THE BOUNDARY SCHWARZ LEMMA AND THE RIGIDITY THEOREM ON REINHARDT DOMAINS B_(p)^(n) OF C^(n)

By introducing the Carathéodory metric,we establish the Schwarz lemma at the boundary for holomorphic self-mappings on the unit p-ball B_(p)^(n) of C^(n).Furthermore,the boundary rigidity theorem for holomorphic self-mappings defined on B_(n)^(p) is obtained.These results cover the boundary Schwarz lemma and rigidity result for holomorphic self-mappings on the unit ball for p=2,and the unit polydisk for p=∞,respectively.

GLOBAL RIGIDITY THEOREMS FOR SUBMANIFOLDS WITH PARALLEL MEAN CURVATURE

In this paper,we mainly study the global rigidity theorem of Riemannian submanifolds in space forms.Let Mn(n≥3)be a complete minimal submanifold in the unit sphere Sn+p(1).Forλ∈[0,n2−1/p),there is an explicit positive constant C(n,p,λ),depending only on n,p,λ,such that,if∫MSn/2dM<∞,∫M(S−λ)n/2+dM<C(n,p,λ),then Mn is a totally geodetic sphere,where S denotes the square of the second fundamental form of the submanifold and∫+=max{0,f}.Similar conclusions can be obtained for a complete submanifold with parallel mean curvature in the Euclidean space Rn+p.

Impairment of rigidity sensing caused by mutant TP53 gain of function in osteosarcoma

Osteosarcoma(OS)is the most common primary malignant pediatric bone tumor and is characterized by high heterogeneity.Studies have revealed a wide range of phenotypic differences among OS cell lines in terms of their in vivo tumorigenicity and in vitro colony-forming abilities.However,the underlying molecular mechanism of these discrepancies remains unclear.The potential role of mechanotransduction in tumorigenicity is of particular interest.To this end,we tested the tumorigenicity and anoikis resistance of OS cell lines both in vitro and in vivo.We utilized a sphere culture model,a soft agar assay,and soft and rigid hydrogel surface culture models to investigate the function of rigidity sensing in the tumorigenicity of OS cells.Additionally,we quantified the expression of sensor proteins,including four kinases and seven cytoskeletal proteins,in OS cell lines.The upstream core transcription factors of rigidity-sensing proteins were further investigated.We detected anoikis resistance in transformed OS cells.The mechanosensing function of transformed OS cells was also impaired,with general downregulation of rigidity-sensing components.We identified toggling between normal and transformed growth based on the expression pattern of rigidity-sensing proteins in OS cells.We further uncovered a novel TP53 mutation(R156P)in transformed OS cells,which acquired gain of function to inhibit rigidity sensing,thus sustaining transformed growth.Our findings suggest a fundamental role of rigidity-sensing components in OS tumorigenicity as mechanotransduction elements through which cells can sense their physical microenvironment.In addition,the gain of function of mutant TP53 appears to serve as an executor for such malignant programs.

Determination of Material Parameters of EVA Foam under Uniaxial Compressive Testing Using Hyperelastic Models

The objective of this research was to determine the mechanical parameter from EVA foam and also investigate its behavior by using Blatz-Ko,Neo-Hookean,Mooney model and experimental test.The physical characteristic of EVA foam was also evaluated by scanning electron microscopy(SEM).The results show that Blatz-Ko and Neo-Hookean model can fit the curve at 5%and 8%strain,respectively.The Mooney model can fit the curve at 50%strain.The modulus of rigidity evaluated from Mooney model is 0.0814±0.0027 MPa.The structure of EVA foam from SEM image shows that EVA structure is a closed cell with homogeneous porous structure.From the result,it is found that Mooney model can adjust the data better than other models.This model can be applied for mechanical response prediction of EVA foam and also for reference value in engineering application.

Motor cortical circuit adaptations in parkinsonism

Parkinson's disease is a chronic and progressive neurodegenerative disorder characterized by the loss of dopaminergic neurons in the substantia nigra pars compacta,which leads to the featured motor impairment of parkinsonism,including akinesia,bradykinesia,rigidity,and tremor(McGregor and Nelson,2019).

Dynamic Analysis of a 10 MW Floating Offshore Wind Turbine Considering the Tower and Platform Flexibility

Recently,semisubmersible floating offshore wind turbine technologies have received considerable attention.For the coupled simulation of semisubmersible floating offshore wind energy,the platform is usually considered a rigid model,which could affect the calculation accuracy of the dynamic responses.The dynamic responses of a TripleSpar floating offshore wind turbine equipped with a 10 MW offshore wind turbine are discussed herein.The simulation of a floating offshore wind turbine under regular waves,white noise waves,and combined wind-wave conditions is conducted.The effects of the tower and platform flexibility on the motion and force responses of the TripleSpar semisubmersible floating offshore wind turbine are investigated.The results show that the flexibility of the tower and platform can influence the dynamic responses of a TripleSpar semisubmersible floating offshore wind turbine.Considering the flexibility of the tower and platform,the tower and platform pitch motions markedly increased compared with the fully rigid model.Moreover,the force responses,particularly for tower base loads,are considerably influenced by the flexibility of the tower and platform.Thus,the flexibility of the tower and platform for the coupled simulation of floating offshore wind turbines must be appropriately examined.

Interaction Mechanisms between Natural Debris Flow and Rigid Barrier Deflectors:A New Perspective for Rational Design and Optimal Arrangement

Rigid barrier deflectors can effectively prevent overspilling landslides,and can satisfy disaster prevention requirements.However,the mechanisms of interaction between natural granular flow and rigid barrier deflectors require further investigation.To date,few studies have investigated the impact of deflectors on controlling viscous debris flows for geological disaster prevention.To investigate the effect of rigid barrier deflectors on impact mechanisms,a numerical model using the smoothed particle hydrodynamics(SPH)method with the Herschel–Bulkley model is proposed to simulate the interaction between natural viscous flow and single/dual barriers with and without deflectors.This model was validated using laboratory flume test data from the literature.Then,the model was used to investigate the influence of the deflector angle and multi-barrier arrangements.The optimal configuration of multi-barriers was analyzed with consideration to the barrier height and distance between the barriers,because these metrics have a significant impact on the viscous flow pile-up,run-up,and overflow mechanisms.The investigation considered the energy dissipation process,retention efficiency,and dead-zone formation.Compared with bare barriers with similar geometric characteristics and spatial distribution,rigid barriers with deflectors exhibit superior effectiveness in preventing the overflow and overspilling of viscous debris flow.Recommendations for the rational design of deflectors and the optimal arrangement of multi-barriers are provided to mitigate geological disasters.

Treadmill training in Parkinson's disease:possible role of prefrontal modifications in the improved cortical-subcortical network function

Parkinson’s disease(PD)is a complex neurodegenerative disorder characterized by a range of motor symptoms such as bradykinesia,resting tremor,rigidity,and postural instability,as well as non-motor symptoms,such as depression,anxiety,sleep disturbances,and fatigue(Bloem et al.,2021).

Field Load Test Based SHM System Safety Standard Determination for Rigid Frame Bridge

The deteriorated continuous rigid frame bridge is strengthened by external prestressing. Static loading tests wereconducted before and after the bridge rehabilitation to verify the effectiveness of the rehabilitation process. Thestiffness of the repaired bridge is improved, and the maximum deflection of the load test is reduced from 37.9 to27.6 mm. A bridge health monitoring system is installed after the bridge is reinforced. To achieve an easy assessmentof the bridge’s safety status by directly using transferred data, a real-time safety warning system is createdbased on a five-level safety standard. The threshold for each safety level will be determined by theoretical calculationsand the outcomes of static loading tests. The highest risk threshold will be set at the ultimate limit statevalue. The remaining levels, namely middle risk, low risk, and very low risk, will be determined usingreduction coefficients of 0.95, 0.9, and 0.8, respectively.

Review on dynamic analysis of road pavements under moving vehicles and plane strain conditions

This paper reviews works on the dynamic analysis of flexible and rigid pavements under moving vehicles on the basis of continuum-based plane strain models and linear theories.The purpose of this review is to provide in-formation about the existing works on the subject,critically discuss them and make suggestions for further research.The reviewed papers are presented on the basis of the various models for pavement-vehicle systems and the various methods for dynamically analyzing these systems.Flexible pavements are modeled by a homogeneous or layered half-plane with isotropic or anisotropic and linear elastic,viscoelastic or poroelastic material behavior.Rigid pavements are modeled by a beam or plate on a homogeneous or layered half-plane with material properties like the ones for flexible pavements.The vehicles are modeled as concentrated or distributed over a finite area loads moving with constant or time dependent speed.The above pavement-vehicle models are dynamically analyzed by analytical,analytical/numerical or purely numerical methods working in the time or frequency domain.Representative examples are presented to illustrate the models and methods of analysis,demonstrate their merits and assess the effects of the various parameters on pavement response.The paper closes with con-clusions and suggestions for further research in the area.The significance of this research effort has to do with the presentation of the existing literature on the subject in a critical and easy to understand way with the aid of representative examples and the identification of new research areas.

Flexible bronchoscopy for foreign body aspiration in children:A single-centre experience

BACKGROUND The technological evolution of bronchoscopy has led to the widespread adoption of flexible techniques and their use for both diagnostic and therapeutic purposes.Currently,there is an active debate regarding the comparative efficacy and safety of rigid vs flexible bronchoscopy in the treatment of foreign body aspiration.AIM To evaluate our experience with tracheobronchial foreign body extraction using flexible bronchoscopy and provide a literature overview.METHODS This was a single-centre retrospective study.Twenty-four patients were enrolled between January 2017 and January 2023.Medical records of patients aged below 18 years who were admitted to authors’affiliated institution with a suspected diagnosis of foreign body aspiration were collected from hospital’s database to Microsoft Excel 2019.Data were analysed using MedCalc Statistical Software.RESULTS Patient ages varied from 9 months to 11 years.The median age was 23.5 months,95%confidence interval(CI)19.49-44.77.We observed age clustering in children with foreign body aspiration at our institution with three age subgroups:(1)0-25 months;(2)40-60 months;and(3)120-140 months.We expectancy of an organic tracheobronchial foreign body was significantly higher in 0-25 months subgroup than that in older ones when subgroups 40-60 and 120-140 months were combined together(odds ratio=10.0,95%CI:1.44-29.26,P=0.0197).Successful foreign body extraction was performed in all cases.Conversion to a rigid bronchoscope was not required in any of the cases.No major complications(massive bleeding,tracheobronchial tree perforation,or asphyxia)were observed.CONCLUSION Flexible bronchoscopy is an effective and safe method for tracheobronchial foreign body extraction in children.

Graphite Carbone Structure

Carbon graphite is a crystalline form of carbon consisting of layers of hexagonal carbon atoms arranged in a two-dimensional “graphene” structure. Graphene layers are stacked on top of each other, forming a three-dimensional structure with a high degree of anisotropy. The carbon atoms within each layer are linked together by strong covalent bonds, creating a strong, stable lattice structure. However, the layers themselves are held together by weak van der Waals forces, enabling them to slide easily over each other. The properties of carbon graphite are highly dependent on the orientation and alignment of the graphene layers. When the layers are aligned parallel to each other, the material exhibits high strength and stiffness along the alignment direction, but is weaker and more flexible in other directions. Carbon graphite is used in a variety of applications where high strength, rigidity and electrical conductivity are required. Some common applications include electrical contacts, electric motor brushes, and as a structural material in aerospace and defense applications. The aim of our work is to describe the structure of graphite, its physical and chemical properties and its applications.

Radial Grip Rigidity of the Matching of Lengthened Shrink-fit Holder and Cutter in High-speed Milling

Though the lengthened shrink-fit holder (LSFH) is widely applied in high speed milling of the parts characterized by deep cavities at present, its design and selection mainly depends on the experience and lacks a correct theoretical guidance. In this paper, attention is focus on the radial grip rigidity of the matching of LSFH and cutter in high speed milling. Based on the experiment modal analysis (EMA) technique, an accurate finite element model of the matching of LSFH and cutter is established firstly. Subsequently, the influence of different interference, grip length and spindle speed on the grip rigidity of LSFH are analyzed. The analysis results show that there is a reasonable interference and grip length between the LSFH and cutter so that to have a steepless grip and have a good radial grip rigidity and at the same time to avoid the strength of LSFH to exceed it’s yield limit which will reduce the precision and service life of LSFH, besides when spindle speed reach a extension the weakening influence of the centrifugal force on the radial grip rigidity of the matching of LSFH and cutter should been taken into account. Finally, the finite element analysis results are verified based on the construction of measurement method of the grip rigidity and the results fit very well. The studies provide a theoretical basis for the design, selection and the serialization and standardization of the matching of LSFH and cutter.

Theoretical analysis of natural frequency of externally prestressed concrete beam based on rigidity correction

A dynamic test on externally prestressed simply supported concrete beams separately with three typical types of tendon distributions was conducted. The results show that the natural frequencies of the beams increase with the increase in the prestressing force at the tensioning stage, and the natural frequencies decrease after the cracks occur in the beams. Following the calculation formula of natural frequency of externally prestressed beam, which was reported in a literature, the natural frequencies of the experimental beams are calculated, and big errors are found between the test results and the calculated ones of natural frequency values. As a result, this paper has tried to adopt two methods to correct the rigidity parameter of the concrete beam in the formula for natural frequency calculation, and to use the corrected formula to calculate the frequencies of the experimental beams. The calculation results indicate a good consistency with the experimental ones, which verifies the feasibility of the corrected formula.

Research on the Structural Rigidity Characteristics of a Reconfigurable TBM Thrust Mechanism

To improve the adaptability of TBMs in diverse geological environments,this paper proposes a reconfigurable Type-V thrust mechanism(V-TM)with rearrangeable working states,in which structural stiffness can be automatically altered during operation.Therefore,millions of configurations can be obtained,and thousands of instances of working status per configuration can be set respectively.Nonetheless,the complexity of configurations and diversity of working states contributes to further complications for the structural stiffness algorithm.This results in challenges such as difficulty calculating the payload compliance index and the environment adaptability index.To solve this problem,we use the configuration matrix to describe the relationship between propelling jacks under reconfiguration and adopt pattern vectors to describe the working state of each hydraulic cylinder.Then,both the dynamic compatible equation between propeller forces of the hydraulic cylinders and driving forces,and the kinematic harmonizing equation between the hydraulic cylinder displacements and their deformations are established.Next,we derive the stiffness analytical equation using Hooke’s law and the Jacobian Matrix.The proposed approach provides an effective algorithm to support structural rigidity analysis,and lays a solid theoretical foundation for calculating the performance indexes of the V-TM.We then analyze the rigidity characteristics of typical configurations under different working states,and obtain the main factors affecting structural stiffness of the V-TM.The results show the deviation degree of structural parameters in hydraulic cylinders within the same group,and the working status of propelling jacks.Finally,our constructive conclusions contribute valuable information for matching and optimization by drawing on the factors that affect the structural rigidity of the V-TM.

On rigidity of Clifford torus in a unit sphere

We extend the scalar curvature pinching theorems due to Peng-Terng, Wei-Xu and Suh-Yang. Let M be an n-dimensional compact minimal hypersurface in S^n＋1 satisfying S f4 - f^2 3 ≤1/nS^3 where S is the squared norm of the second fundamental form of M, and fk = ∑λi^k and λi（1 ≤ i ≤ n） are the principal curvatures of M. We prove that there exists a positive constant δ（n）（≥ n/2） depending only on n such that if n ≤ S ≤ n ＋δ（n）, then S ≡ n, i.e., M is one of the Clifford torus S^K （√k/n） × S^n-k （V√n-k/n） for 1≤ k ≤ n - i. Moreover, we prove that if S is a constant, then there exists a positive constant T（n）（≥ n -2/3） depending only on n such that ifn ≤ S 〈 n ＋ τ（n）, then S ≡n, i.e.. M is a Clifford torus.

Chain Conformation and Local Rigidity of Soluble Polyimides(II):Isomerized Polyimides in THF

Two soluble isomerized polyimides（PIs） synthesized from 2,2＇-bis（3,4-dicarboxyphenyl）hexafluoropropane dianhydride（6FDA） with either 2,2＇-dimethylbenzidine（2,2＇-DMB） or 3,3＇-DMB were investigated by means of size-exclusion chromatography coupled with multi-angle laser light scattering,a viscometer and a refractive index detector in tetrahydrofuran（THF） with tetrabutylammonium bromide（TBAB） at 35 ℃.The corresponding parameters related to conformations α and ν,evaluated from the scaling relationships [η]=K η M α and R g =K g M ν,respectively,were 0.66±0.01 and 0.55±0.02 for poly（6FDA/3,3＇-DMB）,and 0.67±0.01 and 0.56±0.01 for poly（6FDA/2,2＇-DMB）,indicating a random coil conformation for both the samples in this mobile system.The persistence length l p and shift factor M L（relative molecular weight per unit contour length） were estimated from the relationship between intrinsic viscosity and molecular weight for the wormlike cylinder model proposed by Bohdanecky.Both l p and M L showed that the two PIs in THF are flexible chains and exhibit some local rigidity to some extent.

Relation between Stress Conditions, Uncertainty and Incongruity Intolerance, Rigidity and Mental Health: Experimental Demonstrations

An innovative critique of existing studies on creativity has revealed the opportunity of distinguishing between different varieties of creative tasks, and namely creativity for “Continuity”, “Opposition” and “Detachment”, considering relations between products and perceived models. This theoretical contribution has led to a specific evaluation procedure: the COD Creativity test. Considering the influences of dynamic processes on creative processes, it is worth experimentally studying the effects of short-term stress or comfort treatments. The similarities and differences between various existing studies are examined. A non-invasive but effective procedure, compared to classic techniques, is described: the “drawing recall” of stressful or relaxing real experiences, accompanied by detailed evaluations of the emotional sphere. In a specific investigation, creativity turned out to be significantly lower after acute stress with respect to comfort treatment. In conclusion, the cognitive, decisional and activity processes involved in creativity operations can be considered as strictly reflecting emotional dynamic processes, as well as the experiences gained during the stress or comfort treatments. Results are explained considering the role of conflict overload in stress as a factor of incongruity and uncertainty intolerance, inhibiting the production of bizarre and unusual ideas and configurations, and thus reducing essential aspects relevant to the evaluation of creativity levels. From clinical point of view, we underline that decades of research has generally shown that being more rigid is associated with poorer mental health. Our experimental study gives confirmation of the link between stress and intolerance of uncertainty and incongruity;this correlation could augment the negative impact of stressors on anxiety levels. In summary, people with high level of intolerance of uncertainty and, generally, with high level of intolerance of incongruity, develop mental rigidity, and this traits constellation represent a risk for mental health.

CALCULATION OF MILL RIGIDITY BY THREE DIMENSION CONTACT BOUNDARY ELEMENT METHOD

Vertical rigidity of the space self adaptive 530 high rigidity mill is calculated by applying the boundary element method (BEM) of three dimension elastic contact problem,which can update the existed deforming separation calculating theory and corresponding methods of material mechanics,elastic mechanics and finite element method.The method has less hypotheses and stronger synthesis in contact type calculating model.The advantages of the method are high calculating rate,high calculating accuracy,etc..

A Single Mooring System with Sag-Extensibility and Flexural Rigidity Applied to Offshore Platform

Floating platform system has been extensively used in ocean exploitation, particularly for a tension-leg platform （TLP） system in deep water. Most of the TLPs are multi-mooring systems, where multi-joints are connected to the tension-legs so that the platform is not allowed to twist freely and may subject to enormous force induced by large incident waves in the weak-direction of the structure. This study aims to exploit a single moored offshore platform system that may attract less force and can be operated with less effort. In our analysis, in addition to mechanical properties of the tether, two important properties are also taken into consideration for the single mooring tether with expanded cross sectional dimension and utilization of stronger material, namely, the sag-extensibility and the flexural rigidity. Finally, the dynamic structural behavior produced by the mechanical effects on the new system is investigated and compared with that of traditional design while the wave-structure interactions of large body are also accounted for. Our study finds that the neglect of sag-extensibility or the flexural rigidity of large, strong mooring cable may result in a conservative but not necessarily safe design.