Hilbert series of Koszul algebras and one-dependent processes

2005 ◽  
pp. 133-152
Author(s):  
Alexander Polishchuk ◽  
Leonid Positselski
Keyword(s):  
Hilbert Series ◽  
Koszul Algebras ◽  
Dependent Processes

scholarly journals COMBINATORICS AND N-KOSZUL ALGEBRAS

2008 ◽  
Vol 05 (08) ◽  
pp. 1205-1214
Author(s):  
ROLAND BERGER
Keyword(s):  
Hilbert Series ◽  
Natural Generalization ◽  
Koszul Algebras ◽  
Polynomial Algebras ◽  
New Type ◽  
Master Theorem

The numerical Hilbert series combinatorics for quadratic Koszul algebras was extended to N-Koszul algebras by Dubois-Violette and Popov [9]. In this paper, we give a striking application of this extension when the relations of the algebra are all the antisymmetric tensors of degree N over given variables. Furthermore, we present a new type of Hilbert series combinatorics, called comodule Hilbert series combinatorics, and due to Hai, Kriegk and Lorenz [15]. When the relations are all the antisymmetric tensors, a natural generalization of the MacMahon Master Theorem (MMT) is obtained from the comodule level, the original MMT corresponding to N = 2 and to polynomial algebras.

Probing the Dynamic Self-Assembly Behaviour of Photoswitchable Wormlike Micelles in Real Time

2018 ◽  
Author(s):  
Elaine A. Kelly ◽  
Judith E. Houston ◽  
Rachel Evans
Keyword(s):  
Real Time ◽  
Absorption Spectroscopy ◽  
Self Assembly ◽  
Uv Light ◽  
Wormlike Micelles ◽  
Tetraethylene Glycol ◽  
Light Illumination ◽  
First Time ◽  
Dependent Processes

Understanding the dynamic self-assembly behaviour of azobenzene photosurfactants (AzoPS) is crucial to advance their use in controlled release applications such as<i></i>drug delivery and micellar catalysis. Currently, their behaviour in the equilibrium <i>cis-</i>and <i>trans</i>-photostationary states is more widely understood than during the photoisomerisation process itself. Here, we investigate the time-dependent self-assembly of the different photoisomers of a model neutral AzoPS, <a>tetraethylene glycol mono(4′,4-octyloxy,octyl-azobenzene) </a>(C<sub>8</sub>AzoOC<sub>8</sub>E<sub>4</sub>) using small-angle neutron scattering (SANS). We show that the incorporation of <i>in-situ</i>UV-Vis absorption spectroscopy with SANS allows the scattering profile, and hence micelle shape, to be correlated with the extent of photoisomerisation in real-time. It was observed that C<sub>8</sub>AzoOC<sub>8</sub>E<sub>4</sub>could switch between wormlike micelles (<i>trans</i>native state) and fractal aggregates (under UV light), with changes in the self-assembled structure arising concurrently with changes in the absorption spectrum. Wormlike micelles could be recovered within 60 seconds of blue light illumination. To the best of our knowledge, this is the first time the degree of AzoPS photoisomerisation has been tracked <i>in</i><i>-situ</i>through combined UV-Vis absorption spectroscopy-SANS measurements. This technique could be widely used to gain mechanistic and kinetic insights into light-dependent processes that are reliant on self-assembly.

Short Generating Functions for some Semigroup Algebras

10.37236/1729 ◽  
2003 ◽  
Vol 10 (1) ◽  
Author(s):  
Graham Denham
Keyword(s):  
Rational Function ◽  
Generating Functions ◽  
Hilbert Series ◽  
Simple Expression ◽  
Arbitrary Field ◽  
Graded Algebra ◽  
Semigroup Algebras ◽  
Positive Integers

Let $a_1,\ldots,a_n$ be distinct, positive integers with $(a_1,\ldots,a_n)=1$, and let k be an arbitrary field. Let $H(a_1,\ldots,a_n;z)$ denote the Hilbert series of the graded algebra k$[t^{a_1},t^{a_2},\ldots,t^{a_n}]$. We show that, when $n=3$, this rational function has a simple expression in terms of $a_1,a_2,a_3$; in particular, the numerator has at most six terms. By way of contrast, it is known that no such expression exists for any $n\geq4$.

THE INTENSITY OF OXIDATIVE MODIFICATION OF PROTEINS AND PEROXIDATION OF LIPIDS IN THE BLOOD SERUM, BRAIN, LIVER AND PANCREAS TISSUES OF RATS WITH INSULIN RESISTANCE AND CONGENITAL IODINE DEFICIENCY

2019 ◽  
pp. 115-120
Author(s):  
V. B. Stetsevyat ◽  
N. M. Voronych-Semchenko
Keyword(s):  
Insulin Resistance ◽  
Iodine Deficiency ◽  
Thiobarbituric Acid ◽  
Oxidative Modification ◽  
Peroxidation Of Lipids ◽  
Diene Conjugates ◽  
Oxidative Modification Of Proteins ◽  
High Fructose ◽  
Liver And Pancreas ◽  
Dependent Processes

The results of the study about the nature of oxygen-dependent processes in rats that were on a high-fructose diet for 8 weeks under conditions of adequate iodine supply and congenital iodine deprivation is presented in the article. The significant activation of peroxide oxidation of proteins (by increasing the aldo- and keto-derivates of a neutral nature) and lipids (increased of diene conjugates content and products, that are responsible to thiobarbituric acid) of animals with insulin resistance was found. An aggravating factor in the course of these processes is a congenital iodine deficiency. The changes of oxidative modification of proteins in animals with congenital iodine deficiency had multidirectional character, and processes of lipid peroxidation mainly increased. The most pronounced changes of the studied processes were observed in the liver and pancreas of animals with insulin resistance against the background of congenital iodine deficiency.

scholarly journals The Hilbert Series of a Linear Symplectic Circle Quotient

2014 ◽  
Vol 23 (1) ◽  
pp. 46-65 ◽  
Author(s):  
Hans-Christian Herbig ◽  
Christopher Seaton
Keyword(s):  
Hilbert Series

scholarly journals 2, 12, 117, 1959, 45171, 1170086, …: a Hilbert series for the QCD chiral Lagrangian

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Lukáš Gráf ◽  
Brian Henning ◽  
Xiaochuan Lu ◽  
Tom Melia ◽  
Hitoshi Murayama
Keyword(s):  
Hilbert Series ◽  
Charge Conjugation ◽  
External Fields ◽  
Dynkin Diagrams ◽  
Non Linear ◽  
Very High ◽  
Chiral Lagrangian

Abstract We apply Hilbert series techniques to the enumeration of operators in the mesonic QCD chiral Lagrangian. Existing Hilbert series technologies for non-linear realizations are extended to incorporate the external fields. The action of charge conjugation is addressed by folding the $$ \mathfrak{su}(n) $$ su n Dynkin diagrams, which we detail in an appendix that can be read separately as it has potential broader applications. New results include the enumeration of anomalous operators appearing in the chiral Lagrangian at order p8, as well as enumeration of CP-even, CP-odd, C-odd, and P-odd terms beginning from order p6. The method is extendable to very high orders, and we present results up to order p16.(The title sequence is the number of independent C-even and P-even operators in the mesonic QCD chiral Lagrangian with three light flavors of quarks, at chiral dimensions p2, p4, p6, …)

scholarly journals Role of Virally-Encoded Deubiquitinating Enzymes in Regulation of the Virus Life Cycle

2021 ◽  
Vol 22 (9) ◽  
pp. 4438
Author(s):  
Jessica Proulx ◽  
Kathleen Borgmann ◽  
In-Woo Park
Keyword(s):  
Immune Response ◽  
Life Cycle ◽  
Deubiquitinating Enzyme ◽  
Deubiquitinating Enzymes ◽  
Antiviral Immune Response ◽  
Cellular Processes ◽  
Virus Life Cycle ◽  
Infected Cells ◽  
Dependent Processes

The ubiquitin (Ub) proteasome system (UPS) plays a pivotal role in regulation of numerous cellular processes, including innate and adaptive immune responses that are essential for restriction of the virus life cycle in the infected cells. Deubiquitination by the deubiquitinating enzyme, deubiquitinase (DUB), is a reversible molecular process to remove Ub or Ub chains from the target proteins. Deubiquitination is an integral strategy within the UPS in regulating survival and proliferation of the infecting virus and the virus-invaded cells. Many viruses in the infected cells are reported to encode viral DUB, and these vial DUBs actively disrupt cellular Ub-dependent processes to suppress host antiviral immune response, enhancing virus replication and thus proliferation. This review surveys the types of DUBs encoded by different viruses and their molecular processes for how the infecting viruses take advantage of the DUB system to evade the host immune response and expedite their replication.

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