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Background and objective: Since industrialization, various communities worldwide have had to deal with the negative effects of pollution. Previous studies have investigated how communities affected by pollution can recover. However, few studies have explored the ways in which recovery takes place over time. This study examined the restoration process of the village of Jangjeom in Iksan, South Korea. The environmental contamination of the air and soil of this area, caused by a fertilizer factory, has been officially recognized. As such, its regional administration is planning its recovery with governmental support.Methods: This study conducted a content analysis of the meeting minutes of the government-civilian committee on environmental emergency measures in the village, using time-series text mining. The main phases and problems in the process of environmental pollution recovery were analyzed.Results: The results of the analysis show that, in the early days of this initiative, there were many discussions regarding the physical and environmental aspects of pollution and the legal framework required to investigate the sources of pollution. However, in later meetings, the focus shifted to how pollution affects the residents, covering topics such as residents’ health check-ups and consultations with experts and administrative agencies.Conclusion: This study shows that for the long-term recovery of communities damaged by pollution, a human-centered approach that goes beyond the physical and environmental aspects of recovery is needed.

Oocyte quality is essential for reproductive capacity, but it rapidly declines with age. In addition to aging, maternal nutrition is a major concern in maintaining oocyte quality. Gliadin, a major component of gluten, causes gluten toxicity, which has been reported in a variety of gluten-related disorders. The basis of gluten toxicity in reproduction is being understood using simple animal models such as

Purpose. To evaluate the clinical outcomes after bilateral mix-and-match cataract surgery using extended depth of focus (EDOF) and diffractive multifocal (DMF) intraocular lenses (IOLs). Setting. Asan Medical Center, Seoul, South Korea. Design. Prospective clinical study. Methods. Thirty-seven patients underwent TECNIS Symfony EDOF IOL (ZXR00) implantation in the dominant eye, and TECNIS +3.25 DMF IOL (ZLB00) implantation in the nondominant eye. Patients were followed up for 3 months; uncorrected and corrected distance visual acuity (UDVA and CDVA), uncorrected intermediate and near visual acuity (UIVA and UNVA), contrast sensitivity, defocus curves, stereopsis, and patient satisfaction were assessed. Results. At 3 months, the mean logarithm of the minimum angle of resolution (logMAR) of UDVA was 0.07 ± 0.09 in EDOF IOL eyes, 0.12 ± 0.11 in DMF IOL eyes, and 0.02 ± 0.05 in both eyes. UIVA was 0.11 ± 0.11 in EDOF IOL eyes, 0.16 ± 0.12 in DMF IOL eyes, and 0.04 ± 0.07 in both eyes. UNVA was 0.25 ± 0.15 in EDOF IOL eyes, 0.22 ± 0.16 in DMF IOL eyes, and 0.13 ± 0.13 in both eyes. Thirty patients (81.1%) were more than satisfied with near vision, and 8 patients (21.6%) complained of severe glare and halo. Spectacle independence for near vision was achieved in 34 patients (91.9%), and 31 patients (83.8%) had better than a 50-second arc of stereopsis. Conclusion. Mix-and-match cataract surgery with EDOF and DMF IOL implantation provided good visual outcomes for all distances. Additionally, excellent patient satisfaction was achieved with a high level of spectacle independence and acceptable photic phenomena.

Since there are various stakeholders related to water in Blue-Green Infrastructure that perform various ecological functions in a given city, there is a need for a plan to manage their interests and conflicts. Previous studies have verified the spatial preferences of many local residents using techniques, such as the public participation geographic information system, but have failed to show how stakeholders vary in regard to their dependence on water and their different spatial preferences. Therefore, this study intended to discuss the direction of collaborative planning by analyzing the Blue-Green Infrastructure of Siheung Hojobul wetland using spatial Q methodology, finding various stakeholders, and identifying the areas they prefer. The analysis results showed that local residents and environmental NGOs want to conserve middle and upper streams, but ecotourism guides and officials want to develop them for ecotourism, demonstrating a great difference in perspectives. However, they all agreed to develop a lower stream for ecotourism. Although this study has limitations as a single case study, the spatial Q methodology used in this study is significant in demonstrating that the use of the Blue-Green Infrastructure planning method for resident participation can reduce conflicts and encourage cooperation among competing parties.

A one-dimensional p-wave topological superconductor deformed by a sine-square-deformation is studied in the framework of machine learning. A supervised learning algorithm is applied with a convolutional neural network to discern the existence of a Majorana zero mode, which is the hallmark of topological superconductivity. The machine learning algorithm learns features of the Majorana zero mode, and the neural network trained with the dataset from the link deformed case turns out to be the most effective.

It is important to identify and manage regional natural resources to maximize ecosystem services. Although several studies have assessed ecosystem services using natural resources, they have failed to interpret the results spatially and to present regional policies. This study used factor analysis to map the results of an assessment of natural resources made by local ecologists to identify the main ecosystem services of the target area and their distribution. Spatial patterns were analyzed in the Namyangju area of South Korea, a water source for the Han River, where ecosystem services are paid for in monetary terms. Analyses revealed that cultural services predominated in the urban area, supporting services predominated in the mountain and river areas, and regulation services were emphasized at the points where mountains meet rivers. Mapping the results of inhabitant participation in the rapid function assessment of ecosystem services complements the mapping of general ecosystem service assessment, and can facilitate practical utilization.

Ecotourism facilities are designed to provide amenities for eco-tourists and spaces for local residents’ activities, but can also generate conflicts with local stakeholders. Using Q methodology, wh...

Ecosystem service valuations provide imperative data that is valuable for policy makers. However, the valuations are seldom adopted in national policymaking. In order to promote the use of ecosystem service valuations in policy and decision-making, a two-mode network analysis was conducted in order to investigate trends in ecosystem service valuation research in South Korea. According to the results, the “contingent valuation method” and “choice experiment” showed high connectivity with ecosystem type and service and were frequently employed by valuators. In contrast, the “net factor income” and “contingent ranking method” showed low connectivity and low frequency of use. The ecosystem types “forest”, “farmland,” and “coastal systems” showed high connectivity with the valuation methodologies and high frequency of use whereas “grassland” and “urban” showed low connectivity and frequency of use. The ecosystem services “aesthetic value/amenities/inspiration” and “recreation/ecotourism” showed high connectivity with the methodologies and high frequency of use whereas “forest products” and “natural resources” showed low connectivity and frequency of use. This study identified trends in ecosystem service valuation research in South Korea, and these trends can be used to guide the direction of future research and aid in the selection of methodologies according to ecosystem type and services.

This study aimed to evaluate the efficacy and safety of transplantation with human corneal limbal epithelial (HCLE) cell sheets cultured on carboxymethyl cellulose (CMC)-dopamine (DA)-coated substrates and harvested via enzymatic digestion of CMC with cellulase in a rabbit animal model of limbal stem cell deficiency (LSCD). Synthesized CMC-DA was pretreated onto the surface of culture plates. Then, HCLE cells were cultured on precoated CMC-DA and HCLE cell sheets were harvested using cellulase-containing cell culture medium. HCLE cell sheets were evaluated using a live/dead assay, histological examination, and immunofluorescence staining. For in vivo assessment, HCLE cell sheets were transplanted in a rabbit model of LSCD for 2 weeks to determine the effectiveness of the repair. Primary culture of HCLE cells stained positively for p63, cytokeratin (CK)15, and CK12. HCLE cell sheets were generated with a well-preserved morphology and transparency ranging in size from 15 to 19 mm after cellulase-assisted cell sheet generation. HCLE cell sheets uniformly stained positively for human mitochondria, p63, CK15, CK12, CK3/2p, and zonula occludens (ZO)-1. HCLE cell sheet transplantation in a rabbit model of LSCD improved the corneal opacity and neovascularization scores. Transplanted HCLE cell sheets stained positively for p63 and CK12. Transplantation of HCLE cell sheets harvested on CMC-DA coating combined with cellulase is a safe and efficient procedure for corneal epithelial regeneration in a rabbit model of LSCD. This system could enable a promising strategy to regenerate corneal epithelium by transplantation in ocular surface disorders.

Purpose To compare the protective effects of cyclosporine A emulsion (Restasis: 0.05% cyclosporine A) (CsAE) and cyclosporine A cationic emulsion (Ikervis: 0.1% cyclosporine A) (CsACE) on cellular inflammation, apoptosis, proliferation, and survival in an in vitro dry eye model. Methods The concentration of CsA in CsAE and CsACE was verified using a liquid chromatography tandem mass spectrometry system. Human corneal epithelial cells were subjected to desiccation stress. Human corneal epithelial cells were incubated with or without 3 groups of cyclosporine A medium (CsAE 1:50, CsACE 1:50, and CsACE 1:100). p-NF-κB p65, p-IκBα, Bax, Bcl-xL, p-Erk1/2, and p-Akt levels were determined using Western blots, and TNF-α levels were quantified using an enzyme-linked immunosorbent assay. Results The CsA concentration of CsACE 1:100 was nearly the same as that of CsAE 1:50. Compared with CsAE 1:50 (0.78 ± 0.19 fold), the p-NF-κB p65 level was further reduced in CsACE 1:50 (0.38 ± 1.20 fold) and 1:100 (0.29 ± 0.11 fold) as well as p-IκBα. Levels of TNF-α were also lower in CsACE 1:50 and 1:100 than in CsAE 1:50. Induction of the apoptotic protein Bax was significantly decreased in CsACE 1:50 and 1:100 compared with CsAE 1:50, whereas that of the antiapoptotic protein Bcl-xL was increased in CsACE 1:50 and 1:100. p-ERK1/2 and p-Akt levels were higher in CsACE 1:50 and 1:100 than in CsAE 1:50. Conclusions CsACE had more potent anti-inflammatory and antiapoptotic effects than CsAE in a transwell desiccation stress model. CsACE also enhanced proliferation and survival factors under desiccation stress compared with CsAE in this in vitro dry eye model.

Recently, incinerators have been shifted to underground complexes because of concerns regarding environmental pollution and declining land prices. In Korea, an underground waste incinerator has been built for the first time, with additional construction being expected in the near future. Therefore, a perception survey was conducted to acquire responses from South Korean experts regarding the impact of underground complex incinerators. The Q-methodology was used in the survey to examine various viewpoints. Academicians showed concerns regarding environmental effects of ground incinerators, and environmental and economic effects of underground complex incinerators, conversely, industrialists were concerned about civil complaints and administrative processing, indicating that the academicians were more concerned about scientific issues, whereas the industrialists were more concerned about democratic issues. Furthermore, both groups expressed concerns regarding land value and civil complaints of ground incinerators, safety issues and resultant social distrust of underground incinerators. The findings suggest that, to address the safety issues involving underground incinerator construction, governance by local experts is required for a holistic evaluation of environmental issues and economic feasibility of underground incinerators. To establish a link between science and democracy, measures for transparently sharing information are necessary.

Environmental pollution causes severe damage to local communities, which is perceived differently by different victims, that is, the damage is discriminatory. However, previous studies have not focused on this aspect. Here, we explored the perceptions of different victims of the Hebei Spirit oil spill incident of Korea. Additionally, we explored the importance of considering discriminatory aspects of damage when planning recovery governance. The damages from the oil spill were analyzed using a text mining technique for each subject based on factor analyses. Women and residents older than 60 years were interested in the social relations of the village community, residents in their 40s, who were raising children and teenagers, were interested in the economic aspects, boat fishermen, who had discontinued fishing to participate in the pollution response activity in the early stages of the incident, were interested in disaster prevention, and women divers were interested in health issues. Hence, restoring the economy and environment and reversing indirect social damages are essential for recovery from pollution damage. Furthermore, governance for recovery must not exclude specific victims based on the discriminatory aspects of damages. A political process is necessary to secure the validity of governance and alternatives by involving different victim groups.

The sine-square deformation of the lattice model of one-dimensional p-wave topological superconductor is studied focusing on the existence of the zero energy Majorana fermion localized at the ends of the superconductor. The deformation is applied in two distinct ways depending on whether the interaction in the Hamiltonian is defined on the lattice link and/or the lattice site. The zero energy Majorana fermion is found to survive both kinds of the deformations while the overall single particle energy spectrum is substantially modified.

Ecotourism planning must consider the location of ecological resources, residents' homes, and infrastructure. In numerous studies using environmental and physical data, efficient ecotourism planning is considered “development-unfriendly and negligent toward the environment” by locals. This study analyzes the preference relationships of stakeholders' spaces through conflict mapping using Q methodology. Such mapping of stakeholder interests between two specific periods in the Maha ecotourism site, Pyeongchang, Korea, where ecotourism development conflicts peaked recently, revealed that minimizing the scale of facilities in accordance with residents’ opinions would also minimize conflict. Additionally, the concerns expressed during the early stages of development pertained to ecotourism facilities and road maintenance, which were assumed to vitalize the local community by attracting tourists. However, in terms of ecological resource maintenance, its improvement, and the use of village public spaces, a strong preference was gradually shown for spaces intended for both tourists and residents.

Ecosystem service assessment maps are an important form of data, showing the flow and characteristics of ecosystem services. However, there has been a lack of research on the spatial boundaries of synergetic and trade-off relationships among different types of ecosystem services based on the microscopic characteristics of ecosystem maps. Therefore, the boundaries of ecosystems were identified in this study using factor analysis of indicators in ecosystem service maps. Ecosystems were mapped for each indicator in each cell, and then factor analysis was used to combine all indicators into one map. Analysis of Seocheon in central South Korea shows the boundaries of two ecosystem types: a mountainous region with abundant underground water and carbon stocks that lack rice paddies, and flatlands with high crop production and a lack of scenic views. The spatial types of ecosystems in which synergy and trade-offs occur were identified by indicator, and these can be used as evidentiary material for spatial planning in order to maximize the function of each ecosystem service.

Biosphere reserves designate ecologically superior and sensitive areas for local biodiversity and sustainable use. Despite their promised benefits, some areas fail to be designated as biosphere reserves due to opposition by local residents. This study investigates the causes of failed biosphere reserve designation using a semantic network analysis of local resident meetings concerning designation of the Baekdudaegan mountain range as a biosphere reserve. The analysis results reveal that the main topics of discussion were legislation of the biosphere reserve, its administration, and the consultation process. The residents made strong demands on the legislative system and administrative operation, whereas the administrative agency attempted to solve this problem through the consultation process. This suggests that the agency in charge of designating biosphere reserves must first ensure transparency in the legislative and administration operation process, which may not be completely successful through the consultation process. When designating biosphere reserves in future, we recommend that authorities first establish guidelines for transparency in the legislation of regulations and the administrative operation process and obtain the trust of local people for the consultation process.

Background To evaluate the effects of lid debris debridement and meibomian gland expression (MGX) on extracellular matrix metalloproteinase-9 (MMP-9) levels and clinical outcomes of moderate and severe MGD. Methods In this retrospective case series study, a total 48 eyes of 24 patients with moderate and severe MGD underwent one session of lid debris debridement using the BlephEx combined with MGX. We evaluated the tear film break-up time (TBUT), corneal and conjunctival fluorescein staining scores, Schirmer 1 test, biomicroscopic examination of lid margins and meibomian gland (MG), ocular surface disease index (OSDI) questionnaire score, and extracellular MMP-9 levels using a point-of-care MMP-9 immunoassay device before and 4 weeks after lid debris debridement and MGX. Linear mixed model and generalized estimating equations model were used to evaluate possible differences. Results There were significant improvements in the TBUT (P = 0.002), SICCA and Oxford staining scores (all P P P P P = 0.026 for upper eyelid, P P P P P = 0.002). MMP-9 immunoassay positivity rate significantly decreased from 83.3 to 50.0% 4 weeks after treatment (P = 0.014). Conclusions In patients with moderate to severe MGD, lid debris debridement using the BlephEx combined with MGX improved clinical findings, subjective symptoms, meibomian gland function, along with ocular surface MMP-9 level. We hereby suggest lid debris debridement using BlephEx combined with MGX as an effective clinical strategy for treatment of moderate to severe MGD.

Purpose: To test the hypothesis that ocular pigment in patients with oculodermal melanocytosis decreases myopia severity. Methods: Refractive and biometric parameters were measured and compared between pigmented eyes and non-pigmented contralateral eyes in oculodermal melanocytosis patients that underwent surgical ocular pigmentation removal. To assess pigmentation, the pigmentation score was measured in each quadrant of the sclera and added together for a cumulative score. For subgroup analyses, patients were categorized into three groups according to the severity of myopia in the non-pigmented eye. Results: Fifty-five patients (110 eyes) were included. Spherical power and spherical equivalent were significantly less myopic in pigmented eyes relative to contralateral non-pigmented eyes. The spherical powers of non-pigmented eyes were positively correlated with the difference in spherical power between contralateral eyes (r = 0.697, p p = .005). In subgroup analyses, pigmented eyes exhibited significantly less myopic spherical powers and spherical equivalents than non-pigmented contralateral eyes in the moderate and high myopia groups. Pigmented eyes exhibited significantly shorter axial length than non-pigmented contralateral eyes in the high myopia group only. Conclusions: In patients with oculodermal melanocytosis, pigmented eyes exhibited less severe myopia relative to non-pigmented contralateral eyes. This suggested that ocular pigmentation inhibited myopic changes, potentially by blocking UV transmission. This study will be helpful in elucidating the mechanisms of myopic progression.

Purpose To compare clinical outcomes of a new monofocal intraocular lens (IOL) with enhanced intermediate function and an extended-depth-of-focus (EDOF) IOL. Setting Asan Medical Center, Seoul, Korea. Design Nonrandomized prospective comparative case series. Methods Patients presenting for cataract surgery and meeting all inclusion and exclusion criteria were implanted with new monofocal IOLs with enhanced intermediate function (Tecnis Eyhance ICB00) or EDOF IOLs (Tecnis Symfony ZXR00) bilaterally. Uncorrected distance visual acuity (UDVA), uncorrected intermediate visual acuity (UIVA), uncorrected near visual acuity (UNVA), corrected distance visual acuity (CDVA), defocus curves, and contrast sensitivity were compared after 3 months. Patients were administered questionnaires regarding visual symptoms, spectacle independence, overall satisfaction, and lens recommendations. Results Twenty-four patients (48 eyes) were enrolled in the Eyhance group and 20 patients (40 eyes) in the Symfony group. Monocular and binocular UDVA, UIVA, and CDVA were similar in the two groups. Monocular UNVA and spectacle independence for near distance were better in the Symfony group, whereas binocular UNVA did not differ significantly in the two groups. Contrast sensitivity, glare and halo, satisfaction, and recommendation rates were similar in the two groups. Although some dissatisfaction and severe glare and halo were reported in the Symfony group, none of these was reported in the Eyhance group. Conclusions Bilateral implantation of the new Eyhance ICB00 IOLs provided comparable clinical performances as bilateral implantation of Symfony ZXR00 IOLs. Binocular UNVA was similar, although spectacle independence was higher in the Symfony group, but this was at the expense of more glare and halos.

Highlights • Among 694 inpatients with COVID-19, 137 patients were classified as severe cases. • No severe case was observed among patients aged ≤ 19 years • Asymptomatic patients accounted for 14.4% of cases. • The first outbreak was mostly associated with younger age groups • The number of severe patients and mortality rate were high in the second outbreak, Objectives The Coronavirus Disease 2019 (COVID-19) outbreak simultaneously occurred at a church and a long-term care facility in Daegu. This study aimed to investigate the epidemiological characteristics of COVID-19 and factors related to severe outcomes. Methods We enrolled all inpatients diagnosed with COVID-19 between February 21 and April 2, 2020 in Daegu Dongsan Hospital, South Korea. We analyzed their clinical and demographic data, laboratory parameters, radiological findings, symptoms, and treatment outcomes. Results Of 694 patients, severe cases accounted for 19.7% (137 patients). No severe case was observed among patients aged ≤19 years. Hypertension was the most common co-morbidity (27%), and cough was the most common symptom (59%). Besides, asymptomatic patients accounted for 14.4% of cases. Lymphopenia, lactate dehydrogenase, C-reactive protein, and albumin were associated with severe outcomes. The first outbreak was mostly associated with younger age groups, and asymptomatic patients mostly showed mild progression. In the second outbreak involving a long-term care facility, both the number of severe patients and the mortality rate were high. Conclusions The overall mortality in Daegu was low, which might have resulted from large scale mass screening to detect patients and starting appropriate treatment, including hospitalization for severe cases, and quarantine for asymptomatic patients.

Purpose: To evaluate clinical outcomes after bilateral mix-and-match cataract surgery using extended depth of focus (EDOF) and diffractive multifocal (DMF) intraocular lenses (IOLs). Methods: Thirty-seven patients received Tecnis Symfony EDOF IOL (ZXR00) implantation in the dominant eye, and Tecnis +3.25 DMF IOL (ZLB00) in the non-dominant eye. Patients were followed for 3 months, and uncorrected and corrected distance visual acuity (UDVA, CDVA) , uncorrected intermediate and near visual acuity (UIVA, UNVA), contrast sensitivity, defocus curves, stereopsis, and patient satisfaction were assessed. Results: At 3 months, mean logMAR UDVA was 0.07 ± 0.09 in EDOF IOL eyes, 0.12 ± 0.11 in DMF IOL eyes, and 0.02 ± 0.05 in both eyes. UIVA was 0.11 ± 0.11 in EDOF IOL eyes, 0.16 ± 0.12 in DMF IOL eyes, and 0.04 ± 0.07 in both eyes. UNVA was 0.25 ± 0.15 in EDOF IOL eyes, 0.22 ± 0.16 in DMF IOL eyes, and 0.13 ± 0.13 in both eyes. Thirty patients(81.1%) were more than satisfied with near vision, and 8 patients(21.6%) complained of severe glare and halo. Spectacle independence for near vision was achieved in 34 patients(91.9%), and 31 patients(83.8%) had better than a 50 second arc of stereopsis. Conclusion: Mix-and-match cataract surgery with EDOF and DMF IOL implantation provided good visual outcomes through all distances. Also excellent patient satisfaction was achieved with high level of spectacle independence and minimal photic phenomena.

Background: To evaluate the clinical outcomes of bilateral mix-and-match implantation of diffractive multifocal intraocular lenses (IOLs) with different add powers.Methods: We retrospectively reviewed the medical records of 18 patients who underwent bilateral mix-and-match implantation of diffractive multifocal IOLs with different add powers. Multifocal IOLs with add powers of +2.75 diopters (D) and +4.00 D were implanted into the patients’ dominant and nondominant eyes, respectively. At 1 and 3-month postoperatively, monocular and binocular visual acuity was measured using logMAR charts and manifest refraction was performed. Specifically, logMAR charts were used to measure uncorrected distance visual acuity (UDVA), uncorrected intermediate visual acuity (UIVA), uncorrected near visual acuity (UNVA), and corrected distance visual acuity (CDVA). Defocus curves, contrast sensitivity, and patient satisfaction were assessed at 3-month postoperatively.Results: Binocular logMAR measurements (mean ± standard deviation) at 3-month postoperatively were 0.01±0.04 (UDVA), 0.16±0.05 (UIVA), and 0.11±0.07 (UNVA). Postoperative spherical equivalent was -0.43±0.35 D and -0.39±0.21 D in the dominant and nondominant eyes, respectively. Defocus curves showed significant differences between -1.50 and -4.00 D among binocular, dominant, and nondominant eye measurements, except between -2.50 and -3.00 D. Eyes implanted with +2.75 and +4.00 D IOLs showed good contrast sensitivity under photopic and mesopic conditions. Over 80% of patients reported high satisfaction with their near vision.Conclusions: Bilateral mix-and-match implantation of diffractive multifocal IOLs with add powers of +2.75 D and +4.00 D showed good near, intermediate, and far vision.Trial registration: Clinical Research Information Service[Internet]; Osong(Chungcheongbuk-do): Korea Centers for Disease Control and Prevention, Ministry of Health and Welfare (Republic of Korea), KCT0003945, Registered 20 May 2019 – Retrospectively registered, https://cris.nih.go.kr/cris/search/search_result_st01_kren.jsp?seq=13946&sLeft=2&ltype=my&rtype=my

The non-equilibrium dynamics of the excitonic insulator order parameter in the excitonic insulator phase of the Falicov–Kimball model excited by ultrashort laser pulse is studied. The Keldysh–Schwinger functional integral method with the saddle point approximation is employed. The numerical solution for the order parameter obtained from the saddle point equation is found to exhibit oscillatory behaviors, whose frequencies are consistent with the energy gap of the excitonic insulator. The fluctuations of the order parameter around the saddle point are identified with the collective modes in non-equilibrium states, and their Green’s functions are explicitly found in terms of the saddle point solution. Also, the interaction vertices responsible for the decay of the non-equilibrium order parameter is found, and the lowest order contribution for the decay process is expressed in terms of the vertices and the Green’s functions of the non-equilibrium collective modes. In the presence of a particular electron–phonon interaction, a hybrid mode of the excitonic order parameter and the phonon can be naturally defined in functional integral and its saddle point equation can be derived. It is shown that the saddle point solution with electron–phonon interaction is consistent with the experimental data and the existing theoretical result.