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外文文献原稿和译文

外文文献原稿和译文
外文文献原稿和译文

外文文献原稿和译文

原稿

Pharmacokinetic study of six flavones in rat plasma and tissues after oral administration of ‘JiangY aBiFeng’ using SPE-HPLC-DAD Abstract

In this study, a high performance liquid chromatography (HPLC) coupled with diode array detection (DAD) for simultaneous determination of six flavones including baicalein, sophoricoside, rutin, baicalin, quercetin and genistein in rat plasma and tissues after oral administration of JiangYaBiFeng (JYBF) tablets was developed. The investigated analytes in plasma and tissues were extracted and purified with liquid -liquid extraction and solid phase extraction (SPE). Chromatographic separation was accomplished on a DIONEX Acclaim C18 column (250mm×4.6mm, 5.0μm particle size) with a simple linear gradient elution. The calibration curves for all the flavones had good linearity in the measured range with R2 higher than 0.9983. The relative errors (REs) of the intra– and inter–day accuracy at different flavones levels were all less than ±10%. The proposed method enables unambiguous identification and quantification of investigated flavones in vivo. This is the first report on determination of the major flavones in rat plasma and tissues after oral administration of JYBF tablets. The result provided a meaningful basis for evaluating the clinical application of this medicine.

Keywords: JiangYaBiFeng tablet; Flavones; HPLC–DAD; Rat plasma; Tissue distribution

1. Introduction

‘JiangYaBiFeng’tablet (JYBF tablet), a new drug for the treatment of hypertension has been widely used in the clinic in china because of its good effect and small side effects. It is composed of two western medicines (pargyline and

hydrochlorothiazide) and three traditional Chinese medicines (TCMs), including Scutellaria baicalensis, Sophora japonica and Arachis hypogaea. According to some reported papers, flavones, such as baicalin, baicalein, sophoricoside, rutin, quercetin and genistein originally from the three TCMs are the main effective components contained in this formulation. Because the therapeutic effects of TCMs are based on the complex interactions of multiple ingredients, investigation of the pharmacokinetic studies of multi flavones after administration of JYBF tablets is essential to understand their role in human health and evaluate the clinical efficacy of this medicine. However, as far as we know, such relevant reports have not been found in the literature.

In this study, a reliable SPE–HPLC–DAD method for the simultaneous determination of six active components (including sophoricoside, rutin, baicalin, baicalein, quercetin and genistein) in rat plasma and tissues after oral administration of JYBF tablet was developed and validated. The pharmacokinetics of this flavones in plasma and tissue were first investigated and the obtained results would be very helpful for evaluating the clinical application of this medicine.

2. Experimental

2.1. Chemicals and reagents

JYBF tablet was supplied by Chinese pharmaceutical manufacturer (Zhongxin, Tianjin, China). Baicalin, baicalein, sophoricoside, rutin, quercetin and genistein were obtained from the National Institute for the Control of Pharmaceutical and Biological Products (Beijing, China). HPLC grade acetonitrile and methanol were purchased from Tianjin Kermel Chemical Regent Company (Tianjin, China). Others reagents were all of analytical grade. Ultrapure water was generated from the Milli-Q system (Millipore, Bedford, MA, USA).

2.2. Instrumentation and analytical conditions

The HPLC system Dionex P680 series (Dionex, USA), equipped with the Chromeleon software (Dionex) and comprised a quaternary pump, an online vacuum degasser, a manual sampler, a thermostated column compartment and a diode array detection (DAD), was used for the chromatographic analysis. All separations were carried out on a DIONEX Acclaim C18 column (250mm×4.6mm id, 5.0μm particle

size) with a gradient elution of the mobile phase system consisting of acetonitrile (A) and 50mM ammonium dihydrogen phosphate (pH 3.0) (B). The elution program was performed as the following: 78-73% A at the beginning of 12min, then 73-67% A within 12-22min and 67% A at the last 10min. The flow rate was 1.0mLmin-1. Column temperature was maintained at 25℃. According to the different absorption spectrums of the described flavones, effluent was monitored at 256nm for sophoricoside, rutin, quercetin, genistein and 280nm for baicalin and baicalein. The injection volume was 20μL. The peak identification was based on the retention time and the DAD spectrum against the standard presented in the chromatogram.

The SPE cartridges (C18, 45μm particle size, 50mg) were purchased from Agela Technologies Inc. (USA). Before used, they were successively preconditioned with 1mL of methanol and 1mL of distilled water.

2.3. Preparation of standard solutions, calibration standards and

quality samples

The stock solutions of the investigated flavones were prepared in methanol, respectively. A series of standard mixture working solutions were obtained by diluting the mixture of the stock standard solutions with mobile phase.

Calibration standards of the mixture flavones were prepared by spiking the appropriate amount of the standard mixture working solutions into 200μL drug-free rat plasma or tissue homogenates to give nominal concentration range of 0.10-62.50μg mL-1for sophoricoside, rutin and quercetin, 0.10-100.00μgmL-1for baicalin and baicalein, 0.10-50.00μg mL-1 for genistein.

Quality control samples were prepared at low, medium and high concentrations (0.5, 5.0 and 50.0μg mL-1) in the same manner as the calibration standards, and used to assess the accuracy and precision of the method. The samples were extracted following the procedure described below.

2.4. Pretreatment of plasma or tissue sample

To 200μL of plasma or tissue homogenate samples, 500μL of 5% trichloroacetic acid was added. After centrifugation at 12000rpm for 10min at 4℃, the supernatant was collected and flowed through a pre-treatment C18 SPE cartridge with gravity. The solid-phase cartridge was washed with 1.0mL 5% methanol and then eluted with 1mL

of methanol. The methanol elute was evaporated to dryness under a stream of nitrogen at 50℃. The residue was dissolved into 100μL methanol for the HPLC analysis.

The extraction recovery analysis was conducted with spiked flavone biosamples at three QC levels and calculated by comparing the flavone peak area in extracted biosamples with those found by direct injection of standard solutions at the same concentration.

2.5. Method validation

The accuracy and precision of the established method were evaluated by QC samples at low, medium and high concentration. The concentration of each QC samples was calculated using calibration curves. Accuracy was defined as the relative deviation in the calculated value of a standard from that of its true value, expressed as relative error (RE). Precision was evaluated as the relative standard deviation (RSD). The intra-day accuracy was determined by assaying six replicates at each concentration level on 1 day, and inter-day accuracy was determined by analyzing QC samples in five duplicates during three separate and successive days.

The stability of flavones in biosamples was investigated under a variety of storage and process conditions. For storage stability, samples (5.0μg mL-1 of flavones in plasma and tissue) were prepared and stored at ﹣20℃ for 30 days. On the 30th day, all samples were thawed and analyzed along with the freshly prepared set of quality control samples; for freeze-thaw stability testing, the QC were determined after three freeze-thaw cycles and the concentration were compared to their nominal concentrations.

2.6. Pharmacokinetic study in rat plasma and tissue

Male and female Sprague-Dawley rats weighing 220-250g were obtained from the Henan Laboratory Animal Center (Zhengzhou, China). After breeding in a controlled environment for 5 days, the rats were orally administrated JYBF tablets at a dose of 2.0gkg-1(approximately 7.56mgkg-1sophoricoside, 17.56mgkg-1rutin, 52.48mgkg-1baicalin, 0.32mgkg-1quercetin, 0.68mgkg-1genistein and 66.05mgkg-1 baicalein). For pharmacokinetic study, the blood samples (0.5mL) of 5 rats were collected from the fossa orbitalis vein according to the specific schedule at times of 10, 20, 30, 45, 60, 90, 120, 180, 240, 360, 480 and 720min after dosing. The blood

samples were immediately transferred to heparinized tubes and centrifuged at 4000rpm for 10min. The separated plasma was frozen at ﹣20℃before assay. For tissue distribution study, 30 rats were assigned randomly to three groups. After administration of JYBF tablets as described above, tissues including heart, liver, spleen, lung, kidney, stomach, small intestine and brain were obtained at 10, 20, 30, 45, 60, 90, 120, 180 and 240min after administration. All samples were thoroughly rinsed of residual blood and other contents with physiological saline solution. Then each sample was blotted on filter paper and then weighed for wet weight and individually homogenized with the same mass of saline solution. The obtained tissue homogenates were stored at ﹣20℃ until analysis.

3. Results and discussion

3.1. Selectivity

The selectivity of the method was tested by comparing the chromatograms of blank plasma and tissue, spiked plasma and tissue and actual plasma and tissue samples after oral administration of JYBF tablets at a dose of 2.0gkg-1. It was indicated that analytes were well separated and no interferences were detected from endogenous substances or metabolites. The representative chromatograms for determination of analytes in plasma and tissues are shown in Figs. 1 and 2, respectively.

3.2. Linearity, limit of detection and limit of quantification

The linear regression of the investigated flavones in rat plasma and tissues was constructed by plotting peak area with concentration of standard solutions. The calibration curves showed good linearity over the concentration range 0.10-62.50μg mL-1for sophoricoside, rutin and quercetin, 0.10-100.00μg mL-1for baicalin and baicalein, and 0.10-50.00μg mL-1 for genistein in all biosamples with a correlation coefficient (R2) larger than 0.9983. The limits of detection (LOD, S/N=3) and the lower limits of quantification (LLOQ, S/N=10) for sophoricoside, rutin, baicalin, quercetin, genistein and baicalein were 0.04, 0.01, 0.05, 0.03, 0.05, 0.02μg mL-1 and 0.13, 0.04, 0.15, 0.08, 0.15, 0.07μg mL-1, respectively.

Fig. 1. Representative chromatograms of blank plasma (A), plasma sample spiked with six flavones (B, 10μg mL-1 sophoricoside, 30μg mL-1 rutin, 20μg mL-1 baicalin, 10μg mL-1quercetin, 10μg mL-1genistein, 10μg mL-1baicalein) and a plasma sample collected from a rat at 1h after an oral administration of JYBF tablet (C). Ⅰ: 256nm; Ⅱ: 280nm. (1) Sophoricoside, (2) rutin, (3) baicalin, (4)

quercetin, (5) genistein and (6) baicalein.

Fig. 2. Representative chromatograms of blank liver tissue (A), liver tissue sample spiked with six flavones (B, 10μg mL-1sophoricoside, 30μg mL-1rutin, 20μg mL-1 baicalin, 10μg mL-1 quercetin, 10μg mL-1 genistein, 10μg mL-1 baicalein) and a liver tissue sample collected from a rat at 1h after an oral administration of JYBF tablet (C). Ⅰ: 256nm; Ⅱ: 280nm. (1) Sophoricoside, (2) rutin, (3)

baicalin, (4) quercetin, (5) genistein and (6) baicalein.

3.3. Method validation

Intra- and inter-day precision and accuracy were determined by measuring QC samples as described in Section 2. The relative errors (REs) were obtained ranging from ﹣9.6% to 8.8% in intra-day accuracy and from ﹣9.8% to 7.0% in inter-day accuracy with RSD less than 9.0%. The results indicated that overall reproducibility of the method was acceptable.

The mean extraction recoveries of the investigated flavones in plasma at three different concentration levels were found to be 90.2-95.96% with RSD less than 8%, and the mean recoveries in all tissue samples were above 88.7%.

The stability of the investigated flavones evaluated by analyzing the QC samples according to the procedures described in Section 2.5. The RSD of the concentrations of the QC samples tested were all within 5%. The results suggested that all the analytes were stable under the indicated storage conditions.

3.4. Pharmacokinetics study

The mean plasma concentration-time profiles of the investigated components were shown in Fig. 3, demonstrating that flavones was rapidly absorbed and then slowly decreased. The pharmacokinetics model and the parameters were calculated by the practical pharmacokinetics program 97 (3P97). It was found that the concentration-time profile was best described by the two-compartment model for all flavones. The main pharmacokinetics parameters are summarized in Table 1.

3.5. Tissues distribution study

The AUC of six investigated flavones is shown in Fig. 4. It was indicated that all flavones could be rapidly absorbed and distributed to all collected tissues except quercetin and genistein. At predetermined times, quercetin and genistein were few or undetectable in both brain and spleen, demonstrating that they have difficulty crossing the blood-brain barrier and spleen might not be the primary absorbent organ of them.

4. Conclusion

In this paper, a SPE-HPLC-DAD method for simultaneous determination of six flavones including baicalein, sophoricoside, rutin, baicalin, quercetin and genistein in rat plasma and tissues after oral administration JYBF tablet was developed and validated. The achieved pharmacokinetics and tissue distribution results may be useful for further study of the bioactive mechanism of a new Chinese medicine-JYBF tablet.

译文

使用固相萃取-高效液相色谱二极管阵列检测法对口服降压避风片后大鼠血浆和组织中六种黄酮类化合物的药物代谢动力学研究

摘要:在这项研究中,采用高效液相色谱与二极管阵列检测器联用技术同时测定口服降压避风片后大鼠血浆和组织中的六种黄酮类化合物,这些化合物分别是黄芩素、槐角苷、芦丁、黄芩甙、槲皮素和染料木黄酮。这项研究是用液-液萃取和固相萃取的方法进行萃取纯化血浆和组织中的被分析物。色谱分离是在DIONEX Acclaim C18 色谱柱(250mm×4.6mm, 填料粒径5.0μm)上用一个简单的线性梯度洗脱完成的。黄酮类化合物的标准曲线在测量范围内线性关系良好,相关系数R2 大于0.9983。不同种类黄酮化合物含量日内及日间精密度的相对误差都在±10%以内。本文所提及的方法能够准确的鉴定体内的黄酮类化合物并测量出它的含量。这是对口服降压避风片后大鼠血浆和组织中的主要黄酮类化合物含量测定的首次报道。此结果为该药的临床应用提供了较好的理论依据。

关键词:降压避风片;黄酮;高效液相色谱-二极管阵列检测法;大鼠血浆;组织分布

1. 引言

降压避风片是一种新的治疗高血压的药物。由于其疗效好、副作用小,在中国这种药物已经广泛的应用于临床上。它是由两种西药(优降宁和氢氯噻嗪)和三种中药(黄芩、中国槐和花生)构成的。根据一些文献的报道,该药剂配方的主要有效成分是黄酮类化合物。这些黄酮类化合物,像是黄芩素、槐角苷、芦丁、黄芩甙、槲皮素和染料木黄酮,最早都来源于这三种中药。因为中药的治疗效果大都是基于多种成分复杂的相互作用,所以对于服用降压避风片后多种黄酮类化合物的药物代谢动力学研究在了解该药剂对人类健康的影响和该药物临床疗效的评价方面起到了至关重要的作用。然而,据我们所知,在文献中还没有发现这样的相关报道。

在这项研究中,一种可靠的固相萃取-高效液相色谱二极管阵列检测法已经被研发并得到了验证。这种检测方法可以同时测定口服降压避风片后大鼠血浆和组织中的六种活性成分(包括槐角苷、芦丁、黄芩甙、黄芩素、槲皮素和染料木

黄酮)。这是首次对于血浆和组织中黄酮类化合物的药代动力学研究,并且所得到的结果对该药的临床应用是非常有帮助的评估。

2. 实验

2.1 化学试剂

降压避风片是由中国制药厂(天津市中兴公司)供应的。黄芩甙、黄芩素、槐角苷、芦丁、槲皮素和染料木黄酮购买于中国药品生物制品检定所(中国北京)。高效液相色谱级乙腈和甲醇从天津科密欧化学试剂公司(中国天津)购买。其他试剂均为分析纯。超纯水由Milli-Q级的超纯水系统供水(微孔过滤器生产于美国麻萨诸塞州贝德福德市)。

2.2 仪器分析条件

进行色谱分析需要一台有着Chromeleon色谱管理软件并且包含四元液相泵配置的Dionex P680的高效液相色谱仪,联机真空脱气装置,手动取样器,恒温柱室以及二极管阵列检测器。所有的分离过程是在DIONEX Acclaim C18 色谱柱(250mm×4.6mm不锈钢柱, 填料粒径5μm)中进行梯度洗脱的。其中流动相A是乙腈,流动相B是pH为3的磷酸二氢铵溶液。洗脱程序如下进行:最初的12min通过78-73%的A,然后通过73-67%的A 12-22min,最后的10min通过67%的A。流速为1.0mLmin-1。柱温保持在25℃。根据所描述的黄酮类化合物的吸收光谱不同,提取液中槐角苷、芦丁、槲皮素的检测波长为256nm,黄芩素、黄芩甙的检测波长为280nm。进样量20μL。谱峰识别是基于色谱图中出现的相对标准的保留时间和二极管阵列检测器光谱。

固相萃取柱(C18, 填料粒径45μm, 50mg)购自美国的博纳艾杰尔科技公司。在使用之前要依次用1mL甲醇和1mL蒸馏水进行预处理。

2.3 标准溶液、校正标准和质量样品的制备

被研究的黄酮类化合物的储备液分别以甲醇为溶剂制得。一系列标准混合溶液是用流动相稀释标准储备液的混合物制得的。

黄酮混合液校正标准的制作方法是在200μL无药物的大鼠血浆或组织匀浆中加入适量的标准混合液。使得槐角苷、芦丁、槲皮素额定的标称浓度范围是0.10-62.50μg mL-1,黄芩甙、黄芩素的标称浓度范围是0.10-100.00μg mg-1, 染料木黄酮的标称浓度范围是0.10-50.00μg mL-1。

分别用低(0.5μg mL-1)、中(5.0μg mL-1)、高(50.0μg mL-1)三种不同质量浓度的样品溶液在相同的条件下制作校正标准,用于评估该方法的准确度和精密度。样

品按照下面描述的步骤进行萃取。

2.4 血浆或组织样品的预处理

在200μL的血浆或组织匀浆样品中加入5%的三氯乙酸500μL。在4℃时以12000转/分的转速离心分离10min后,收集上层清液,由于重力的作用流经C18固相萃取柱进行预处理。固定相色谱柱要先用1.0mL 5%的甲醇溶液淋洗,再用1mL 甲醇洗脱。该甲醇的流出液在50℃的氮气流中蒸发至干。将残留物溶解在200μL 甲醇中进行高效液相色谱分析。

提取回收率的计算方法是,对加标黄酮生物样本进行三个水平的质量鉴定,其结果与直接注射相同浓度标准溶液所得结果进行对比,通过黄酮类化合物的峰面积进行计算。

2.5 方法验证

通过进行低、中、高三种浓度水平的质量鉴定对所建立的方法进行准确度和精密度的评估。使用标准曲线计算每个品质控制样品的浓度。准确度是计算值与真值之间的相对偏差,用相对误差来表示。精密度用相对标准偏差来衡量。日内精密度由一日之内每种浓度水平的六次平行试验结果确定,而日间精密度由连续三天中五次对样品的质量鉴定分析结果确定。

在各种各样的储存工艺条件下研究生物样品中黄酮类化合物的稳定性。对于储存稳定性来说,提取5.0μg mL-1血浆和组织中的黄酮类化合物并在﹣20℃的条件下保存30天。到第30天时,把所有样品解冻后与新制备的一组质控样品一同分析;在冻融稳定性试验中,质量控制在三个冻融周期后进行并将其浓度与标准浓度比较。

2.6 大鼠血浆和组织中的药代动力学研究

体重为220-250g的雄性和雌性SD大鼠由河南省实验动物中心(中国郑州)提供。大鼠在特定的环境下生长5天后口服剂量为2.0gkg-1的降压避风片(大约含槐角苷7.56mgkg-1,芦丁17.56mgkg-1,黄芩甙52.48mgkg-1,槲皮素0.32mgkg-1,染料木黄酮0.68mgkg-1,黄芩素66.05mgkg-1)。5只大鼠在服药10、20、30、45、60、90、120、180、240、360、480、720min后,从眼眶静脉中分别抽取0.5mL血浆样本进行药代动力学研究。血样被立即转移到肝素管中并以4000转/分的转速离心10min。已分离的血浆在﹣20℃冷冻后进行检测。在组织分布的研究中30只大鼠被随机分为3组。如上述方法服用降压避风片,在服药10、20、30、45、60、90、120、180、240min后分别获取心脏、肝、脾、肺、肾、胃、小肠和脑中的组

织。所有的样品都要用生理盐水把残留的血液和其它杂物冲洗干净。然后把每个样品涂抹在滤纸上称量湿重并且用相同质量的生理盐水匀浆。获得的均匀组织在﹣20℃时保存直至进行分析。

3. 结果与讨论

3.1 分离度

通过比较口服剂量为2.0gkg-1降压避风片后空白的血浆和组织、加入标样的血浆和组织以及实际样品的色谱图,测试出该方法的分离度。结果表明分析物已被很好的分离且内源性物质和代谢产物不干扰测定。图1和图2是测定血浆和组织中分析物最具有代表性的色谱图。

图1.(A)空白血浆的色谱图(B)血浆样品中添加六种黄酮类化合物(槐角苷10μg mL-1,芦丁30μg mL-1,黄芩甙20μg mL-1,槲皮素10μg mL-1,染料木黄酮10μg mL-1,黄芩素10μg mL-1)的色谱图(C)口服降压避风片一小时后大鼠血浆样品的色谱图。Ⅰ: 256nm; Ⅱ: 280nm。(1)槐角苷,(2)芦丁,(3)黄芩甙,(4)槲皮素,(5)染料木黄酮,(6)黄芩素。

图 2. (A)空白肝组织的色谱图(B)肝组织样品中添加六种黄酮类化合物(槐角苷10μg mL-1,芦丁30μg mL-1,黄芩甙20μg mL-1,槲皮素10μg mL-1,染料木黄酮10μg mL-1,黄芩素10μg mL-1)的色谱图(C)口服降压避风片一小时后大鼠肝组织样品的色谱图。Ⅰ: 256nm; Ⅱ: 280nm。(1)槐角苷,(2)芦丁,(3)黄芩甙,(4)槲皮素,(5)染料木黄酮,(6)黄芩素。

3.2 线性度、检出限和定量限

大鼠血浆和组织中黄酮类化合物的线性回归关系通过测量一定浓度标准溶液峰面积得到。标准曲线在生物样品中槐角苷、芦丁、槲皮素0.10-62.50μg mL-1,黄芩甙、黄芩素0.10-100.00μg mL-1,染料木黄酮0.10-50.00μg mL-1的浓度范围内线性关系良好,且相关系数大于0.9983。槐角苷、芦丁、黄芩甙、槲皮素、染料木黄酮、黄芩素的检出限(LOD, S/N=3)和定量限(LLOQ, S/N=10)分别是0.04、0.01、0.05、0.03、0.05、0.02μg mL-1和0.13、0.04、0.15、0.08、0.15、0.07μg mL-1。

3.3 方法验证

日内及日间精密度和准确度通过测量第二部分讲述的质量样品得到。日内精密度的相对误差范围是﹣9.6% to 8.8%,日间精密度的相对误差范围是﹣9.8% to 7.0%,且相对标准偏差都小于9.0%。结果表明该方法的整体重现性良好。

三个不同浓度水平的血浆中黄酮的平均提取率在90.2-95.96%之间且相对标

准偏差小于8%,同时所有组织样品的平均提取率在88.7%以上。

根据第2.5部分描述的步骤分析质量样品来评价所研究的黄酮类化合物的稳定性。不同浓度质量样品测定结果的相对标准偏差都在5%以内。结果表明,所有的分析物在指定的存储条件下都是稳定的。

3.4 药代动力学研究

研究组成的平均血浆浓度-时间曲线如图3所示。图中表明黄酮类化合物被迅速吸收,然后吸收速率缓慢下降。通过3P97药代动力学软件计算药代动力学模型和参数。研究发现,浓度-时间曲线是最好的描述所有黄酮类化合物的二室模型。主要的药代动力学参数在表1中列出。

图3.口服降压避风片后血液中六种黄酮类化合物的浓度-时间曲线。每个数据由五次实验的平均偏差得到。

表1.口服降压避风片后六种黄酮类化合物的药代动力学参数

3.5 组织分布研究

六种黄酮类化合物的曲线下面积如图4所示。结果表明,所有的黄酮类化合物都能被迅速吸收,且除了槲皮素和染料木黄酮都能分散到各组织中去。在之前的研究中,槲皮素和染料木黄酮在大脑和脾脏中的含量很少或检测不出来。这说明槲皮素和染料木黄酮有难以跨越的血脑屏障,同时脾脏可能不是它们的主要吸收器官。

图4.口服降压避风片后各组织中六种黄酮类化合物的曲线下面积

4. 结论

在本文中,对口服降压避风片后大鼠血浆和组织中六种黄酮类化合物(黄芩素、槐角苷、芦丁、黄芩甙、槲皮素和染料木黄酮)同时测定的固相萃取-高效液相色谱二极管阵列检测技术已得到发展和验证。在药代动力学和组织分布方面的研究成果为进一步研究新型中药-降压避风片提供了一个可能的生物活性机理。

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(2) w 12… . (3) R 1,2, … (4) Δ ? ? ?others toprojectQ rcer humanresou i k 01 (5) . I t I t . (6) △ I ’s a .( ’t .) (7) (5) t I △ ,( △ ). , – a . (8) (6) (7), I ( = △* △ ). (9) =ηi / * , ηi I ; * I , * =∑=R k ki 1 δ . , . , , . 3.3 , , : = ∑∑==N i i N i Ci 11 ω i i N i i N i c t ??∑∑==1 1 ω (2) ∑∑ ==N i i N i 1 1 ω ) E i R i ki i t - ?? ∑=1 δη i c ? 2F Z 2()i t ? ) E i R i ki i t - ??∑=1 δη (3) () ,(N j i K 3,2,1,=?) (4)

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