Reduction Of Group Research Articles

G-connections on principal bundles over complete G-varieties

Let X be a complete variety over an algebraically closed field k of characteristic zero, equipped with an action of an algebraic group G. Let H be a reductive group. We study the notion of G-connection on a principal H-bundle. We give necessary and sufficient criteria for the existence of G-connections extending the Atiyah-Weil type criterion for holomorphic connections obtained by Azad and Biswas. We also establish a relationship between the existence of G-connection and equivariant structure on a principal H-bundle, under the assumption that G is semisimple and simply connected. These results have been obtained by Biswas et al. when the underlying variety is smooth.

Correction: Stability, Analytic Stability for Real Reductive Lie Groups

Correction: Stability, Analytic Stability for Real Reductive Lie Groups

High mechanical, self-adhesive oxidized guar gum/chitosan hydrogel prepared at room temperature based on a nickel-urushiol catalytic system for wireless wearable sensors

Recently, sensors constructed on the basis of hydrogel are playing a major role in health detection such as motion detection and breathing monitoring. However, the common hydrogels have poor mechanical properties, insufficient adhesion and complex preparation processes, which hinder the further use of such sensors. In this paper, the conductive hydrogel (P(AA-UH)-OGG-CS/NiCl2) composed of acrylic acid (AA), oxidized guar gum (OGG) and chitosan (CS) was prepared at room temperature through the dynamic redox reaction of nickel chloride (NiCl2) and urushiol (UH). In detail, the reduction group (phenolic hydroxyl) of UH and Ni2+/Ni3+ pair form a semi-quinone/quinone redox dynamic cycle system, allowing the hydrogel to quickly gel at room temperature for 3 min. The catechol group in UH also promotes the hydrogel to have a superior adhesion strength of 25.23 kPa to pig skin and a strong repeated adhesion performance. In addition, the dynamic Schiff base bond created by the interaction of OGG and CS elevated the tensile stress of the hydrogel to 67.54 kPa. After the hydrogel is assembled into the sensor, it has high sensitivity and high stability to different strains, and has great application prospects in the field of actual human health monitoring.

A note on the Loewy lengths of baby Verma modules for modular Lie algebras

Let G be a connected reductive algebraic group over an algebraically closed field k of prime characteristic p, and g=Lie(G). We study the representations of the reductive Lie algebra g with p-character χ of standard Levi-form in this note. We obtain the similar results about the translation functor and the wall-crossing functor of simple modules parallelling to the representations of algebraic groups (cf. [16, II.Lem.7.20]). Moreover, we get the Loewy lengths of baby Verma modules provided the Vogan Conjecture holds.

Galois automorphisms and a unique Jordan decomposition in the case of connected centralizer

We show that the Jordan decomposition of characters of finite reductive groups can be chosen so that if the centralizer of the relevant semisimple element in the dual group is connected, then the map is Galois-equivariant. Further, in this situation, we show that there is a unique Jordan decomposition satisfying conditions analogous to those of Digne–Michel's unique Jordan decomposition in the connected center case.

Biomechanical comparison of Gofried positive support reduction of Pauwels type III femoral neck fractures: A finite elements analysis

ObjectiveThis study aims to investigate the biomechanical characteristics of non-anatomical reduction and different screw positions on the stability of Pauwels type III femoral neck fractures. MethodsThree-dimensional finite element models of femoral neck fractures were constructed using CT images. Four types of internal fixation methods were simulated, including biplane double-supported screw fixation (BDSF), three inverted triangular parallel cannulated screws (3CS), new parallel cannulated screws with posterior screws moving down (New 3CS), and two parallel cannulated screws (2CS). von Mises stress and total displacement were compared between the fracture models after the femoral head was subjected to an axial load of 2100 N. Stress and displacement data for the implants and the femur were recorded for each fixation method and compared. ResultsThe results demonstrated that positive reduction of a Pauwels type III femoral neck fracture provided greater stability than neutral or negative reduction. Specifically, the BDSF group showed the lowest maximum von Mises stress in the femur (17.66 MPa) in positive reduction, compared to 3CS (21.08 MPa), New 3CS (22.14 MPa), and 2CS (36.57 MPa). The total displacement of positive reduction in the BDSF group was 0.3143 mm, which was lower than in the 3CS (0.3498 mm), New 3CS (0.3343 mm), and 2CS (0.4533 mm) groups. The stress distribution in the positive support reduction group was lower than that of the other groups, indicating better load distribution. Among the three-screw fixation methods, the New 3CS system exhibited the highest stress in the screws (with a peak of 28.62 MPa), while the 2CS group displayed the highest stresses overall, both in the femur and the screws. ConclusionFor Pauwels type III femoral neck fractures, a positive support reduction with BDSF fixation exhibited superior biomechanical performance than negative reduction. Based on the finite element analysis conducted in this study, the positive support reduction with BDSF fixation can enhance fixation stability, suggesting that non-anatomical reduction is recommended.

Modulo ℓ distinction problems

Let $F$ be a non-archimedean local field of characteristic different from 2 and residual characteristic $p$ . This paper concerns the $\ell$ -modular representations of a connected reductive group $G$ distinguished by a Galois involution, with $\ell$ an odd prime different from $p$ . We start by proving a general theorem allowing to lift supercuspidal $\overline {\mathbf {F}}_{\ell }$ -representations of $\operatorname {GL}_n(F)$ distinguished by an arbitrary closed subgroup $H$ to a distinguished supercuspidal $\overline {\mathbf {Q}}_{\ell }$ -representation. Given a quadratic field extension $E/F$ and an irreducible $\overline {\mathbf {F}}_{\ell }$ -representation $\pi$ of $\operatorname {GL}_n(E)$ , we verify the Jacquet conjecture in the modular setting that if the Langlands parameter $\phi _\pi$ is irreducible and conjugate-selfdual, then $\pi$ is either $\operatorname {GL}_n(F)$ -distinguished or $(\operatorname {GL}_{n}(F),\omega _{E/F})$ -distinguished (where $\omega _{E/F}$ is the quadratic character of $F^\times$ associated to the quadratic field extension $E/F$ by the local class field theory), but not both, which extends one result of Sécherre to the case $p=2$ . We give another application of our lifting theorem for supercuspidal representations distinguished by a unitary involution, extending one result of Zou to $p=2$ . After that, we give a complete classification of the $\operatorname {GL}_2(F)$ -distinguished representations of $\operatorname {GL}_2(E)$ . Using this classification we discuss a modular version of the Prasad conjecture for $\operatorname {PGL}_2$ . We show that the ‘classical’ Prasad conjecture fails in the modular setting. We propose a solution using non-nilpotent Weil–Deligne representations. Finally, we apply the restriction method of Anandavardhanan and Prasad to classify the $\operatorname {SL}_2(F)$ -distinguished modular representations of $\operatorname {SL}_2(E)$ .

Rationality of extended unipotent characters

We determine the rationality properties of unipotent characters of finite reductive groups arising as fixed points of disconnected reductive groups under a Frobenius map. In the proof, we use realisations of characters in ℓ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\ell $$\\end{document}-adic cohomology groups of Deligne–Lusztig varieties as well as block theoretic considerations.

Dose compliance of estramustine phosphate in neoadjuvant chemohormonal therapy combined with degarelix acetate predicts the biochemical recurrence in patients with very high-risk prostate cancer who underwent robot-assisted radical prostatectomy.

The objective of this study is to evaluate the safety and efficacy of neoadjuvant degarelix acetate and low-dose estramustine phosphate for high-/very high-risk prostate cancer. Overall, 187 patients diagnosed with National Comprehensive Cancer Network high-/very high-risk cTanyN0M0 localized prostate cancer who consented to undergo robot-assisted radical prostatectomy after receiving neoadjuvant chemohormonal therapy for 6 months were prospectively enrolled between December 2017 and March 2023. Adverse events, perioperative and histopathological outcomes, and biochemical recurrence-free survival rates were examined. Survival analysis compared the estramustine phosphate completion and reduction groups. Thirty-six patients discontinued neoadjuvant therapy in <5 months owing to adverse events (n = 34) or other reasons (n = 2). Eleven were excluded for being in the postoperative castration range. Of the 140 patients who underwent surgery, 124 continued with two tablets of estramustine phosphate and 16 with one tablet. Overall, 82 patients were very high-risk. Histopathological outcomes were significantly worse in the very high-risk group than those in the high-risk group. Very high-risk status and estramustine phosphate reduction were significant factors in biochemical recurrence in multivariate analysis. The biochemical recurrence-free survival rate in very high-risk patients was significantly lower in the estramustine phosphate dose reduction group than in the completion group but not significant in high-risk patients. Major adverse events were anemia (n = 174), elevated transaminase levels (n = 68), and deep vein thrombosis (n = 24). Severe adverse events included acute coronary syndrome (n = 4) and pulmonary embolism (n = 3). Dose compliance with estramustine phosphate predicted biochemical recurrence in patients with very high-risk prostate cancer undergoing robot-assisted radical prostatectomy with neoadjuvant chemohormonal therapy.

A Comparative Study of Stress Reduction Groups With and Without Therapy Dogs in a Rural Pennsylvania Jail

Individuals who are incarcerated are often stressed, hopeless, and overwhelmed by this challenging life circumstance. Unfortunately, jails offer little treatment to assist in enhancing coping and fostering hope and resilience. This research study in a rural Pennsylvania jail provided four six-week coping and stress reduction groups, two with and two without therapy dogs. Findings indicate that all group participants experienced significant reductions in stress, improved resilience, and an increased sense of hope as measured by standardized scales. All four groups rated the interventions as very helpful.

Open Reduction in Traumatic Cervical Facet Dislocation Does Not Delay Time to Treatment.

Background Cervical facet dislocation is a serious injury that can result in permanent neurologic damage. Current guidelines recommend immediate closed reduction of cervical dislocations, though the efficacy of this practice remains a debate. This study aims to evaluate whether immediate open reduction and fixation of cervical dislocations offer equal or better outcomes for patients and limit the need for follow-up operations. Methods This is a retrospective study including patients who presented to the emergency department of a single institution from 2008 to 2023 with cervical facet dislocation. Patients were divided into groups based on initial treatment: either open or closed reduction. Time to surgery was calculated as the time between arrival to the ED and incision time in the OR. Primary outcomes were improvement in motor and sensory deficits at six-week post-operative follow-up. Results There were 31 patients who met the inclusion criteria. Time to treatment did not differ significantly between the open versus closed reduction groups. There were no differences between groups in improvement in motor function, sensory function, or pain at the six-week follow-up. All patients treated with initial closed reduction ultimately required surgical stabilization. Conclusions Open reduction as a first-line treatment did not increase the time to treatment for patients with cervical facet dislocations. Patients had equivalent functional outcomes in both treatment groups. The findings suggest that current practice guidelines may delay definitive treatment without improving patient safety or outcomes.

The effects of acupressure, laughter yoga, and a mindfulness-based stress reduction program applied to postmenopausal women for menopause symptoms and quality of life.

This research was conducted to determine the effects of acupressure, laughter yoga, and a mindfulness-based stress reduction program applied to postmenopausal women for menopause symptoms and quality of life. A randomized controlled design was used. The study was conducted with a total of 146 women, including 41 acupressure, 31 laughter yoga, 37 mindfulness-based stress reduction, and 37 control group women. The women in the acupressure group were administered acupressure twice a week, which accounted for 16 sessions in total. Women in the laughter yoga and mindfulness-based stress reduction groups received a total of eight sessions of the related intervention, which was performed once a week. Study data were collected using a participant information form, the Menopause Rating Scale (MRS), and the Menopause-Specific Quality of Life Scale (MENQOL). Descriptive statistics, paired-samples t test, χ 2 test, analysis of variance test, and intention to treat analysis were used to analyze the data. Before the intention to treat analysis was performed, the multiple imputation method was employed to deal with missing data. In the study, it was found that there was a decrease in the MRS total score after the intervention in women in all three intervention groups compared to the control group ( P < 0.05). In the laughter yoga group, total MRS scores decreased by 3.16 points ( P < 0.05). In the acupressure group, total MRS scores decreased by 5.46 points ( P < 0.05). In the mindfulness-based stress reduction (MBSR) program group, total MRS scores decreased by 4.65 points ( P < 0.05). It was determined that the mean scores of women in the laughter yoga and acupressure groups on all subscales of the MENQOL decreased after the intervention compared to the control group ( P < 0.05). The comparison of the MBSR group and the control group showed that there was a decrease only in the psychosocial domain subdimension of the MENQOL ( P < 0.05). In conclusion, it was determined that laughter yoga, acupressure, and MBSR could be effective in reducing menopause symptoms and improving quality of life, although findings require further testing in a rigorously controlled study and in a study with only a single prespecified outcome.

Biomimetic Phthalocyanine-Based Covalent Organic Frameworks with Tunable Pendant Groups for Electrocatalytic CO2 Reduction.

Electrocatalytic carbon dioxide reduction reaction (CO2RR) is an effective way of converting CO2 into value-added products using renewable energy, whose activity and selectivity can be in principle maneuvered by tuning the microenvironment near catalytic sites. Here, we demonstrate a strategy for tuning the microenvironment of CO2RR by learning from the natural chlorophyll and heme. Specifically, the conductive covalent organic frameworks (COFs) linked by piperazine serve as versatile supports for single-atom catalysts (SACs), and the pendant groups modified on the COFs can be readily tailored to offer different push-pull electronic effects for tunable microenvironment. As a result, while all the COFs exhibit high chemical structure stability under harsh conditions and good conductivity, the addition of -CH2NH2 can greatly enhance the activity and selectivity of CO2RR. As proven by experimental characterization and theoretical simulation, the electron-donating group (-CH2NH2) not only reduces the surface work function of COF, but also improves the adsorption energy of the key intermediate *COOH, compared with the COFs with electron-withdrawing groups (-CN, -COOH) near the active sites. This work provides insights into the microenvironment modulation of CO2RR electrocatalysts at the molecular level.

Bessel functions on GL(n), I

In the context of the Kuznetsov trace formula, we outline the theory of the Bessel functions on GL(n) as a series of conjectures designed as a blueprint for the construction of Kuznetsov-type formulas with given ramification at infinity. We are able to prove one of the conjectures at full generality on GL(n) and most of the conjectures in the particular case of the long Weyl element; as with previous papers, we give some unconditional results on Archimedean Whittaker functions, now on GL(n) with arbitrary weight. We expect the heuristics here to apply at the level of real reductive groups. A forthcoming paper will address the initial conjectures up to Mellin-Barnes integral representations in the case of GL(4) Bessel functions.

Colored vertex models and Iwahori Whittaker functions

We give a recursive method for computing all values of a basis of Whittaker functions for unramified principal series invariant under an Iwahori or parahoric subgroup of a split reductive group G over a nonarchimedean local field F. Structures in the proof have surprising analogies to features of certain solvable lattice models. In the case G=GLr\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$G=\ extrm{GL}_r$$\\end{document} we show that there exist solvable lattice models whose partition functions give precisely all of these values. Here ‘solvable’ means that the models have a family of Yang–Baxter equations which imply, among other things, that their partition functions satisfy the same recursions as those for Iwahori or parahoric Whittaker functions. The R-matrices for these Yang–Baxter equations come from a Drinfeld twist of the quantum group Uq(gl^(r|1))\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$U_q(\\widehat{\\mathfrak {gl}}(r|1))$$\\end{document}, which we then connect to the standard intertwining operators on the unramified principal series. We use our results to connect Iwahori and parahoric Whittaker functions to variations of Macdonald polynomials.

Nonanatomical reduction of femoral neck fractures in young patients with different Pauwels classifications: a retrospective study and finite element analysis

BackgroundPrevious studies have reported that positive buttress is as effective as anatomical reduction in treating young femoral neck fractures, but whether this effect is related to the Pauwels classification remains unclear. The purpose of this study was to retrospectively analyze the clinical prognosis of positive buttress in young femoral neck fractures with different Pauwels classifications, as well as to assess its biomechanical properties.MethodsA total of 170 young patients with femoral neck fractures who were treated with three cannulated screws were included in this study. Patients were divided into three groups based on their preoperative Pauwels classification. Each group was divided into three subgroups based on the reduction quality: positive buttress, negative buttress and anatomical reduction. The femoral neck shortening, the incidence of necrosis of the femoral head (AVN) and the Harris hip scores at the last follow-up were compared across the three reduction quality within each Pauwels classification. Subsequently, a volunteer was recruited, CT data of the hip was obtained, and finite element models representing different reduction quality under varying Pauwels classifications were established. The biomechanical properties of each model were then evaluated following the application of strains.ResultsIn Pauwels type I, there were no significant differences in postoperative femoral neck shortening, incidence of AVN, or Harris score among the three types of reduction quality (P > 0.05). However, positive buttress provided superior biomechanical stability compared to negative buttress and anatomical reduction. In Pauwels type II, the incidence of AVN was similar between the positive buttress and the anatomical reduction groups, and both were significantly lower than that in the negative buttress (P < 0.05). The Harris score of the positive buttress was higher than that of the negative buttress, and there was no significant difference in the occurrence of femoral neck shortening between the three groups (P > 0.05). Finite element analysis showed that the biomechanical stability of positive buttress was equivalent to anatomical reduction, and both were better than negative buttress. In Pauwels type III, the incidence of AVN in the anatomical reduction group was lower than that in both the positive buttress and negative buttress (P < 0.05). There was no significant difference in the occurrence of AVN or femoral neck shortening between positive buttress and negative buttress (P > 0.05). There was also no difference in postoperative Harris scores between the three reduction qualities (P > 0.05). Both positive buttress and negative buttress exhibited identical biomechanical qualities and were inferior to anatomical reduction.ConclusionsThe biomechanical and clinical dominance of positive buttress correlates with Pauwels type. Specifically, Positive buttress is biomechanically stable in Pauwels types I and II. In Pauwels type III, positive buttress is not advantageous. As the Pauwels angle increases, the biomechanical benefit of the positive buttress is lost. Therefore, regardless of the Pauwels classification, negative buttress should be avoided after reduction of femoral neck fractures in young patients.

The simplicial complex of Brauer pairs of a finite reductive group

In this paper we study the simplicial complex induced by the poset of Brauer pairs ordered by inclusion for the family of finite reductive groups. In the defining characteristic case the homotopy type of this simplicial complex coincides with that of the Tits building thanks to a well-known result of Quillen. On the other hand, in the non-defining characteristic case, we show that the simplicial complex of Brauer pairs is homotopy equivalent to a simplicial complex determined by generalised Harish-Chandra theory. This extends earlier results of the author on the Brown complex and makes use of the theory of connected subpairs and twisted block induction developed by Cabanes and Enguehard.

Intra-articular fracture reduction: a comparative observational study of clinical results after the surgical treatment of distal radius fractures

Purpose: This study compared the outcomes of intra-articular fracture reduction for distal radius fractures. Methods: Among 180 patients who underwent open reduction and plate fixation, the exclusion criteria were as follows: non-acute fracture (&gt;1 month), an accompanying ulnar neck fracture, a distal ulnar fracture requiring fixation, fixation through the dorsal approach, other accompanying hand fractures, the absence of preoperative or postoperative computed tomography (CT), and follow-up for &lt;1 year. Intra-articular fractures were evaluated through CT. Forty-eight patients with intra-articular fractures were studied. Displaced intra-articular fractures were defined as: (1) articular step-off ≥1 mm, (2) fracture gap ≥2 mm, or (3) gross incongruence. Reduction was classified as good (n=23) or poor (n=25) based on postoperative CT. The pain visual analogue scale (pVAS), the quick Disabilities of the Arm, Shoulder, and Hand (DASH) questionnaire, and range of motion of the wrist joint were compared between both groups.Results: No significant between-group differences were found in the preoperative demographic data and the postoperative pVAS and quick DASH scores (pVAS: 0.6 vs. 0.8 and quick DASH: 9.4 vs. 10.2 in the good vs. poor reduction groups, respectively). However, the flexion-extension arc was significantly restricted in the poor reduction group (162° in the good reduction group vs. 146° in the poor reduction group, p&lt;0.001).Conclusion: The reduction of the articular surface was not related to pain and functional results at the mid-term follow-up after the surgical treatment of intra-articular distal radius fractures. However, insufficient fracture reduction affected the postoperative range of motion.

The Steinberg character in the principal block of a finite reductive group

We give a generic description of the non-defining primes l , for which the Steinberg character lies in the principal l -block of a finite reductive group.

A Study of Omentum Reduction on the Improvement of Nausea and vomiting and Gastroesophageal Reflux Symptoms After Laparoscopic Gastric Sleeve Resection.

To investigate the effect of omentum reduction in laparoscopic sleeve gastrectomy (LSG) on the improvement of postoperative nausea and vomiting and gastroesophageal reflux symptoms. A retrospective study was performed on the case data of 198 obese patients who underwent LSG in the Department of Obesity and Metabolic Diseases of Xiaolan People's Hospital of Zhongshan from March 2021 to March 2022 and were divided into omentum reduction group and control group, with 99 cases in each group, and the preoperative body mass index (BMI) of the patients was recorded. Age, gender, comorbidities, and comparative analysis of operation time, blood loss, length of hospital stay, postoperative nausea and vomiting score, gastroesophageal reflux GerdQ score, postoperative pain score, weight, and postoperative complications were analyzed. There were no significant differences in preoperative BMI, age, gender and comorbidities between the two groups (P > 0.05), but there were significant differences in intraoperative blood loss and operation time (P < 0.05). There were differences in postoperative nausea and vomiting scores and VAS pain scores between the two groups (P < 0.05). The GerdQ scores of the omental reduction group were 8.11 ± 2.84 points at 1year, and those in the control group were 7.56 ± 2.67 points, which were 3.97 ± 4.09 points higher than those in the preoperative omentum reduction group and 3.42 ± 3.41 in the control group, with no significant difference (P > 0.05). There was no significant difference in the postoperative excess weight loss rate %EWL and postoperative complications (p > 0.05). Omentum reduction can improve short-term nausea and vomiting after LSG, but it cannot significantly improve long-term reflux symptoms.