Characterizations based on conditional expectations of the doubled truncated distribution

The expression of the continuous distribution function F(x) is obtained whenever % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaerbhv2BYDwAHbacfiGaa8xBaiaabIcacaWG4bGaaiilaiaadMha% caqGPaGaa8hiaiaab2dacaWFGaGaa8xraiaa-HcacaWFybGaa8hiai% aa-XhacaWFGaGaa8hEaiaa-bcacqGHKjYOcaWFGaGaa8hwaiaa-bca% cqGHKjYOcaWFGaGaa8xEaiaa-Lcaaaa!53EE!\[m{\rm{(}}x,y{\rm{)}} {\rm{ = }} E(X | x \le X \le y)\]is known. Moreover, we obtain the necessary and sufficient conditions so that any function m: ² is the conditional expectation % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiaadweacaGGOaGaamiwaerbhv2BYDwAHbacfiGaa8hiaiaacYha% caWFGaGaa8hEaiaa-bcacqGHKjYOcaWFGaGaa8hwaiaa-bcacqGHKj% YOcaWFGaGaa8xEaiaacMcaaaa!4D0D!\[E(X | x \le X \le y)\]of a random variable X with continuous distribution function. Furthermore, we relate m(x,y) to order statistics.     

STUDY ON THE DUCTILE DEFORMATION DOMAIN OF THE SIMPLE SHEAR IN ROCKS——TAKING BRITTLE FAULTS OF THE COVERING STRATA IN THE SOUTHERN JIANGSU AREA AS AN EXAMPLE

A study on the ductile deformation domain of the brittle fault in the shallow level ofthe crust is a new probe field for the modern structural geology. Taking the southern Jiang-su Province area as an example the orientation measurement of quartz crystals, the com-positional texture observation of three pressure sensitive minerals and the rheological param-eter determination of dislocation densities, etc. have been demonstrated and analysed basedon typical samples in the present paper. In addition, their generation mechanisms arealso discussed from the cataclastic rheology, the dynamic differentiation and the simpleshearing, specially, from the Ode strength theory. Finally, a generative relationship betweenthe ductile deformation domain of the brittle fault system, in the regional layer--slip andthe formation of the stratabound ore deposit is shown as well.     

Molecular structure of ethynylbenzene from electron diffraction and ab initio molecular orbital calculations

The molecular structure and benzene ring distortions of ethynylbenzene have been investigated by gas-phase electron diffraction and ab initio MO calculations at the HF/6-31G^* and 6-3G^** levels. Least-squares refinement of a model withC _2v, symmetry, with constraints from the MO calculations, yielded the following important bond distances and angles:r _g(C _i -C _o )=1.407±0.003 Å,r _g(C _o -C _m )=1.397±0.003 Å,r _g(C _m -C _p )=1.400±0.003 Å,r _g(Cr _i -CCH)=1.436 ±0.004 Å,r _g(C=C)=1.205±0.005 Å, C _o -C _i -C _o =119.8±0.4°. The deformation of the benzene ring of ethynylbenzene given by the MO calculations, including o-C_i-C_o=119.4°, is insensitive to the basis set used and agrees with that obtained by low-temperature X-ray crystallography for the phenylethynyl fragment, C₆H₅-CC-, in two different crystal environments. The partial substitution structure of ethynylbenzene from microwave spectroscopy is shown to be inaccurate in the ipso region of the benzene ring.     

Plastic deformation kinetics for glassy polymers and blends

Measurements of the plastic deformation kinetics for several glassy (PS, PC, PI-polyimide, PET, epoxy-amine network), semi crystalline polymers (PBT, PET) and blends (ABS, PC:ABS, PC: PBT) were performed for the unidirectional compression loading conditions by using constant temperature deformation calorimetry. The experiments have permitted us to follow the changes of the mechanical work (A), the heat of deformation (Q) and differences between these quantities, i.e., internal energy (U) stored in samples during their loading and unloading. Experiments have shown that the large portion (45–85%) of the mechanical work of deformation (A) is converted to heat (Q). The rest ofA is converted to internal energy (U) stored in deformed samples. U is quite high as compared with metals [1,2]. After complete unloading of plastically deformed samples, i.e., samples carrying irreversible atT _def plastic deformation ( _irr ), some amount (U) of stored energy disappeared. The amount of (U and (U) are different for different polymers. All data are analyzed in the framework of the model proposed in [3,4]. The experiments support the deformation model where the plasticity of glassy polymers is the process of nucleation and development of so-called PDs-plastic local shear defects of nonconformational and nondilatational nature.Dedicated to Prof. Dr. W. Pechhold on the occasion of his 60th birthday     

氯化聚乙烯弹性体的固相法合成

讨论了以固相法合成氯化聚乙烯（ＣＰＥ）弹性体的过程．实验结果表明，以固相氯化反应所得的ＣＰＥ，其大分子链上Ｃｌ取代基的分布比水相悬浮法更均匀．氯化过程的温度直接影响氯化速度及分子结构，如残留结晶、氯分布等．而聚乙烯颗粒表面与内部的氯化程度取决于氯化速度．大分子链上Ｃｌ取代基对邻近基团的氯化起阻碍作用     

The absolute sign of J coupling constants determined using the order matrix calculation

A novel methodology using the order matrix calculation to determine the absolute sign of spin-spin couplings based on the structure of organic compounds is presented. The sign of the residual dipolar coupling (RDC) depends on the sign of corresponding scalar spin-spin coupling constant and the sign of the RDC has a dramatic influence on the order matrix calculation. Therefore, the sign of the spin-spin coupling constant can be obtained by an order matrix calculation through the corresponding RDC. Six types of spin-spin coupling constants, including 2J(H,H), 1J(C,F), 2J(C,F), 3J(C,F), 2J(F,H) and 3J(F,H), were obtained simultaneously. Except for 3J(C,F) where the measured RDCs have very small magnitudes, the signs were determined unambiguously.     

On the deformation mechanisms of oriented PET and PP films under load

Uniaxially orienred semicrystalline poly(ethylene terephthalate) (PET) and poly(propylene) (PP) films were loaded parallel to draw direction at various temperatures. Changes in the submicroscopical structure of the films under load were examined by small and wide-angle x-ray scattering (SAXS; WAXS) and birefringence measurements. WAXS measurements reveal a decrease of the initial high orientation of the chains in the crystallites during deformation. Simultaneously, an increase of the birefringence was detected, indicating an orientation of chains in the amorphous regions. The alteration of the long period reflections in the SAXS patterns give strong evidence that lamellar stacks with different orientation angles according to load direction are present. Depending on the orientation of stacks, the contribution of lamellar separation to sample deformation alters, giving rise to different amounts of density changes in the stacks. Absolute intensity measurements of SAXS using a Kratky apparatus reveal that lamellar separation occurs preferentially below or in the range of the glass-transition temperature at small strain. With increasing strain and temperatures above the glass-transition slip deformation mechanisms become more important. The formation of microvoids was observed at strain near to elongation at break below or in the range of glass-transition temperature.     

Determination of various deformation processes in impact-modified PMMA at strain rates up to 105%/min

The deformation processes in impact-modified PMMA, which deforms homogeneously, were determined by means of the stress/strain experiment (, ) with simultaneous lateral strain measurement (_lat) in a wide range of strain rates () up to 10⁵%/min (impact stress). The elastic, plastic cavitation and plastic shear processes were determined as a function of strain. Therefore we calculated the elastic strain ( _el), the elastic volume expansion ( _{vol el}), the cavitation strain ( _cav), which is identical with the plastic volume expansion ( _{vol pl}), the shear strain ( _sh) and the energy densities (W_el, W_cav, W_sh) related to these three processes.For strains of 3 % onward it was found that plastic shear processes and plastic cavitation processes are responsible for a partial loss of elastically stored energy. Both plastic processes turn out to be mostly anelastic deformations, their amount depending strongly on the strain rate. The contributions of the processes to the total deformation of the unmodified PMMA in its strain range are similar to those of the impact-modified PMMA, and the high impact strength is caused by a shift of the catastrophic rupture to very high strains.     

VISCOELASTIC BEHAVIOR OF THE NON-HOOKE DEFORMATION BEFORE YIELDING IN UNIAXIAL DRAWING OF AMORPHOUS POLY(ETHYLENE TEREPHTHALATE)*

Viscoelastic behavior of the non-Hooke deformation of amorphous PET film before yield was investigated in thetemperature region 74--80.5℃ around the glass transition temperature. The film specimen was drawn to yield point followedby unloading to zero stress, then the residual deformation was held constant, while the subsequent evolution of the stress wasrecorded. An induction period was found in the course of stress evolution fol1owed by a stress step-increase. The inductionperiod decreases with increasing drawing temperature with an activation energy of 1.10 MJ/mol·K, which is attributed tothe time needed for the relaxation of rubbery deformation through cooperative internal rotations. At temperatures lower than74℃, there is no stress increase or the induction period becomes too long to be observed. Thus the nature of anelasticity inthe non-Hooke region before yielding is attributed to stress induced rubbery deformation. The experimental results areinterpreted in terms of Perez' rheological model of a series connected Hooke spring and a Voigt element consisting of aparallel connected elastic spring and a dashpot.     

Uniaxial deformation and orientation of ethylene–tetrafluoroethylene films

This study concerns the thermal and mechanical response of several commercial grades of ethylene – tetrafluoroethylene copolymer films. Differential scanning calorimetry was used to show that, although films have similar degrees of crystallinity and melting temperature, the melting endotherms and crystallisation exotherms differ between materials, suggesting small changes in composition between manufacturers. Films were deformed in tension at a range of temperatures and rates. Selected films were unloaded immediately after stretching, and measurement of the elastic recovery highlighted further differences between materials. Batches of films were pre-drawn uniaxially above the glass transition and immediately quenched. When these materials were subsequently re-drawn below the glass transition temperature, most of them exhibited much improved yield stress, modulus and tensile strength (improving by factors of 5, 5 and 4, respectively at a draw ratio of 3), but a reduced strain to failure. In most of the films, the pre-drawing, as well as the initial orientation of the films, is accounted for by a simple shift in the true strain axis. This is indicative of a material response dominated by entropic network stretch. It also suggests that, in the cases where strain superposition does not work, a different arrangement of crystalline lamellae may be present, limiting the extent to which improved properties can be achieved in some materials.