scholarly journals Limit Densities of Patterns in Permutation Inflations

10.37236/8234 ◽  
2021 ◽  
Vol 28 (1) ◽  
Author(s):  
Tanya Khovanova ◽  
Eric Zhang
Keyword(s):  
General Formula ◽  
Tensor Products ◽  
Convergent Sequence ◽  
Point Pattern ◽  
Random Permutations

Call a permutation $k$-inflatable if the sequence of its tensor products with uniform random permutations of increasing lengths has uniform $k$-point pattern densities. Previous work has shown that nontrivial $k$-inflatable permutations do not exist for $k \geq 4$. In this paper, we derive a general formula for the limit densities of patterns in the sequence of tensor products of a fixed permutation with each permutation from a convergent sequence. By applying this result, we completely characterize $3$-inflatable permutations and find explicit examples of $3$-inflatable permutations with various lengths, including the shortest examples with length $17$.

Synthesis of B-ring-fluorinated (−)-epicatechin gallate derivatives

2020 ◽  
Vol 18 (21) ◽  
pp. 4024-4028
Author(s):  
David D. S. Thieltges ◽  
Kai D. Baumgarten ◽  
Carina S. Michaelis ◽  
Constantin Czekelius
Keyword(s):  
Kinetic Resolution ◽  
Convergent Sequence ◽  
Epicatechin Gallate

Electronically modified, fluorinated catechins and epicatechins are enantioselectively synthesized in a short, convergent sequence via kinetic resolution.

X-ray Structure Refinement and Vibrational Spectroscopy of Ca8Gd2 (PO4)6 O2

2013 ◽  
Vol 12 (10) ◽  
pp. 719-726
Author(s):  
R. Ayadi ◽  
Mohamed Boujelbene ◽  
T. Mhiri
Keyword(s):  
Solid State ◽  
General Formula ◽  
Vibrational Spectroscopy ◽  
Powder Diffraction ◽  
Infrared Spectra ◽  
Solid State Reaction ◽  
Structure Refinement ◽  
Unit Cell ◽  
Cell Group ◽  
X Ray

The present paper is interested in the study of compounds from the apatite family with the general formula Ca10 (PO4)6A2. It particularly brings to light the exploitation of the distinctive stereochemistries of two Ca positions in apatite. In fact, Gd-Bearing oxyapatiteCa8 Gd2 (PO4)6O2 has been synthesized by solid state reaction and characterized by X-ray powder diffraction. The site occupancies of substituents is0.3333 in Gd and 0.3333 for Ca in the Ca(1) position and 0. 5 for Gd in the Ca (2) position.  Besides, the observed frequencies in the Raman and infrared spectra were explained and discussed on the basis of unit-cell group analyses.

Isn't it eyeronic? Little evidence for consistent eye colour choices across relationships

2018 ◽  
Author(s):  
Amy Victoria Newman ◽  
Thomas V. Pollet ◽  
Kristofor McCarty ◽  
Nick Neave ◽  
Tamsin Saxton
Keyword(s):  
Good Evidence ◽  
Random Permutations ◽  
Three Samples ◽  
Eye Colour ◽  
A Priority

This study examined the anecdotal notion that people choose partners based on preferred characteristics that constitute their ‘type’. We gathered the eye colours of participants’ partners across their entire romantic history in three samples (student-centred, adult, and celebrity). We calculated the proportion of partners’ eye colours, and compared that to 100,000 random permutations of our observed dataset using t-tests. This was to investigate if the eye colour choices in the original datasets had greater consistency than in the permutations. Across all samples, we observed no good evidence that individuals make consistent eye colour choices, suggesting that eye colour may not be a priority when choosing a partner.

Toxicity of Para-Chloro Substituted Benzene Derivatives in the Microtox™ Test

1985 ◽  
Vol 20 (2) ◽  
pp. 36-43 ◽  
Author(s):  
Klaus L.E. Kaiser ◽  
Juan M. Ribo ◽  
Brian M. Zaruk
Keyword(s):  
General Formula ◽  
Functional Group ◽  
Structural Parameters ◽  
Systematic Investigation ◽  
Photobacterium Phosphoreum ◽  
Benzene Derivatives ◽  
Quantitative Structure ◽  
Chlorinated Benzenes ◽  
Chloro Derivatives ◽  
Derivatives Of

Abstract This paper gives the results of part of a systematic investigation into contaminant toxicity to Photobacterium phosphoreum in the Microtox™ test. Reported are the toxicity values for 39 para-chloro substituted benzene derivatives of the general formula l-Cl-C6h4-4-X=CH2CH(NH2)COOH, F, SO2NH2, OCH2COOH, CH2COOH, CONHNH2, NHCOCH3, CONH2, CH=CHCOOH, SeOOH, CH2NH2, CH2CH2NH2, NO2, H, CF3, CHO, CH2OH, OH, CH3, CCl3, COCH3, COOH, NH2, SO2C6H5, Cl, CH2COCH3, COCl, CN, OCH3, NCO, NHCH3, I, COC6H5, CH2Cl, SH, CH2SH, NCS, CH2CN and SO2C6H4Cl. Except for the last compound, whose solubility is below the required concentration, the toxicities increase in the presented order with a total range of more than three orders of magnitude. The data are discussed in terms of quantitative structure-toxicity correlations with compound-specific structural parameters. In combination with a previously developed submodel on chlorinated benzenes, phenols, nitrobenzenes and anilines, the observed relationships allow the prediction of the toxicity of some 780 possible chloro derivatives of the general formula C6H5-nClnX, where n=<5 and X is a functional group as listed above.

Synthesis of isomeric 1,1'-phenylene-bis(6-azauracil-5-carbonitriles)

1990 ◽  
Vol 55 (12) ◽  
pp. 2967-2976 ◽  
Author(s):  
Jan Slouka
Keyword(s):  
General Formula ◽  
Mutual Distance ◽  
Planar Molecules ◽  
Amino Derivatives

The described synthesis of all three isomeric 1,1'-phenylene-bis(6-azauracil-5-carbonitriles) IVa-IVc starts from the respective 1-nitrophenyl-6-azauracil-5-carbonitriles Ia-Ic which were reduced to the corresponding amino derivatives IIa-IIc, diazotized, and coupled with ethyl cyanoacetylcarbamate to give the isomeric hydrazones IIIa-IIIc which were finally cyclized to the title compounds containing two 6-azauracil rings. A general formula is presented for calculation of mutual distance of arbitrary atoms in any planar molecules.

The Coordination Chemistry of Phosphoryl Compounds Containing the — N(CH3)2 Group, Part VIII

1972 ◽  
Vol 27 (7) ◽  
pp. 759-763 ◽  
Author(s):  
M. W. G. De Bolster ◽  
W. L. Groeneveld
Keyword(s):  
Coordination Chemistry ◽  
General Formula ◽  
Ligand Field ◽  
Chemical Analyses ◽  
X Ray ◽  
Physical Measurements ◽  
Ligand Field Spectra ◽  
Chloride Adduct ◽  
Ligand Field Parameters ◽  
Group Part

A number of new solvates and adducts containing bisphenyldimethylaminophosphine oxide is reported. The solvates have the general formula M[(C6H5)2P(O)N(CH3)2]42+(anion-)2, in which M = Mg, Ca, Mn, Fe, Co, Ni, Cu, Zn and Cd, and the anions are ClO4- and BF4-. The adducts have the general formula M[(C6H5)2P(O)N(CH3)2]2Cl2, where M stands for the same series of metals.The compounds are characterized and identified by chemical analyses and physical measurements.Ligand-field and vibrational spectra have been investigated; values for the ligand-field parameters are reported. It is concluded that coordination takes place via the oxygen atom of the ligand.X-ray powder patterns were used in combination with ligand-field spectra to deduce the coordination around the metal ions.The interesting behaviour of the nickel (II) chloride adduct upon heating is discussed and it is shown that both a square pyramidal and a tetrahedral modification exists.

scholarly journals Does fluvial channel-belt clustering predict net sand to gross rock volume? Architectural metrics and point-pattern analysis of a digital outcrop model

2019 ◽  
Vol 89 (11) ◽  
pp. 1109-1126
Author(s):  
Alexander R. Koch ◽  
Cari L. Johnson ◽  
Lisa Stright
Keyword(s):  
Large Scale ◽  
Small Scale ◽  
Point Pattern ◽  
Point Patterns ◽  
Spatial Point ◽  
Channel Belt ◽  
John Henry Member ◽  
Scale Point ◽  
Belt Width ◽  
Digital Outcrop

ABSTRACT Spatial point-pattern analyses (PPAs) are used to quantify clustering, randomness, and uniformity of the distribution of channel belts in fluvial strata. Point patterns may reflect end-member fluvial architecture, e.g., uniform compensational stacking and avulsion-generated clustering, which may change laterally, especially at greater scales. To investigate spatial and temporal changes in fluvial systems, we performed PPA and architectural analyses on extensive outcrops of the Cretaceous John Henry Member of the Straight Cliffs Formation in southern Utah, USA. Digital outcrop models (DOMs) produced using unmanned aircraft system-based stereophotogrammetry form the basis of detailed interpretations of a 250-m-thick fluvial succession over a total outcrop length of 4.5 km. The outcrops are oriented roughly perpendicular to fluvial transport direction. This transverse cross-sectional exposure of the fluvial system allows a study of the system's variation along depositional strike. We developed a workflow that examines spatial point patterns using the quadrat method, and architectural metrics such as net sand to gross rock volume (NTG), amalgamation index, and channel-belt width and thickness within moving windows. Quadrat cell sizes that are ∼ 50% of the average channel-belt width-to-thickness ratio (16:1 aspect ratio) provide an optimized scale to investigate laterally elongate distributions of fluvial-channel-belt centroids. Large-scale quadrat point patterns were recognized using an array of four quadrat cells, each with 237× greater area than the median channel belt. Large-scale point patterns and NTG correlate negatively, which is a result of using centroid-based PPA on a dataset with disparately sized channel belts. Small-scale quadrat point patterns were recognized using an array of 16 quadrat cells, each with 21× greater area than the median channel belt. Small-scale point patterns and NTG correlate positively, and match previously observed stratigraphic trends in the fluvial John Henry Member, suggesting that these are regional trends. There are deviations from these trends in architectural statistics over small distances (hundreds of meters) which are interpreted to reflect autogenic avulsion processes. Small-scale autogenic processes result in architecture that is difficult to correlate between 1D datasets, for example when characterizing a reservoir using well logs. We show that 1D NTG provides the most accurate prediction for surrounding 2D architecture.

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