scholarly journals On ordered k-paths and rims for certain families of Kazhdan–Lusztig cells of Sn

2020 ◽  
pp. 2150181
Author(s):  
T. P. McDonough ◽  
C. A. Pallikaros
Keyword(s):  
Symmetric Group ◽  
Parabolic Subgroup ◽  
Composition Formula ◽  
Standard Parabolic Subgroup ◽  
Reduced Forms

For a composition [Formula: see text] of [Formula: see text] we consider the Kazhdan–Lusztig cell in the symmetric group [Formula: see text] containing the longest element of the standard parabolic subgroup of [Formula: see text] associated to [Formula: see text]. In this paper, we extend some of the ideas and results in [Beiträge zur Algebra und Geometrie, 59(3) (2018) 523–547]. In particular, by introducing the notion of an ordered [Formula: see text]-path, we are able to obtain alternative explicit descriptions for some additional families of cells associated to compositions. This is achieved by first determining the rim of the cell, from which reduced forms for all the elements of the cell are easily obtained.

Effect of carvedilol on the redox-status of plasma low-molecular-weight aminothyols in rats with acute cerebral ischemia

2018 ◽  
pp. 12-18
Author(s):  
К.А. Никифорова ◽  
В.В. Александрин ◽  
П.О. Булгакова ◽  
А.В. Иванов ◽  
Э.Д. Вирюс ◽  
...  
Keyword(s):  
Molecular Weight ◽  
Cerebral Ischemia ◽  
Carotid Arteries ◽  
Redox Status ◽  
Global Cerebral Ischemia ◽  
Low Molecular Weight ◽  
Adrenergic Antagonist ◽  
Acute Cerebral Ischemia ◽  
Common Carotid Arteries ◽  
Reduced Forms

Цель. Установить влияние неспецифического адреноблокатора карведилола на редокс-статус низкомолекулярных аминотиолов (цистеин, гомоцистеин, глутатион) в плазме крови при моделировании глобальной ишемии головного мозга у крыс. Методика. Нами была использована модель глобальной ишемии (пережатие общих сонных артерий с геморрагией длительностью 15 мин). Препарат вводили за 1 ч до операции. Уровни аминотиолов измеряли через 40 мин после начала реперфузии. Анализ уровня аминотиолов проводили методом жидкостной хроматографии. Результаты. Установлено, что у крыс, не подвергавшихся ишемии, карведилол в дозе 10 мг/кг вызывает рост редокс-статуса цистеина и глутатиона (в 3 и 3,5 раза соответственно по сравнению с контролем, p = 0,04 и p = 0,008) за счет увеличения их восстановленных форм. При ишемии данного эффекта не наблюдалось. Редокс-статус у крыс с ишемией на фоне карведилола (Цис = 0,85 ± 0,14%, Глн = 1,8 ± 0,7%, Гцис = 1,1 ± 0,8%) оставался таким же низким, как и у крыс с ишемией без введения карведилола (р > 0,8). Заключение. Полученный результат демонстрирует, что в условиях ишемии головного мозга карведилол не оказывает эффекта на гомеостаз аминотиолов плазмы крови, несмотря на выраженный антиоксидантный эффект в нормальных условиях. Aim. Effect of a nonspecific adrenergic antagonist carvedilol on the redox status of plasma low-molecular-weight aminothiols (cysteine, homocysteine, glutathione) was studied in rats with global cerebral ischemia (occlusion of common carotid arteries with hemorrhage). Methods. A model of global ischemia (occlusion of common carotid arteries with 15-min hemorrhage) was used. The drugs were administered one hour before the operation. Aminothiol levels were measured by HPLC with UV detection at 40 minutes after the onset of reperfusion. Results. Carvedilol 10 mg/kg increased the redox status of cysteine and glutathione in rats not exposed to ischemia (3 and 3.5 times, respectively, compared with the control, p = 0.04 and p = 0.008, respectively) but not of homocysteine, by increasing their reduced forms. However, this effect was not observed in ischemia. In rats with ischemia treated with carvedilol, the redox status (Cys = 0.85 ± 0.14%, GSH = 1.8 ± 0.7%, Hcys = 1.1 ± 0.8%) remained low similar to that in rats with ischemia not treated with carvedilol (p >0.8, 0.8, and 0.9, respectively). Conclusion. Carvedilol did not affect the homeostasis of blood plasma thiols in cerebral ischemia despite the pronounced antioxidant effect under the normal conditions.

Type 2 diabetes mellitus in patients with acute ischemiс stroke is associated with a decrease in plasma glutathione levels

2020 ◽  
Vol 25 (5) ◽  
pp. 29-35
Author(s):  
M. Yu. Maksimova ◽  
A. V. Ivanov ◽  
K. A. Nikiforova ◽  
F. R. Ochtova ◽  
E. T. Suanova ◽  
...  
Keyword(s):  
Diabetes Mellitus ◽  
Type 2 Diabetes ◽  
Type 2 Diabetes Mellitus ◽  
Redox Status ◽  
Reduced Form ◽  
Glutathione Level ◽  
Total Glutathione ◽  
Diabetes Mellitus Group ◽  
Reduced Forms

Ischemic stroke (IS) and type 2 diabetes mellitus are factors that affect the homeostasis of low-molecularweight aminothiols (cysteine, homocysteine, glutathione etc.). It has already been shown that IS in the acute period led to a decrease a level of reduced forms of aminothiols, but it is not clear whether type 2 diabetes mellitus has a noticeable effect there. Objective: to reveal the features of homeostasis of aminothiols in patients with type 2 diabetes mellitus in acute IS. Material and methods. The study involved 76 patients with primary middle cerebral artery IS in the first 10–24 hours after development of neurological symptoms. Group 1 included 15 patients with IS and type 2 diabetes mellitus, group 2 — 61 patients with IS and stress hyperglycemia. Their total plasma levels of cysteine, homocysteine, and glutathione, their reduced forms, and redox status were determined at admission (in the first 24 hours after IS). Results. There was a decrease in the level of total glutathione level (1.27 vs. 1.65 μM, p = 0.021), as well as its reduced form (0.03 vs. 0.04 μM, p = 0.007) in patients with IS and type 2 diabetes mellitus. Patients with type 2 diabetes mellitus who had a low redox status of homocysteine (0.65–1.2%) and glutathione (0.7–2.0%) were also characterized by a decrease in total glutathione level (p = 0.02; p = 0.03). Conclusion. Thus, type 2 diabetes mellitus is associated with a decrease in the level of total glutathione in acute IS. Probably, type 2 diabetes mellitus is characterized by a particular relationship between the metabolism of homocysteine, glutathione and glucose. Therefore, the search for homocysteine-dependent approaches to correct glutathione metabolism in type 2 diabetes mellitus may be of interest as an adjuvant therapy for IS.

The Transition Matrix Between the Specht and 𝔰𝔩3 Web Bases is Unitriangular With Respect to Shadow Containment

2020 ◽  
Author(s):  
Heather M Russell ◽  
Julianna Tymoczko
Keyword(s):  
Symmetric Group ◽  
Partial Order ◽  
Transition Matrix ◽  
Group Representation ◽  
Jones Polynomial ◽  
Basis Matrix ◽  
Combinatorial Structures ◽  
Quantum Invariants ◽  
One Dimensional ◽  
Link Diagrams

Abstract Webs are planar graphs with boundary that describe morphisms in a diagrammatic representation category for $\mathfrak{sl}_k$. They are studied extensively by knot theorists because braiding maps provide a categorical way to express link diagrams in terms of webs, producing quantum invariants like the well-known Jones polynomial. One important question in representation theory is to identify the relationships between different bases; coefficients in the change-of-basis matrix often describe combinatorial, algebraic, or geometric quantities (e.g., Kazhdan–Lusztig polynomials). By ”flattening” the braiding maps, webs can also be viewed as the basis elements of a symmetric group representation. In this paper, we define two new combinatorial structures for webs: band diagrams and their one-dimensional projections, shadows, which measure depths of regions inside the web. As an application, we resolve an open conjecture that the change of basis between the so-called Specht basis and web basis of this symmetric group representation is unitriangular for $\mathfrak{sl}_3$-webs ([ 33] and [ 29].) We do this using band diagrams and shadows to construct a new partial order on webs that is a refinement of the usual partial order. In fact, we prove that for $\mathfrak{sl}_2$-webs, our new partial order coincides with the tableau partial order on webs studied by the authors and others [ 12, 17, 29, 33]. We also prove that though the new partial order for $\mathfrak{sl}_3$-webs is a refinement of the previously studied tableau order, the two partial orders do not agree for $\mathfrak{sl}_3$.

SYMMETRIC GROUP BLOCKS OF DEFECT TWO

1995 ◽  
Vol 46 (2) ◽  
pp. 201-234 ◽  
Author(s):  
JOANNA SCOPES
Keyword(s):  
Symmetric Group

scholarly journals Dynamics of Oxidation of Reduced Forms of CO2 under Electrochemical and Open-Сircuit Conditions on Polycrystalline Pt in H2CO3

Metals ◽  
2021 ◽  
Vol 11 (2) ◽  
pp. 274
Author(s):  
Alexander V. Smolin ◽  
Мikhail N. Mikhailov ◽  
Aleksey F. Gadzaov ◽  
Leonid M. Kustov
Keyword(s):  
Quantum Chemical ◽  
Preliminary Analysis ◽  
Oxidation Reaction ◽  
Density Functional ◽  
Oxidation Process ◽  
Open Circuit ◽  
Organic Substances ◽  
Oxidation Of Co ◽  
Reduced Forms

The problem of identifying correlations between catalytic and electrocatalytic processes is one of the fundamental problems of catalysis among “simple” organic substances, and the oxidation of CO and rCO2 is of great interest, since CO and CO2 are considered in pairs both during catalytic and electrocatalytic transformations. In the case of electrocatalysis, this analysis is important in the study of fuel cells. In this paper, we studied the correlation between the oxidation of reduced forms of CO2 (rCO2) under potentiodynamic-galvanoctatic electrochemical and open-circuit conditions of measurements on polycrystalline (pc)Pt in H2CO3. Periodic oscillations are revealed at the oxidation of Had and rCO2 on (pc)Pt. Quantum chemical calculations were carried out on the Pt13 cluster in order to identify the mechanisms of the rCO2 oxidation reaction. The correspondence in the energy parameters of the oxidation process of rCO2 under open-circuit conditions and electrochemical conditions is shown. The preliminary analysis of the system using density functional (DFT) calculations is carried out and the most stable systems that are based on Pt13 are found, namely rOH-Pt13-(CO)n, rOH-Pt13-(COH) and rOH-Pt13-(rCOOH). OH• species was chosen as the most likely candidate for the role of the oxidant for rCO2. Preliminary calculations for the expected reactions were carried out, and the optimal PES is revealed.

scholarly journals Peptide-Bound Methionine Sulfoxide (MetO) Levels and MsrB2 Abundance Are Differentially Regulated during the Desiccation Phase in Contrasted Acer Seeds

Antioxidants ◽  
2020 ◽  
Vol 9 (5) ◽  
pp. 391 ◽  
Author(s):  
Natalia Wojciechowska ◽  
Shirin Alipour ◽  
Ewelina Stolarska ◽  
Karolina Bilska ◽  
Pascal Rey ◽  
...  
Keyword(s):  
Desiccation Tolerance ◽  
Methionine Sulfoxide ◽  
Redox Status ◽  
Embryonic Axes ◽  
Seed Desiccation ◽  
Methionine Sulfoxide Reductases ◽  
Norway Maple ◽  
Orthodox Seeds ◽  
Oxidation Of Methionine ◽  
Reduced Forms

Norway maple and sycamore produce desiccation-tolerant (orthodox) and desiccation-sensitive (recalcitrant) seeds, respectively. Drying affects reduction and oxidation (redox) status in seeds. Oxidation of methionine to methionine sulfoxide (MetO) and reduction via methionine sulfoxide reductases (Msrs) have never been investigated in relation to seed desiccation tolerance. MetO levels and the abundance of Msrs were investigated in relation to levels of reactive oxygen species (ROS) such as hydrogen peroxide, superoxide anion radical and hydroxyl radical (•OH), and the levels of ascorbate and glutathione redox couples in gradually dried seeds. Peptide-bound MetO levels were positively correlated with ROS concentrations in the orthodox seeds. In particular, •OH affected MetO levels as well as the abundance of MsrB2 solely in the embryonic axes of Norway maple seeds. In this species, MsrB2 was present in oxidized and reduced forms, and the latter was favored by reduced glutathione and ascorbic acid. In contrast, sycamore seeds accumulated higher ROS levels. Additionally, MsrB2 was oxidized in sycamore throughout dehydration. In this context, the three elements •OH level, MetO content and MsrB2 abundance, linked together uniquely to Norway maple seeds, might be considered important players of the redox network associated with desiccation tolerance.

scholarly journals A decomposition formula for representations

1987 ◽  
Vol 107 ◽  
pp. 63-68 ◽  
Author(s):  
George Kempf
Keyword(s):  
Irreducible Representation ◽  
General Formula ◽  
Parabolic Subgroup ◽  
Characteristic Zero ◽  
Maximal Torus ◽  
Reductive Group ◽  
Irreducible Representations ◽  
Levi Subgroup ◽  
Know How ◽  
Decomposition Formula

Let H be the Levi subgroup of a parabolic subgroup of a split reductive group G. In characteristic zero, an irreducible representation V of G decomposes when restricted to H into a sum V = ⊕mαWα where the Wα’s are distinct irreducible representations of H. We will give a formula for the multiplicities mα. When H is the maximal torus, this formula is Weyl’s character formula. In theory one may deduce the general formula from Weyl’s result but I do not know how to do this.

Reduced forms in the nominal morphology of the Lindisfarne Gospel Gloss. A case of accusative/dative syncretism?

2020 ◽  
Vol 54 (s41) ◽  
pp. 37-65
Author(s):  
Julia Fernández-Cuesta ◽  
Nieves Rodríguez-Ledesma
Keyword(s):  
Statistical Analysis ◽  
Old English ◽  
Frequency Condition ◽  
Facsimile Edition ◽  
Noun Class ◽  
Characteristic Features ◽  
Nominal Morphology ◽  
Reduced Forms ◽  
Syntactic Context

Abstract One of the most characteristic features of the grammar of the Lindisfarne Gospel gloss is the absence of the etymological -e inflection in the dative singular in the paradigm of the strong masculine and neuter declension (a-stems). Ross (1960: 38) already noted that endingless forms of the nominative/accusative cases were quite frequent in contexts where a dative singular in -e would be expected, to the extent that he labeled the forms in -e ‘rudimentary dative.’ The aim of this article is to assess to what extent the dative singular is still found as a separate case in the paradigms of the masculine and neuter a-stems and root nouns. To this end a quantitative/statistical analysis of nouns belonging to these classes has been carried out in contexts where the Latin lemma is either accusative or dative. We have tried to determine whether variables such as syntactic context, noun class, and frequency condition the presence or absence of the -e inflection, and whether the distribution of the inflected and uninflected forms is different in the various demarcations that have been identified in the gloss. The data have been retrieved using the Dictionary of Old English Corpus. All tokens have been checked against the facsimile edition and the digitised manuscript in order to detect possible errors.

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