CXLIX.—Studies of dynamic isomerism. Part IX. The relationship between absorption spectra and isomeric change. Absorption spectra of sulphonic derivatives of camphor

1909 ◽  
Vol 95 (0) ◽  
pp. 1340-1346
Author(s):  
Thomas Martin Lowry ◽  
Cecil Henry Desch
Keyword(s):  
Absorption Spectra ◽  
The Relationship ◽  
Derivatives Of

Infrared spectra and substituent effects in 2-(3-, and 4-substituted phenylmethylene)-1,3-cycloheptanediones

1983 ◽  
Vol 48 (2) ◽  
pp. 586-595 ◽  
Author(s):  
Alexander Perjéssy ◽  
Pavol Hrnčiar ◽  
Ján Šraga
Keyword(s):  
Substituent Effects ◽  
Phenyl Group ◽  
Wave Number ◽  
Vibrational Coupling ◽  
Wave Numbers ◽  
Stretching Vibration ◽  
Stretching Vibrations ◽  
The Relationship ◽  
Derivatives Of ◽  
Effect Of Structure

The wave numbers of the fundamental C=O and C=C stretching vibrations, as well as that of the first overtone of C=O stretching vibration of 2-(3-, and 4-substituted phenylmethylene)-1,3-cycloheptanediones and 1,3-cycloheptanedione were measured in tetrachloromethane and chloroform. The spectral data were correlated with σ+ constants of substituents attached to phenyl group and with wave number shifts of the C=O stretching vibration of substituted acetophenones. The slope of the linear dependence ν vs ν+ of the C=C stretching vibration of the ethylenic group was found to be more than two times higher than that of the analogous correlation of the C=O stretching vibration. Positive values of anharmonicity for asymmetric C=O stretching vibration can be considered as an evidence of the vibrational coupling in a cyclic 1,3-dicarbonyl system similarly, as with derivatives of 1,3-indanedione. The relationship between the wave numbers of the symmetric and asymmetric C=O stretching vibrations indicates that the effect of structure upon both vibrations is symmetric. The vibrational coupling in 1,3-cycloheptanediones and the application of Seth-Paul-Van-Duyse equation is discussed in relation to analogous results obtained for other cyclic 1,3-dicarbonyl compounds.

Private and Public Law

2020 ◽  
pp. 574-592
Author(s):  
Thomas W. Merrill
Keyword(s):  
Law And Economics ◽  
Public Law ◽  
Private Law ◽  
General Criterion ◽  
The Public ◽  
Private Ordering ◽  
Public Rights ◽  
Private And Public ◽  
The Relationship ◽  
Derivatives Of

This chapter explores the relationship between private and public law. In civil law countries, the public-private distinction serves as an organizing principle of the entire legal system. In common law jurisdictions, the distinction is at best an implicit design principle and is used primarily as an informal device for categorizing different fields of law. Even if not explicitly recognized as an organizing principle, however, it is plausible that private and public law perform distinct functions. Private law supplies the tools that make private ordering possible—the discretionary decisions that individuals make in structuring their lives. Public law is concerned with providing public goods—broadly defined—that cannot be adequately supplied by private ordering. In the twentieth and twenty-first centuries, various schools of thought derived from utilitarianism have assimilated both private and public rights to the same general criterion of aggregate welfare analysis. This has left judges with no clear conception of the distinction between private and public law. Another problematic feature of modern legal thought is a curious inversion in which scholars who focus on fields of private law have turned increasingly to law and economics, one of the derivatives of utilitarianism, whereas scholars who concern themselves with public law are increasingly drawn to new versions of natural rights thinking, in the form of universal human rights.

On derivatives of fuzzy multi-dimensional mappings and applications under generalized differentiability

2021 ◽  
pp. 1-19
Author(s):  
M. Miri Karbasaki ◽  
M. R. Balooch Shahriari ◽  
O. Sedaghatfar
Keyword(s):  
Linear Function ◽  
Level Set ◽  
Fuzzy Numbers ◽  
Sufficient Condition ◽  
Continuous Linear ◽  
Generalized Differentiability ◽  
Relationship Of ◽  
The Relationship ◽  
Derivatives Of ◽  
Dimensional Mapping

This article identifies and presents the generalized difference (g-difference) of fuzzy numbers, Fréchet and Gâteaux generalized differentiability (g-differentiability) for fuzzy multi-dimensional mapping which consists of a new concept, fuzzy g-(continuous linear) function; Moreover, the relationship between Fréchet and Gâteaux g-differentiability is studied and shown. The concepts of directional and partial g-differentiability are further framed and the relationship of which will the aforementioned concepts are also explored. Furthermore, characterization is pointed out for Fréchet and Gâteaux g-differentiability; based on level-set and through differentiability of endpoints real-valued functions a characterization is also offered and explored for directional and partial g-differentiability. The sufficient condition for Fréchet and Gâteaux g-differentiability, directional and partial g-differentiability based on level-set and through employing level-wise gH-differentiability (LgH-differentiability) is expressed. Finally, to illustrate the ability and reliability of the aforementioned concepts we have solved some application examples.

scholarly journals Permutation Matrices, Their Discrete Derivatives and Extremal Properties

2020 ◽  
Vol 48 (4) ◽  
pp. 719-740
Author(s):  
Richard A. Brualdi ◽  
Geir Dahl
Keyword(s):  
Permutation Matrix ◽  
Permutation Matrices ◽  
Discrete Derivative ◽  
The Relationship ◽  
Derivatives Of ◽  
Extremal Properties

AbstractFor a permutation π, and the corresponding permutation matrix, we introduce the notion of discrete derivative, obtained by taking differences of successive entries in π. We characterize the possible derivatives of permutations, and consider questions for permutations with certain properties satisfied by the derivative. For instance, we consider permutations with distinct derivatives, and the relationship to so-called Costas arrays.

The photodegradation of metronidazole in the presence of coexisting pharmaceuticals

2012 ◽  
Vol 66 (4) ◽  
pp. 735-740 ◽  
Author(s):  
Bo Wu ◽  
Ting Zhang ◽  
Jinxia Li ◽  
Yong Ye ◽  
Huaixia Chen
Keyword(s):  
Surface Water ◽  
Absorption Spectra ◽  
Environmental Water ◽  
Ultraviolet Absorption ◽  
Solar Irradiation ◽  
Batch Experiments ◽  
The Relationship

The objective of this study was to investigate if coexisting compounds could affect the fate of pharmaceuticals in surface water under solar irradiation. The degradation of metronidazole (MET) in the presence of different coexisting pharmaceuticals was investigated in batch experiments with exposure to sunlight. Tinidazole, which has a similar structure to MET, was employed as an analogue. The results indicated that the presence of an analogue with a similar photosensitive group to MET could inhibit the photodegradation of MET. In addition, the effect of coexisting pharmaceuticals with different absorption spectra on the degradation of MET was investigated. The results showed that the effect depended on the degree of overlapping absorption spectra between MET and the coexisting pharmaceuticals. The relationship between the degree of the influence and the ultraviolet absorption spectra of coexisting pharmaceuticals found in this study could give guidance in assessing the fate of pharmaceuticals in environmental water.

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