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.

Energetic Nature of Rigidity

The work is to present the energetic nature of the rigidity. It starts with the definition by introducing the notion of sensual magnitudes with the pyramidal structure of all surrounding magnitudes known by a human being. Next the selection of the subject is provided in view of a smooth categorization of magnitudes describing the reality. The adequate description of the considered mechanical phenomenon is presented by formulating general stiffness characteristics. There are several characteristics analyzed, both functional and parametric. An essential, quite a new one is the characteristic of stiffness energy measure which is the stiffness potential. The proper and gained stiffness potentials situated on stable and unstable potential fields have been analyzed. An example of using of this theory to practice is given. It has been referred to a cylindrical grinder case. The presented theory allowed describing the entire stiffness characteristics, including its initial very essential course which has been usually, though inequitably, extrapolated by a straight line segment coming out of zero point with zero coordinates.

Numerical evaluation of buckling behavior in space structure considering geometrical parameters with joint rigidity

The buckling behavior of single layer space structure is very sensitive. The joint rigidity, moreover, is one of the main factors of stability which may determine the entire failure behavior. Thus, the reasonable stiffness of joint system, which is neither total pin assumption nor perfect fix condition, is very important to apply to the real single layer space one. Therefore, the purpose of this work was to investigate the buckling behavior of single layer space structure, using the development of the upgraded stiffness matrix for the joint rigidity. To derive tangential stiffness matrix, a displacement function was assumed using translational and rotational displacement at the node. The geometrical nonlinear analysis was simulated not only with perfect model but also with imperfect one. As a result, the one and two free nodal numerical models were investigated using derived stiffness matrix. It was figured out that the buckling load increases in proportion to joint rigidity with rise-span ratio. The stability of numerical model is very sensitive with the initial imperfection, responding of bifurcation in the structure.

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.

Voltage adjustment improves rigidity and tremor in Parkinson's disease patients receiving deep brain stimulation

Deep brain stimulation of the subthalamic nucleus is recognized as the most effective treatment for moderate and advanced Parkinson＇s disease. Programming of the stimulation parameters is important for maintaining the efficacy of deep brain stimulation. Voltage is consid- ered to be the most effective programming parameter. The present study is a retrospective analysis of six patients with Parkinson＇s disease （four men and two women, aged 37-65 years）, who underwent bilateral deep brain stimulation of the subthalamic nucleus at the First Affiliated Hospital of Sun Yat-sen University, China, and who subsequently adjusted only the stimulation voltage. We evaluated motor symptom severity using the Unified Parkinson＇s Disease Rating Scale Part III, symptom progression using the Hoehn and Yahr scale, and the levodopa equivalent daily dose, before surgery and 1 and 2 years after surgery. The 2-year follow-up results show that rigidity and tremor improved, and clinical symptoms were reduced, while pulse width was maintained at 60 ps and frequency at 130 Hz. Voltage adjust- ment alone is particularly suitable for patients who cannot tolerate multiparameter program adjustment. Levodopa equivalent daily dose was markedly reduced 1 and 2 years after surgery compared with baseline. Our results confirm that rigidity, tremor and bradykinesia can be best alleviated by voltage adjustment. The trial was registered at ClinicalTrials.gov （identifier： NCT01934881）.

An optimal rigidity theorem for complete submanifolds in a sphere

It is proved that if M^n is an n-dimensional complete submanifold with parallel mean curvature vector and flat normal bundle in S^n＋p（1）, and if supM S 〈 α（n, H）, where α（n,H）=n＋n^3/2（n-1）H^2-n（n-2）/n（n-1）√n^2H^4＋4（n-1）H^2,then M^n must be the totally urnbilical sphere S^n（1/√1＋H^2）.An example to show that the pinching constant α（n, H） appears optimal is given.

Flexural rigidity of honeycomb consisting of hexagonal cells

In this study,the flexural rigidity of a honeycomb consisting of regular hexagonal cells is investigated.It is found that the honeycomb bending can not be evaluated by using the equivalent elastic moduli obtained from the in-plane deformation because the moments acting on the inclined cell wall are different for in-plane deformation and bending deformation.Based on the fact that the inclined wall is twisted under the condition of the rotation angle in both connection edges being zero,a theoretical technique for calculating the flexural rigidity of honeycombs is proposed,and the validity of the present analysis is demonstrated by numerical results obtained by BFM.

Graph rigidity and localization of multi-robot formations

This paper provides theoretical foundation for the problem of localization in multi-robot formations. Sufficient and necessary conditions for completely localizing a formation of mobile robots/vehicles in SE(2) based on distributed sensor networks and graph rigidity are proposed. A method for estimating the quality of localizations via a linearized weighted least-squares algorithm is presented, which considers incomplete and noisy sensory information. The approach in this paper had been implemented in a multi-robot system of five car-like robots equipped with omni-directional cameras and IEEE 802.11b wireless network.

On Intrinsic Rigidity for Submanifolds with Constant Scalar Curvature in Space Forms

Under the assumption that the normalized mean curvature vector is parallel in the normal bundle, by using the generalized ChengYau＇s self-adjoint differential operator, here we obtain some rigidity results for compact submanifolds with constant scalar curvature and higher codimension in the space forms.

RIGIDITY RESULTS FOR SELF-SHRINKING SURFACES IN R^(4)

In this paper,we give some rigidity results for complete self-shrinking surfaces properly immersed in R^(4) under some assumptions regarding their Gauss images.More precisely,we prove that this has to be a plane,provided that the images of either Gauss map projection lies in an open hemisphere or S^(2)(1/2–√)∖S^(-1)+(1/2–√).We also give the classification of complete self-shrinking surfaces properly immersed in R^(4) provided that the images of Gauss map projection lies in some closed hemispheres.As an application of the above results,we give a new proof for the result of Zhou.Moreover,we establish a Bernstein-type theorem.

Rigidity based formation tracking for multi-agent networks

This paper considers the formation tracking problem under a rigidity framework, where the target formation is specified as a minimally and infinitesimally rigid formation and the desired velocity of the group is available to only a subset of the agents. The following two cases are considered： the desired velocity is constant, and the desired velocity is timevarying. In the first case, a distributed linear estimator is constructed for each agent to estimate the desired velocity. The velocity estimation and a formation acquisition term are employed to design the control inputs for the agents, where the rigidity matrix plays a central role. In the second case, a distributed non-smooth estimator is constructed to estimate the time-varying velocity, which is shown to converge in a finite time. Theoretical analysis shows that the formation tracking problem can be solved under the proposed control algorithms and estimators. Simulation results are also provided to show the validity of the derived results.