unisolvability (using the unimathematical unierrors, unireserves, unireliabilities, and unirisks, as well as uniproblem unisolving methods, theories, doctrines, and sciences).
4. Unicomputability (using the computer fundamental sciences system, the overcoming complication fundamental sciences system, and the unimathematical data processing fundamental sciences system).
The Other Principles of Uniphysics
Among the other principles of uniphysics are the following:
1. The efficiency of transparency and ergonomicity (the analytical, numerical, and graphical unity, clarity, visibility, observability, and reviewability of knowledge, information, data, conditions, and results).
2. Creative inheritance efficiency (refining, correcting, improving, generalizing, and universalizing classical results, establishing the limits of their applicability, acceptability, adequacy, and efficiency).
3. Comprehensive self-responsibility concentration (the unity and indivisibility of research, expressing, interpreting, explaning, and presenting the results with the creative and efficient utilization of routine).
The Principles of Unimetrology
The principles of unimetrology build a system of revolutions in the principles of mathematics, physics, and metrology and include the following subsystems:
1) the universalizability subsystem of metrological revolutions, in particular, the following principles of unimetrology:
the universalizability of the numbers via the unimathematical uninumbers;
the universalizability of the measures via the unimathematical uniquantities (without absorption and violations of the conservation laws) perfectly sensitive to the overinfinite, the infinite, the finite, the infinitesimal, and the overinfinitesimal;
the universalizability of the errors via the unimathematical unierrors;
the universalizability of physical quantities, e.g. of mechanical stresses via universal mechanical stresses and of ion implantation doses via universal ion implantation doses;
the universalizability of measurement data processing;
2) the physical quantity measurability subsystem of metrological revolutions, in particular, the following principles of unimetrology:
the definability, determinability, measurability, and estimability of the averaging errors of partitioning objects and systems;
the definability, determinability, and estimability of the averaging errors of measurements using namely actual physical devices;
approximation quality definability, determinability, measurability, estimability, and improvability;
the reliable definability, determinability, and estimability of true measurement data using incomplete distorted information;
the discoverability of new phenomena and laws of nature due to metrology universalizability.
Unimetrology is a system of fundamental mathematical, physical, and metrological sciences such as:
the fundamental mathematical and physical science of using unimathematical uninumbers in unimeasurement;
the fundamental mathematical and physical science of using uniquantities in unimeasurement;
the fundamental mathematical and physical science of using unierrors, unireserves, unireliabilities, and unirisk in unimeasurement;
the fundamental mathematical and physical science of universalizing physical quantities;
the fundamental mathematical and physical science of the averaging errors of partitioning objects and systems;
the fundamental mathematical, physical, and metrological science of transforming measurement data;
the fundamental mathematical, physical, and metrological science of measurement data processing;
the fundamental mathematical and physical science of universalizing data processing in unimeasurement.
The fundamental mathematical and physical science of using unimathematical uninumbers in unimeasurement includes the general theories of applying unimathematical uninumbers to diversely unimeasuring universal physical quantities in various fields of mathematics and physics.
The fundamental mathematical and physical science of using uniquantities in unimeasurement includes the general theories of applying perfectly sensitive uniquantities as universal measures without absorption and violations of conservation laws in the overinfinite, the infinite, the finite, the infinitesimal, and the overinfinitesimal to diversely unimeasuring universal physical quantities in different areas of mathematics and physics.
The fundamental mathematical and physical science of using unierrors, unireserves, unireliabilities, and unirisks in unimeasurement includes the general theories of applying unierrors, unireserves, unireliabilities, and unirisks as the universal measurers and estimators of measurement and approximation quality especially precision in the overinfinite, the infinite, the finite, the infinitesimal, and the overinfinitesimal to diversely unimeasuring universal physical quantities in different areas of mathematics and physics.
The fundamental mathematical and physical science of universalizing physical quantities includes the general theories of various universal transformations of physical quantities in different areas of mathematics and physics. This applies, in particular, to unimeasures and mechanical unistresses, as well as to ion implantation unidoses as implantation unimultiplicities. Such a (possibly noninteger) unimultiplicity introduced as the ratio of the total area of the cross sections of the implanted ions to the surface area of the target subjected to ion implantation. If ion implantation is inhomogeneous, then its unimultiplicity is introduced locally as the ratio of the differentials of those areas. It turns out that by small, medium, and high ion implantation doses, their unimultiplicities orders correspond to one-hundredth, unity, and one hundred, respectively, which seems to be quite natural. Namely unimultiplicities having clear physical sense like unistresses provide discovering, explaining, interpreting, and justifying new phenomena and laws of nature.
The fundamental mathematical and physical science of the averaging errors of partitioning objects and systems includes the general theories of measuring and estimating such errors and of corresponding directed test systems in different areas of mathematics and physics. This holds in particular for replacing integrals via integral sums and is especially important for systems with many elements such as airplanes and helicopters with their decompositions into so-called stations of inch lengths, widths, and heights.
The fundamental mathematical, physical, and metrological science of transforming measurement data includes the general theories of such transformations and of corresponding directed test systems in different areas of mathematics, physics, and metrology. Measuring any physical quantity not invariant in the space and/or time via actual physical devices sensors having finite sizes and inertia gives measurement information distorted by modulation with the specific law and, generally speaking, by the time delay. It is therefore important to establish the true value of the measured physical quantity (the preimage) via measuring distorted information (the image of the measurement operator as a measurement information converter). The delay is usually constant and can be simply excluded via shifting measurement data as a whole into the past. It is much more complicated to provide demodulation as correcting modulation errors nonuniversal due to their dependence not only on the properties of the physical device but also on the specific features of the measured physical quantity itself. The fundamental laws of modulation and demodulation become clear in the simplest case of modulation, namely by averaging a one-parameter continuous variable with a weight function continuous on a segment of a certain length (a measuring instrument constant) whose center coincides with the value of the parameter. This leads to the general theories of correcting averaging errors in the measurements of static and dynamic nonuniform distributions via inverting the averaging operator with determining the corresponding equivalent factors for standard functions such as linear, trigonometric, exponential, and hyperbolic.
The fundamental mathematical, physical, and metrological science of measurement data processing includes the general theories of the corresponding transformations and directed test systems in various areas of mathematics, physics, and metrology. In particular, applying the fundamental mathematical, physical, and metrological science of transforming measurement data to the electric tensiometry of stress concentration zones showed that the maximum true strain is determined by the product of the measured strain and of the corresponding equivalent factor. This factor greately depends on the relative characteristic size of the strain gage of the electric tensiometer and on the relative distance of this strain gage from the stress concentrator so that these both relative quantities are the corresponding usual quantities divided by the characteristic size of the stress concentrator.
The fundamental mathematical and physical science of universalizing data processing in unimeasurement includes the corresponding general theories of defining, determining, and applying data unierrors, scatter, directionality, and approximation, as well as its estimability and improvability.
The System of Metrological Revolutions
The system of metrological revolutions in physics and mathematics includes:
1) the number and measure universalization subsystem of metrological revolutions, in particular:
using the unimathematical uninumbers;
using perfectly sensitive uniquantities as universal measures without any absorption and violations of conservation laws in the overinfinite, the infinite, the finite, the infinitesimal, and the overinfinitesimal;
2) the unimeasurement quality estimation universalization subsystem of metrological revolutions, in particular:
physical quantity unimeasurement and uniapproximation unierrors;
physical quantity unimeasurement and uniapproximation unireserves;
physical quantity unimeasurement and uniapproximation unireliabilities;
physical quantity unimeasurement and uniapproximation unirisks;
3) the physical quantity universalization subsystem of metrological revolutions, in particular:
universalizing mechanical stresses;
universalizing ion implantation doses;
4) the partitioning subsystem of metrological fundamental innovations, in particular:
exactly measuring significant averaging errors of partitioning objects and systems;
the possibility to use macroelements or even a single macroelement;
5) the physical quantity measurement subsystem of metrological fundamental innovations, in particular:
exactly measuring significant averaging errors of measurements using namely actual physical devices;
reliably determining the true measurement data using incomplete distorted information such as by the electric tensiometry of stress concentration zones;
6) the measurement data processing subsystem of metrological revolutions, in particular:
universalizing measurement data errors, scatter, and directionality, as well as approximation;
universalizing measurement data processing;
measurement data approximation quality uniestimability;
measurement data approximation quality uniimprovability;
7) the phenomenon and law discovery, explanation, interpretation, and justification subsystem of metrological fundamental innovations, in particular:
the invertibility of the linear integral operator of averaging by the differentiability of the image;
the uniqueness of the inversion of the linear integral operator of averaging up to functions for which the measurement instrument sensor base is a period with zero mean integral value on it;
the existence of the first critical ion implantation dose;
the existence of the second critical ion implantation dose;
the existence of the critical ion implantation energy whose excess leads to the nonuniform strength of the target surface layer;
the abrupt supercritical collapse of the target strength;
the coincidence and joint movement of all the depths of the main implantation maxima of different particles (ions with different sizes, initial energies, etc.).
Basic Results and Conclusions
References
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3. Lebedev A. A., Koval'chuk B. I., Giginyak F. F., Lamashevsky V. P. Mechanical Properties of Structural Materials at a Complex Stress State. Handbook. – Kiev, Naukova Dumka, 1983. – 366 pp. – In Russian.
4. Troshchenko V. T., Sosnovsky L. A. Strength of Metals and Alloys. Handbook in 2 parts. – Kiev, Naukova Dumka, 1987. – Part 1. – 509 pp. – Part 2. – 1304 pp. – In Russian.
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In this paper the problem. Dry to handle. for 1978 is a fact - the destruction, where a rigid scheme of stress ..
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In the work 67 - tity of rooms specimen for mechanical testing in conditions of mild stress.
L. B. Tsvik. Specimen for mechanical testing of structural steel under cyclic loading [In Russian]. Track Facilities Problems in Eastern Siberia. Scientific papers of IrGUPS, 2005, 3, 200-203