Music from the "Radical Center"

1964 ◽  
Vol 3 (1) ◽  
pp. 131 ◽  
Author(s):  
David Cohen ◽  
Gordon Binkerd
Keyword(s):  
Radical Center

Circles on the Complex Plane

2021 ◽  
pp. 3-12
Author(s):  
A. Girsh
Keyword(s):  
Euclidean Space ◽  
Complex Plane ◽  
Euclidean Plane ◽  
Complex Space ◽  
Radical Center ◽  
Special Cases ◽  
Different Types ◽  
Different Dimensions ◽  
The Given ◽  
Made In

The Euclidean plane and Euclidean space themselves do not contain imaginary elements by definition, but are inextricably linked with them through special cases, and this leads to the need to propagate geometry into the area of imaginary values. Such propagation, that is adding a plane or space, a field of imaginary coordinates to the field of real coordinates leads to various variants of spaces of different dimensions, depending on the given axiomatics. Earlier, in a number of papers, were shown examples for solving some urgent problems of geometry using imaginary geometric images [2, 9, 11, 13, 15]. In this paper are considered constructions of orthogonal and diametrical positions of circles on a complex plane. A generalization has been made of the proposition about a circle on the complex plane orthogonally intersecting three given spheres on the proposition about a sphere in the complex space orthogonally intersecting four given spheres. Studies have shown that the diametrical position of circles on the Euclidean E-plane is an attribute of the orthogonal position of the circles’ imaginary components on the pseudo-Euclidean M-plane. Real, imaginary and degenerated to a point circles have been involved in structures and considered, have been demonstrated these circles’ forms, properties and attributes of their orthogonal position. Has been presented the construction of radical axes and a radical center for circles of the same and different types. A propagation of 2D mutual orthogonal position of circles on 3D spheres has been made. In figures, dashed lines indicate imaginary elements.

Structure et réactivité. III., Evolutions stéréochimiques et chemins réactionnels des radicaux cyclohexyles substitués en 2 et cyclohexényles substitués en 3 (réaction de Kochi)

1979 ◽  
Vol 57 (10) ◽  
pp. 1257-1261 ◽  
Author(s):  
Maurice Monnier ◽  
Jean-Pierre Aycard
Keyword(s):  
Carboxylic Acids ◽  
Steric Hindrance ◽  
High Energy ◽  
Radical Center ◽  
The Difference

The chlorodecarboxylation reaction (Kochi reaction) of a series of cyclohexane and cyclohexene carboxylic acids was investigated. Competitive acetoxy decarboxylation occurs, and the proportion of acetates is shown to increase with steric hindrance due to the R-substituent relative to the radical center. A partial evolution involving high energy conformers is suggested to explain the difference of stereoselectivities in the formation of acetates and chlorides.

A Noble Photo-Grafting Technique of Perfluoropolyether Molecular Chains to the Carbon Overcoat

2007 ◽  
Author(s):  
Paul H. Kasai ◽  
A. Wakabayashi
Keyword(s):  
Uv Curing ◽  
Carbon Layer ◽  
Molecular Chain ◽  
Fluoride Anion ◽  
Radical Center ◽  
Curing Process ◽  
Carbon Overcoat ◽  
Radical Chain ◽  
Polymer Backbone ◽  
Uv Curing Process

The technique of enhancing adhesion of PFPE (perfluoropolyether) lubricants to the carbon overcoat of magnetic media discs by irradiation with far-UV (185 nm) was reported some time ago.[1] It was later suggested that photoelectrons emanating from the carbon layer was responsible for the observed efficacy.[2] Capture of these low energy electrons by PFPE molecular chains would lead to detachment of a fluoride anion and formation of a radical center on the polymer backbone. Adhesion occurs when the radical center reacts with the carbon layer. Most recently this mechanism was challenged, and photo-cleavage of a CF2O unit from the molecular chain thus generating two radical chain fragments was proposed as the primary happening.[3] In either case the reaction commences at a point randomly selected on the molecular chain. The UV-curing process was not adopted into the production process until recently. The process is now being used for such lubricant mixtures as A20H/Z-dol and A20H/Z-tetraol. In these mixtures, however, an electro- or photo-chemistry involving the phosphazene moiety of A20H appears to play a major role.[4] One negative issue with the far-UV curing process is production of ozone if oxygen is present.

Content Area Reading and Disciplinary Literacy: A Case for The Radical Center

2013 ◽  
Vol 56 (5) ◽  
pp. 353-357 ◽  
Author(s):  
William G. Brozo ◽  
Gary Moorman ◽  
Carla Meyer ◽  
Trevor Stewart
Keyword(s):  
Content Area Reading ◽  
Disciplinary Literacy ◽  
Content Area ◽  
Radical Center

Theoretical examination of competitive β-radical-induced cleavages of N–Cα and Cα–C bonds of peptides

2015 ◽  
Vol 93 (12) ◽  
pp. 1355-1362 ◽  
Author(s):  
Wai-Kit Tang ◽  
Chun-Ping Leong ◽  
Qiang Hao ◽  
Chi-Kit Siu
Keyword(s):  
Amino Acid ◽  
Density Functional ◽  
Bond Cleavage ◽  
Radical Cations ◽  
Radical Center ◽  
Amino Acid Residues ◽  
Mobile Proton ◽  
Aromatic Side Chain ◽  
Heterolytic Cleavage ◽  
Terminal Fragment

Selective cleavages of N–Cα and Cα–C bonds of β-radical tautomers of amino acid residues in radical peptides have been examined theoretically by means of the density functional theory at the M06-2X/6-311++G(d,p) level. The majority of the bond cleavages are homolytic via β-scission. Their energy barriers depend largely on the ability of the radical being stabilized in the transition structures and the availability of a mobile proton in the vicinity of the β-radical center. The N–Cα bond is less favorably cleaved than the Cα–C bond (except Ser and Thr) for systems without a mobile proton. It is because, firstly, the homolytic cleavage is less favorable for the more polar N–Cα bond than for the less polar Cα–C bond. Secondly, a less stable σ-radical localized on the amide nitrogen atom of the incipient N-terminal fragment is formed for the former, while a more stable radical delocalized in a π*(CO)-like orbital of the incipient C-terminal fragment is formed for the latter. In the presence of a mobile proton N-terminal to the β-radical center, some degrees of heterolytic cleavage character, as preferred by the polar N–Cα bond, are observed. Consequently, its barrier is reduced. If the mobile proton is located at the C-terminal amide oxygen of the β-radical center, the Cα–C bond cleavage will be significantly suppressed. It is because the radical in the incipient C-terminal fragment becomes more localized as a σ-radical on the carbon atom of its protonated amide group. With basic amino acid residues, the Cα–C bond cleavage can be reactivated. Heterolytic cleavage of the polar N–Cα bond can be largely facilitated if a mobile proton N-terminal to the β-radical center is available and the radical in the incipient C-terminal fragment is sufficiently stabilized, for instance, by the aromatic side chain of Trp and Tyr. Therefore, cleavages of the N–Cα bond induced by the β-radical tautomer of Trp and Tyr are often preferred as compared with cleavages of the Cα–C bond in peptide radical cations containing mobile protons.

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