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.

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.

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..

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.

TORSIONAL RIGIDITY OF SHELLS OF REVOLUTION

In this paper,the general equations of equilibrium for axisymmetrical deformationincluding the torsional deformation of revolutional shells are derived.It is shown that theshearing stress distribution due to torsion is independent of other stress componentsincluding those of membrane stress and bending stress.In this paper,the torsional deformation is considered to be represented by membraneaction only,and also by the combined action of bending membrane deformation.It is shownthat the main contribution of torsional rigidity is that related to membrane action.

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.

Effects of Break-through State and System Rigidity on Vibration and Noise in Blanking

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STUDY OF STRUCTURE AND RIGIDITY OF AIR-JET TEXTURED YARN(ATY)

This paper deals with the structure of air-jet textured yarn(ATY),especilly its core structurein dedail.It is described that overfeed of supply yarn does influence the ATY structure.Then thebending rigidity of ATY has been measured and analyzed.The results shows that various supplyyarns affect the core structure and bending rigidity of ATY.

A Rigidity Measurement of Pseudo-Rapidity Spectrum of Produced Particles in High Energy Nucleus-Nucleus Collisions

A new concept,rigidity of pseudo-rapidity spectrum,is extended into the study of the multiplicity fluctuations in high energy nucleus-nucleus interactions.In using the novel method to analyze the data of l6O-Em at 14.6,60,and 200A GeV,and ^(32)S-Em at 200A GeV,it is found that the rigidity of pseudo-rapidity spectrum in the central domain of pseudo-rapidity might be a mixture of Poisson type and Wigner one.

A NOTE ON MEASURE-THEORETIC EQUICONTINUITY AND RIGIDITY

Given a topological dynamical system(X,T)and a T-invariant measureμ,let B denote the Borel σ-algebra on X.This paper proves that(X,B,μ,T)is rigid if and only if(X,T)isμ-A-equicontinuous in the mean for some subsequence A of N,and a function f∈L^(2)(μ)is rigid if and only if f is μ-A-equicontinuous in the mean for some subsequence A of N.In particular,this gives a positive answer to Question 4.11 in[1].

RIGIDITY THEOREMS OF COMPLETE K?HLER-EINSTEIN MANIFOLDS AND COMPLEX SPACE FORMS

We concentrate on using the traceless Ricci tensor and the Bochner curvature tensor to study the rigidity problems for complete K?hler manifolds. We derive some elliptic differential inequalities from Weitzenb?ck formulas for the traceless Ricci tensor of K?hler manifolds with constant scalar curvature and the Bochner tensor of K?hler-Einstein manifolds respectively. Using elliptic estimates and maximum principle, several L^p and L~∞ pinching results are established to characterize K?hler-Einstein manifolds among K?hler manifolds with constant scalar curvature and complex space forms among K?hler-Einstein manifolds.Our results can be regarded as a complex analogues to the rigidity results for Riemannian manifolds. Moreover, our main results especially establish the rigidity theorems for complete noncompact K?hler manifolds and noncompact K?hler-Einstein manifolds under some pointwise pinching conditions or global integral pinching conditions. To the best of our knowledge,these kinds of results have not been reported.

THE UNIQUENESS OF THE L_(p) MINKOWSKI PROBLEM FOR q-TORSIONAL RIGIDITY

In this paper,we prove the uniqueness of the Lp Minkowski problem for q-torsional rigidity with p>1 and q>1 in smooth case.Meanwhile,the Lp Brunn-Minkowski inequality and the Lp Hadamard variational formula for q-torsional rigidity are established.

Cable flexural rigidity influence on suspension bridges static properties

In order to figure out the cable flexural rigidity influence on suspension bridges,a contrast model experiment is made:a chain cable model with no flexural rigidity and a wire cable model with some flexural rigidity.And then,four finite element models of a same long-span suspension bridge with different cable element are set up to be analyzed.Both experimental and numerical simulation results show that,with the increase of the span and the decrease of sag-span ratio,the influence of the cable flexural rigidity is significant.The difference of nodes displacement reaches more than 10 cm in construction analysis,which will bring some trouble to the construction.And the difference of the maximum section edge normal stress may reach 15%,which may have an adverse impact onto the bridge.Therefore,considering the cable flexural rigidity is necessary on some analysis of suspension bridges.

The error research on vertical rigidity theory’s formula of airborne air spring

On the basis of analyzing the result of numerical simulation and that of theoretical analysis,the systematic error of some air spring's theoretical formula is researched. The result shows that the vertical stiffness's theoretical formula of air spring owes the systematic error. And the systematic error is relative to the three supposed conditions which are used in the process of theoretical deduction. However,the systematic error is small enough so that the supposed conditions of theoretical formula are reasonable. Moreover,with the increase of initial inner pressure,the systematical error increases.

Rigidity in Subclasses of Transitive and Mixing Systems

We will present some restrictions for a rigidity sequence of a nontrivial topological dynamical system. For instance, any finite linear combination of a rigidity sequence by integers has upper Banach density zero. However, there are rigidity sequences for some uniformly rigid systems whose reciprocal sums are infinite. We also show that if F is a family of subsets of natural numbers whose dual F* is filter, then a minimal F*-mixing system does not have F+-rigid factor for F∈F.

Effects of <i>Nigella sativa</i>Seed Extract on Perphenzine-Induced Muscle Rigidity in Male Mice

Parkinson’s disease (PD) is a degenerative disorder of the central nervous system. Early in the course of the disease, the most obvious symptoms are movement-related, including: shaking, rigidity, slowness of movement and difficulty with walking and gait. Rigidity is stiffness and resistance to limb movement caused by increased muscle tone, an excessive and continuous contraction of muscles. Effects of different herbal preparations have been evaluated on muscle rigidity so far and some of them are approved in clinic. In the present research, the effects of Nigella sativa hydroalcoholic seed extract on muscle stiffness in perphenazine-induced muscle rigidity were evaluated in adult male mice. In this experimental study, L-dopa 10 mg/kg, Nigella sativa hydroalcoholic seed extract at 50, 100, and 200 mg/kg were administered orally to male Balb/c mice for 12 days. Control group only received water. Muscle rigidity scores were then measured and compared. The muscle rigidity score in group receiving extract at 50 mg/kg had no significant difference with control group but at 100 mg/kg it had been significantly improved starting at the 40th minute. The extract at 200 mg/kg had significant difference in all times measured in comparison with control group that also showed lower scores compared to L-dopa treated group. According to the obtained results in this study, it can be concluded that Nigella sativa hydroalcoholic extract has good effects on muscle rigidity in dose-dependent pattern.