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.

scholarly journals Aztec Diamonds and Baxter Permutations

10.37236/377 ◽  
2010 ◽  
Vol 17 (1) ◽  
Author(s):  
Hal Canary
Keyword(s):  
Permutation Matrix ◽  
Enumerative Combinatorics ◽  
Alternating Sign Matrices ◽  
Domino Tilings ◽  
Permutation Matrices ◽  
Pattern Avoiding Permutations ◽  
The Relationship

We present a proof of a conjecture about the relationship between Baxter permutations and pairs of alternating sign matrices that are produced from domino tilings of Aztec diamonds. It is shown that a tiling corresponds to a pair of ASMs that are both permutation matrices if and only if the larger permutation matrix corresponds to a Baxter permutation. There has been a thriving literature on both pattern-avoiding permutations of various kinds [Baxter 1964, Dulucq and Guibert 1988] and tilings of regions using dominos or rhombuses as tiles [Elkies et al. 1992, Kuo 2004]. However, there have not as of yet been many links between these two areas of enumerative combinatorics. This paper gives one such link.

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 Covalent labelling of ligand binding sites of human placental S-adenosylhomocysteine hydrolase with 8-azido derivatives of adenosine and cyclic AMP

1985 ◽  
Vol 232 (3) ◽  
pp. 643-650 ◽  
Author(s):  
V N Aiyar ◽  
M S Hershfield
Keyword(s):  
Cyclic Amp ◽  
Binding Sites ◽  
Catalytic Mechanism ◽  
Periodate Oxidation ◽  
Regulatory Subunit ◽  
Adenosylhomocysteine Hydrolase ◽  
Dependent Protein ◽  
Covalently Linked ◽  
The Relationship ◽  
Derivatives Of

S-Adenosylhomocysteine hydrolase (AdoHcyase) has previously been identified as a cytoplasmic adenosine and cyclic AMP binding protein. In order to examine the relationship between the adenosine and cyclic AMP binding sites on this enzyme we have explored the use of 8-azido analogues of adenosine and cyclic AMP as photoaffinity reagents for covalently labelling AdoHcyase purified from human placenta. 8-Azidoadenosine (8-N3-Ado), like adenosine, inactivated AdoHcyase, and the rate of inactivation was greatly increased by periodate oxidation. In addition, 8-N3-Ado was found to participate in the first step in the catalytic mechanism for AdoHcyase, resulting in conversion of enzyme-bound NAD+ to NADH, although it was not a substrate for the full enzyme-catalysed reaction. Radioactively labelled 8-N3-Ado, its periodate-oxidized derivative and 8-azidoadenosine 3′, 5′-phosphate (8-N3-cAMP) bound specifically to adenosine binding sites on AdoHcyase and, after irradiation, became covalently linked to the enzyme. Photoaffinity-labelled enzyme could be precipitated by monoclonal antibody to human AdoHcyase. Two observations suggested that cyclic AMP and adenosine bind to the same sites on AdoHcyase. First cyclic AMP and adenosine each blocked binding of both radioactively labelled 8-N3-Ado and 8-N3-cAMP, and second, digestion with V8 proteinase generated identical patterns of peptides from AdoHcyase that had been photolabelled with [32P]8-N3-cAMP and [3H]8-N3-Ado. Binding sites for cyclic AMP on AdoHcyase were found to differ functionally and structurally from cyclic AMP binding sites on the R1 regulatory subunit of cyclic AMP-dependent protein kinase.

On the new Narayana polynomials, the Gauss Narayana numbers and their polynomials

2020 ◽  
pp. 2150100
Author(s):  
Engi̇n Özkan ◽  
Bahar Kuloğlu
Keyword(s):  
Hankel Transform ◽  
Pell Numbers ◽  
Pascal’S Triangle ◽  
Narayana Numbers ◽  
Definition Of ◽  
Pascal's Triangle ◽  
The Relationship ◽  
Derivatives Of

We give a new definition of Narayana polynomials and show that there is a relationship between the coefficient of the new Narayana polynomials and Pascal’s triangle. We define the Gauss Narayana numbers and their polynomials. Then we show that there is a relationship between the Gauss Narayana polynomials and the new Narayana polynomials. Also, we show that there is a relationship between the derivatives of the new Narayana polynomials and Pascal’s triangle. We also explain the relationship between the new Narayana polynomials and the known Pell numbers. Finally, we give the Hankel transform of the new Narayana polynomials.

A Statistical Analysis of Corrosion Wastage of Transverse Members in Single Hull Tankers

2006 ◽  
Author(s):  
Swieng Thuanboon ◽  
David S. Tordonato ◽  
William Navidi ◽  
David L. Olson ◽  
Brajendra Mishra ◽  
...  
Keyword(s):  
Statistical Analysis ◽  
Weibull Function ◽  
Structural Members ◽  
Ship Structure ◽  
Corrosion Rates ◽  
Protection Systems ◽  
Oil Tankers ◽  
The Relationship ◽  
Derivatives Of ◽  
Best Fit

Corrosion wastage of structural members in oil tankers over the time causes variability in structural properties. Corrosion is a function of many variables and uncertainties, such as the types of corrosion protection systems used, types of cargo, temperature, humidity, etc. The traditional engineering and analysis, which uses simplified deterministic approaches to account for this time-dependent reliability or risk of aging ship structure, is not suitable. This investigation explores the use of statistical analysis approaches to predict corrosion wastage in oil carrying tankers. Corrosion wastage measurements from transverse members of 115 oil tankers were collected to add to an extensive corrosion wastage database. Lognormal function was found to best fit the collected data when compared to other methods, such as the Weibull function. Linear regression in the form of three mathematical models of corrosion wastage, developed by considering age of ship, coating life, and the location of the transverse members, is used to indicate the relationship between corrosion wastage and age of ship. Corrosion rates were determined by the derivatives of the corrosion wastage. The results show that corrosion wastage may accelerate after twenty years of service. It is expected that the study will help identify which structural members may be more susceptible to corrosion wastage and require more frequent inspection.

scholarly journals EXACT NONNULL WAVELIKE SOLUTIONS TO GRAVITY WITH QUADRATIC LAGRANGIANS

1994 ◽  
Vol 09 (02) ◽  
pp. 167-179 ◽  
Author(s):  
M.D. ROBERTS
Keyword(s):  
Gravitational Radiation ◽  
Riemann Tensor ◽  
Gravitational Energy ◽  
Cross Terms ◽  
Linearized Theory ◽  
Relationship Of ◽  
The Relationship ◽  
Poynting Vectors ◽  
Derivatives Of

Solutions to gravity with quadratic Lagrangians are found for the simple case where the only nonconstant metric component is the lapse N and the Riemann tensor takes the form [Formula: see text] thus these solutions depend on cross terms in the Riemann tensor and therefore complement linearized theory where it is the derivatives of the Riemann tensor that matter. The relationship of this metric to the null gravitational radiation metric of Peres is given. Gravitational energy Poynting vectors are constructed for the solutions and one of these, based on the Lanczos tensor, supports the indication in the linearized theory that nonnull gravitational radiation can occur.

CARNAP ON EXTREMAL AXIOMS, “COMPLETENESS OF THE MODELS,” AND CATEGORICITY

2012 ◽  
Vol 5 (4) ◽  
pp. 613-641 ◽  
Author(s):  
GEORG SCHIEMER
Keyword(s):  
The Relationship ◽  
Extremal Properties

AbstractThis paper provides a historically sensitive discussion of Carnap’s theory of extremal axioms developed first in the late 1920s. The main focus is set on the unpublished documents of the projected second part of his manuscript Untersuchungen zur allgemeinen Axiomatik (RC 081-01-01 to 081-01-33). Carnap’s theory will be assessed with respect to two interpretive issues. The first concerns his mathematical sources, that is, the mathematical axioms on which his extremal axioms were based. The second concerns Carnap’s understanding of the relationship between the “completeness of the models” and other metatheoretic notions investigated by him at the time, most notably that of categoricity. The paper surveys Carnap’s different attempts to explicate the extremal properties of a theory and puts his results in context with related metamathematical research at the time.

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