Quadratic Reciprocity and the Group Orders of Particle States
Abstract
The construction of inverse states in a finite field F{sub P{sub P{alpha}}} enables the organization of the mass scale by associating particle states with residue class designations. With the assumption of perfect flatness ({Omega}total = 1.0), this approach leads to the derivation of a cosmic seesaw congruence which unifies the concepts of space and mass. The law of quadratic reciprocity profoundly constrains the subgroup structure of the multiplicative group of units F{sub P{sub {alpha}}}* defined by the field. Four specific outcomes of this organization are (1) a reduction in the computational complexity of the mass state distribution by a factor of {approximately}10{sup 30}, (2) the extension of the genetic divisor concept to the classification of subgroup orders, (3) the derivation of a simple numerical test for any prospective mass number based on the order of the integer, and (4) the identification of direct biological analogies to taxonomy and regulatory networks characteristic of cellular metabolism, tumor suppression, immunology, and evolution. It is generally concluded that the organizing principle legislated by the alliance of quadratic reciprocity with the cosmic seesaw creates a universal optimized structure that functions in the regulation of a broad range of complex phenomena.
 Authors:
 Publication Date:
 Research Org.:
 Sandia National Labs., Albuquerque, NM (US); Sandia National Labs., Livermore, CA (US)
 Sponsoring Org.:
 US Department of Energy (US)
 OSTI Identifier:
 782710
 Report Number(s):
 SAND20011534
TRN: AH200126%%190
 DOE Contract Number:
 AC0494AL85000
 Resource Type:
 Technical Report
 Resource Relation:
 Other Information: PBD: 1 Jun 2001
 Country of Publication:
 United States
 Language:
 English
 Subject:
 59 BASIC BIOLOGICAL SCIENCES; CONSTRUCTION; DISTRIBUTION; GENETICS; IMMUNOLOGY; MASS NUMBER; METABOLISM; NEOPLASMS; ORGANIZING; RESIDUES; TAXONOMY
Citation Formats
DAI,YANG, BORISOV,ALEXEY B., LONGWORTH,JAMES W., BOYER,KEITH, and RHODES,CHARLES K.. Quadratic Reciprocity and the Group Orders of Particle States. United States: N. p., 2001.
Web. doi:10.2172/782710.
DAI,YANG, BORISOV,ALEXEY B., LONGWORTH,JAMES W., BOYER,KEITH, & RHODES,CHARLES K.. Quadratic Reciprocity and the Group Orders of Particle States. United States. doi:10.2172/782710.
DAI,YANG, BORISOV,ALEXEY B., LONGWORTH,JAMES W., BOYER,KEITH, and RHODES,CHARLES K.. 2001.
"Quadratic Reciprocity and the Group Orders of Particle States". United States.
doi:10.2172/782710. https://www.osti.gov/servlets/purl/782710.
@article{osti_782710,
title = {Quadratic Reciprocity and the Group Orders of Particle States},
author = {DAI,YANG and BORISOV,ALEXEY B. and LONGWORTH,JAMES W. and BOYER,KEITH and RHODES,CHARLES K.},
abstractNote = {The construction of inverse states in a finite field F{sub P{sub P{alpha}}} enables the organization of the mass scale by associating particle states with residue class designations. With the assumption of perfect flatness ({Omega}total = 1.0), this approach leads to the derivation of a cosmic seesaw congruence which unifies the concepts of space and mass. The law of quadratic reciprocity profoundly constrains the subgroup structure of the multiplicative group of units F{sub P{sub {alpha}}}* defined by the field. Four specific outcomes of this organization are (1) a reduction in the computational complexity of the mass state distribution by a factor of {approximately}10{sup 30}, (2) the extension of the genetic divisor concept to the classification of subgroup orders, (3) the derivation of a simple numerical test for any prospective mass number based on the order of the integer, and (4) the identification of direct biological analogies to taxonomy and regulatory networks characteristic of cellular metabolism, tumor suppression, immunology, and evolution. It is generally concluded that the organizing principle legislated by the alliance of quadratic reciprocity with the cosmic seesaw creates a universal optimized structure that functions in the regulation of a broad range of complex phenomena.},
doi = {10.2172/782710},
journal = {},
number = ,
volume = ,
place = {United States},
year = 2001,
month = 6
}

Calibration of photographic and spectroscopic films. 1: Film batch variations of reciprocity failure in IIaO film. 2: Thermal and aging effects in relationship to reciprocity failure. 3: Shifting of reciprocity failure points as a function of thermal and aging effects. Semiannual report, December 1986
Reciprocity failure was examined for IIaO spectroscopic film. Three separate experiments were performed in order to study film batch variations, thermal and aging effects in relationship to reciprocity failure, and shifting of reciprocity failure points as a function of thermal and aging effects. The failure was examined over ranges of time between 5 and 60 seconds. The variation to illuminance was obtained by using thirty neutral density filters. A standard sensitometer device imprinted the wedge pattern on the film as exposure time was subjected to variation. The results indicate that film batch differences, temperature, and aging play an important rolemore » 
An invariant imbedding, ordersofscattering approach to particle transport in a slab. Physical sciences research papers
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