SEMI-DEFINITE RELAXATION ALGORITHM OF MULTIPLE KNAPSACK PROBLEM

The multiple knapsack problem denoted by MKP (B,S,m,n) can be defined as fol- lows.A set B of n items and a set Sof m knapsacks are given such thateach item j has a profit pjand weightwj,and each knapsack i has a capacity Ci.The goal is to find a subset of items of maximum profit such that they have a feasible packing in the knapsacks.MKP(B,S,m,n) is strongly NP- Complete and no polynomial- time approximation algorithm can have an approxima- tion ratio better than0 .5 .In the last ten years,semi- definite programming has been empolyed to solve some combinatorial problems successfully.This paper firstly presents a semi- definite re- laxation algorithm (MKPS) for MKP (B,S,m,n) .It is proved that MKPS have a approxima- tion ratio better than 0 .5 for a subclass of MKP (B,S,m,n) with n≤ 1 0 0 ,m≤ 5 and maxnj=1{ wj} minmi=1{ Ci} ≤ 2 3 .

SEMI-DEFINITE RELAXATION ALGORITHM FOR SINGLE MACHINE SCHEDULING WITH CONTROLLABLE PROCESSING TIMES

The authors present a semi-definite relaxation algorithm for the scheduling problem with controllable times on a single machine. Their approach shows how to relate this problem with the maximum vertex-cover problem with kernel constraints (MKVC).The established relationship enables to transfer the approximate solutions of MKVCinto the approximate solutions for the scheduling problem. Then, they show how to obtain an integer approximate solution for MKVC based on the semi-definite relaxation and randomized rounding technique.

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.

Theory analysis and vestigial information of surface relaxation of natural chalcopyrite mineral crystal

X-ray diffraction was used to measure the unit cell parameters of chalcopyrite crystal.The results showed that the chalcopyrite crystal is perfect,and the arrangement of its atoms is regular.A qualitative analysis of molecular mechanics showed that surface relaxation causes the chalcopyrite surface to be sulfur enriched.Atomic force microscope（AFM） was used to obtain both a microscopic three-dimensional topological map of chalcopyrite surface and a two-dimensional topological map of its electron cloud.The AFM results revealed that the horizontal and longitudinal arrangements of atoms on the chalcopyrite surface change dramatically compared with those in the interior of the crystal.Longitudinal shifts occur among the copper,iron and sulfur atoms relative to their original positions,namely,surface relaxation occurs,causing sulfur atoms to appear on the outermost surface.Horizontally,AFM spectrum showed that the interatomic distance is irregular and that a reconstruction occurs on the surface.One result of this reconstruction is that two or more atoms can be positioned sufficiently close so as to form atomic aggregates.The lattice properties of these models were calculated based on DFT theory and compared with the experimental results and those of previous theoretical works.On analyzing the results,the atomic arrangement on the（001） surface of chalcopyrite is observed to become irregular,S atoms move outward along the Z-axis,and the lengths of Cu—S and Fe—S bonds are enlarged after geometry optimization because of the surface relaxation and reconstruction.The sulfur-rich surface and irregular atomic aggregates caused by the surface relaxation and reconstruction greatly influence the bulk flotation properties of chalcopyrite.

Parallel rapid relaxation inversion of 3D magnetotelluric data

We implement a parallel algorithm with the advantage of MPI （Message Passing Interface） to speed up the rapid relaxation inversion for 3D magnetotelluric data. We test the parallel rapid relaxation algorithm with synthetic and real data. The execution efficiency of the algorithm for several different situations is also compared. The results indicate that the parallel rapid relaxation algorithm for 3D magnetotelluric inversion is effective. This parallel algorithm implemented on a common PC promotes the practical application of 3D magnetotelluric inversion and can be suitable for the other geophysical 3D modeling and inversion.

Dielectric Relaxation of Adsorbed Water in Wood Cell Wall under Equilibrium and Non-Equilibrium State

This article summarized systematically the previous investigations on t he dielectric relaxation of wood, the main substances and extractives in wood at oven-dry state, and the dielectric relaxation based on the adsorbed water in w o od cell wall under equilibrium and non-equilibrium state. Moreover, some expect a tions for future research were proposed on this basis. The purpose of this artic le is to provide other researchers an overall understanding about the research i n this region, and further to promote the research onto a new and higher level.

Formation and evolution characteristics of bcc phase during isothermal relaxation processes of supercooled liquid and amorphous metal Pb

The formation and evolution characteristics of bcc phase during the isothermal relaxation processes for supercooled-liquid and amorphous Pb were investigated by molecular dynamics simulation and cluster-type index method （CTIM）. It is found that during the relaxation process, the formation and evolution of bcc phase are closely dependent on the initial temperature and structure. During the simulation time scale, when the initial temperature is in the range of supercooled liquid region, the bcc phase can be formed and kept a long time; while it is in the range of glassy region, the bcc phase can be formed at first and then partially transformed into hcp phase; when it decreases to the lower one, the hcp and fcc phases can be directly transformed from the glassy structure without undergoing the metastable bcc phase. The Ostwald＇s ＂step rule＂ is impactful during the isothermal relaxation process of the supercooled and glassy Pb, and the metastable bcc phase plays an important role in the precursor of crystallization.

RTD’s Relaxation Oscillation Characteristics with Applied Pressure

The relaxation oscillation characteristics of a resonant tunneling diode （RTD） with applied pressure are reported. The oscillation circuit is simulated and designed by Pspice 8. 0, and the measured oscillation frequency is up to 200kHz. Using molecular beam epitaxy （MBE） ,AIAs/lnx Ga1-x As/GaAs double barrier resonant tunneling structures （DBRTS） are grown on （100） semi-insulated （SI） GaAs substrate,and the RTD is processed by Au/Ge/Ni/Au metallization and an airbridge structure. Because of the piezoresistive effect of RTD,with Raman spectrum to measure the applied pressure, the relaxation oscillation characteristics have been studied, which show that the relaxation oscillation frequency has approxi- mately a - 17.9kHz/MPa change.

RELAXATION BEHAVIOUR OF GFRP UNIDIRECTIONAL LAMINATES

In this paper two set of GFRP specimens are manufactured and tested to investigate the relaxation behaviour under cyclic loading in the longitudinal and transversel direction. The relaxation of GFRP unidirectional laminates is evident for both cyclic loadings. Under longitudinal cyclic loading the relaxation is dependent on the number of loading cycles. Under transverse loading the relaxation depends on the loading cycles as well as the time of loading. Two expressions are set up to describe the relaxation for the longitudinal and transverse loading, and the predictions agree well with the experimental data.

Energy Dependence of Interface Trap Density——Investigated by Relaxation Spectral Technique

According to the definition of interface traps,a new application of relaxation spectral technique to sub-threshold swing shift and sub-threshold gate voltage shift is proposed to extract interface trap density in 1.9nm MOSFET.And thus the energy distribution of interface trap can be determined.According to the two methods,the energy profile of interface traps agrees with those reported in literature.Compared to other methods,this method is simpler and more convenient.

Correlation of Cooperatively Localized Rearrangement on the ＂Fluidized Domain＂ of Polymers to Their Nonexponentially Viscoelastic Behaviors at Double Aging Processes （I）： A Set of Reduced Universal Equations on the Stress Relaxation Modulus and Creep Comp

Based on the structure of glass （or liquid） polymers consisting of α-domain, β-co-domain, and entanglement constituent chain networks, and the nonexponentially viscoelastic behavior, a “heterophase fluctuation” model was proposed. It was found that the dynamics of cooperative rearrangement on the “fluidized domain” has a great shear rate, domain size, and temperature dependences. When the shear rate, domain size, and temperature dependences were taken account into the cooperatively localized rearrangement on the fluidized domain by the degradation of primary α-domain and the reformation of secondary β-co-domain constituent chains. A new dynamic theory of cooperatively localized rearrangement on the fluidized domain constituent chains with different size and different network chain length during physical and mechanical aging was established. The total viscoelastic free en-ergy of deformation resulting from the change in conformations of α-domain, β-co-domain, crytallite, crosslinked, and trapped entanglement constituent chains during aging processes was calculated by the combining method of kinetics and statistical mechanics. The constitu- tive equations and reduced stress relaxation modulus and creep compliances for three types of polymers were also derived. Finally, two reduced universal equations on creep compliance and stress relaxation modulus with a non-linear and two nonexponential parameters α and β were theoretically derived from the dynamic theory and a statistically extended mode coupling theory for double aging effects of polymers was developed. Results show that the two reduced universal equations have the same form as Kohlraush-Williams-Watts （K-W-W） stretched exponential function. The nonlinearity and the nonexponentiality are, respectively, originated from the memory effects of nonthermal and thermal history. The correlation of nonlinearity, α and β to the aging time, aging temperature, and the mesomorphic structure of fluidized domains was also established.