STRONGLY CONVERGENT INERTIAL FORWARD-BACKWARD-FORWARD ALGORITHM WITHOUT ON-LINE RULE FOR VARIATIONAL INEQUALITIES

This paper studies a strongly convergent inertial forward-backward-forward algorithm for the variational inequality problem in Hilbert spaces.In our convergence analysis,we do not assume the on-line rule of the inertial parameters and the iterates,which have been assumed by several authors whenever a strongly convergent algorithm with an inertial extrapolation step is proposed for a variational inequality problem.Consequently,our proof arguments are different from what is obtainable in the relevant literature.Finally,we give numerical tests to confirm the theoretical analysis and show that our proposed algorithm is superior to related ones in the literature.

Impact of strain relaxation on the growth rate of heteroepitaxial germanium tin binary alloy

The growth of high-quality germanium tin(Ge_(1–y)Sn_(y))binary alloys on a Si substrate using chemical vapor deposition(CVD)techniques holds immense potential for advancing electronics and optoelectronics applications,including the development of efficient and low-cost mid-infrared detectors and light sources.However,achieving precise control over the Sn concentration and strain relaxation of the Ge_(1–y)Sn_(y)epilayer,which directly influence its optical and electrical properties,remain a significant challenge.In this research,the effect of strain relaxation on the growth rate of Ge_(1–y)Sn_(y)epilayers,with Sn concentration>11at.%,is investigated.It is successfully demonstrated that the growth rate slows down by~55%due to strain relaxation after passing its critical thickness,which suggests a reduction in the incorporation of Ge into Ge_(1–y)Sn_(y)growing layers.Despite the increase in Sn concentration as a result of the decrease in the growth rate,it has been found that the Sn incorporation rate into Ge_(1–y)Sn_(y)growing layers has also decreased due to strain relaxation.Such valuable insights could offer a foundation for the development of innovative growth techniques aimed at achieving high-quality Ge_(1–y)Sn_(y)epilayers with tuned Sn concentration and strain relaxation.

3D digital-image correlation insight into generalized relaxation behavior of sandstone under stress and pore pressure coupling

The occurrence of geological hazards and the instability of geotechnical engineering structures are closely related to the time-dependent behavior of rock.However,the idealization boundary condition for constant stress in creep or constant strain in relaxation is not usually attained in natural geological systems.Therefore,generalized relaxation tests that explore the simultaneous changes of stress and strain with time under different stress levels with constant pore-water pressure are conducted in this study.The results show that in area Ⅰ,area Ⅱ,and area Ⅲ,the stress and strain both change synchronously with time and show similar evolutionary laws as the strain-time curve for creep or the stress-time curve for relaxation.When the applied stress level surpasses the δ_(ci) or δ_(cd) threshold,the variations in stress and strain and their respective rates of change exhibit a significant increase.The radial deformation and its rate of change exhibit greater sensitivity in response to stress levels.The apparent strain deforms homogeneously at the primary stage,and subsequently,gradually localizes due to the microcrack development at the secondary stage.Ultimately,interconnection of the microcracks causes the formation of a shear-localization zone at the tertiary stage.The strain-time responses inside and outside the localization zone are characterized by local strain accumulation and inelastic unloading during the secondary and tertiary stages,respectively.The width of the shear-localization zone is found to range from 4.43 mm to 7.08 mm and increased with a longer time-to-failure.Scanning electron microscopy(SEM)reveals a dominant coalescence of intergranular cracks on the fracture surface,and the degree of physiochemical deterioration caused by water-rock interaction is more severe under a longer lifetime.The brittle sandstone’s time-dependent deformation is essentially controlled by microcrack development during generalized relaxation,and its expectancy-life is determined by its initial microstructural state and the rheological path.

Analytical solutions to the precession relaxation of magnetization with uniaxial anisotropy

Based on the Landau-Lifshitz-Gilbert(LLG)equation,the precession relaxation of magnetization is studied when the external field H is parallel to the uniaxial anisotropic field H_(k).The evolution of three-component magnetization is solved analytically under the condition of H=nH_(k)(n=3,1 and 0).It is found that with an increase of H or a decrease of the initial polar angle of magnetization,the relaxation time decreases and the angular frequency of magnetization increases.For comparison,the analytical solution for H_(k)=0 is also given.When the magnetization becomes stable,the angular frequency is proportional to the total effective field acting on the magnetization.The analytical solutions are not only conducive to the understanding of the precession relaxation of magnetization,but also can be used as a standard model to test the numerical calculation of LLG equation.

Solid-state impedance spectroscopy studies of dielectric properties and relaxation processes in Na_(2)O–V_(2)O_(5)–Nb_(2)O_(5)–P_(2)O_(5) glass

Solid-state impedance spectroscopy(SS-IS)was used to investigate the influence of structural modifications resulting from the addition of Nb2O5 on the dielectric properties and relaxation processes in the quaternary mixed glass former(MGF)system 35Na_(2)O–10V_(2)O_(5)–(55-x)P_(2)O_(5)–xNb_(2)O_(5)(x=0–40,mol%).The dielectric parameters,including the dielectric strength and dielectric loss,are determined from the frequency and temperature-dependent complex permittivity data,revealing a significant dependence on the Nb2O5 content.The transition from a predominantly phosphate glass network(x<10,region I)to a mixed niobate–phosphate glass net-work(10≤x≤20,region II)leads to an increase in the dielectric parameters,which correlates with the observed trend in the direct-cur-rent(DC)conductivity.In the predominantly niobate network(x≥25,region III),the highly polarizable nature of Nb5+ions leads to a fur-ther increase in the dielectric permittivity and dielectric strength.This is particularly evident in Nb-40 glass-ceramic,which contains Na_(13)Nb_(35)O_(94) crystalline phase with a tungsten bronze structure and exhibits the highest dielectric permittivity of 61.81 and the lowest loss factor of 0.032 at 303 K and 10 kHz.The relaxation studies,analyzed through modulus formalism and complex impedance data,show that DC conductivity and relaxation processes are governed by the same mechanism,attributed to ionic conductivity.In contrast to glasses with a single peak in frequency dependence of imaginary part of electrical modulus,M″(ω),Nb-40 glass-ceramic exhibits two distinct contributions with similar relaxation times.The high-frequency peak indicates bulk ionic conductivity,while the additional low-fre-quency peak is associated with the grain boundary effect,confirmed by the electrical equivalent circuit(EEC)modelling.The scaling characteristics of permittivity and conductivity spectra,along with the electrical modulus,validate time-temperature superposition and demonstrate a strong correlation with composition and modification of the glass structure upon Nb_(2)O_(5) incorporation.

Effectiveness of aromatherapy with lavender compared to progressive muscle relaxation on anxiety and vital signs in patients under spinal anesthesia:A randomized clinical trial

Objective:This study aimed to determine the effectiveness of aromatherapy with lavender essential oil compared to progressive muscle relaxation(PMR)on anxiety and vital signs of patients under spinal anesthesia.Materials and Methods:This clinical trial was conducted on 120 spinal anesthesia candidates who were randomly assigned into three groups of 40 including control,PMR(Jacobsen group),and aromatherapy.The state-trait anxiety inventory was completed on surgery day and 15 min after the end of the intervention by the samples of all three groups,and at the same time as completing the questionnaire,vital signs were also measured and recorded.Results:The mean score of anxiety after intervention was lower than that before the intervention in the aromatherapy group(P<0.001).The mean score of anxiety in the aromatherapy group was significantly lower than that in the Jacobsen group(P<0.001).Moreover,data analysis showed a significant decrease in the mean arterial blood pressure scores of the PMR(P=008)and aromatherapy(P<0.001)groups and a statistically significant increase in the mean heart rate scores in the control group(P=0.002).Conclusion:The use of aromatherapy with lavender is more effective than PMR therapy in reducing the anxiety level of patients undergoing spinal anesthesia.Due to the high level of anxiety and its serious effects on the patient’s hemodynamics,aromatherapy with lavender can be used as an easy and cheap method to reduce anxiety in operation rooms.

Photoelectric State with Long-Term Relaxation in CdTe:(Ag, Cu, Cd) and Sb2Se3:Se Photovoltaic Films

The results of an experimental study of long-term relaxation of the photoelectret state of polycrystalline CdTe:(Ag, Cu, Cd) and Sb2Se3:Se films with an anomalous photovoltaic property are presented. In such films, the residual photovoltage is caused by the separation of photocarriers by the built-in electrostatic field of the near-surface region of space charges and their asymmetric capture by deep levels of impurities or complexes, including impurity atoms and intrinsic defects, both in the bulk and on the surface of crystal grains. It has been shown that in activated films, a two-step exponential temporary relaxation of the initial photovoltage of the order of VAPV ≈ (500-600) V is detected, and only 10% of it experiences long-term relaxation (t ≈ 100-120 min).

Improved Algorithm for Efficient Extraction of Relaxation Parameter Values from Wideband Permittivity of Baijiu

The complex permittivity of baijiu varies with frequency,and dielectric spectroscopy has been used to evaluate the quality.To simplify the analysis and reduce the number of the parameters,a dielectric relaxation model is often used to fit the permittivity data.However,existing fitting methods such as the least squares and particle swarm optimization methods are often computationally complex and require preset initial values.Therefore,a simpler calculation method of the relaxation parameters considering the geometric characteristics of the permittivity spectrum is proposed.It is based on the relationship between the Cole-Cole relaxation parameters and the Cole-Cole diagram,which is fitted by a geometric method.First,the concepts of the Cole-Cole parameters and the diagram are introduced,and then the process of obtaining the parameters from the complex permittivity measurement data is explained.Taking baijiu with 56%alcohol by volume(ABV)as an example,the fitting is better than the least squares method and similar to the particle swarm optimization.This method is then used for the parameter fitting of baijiu with ABV of 42-52%,and the average error is less than 1%,demonstrating its wider applicability.Finally,a prediction model is used for baijiu with 53%ABV,and the error is only 1.51%.Hence,the method can be applied to the measurement of ABV of baijiu.

Effects of relaxation breathing exercise on fatigue and cortisol level among Indonesian gynecological cancer patients undergoing chemotherapy:a pilot study

Objective:This study aimed to determine the effect of the relaxation breathing exercise(RBE)on fatigue and cortisol levels among Indonesian women with gynecological cancer undergoing chemotherapy.Methods:This pilot study consecutively recruited 44 gynecological cancer patients to receive RBE(22)or usual care(22).Cortisol level was measured before and after completion of the intervention(day 8).Fatigue was measured using the Piper Fatigue Scale(PFS).Anxiety and depression were assessed using the Hospital Anxiety and Depression Scale(HADS)at the baseline days of the study for days 1,4,and 8.The obtained data were analyzed using Fisher’s exact test,the independent t-test,and the Mann-Whitney U test.Results:There were significant increases in cortisol levels within the groups,either the intervention or control groups,respectively(P-value=0.0003 and 0.001).Despite there being no statistical significance between the intervention and control groups,there were noticeable differences in the cortisol levels,indicating the extreme increase in cortisol levels in the control group(Median[IQR1-IQR3]:2.30[0.99-9.09];Min-Max:0.43-23.38)compared with the intervention group(Median[IQR1-IQR3]=2.97[1.26-5.18];Min-Max=0.39-6.91).Conclusions:RBE helps prevent a significant increase in cortisol levels that can alleviate fatigue for women with gynecological cancer.Further research was recommended to compare several intervention modalities for fatigue and cancer-related symptom management based on cortisol level changes.

A Bibliometric Study on The Application of Progressive Muscle Relaxation Training in The Nursing Field in China

Objective:To systematically analyze the research status and application of progressive muscle relaxation training(PMRT)in the nursing field in China,and provide a reference basis for scientific research in this field.Methods:The bibliometric method was adopted in“progressive muscle relaxation training”or“PMRT,”and“nursing.”The established database was included in the China National Knowledge Infrastructure(CNKI)and the Wanfang Medical Network.The relevant articles in the Chinese Science and Technology Periodical Database(VIP)were analyzed.Results:A total of 169 literatures were included.The journals,years,and regions of literature publication were uneven,mainly originating from the eastern region(43.19%),and listed the application of progressive muscle relaxation training in the field of nursing in China.Intervention literature information was mainly dominated by experimental studies(97%).Conclusion:The related research and application of progressive muscle relaxation training in nursing in China is increasing,but there is a lack of objective evaluation of outcome indicators and a short intervention period.Further research should be conducted in the future to effectively guide the development of PMRT in the field of nursing in China.

Effects of Progressive Muscle Relaxation Training on Anxiety, Depression, and Quality of Life in Patients with Cerebral Small Vessel Disease

Objective:To explore the effects of progressive muscle relaxation training on anxiety,depression,and quality of life in patients with cerebral small vessel disease(CSVD).Methods:Sixty-one patients with CSVD in the Department of Neurology of a tertiary hospital were divided into an observation group(28 patients)and a control group(33 patients)by lottery method.The control group received conventional nursing care,while the observation group received progressive muscle relaxation training interventions in addition to the conventional care.The Hamilton Anxiety Scale(HAMA),the Hamilton Depression Scale(HAMD),and the Stroke-Specific Quality of Life Scale(SS-QOL)were used to compare the effects before the intervention,7 days after the intervention,and 30 days after the intervention.Results:Over time,at different time points after the intervention,the anxiety and depression scores of patients with CSVD in the observation group were significantly lower than those in the control group(P<0.05).The quality of life scores were significantly higher in the observation group compared to the control group(P<0.05),and these differences were statistically significant.Conclusion:Progressive muscle relaxation training can improve anxiety and depression in patients with cerebral small vessel disease and can effectively enhance their quality of life.

Functional group resolved NMR relaxation of 3-carbon adsorbates in mesoporous alumina

NMR relaxation analysis provides a unique and non-invasive probe of fluid dynamics within porous materials,and may be applied to the interpretation of a wide variety of material and interfacial characteristics.Here,we report two-dimensional^(1)H T_(1)-T_(2)relaxation correlation measurements of a range of three-carbon adsorbates(1-propanol,2-propanol and propanoic acid)imbibed within the mesoporous metal oxide gamma-alumina.Our data,acquired across field strengths of 2 MHz,12.7 MHz and 43 MHz,clearly reveal two populations in each measurement,identified as the alkyl and hydroxyl moieties of each adsorbate.These results expand the range of materials in which such functional group resolved relaxation is known to occur,and demonstrate the clear persistence of such phenomena using a range of typical benchtop NMR systems employed to study fluid-saturated porous media.

The dynamic relaxation form finding method aided with advanced recurrent neural network

How to establish a self‐equilibrium configuration is vital for further kinematics and dynamics analyses of tensegrity mechanism.In this study,for investigating tensegrity form‐finding problems,a concise and efficient dynamic relaxation‐noise tolerant zeroing neural network(DR‐NTZNN)form‐finding algorithm is established through analysing the physical properties of tensegrity structures.In addition,the non‐linear constrained opti-misation problem which transformed from the form‐finding problem is solved by a sequential quadratic programming algorithm.Moreover,the noise may produce in the form‐finding process that includes the round‐off errors which are brought by the approximate matrix and restart point calculating course,disturbance caused by external force and manufacturing error when constructing a tensegrity structure.Hence,for the purpose of suppressing the noise,a noise tolerant zeroing neural network is presented to solve the search direction,which can endow the anti‐noise capability to the form‐finding model and enhance the calculation capability.Besides,the dynamic relaxation method is contributed to seek the nodal coordinates rapidly when the search direction is acquired.The numerical results show the form‐finding model has a huge capability for high‐dimensional free form cable‐strut mechanisms with complicated topology.Eventually,comparing with other existing form‐finding methods,the contrast simulations reveal the excellent anti‐noise performance and calculation capacity of DR‐NTZNN form‐finding algorithm.

Prediction of impedance responses of protonic ceramic cells using artificial neural network tuned with the distribution of relaxation times

A deep-learning-based framework is proposed to predict the impedance response and underlying electrochemical behavior of the reversible protonic ceramic cell(PCC) across a wide variety of different operating conditions.Electrochemical impedance spectra(EIS) of PCCs were first acquired under a variety of opera ting conditions to provide a dataset containing 36 sets of EIS spectra for the model.An artificial neural network(ANN) was then trained to model the relationship between the cell operating condition and EIS response.Finally,ANN model-predicted EIS spectra were analyzed by the distribution of relaxation times(DRT) and compared to DRT spectra obtained from the experimental EIS data,enabling an assessment of the accumulative errors from the predicted EIS data vs the predicted DRT.We show that in certain cases,although the R^(2)of the predicted EIS curve may be> 0.98,the R^(2)of the predicted DRT may be as low as~0.3.This can lead to an inaccurate ANN prediction of the underlying time-resolved electrochemical response,although the apparent accuracy as evaluated from the EIS prediction may seem acceptable.After adjustment of the parameters of the ANN framework,the average R^(2)of the DRTs derived from the predicted EIS can be improved to 0.9667.Thus,we demonstrate that a properly tuned ANN model can be used as an effective tool to predict not only the EIS,but also the DRT of complex electrochemical systems.

Data-driven optimization study of the multi-relaxation-time lattice Boltzmann method for solid-liquid phase change

Sharp phase interfaces and accurate temperature distributions are important criteria in the simulation of solid-liquid phase changes.The multi-relaxation-time lattice Boltzmann method(MRT-LBM)shows great numerical performance during simulation;however,the value method of the relaxation parameters needs to be specified.Therefore,in this study,a random forest(RF)model is used to discriminate the importance of different relaxation parameters to the convergence,and a support vector machine(SVM)is used to explore the decision boundary of the convergent samples in each dimensional model.The results show that the convergence of the samples is consistent with the sign of the decision number,and two types of the numerical deviations appear,i.e.,the phase mushy zone and the non-physical heat transfer.The relaxation parameters chosen on the decision boundary can further suppress the numerical bias and improve numerical accuracy.

One-step Eco-friendly Fabrication of Antibacterial Polyester Via On-line Amination Reaction by Melt Coextrusion

The work is dedicated to develop a one-step eco-friendly method to prepare antibacterial polyethylene terephthalate(PET).We report a one-step eco-friendly method to manufacture antibacterial PET via on-line amination reaction by melt coextrusion.Beside evenly mixing of poly(hexamethylene guanidine)(PHMG)and PET in the melt coextrusion procedure,the amination reaction also occurred between PHMG and PET under high temperature(230-270℃).The antibacterial ability of composite PET showed obvious PHMG concentration dependence,and antibacterial activity reached more than 99%when PHMG content was 2.5 wt%.Moreover,LIVE/DEAD fluorescence test further confirmed that the composite PET could kill bacteria quickly and efiectively(within 30 min);while negligible cytotoxicity was observed to HSF and HUVEC cells.Onestep eco-friendly fabrication of composite antibacterial PET was accomplished by on-line melt coextrusion.The composite antibacterial PET has potential use in multiple fields to combat with pathogenic including textiles,packaging materials,decoration materials and biomedical devices,etc.

Unusual magnetic relaxation in a single-molecule magnet with toroidal magnetic moments

We report the synthesis and characterization of a single-molecule magnet composed of triangular clusters of dysprosium ions.The structural study shows that the symmetry changes from one polar point group(mm2)at room temperature to another polar point group(m)at low temperature.Magnetic studies and theory calculations illustrate that the vortex distribution of magnetic dipoles in the triangular dysprosium clusters forms a toroidal magnetic moment.Interestingly,the analysis of AC magnetic susceptibility reveals the coexistence of three distinct magnetic relaxation processes,corresponding to the Raman,Orbach,and QTM relaxation pathways,respectively.The sum of three modified Debye functions is successfully used to describe the multiple relaxation behavior.

Relaxation of Ne^(1+)1s^(0)2s^(2)2p^(6)np produced by resonant excitation of an ultraintense ultrafast x-ray pulse

The creation and relaxation of double K-hole states 1s^(0)2s^(2)2p^(6)np(n≥3)of Ne^(1+)in the interaction with ultraintense ultrafast x-ray pulses are theoretically investigated.The x-ray photon energies are selected so that x-rays first photoionize1s^(22)s^(22)p^(6) of a neon atom to create a single K-hole state of 1s2s^(22)p^(6) of Ne^(1+),which is further excited resonantly to double K-hole states of ls^(0)2s^(2)2p^(6)np(n≥3).A time-dependent rate equation is used to investigate the creation and relaxation processes of 1s^(0)2s^(2)2p^(6)np,where the primary microscopic atomic processes including photoexcitation,spontaneous radiation,photoionization and Auger decay are considered.The calculated Auger electron energy spectra are compared with recent experimental results,which shows good agreement.The relative intensity of Auger electrons is very sensitive to the photon energy and bandwidth of x-ray pulses,which could be used as a diagnostic tool for x-ray free electron laser and atom experiments.

GLOBAL SOLUTIONS TO A HYDRODYNAMIC MODEL FOR SEMICONDUCTORS WITH VELOCITY RELAXATION

In this paper,we apply the method given in the paper“Zero relaxation time limits to a hydrodynamic model of two carrier types for semiconductors”(Mathematische Annalen,2022,382:1031–1046)to study the Cauchy problem for a one dimensional inhomogeneous hydrodynamic model of two-carrier types for semiconductors with the velocity relaxation.

Binary fluids in mesoporous materials: Phase separation studied by NMR relaxation and diffusion

Relaxation and diffusion measurements were carried out on single and binary liquids filling the pore space of controlled porous glass Vycor with an average pore size of about 4 nm.The dispersion of the longitudinal relaxation time Tr is discussed as a means to identify liquid-surface interaction based on existing models developed for metal-free glass surfaces.In addition,the change of T1 and T2 with respect to their bulk values is discussed,in particular T2 serves as a probe for the strength of molecular interactions.As the native glass surface is polar and contains a large amount of hydroxyl groups,a pronounced interaction of polar and protic adsorbate liquids is expected;however,the T dispersion,and the corresponding reduction of T2,are also observed for non-polar liquids such as alkanes and cyclohexane.Deuterated liquids are employed for simplifying data analysis in binary systems,but also for separating the respective contributions of intra-and intermolecular interactions to the overall relaxation rate.Despite the lack of paramagnetic impurities in the glass material,H and 2H relaxation dispersions of equivalent molecules are frequently found to differ from each other,suggesting intermolecular relaxation mechanisms for the'H nuclei.The variation of the T dispersion when comparing single and binary systems gives clear evidence for the preferential adsorption of one of the two liquids,suggesting complete phase separation in several cases.Measurement of the apparent tortuosity by self-diffusion experiments supports the concept of a local variation of sample composition within the porespace.