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Robert A. Herrmann

Publications and source records attributed to Robert A. Herrmann.

27 records · Page 2Linked to original sources
arXiv2008

Modern Infinitesimal Analysis Applied to the Physical Metric dS and a Theoretical Verification of a Time-dilation Conjecture

In this paper, the modern theory of infinitesimals is applied to the General Relativity metric dS and its geometric and physical meanings are rigorously investigated. Employing results obtained via the time-dependent Schrodinger equation, gravitational time-dilation expressions are obtained and are shown to be caused by gravitationally altered photon interactions with atomic structures.

physics.gen-ph↗
arXiv2007

Nonstandard Analysis Applied to Advanced Undergraduate Mathematics - Infinitesimal Modeling

This is a Research and Instructional Development Project from the U. S. Naval Academy. In this monograph, the basic methods of nonstandard analysis for n-dimensional Euclidean spaces are presented. Specific rules are deveoped and these methods and rules are applied to rigorous integral and differential modeling. The topics include Robinson infinitesimals, limited and infinite numbers; convergence theory, continuity, *-transfer, internal definition, hyprefinite summation, Riemann-Stieltjes integration over Jordan-measurable regions; modeling with integrals via Infinite Sum Theorems; the nonstandard integral modeling rules - the method of constants, the methods of max. and min., and the hyperfinite sum; pure infinitesimal integral modeling via geometric elements; microgeometry, line and surface integrals, gauge integrals, fluxions and their relations to dynamic geometry. These rigorous results are also applied to lengths of curves, areas and volumes for Jordan-measurable regions, incompressible fluids, moments of inertia, electric field vectors, force fields and very elementary physics. Also presented are rigorous differential derivations for the partial differential equations for internal heat transfer and the vibrating membrane. All results are rigorously established and, mostly, all proofs appear in the appendix.

math.GM↗
arXiv2006

General Logic-Systems and Consequence Operators

In this paper, general logic-systems are investigated. It is shown that there are infinitely many finite consequence operators defined on a fixed language L that cannot be generated from a finite logic-system. It is shown that a set map is a finite consequence operator iff it is defined by a general logic-system.

math.GM↗
arXiv2006

Logic for Everyone

Presented, in this monograph, are the results of the U. S. Naval Academy Mathematical Logic Course Project. The propositional and predicate calculus is presented in a unique manner. All aspects are rigorously established using the the fewest mathematical techniques. The propositional calculus is expanded considerably and many of the proof methods are used to establish the predicate calculus results. Consequnce operators are also introduced. Further, the material is considered to be a terminal experience and is directed towards applications such as logic-networks, procedures to determine the validity of arguments, the simple consistency of some sets of hypotheses, some concrete and abstract model theory and, by the Compactness Theorem, the generation of infinitesimals, ultrawords and ultralogics.

math.GM↗
arXiv2004

Nonstandard Analysis and Generalized Functions

This application of nonstandard analysis utilizes the notion of the highly-staturated enlargement. These nonstandard methods clarify many aspects of the theory of generalized functions (distributions).

math.FA↗
arXiv2003

The Wondrous Design and Non-random Character of "Chance" Events

In this article, it is shown specifically that natural system chance events as represented by theory predicted (a priori) probabilistic statements used in such realms as modern particle physics, among others, are only random relative to the restricted language of the theory that predicts such behavior. It is shown that all such "chance" natural events are related one to another by a remarkably designed, systematic and wondrous collection of equations that model how the natural laws and processes specifically yield such natural events. A second result shows theoretically that all such "chance" behavior is caused by application of well-defined ultralogics. These results show specifically that the fundamental underlying behavior associated with all natural systems that comprise our universe is controlled internally by processes that cannot be differentiated from those that mirror the behavior of an infinitely powerful mind.

physics.gen-ph↗
arXiv2002

General Relativity and Contrary Predictions

Using the accepted methods to extract natural system behavior from the Einstein-Hilbert gravitational field tensor equation, a new coordinate transformation is analyzed. It is demonstrated that these extraction methods yield specific contradictions. Two such contradictions are that for an electrically neutral (non-rotating) Schwarzschild configuration there is an infinite redshift surface that is not an event horizon and, for the same Schwarzschild configuration, no dustlike particle external to this configuration will, with respect to proper time, ever gravitationally collapse radially to the surface of the configuration.

physics.gen-ph↗
arXiv2001

An Ultralogic Unification for All Physical Theories

In this paper, the set of all physical theories is represented by a countable collection of consequence operators. It is established that in the Grundlegend Structure, a nonstandard structure, there exists a function S such that for any subset W of L, S selects an ultralogic C such that C(*W) restrictred to L is a unification for the set of all physical theories as they are applied to W.

physics.gen-ph↗