學(xué)生學(xué)習(xí)狀況的評(píng)價(jià)模型

word文檔可自由復(fù)制編輯word文檔可自由復(fù)制編輯word文檔可自由復(fù)制編輯北方民族大學(xué)第八屆數(shù)學(xué)建模競(jìng)賽競(jìng)賽論文競(jìng)賽分組：競(jìng)賽題目：組員：所在學(xué)院:數(shù)學(xué)與信息科學(xué)學(xué)院制版北方民族大學(xué)第八屆數(shù)學(xué)建模競(jìng)賽承諾書為保證競(jìng)賽的公平、公正，維護(hù)競(jìng)賽的嚴(yán)肅性，在競(jìng)賽期間，我們承諾遵守以下競(jìng)賽規(guī)定：只在本參賽隊(duì)的三人之間進(jìn)行問題的討論，絕不與本參賽隊(duì)外的其他人討論與競(jìng)賽題目相關(guān)的任何問題，不抄襲、剽竊他人的成果，引用的參考文獻(xiàn)在答卷中進(jìn)行標(biāo)注。承諾人簽名：承諾人所在分組：2014JMZ02承諾人所在學(xué)院：數(shù)學(xué)與信息科學(xué)學(xué)院2014年6月23日學(xué)生學(xué)習(xí)狀況的評(píng)價(jià)模型摘要本文通過對(duì)學(xué)生的實(shí)際成績(jī)、進(jìn)步程度以及學(xué)生每學(xué)期的綜合排名三個(gè)方面來(lái)綜合評(píng)價(jià)學(xué)生的學(xué)習(xí)情況。針對(duì)題目中所提出的三個(gè)問題，本文用相應(yīng)的方法和數(shù)學(xué)軟件做出了合理的解釋。對(duì)于問題一：①用到Excel做描述性統(tǒng)計(jì)分析，對(duì)學(xué)生整體作分析，得出以下結(jié)論：學(xué)生三個(gè)學(xué)期考試的及格率大于等于89%且呈上升趨勢(shì)；學(xué)生三個(gè)學(xué)期的的平均分和中位數(shù)都在71~75分之間，說(shuō)明絕大部分學(xué)生具備較好的學(xué)習(xí)能力且整體學(xué)習(xí)能力逐漸提高。②用spss軟件對(duì)三個(gè)學(xué)期的學(xué)生成績(jī)做了“人數(shù)——分?jǐn)?shù)直方圖”，從圖上可以看出學(xué)生的成績(jī)近似服從正態(tài)分布。也反映了一個(gè)問題：優(yōu)等生較少。針對(duì)問題二：我們采用了層次分析法，把實(shí)際成績(jī)、進(jìn)步程度以及綜合排名做為準(zhǔn)則層，找出各因素所占權(quán)重，進(jìn)而對(duì)所有的學(xué)生做了系統(tǒng)的排名。注：本學(xué)期的進(jìn)步度=本學(xué)期成績(jī)-上學(xué)期成績(jī)，綜合排名用學(xué)生學(xué)期排名得分（排名前10%的得分為100，處于10%-60%之間的得分為80，處于60%-90%之間的得分為60，后10%的得分為40）表示。得出組合權(quán)向量為ω=(0.080,0.160,0.080,0.140,0.419,0.012,0.069,0.040)。針對(duì)問題三：我們對(duì)前三個(gè)學(xué)期成績(jī)做了多元線性回歸預(yù)測(cè)模型，用Excel做線性回歸分析，最終調(diào)整后的擬合系數(shù)為0.722914274，能夠較好的擬合，得出的預(yù)測(cè)模型為：y=0.377253547x+0.347485052x+20.99585486，很好的預(yù)測(cè)了第四學(xué)期和第五學(xué)期的成績(jī)。 1 2關(guān)鍵字：描述性統(tǒng)計(jì)分析層次分析法多元線性回歸權(quán)重組合權(quán)向量目錄一、問題重述............................................3二、模型的假設(shè)及符號(hào)說(shuō)明.................................32.1模型的假設(shè)................................................32.2符號(hào)說(shuō)明..................................................3模型的建立與求解....................................43.1對(duì)學(xué)生整體成績(jī)的分析......................................43.2對(duì)學(xué)生學(xué)習(xí)狀況的評(píng)價(jià)......................................63.2.1數(shù)據(jù)處理.....................................................................................3.2.2層次分析模型...............................................................................3.3對(duì)以后兩學(xué)期成績(jī)的預(yù)測(cè)....................................93.3.1多元線性回歸模型............................................................................3.4預(yù)測(cè)接下來(lái)兩學(xué)期的學(xué)習(xí)狀況...............................113.4.2學(xué)習(xí)狀況評(píng)價(jià)預(yù)測(cè)............................................................................模型結(jié)果分析與檢驗(yàn).................................12五、模型的優(yōu)化與推廣...................................12六、參考文獻(xiàn)...........................................13七、附錄...............................................14問題重述現(xiàn)行的評(píng)價(jià)方式單純的根據(jù)“絕對(duì)分?jǐn)?shù)”評(píng)價(jià)學(xué)生的學(xué)習(xí)狀況，忽略了基礎(chǔ)條件的差異；只對(duì)基礎(chǔ)條件較好的學(xué)生起到促進(jìn)作用，對(duì)基礎(chǔ)條件相對(duì)薄弱的學(xué)生很難起到鼓勵(lì)作用。為了激勵(lì)優(yōu)秀學(xué)生取得更好的成績(jī)，同時(shí)對(duì)基礎(chǔ)薄弱的學(xué)生樹立信心，建立合理的數(shù)學(xué)模型來(lái)解決這一問題是有必要的。題目中提到以下三個(gè)問題：1.請(qǐng)根據(jù)附件數(shù)據(jù)，對(duì)這些學(xué)生的整體情況進(jìn)行分析說(shuō)明；2.請(qǐng)根據(jù)附件數(shù)據(jù)，全面、客觀、合理的評(píng)價(jià)這些學(xué)生的學(xué)習(xí)狀況；3.根據(jù)你的評(píng)價(jià)情況，請(qǐng)預(yù)測(cè)這些學(xué)生后面一個(gè)學(xué)期或兩個(gè)學(xué)期的學(xué)習(xí)情況。針對(duì)以上問題由于附件中只給出了300名學(xué)生連續(xù)三個(gè)學(xué)期的成績(jī)，如果從多個(gè)因素著手就會(huì)脫離客觀現(xiàn)實(shí)，具有不可操作性。因此我們主要著眼于學(xué)生的實(shí)際成績(jī)、進(jìn)步程度以及綜合排名，本文所使用的兩個(gè)模型只針對(duì)這三個(gè)因素展開。模型的假設(shè)及符號(hào)說(shuō)明2.1模型的假設(shè)①.成績(jī)、進(jìn)步程度和排名都實(shí)行百分制；②.每個(gè)學(xué)生的學(xué)習(xí)能力保持不變；③.每個(gè)學(xué)生的學(xué)習(xí)考試環(huán)境相同；④.綜合排名分等級(jí)并且計(jì)分，方式如下：將學(xué)生實(shí)際成績(jī)排名后，取前10%的學(xué)生分?jǐn)?shù)記為100，接下來(lái)50%的學(xué)生分?jǐn)?shù)記為80，再接下來(lái)30%的學(xué)生成績(jī)記為60，最后10%的學(xué)生成績(jī)記為40；2.2符號(hào)說(shuō)明x第一學(xué)期的實(shí)際成績(jī)1第二學(xué)期的實(shí)際成績(jī)2第三學(xué)期的實(shí)際成績(jī)?chǔ)亟M合權(quán)向量k第j個(gè)權(quán)占的權(quán)重jC第j個(gè)學(xué)期的實(shí)際成績(jī)（j=1,2,3）j第j-2個(gè)學(xué)期的進(jìn)步程度（j=4,5）第j-5個(gè)學(xué)期的綜合排名分?jǐn)?shù)（j=6,7,8）S第i個(gè)學(xué)生三個(gè)學(xué)期的綜合成績(jī)iC第i個(gè)學(xué)生第j個(gè)學(xué)期的實(shí)際成績(jī)i,jrank學(xué)生每學(xué)期實(shí)際成績(jī)排名a，b，c多元線性回歸系數(shù)三、模型的建立與求解3.1對(duì)學(xué)生整體成績(jī)的分析⑴.根據(jù)附件中所給的300組數(shù)據(jù)，用Excel做描述性統(tǒng)計(jì)分析并做相應(yīng)的處理得出下表:表一：學(xué)生三學(xué)期成績(jī)分析表及格率89%89.70%92.30%平均分71.2756412172.717008572.40156629中位數(shù)72.7242346974.8572.98357143標(biāo)準(zhǔn)差9.25801059811.291106619.647327595最低分24.34375016.25最高分最高分與最低89.4590.2535714390.61584906分差值65.1062590.2535714374.36584906觀測(cè)數(shù)300300300由表一我們可以得出以下結(jié)論：①學(xué)生三個(gè)學(xué)期考試的及格率大于等于89%且呈上升趨勢(shì)，說(shuō)明約九成的學(xué)生都能及格，絕大部分學(xué)生具備較好的學(xué)習(xí)能力，上升趨勢(shì)說(shuō)明整體學(xué)習(xí)能力逐漸提高。②學(xué)生三個(gè)學(xué)期的的平均分和中位數(shù)都在71~75分之間，說(shuō)明整體的學(xué)習(xí)情況還不錯(cuò)。③第二學(xué)期的標(biāo)準(zhǔn)差比第一學(xué)期的標(biāo)準(zhǔn)差大，說(shuō)明第二學(xué)期總體成績(jī)較向兩端分散；第三學(xué)期的標(biāo)準(zhǔn)差比帶一學(xué)期的大，但比第二學(xué)期的小，說(shuō)明第三學(xué)期總體成績(jī)比起第一學(xué)期要分散，比起第二學(xué)期要集中。④從最高分與最低分的差值來(lái)看，有增大的趨勢(shì)。⑵.對(duì)學(xué)生三個(gè)學(xué)期的成績(jī)用spss軟件做出人數(shù)——分?jǐn)?shù)直方圖如下：圖一:300圖一:300名學(xué)生第一學(xué)期人數(shù)——分?jǐn)?shù)直方圖圖二:300名學(xué)生第二學(xué)期人數(shù)——分?jǐn)?shù)直方圖圖三:300名學(xué)生第三學(xué)期人數(shù)——分?jǐn)?shù)直方圖由上面三個(gè)圖可以直觀的得出以下結(jié)論：①這300個(gè)人當(dāng)中85分以上的人數(shù)較少，且優(yōu)等生的分?jǐn)?shù)不高，最高分不到91分，學(xué)校需加強(qiáng)對(duì)優(yōu)等生的拔尖培養(yǎng)。②學(xué)生成績(jī)分布近似服從正態(tài)分布，數(shù)據(jù)比較合理。③第三個(gè)圖與前兩個(gè)圖相比70分左右分布的人較多，不及格的人明顯減少，體現(xiàn)了教學(xué)的良性發(fā)展。3.2對(duì)學(xué)生學(xué)習(xí)狀況的評(píng)價(jià)3.2.1數(shù)據(jù)處理其中進(jìn)步程度表達(dá)式為：CCC,CCC；4 2 1 5 3 2綜合成績(jī)排名表達(dá)式為： rank 100， 3000.1; 80, 0.1rank0.6; 300C= 其中j(6,7,8).j rank 60, 0.6 0.9; 300 rank 40, 0.9 1 3003.2.2層次分析模型學(xué)習(xí)狀況評(píng)價(jià)實(shí)際成績(jī)進(jìn)步程度第一學(xué)期成績(jī)第二學(xué)期成績(jī)第三學(xué)期成績(jī)第二學(xué)期進(jìn)步程度第三學(xué)期進(jìn)步程度綜合排名第一學(xué)期綜合排名第二學(xué)期綜合排名第三學(xué)期綜合排名目標(biāo)層準(zhǔn)則層方案層圖四：層次分析模型構(gòu)造優(yōu)先關(guān)系矩陣矩陣如下： 1 1 123 121 AB:214BC:212 11 11 1 11 34 2 111541BC:13BC:512 231 31 41 2 運(yùn)用matlab軟件，所有構(gòu)造的矩陣都通過了一致性檢驗(yàn)，并且得到B層各指標(biāo)相對(duì)于A層的權(quán)值從左到右依次為（0.3196,0.5584,0.122），C層各指標(biāo)相對(duì)于B層各指標(biāo)的權(quán)值從左到右依次為（0.25,0.50,0.25,0.25,0.75,0.0974,0.5696,0.3331），因此組合權(quán)向量為：ω=(0.080,0.160,0.080,0.140,0.419,0.012,0.069,0.040)，即如下面的關(guān)系圖：學(xué)習(xí)狀況學(xué)習(xí)狀況評(píng)價(jià)第一學(xué)期成績(jī)0.080第二學(xué)期成績(jī)0.160第三學(xué)期成績(jī)0.080第二學(xué)期進(jìn)步程度0.140第三學(xué)期進(jìn)步程度0.419第一學(xué)期綜合排名0.012第二學(xué)期綜合排名0.069第三學(xué)期綜合排名0.040圖五因此對(duì)于學(xué)號(hào)為i的學(xué)生的學(xué)習(xí)狀況的綜合評(píng)定定量表示如下：S8kC，其中(j1,2,3...8),i(1,2,3...300) i jj j1 根據(jù)該表達(dá)式算出結(jié)果并排名，下表列出的是學(xué)號(hào)為1~20的20名學(xué)生的信息（所有學(xué)生的信息參見附表）：表二：學(xué)號(hào)為1~20的20名學(xué)生的信息學(xué)學(xué)學(xué)學(xué)進(jìn)進(jìn)排排排綜綜生期期期步步名名名合合序123度度分分分評(píng)排號(hào)成 成 成 1 2 值1值值3價(jià) 名 績(jī) 績(jī) 績(jī) 266.87554.371470.5266-12.503616.155260406030.590119762.12561.571465.9792-0.55364.407860606029.129124174.37579.108974.61504.7339 -4.493980808033.036412962.93860.339369.4200-2.59829.080760606030.944018782.07578.350081.9151-3.72503.5651100808036.54753968.17570.025071.22501.8500 1.200060606030.377820652.37553.250057.83930.8750 4.589340404024.222628470.22564.915770.2500-5.30935.334360606030.376320779.30085.332179.66606.0321 -5.6661801008035.90085071.52568.467973.9650-3.05715.497180608032.769413977.35077.403675.13110.0536 -2.272480808033.318412275.40080.935782.26795.5357 1.332280808036.57633860.50047.207156.5050-13.29299.297960404024.028328568.67563.932174.0755-4.742910.143360608033.295212354.29564.821464.458010.5264-0.363440606028.213125989.45088.671490.6158-0.77861.944410010010041.3984275.12578.653683.66603.5286 5.0125808010038.36211978.07579.403681.21501.3286 1.811480808036.07284873.05073.914374.85500.8643 0.940780808033.853810779.92586.903685.26086.9786 -1.64278010010039.268111表1：學(xué)號(hào)為1~20的20名學(xué)生的信息:由表1的計(jì)算結(jié)果可以看出：在這20名學(xué)生中，16號(hào)學(xué)生綜合成績(jī)最好，考試成績(jī)突出且其學(xué)習(xí)狀態(tài)也比較穩(wěn)定；而13號(hào)學(xué)生綜合成績(jī)最差，該同學(xué)雖然第三學(xué)期進(jìn)步較大，但其第二學(xué)期退步很大，又因?yàn)榈诙W(xué)期的考試難度是這三學(xué)期中最大的，該同學(xué)三次成績(jī)也比較低，說(shuō)明該同學(xué)學(xué)習(xí)狀況較差，對(duì)于這種情況，老師有必要采取一定的措施，幫助該同學(xué)擺脫差的學(xué)習(xí)狀況。因此，通過層次分析模型可以客觀、全面、正確地評(píng)價(jià)學(xué)生的學(xué)習(xí)狀況。3.3對(duì)以后兩學(xué)期成績(jī)的預(yù)測(cè)3.3.1多元線性回歸模型用Cij來(lái)表示第i個(gè)學(xué)生第j個(gè)學(xué)期的實(shí)際成績(jī)，在理想化的情況下假設(shè)學(xué)生第三學(xué)期的成績(jī)由前兩學(xué)期決定，此三者符合一定的線性關(guān)系，建立如下線性方程：Ca*Cb*Cc.i3 i1 i2 用spss得出線性系數(shù)：a=0.467887b=0.322979c=15.56655則有多元線性回歸方程：C0.467887*C0.322979*C15.56655. i3 i1 i2 回歸的結(jié)果如下：表三回歸統(tǒng)計(jì) MultipleR 0.775552 RSquare 0.601481AdjustedRSquare0.598798標(biāo)準(zhǔn)誤差 6.110668 觀測(cè)值 300其中，我們看到調(diào)整的R平方為0.5987980.6，說(shuō)明該模型可以模擬真實(shí)成績(jī)的60%，效果不是太好，且用matlab畫出殘差分析圖，可見大部分殘差在[-9,9]之間波動(dòng)，有部分?jǐn)?shù)據(jù)在此區(qū)間之外，這部分學(xué)生成績(jī)波動(dòng)較大（星型圖標(biāo)所示的數(shù)據(jù)），因此不能用線性模型來(lái)擬合，需要剔除該類數(shù)據(jù)來(lái)優(yōu)化模型，提高模型的逼真性。.圖六：總評(píng)分?jǐn)?shù)殘差通過對(duì)數(shù)據(jù)殘差進(jìn)行篩選，剔除部分異常值點(diǎn)（殘差值在[-9,9]之間的值），其分別為學(xué)生序列為21、60、76、100、123、154、174、184、196、205、220、221、227、237、239、247、256、268、282、290的學(xué)生成績(jī)，得到的新的數(shù)據(jù)將在附錄中給出。根據(jù)剔除部分極值得到的新的數(shù)據(jù)，再次進(jìn)行多元線性擬合，得到的效果如下：表四回歸統(tǒng)計(jì) MultipleR 0.851410918 RSquare 0.724900551AdjustedRSquare0.722914274標(biāo)準(zhǔn)誤差 3.760439965 觀測(cè)值 280其中，調(diào)整的R平方達(dá)到了72%的精度，說(shuō)明模型的逼真性有了很大的提高。新的模型線性系數(shù)分別為：a0.3772535,b0.3474851,c20.9958549線性擬合方程為：C=0.3772535*C+0.3474851*C+20.9958549.i,j i,j-1 i,j-2運(yùn)用此模型可以模擬出第四、五學(xué)期的成績(jī)。從預(yù)測(cè)值來(lái)看，與真實(shí)值的差值在7左右波動(dòng)，在不考慮極少數(shù)異常的情況下，該模型能夠很好地預(yù)測(cè)學(xué)生后幾學(xué)期的成績(jī)，下面給出部分預(yù)測(cè)數(shù)據(jù)，具體詳見附錄。表五：10名學(xué)生第四學(xué)期和第五學(xué)期的預(yù)測(cè)成績(jī)學(xué)生序號(hào)學(xué)生序號(hào)學(xué)期四成績(jī)學(xué)期五成績(jī)166.014622970.54137531267.150696369.22062245376.76757675.82021351467.881476870.7725947579.017941279.35616825672.162657472.94118361761.182893564.0760716869.896363371.78585808980.870465879.151428281072.527328874.10157618根據(jù)預(yù)測(cè)的成績(jī)值，同前幾學(xué)期相比，總體平均分逐漸上漲，說(shuō)明大部分學(xué)生成績(jī)有穩(wěn)步的提升。同時(shí)，數(shù)據(jù)的方差變小，說(shuō)明學(xué)生間的差距在逐漸減小，學(xué)生總體情況良好，達(dá)到了教學(xué)的目的。3.4預(yù)測(cè)接下來(lái)兩學(xué)期的學(xué)習(xí)狀況3.4.1數(shù)據(jù)處理引用層次分析模型，利用多元線性模型預(yù)測(cè)出的接下來(lái)兩學(xué)期的成績(jī)，進(jìn)行加權(quán)分析，其中各權(quán)的權(quán)重均已在層次分析模型中得出，第四五學(xué)期的進(jìn)步程度在理想狀態(tài)下等于第二三學(xué)期既不讀的加權(quán)平均，即：0.25*CC*0.75 4 53.4.2學(xué)習(xí)狀況評(píng)價(jià)預(yù)測(cè)由此得出接下來(lái)兩學(xué)期的學(xué)習(xí)綜合評(píng)定量的值：S0.3196*C0.5584*[0.25*CC*0.75]i,j i,j 4 50.122*[0.0974*C0.5696*C0.3331*C] 6 7 8j(4,5)將學(xué)生數(shù)據(jù)代入該方程，得出每個(gè)學(xué)生接下來(lái)兩學(xué)期的綜合評(píng)定量（見附錄）。由預(yù)測(cè)值進(jìn)行排名可以看到，與前幾學(xué)期相比，接下來(lái)兩學(xué)期，部分學(xué)生進(jìn)步較大，學(xué)習(xí)狀況良好，整體來(lái)看，較前幾學(xué)期綜合評(píng)定分有所提高，說(shuō)明整體的學(xué)習(xí)狀況有提高的趨勢(shì)。模型結(jié)果分析與檢驗(yàn)針對(duì)上述模型得出的結(jié)果，我們用300名學(xué)生的綜合成績(jī)做折線圖如下：19241924293439114274053667992105118131144157170183196209222235248261274圖七:300名學(xué)生的綜合評(píng)價(jià)成績(jī)由上圖可以看出大多數(shù)學(xué)生的水平是比較相近的，但仍有個(gè)別學(xué)生的成績(jī)比較低，老師應(yīng)該加強(qiáng)對(duì)這部分學(xué)生的關(guān)心。模型的優(yōu)化與推廣層次分析法優(yōu)點(diǎn)：層次分析法利用權(quán)重關(guān)系比較進(jìn)行分析可以學(xué)生學(xué)習(xí)情況綜合評(píng)價(jià)指標(biāo)權(quán)重值的科學(xué)性和可信性，從而能夠很好的反應(yīng)學(xué)生實(shí)際的學(xué)習(xí)情況，避免了傳統(tǒng)的將各項(xiàng)分?jǐn)?shù)相加求和的不合理做法，從而使教育管理者能更全面地了解學(xué)生的學(xué)習(xí)狀態(tài)，從而進(jìn)行有效地教學(xué)管理。缺點(diǎn)：此方法仍在一定程度上受主觀因素的影響，如一開始各個(gè)因素的各項(xiàng)指標(biāo)權(quán)重是已經(jīng)確定再進(jìn)行求解的，這里就有一定的主觀性。改進(jìn)：在對(duì)剛開始的各個(gè)因素的各項(xiàng)指標(biāo)權(quán)重賦值上，可以根據(jù)不同學(xué)校的標(biāo)準(zhǔn)進(jìn)行設(shè)定，或者查閱相關(guān)的資料進(jìn)行確定。多元線性回歸預(yù)測(cè)優(yōu)點(diǎn)：用多變量線性回歸模型，通過多組數(shù)據(jù)，可直觀、快速分析出三者之間的線性關(guān)系。回歸分析可以準(zhǔn)確的劑量各個(gè)因素之間的相關(guān)程度與擬合程度的高低，提高預(yù)測(cè)方程式的效果。缺點(diǎn)：可能忽略了交互效應(yīng)和非線性的因果關(guān)系，擬合程度差會(huì)導(dǎo)致預(yù)測(cè)效果差。如一開始調(diào)整后的擬合系數(shù)只有0.5左右，擬合程度較低。改進(jìn)：對(duì)原始數(shù)據(jù)進(jìn)行篩選，排除一些異常值后得到的調(diào)整后的擬合系數(shù)為0.7左右，大大提高了預(yù)測(cè)效果。六、參考文獻(xiàn)姜啟源謝金星葉俊編著《數(shù)學(xué)模型》高等教育出版社2003年8月第三版；熊啟才曹吉利張東生趙臨龍編著《數(shù)學(xué)模型方法及應(yīng)用》重慶大學(xué)出版社2005.3；周義倉(cāng)郝孝良編著《數(shù)學(xué)建模實(shí)驗(yàn)》西安交通大學(xué)出版社1999七、附錄 平均排名分 學(xué)期四綜合評(píng)學(xué)期五綜合評(píng)序號(hào)學(xué)期四成績(jī)學(xué)期五成績(jī)平均進(jìn)步度值 價(jià) 價(jià)66.01462370.5413758.97770048.59504132.04001633.48676667.15069669.2206223.16525160.00000030.54883931.21038776.76757675.820214-2.18283780.00000033.07602132.77324467.88147770.7725956.15575960.00000032.45229633.37629779.01794179.3561681.73931081.98347136.22734836.33544672.16265772.9411841.36279160.00000031.14416831.39298561.18289464.0760723.65905340.00000026.47726827.40192869.89636371.7858582.66863360.00000031.14904231.75292580.87046679.151428-2.73631191.40495935.46965034.92024572.52732974.1015763.35474668.59504133.42161933.92474976.30357275.853692-1.68989680.00000033.20298433.05920280.11601479.8708392.38496680.00000036.69684336.61848558.43956062.6194403.64007541.98347125.83188527.16777570.85460273.5620046.41512566.61157034.35394835.21923467.84816768.8890952.36392058.01652930.08230430.41498485.93511985.0421751.262455100.00000040.36981940.08443479.74089180.2679324.64082986.61157038.64323938.81168279.17213279.1456341.69049880.00000036.00738835.99891974.89127575.2587680.92157380.00000034.20985834.32730983.40740682.1436400.51645798.01652938.90341338.49951372.98222872.9645640.79297971.40495932.47932532.47367969.08065170.5998490.51658261.98347129.92861930.41415575.33930374.616560-3.26814080.00000032.01351231.78252374.75236174.382426-1.17333180.00000032.99566632.87743573.69042773.855187-1.94108080.00000032.22756132.2802192775.61616875.8778391.59659780.00000034.81846734.90209775.41533376.2233874.16412678.01652935.94600536.20425964.00995267.7107948.23935246.61157030.74504631.92783666.95929868.4592201.16059860.00000029.36827029.84764574.34612575.2176401.38562980.00000034.29475734.57329361.82786563.9911110.03684141.98347124.90274125.59411568.18233170.1754451.51429360.00000029.95665430.59365479.89928180.1204644.59610386.61157038.66888638.73957680.27876278.658876-2.59778791.40495935.35789334.84017879.80020378.941373-0.51355180.00000034.97737834.70289653.61943756.993572-0.19317340.00000021.90890422.98727873.93683673.534729-1.79058573.38843031.58373931.45522554.82919061.4473319.87047340.00000027.91508130.03023973.45241473.587947-1.10947880.00000032.61585932.65917570.08289270.9603561.62789660.00000030.62750930.90794781.15945680.4754310.14608988.59504136.82873336.61011976.98457376.029542-3.61218880.00000032.34722432.04199681.55835380.502965-0.35577186.61157036.43399936.09669777.27571077.0122892.01546078.01652935.34076735.25657784.22492183.2977100.940092100.00000039.64323239.34689672.58878872.661075-1.34989373.38843031.39898531.42208860.90405163.4350933.17926140.00000026.12023426.92915584.72520882.961513-1.206435100.00000038.60450338.04082676.85182476.254716-2.14115080.00000033.12622532.93538971.18543672.2413370.34873861.98347130.50758430.84505068.52217471.1159496.34311860.00000032.76168433.59065470.54582370.600607-4.02813661.98347127.85911727.87662780.64880180.1151250.54232680.00000035.83819135.66762872.51142472.9436822.07368060.00000031.65259431.79074474.16140773.098133-5.43410473.38843029.62097029.2811485774.66357175.072127-0.04221280.00000033.59890633.72948077.33998177.296297-0.69321181.98347134.33275234.31879168.68998871.1648306.41645058.01652932.61428333.40524271.33427873.3820393.74895768.59504133.26044833.91491277.21992077.6467432.12163280.00000035.62420635.76061864.79112366.182740-0.15897651.40495926.88987527.33463677.60877978.0855552.08958280.00000035.73058935.88296684.21282083.4134791.760173100.00000040.09729839.84182876.50096677.1649073.21550680.00000036.00524736.21744377.72494779.3213175.69882386.61157038.58972839.09992874.69065075.3727690.96193980.00000034.16827934.38628464.28950265.433122-3.17400353.38843025.28795025.65345176.56721476.5906381.63276980.00000035.14262035.15010678.54938378.5434971.93533580.00000035.94507435.94319280.93140580.034503-0.51746780.00000035.33672335.05007469.83436572.3075604.66106466.61157033.04841333.83884680.94027279.143227-2.70730591.40495935.50815734.93382171.69779171.847833-2.31768761.98347129.18240129.23035476.97722676.4505260.00919280.00000034.36705434.19872173.58832074.4928901.47889168.59504132.71323533.00233575.80598275.766630-0.23048080.00000033.85889233.84631568.04359669.8244911.98589360.00000030.17565630.74483076.02365274.642156-4.57199580.00000031.50415731.06263176.77399375.796498-2.16805380.00000033.08632732.77392078.18065677.9784851.11665880.00000035.37007935.30546583.16685982.6136552.44646398.01652939.90425039.72744571.78013472.8866492.27040466.61157032.33533632.68897875.46378574.535322-1.35872378.01652932.87753132.58079472.91090572.763610-1.90634873.38843031.19120931.14413372.25082473.5414735.46392364.62809934.02704634.4395378971.65748772.5697222.08557460.00000031.38631831.67786862.00924666.4817657.55977348.59504129.96812731.39754475.67390674.796962-4.03118080.00000031.69436931.41409878.40654677.729551-0.84535080.00000034.34668934.13032172.01196872.6345310.48406460.00000030.60532630.80429775.69725574.221187-3.99900473.38843030.91318730.44143676.89660976.068767-0.96798180.00000033.79563633.53105778.79610678.8349213.58310978.01652936.70206036.71446582.40182281.493835-0.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