scholarly journals Embedding of dendriform algebras into Rota-Baxter algebras

2013 ◽  
Vol 11 (2) ◽  
Author(s):  
Vsevolod Gubarev ◽  
Pavel Kolesnikov
Keyword(s):  
Recent Work ◽  
Dendriform Algebra ◽  
Dendriform Algebras

AbstractFollowing a recent work [Bai C., Bellier O., Guo L., Ni X., Splitting of operations, Manin products, and Rota-Baxter operators, Int. Math. Res. Not. IMRN (in press), DOI: 10.1093/imrn/rnr266] we define what is a dendriform dior trialgebra corresponding to an arbitrary variety Var of binary algebras (associative, commutative, Poisson, etc.). We call such algebras di- or tri-Var-dendriform algebras, respectively. We prove in general that the operad governing the variety of di- or tri-Var-dendriform algebras is Koszul dual to the operad governing di- or trialgebras corresponding to Var!. We also prove that every di-Var-dendriform algebra can be embedded into a Rota-Baxter algebra of weight zero in the variety Var, and every tri-Var-dendriform algebra can be embedded into a Rota-Baxter algebra of nonzero weight in Var.

scholarly journals Free dendriform algebras. Part I. A parenthesis setting

2006 ◽  
Vol 2006 ◽  
pp. 1-16
Author(s):  
Philippe Leroux
Keyword(s):  
Free Probability ◽  
Dendriform Algebra ◽  
Dendriform Algebras

We propose both a reformulation of some known results on the free dendriform algebra on one generator from a parenthesis setting instead of using permutations and some developments as well. Moreover, by introducing the concept of NCP-operad, we show how to use the free dendriform algebra on one generator to reformulate some results obtained by Speicher in free probability.

scholarly journals Typed Angularly Decorated Planar Rooted Trees and Ω-Rota-Baxter Algebras

Mathematics ◽  
2022 ◽  
Vol 10 (2) ◽  
pp. 190
Author(s):  
Yi Zhang ◽  
Xiaosong Peng ◽  
Yuanyuan Zhang
Keyword(s):  
Rooted Trees ◽  
Integral Analysis ◽  
Dendriform Algebra ◽  
Dendriform Algebras ◽  
Definition Of ◽  
The Relationship ◽  
Planar Rooted Trees

As a generalization of Rota–Baxter algebras, the concept of an Ω-Rota–Baxter could also be regarded as an algebraic abstraction of the integral analysis. In this paper, we introduce the concept of an Ω-dendriform algebra and show the relationship between Ω-Rota–Baxter algebras and Ω-dendriform algebras. Then, we provide a multiplication recursion definition of typed, angularly decorated rooted trees. Finally, we construct the free Ω-Rota–Baxter algebra by typed, angularly decorated rooted trees.

What sentimentalists should say about emotion

2019 ◽  
Vol 42 ◽  
Author(s):  
Charlie Kurth
Keyword(s):  
Moral Judgment ◽  
Recent Work ◽  
Relevant Information ◽  
Moral Cognition ◽  
Multilevel Structure

Abstract Recent work by emotion researchers indicates that emotions have a multilevel structure. Sophisticated sentimentalists should take note of this work – for it better enables them to defend a substantive role for emotion in moral cognition. Contra May's rationalist criticisms, emotions are not only able to carry morally relevant information, but can also substantially influence moral judgment and reasoning.

The Sun as a Magnetic Star

1976 ◽  
Vol 32 ◽  
pp. 457-463
Author(s):  
John M. Wilcox ◽  
Leif Svalgaard
Keyword(s):  
Recent Work ◽  
Rotation Axis ◽  
Polar Field ◽  
Magnetic Star ◽  
Rotational Axis ◽  
Field Variation ◽  
The Sun ◽  
Arbitrary Angle ◽  
Solar Magnetism ◽  
Oblique Rotator

SummaryThe sun as a magnetic star is described on the basis of recent work on solar magnetism. Observations at an arbitrary angle to the rotation axis would show a 22-year polar field variation and a 25-day equatorial sector variation. The sector variation would be similar to an oblique rotator with an angle of 90° between the magnetic and rotational axis.

Microstructural comparison of synthetic bioceramics with natural bioceramics

1991 ◽  
Vol 49 ◽  
pp. 38-39
Author(s):  
Shulin Wen ◽  
Jingwei Feng ◽  
A. Krajewski ◽  
A. Ravaglioli
Keyword(s):  
Recent Work ◽  
Human Body ◽  
Human Tissues ◽  
Main Constituent ◽  
Laboratory Furnace ◽  
Chinese Adult ◽  
Human Enamel ◽  
Biological Compatibility ◽  
Synthetic Hydroxyapatite ◽  
Synthetic Work

Hydroxyapatite bioceramics has attracted many material scientists as it is the main constituent of the bone and the teeth in human body. The synthesis of the bioceramics has been performed for years. Nowadays, the synthetic work is not only focused on the hydroapatite but also on the fluorapatite and chlorapatite bioceramics since later materials have also biological compatibility with human tissues; and they may also be very promising for clinic purpose. However, in comparison of the synthetic bioceramics with natural one on microstructure, a great differences were observed according to our previous results. We have investigated these differences further in this work since they are very important to appraise the synthetic bioceramics for their clinic application.The synthetic hydroxyapatite and chlorapatite were prepared according to A. Krajewski and A. Ravaglioli and their recent work. The briquettes from different hydroxyapatite or chlorapatite powders were fired in a laboratory furnace at the temperature of 900-1300°C. The samples of human enamel selected for the comparison with synthetic bioceramics were from Chinese adult teeth.

Substrate specificity and inducibility of TACE (tumour necrosis factor α-converting enzyme) revisited: the Ala-Val preference, and induced intrinsic activity

2003 ◽  
Vol 70 ◽  
pp. 39-52 ◽  
Author(s):  
Roy A. Black ◽  
John R. Doedens ◽  
Rajeev Mahimkar ◽  
Richard Johnson ◽  
Lin Guo ◽  
...  
Keyword(s):  
Substrate Specificity ◽  
Recent Work ◽  
Tumour Necrosis Factor ◽  
Tumour Necrosis ◽  
Transforming Growth Factor ◽  
Intrinsic Activity ◽  
Converting Enzyme ◽  
Tumour Necrosis Factor Α ◽  
Factor Α ◽  
Necrosis Factor

Tumour necrosis factor α (TNFα)-converting enzyme (TACE/ADAM-17, where ADAM stands for a disintegrin and metalloproteinase) releases from the cell surface the extracellular domains of TNF and several other proteins. Previous studies have found that, while purified TACE preferentially cleaves peptides representing the processing sites in TNF and transforming growth factor α, the cellular enzyme nonetheless also sheds proteins with divergent cleavage sites very efficiently. More recent work, identifying the cleavage site in the p75 TNF receptor, quantifying the susceptibility of additional peptides to cleavage by TACE and identifying additional protein substrates, underlines the complexity of TACE-substrate interactions. In addition to substrate specificity, the mechanism underlying the increased rate of shedding caused by agents that activate cells remains poorly understood. Recent work in this area, utilizing a peptide substrate as a probe for cellular TACE activity, indicates that the intrinsic activity of the enzyme is somehow increased.

Recent work on group III antimonides and arsenides

Physica ◽  
1954 ◽  
Vol 3 (7-12) ◽  
pp. 1065-1067
Author(s):  
H HROSTOWSKI ◽  
M TANENBAUM
Keyword(s):  
Recent Work ◽  
Group Iii

MANUSCRIPT EVIDENCE FOR ALPHABET-SWITCHING IN THE WORKS OF CICERO: COMMON NOUNS AND ADJECTIVES

2018 ◽  
Vol 68 (2) ◽  
pp. 498-516
Author(s):  
Neil O'Sullivan
Keyword(s):  
Recent Work ◽  
Code Switching ◽  
Consistent Pattern ◽  
Current Interest ◽  
Reliable Transmission ◽  
Accurate Record ◽  
The Way

Of the hundreds of Greek common nouns and adjectives preserved in our MSS of Cicero, about three dozen are found written in the Latin alphabet as well as in the Greek. So we find, alongside συμπάθεια, also sympathia, and ἱστορικός as well as historicus. This sort of variation has been termed alphabet-switching; it has received little attention in connection with Cicero, even though it is relevant to subjects of current interest such as his bilingualism and the role of code-switching and loanwords in his works. Rather than addressing these issues directly, this discussion sets out information about the way in which the words are written in our surviving MSS of Cicero and takes further some recent work on the presentation of Greek words in Latin texts. It argues that, for the most part, coherent patterns and explanations can be found in the alphabetic choices exhibited by them, or at least by the earliest of them when there is conflict in the paradosis, and that this coherence is evidence for a generally reliable transmission of Cicero's original choices. While a lack of coherence might indicate unreliable transmission, or even an indifference on Cicero's part, a consistent pattern can only really be explained as an accurate record of coherent alphabet choice made by Cicero when writing Greek words.

Recent Work of the Russian Academy of Science

1921 ◽  
Vol 3 (6supp) ◽  
pp. 561-562
Author(s):  
Vernon Kellogg ◽  
R. M. Yerkes ◽  
H. E. Howe
Keyword(s):  
Recent Work

Excavation at Montfode Mount Motte, Ayrshire

1986 ◽  
Vol 13 (1) ◽  
pp. 78-85 ◽  
Author(s):  
Heather F James
Keyword(s):  
Recent Work ◽  
Aerial Photographs ◽  
Formed Part

Summary A two week excavation in two areas around the Scheduled Monument known as Montfode Mount confirmed the existence of the arcs of two outer concentric ditches noted on aerial photographs and an inner ditch at the base of the motte. There was no stratigraphical relationship between the outer ditches and the motte, and the excavation did not provide dating evidence for any of these features. While allowing for the fact that the outer ditches may be Medieval in date the excavator suggests that the ditches formed part of the defenses of a promontory fort of prehistoric date. In the light of recent work the interpretation of the mound as a motte is also discussed.

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