Rigid Groups Research Articles

Isobar hybrid dynamic stabilization with posterolateral fusion in mild and moderate lumbar degenerative disease

ObjectiveThe aim of this study was to investigate the feasibility of using the Isobar TTL system and posterolateral fusion in a two-segment hybrid fixation approach, combined with spinal decompression, for treating mild and moderate lumbar degenerative disease. Specifically, we sought to evaluate the effectiveness of this approach for managing two-segment mild and moderate lumbar degenerative disease, and to determine whether it could provide a safe and reliable alternative to traditional surgical methods.MethodsThis retrospective study included 45 consecutive patients with two-level lumbar disc herniation or spinal stenosis, 24 of whom underwent the TTL system and posterolateral fusion combined (TTL group), and 21 of whom underwent posterolateral fusion alone (Rigid group). The surgical segment, admission diagnosis, operation time, and intraoperative bleeding were recorded separately for the two groups of patients. Imaging studies included pre- and postoperative radiography, magnetic resonance imaging, and computed tomography. The clinical outcomes were measured by Oswestry Disability Index (ODI) scores, and a visual analogue scale (VAS) for back and leg pain.ResultsAll patients completed the surgery successfully with a mean follow-up of 56.09 months. The operative time and intraoperative bleeding were lower in the TTL group than in the Rigid group (p < 0.05). All patients showed significant improvements in clinical outcomes, including VAS for back and leg pain, and ODI scores (p < 0.05). ODI scores, the TTL group was better than the Rigid group at 1 year after surgery and at the final follow-up (p < 0.05). Postoperative surgical segment range of motion (ROM) decreased in both groups (p < 0.05). The postoperative ROM of the upper adjacent segment increased in both groups and was significantly higher in both groups at the last follow-up compared with the preoperative period (p < 0.05), and the superior adjacent segment rom of the TTL group was lower than the Rigid group (p < 0.05). The modified Pfrrmann classification of the superior adjacent segment was significantly increased in both groups at the last follow-up (p < 0.05). And in the TTL group, ROM, DH, and modified Pfrrmann grading of dynamic segment outperformed fusion segments. According to the UCLA classification, the incidence of adjacent segment degeneration (ASD) was 4.2% in the TTL group and 23.8% in the Rigid group, and the incidence of ASD was lower in the TTL group than in the Rigid group (P < 0.05).ConclusionThe Isobar TTL System was utilized in two-level lumbar hybrid surgery, resulting in no evident indications of lumbar instability being detected on X-rays captured at a minimum of 4 years after the operation, while retaining partial range of motion of the surgical segment. The general clinical efficacy is equivalent to titanium rod fusion surgery, presenting an alternative treatment for individuals with mild and moderate lumbar degenerative disease.

Image Registration using the Rigid Group

Image registration is the process of approximate matching of the source image to the target so that they resemble each other. In this study, two-dimensional image registration is presented using the rigid group. This group is a finite dimensional group (four-dimensional in this case) under composition. The dimensions of the rigid group are scaling, rotation, and translations along the axes. In this paper, an algorithm for the construction of rigid transformation is presented using the discretized objective function. This objective function is based on SSD (sum of the squares of the distances between the pixels intensities) and calculates the discrepancy between the images. The coarse search and the gradient descent approaches have been used for the optimization. The proposed algorithm is implemented on variety of images. The numerical examples illustrate the ability of the proposed algorithm.

Aliphatic Polybenzimidazoles: Synthesis, Characterization and High-Temperature Shape-Memory Performance

A series of aliphatic polybenzimidazoles (PBIs) with methylene groups of varying length were synthesized by the high-temperature polycondensation of 3,3'-diaminobenzidine (DAB) and the corresponding aliphatic dicarboxylic acid in Eaton's reagent. The influence of the length of the methylene chain on PBIs' properties was investigated by solution viscometry, thermogravimetric analysis, mechanical testing and dynamic mechanical analysis. All PBIs exhibited high mechanical strength (up to 129.3 ± 7.1 MPa), glass transition temperature (≥200 °C) and thermal decomposition temperature (≥460 °C). Moreover, all of the synthesized aliphatic PBIs possess a shape-memory effect, which is a result of the presence of soft aliphatic segments and rigid bis-benzimidazole groups in the macromolecules, as well as strong intermolecular hydrogen bonds that serve as non-covalent crosslinks. Among the studied polymers, the PBI based on DAB and dodecanedioic acid has high adequate mechanical and thermal properties and demonstrates the highest shape-fixity ratio and shape-recovery ratio of 99.6% and 95.6%, respectively. Because of these properties, aliphatic PBIs have great potential to be used as high-temperature materials for application in different high-tech fields, including the aerospace industry and structural component industries.

Collaborative modification strategy to develop a highly selective fluorescent probe for human UDP-glucuronosyltransferase 1A10

UDP-glucuronosyltransferase 1A10 (UGT1A10) is an important phase II human metabolic enzyme. However, few methods are available to facilely monitor the function of UGT1A10 in biological systems. Here we report the first sensitive and selective fluorescent “off–on” UGT1A10 probe substrate UPr6. Using a collaborative modification strategy, we introduced a rigid propyl morpholine group to the amide and a methoxy group next to 4′-phenoxy of the 4-phenyl-1,8-naphthalimide skeleton to obtain UPr6. Visualization methods were established to evaluate the function of UGT1A10 in living cells, rat tissues, and zebrafish. From a Chinese herbal medicine compound library, two natural products EUC and DAP from licorice were discovered as potent UGT1A10 inhibitors, which remarkably improved the sensitivity of CPT-11 against a resistant human cancer cell line. This work established a feasible strategy to rationally design isoform-specific UGT probe substrates.

Efficient Toughening of DGEBA with a Bio-Based Protocatechuic Acid Derivative.

In this work, a bio-based epoxy resin, protocatechuic acid diester epoxy resin, (PDEP), was synthesized using protocatechuic acid. The structure and properties of PDEP have been characterized by 1H NMR, 13C NMR, and Fourier transform infrared. After different contents of PDEP were added to diglycidyl ether of bisphenol A (DGEBA), the modified epoxy resins were cured by 4,4'-diaminodiphenylmethane (DDM). With the addition of a flexible long-chain bio-based monomer to improve toughness, the impact strength was 50 kJ·m-2 with only 5.0 wt % PDEP; compared with pure DGEBA, the impact strength was 27 kJ·m-2. Further, an increase in T g should be confirmed from the mechanical cross-linking density and rigidity group content. The single T g proved the homogeneous phase structure of the PDEP-cured resin. Morphology exhibiting the ductile fracture of the cured resin was confirmed by scanning electron microscopy. Overall, this work demonstrates the utilization of renewable protocatechuic acid as an effective modifier for epoxy resin, which reflects its potential application.

Generic Types and Generic Elements in Divisible Rigid Groups

Generic Types and Generic Elements in Divisible Rigid Groups

Aza-phenol Based Macrocyclic Probes Design for "CHEF-on" Multi Analytes Sensor: Crystal Structure Elucidation and Application in Biological Cell Imaging.

Metal bound macrocyclic compounds found in biological systems inspired us to design and synthesize two Robson-type macrocyclic Schiff-base chemosensors, H 2 L1 (H 2 L1=1,11-dimethyl-6,16-dithia-3,9,13,19-tetraaza-1,11(1,3)-dibenzenacycloicosaphane-2,9,12,19-tetraene-1,11-diol) and H 2 L2 (H 2 L2=1,11-dimethyl-6,16-dioxa-3,9,13,19-tetraaza-1,11(1,3)-dibenzenacycloicosaphane-2,9,12,19-tetraene-1,11-diol). Both the chemosensors have been characterized with different spectroscopic techniques. They act as multianalyte sensor and exhibit "turn-on" fluorescence toward different metal ions in 1X PBS (Phosphate Buffered Saline) solution. In presence of Zn2+, Al3+, Cr3+ and Fe3+ ions, H 2 L1 exhibits ∼6-fold enhancement of emission intensity, while H 2 L2 shows ∼6-fold enhancement of emission intensity in the presence of Zn2+, Al3+ and Cr3+ ions. The interaction between the different metal ion and chemosensor have been examined by absorption, emission, and 1H NMR spectroscopy as well as by ESI-MS+ analysis. We have successfully isolated and solved the crystal structure of the complex [Zn(H 2 L1)(NO3)]NO3 (1) by X-ray crystallography. The crystal structure of 1 shows 1:1 metal:ligand stoichiometry and helps to understand the observed PET-Off-CHEF-On sensing mechanism. LOD values of H 2 L1 and H 2 L2 toward metal ions are found to be ∼10-8 and ∼10-7 M, respectively. Large Stokes shifts of the probes against analytes (∼100 nm) make them a suitable candidate for biological cell imaging studies. Robson type phenol based macrocyclic fluorescence sensors are very scarce in the literature. Therefore, the tuning of structural parameters as the number and nature of donor atoms, their relative locations and presence of rigid aromatic groups can lead to the design of new chemosensors, which can accommodate different charged/neutral guest(s) inside its cavity. The study of the spectroscopic properties of this type of macrocyclic ligands and their complexes might open a new avenue of chemosensors.

P/N Flame Retardant Based on a Pyrimidine Ring for Improving the Flame Retardancy, Mechanical Properties, and Smoke Suppression of Epoxy Resin

A P/N flame-retardant TBD based on a pyrimidine ring was devised and developed by reacting 2,4,6-triaminopyrimidine, benzaldehyde, and 9,10-dihydro-9-oxa-10-phosphaphenanthrene-10-oxide to create a less toxic, low-smoke, and mechanically improved the flame-retardant epoxy resin (EP). The EP modified using TBD exhibited good transparency, which was attributed to the outstanding compatibility of TBD with the EP. With a phosphorus content of only 0.65%, EP/TBD10 passed the V-0 rating of the UL-94 test, and the limited oxygen index increased from 27.1% (pure EP) to 38.1%. In the cone calorimetry test (CCT), the peak heat release rate and the total heat release decreased by 34.9 and 45.7%, respectively, compared to pure EP. In addition, the modified cured EP exhibited good mechanical properties owing to the action of rigid groups and the formation of hydrogen bonds, and the tensile strength and modulus as well as the flexural strength and modulus of the samples were improved. In the smoke density test, EP/TBD20 received the ratings of HL1 and HL2 in Ds(4) and VOF4, respectively, according to EN45545-2. All results indicate that TBD is an efficient flame retardant that can enhance the flame retardancy and mechanical properties of the curing EP and reduce its smoke density, making it suitable for use in the rail transportation industry.

Role of the Intramolecular‐Locking Strategy in the Construction of Organic Thermally Activated Delayed Fluorescence Emitters with Rotation‐Restricted Acceptors

AbstractConstructing highly twisted and rigid donor–acceptor systems is important for obtaining highly efficient thermally activated delayed fluorescence (TADF) emitters. In the traditional framework of structurally twisted charge‐transfer TADF molecular design, increasing the rigidity of the molecule through constructing rigid groups guarantees the minimized overlap integral between their highest occupied molecular orbitals and lowest unoccupied molecular orbitals for a small singlet and triplet energy gap, which ensures efficient reverse intersystem crossing. Increasing rigidity also prevents the molecule from deforming when in the excited state, effectively suppresses non‐radiative energy dissipation, and improves the photoluminescence quantum yield. As one of the important fragments for TADF emitters, the development of acceptor units with rigid structure deserves in‐depth understanding. Therefore, this review offers a comprehensive summary of the designs and developments of rigid TADF acceptors with “intramolecular locks” including covalent bonds, coordination bonds, and non‐covalent bonds, via the intramolecular‐locking strategy. The mechanism of TADF based on results from density functional theory is also described. Finally, the role of the intramolecular‐locking strategy in the construction of pure organic TADF emitters with rotation‐restricted acceptors and in improving the efficiency of all‐organic TADF‐based organic light‐emitting diodes is discussed.

Improved syntheses of doubly naphthalene-bridged diphosphine and its diiminodiphosphorane derivatives linking two Cu(I) centers

An improved method for preparing bis(1,8-naphthalenediyl)diphosphine, 1, was developed. A phosphino-naphthalene unit of a precursor, iPr2NP-peri-bridged naphthalene, was dimerized in an acetic acid medium, while the precursor in a previously reported method was heated in toluene. The reaction time was reduced from 48 h to 1 h, and an increase to the gram scale was achieved. The diphosphine, 1, comprised a unique PP bond, which was clamped by two 1,8-naphthalene units and was used to synthesize the diiminodiphosphorane derivatives. Thereafter, the two imino-donating groups comprising Ph, p-nBu–C6H4, Mes, and 2,6-iPr2–C6H3 were introduced into two phosphorus centers via the Staudinger reaction using the corresponding R−N3 group (R = Ph, p-nBu–C6H4, Mes, and 2,6-iPr2–C6H3). The result revealed that they did not function as a chelating pair to a single metal center; rather, they acted as a bridging ligand that linked the two metal centers, as demonstrated by the formation of dicopper complexes, except for the bulky 2,6-iPr2–C6H3 case. The two rigid naphthalene groups forced the PPC(naphthalene) angles of five-membered rings to be ca. 90°, thereby increasing the P−PN bond angles (ca. 130°). These increased P−PN bond angles forced the two imino nitrogen to trigger each other. This accounted for the bridging and nonchelating functionalities of the synthesized diiminodiphosphoranes. Both iminophosphorane groups of the synthesized diiminodiphosphorane were directly linked; they could facilitate the binding of two neighboring metal units.

Vertebral refracture after percutaneous vertebroplasty for osteoporotic vertebral compression fractures with and without brace wearing: A retrospective study of 300 patients.

The aim of the study was to examine the clinical incidence rate of vertebral body fractures after percutaneous vertebroplasty (PVP) with and without brace wearing and provide a new guiding ideology for preventing vertebral fractures after clinical surgeries. The retrospective analysis included 100 outpatients who underwent PVP between January 2017 and December 2018 without bracing after PVP surgeries (non-brace-wearing group). In total, 100 patients were paired into the rigid brace group and 100 patients were paired into the soft braces group according to propensity score matching. Seven independent variables were used in the soft and rigid brace group: age, sex, body mass index (BMI), visual analog scale (VAS), Oswestry Disability Index (ODI), and Cobb angle. The VAS, ODI, and Japanese Orthopaedic Association (JOA) scores were recorded preoperatively on the second day, after 1 month, after 3 months, and during the last follow-up postoperatively. We recorded the incidence of vertebral refracture in each of the three groups of patients and evaluated the effect of braces on postoperative fractures based on the ODI, VAS, and JOA scores. All patients were followed up for 8-24 months (mean 22.4 months). Compared with the preoperative values, the age, sex, BMI, bone density, ODI, VAS, and Cobb angle between refracture and non-refracture were not statistically significant. The VAS, ODI, and JOA scores significantly increased in the brace-wearing group compared with those of the non-brace-wearing group (p < 0.05). The incidence of vertebral refracture in the brace-wearing group was lower than that in the non-brace-wearing group, between which there was a significant difference (p < 0.05). Three months postoperatively, the JOA score of the soft brace group was significantly higher than that of the rigid brace group (p < 0.05). During the last follow-up, it was found that there was no difference in the VAS score, the incidence of refracture, or ODI between the soft brace group and the rigid brace group (p > 0.05). The improvement in the JOA score of the soft brace group was better than that of the rigid brace group, between which there was a significant difference (p < 0.05). Braces can improve the prognosis of quality of life and postoperative subjective perception, whose presence can relieve postoperative residual pains. In contrast, patients can have a better medical experience wearing a soft brace.

Comparative analysis of mid-term outcomes of Rigid and NeoRing support rings in mitral regurgitation surgery: a prospective randomized trial

Highlights. For the first time, as part of a prospective randomized study, a comparative assessment of the mid-term results of mitral valve annuloplasty using a new biological NeoRing ring (CJSC NeoKor, Kemerovo) and a RIGID ring (CJSC NPP MedInzh, Penza) in patients with connective tissue dysplasia was carried out. Predictors of the conversion of sinus rhythm to atrial fibrillation and residual mitral insufficiency in the medium-term follow-up period were determined.Aim. To analysis and compare mid-term results of mitral valve annuloplasty conducted using NeoRing и RIGID rings.Methods. From November 2019 to March 2022, 62 patients with mitral valve (MV) dysplasia underwent MV annuloplasty using NeoRing semi-rigid rings (CJSC NeoKor, Kemerovo, n = 31) and rigid RIGID rings (CJSC NPP MedInzh, Penza, n = 31). There were no differences between the groups at baseline.Results. Two deaths were registered during inpatient treatment in the RIGID group. Both devices showed a satisfactory outcome during inpatient treatment in the form of restoration of MV function (p&lt;0.001) and the frequency of detected maximum residual mitral regurgitation (MR) up to grade 1 in the NeoRing group 9.7% and in the RIGID group 29%, respectively, no statistically significant intergroup differences were noted (p = 0.292). After 12 months, freedom from ≥2 grade MR in the NeoRing group was 93.5% and 77.4% in the RIGID group (p = 0.147). In the RIGID group, patients had higher values of the transvalvular mitral diastolic gradient – PAV 3.70 [3.00–4.40] mm Hg vs. NeoRing group 2.3 [2.05–2.85] mmHg (p&lt;0.001), as well as a higher transvalvular flow rate – VAV 79 [71–94] cm/sec vs. 70 [64–79] cm/sec (p = 0.017). The analysis of the achievement of composite primary endpoint (recurrence of ≥2 grade MR, MACCE, new onset arrhythmias, reoperations) by the device was carried out. The composite endpoint rate in the RIGID group was 3.067 times higher compared to the NeoRing group, odds differences were statistically significant (p = 0.037, 95% CI: 1.053–8.934).Conclusion. The outcome of MV annuloplasty conducted using rigid and semi-rigid rings revealed no significant differences in long-term survival and recurrence of MR between groups. Given the statistically significant difference in achieving the combined endpoint, lower inpatient and long-term indicators of transmitral pressure gradient, and a positive effect on cardiac chambers reverse remodeling, it was concluded that the use of semi-rigid NeoRing rings for MV annuloplasty when performing valvepreserving operations for connective tissue dysplasia is preferable.

Curves of stationary acceleration according to alternative frame

This paper investigates curves of stationary acceleration by using alternative frame which includes the principal normal vector, the derivative of principal normal vector and the Darboux vector. Mentioned curves are studied by the way of rigid body motions, that is to say a point in the moving body follows the curve and the alternative frame in the moving body stays aligned with the members of frame. It is determined that in which condition this special motion becomes to stationary acceleration motion. The matrix representations of a constant vector related to velocity vector of the motion which is used to characterize stationary acceleration is obtained by means of alternative frame curvatures. Some examinations are developed with some solutions of differential equations. The main result is attained as: general helix curves with linear curvature and torsion functions are curves of stationary acceleration which are curves in the rigid body motions group SE(3) correlated with robotics. The paths designed as stationary acceleration curves can lead the way to control the end-effectors of robots. Finally, some explanatory examples are imputed.

The Panel Method for Rigid Section Group Added Mass Coefficients and Its Application to Fuel Assemblies

This paper develops a numerical method based on the panel method which can apply to calculate the added fluid mass coefficients of a group of rigid sections with arbitrarily complex shapes. It has been successfully applied to the PWR fuel assemblies, which analyzed the variation law of added mass coefficients caused by position deviation in the (1 × 5) fuel assembly’s seismic test. Results show that this method is suitable for the calculation of the added mass coefficients of a group of rigid sections which have a complex continuous boundary. Compared with the gap between assemblies, the gap between baffles and assemblies has a dominant influence on the added mass coefficients; Regardless of the position deviation, the sum of the added mass coefficients of all assemblies and baffles along the assumed motion direction is approximately equal to −1, the sum of the coefficients perpendicular to the assumed motion is approximately equal to 0.

Short-term Endoscopic Outcomes of Balloon and Rigid Bronchoplasty in the Management of Benign Subglottic and Tracheal Stenosis.

Endoscopic therapies are firmly established in the management algorithm of benign subglottic and tracheal stenosis (SGTS). The optimal dilation strategy, however, has yet to be elucidated. The objective of this study was to compare the efficacy and safety of balloon versus rigid bronchoplasty in the treatment of benign SGTS. De novo cases of benign SGTS at our institution over a 9-year period were retrospectively identified. Patients were divided into 2 groups based on the initial dilation strategy of balloon or rigid bronchoplasty. Demographics, clinical findings, concurrent interventions, lesion characteristics, and complications were analyzed. Two reviewers independently assigned an index and follow-up endoscopic stenosis grade for each case. The mean stenosis grade at follow-up in both groups was then calculated and compared. Sixty-three patients with benign SGTS were included. Most stenoses in the rigid (80%) and balloon (63%) bronchoplasty groups were complex (P=0.174). In addition, 94% (59/63) of index stenoses were classified as Cotton Myer Grade 3. At follow-up, no significant difference was found in the mean stenosis grade between dilation strategies (1.97 vs. 2.2,P=0.287). Furthermore, no procedural-related complications were observed in either group. Balloon and rigid bronchoplasty are safe and effective endoscopic tools in the early management of benign SGTS. A multimodality approach centered around mucosal sparing techniques remains vitally important to the overall and likely long-term success of treating this challenging disease entity.

Некоторые вопросы теории моделей делимых жестких групп

A brief review of some of the author's results on the theory of models of divisible rigid groups is given. A theorem is presented that describes algebraic closures of subsets in a divisible rigid group.

Preparation of Quaternary Ammonium Gemini Surfactant and Its Application in Insulator Cleaning

In this paper, quaternary ammonium salt type Gemini surfactant G12 was designed and synthesized, and its structure was characterized by infrared and nuclear magnetic resonance. The surface tension, permeability, emulsification ability and cleaning of insulator surface contamination in the composite system were tested, and the test results showed that it had low critical micelle concentration (cmc) and good emulsification performance. Due to the presence of rigid groups, the permeability is average. When quaternary ammonium Gemini surfactant G12 is mixed with permeant JFC-E, and is combined with auxiliary and organic solvent, the cleaning rate of insulators can reach more than 90%.

Naphthalimide-based conjugated macrocycles possessing tunable self-assembly and supramolecular binding behaviours.

The special geometric configurations and optoelectronic properties of p-conjugated macrocycles have always been the focus of materials science. The incorporation of building moieties with different features into macrocycles can not only change their geometric configurations, but also realize the regulation of intramolecular charge transfer, which is expected to bring unusual performance in supramolecular chemistry and optoelectronic devices. Herein, four novel p-conjugated macrocycles based on typical electron acceptor units naphthalimide (NMI) with aryl or alkyl substitutions were reported. The different substitutions on NMI had greatly affected the self-assembly behaviours of these macrocycles. Alkyl substituted NP2b and NP3b showed obvious self-aggregation in solution, while similiar phenomenon was not found in aryl substituted macrocycles NP2a and NP3a, which can be attributed to the steric hindrance caused by rigid aryl groups that could affect the aggregation of macrocycles in solution. In addition, all the macrocycles exhibited supramolecular encapsulation with C70, in which the larger macrocycles NP3a and NP3b with twisted geometries showed stronger binding affinity towards C70 than the corresponding small-size macrocycles NP2a and NP2b with near-planar geometries. Our studies have greatly extended the family of macrocycles based on NMI, pointing out the direction for further supramolecular studies and applications on p-conjugated macrocycles.

Locally Rigid Right-angled Coxeter Groups with Fuchsian Ends in Dimension 5

In this paper, we construct a right-angled 5-polytope P of finite volume such that all the right-angled Coxeter groups with Fuchsian ends obtained from P are locally rigid. This is the first explicit example of locally rigid discrete subgroups of Isom(ℍ5) with Fuchsian ends.

Explicit Methods in Number Theory

The series of Oberwolfach meetings on ‘Explicit methods in number theory’ brings together people attacking key problems in number theory via techniques involving concrete or computable descriptions. Here, number theory is interpreted broadly, including algebraic and analytic number theory, Galois theory and inverse Galois problems, arithmetic of curves and higherdimensional varieties, zeta and L -functions and their special values, modular forms and functions. The 2021 meeting featured a seven-lecture minicourse on the distribution of class groups and Selmer groups. The other talks covered a broad range of topics in number theory ranging, for instance, from deterministic integer factorisation to the inverse Galois problem, rational points, and integrality of instanton numbers.