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Ebrahimi-Fard Kurusch José M. Gracia-Bondía Frédéric Patras 《Letters in Mathematical Physics》2007,81(1):61-75
The word problem for an arbitrary associative Rota–Baxter algebra is solved. This leads to a noncommutative generalization
of the classical Spitzer identities. Links to other combinatorial aspects are indicated.
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Dhont Guillaume Cassam-Chenaï Patrick Patras Frédéric 《Journal of mathematical chemistry》2021,59(10):2294-2326
Journal of Mathematical Chemistry - The construction of integrity bases for invariant and covariant polynomials built from a set of three dimensional vectors under the $${{\mathrm {SO(3)}}}$$ and... 相似文献
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Aliona Ghendov-Mosanu Daniela Cojocari Greta Balan Antoanela Patras Ildiko Lung Maria-Loredana Soran Ocsana Opri Elena Cristea Rodica Sturza 《Molecules (Basel, Switzerland)》2022,27(5)
The article focuses on the optimization of the extraction process of biologically active compounds (BAC) from grape marc—a by-product of the wine industry. The influence of temperature, specifically 30 °C, 45 °C and 65 °C, and ethanol concentration in solutions, specifically 0–96% (v/v) on the extraction yield of polyphenols, flavonoids, tannins and anthocyanins, were investigated. The composition of individual polyphenols, anthocyanins and organic acids, antioxidant activity (DPPH and ABTS) and CIELab chromatic characteristics of the grape marc extracts (GME), were characterized. The microbiostatic and microbicidal effects in direct contact of GME with pathogenic microorganisms, Bacillus subtilis, Staphylococcus aureus, Escherichia coli, Klebsiella pneumoniae, were determined in vitro. The influence of extraction parameters on the total polyphenol content (TPC), total flavonoid content (TFC), tannin content (TC), total anthocyanin content (TAC) and their interdependencies were studied using information analysis. A mathematical model was developed on cubic spline functions. The analysis of individual compounds showed the presence of a wide range of flavonoids (procyanidin B2, procyanidin B1, hyperoside and quercetin), flavones (catechin), hydroxybenzoic acid derivatives (gallic, protocatechuic, p-hydroxybenzoic acids, m-hydroxybenzoic acid, syringic acid), hydroxycinic acid derivatives and ferulic acid methyl ester. The malvidol-3-glucoside was the main anthocyanin identified in the extract. A high amount of tartaric acid was also found. GME showed significant antimicrobial activity against Gram-positive bacteria and lower activity against Gram-negative bacteria. 相似文献
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We introduce and study a Hopf algebra containing the descent algebra as a sub-Hopf-algebra. It has the main algebraic properties of the descent algebra, and more: it is a sub-Hopf-algebra of the direct sum of the symmetric group algebras; it is closed under the corresponding inner product; it is cocommutative, so it is an enveloping algebra; it contains all Lie idempotents of the symmetric group algebras. Moreover, its primitive elements are exactly the Lie elements which lie in the symmetric group algebras. 相似文献
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We first show that increasing trees are in bijection with set compositions, extending simultaneously a recent result on trees
due to Tonks and a classical result on increasing binary trees. We then consider algebraic structures on the linear span of
set compositions (the twisted descent algebra). Among others, a number of enveloping algebra structures are introduced and
studied in detail. For example, it is shown that the linear span of trees carries an enveloping algebra structure and embeds
as such in an enveloping algebra of increasing trees. All our constructions arise naturally from the general theory of twisted
Hopf algebras. 相似文献
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Michel Bauer Raphael Chetrite Kurusch Ebrahimi-Fard Frédéric Patras 《Letters in Mathematical Physics》2013,103(3):331-350
Both the classical time-ordering and the Magnus expansion are well known in the context of linear initial value problems. Motivated by the noncommutativity between time-ordering and time derivation, and related problems raised recently in statistical physics, we introduce a generalization of the Magnus expansion. Whereas the classical expansion computes the logarithm of the evolution operator of a linear differential equation, our generalization addresses the same problem, including, however, directly a non-trivial initial condition. As a by-product we recover a variant of the time-ordering operation, known as ${\mathsf{T}^\ast}$ -ordering. Eventually, placing our results in the general context of Rota–Baxter algebras permits us to present them in a more natural algebraic setting. It encompasses, for example, the case where one considers linear difference equations instead of linear differential equations. 相似文献
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The usual time-ordering operation and the corresponding time-ordered exponential play a fundamental role in physics and applied mathematics. In this work, we study a new approach to the understanding of time-ordering relying on recent progress made in the context of enveloping algebras of pre-Lie algebras. Various general formulas for pre-Lie and Rota–Baxter algebras are obtained in the process. Among others, we recover the noncommutative analog of the classical Bohnenblust–Spitzer formula, and get explicit formulae for operator products of time-ordered exponentials. 相似文献
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