Influence of Omega 3 Fatty Acid Supplementation on Phase Angle Values of People Living with HIV/AIDS with Lipodystrophy Secondary to Antiretroviral Therapy: A Randomized Clinical Trial

Objective: The measurement of phase angles is an important monitoring parameter and supplementation with omega-3 could promote benefits by modulating the electrical potential of membranes and increasing body cell mass. This study aimed to evaluate the effectiveness of omega-3 fatty acid supplementation on the phase angle of people living with HIV/AIDS. Methods: In this study, 63 individuals of all genders who were undergoing outpatient follow-up and showed lipodystrophy due to highly active antiretroviral therapy were analyzed. Our sample consisted of two groups, one that received supplementation containing 2550 mg of omega-3/day (1080 mg of eicosapentaenoic acid and 720 mg of docosahexaenoic acid) for three months (n = 32) and another that underwent nutrition guidance (n = 31). Phase angle and body cell mass were assessed for both groups and compared at the beginning of research (T0) and after our intervention (T1) for each group separately. Results: Phase angle averaged 6.45° ± 1.06 SD. The comparison between T0 and T1 showed a significant increase in phase angle and body cell mass, whereas the guidance group showed a decrease in body cell mass at T1 in relation to T0, with a significant p-value. Variance in phase angle between moments showed significant values between T0 and T1 in the supplementation group for all genders. Conclusion: Omega-3 positively modulated patients phase angle and body cell mass, but we emphasize the need for other studies that can solidify knowledge about supplementation dosage and intervention time.

Role of the phase angle in the prognosis of the cirrhotic patient:15 years of follow-up

BACKGROUND In 2019,cirrhosis accounted for 2.4%of global deaths.The projection for 2030 is an increase in this index.In recent years,hospitalization costs have escalated by 36%for compensated cirrhosis and 24%for decompensated cirrhosis.Therefore,it is necessary to identify a tool capable of predicting the mortality of these patients according to their clinical condition and consequently extending their survival time.Different studies have shown that the phase angle(PA)can be a feasible method in clinical practice,with the potential to guide assertive patient management in the therapeutic of chronic liver disease.AIM To evaluate the prognostic role of PA in cirrhotic patients over a 15-year followup period.METHODS Retrospective cohort study with 129 cirrhotic patients of both sexes over 18 years old.Diagnosis of cirrhosis by liver biopsy.The first year of data collection was 2007,and data regarding outcomes was collected in 2023.Data were gathered from medical records,such as esophageal varices(EV),EV bleeding,ascites,spontaneous bacterial peritonitis(SBP),encephalopathy,laboratory findings and PA.The cut-off value for the PA was 5.4°,a value described in 2012 by Fernandes et al for 129 patients evaluated in this study and the cut-off points for the Brazilian population presented in percentiles(P),as described by Mattiello et al.The mortality was assessed using the PA percentile through Kaplan-Meier curves and multivariate binary logistic regression models.RESULTS Patients were divided into two groups according to the PA 5.4th(PA>5.4°,n=40;PA≤5.4°,n=89)PA percentile(<P50,n=56;≥P50 n=73).The percentile classification was more accurate in identifying long-term deaths than the 5.4ºPA.Patients with<P50 had a higher number of relevant complications such as ascites,SBP,liver encephalopathy and HCC.PA is strongly correlated with serum albumin(P<0.001),International Normalized Ratio(P=0.01),total bilirubin(P=0.02)and direct bilirubin(P=0.003).PA is correlated with survival time(P<0.001)and length of stay(P=0.02).Logistic regression analysis shows that an increase of 1°in PA enlarges the cirrhotic patient's chance of survival by 17.7%.CONCLUSION PA is a good predictor of morbidity and mortality for cirrhotic patients.The PA by percentile showed greater sensitivity in predicting mortality compared to the cut-off point of 5.4º.

Phase angle obtained by bioelectrical impedance analysis independently predicts mortality in patients with cirrhosis

AIM To evaluate the prognostic value of the phase angle(PA)obtained from bioelectrical impedance analysis(BIA) for mortality prediction in patients with cirrhosis. METHODS In total, 134 male cirrhotic patients prospectively completed clinical evaluations and nutritional assessment by BIA to obtain PAs during a 36-mo follow-up period. Mortality risk was analyzed by applying the PA cutoff point recently proposed as a malnutrition marker(PA ≤ 4.9°) in Kaplan-Meier curves and multivariate Cox regression models. RESULTS The patients were divided into two groups according to the PA cutoff value(PA > 4.9°, n = 73; PA ≤ 4.9°, n = 61). Weight, height, and body mass index were similar in both groups, but patients with PAs > 4.9° were younger and had higher mid-arm muscle circumference, albumin, and handgrip-strength values and lower severe ascites and encephalopathy incidences, interleukin(IL)-6/IL-10 ratios and C-reactive protein levels than did patients with PAs ≤ 4.9°(P ≤ 0.05). Forty-eight(35.80%) patients died due to cirrhosis, with a median of 18 mo(interquartile range, 3.3-25.6 mo) follow-up until death. Thirty-one(64.60%) of these patients were from the PA ≤ 4.9° group. PA ≤ 4.9° significantly and independently affected the mortality model adjusted for Model for End-Stage Liver Disease score and age(hazard ratio = 2.05, 95%CI: 1.11-3.77, P = 0.021). In addition, Kaplan-Meier curves showed that patients with PAs ≤ 4.9° were significantly more likely to die. CONCLUSION In male patients with cirrhosis, the PA ≤ 4.9° cutoff was associated independently with mortality and identified patients with worse metabolic, nutritional, and disease progression profiles. The PA may be a useful and reliable bedside tool to evaluate prognosis in cirrhosis.

Low phase angle is associated with the development of hepatic encephalopathy in patients with cirrhosis

AIM Evaluate the association between phase angle and the development of hepatic encephalopathy in the longterm follow-up of cirrhotic patients.METHODS This was a prospective cohort study. Clinical, nutritional and biochemical evaluations were performed. MannWhitney's U and χ2 tests were used as appropriate. Kaplan-Meier curves and Cox proportional Hazards analysis were used to evaluate the prediction and incidence of hepatic encephalopathy.RESULTS Two hundred and twenty were included; the most frequent etiology of cirrhosis was hepatitis C infection, 52% of the patients developed hepatic encephalopathy(18.6% covert and 33.3% overt); the main precipitating factors were infections and variceal bleeding. KaplanMeier curves showed a higher proportion of HE in the group with low phase angle(39%) compared to the normal phase angle group(13%)(P = 0.012). Furthermore, creatinine and phase angle remained independently associated to hepatic encephalopathy in the Cox regression multivariate analysis [hazard ratio = 1.80(1.07-3.03)]. CONCLUSION In our cohort of patients low phase angle was associated with an increased incidence of hepatic encephalopathy. Phase angle is a useful nutritional marker that evaluates cachexia and could be used as a part of the integral assessment in patients with cirrhosis.

Nutritional evaluation in cirrhosis: Emphasis on the phase angle

Protein-calorie malnutrition (PCM) is a common condition in cirrhotic patients, leading to a worse prognosis, complications, poor quality of life and lower survival rates. Among ways of assessing nutritional status, there are anthropometric methods such as the evaluation of the triceps skinfold, the arm circumference, the arm muscle circumference and the body mass index, and non-anthropometric methods such as the subjective global assessment, the handgrip strength of non-dominant hand, and the bioelectrical impedance analysis (BIA). PCM is frequently under-diagnosed in clinical settings in patients with cirrhosis due to the limitations of nutritional evaluation methods in this population. BIA is a useful method, but cannot be indicated in patients with abnormal body composition. In these situations, the phase angle (PA) has been used, and can become an important tool in assessing nutritional status in any situation. The PA is superior to anthropometric methods and might be considered as a nutritional indicator in cirrhosis. The early characterization of the nutritional status in patients with cirrhosis means an early nutritional intervention, with a positive impact on patients&rsquo; overall prognosis. Among the usually accepted methods for nutritional diagnosis, the PA provides information in a quick and objective manner.

Variations in electrical impedance and phase angle among seedlings of Pinus densata and parental species in Pinus tabuliformis habitat environment

Electrical impedance （El） and phase angle （PHI） parameters in AC impedance spectroscopy are important electrical parameters in the study of medical pathology. However, little is known about their application in variation and genetic relationship studies of forest trees. In order to test whether impedance parameters could be used in genetic relationship analysis among conifer species, E1 and PHI were measured in a seedling experiment test composed of Pinus tabuliformis, Pinus yunnanensis, and Pinus densata in a habitat of Pinus tabuliformis. The results showed that variations in both EI and PHI among species were sig- nificant in different electric frequencies, and the EI and PHI values measured in the two populations of P. densata were between the two parental species, P. yunnanensis and P. tabuliformis. These results show that these two impedance parameters could reflect the genetic relationship among pine species. This was the first time using the two AC impedance spectroscopy parameters to test the genetic relationship analysis between tree species, and would be a hopeful novelreference methodology for future studies in evolution and genetic variation of tree species.

Bioelectrical Impedance Phase Angle as a Predictors of Mortality in Patients with Lung Cancer:a Prospective Study

Objective Bioelectrical impedance analysis(BIA)is used to measure a patient's body composition.The phase angle(PA),the major parameter in BIA,is one of the most sensitive indicators of malnutrition.The aim of the current study was to investigate whether the PA can be used to predict survival in lung cancer patients.Methods One hundred sixty-six lung cancer patients were prospectively included from January 2014 to August 2016 in Daping Hospital.Anthropometric measurements,hematological values,the nutritional risk screening(NRS 2002)score,patient generated-subjective global assessment(PG-SGA)score,Karnofsky performance status(KPS)scale,European Organization for Research and Treatment of Cancer Core Quality of Life Questionnaire(EORTC QLQ C-30)score,and BIA were investigated within 48 hours after admission to the hospital.A Spearman correlation analysis was applied to test the correlations between the study characteristics and PA.A Kaplan-Meier analysis and log-rank test were conducted to analyze the association between the overall survival(OS)and PA.Results The mean age for all patients was 63 years old(42 females and 124 males).The median PA was 5.5°(4.70°,6.23°).The PA was positively associated with the body mass index,hand grip strength,mid-arm circumference,mid-arm muscle circumference,albumin,prealbumin,C-reactive protein,red blood cells,hemoglobin and KPS score.The PG-SGA scores,QLQ-C30 score,and NRS2002 score showed a significant negative association with the PA.According to a multivariate analysis,the PA(HR=0.47;95%CI:0.27-0.81)was independent predictor of the lung cancer patients'long-term OS.Patients with a higher PA(≥5°)had better overall survival(median=426 days)compared to those with a lower PA(<5°)(median=96 days)based on the one-year follow-up data(P<0.0001).Conclusions These studies indicate that the PA is a sensitive and early indicator to predict survival in lung cancer patients.

Low Phase Angle Predicts Poor Survival in Patients with Hepatocellular Carcinoma:A Retrospective Study

Background The phase angle(PA)is an indicator of nutritional status derived from bioelectrical impedance analysis(BIA).Studies have shown that the PA is one of several factors related to the survival of cancer patients.However,the correlation between the PA and prognosis in patients with hepatocellular carcinoma(HCC)has not been reported.This study aimed to explore the relationship between the PA,nutrition-related indicators,and patient prognosis.Methods The data from 248 HCC patients who underwent BIA between January 2015 and December 2019 at the First Hospital of Jilin University were retrospectively analyzed.Patients were divided into two groups according to the median PA value,then the nutrition-related indicators and overall survival(OS)were compared between the two groups.The correlations between the PA and laboratory test nutrition-related indicators and the results of a body composition analysis were determined using Pearson correlation analysis.Independent predictors of the patient prognosis were identified using univariate and multivariate analyses.Results The median OS in the high and low PA groups were 70 and 54.6 months,respectively(P=0.004).The Pearson correlation analysis revealed that the PA was associated with both laboratory test nutrition-related indicators and the results of a body composition analysis.The multivariable Cox regression analysis identified the PA as an independent risk factor affecting the prognosis of patients with Barcelona Clinic Liver Cancer stage A or B.Conclusion The PA is a good biomarker for the nutritional status.We found that the PA was associated with the prognosis in patients with HCC,with a low PA indicating a poor nutritional status and worse prognosis.

Relationship between phase angle,steatosis,and liver fibrosis in patients coinfected with human immunodeficiency virus/hepatitis C virus

BACKGROUND Malnutrition,lipodystrophy,and dyslipidemia are prevalent characteristics in patients with human immunodeficiency virus(HIV)infection with or without previous treatment.Such a clinical condition can lead to the hypothesis of the presence of hepatic steatosis with possible progression to fibrosis and the risk of hepatocellular carcinoma.Notably,a low phase angle(PA),evaluated by bioelectrical impedance analysis(BIA),is an independent prognostic marker of clinical progression and survival in HIV-infected patients.AIM To evaluate the relationship between PA and body composition with steatosis and hepatic fibrosis in HIV/hepatitis C virus(HCV)-coinfected patients.METHODS A retrospective observational study by convenience sampling of coinfected HIV/HCV patients,in which all patients underwent transient elastography(Fibroscan)and BIA evaluation.Student’s t test was used for group comparisons,and Spearman’s or Pearson’s correlation test was used when appropriate.The significance level was set at 5%,and analyses were performed using SPSS version 21.0.RESULTS Forty-three patients who received antiretroviral therapy met the inclusion criteria,and 23(53.5%)were under treatment with protease inhibitors(PIs).There was no difference in PA between those who used PIs and those who did not(P=0.635).There was no correlation between fibrosis grade and PA(P=0.355)or lean mass(P=0.378).There was a significant inverse correlation between the controlled attenuation parameter(CAP)and lean mass(P=0.378),positive correlation between PA and lean mass(P=0.378),and negative correlation between PA and fatty mass(P=0.378),although the CAP and PA were not correlated.When evaluated by sex,no significant correlations were found.CONCLUSION PA determines the muscle function of HIV/HCV-coinfected patients,and the CAP values reinforce the association with lean mass,suggesting that patients require early nutritional interventions.

Phase angle and non-alcoholic fatty liver disease before and after bariatric surgery

BACKGROUND Obesity is a global health problem that is continuing to increase in the young population.In Brazil,the frequency of obesity in 2018 was 19.8%.Several comorbidities are directly associated with obesity,such as non-alcoholic fatty liver disease(NAFLD),which is considered the most common liver disorder in Western countries and affects up to 46%of adults.Bariatric surgery is effective in treating obesity and can improve NAFLD;however,the effect of bariatric surgery on body composition,phase angle(PA),and improving NAFLD needs to be further studied.AIM To analyze the PA in the postoperative period of bariatric surgery and to correlate it with changes in body composition and liver disease.METHODS This study is a retrospective cohort study of the analysis of the medical records of patients undergoing bariatric surgery in a reference center of a teaching hospital in Porto Alegre over a 2-year period.Patients older than 18 years whose record contained all information relevant to the study were included.The data analyzed were body composition and PA through electrical bioimpedance and NAFLD through liver biopsy in the pre-and postoperative period.The level of significance adopted for the statistical analyses was 5%.RESULTS We evaluated 379 patients with preoperative data.Regarding PA,169 patients were analyzed,and 33 patients had liver biopsy pre-and postoperatively with NAFLD information.In total,79.4%were female,with a mean age of 39.1±10.6 years.The average body mass index(BMI)was 45.9±7.5 kg/m².The PA showed a mean of 5.8±0.62°in the preoperative period and a significant reduction in the postoperative period.A postoperative reduction in body composition data(skeletal muscle mass,fat percentage,fat mass,body cell mass,BMI and visceral fat area)was shown as well.Regarding liver disease,all patients presented a reduction in the degrees and stages of liver disease in the postoperative period,and some had no degree of liver disease at all.CONCLUSION PA decreased after bariatric surgery,with a direct correlation with weight loss and changes in body composition.The decrease in PA was not correlated with the improvement in NAFLD.

Phase angle through electrical bioimpedance as a predictor of cellularity in inflammatory bowel disease

It is estimated in Western industrialized countries that inflammatory bowel disease(IBD)has a prevalence of 1 for every 200 inhabitants.In the past,the fat mass disproportionate increase in relation to the fat-free mass was considered uncommon in patients with IBD,due to the observation of the disease being more common with weight loss and malnutrition.However,more in-depth investigations demonstrate that the fat/lean mass disproportion stands out both in prevalence in patients with new diagnoses of ulcerative colitis or Crohn's disease as well as a factor of poor prognosis to the natural evolution of the disease or to the therapeutic response.Another important aspect associated with obesity in IBD is the increased risk of drug clearance[including anti-tumor necrosis factor(TNF)and anti-integrin agents],resulting in short half-life and low trough drug concentrations,since the levels of TNF secreted by adipocytes sequester anti-TNF agents,which could result in suboptimal response to biologics.In view of these characteristic aspects of the inflammatory process of IBD,the identification of cellular functioning is necessary,which can be associated with the staging of the underlying disease,biochemical parameters,and body composition,helping as an indicator for a more accurate clinical and nutritional conduct.

Application of the Phase Angle in Patients with Malignant Tumors

Bioelectrical impedance analysis(BIA)is a noninvasive and reproducible technique for assessing changes in body composition and nutritional status.The phase angle(PA),a major parameter of BIA,is one of the most sensitive indicators used to detect malnutrition in patients,and is also a prognostic marker in various clinical diseases.The incidence of malnutrition in cancer patients is high,and malnutrition seriously affects the treatment process and prognosis of patients.Reasonable and effective nutritional interventions are therefore of great significance for cancer patients.Compared with traditional nutritional assessment tools,the PA has unique advantages in the nutritional assessment,efficacy monitoring and prognostic prediction of patients with malignant tumors,and it has broad application prospects in clinical practice.This article reviews the research progress on the application of the PA in patients with malignant tumors to provide clinicians with a tool to predict malnutrition,and provide a more favorable basis for the nutritional assessment,treatment and prognostic prediction of cancer patients.

Suppression of Multi-Harmonic Currents in the High-Speed Magnetically Suspended Motor Based on Adaptive Cascaded Notch Filters with Variable Phase Angle

Rotor imbalance is identified as one of the predominant vibration sources in high-speed magnetically suspended motors.Due to factors such as rotor machining accuracy errors and uneven material distribution,synchronous vibration interference is caused.Moreover,sensor runout generates harmonic currents,which are attributed to material irregularities and inhomogeneity in the roundness of the sensor detection surface.Harmonic currents can generate harmonic vibrational forces that are transmitted to the motor housing,jeopardizing control accuracy and the device's operational lifespan.In order to achieve real-time reduction of harmonic currents at specified frequencies and improve the accuracy of harmonic suppression,this paper proposes an algorithm for variable phase anglefiltering of an adaptive cascaded mode notchfilter.This paper performed dynamic modeling and analysis of the magnetically suspended rotor system with rotor imbalance and verified the correctness of the dynamic model.Subsequently,the structure of an adaptive notchfilter with variable phase angle is introduced,highlighting the capability to maintain stability by adjusting the compensatory phase of the system.By comparing the harmonic current suppression performance of cascaded and parallel mode notchfilters,the cascaded method can better enhance the overall frequency selectivity,emphasizing its ability to adjust the compensation phase based on the phase angle of the input signal at different frequencies to maintain system stability.Simulation and experimental results show that harmonic currents can be successfully suppressed in the cascade mode,and the amplitude of the synchronous frequency current is reduced by 94.4%.

Correction of Time-varying PMU Phase Angle Deviation with Unknown Transmission Line Parameters

Phasor measurement units(PMUs)provide useful data for real-time monitoring of the smart grid.However,there may be time-varying deviation in phase angle differences(PADs)between both ends of the transmission line(TL),which may deteriorate application performance based on PMUs.To address that,this paper proposes two robust methods of correcting time-varying PAD deviation with unknown parameters of TL(ParTL).First,the phenomena of time-varying PAD deviation observed from field PMU data are presented.Two general formulations for PAD estimation are then established.To simplify the formulations,estimation of PADs is converted into the optimal problem with a single ParTL as the variable,yielding a linear estimation of PADs.The latter is used by second-order Taylor series expansion to estimate PADs accurately.To reduce the impact of possible abnormal amplitude data in field data,the IGG(Institute of Geodesy&Geophysics,Chinese Academy of Sciences)weighting function is adopted.Results using both simulated and field data verify the effectiveness and robustness of the proposed methods.

Fault Ride Through Strategy of DFIG Using Rotor Voltage Direct Compensation Control Under Voltage Phase Angle Jump

Wind power has developed rapidly in recent years,and large-scale wind power facilities connected to power grids will bring many new challenges.Some new operation charac-teristics of power grids with doubly-fed induction generator(DFIG)may exhibit,for example voltage phase angle jumps(VPAJ).VPAJ can negatively impact the fault ride through(FRT)performance of DFIG.This paper firstly investigates the physical mechanism and the operation characteristics of DFIG with VPAJ.It is noted that the current control strategies designed for voltage amplitude changes are not suitable for VPAJ.Secondly,the paper develops an FRT optimization control strategy under VPAJ which optimizes the DFIG operation characteristics.Finally,simulations of a 250 MW wind farm are presented which validate the proposed FRT strategy.

Voltage phase angle jump characteristic of DFIGs in case of weak grid connection and grid fault

In the condition of connecting large scale doubly-fed induction generators (DFIGs) into weak grid,the closely coupled interactions between wind generators and power grid becomes more severe.Some new fault characteristics including voltage phase angle jump will emerge,which will influence the power quality of power system.However,there are very few studies focusing on the mechanism of voltage phase angle jump under grid fault in a weak grid with wind turbine integration.This paper focuses on the scientific issues and carries out mechanism studies from different aspects,including mathematical deduction,field data analysis and time domain simulation.Based on the analysis of transientcharacteristics of DFIGs during the grid fault,this paper points out that the change of terminal voltage phase angle in DFIGs is an electromagnetism transition process,which is different from conventional synchronous generator.Moreover,the impact on transient characteristics of voltage phase angle are revealed in terms of fault ride through(FRT) control strategies,control parameters of current inner-loop of rotor-side converter and grid strength.

Transient characteristics and adaptive fault ride through control strategy of DFIGs considering voltage phase angle jump

Wind power in China has experienced fast development in recent years. However, areas rich in wind power resources are often far away from loads centers,which leads to weak connection between wind turbines and power grid. When a grid fault occurs, new transient characteristics in weak grid integrated with doubly-fed induction generators(DFIGs) may present, such as voltage phase angle jump. Current control strategies for wind turbine with strong grid connection are hard to be adapted under weak gird connection. This paper explores the transient characteristics of DFIGs under voltage phase angle jump through analyzing the operation and control characteristics of DFIGs connected into weak grid when the voltage phase angle jumps. Fault ride through(FRT) control strategy of DFIGs based on adaptive phase-locked loop is proposed to adapt weak grid condition. The reference frame of the proposed strategy will be changed in real-time to track the operation condition of DFIGs according to the terminal voltage, and different phase tracking method is adopted during the grid fault. Field data analysis and time domain simulation are carried out. The results show that voltage phase angle jumps when a grid fault occurs, which weakens the FRT capability of DFIGs, and the proposed FRT control strategy can optimize transient characteristics of DFIGs, and improve the FRT capability of DFIGs.

Numerical Investigation of Flutter Stability in Subsonic Space Turbine Blisk with Emphasis on Cut-on/Cut-off Modes and Interblade Phase Angles

The so-called blisks,i.e.integrally bladed disks,are characterized by very low viscous material damping and make the flutter prediction much more critical.In that framework,a two-dimensional numerical study of a space turbine blisk featuring complex deformation of blades and high eigenfrequency(>40kHz)is performed.The simulations are based on unsteady Reynolds Averaged Navier Stokes computations linearized in the frequency domain and consist in the superposition of an unsteady linear(in time)pressure field,generated by a harmonic perturbation,upon a steady nonlinear(in space)flow.The aerodynamic damping coefficient is calculated over a range of nodal diameters,and the blades are predicted aeroelastically stable.However,violent changes occur and are rather critical since sudden and large deviations in stability appear.In that context,the nature of the waves propagating from the cascade are evaluated.Such an approach provides fundamental knowledge about the perturbations which can either propagate to the far-field(cut-on mode)or decay(cut-off mode).It is expected that the ability of the flow to damp or to amplify the blade motion is strongly affected by the way unsteady perturbations are transferred from the cascade to the far-field.The nature of the waves are first assessed from the aforementioned linearized results,then they are evaluated analytically and finally compared.A good agreement is found despite the strong assumptions of the analytical model.The results show a clear correlation between the cut-on/cut-off conditions and stability.The least stable configuration corresponds to cut-off mode at the inlet and no wave at the outlet.Without outgoing waves from the cascade,the blade is prone to be less stable:the energy from the blades vibration is necessarily dissipated or sent out by the cascade.

Phase Properties of Two-Mode Squeezing-Rotating Entangled Representation

By virtue of the squeezing-rotating entangled representation, we mainly establish the new two-mode phase operator and phase angle operat, or, which is a general form including the foregoing formalist in two-mode Fock space. In addition, the corresponding phase distribution function is given in the entangled representation. In terms of this definition, we also analyze the phase behavior of some simple two-mode states such as squeezing-rotatlng coherent state, squeezing-rotating vacuum state, and so on. It is found that the results exactly agree with the foregoing phase theory.

Thyristor Controlled Phase Shifter:A Comprehensive Survey

Thyristor control phase shifter (TCPS) is one of the new facilities implemented in power network, leading to the development of economically efficient and technically reliable system. This paper introduces the function of TCPS in power system, describes its working principle and structure, and suggests some simple models used in its study and briefly presents the comparison between different types of TCPSs and their applications.