Beta Transformation Research Articles

Out-of-sample density forecasts with affine jump diffusion models

We conduct out-of-sample density forecast evaluations of the affine jump diffusion models for the S&P 500 stock index and its options’ contracts. We also examine the time-series consistency between the model-implied spot volatilities using options & returns and only returns. In particular, we focus on the role of the time-varying jump risk premia. Particle filters are used to estimate the model-implied spot volatilities. We also propose the beta transformation approach for recursive parameter updating. Our empirical analysis shows that the inconsistencies between options & returns and only returns are resolved by the introduction of the time-varying jump risk premia. For density forecasts, the time-varying jump risk premia models dominate the other models in terms of likelihood criteria. We also find that for medium-term horizons, the beta transformation can weaken the systematic effect of misspecified AJD models using options & returns.

On Schmidt's game and the set of points with non-dense orbits under a class of expanding maps

Given an expanding interval map, we consider sets of points whose forward orbits are bounded away from a given point. It is shown that such sets are 1/2-winning in the sense of Schmidt's game for a class of expanding interval maps including the Gauss transformation and all beta transformations. This improves upon several results dating back to a work of W. Schmidt.

Arterial stiffness parameters: How do they differ?

BackgroundCarotid-femoral pulse wave velocity (PWV), as a parameter of aortic stiffness, is an established marker of cardiovascular risk. There has been increasing use of arterial stiffness parameters combining aortic and muscular stiffness or a parameter derived from PWV – the stiffness index beta (BETA = ln(systolic/diastolic pressure) × 2 blood viscosity/pulse pressure × PWV2). The aim of this study was to compare different arterial stiffness parameters in a general population random sample. Methods and resultsIn 809 individuals from the Czech post-MONICA study (aged 54 ± 13.5 years, 47% men), we compared the association of carotid-femoral PWV (cfPWV), carotid-ankle PWV (caPWV), and BETA with cardiovascular risk factors, parameters of subclinical organ damage, and presence of manifest cardiovascular disease.Both cfPWV and caPWV were similarly associated with blood pressure and glucose level, while cfPWV was more strongly associated with age, cholesterol level and glomerular filtration rate whereas caPWV with Sokolow-Lyon index. BETA derived from cfPWV and caPWV was less dependent on blood pressure, while it showed a closer association with coronary heart disease presence, as compared to cfPWV and caPWV. ConclusionsAddition of lower extremity to aortic stiffness has an effect on the association with cardiovascular risk factors while having no effect on the association with manifest cardiovascular disease. Beta transformation of PWV decreases its dependence on blood pressure and may increase its power in cardiovascular risk prediction.

Prediction of phase transformation of Ti-6Al-4V titanium alloy during hot-forging processes using a numerical model

In this article numerical model for prediction of phase evolution of Ti-6Al-4V titanium alloy was presented. In particular, attention was focused on alpha to beta and beta to alpha+beta phase transformations. The analysis was conducted using a commercial implicit finite element method code, considering the data and the parameters of a real case study to check the quality of the numerical model. The alpha to beta transformation was developed using the simplified form of the Avrami model and the beta to alpha+beta transformation was controlled through the generalized Avrami model. The model so-thought has been used to conduct a 2D simulation of a forging process. A comparison between the numerical and experimental data indicates that the model can be utilized as base for a design tool in complex hot-forging processes of titanium alloys.

Research on Dehydrogenation and Sintering Process of Titanium Hydride for Manufacture Titanium and Titanium Alloy

In this paper, unlike the traditional powder metallurgy technology, the titanium hydride is directly used as the starting material to manufacture the titanium and titanium alloy. Thermogravimetric and dilatometric techniques are performed to study the dehydrogenation and shrinkage of TiH2 powders with different particle sizes. The process factors such as the sintering temperature, the sintering time, the heating rate, the compaction density, the compaction methods, and the alloy system, would affect the sintering densification of TiH2 powders and TiH2-Al-V alloy powder. The results shown that the dehydrogenation temperature of the starting and ending of the ball milling TiH2 is lower than that of the coarse TiH2 powders, the finer the TiH2 powder, the lower the temperature. The densification of TiH2 powders is easy due to the combination of dehydrogenation and shrinkage of α-Ti in one process, which creates the fresh dehydrided titanium uniform during sintering, thus leads to rapid densification and very high sintering relative density, higher than 99%. In contrast, it is difficult to achieve a full densification of TiH2-Al-V alloy powder during sintering, which requires dissolution of alloy elements during sintering above its beta transformation temperature. The sintered microstructure of Ti-6Al-4V shows the typical lamellar shaped α+β characteristics, with a uniform alloy element distribution.

Dependence of the Up-Conversion Properties of NaYF4:Yb3+/Er3+ Nanopowders on the Structure and Particle Size

NaYF4:Yb3+/Er3+ powders were synthesized by a solvothermal method. The effects of an amount of NaF, solvothermal temperatures, and solvothermal time on the up-conversion emission and the phase transition were investigated. Hexagonal rods (beta-form) with well-defined facets were obtained at the solvothermal condition of 210 degrees C and 24 h, whereas cubic nanocrystals (alpha-form) were produced at the low solvothermal temperature and short solvothermal time. These results demonstrated that the high solvothermal temperature of 210 degrees C supplied the enough thermodynamic energy to activate the alpha --> beta transformation, while long solvothermal time was necessary to complete the kinetic process for this phase transition. An amount of NaF obviously contributed to the phase transition, particle size, and the particle morphology. The beta-form with irregular shapes was superior to the well-defined beta-form in the emission intensity due to the enhanced surface scattering. This work suggested that the beta-form could not be obtained through its own nucleation and growth in the solutions during the solvothermal treatment, but could be produced through the alpha --> beta phase transition.

Effect of Annealing and Cold Work on Mechanical Properties of Beta III Titanium

Experiments have been carried out to study the effect of annealing and cold work (CW) on the mechanical properties of beta III Ti alloy. Material was annealed at different temperatures above the beta transformation temperature, and then cold drawn to about 53% area reduction. Cyclic tensile test was performed to study the evolution of mechanical properties and the recoverable strain during process. Results show that the effect of annealing and CW is closely related to the stress-induced martensite (SIM) phase transformation. Lower annealing temperature results in higher strength and recoverable strain, which is further increased by CW. A total recoverable strain of ~3.2% was obtained from the annealed and CW sample.

Orientation dependency of the alpha to omega plus beta transformation in commercially pure zirconium by high-pressure torsion

The alpha (α) to omega (ω) plus beta (β) phase transformation in pure zirconium by high-pressure torsion depends on the orientation of the polycrystalline aggregate with respect to the applied stress. The transformation can be triggered without any applied shear at 1 GPa when the pressure is perpendicular to the c -axes. Twinning plays a major role in the transformation, as it gives rise to new boundaries, which are favorable sites for dislocation pile-ups and therefore constitute potent stress-concentration points.

Comparison of modeling methods for Loss Given Default

We compare six modeling methods for Loss Given Default (LGD). We find that non-parametric methods (regression tree and neural network) perform better than parametric methods both in and out of sample when over-fitting is properly controlled. Among the parametric methods, fractional response regression has a slight edge over OLS regression. Performance of the transformation methods (inverse Gaussian and beta transformation) is very sensitive to ε, a small adjustment made to LGDs of 0 or 1 prior to transformation. Model fit is poor when ε is too small or too large, although the fitted LGDs have strong bi-modal distribution with very small ε. Therefore, models that produce strong bi-model pattern do not necessarily have good model fit and accurate LGD predictions. Even with an optimal ε, the performance of the transformation methods can only match that of the OLS.

Interplay of atomic displacements in the quantum magnet(CuCl)LaNb2O7

We report on the crystal structure of the quantum magnet (CuCl)LaNb2O7 that was controversially described with respect to its structural organization and magnetic behavior. Using high-resolution synchrotron powder x-ray diffraction, electron diffraction, transmission electron microscopy, and band structure calculations, we solve the room-temperature structure of this compound [alpha-(CuCl)LaNb2O7] and find two high-temperature polymorphs. The gamma-(CuCl)LaNb2O7 phase, stable above 640K, is tetragonal with a(sub) = 3.889 A, c(sub) = 11.738 A, and the space group P4/mmm. In the gamma-(CuCl)LaNb2O7 structure, the Cu and Cl atoms are randomly displaced from the special positions along the {100} directions. The beta-phase [a(sub) x 2a(sub) x c(sub), space group Pbmm] and the alpha-phase [2a(sub) x 2a(sub) x c(sub), space group Pbam] are stable between 640 K and 500 K and below 500 K, respectively. The structural changes at 500 K and 640 K are identified as order-disorder phase transitions. The displacement of the Cl atoms is frozen upon the gamma --> beta transformation, while a cooperative tilting of the NbO6 octahedra in the alpha-phase further eliminates the disorder of the Cu atoms. The low-temperature alpha-(CuCl)LaNb2O7 structure thus combines the two types of the atomic displacements that interfere due to the bonding between the Cu atoms and the apical oxygens of the NbO6 octahedra. The precise structural information resolves the controversy between the previous computation-based models and provides the long-sought input for understanding the magnetic properties of (CuCl)LaNb2O7.

ANIONIC EMULSION-MEDIATED SYNTHESIS OF ZEOLITE BETA

Well-crystallized zeolite beta is first synthesized in the anionic emulsion systems of cyclohexane/sodium dodecylbenzenesulfonate(SDBS)/pentanol/zeolite synthesis mixture. Beta materials are then characterized by XRD, SEM, and N 2-adsorption techniques. Compared to beta samples grown using the same synthesis mixture in the absence of the anionic emulsion, the as-synthesized beta presents uniform and well-defined larger crystals. Interestingly, N 2-adsorption results show that such beta sample possesses both ordered mesopores at 3.9 nm and macropores centered at 60.5 nm. These pores combined with the intricate micropores of the Beta crystal comprise the hierarchical porosity. The hierarchical pore-structured zeolite beta may have potential catalysis application in reactions involving large molecules. Additionally, control experiments are also performed to ascertain the effects of the individual emulsion components. Further synthesis study finds the transformation of zeolite beta to ZSM-5 through increasing oil contents, crystallization temperature and time.

Preparation, microstructures, mechanical properties, and cytocompatibility of TiMn alloys for biomedical applications

The titanium-manganese (TiMn) alloys have been extensively used in aerospace and hydrogen storage. In this study, the TiMn alloys with various manganese contents ranging from 2 to 12 wt % were prepared by using mechanical alloying and spark plasma sintering (SPS) techniques. The microstructures, mechanical properties including hardness, elastic modulus and ductility, cytotoxicity and cell proliferation properties of the TiMn alloys were investigated to explore their biomedical applications. The addition of manganese to the titanium reduced the alpha to beta transformation temperature and was confirmed as a beta stabilizer element. The manganese increased the relative density of the alloy and thus high density TiMn alloys with alpha+beta structure were prepared by using SPS at 700 degrees C. The hardness increased significantly ranging from 2.4 GPa (Ti2Mn) to 5.28 GPa (Ti12Mn) and the elastic modulus ranging from 83.3 GPa (Ti2Mn) to 122 GPa (Ti12Mn), the ductility decreased ranging from 21.3% (Ti2Mn) to 11.7% (Ti12Mn) with increasing manganese content in the Ti. Concentrations of Mn below 8 wt % in titanium reveal negligible effects on the metabolic activity and the cell proliferation of human osteoblasts. The Mn could be used in lower concentrations as an alloying element for biomedical titanium. The Ti2Mn, Ti5Mn, and Ti8Mn alloys with supervisor mechanical properties and acceptable cytocompatibility have a potential for use as bone substitutes and dental implants.

Crystal Structure and Phase Transitions in Sr3WO6

The crystal structures of the beta and gamma polymorphs of Sr(3)WO(6) and the gamma<-->beta phase transition have been investigated using electron diffraction, synchrotron X-ray powder diffraction, and neutron powder diffraction. The gamma-Sr(3)WO(6) polymorph is stable above T(c) approximately 470 K and adopts a monoclinically distorted double perovskite A(2)BB'O(6) = Sr(2)SrWO(6) structure (space group Cc, a = 10.2363(1)A, b = 17.9007(1)A, c = 11.9717(1)A, beta = 125.585(1)(o) at T = 1373 K, Z = 12, corresponding to a = a(p) + 1/2b(p) - 1/2c(p), b = 3/2b(p) + 3/2c(p), c = -b(p) + c(p), a(p),b(p), c(p), lattice vectors of the parent Fm3m double perovskite structure). Upon cooling it undergoes a continuous phase transition into the triclinically distorted beta-Sr(3)WO(6) phase (space group C1, a = 10.09497(3)A, b = 17.64748(5)A, c = 11.81400(3)A, alpha = 89.5470(2)(o), beta = 125.4529(2)(o), gamma = 90.2889(2)(o) at T = 300 K). Both crystal structures of Sr(3)WO(6) belong to a family of double perovskites with broken corner sharing connectivity of the octahedral framework. A remarkable feature of the gamma-Sr(3)WO(6) structure is a non-cooperative rotation of the WO(6) octahedra. One third of the WO(6) octahedra are rotated by approximately 45 degrees about either the b(p) or the c(p) axis of the parent double perovskite structure. As a result, the WO(6) octahedra do not share corners but instead share edges with the coordination polyhedra of the Sr cations at the B positions increasing their coordination number from 6 to 7 or 8. The crystal structure of the beta-phase is very close to the structure of the gamma-phase; decreasing symmetry upon the gamma-->beta transformation occurs because of unequal octahedral rotation angles about the b(p) and c(p) axes and increasing distortions of the WO(6) octahedra.

A New Multinomial Model and a Zero Variance Estimation

The analysis of categorical response data through the multinomial model is very frequent in many statistical, econometric, and biometric applications. However, one of the main problems is the precise estimation of the model parameters when the number of observations is very low. We propose a new Bayesian estimation approach where the prior distribution is constructed through the transformation of the multivariate beta of Olkin and Liu (2003). Moreover, the application of the zero-variance principle allows us to estimate moments in Monte Carlo simulations with a dramatic reduction of their variances. We show the advantages of our approach through applications to some toy examples, where we get efficient parameter estimates.

Diffusion bonding of mismatch dental alloys

The diffusion bonding of Ti-6Al-4V and Co-Cr-Mo dental alloys has been investigated in terms of the atoms diffusion, the microstructure evolution, and the bonding strength. The bonding performance reveals asymmetry diffusion profiles for both the Co and Cr in Ti-6Al-4V and the Ti in Co-Cr-Mo alloy. Their diffusion coefficients (Arrhenius relations) have been established based on the experiments. Co and Cr diffusion into Ti-6Al-4V leads to alpha --> beta transformation and the intermetallics-formation. Maximum bonding strength occurs at about 840 degrees C. The bonding joint fails under the shear stress in the Ti-6Al-4V side near the bonding interface in brittle manner. The intermetallics in the diffusion layer together with the unbonded areas and other flaws in the bonding interface are responsible for the shear brittle fracture, which also weaken the bonding strength.

First Experimental Observation of Shear Induced hcp to bcc Transformation in Pure Zr

Shear stresses are shown to induce the alpha (hcp) to omega (simple hexagonal) plus beta (bcc) transformation in pure Zr at room temperature. The beta Zr thus fabricated is stable at 1 atm and room temperature. This phase has so far only been found to occur at high pressures (P>30 GPa) and/or at high temperatures (T>1135 K). This experimental observation provides new insights about the physical processes underlying allotropic transformations and opens the door to future investigations aiming to stabilize high temperature or pressure phases at ambient conditions.

Temperature distribution for electrically conductive and non-conductive materials during Field Assisted Sintering (FAST)

During Field Assisted Sintering Technology (FAST) the temperature differences at two different positions were investigated using two pyrometers, an internal and an external one. Two substances, an electrically conductive (tungsten carbide) and a non-conductive material (96 wt.% silicon nitride with 2 wt.% alumina and yttria) were used to monitor the temperature differences between both pyrometers during heating, sintering shrinkage and dwell time by varying die geometry and heating rate. It was shown that the temperature distribution is strongly influenced by the electrical conductivity of the material as well as by tool design and setup. The alpha–beta transformation of silicon nitride was analyzed to predict the radial temperature distribution within the sample. For comparison and for visualization a dynamical FE model including piston movement for simulating sintering shrinkage was introduced. With this, a complete time dependent FAST run could be simulated. The modeled differences in temperature distribution are in good agreement with real temperature measurements as well as phase analyses.

Melting behavior of polymorphic crystals of poly(trimethylene 2,6-naphthalate) studied by simultaneous synchrotron X-ray scattering and thermal analysis

The polymorphic crystallization and melting behavior of poly(trimethylene 2,6-naphthalate) (PTN) have been investigated using small-angle X-ray scattering and simultaneous wide-angle X-ray scattering (WAXS) and differential scanning calorimetry (DSC). The α-crystal, the β-crystal and the coexistence of both crystal forms of PTN develop at an isothermal temperature below 393 K, above 453 K and between these two temperatures, respectively. The simultaneous WAXS/DSC measurement provides a good way to identify the origin of multiple melting peaks and to get equilibrium melting temperatures. During the PTN melting process, the thermal evolutions of crystallinities, Bragg diffraction intensities and DSC thermograms reveal that the \alpha \rightarrow \beta phase transformation and primary and secondary crystallizations arise to generate the multiple melting peaks. The β-crystal with high equilibrium melting temperature (T^{0}_{{\rm m},\beta}} = 510 K) is a structurally stable phase while the α-crystal with low equilibrium melting temperature (T^{0}_{{\rm m},\alpha}} = 488 K) is a metastable phase. The temperature-dependent structural parameters such as the long period, lamellar thickness and amorphous thickness were extracted from the interface distribution function. Two-step changes in the lamellar thickness and the invariant during the subsequent melting of PTN crystallized at 383 K are consistent with the \alpha \rightarrow \beta transformation obtained by WAXS/DSC. The \alpha \rightarrow \beta transformation, a typical melting–recrystallization, proceeds firstly via surface melting of α-lamellae, and then the PTN chains near the boundaries of surviving α-lamellae modify their conformation to form the β-crystal resulting in thickening lamellae.

Thermal stability of the martensitic transformation of Cu–Al–Ni–Mn–Ti

The development of new shape memory alloys with high martensitic transformation temperature increases the potential for applications. The development and use of these new alloys depends on the stability of the structure during cycling at high temperatures. If it is possible to guarantee that on alloys keeps the structure during cycling, then the alloy can be used because of the shape memory properties. The aim of this work is to obtain a kinetic model of the forward and backward martensitic transformation of two Cu–Al–Ni–Mn–Ti alloys. Differential scanning calorimetry has been performed in order to establish the kinetic stability of the martensite and the beta transformation.

Phase transformation and mechanical properties of the Ti 50Zr 30Nb 10Ta 10 alloy with low modulus and biocompatible

The beta transformation characteristics and mechanical properties of the β titanium alloy Ti 50Zr 30Nb 10Ta 10 in the temperature range between 200 and 900 °C have been studied by means of X-ray diffraction (XRD), Vickers hardness (HV), and tensile test techniques. In the as-rolled state, only β-phase was identified by XRD. Upon heat-treating at 250 °C for 4 h, the α-phase was precipitated from the β-phase matrix, and leading to an increase of Vickers hardness. A maximum HV value was observed at 400 °C, and then HV value decreased with increasing heat-treating temperature. Above 650 °C, HV value remained almost constant. During heat-treating at 300–650 °C, the decomposition of the metastable β-phase has been found to proceed through a phase separation reaction leading to the formation of β-Ti and β-Zr b.c.c. solid solution phases rather than the formation of solute rich and solute lean b.c.c. phases as has been previously reported, leading to little or no increase in HV value. The tensile strength, elongation and elastic modulus of Ti 50Zr 30Nb 10Ta 10 alloy for as-solution-treated samples are 741 MPa, 28.6% and 44 GPa, which is better than required values already reported.