ON THE CONVERGENCE PROBLEMS OF ISHIKAWA AND MANN ITERATIVE PROCESSES WITH ERROR FOR Φ-PSEUDO CONTRACTIVE TYPE MAPPINGS

The purpose of this paper is to introduce the concept of Φ_pseudo contractive type mapping and to study the convergence problem of Ishikawa and Mann iterative processes with error for this kind of mappings. The results presented in this paper improve and extend many authors'recent results.

Investigation of FRP and SFRC Technologies for Efficient Tunnel Reinforcement Using the Cohesive Zone Model

Amid urbanization and the continuous expansion of transportation networks,the necessity for tunnel construction and maintenance has become paramount.Addressing this need requires the investigation of efficient,economical,and robust tunnel reinforcement techniques.This paper explores fiber reinforced polymer(FRP)and steel fiber reinforced concrete(SFRC)technologies,which have emerged as viable solutions for enhancing tunnel structures.FRP is celebrated for its lightweight and high-strength attributes,effectively augmenting load-bearing capacity and seismic resistance,while SFRC’s notable crack resistance and longevity potentially enhance the performance of tunnel segments.Nonetheless,current research predominantly focuses on experimental analysis,lacking comprehensive theoretical models.To bridge this gap,the cohesive zone model(CZM),which utilizes cohesive elements to characterize the potential fracture surfaces of concrete/SFRC,the rebar-concrete interface,and the FRP-concrete interface,was employed.A modeling approach was subsequently proposed to construct a tunnel segment model reinforced with either SFRC or FRP.Moreover,the corresponding mixed-mode constitutive models,considering interfacial friction,were integrated into the proposed model.Experimental validation and numerical simulations corroborated the accuracy of the proposed model.Additionally,this study examined the reinforcement design of tunnel segments.Through a numerical evaluation,the effectiveness of innovative reinforcement schemes,such as substituting concrete with SFRC and externally bonding FRP sheets,was assessed utilizing a case study from the Fuzhou Metro Shield Tunnel Construction Project.

Convergence Theorems of φ-pseudo Contractive Type Mappings in Normed Linear Spaces

In this paper, by virtue of an inequality and sane analysis techniques, we prove sane convergence theorems cm the iterative process for nonlinear mappings of-pseudo contractive type in named linear spaces, which extend and improve the corresponding results obtained by others recently.

Self-contraction process and hot spot formation in the SHOTGUN III-U divergent gas-puff Z pinch

A divergent gas-puff Z pinch has been devised for the realization of an efficient soft x-ray point source.In this device,a divergent hollow annular gas puff is ejected outward from the surface of the inner electrode,and the plasma is compressed three-dimensionally to generate a soft x-ray point source.In the SHOTGUN III-U device at Nihon University,the power supply was enhanced,and experiments were conducted over a larger current range.The peak current at the charging voltage of−25 kV was−190 kA.Ar was used as the discharge gas.The self-contraction process of the plasma was investigated in detail using a gated camera.Near the peak current,local contraction occurred in front of the inner electrode.The contraction velocity of the plasma was 5.53×10^(4)m/s.As the plasma contracted,the discharge current decreased.The energy input was analyzed by induction acceleration.The net input energy was found to be 750 J,which corresponded to 13.3%of the stored energy of the capacitor,5630 J.The soft x-ray source was observed using a soft x-ray CCD camera.A point source was observed 7mmin front of the inner electrode.The size of the source was 35μm in the axial direction and 14μm in the radial direction.

Hot deformation behavior and processing map of Cu-Ni-Si-P alloy

The high-temperature deformation behavior of Cu-Ni-Si-P alloy was investigated by using the hot compression test in the temperature range of 600-800 ℃ and strain rate of 0.01-5 s-1. The hot deformation activation energy, Q, was calculated and the hot compression constitutive equation was established. The processing maps of the alloy were constructed based on the experiment data and the forging process parameters were then optimized based on the generated maps for forging process determination. The flow behavior and the microstructural mechanism of the alloy were studied. The flow stress of the Cu-Ni-Si-P alloy increases with increasing strain rate and decreasing deformation temperature, and the dynamic recrystallization temperature of alloy is around 700 ℃. The hot deformation activation energy for dynamic recrystallization is determined as 485.6 kJ/mol. The processing maps for the alloy obtained at strains of 0.3 and 0.5 were used to predict the instability regimes occurring at the strain rate more than 1 s-1 and low temperature （〈650 ℃）. The optimum range for the alloy hot deformation processing in the safe domain obtained from the processing map is 750-800 ℃ at the strain rate of 0.01-0.1 s i The characteristic microstructures predicted from the processing map agree well with the results of microstructural observations.

Processing map and hot deformation mechanism of novel nickel-free white copper alloy

Hot compression test of a novel nickel-free white alloy Cu?12Mn?15Zn?1.5Al?0.3Ti?0.14B?0.1Ce (mass fraction, %) was conducted on a Gleeble?1500 machine in the temperature range of 600?800 °C and the strain rate range of 0.01?10 s?1. The constitutive equation and hot processing map of the alloy were built up according to its hot deformation behavior and hot working characteristics. The deformation activation energy of the alloy is 203.005 kJ/mol. An instability region appears in the hot deformation temperature of 600?700 °C and the strain rate range of 0.32?10 s?1 when the true strain of the alloy is up to 0.7. Under the optimal hot deformation condition of 800 °C and 10 s?1 the prepared specimen has good surface quality and interior structure. The designed nickel-free alloy has very similar white chromaticity with the traditional white copper alloy (Cu?15Ni?24Zn?1.5Pb), and the color difference between them is less than 1.5, which can hardly be distinguished by human eyes.

Hot deformation behavior and processing maps of Mg-Zn-Cu-Zr magnesium alloy

The deformation behaviors of a new quaternary Mg-6Zn-1.5Cu-0.5Zr alloy at temperatures of 523-673 K and strain rates of 0.001-1 s-1 were studied by compressive tests using a Gleeble 3800 thermal-simulator.The results show that the flow stress increases as the deformation temperature decreases or as the strain rate increases.A strain-dependent constitutive equation and a feed-forward back-propagation artificial neural network were used to predict flow stress,which showed good agreement with experimental data.The processing map suggests that the domains of 643-673 K and 0.001-0.01 s-1 are corresponded to optimum conditions for hot working of the T4-treated Mg-6Zn-1.5Cu-0.5Zr alloy.

Convergence theorem of common fixed points for Lipschitzian pseudo-contraction semi-groups in Banach spaces

The purpose of this paper is to study the weak convergence problems of the implicity iteration process for Lipschitzian pseudocontractive semi-groups in the general Banach spaces. The results presented in this paper extend and improve the corresponding results of some people.

A Modified Averaging Composite Implicit Iteration Process for Common Fixed Points of a Finite Family of k-Strictly Asymptotically Pseudocontractive Mappings

The composite implicit iteration process introduced by Su and Li [J. Math. Anal. Appl. 320 (2006) 882-891] is modified. A strong convergence theorem for approximation of common fixed points of finite family of k-strictly asymptotically pseudo-contractive mappings is proved in Banach spaces using the modified iteration process.

Application of combination weighting method in contract risk's evaluation of third party logistics

First,the analytical hierarchy process(AHP),which stands for the subjective weighting method,and the entropy method,which stands for the objective weighting method,are chosen to calculate the index weights of the contract risks of third party logistics(TPL),respectively.Then,they can determine the combination weights using the combination weighting method.Second,using the combination weights,the contract risks of TPL are evaluated through the fuzzy comprehensive evaluation method.According to the combination weights,the most important risk factor of the contract risks of TPL is choosing sub-contractors.The results are basically consistent with the facts and show that the weights determined by the combination weighting method can avoid the man-made deviations of the subjective weighting method on the one hand,and prevent results opposite to the reality brought about by the objective weighting method on the other hand.Meanwhile,the results of the fuzzy comprehensive evaluation are that the contract risks of TPL are at a high risk level.Roughly this matches real situations,and it indicates that the combination weighting method can generate the comprehensive assessment more scientifically and more reasonably as well.

Constitutive behavior, microstructural evolution and processing map of extruded Al-1.1Mn-0.3Mg-0.25RE alloy during hot compression

Hot compression tests of an extruded Al-1.1Mn-0.3Mg-0.25RE alloy were performed on Gleeble-1500 system in the temperature range of 300-500 ℃ and strain rate range of 0.01-10 s-l. The associated microstructural evolutions were studied by observation of optical and transmission electron microscopes. The results show that the peak stress level decreases with increasing deformation temperature and decreasing strain rate, which can be represented by a Zener-Hollomon parameter in the hyperbolic-sine equation with the hot deformation activation energy of 186.48 kJ/mol. The steady flow behavior results from dynamic recovery whereas flow softening is associated with dynamic recrystallization and dynamic transformation of constituent particles. The main constituent particles are enriched rare earth phases. Positive purifying effects on impurity elements of Fe and Si are shown in the Al-l.lMn-0.3Mg-0.25RE alloy, which increases the workability at high temperature. Processing map was calculated and an optimum processing was determined with deformation temperature of 440-450 ℃ and strain rate of 0.01 s-1.

Characterization of hot deformation behavior of AA2014 forging aluminum alloy using processing map

The hot deformation behavior of AA2014forging aluminum alloy was investigated by isothermal compression tests attemperatures of350-480°C and strain rates of0.001-1s-1on a Gleeble-3180simulator.The corresponding microstructures of thealloys under different deformation conditions were studied using optical microscopy(OM),electron back scattered diffraction(EBSD)and transmission electron microscopy(TEM).The processing maps were constructed with strains of0.1,0.3,0.5and0.7.The results showed that the instability domain was more inclined to occur at strain rates higher than0.1s-1and manifested in theform of local non-uniform deformation.At the strain of0.7,the processing map showed two stability domains:domain I(350-430°C,0.005-0.1s-1)and domain II(450-480°C,0.001-0.05s-1).The predominant softening mechanisms in both of the twodomains were dynamic recovery.Uniform microstructures were obtained in domain I,and an extended recovery occurred in domainII,which would lead to the potential sub-grain boundaries progressively transforming into new high-angle grain boundaries.Theoptimum hot working parameters for the AA2014forging aluminum alloy were determined to be370-420°C and0.008-0.08s-1.

Constitutive behavior and processing maps of a new wrought magnesium alloy ZE20 (Mg-2Zn-0.2Ce)

ZE20(Mg-2Zn-0.2Ce)^2 is a new wrought magnesium alloy with improved extrudability and mechanical properties[1].To understand the constitutive behavior and workability of this new alloy,Gleeble thermomechanical testing has been carried out in this study.The flow stress behavior of ZE20 was investigated between 250℃–450℃ and 10^–3 s^–1–1.0 s^–1 in isothermal compression.Constitutive descriptions of the flow stress are provided.A new general approach at application of the extended Ludwik equation is demonstrated and was found to be more accurate than the hyperbolic sine Arrhenius model while having a similar number of model constants.Processing maps were developed based on the experimental results and are verified with microstructural investigation.A region of safe processing with non-basal texture and high activity of dynamic recrystallization(DRX)was found between 375℃ and 450℃,from 10^–1 s^–1 to 10^–2.5 s^–1.A region of potentially safe processing with annealing that is associated with shear band nucleation of non-basal grains was identified for temperatures as low as 300℃ and rates as high as 10^–1 s^–1.

Hot deformation behaviors and processing maps of Mg-Zn-Er alloys based on Gleeble-1500 hot compression simulation

The hot deformation behaviors of as-solution Mg?xZn?yEr alloys (x/y=6, x=3.0, 4.5 and 6.0; y=0.50, 0.75 and 1.00) wereinvestigated on Gleeble?1500 thermal simulator in a temperature range of 200?450 °C at a strain rate of 0.001?1 s?1. The truestress?strain curves showed the dynamic competition between the working hardening and working softening mainly due to thedynamic recrystallization (DRX) occurring during hot compression. The constitutive equations were constructed which couldaccurately predict the peak stress of the alloys. The addition of Zn and/or Er resulted in higher deformation activation energy forMg?3Zn?0.5Er (alloy A). The processing maps were constructed as function of the temperature and the strain rate, providing theoptimum hot working conditions (i.e., at strain of 0.3, Mg?3Zn?0.5Er (alloy A): 380?430 ?C, <0.1 s?1; Mg?4.5Zn?0.75Er (alloy B):380?450 ?C, 0.01?0.1 s?1; Mg?6Zn?1Er (alloy C): 390?440 ?C, 0.01?0.1 s?1). The as-solution treated Mg?4.5Zn?0.75Er (alloy B)demonstrated more optimum hot working window comparing with Mg?3Zn?0.5Er (alloy A) and Mg?6Zn?1Er (alloy C).

Hot deformation behavior of a Sr-modified Al-Si-Mg alloy:Constitutive model and processing maps

Isothermal compression experiments were conducted to study the hot deformation behaviors of a Sr-modified Al-Si-Mg alloy in the temperature range of 300-420°C and strain rate range of 0.01-10 s-1.A physically-based model was developed to accurately predict the flow stress.Meanwhile,processing maps were established to optimize hot working parameters.It is found that decreasing the strain rate or increasing the deformation temperature reduces the flow stress.The high activation energy is closely related to the pinning of dislocations from Si-containing dispersoids.Moreover,the deformed grains and the Si-containing dispersoids in the matrix are elongated perpendicular to the compression direction,and incomplete dynamic recrystallization(DRX)is discovered on the elongated boundaries in domain with peak efficiency.The flow instability is mainly attributed to the flow localization,brittle fracture of eutectic Si phase,and formation of adiabatic shear band.The optimum hot working window is 380-420°C and 0.03-0.28 s-1.

Production sharing contract: An analysis based on an oil price stochastic process

Assuming that oil price follows the stochastic processes of Geometric Brownian Motion （GBM） or the Mean-Reverting Process （MRP）, this paper takes the net present value （NPV） as an economic index and models the PSC in 11 different scenarios by changing the value of each contract element （i.e. royalty, cost oil, profit oil as well as income tax）. Then the NPVs are shown in probability density graphs to investigate the effect of different elements on contract economics. The results show that under oil price uncertainty the influence of profit oil and income tax on NPV are more significant than those of royalty and cost oil, while a tax holiday could improve the contractor＇s financial status remarkably. Results also show that MRP is more appropriate for cases with low future oil price volatility, and GBM is best for high future oil price volatility.

Processing map and dynamic recrystallization behaviours of 316LN-Mn austenitic stainless steel

The hot deformation behaviours of 316LN-Mn austenitic stainless steel were investigated by uniaxial isothermal compression tests at different temperatures and strain rates.The microstructural evolutions were also studied using electron backscatter diffraction.The flow stress decreases with the increasing temperature and decreasing strain rate.A constitutive equation was established to characterize the relationship among the deformation parameters,and the deformation activation energy was calculated to be 497.92 k J/mol.Processing maps were constructed to describe the appropriate processing window,and the optimum processing parameters were determined at a temperature of 1107-1160℃ and a strain rate of 0.005-0.026 s^(-1).Experimental results showed that the main nucleation mechanism is discontinuous dynamic recrystallization(DDRX),followed by continuous dynamic recrystallization(CDRX).In addition,the formation of twin boundaries facilitated the nucleation of dynamic recrystallization.

Effect of Cr elimination on flow behavior and processing map of newly developed ECO-7175 aluminum alloy during hot compression

ECO-Al alloys are introduced as a game-changer for the aluminum industry and it is of utmost importance to determine the role of alloying elements in their processing characteristics.In this study,the effects of Cr on the hot deformation behavior of newly-developed ECO-7175 alloy were investigated.ECO-7175 samples with and without Cr were hot-compressed using a Gleeble simulator(temperature range of 350−500℃ and strain rates of 0.001−1 s^(−1)).The results were used to study the constitutive equations,the processing maps,and the microstructural evolution of the alloys.In Cr-containing alloy,the analysis of the deformation activation energy reveals that the rate-controlling mechanisms of the deformation change gradually from self-diffusion of Al(or diffusion of Mg in Al)to diffusion of Cr in Al by decreasing the Zener−Hollomon parameter.The analysis of the processing maps of Cr-containing alloy shows that the dynamic recrystallization(DRX)zone is limited to the deformation at high temperatures and low strain rates and expands with increasing applied strain.On the other hand,it is found that the self-diffusion of Al(or Mg in Al)is the only rate-controlling mechanism during hot deformation of Cr-free alloy in all processing conditions and its DRX zone is independent of the plastic strain.

Constitutive equation and processing map of equiatomic NiTi shape memory alloy under hot plastic deformation

In order to describe the deformation behavior and the hot workability of equiatomic NiTi shape memory alloy (SMA) during hot deformation, Arrhenius-type constitutive equation and hot processing map of the alloy were developed by hot compression tests at temperatures ranging from 500 to 1100 °C and strain rates ranging from 0.0005 to 0.5 s?1. The results show that the instability region of the hot processing map increases with the increase of deformation extent. The instability occurs in the low and high temperature regions. The instability region presents the adiabatic shear bands at low temperatures, but it exhibits the abnormal growth of the grains at high temperatures. Consequently, it is necessary to avoid processing the equiatomic NiTi SMA in these regions. It is preferable to process the NiTi SMA at the temperatures ranging from 750 to 900 °C.

Isothermal compression behavior and constitutive modeling of Ti-5Al-5Mo-5V-1Cr-1Fe alloy

Hot compression behavior of Ti-5 Al-5 Mo-5 V-1 Cr-1 Fe alloy with an equiaxed（α＋β） starting microstructure was investigated by isothermal compression test and optical microscopy. Based on the true strain-stress data with temperature correction, constitutive models with a high accuracy were developed and processing maps were established. Strain inhomogeneity at different locations in the compressed sample is reduced by raising temperature, leading to a uniform distribution of α phases. For the temperature range of 800-840 ℃ with a strain rate of 10 s^-1, the transformed volume fraction of α phase increases and the average grain size of α phase decreases slightly with increasing the temperature, indicating co-existence of dynamic recovery and dynamic recrystallization. Flow localization and faint β grain boundaries are observed at the strain rate of 10 s^-1 in the temperature range of 860-900 ℃. The processing map analysis shows that hot working of Ti-5 Al-5 Mo-5 V-1 Cr-1 Fe alloy should be conducted with the strain rate lower than 0.01 s^-1 to extend its workability.