KK关系计算方法

KK关系计算方法

使用软件：Mathematice6.0

计算数据：反射光谱

计算目标：折射率、消光系数（复折射率）、介电常数（实部、虚部）、吸收系数

计算步骤：步

第一步不做任何处理的原始数据拟合

1数据处理

把反射谱中的一一对应的数据点做如下形式：

{x1,y1},{x2,y2},…{xn,yn}

这一步可用Excel完成，如图所示：

复制需要拟合的数据到mathematice中。先打开“未做任何处理的200-2500的原始数据拟合.nb”。以我的数据为例，我只取了其中200－800nm数据。需要说明的文字我用红字标出。如图所示：

f={{200,9.28083},{204,10.67989},{208,10.68956},{212,11.35133},{216,11.94466}, {220,11.97739},{224,12.44642},{228,12.79128},{232,13.17627},{236,13.33227},{2 40,13.64892},{244,14.02046},{248,14.1844},{252,14.43982},{256,14.59005},{260, 14.93265},{264,15.08296},{268,15.44994},{272,15.63906},{276,15.83285},{280,16 .0089},{284,16.18497},{288,16.4413},{292,16.5467},{296,16.80329},{300,17.0636 },{304,17.37439},{308,17.24754},{312,17.53314},{316,17.54477},{320,17.88985}, {324,18.20747},{328,18.15253},{332,18.29901},{336,18.48072},{340,18.63027},{3 44,18.68853},{348,18.93796},{352,18.87828},{356,18.97925},{360,19.07318},{364 ,19.20597},{368,19.46847},{372,19.4527},{376,19.63037},{380,19.45939},{384,19. 54249},{388,19.50909},{392,19.71648},{396,19.72745},{400,19.86541},{404,19.88 394},{408,19.94855},{412,19.99085},{416,20.10268},{420,20.17271},{424,20.2437 6},{428,20.28775},{432,20.33652},{436,20.36746},{440,20.45098},{444,20.51344} ,{448,20.56255},{452,20.61329},{456,20.59809},{460,20.61791},{464,20.712},{46 8,20.75117},{472,20.80953},{476,20.84951},{480,20.91447},{484,21.04063},{488, 21.0387},{492,21.05206},{496,21.08511},{500,21.08685},{504,21.14488},{508,21. 14559},{512,21.17371},{516,21.2372},{520,21.27362},{524,21.31675},{528,21.37} ,{532,21.39788},{536,21.45977},{540,21.49712},{544,21.54286},{548,21.58125},{ 552,21.63051},{556,21.68476},{560,21.71518},{564,21.74266},{568,21.77074},{57 2,21.79919},{576,21.8478},{580,21.87746},{584,21.91433},{588,21.96476},{592,2

1.95952},{596,21.99251},{600,2

2.01649},{604,22.06857},{608,22.05836},{612,22.10567},{616,22.13445},{620,22.11847},{624,22.16107},{628,22.18187},{632,22.21075},{636,22.22322},{640,22.21166},{644,22.26408},{648,22.26516},{652,22.27371},{656,22.28789},{660,22.33599},{664,22.33009},{668,22.35576},{672,22.37441},{676,22.38908},{680,22.4118},{684,22.43644},{688,22.39334},{692,22.45349},{696,22.45548},{700,22.46142},{704,22.50477},{708,22.50623},{712,22.51435},{716,22.56872},{720,22.56509},{724,22.57602},{728,22.59907},{732,22.6267},{736,22.63849},{740,22.69148},{744,22.6825},{748,22.70658},{752,22.73869},{756,22.79487},{760,22.8029},{764,22.835},{768,22.86978},{772,22.87246},{776,22.93132},{780,22.98215},{784,22.99017},{788,2

3.03298},{792,23.06776},{796,23.10254},{800,23.12929}}（f 为定义的一个变量，值为原始数据。你使用时，只需覆盖我原来的数据就行） F = FindFit [f ,u 1010

T u x u ,Table[T u ,{u,-10,10 } ],x ]（表示寻找一个多项式来拟合数据，求和号上下为正负10，表明，从负10次方，到正10次方。这里只要改变需要拟合的次数就行，即改多少次方就行了。） u 1010

T u x

u /.F （这一个命令可以不管它，但必须保持与上一命令相同的次数） p =ListPlot[f]（这个命令的意思是将原始数据以点的形式画出）

Plot [u 1010

T u x u /.F,{x,200,800}]（这个命令的意思是在指定区间内画出拟合的函数的图形。区间为（200,800），可改动，但最好与你的原始数据区间相同，本例中采用200－800nm 。）

Show[%,p]（这个命令是将原始数据与拟合曲线画在一起，用以判断拟合效果如何）

（以下为输出结果）

{{200,9.28083},{204,10.6799},{208,10.6896},{212,11.3513},{216,11.9447},{220,1

1.9774},{224,1

2.4464},{228,12.7913},{232,1

3.1763},{236,13.3323},{240,13.6489},{244,1

4.0205},{248,14.1844},{252,14.4398},{256,14.5901},{260,14.9327},{264,1

5.083},{268,15.4499},{272,15.6391},{276,15.8329},{280,1

6.0089},{284,16.185},{288,16.4413},{292,16.5467},{296,16.8033},{300,1

7.0636},{304,17.3744},{308,17.2475},{312,17.5331},{316,17.5448},{320,17.8899},{324,1

8.2075},{328,18.1525},{332,18.299},{336,18.4807},{340,18.6303},{344,18.6885},{348,18.938},{352,18.8783},{356,18.9793},{360,1

9.0732},{364,19.206},{368,19.4685},{372,19.4527},{376,19.6304},{380,19.4594},{384,19.5425},{388,19.5091},{392,19.7165},{396,19.7275},{400,19.8654},{404,19.8839},{408,19.9486},{412,19.9909},{416,20.1027},{420,20.1727},{424,20.2438},{428,20.2878},{432,20.3365},{436,20.3675},{440,20.451},{444,20.5134},{448,20.5626},{452,20.6133},{456,20.5981},{460,20.6179},{464,20.712},{468,20.7512},{472,20.8095},{476,20.8495},{480,20.9145},{484,21.0406},{488,21.0387},{492,21.0521},{496,21.0851},{500,21.0869},{504,21.1449},{508,21.1456},{512,21.1737},{516,21.2372},{520,21.2736},{524,21.3168},{528,21.37},{532,21.3979

},{536,21.4598},{540,21.4971},{544,21.5429},{548,21.5813},{552,21.6305},{556,2 1.6848},{560,21.7152},{564,21.7427},{568,21.7707},{572,21.7992},{576,21.8478}, {580,21.8775},{584,21.9143},{588,21.9648},{592,21.9595},{596,21.9925},{600,22. 0165},{604,22.0686},{608,22.0584},{612,22.1057},{616,22.1345},{620,22.1185},{ 624,22.1611},{628,22.1819},{632,22.2108},{636,22.2232},{640,22.2117},{644,22.2 641},{648,22.2652},{652,22.2737},{656,22.2879},{660,22.336},{664,22.3301},{66 8,22.3558},{672,22.3744},{676,22.3891},{680,22.4118},{684,22.4364},{688,22.393 3},{692,22.4535},{696,22.4555},{700,22.4614},{704,22.5048},{708,22.5062},{712, 22.5144},{716,22.5687},{720,22.5651},{724,22.576},{728,22.5991},{732,22.6267}, {736,22.6385},{740,22.6915},{744,22.6825},{748,22.7066},{752,22.7387},{756,22. 7949},{760,22.8029},{764,22.835},{768,22.8698},{772,22.8725},{776,22.9313},{7 80,22.9822},{784,22.9902},{788,23.033},{792,23.0678},{796,23.1025},{800,23.129 3}}（原始数据输出，可以不管这个结果）

{T-10→-1.26756 1031,T-9→5.27225 1029,T-8→-9.89949 1027,T-7→1.10041 1026,T →-7.92496 1023,T-5→3.73215 1021,T-4→-1.02308 1019,T-3→3.39511 1015,T-2→-6

1.08241 1014,T-1→-5.4828 1011,T0→1.52085 109,T1→-

2.6332 106,T2→2370.82, T3→1.04202,T4→-0.00721988,T5→0.00001255,T6→-1.31978 10-8,T7→9.22389 1 0-12,T8→-4.22857 10-15,T9→1.1615 10-18,T10→-1.45878 10-22}（多项式相应的系数，可以不管这个结果）

1.52085 109-1.26756 1031/x10+5.27225 1029/x9-9.89949 1027/x8+1.10041 1026/x 7-7.92496 1023/x6+3.73215 1021/x5-1.02308 1019/x4+3.39511 1015/x3+1.08241 1 014/x2-5.4828 1011/x-

2.6332 106 x+2370.82 x2+1.04202 x3-0.00721988

x4+0.00001255 x5-1.31978 10-8 x6+9.22389 10-12 x7-4.22857 10-15

x8+1.1615 10-18 x9-1.45878 10-22 x10（拟合函数表达式，在word里，可能看不清楚，请看我的原程序）

以下为第二次操作：

a=Table[1.5208520266172135`*^9-1.2675581804893597`*^31/x10+5.272248205187 29`*^29/x9-9.899490662109208`*^27/x8+1.1004074726951989`*^26/x7-7.92496324 1331437`*^23/x6+3.7321468261159687`*^21/x5-1.023076110480841`*^19/x4+3.395 110161290293`*^15/x3+1.0824109439997714`*^14/x2-5.482795964973215`*^11/x-2.633201*********`*^6 x+2370.817263501473` x2+1.0420215704202724`

x3-0.007219884471347927` x4+0.000012550049332281336`

x5-1.3197768147930983`*^-8 x6+9.223889143423574`*^-12

x7-4.22856898484929`*^-15 x8+1.161504051032442`*^-18

x9-1.4587766069643154`*^-22 x10,{x,200,800,1}]（此命令的作用是将拟合出来的函数数值化）

{9.30477,9.79019,10.1304,10.3698,10.5415,10.6697,10.7718,10.86,10.9424,11.0243, 11.1087,11.1972,11.2902,11.3874,11.4882,11.5916,11.6966,11.8022,11.9075,12.011 7,12.1141,12.2141,12.3114,12.4056,12.4968,12.5848,12.6697,12.7516,12.8307,12.90 72,12.9814,13.0535,13.1239,13.1927,13.2602,13.3267,13.3924,13.4574,13.522,13.58 63,13.6505,13.7145,13.7785,13.8426,13.9067,13.971,14.0353,14.0997,14.1642,14.22 87,14.2931,14.3575,14.4218,14.4858,14.5496,14.6132,14.6764,14.7392,14.8015,14.8 634,14.9248,14.9856,15.0458,15.1054,15.1644,15.2227,15.2805,15.3375,15.394,15.4 498,15.505,15.5596,15.6136,15.667,15.7199,15.7723,15.8242,15.8756,15.9266,15.97 72,16.0275,16.0773,16.1269,16.1762,16.2252,16.2739,16.3225,16.3708,16.419,16.46 7,16.5149,16.5626,16.6103,16.6578,16.7052,16.7525,16.7998,16.8469,16.8939,16.94 09,16.9877,17.0344,17.081,17.1275,17.1738,17.22,17.266,17.3118,17.3574,17.4028, 17.4479,17.4929,17.5375,17.5819,17.6259,17.6697,17.713,17.7561,17.7987,17.841,1 7.8828,17.9243,17.9653,18.0058,18.0458,18.0854,18.1245,18.1631,18.2011,18.2387, 18.2757,18.3121,18.348,18.3834,18.4182,18.4524,18.4861,18.5192,18.5518,18.5838, 18.6152,18.6461,18.6764,18.7062,18.7355,18.7642,18.7924,18.82,18.8472,18.8739,1 8.9,18.9257,18.9509,18.9756,18.9999,19.0238,19.0473,19.0703,19.0929,19.1152,19. 137,19.1586,19.1797,19.2006,19.2211,19.2413,19.2612,19.2809,19.3002,19.3194,19. 3382,19.3569,19.3753,19.3935,19.4116,19.4294,19.4471,19.4646,19.482,19.4992,19. 5163,19.5333,19.5501,19.5669,19.5835,19.6001,19.6166,19.633,19.6493,19.6655,19. 6817,19.6979,19.714,19.73,19.746,19.7619,19.7778,19.7937,19.8095,19.8253,19.841 1,19.8569,19.8726,19.8883,19.9039,19.9195,19.9351,19.9507,19.9662,19.9817,19.99 72,20.0126,20.028,20.0434,20.0587,20.074,20.0893,20.1045,20.1196,20.1347,20.149 8,20.1648,20.1797,20.1946,20.2094,20.2242,20.2388,20.2535,20.268,20.2825,20.296 9,20.3112,20.3255,20.3396,20.3537,20.3677,20.3816,20.3955,20.4092,20.4228,20.43 64,20.4499,20.4632,20.4765,20.4897,20.5027,20.5157,20.5286,20.5414,20.554,20.56 66,20.5791,20.5915,20.6038,20.616,20.6281,20.6401,20.652,20.6638,20.6755,20.687 2,20.6987,20.7102,20.7215,20.7328,20.744,20.7551,20.7662,20.7771,20.788,20.7988 ,20.8096,20.8202,20.8308,20.8414,20.8519,20.8623,20.8726,20.883,20.8932,20.9034 ,20.9136,20.9237,20.9338,20.9438,20.9538,20.9638,20.9737,20.9836,20.9935,21.003 4,21.0132,21.023,21.0328,21.0426,21.0524,21.0621,21.0719,21.0816,21.0914,21.101 1,21.1108,21.1206,21.1303,21.1401,21.1498,21.1596,21.1693,21.1791,21.1889,21.19 86,21.2084,21.2182,21.2281,21.2379,21.2477,21.2576,21.2675,21.2774,21.2873,21.2 972,21.3071,21.3171,21.327,21.337,21.347,21.357,21.367,21.377,21.3871,21.3971,2 1.4072,21.4172,21.4273,21.4374,21.4474,21.4575,21.4676,21.4777,21.4877,21.4978, 21.5079,21.5179,21.528,21.538,21.548,21.558,21.568,21.578,21.588,21.5979,21.607 8,21.6177,21.6276,21.6374,21.6472,21.6569,21.6667,21.6764,21.686,21.6956,21.705 2,21.7147,21.7242,21.7336,21.743,21.7523,21.7615,21.7707,21.7799,21.789,21.798, 21.807,21.8158,21.8247,21.8334,21.8421,21.8507,21.8593,21.8678,21.8761,21.8845, 21.8927,21.9009,21.909,21.917,21.9249,21.9327,21.9405,21.9482,21.9558,21.9633,2

1.9707,21.9781,21.9853,21.9925,21.9996,2

2.0066,22.0135,22.0203,22.0271,22.0338, 22.0403,22.0468,22.0532,22.0596,22.0658,22.072,22.0781,22.0841,22.09,22.0959,22 .1017,22.1074,22.113,22.1185,22.124,22.1294,22.1348,22.14,22.1452,22.1504,22.15 54,22.1604,22.1654,22.1703,22.1751,22.1799,22.1846,22.1893,22.1939,22.1984,22.2 03,22.2074,22.2118,22.2162,22.2206,22.2249,22.2291,22.2333,22.2375,22.2417,22.2 458,22.2499,22.254,22.258,22.262,22.266,22.27,22.274,22.2779,22.2818,22.2857,22. 2896,22.2935,22.2974,22.3013,22.3051,22.309,22.3128,22.3167,22.3205,22.3243,22. 3282,22.332,22.3359,22.3397,22.3436,22.3474,22.3513,22.3551,22.359,22.3629,22.3 668,22.3707,22.3746,22.3785,22.3825,22.3864,22.3904,22.3944,22.3984,22.4024,22. 4064,22.4104,22.4145,22.4185,22.4226,22.4267,22.4308,22.4349,22.4391,22.4432,2 2.4474,22.4516,22.4558,22.4601,22.4643,22.4686,22.4728,22.4771,22.4815,22.4858, 22.4902,22.4945,22.4989,22.5033,22.5078,22.5122,22.5167,22.5212,22.5257,22.530 2,22.5348,22.5394,22.544,22.5486,22.5533,22.558,22.5627,22.5674,22.5722,22.577, 22.5818,22.5867,22.5916,22.5965,22.6015,22.6065,22.6115,22.6166,22.6217,22.626 9,22.6321,22.6374,22.6427,22.6481,22.6536,22.6591,22.6646,22.6702,22.6759,22.68 16,22.6875,22.6933,22.6993,22.7053,22.7115,22.7176,22.7239,22.7303,22.7367,22.7 433,22.7499,22.7566,22.7635,22.7704,22.7774,22.7845,22.7918,22.7991,22.8065,22. 814,22.8217,22.8294,22.8373,22.8452,22.8533,22.8614,22.8697,22.878,22.8864,22.8 95,22.9036,22.9122,22.921,22.9298,22.9387,22.9476,22.9566,22.9656,22.9747,22.98 37,22.9927,2

3.0017,23.0107,23.0197,23.0285,23.0373,23.0459,23.0544,23.0628,23.0 71,23.0789,23.0867,23.0941,23.1012,23.108,23.1143,23.1203,23.1258}（这便是拟合函数数值化的结果）

Log[a]

{2.23053,2.28138,2.31554,2.3389,2.35532,2.36741,2.37694,2.38509,2.39265,2.4 001,2.40773,2.41567,2.42393,2.43251,2.44132,2.45028,2.4593,2.46829,2.47717,2.48 588,2.49437,2.50259,2.51052,2.51815,2.52547,2.53249,2.53921,2.54565,2.55184,2.5 5779,2.56352,2.56906,2.57443,2.57966,2.58477,2.58977,2.59469,2.59953,2.60432,2. 60906,2.61377,2.61845,2.62311,2.62775,2.63237,2.63698,2.64158,2.64616,2.65072, 2.65526,2.65978,2.66427,2.66874,2.67317,2.67757,2.68192,2.68624,2.69051,2.6947 3,2.6989,2.70302,2.70709,2.7111,2.71505,2.71895,2.72279,2.72658,2.7303,2.73398, 2.7376,2.74116,2.74468,2.74814,2.75156,2.75493,2.75826,2.76154,2.76479,2.76799, 2.77116,2.7743,2.77741,2.78049,2.78354,2.78656,2.78956,2.79254,2.7955,2.79844,2 .80136,2.80426,2.80715,2.81002,2.81288,2.81572,2.81855,2.82136,2.82417,2.82695, 2.82973,2.83249,2.83523,2.83797,2.84068,2.84338,2.84607,2.84874,2.85139,2.8540 2,2.85663,2.85922,2.86179,2.86434,2.86687,2.86937,2.87185,2.8743,2.87673,2.8791 3,2.8815,2.88384,2.88616,2.88844,2.89069,2.89292,2.89511,2.89726,2.89939,2.9014 8,2.90354,2.90557,2.90756,2.90952,2.91145,2.91334,2.9152,2.91702,2.91881,2.9205 7,2.92229,2.92398,2.92564,2.92726,2.92886,2.93042,2.93195,2.93345,2.93492,2.936 36,2.93778,2.93916,2.94052,2.94185,2.94316,2.94444,2.94569,2.94692,2.94813,2.94 932,2.95048,2.95163,2.95275,2.95385,2.95494,2.95601,2.95706,2.95809,2.95911,2.9 6012,2.96111,2.96208,2.96305,2.964,2.96494,2.96587,2.96679,2.9677,2.9686,2.9694 9,2.97037,2.97125,2.97212,2.97298,2.97384,2.97469,2.97553,2.97638,2.97721,2.978 04,2.97887,2.97969,2.98051,2.98133,2.98214,2.98295,2.98376,2.98456,2.98536,2.98 616,2.98696,2.98776,2.98855,2.98934,2.99013,2.99092,2.9917,2.99248,2.99326,2.99

404,2.99482,2.99559,2.99636,2.99713,2.9979,2.99866,2.99943,3.00019,3.00094,3.00 169,3.00245,3.00319,3.00394,3.00468,3.00541,3.00615,3.00688,3.0076,3.00833,3.00 904,3.00976,3.01047,3.01117,3.01188,3.01257,3.01326,3.01395,3.01463,3.01531,3.0 1599,3.01665,3.01732,3.01798,3.01863,3.01928,3.01992,3.02056,3.02119,3.02182,3. 02244,3.02306,3.02367,3.02428,3.02488,3.02548,3.02607,3.02665,3.02724,3.02781, 3.02838,3.02895,3.02951,3.03007,3.03062,3.03117,3.03172,3.03226,3.03279,3.0333 2,3.03385,3.03438,3.0349,3.03541,3.03593,3.03643,3.03694,3.03744,3.03794,3.0384 4,3.03893,3.03942,3.03991,3.0404,3.04088,3.04136,3.04184,3.04232,3.0428,3.04327 ,3.04374,3.04421,3.04468,3.04515,3.04562,3.04608,3.04655,3.04701,3.04748,3.0479 4,3.0484,3.04886,3.04933,3.04979,3.05025,3.05071,3.05117,3.05163,3.05209,3.0525 5,3.05301,3.05348,3.05394,3.0544,3.05486,3.05532,3.05579,3.05625,3.05671,3.0571 8,3.05764,3.05811,3.05858,3.05904,3.05951,3.05998,3.06044,3.06091,3.06138,3.061 85,3.06232,3.06279,3.06326,3.06373,3.0642,3.06467,3.06514,3.0656,3.06607,3.0665 4,3.06701,3.06748,3.06795,3.06842,3.06889,3.06935,3.06982,3.07028,3.07075,3.071 21,3.07167,3.07214,3.0726,3.07306,3.07351,3.07397,3.07442,3.07488,3.07533,3.075 78,3.07622,3.07667,3.07711,3.07755,3.07799,3.07843,3.07886,3.07929,3.07972,3.08 014,3.08057,3.08099,3.0814,3.08182,3.08223,3.08264,3.08304,3.08344,3.08384,3.08 423,3.08463,3.08501,3.0854,3.08578,3.08615,3.08653,3.0869,3.08726,3.08762,3.087 98,3.08833,3.08868,3.08903,3.08937,3.08971,3.09004,3.09037,3.0907,3.09102,3.091 34,3.09166,3.09197,3.09227,3.09258,3.09287,3.09317,3.09346,3.09375,3.09403,3.09 431,3.09459,3.09486,3.09513,3.09539,3.09565,3.09591,3.09616,3.09642,3.09666,3.0 9691,3.09715,3.09739,3.09762,3.09785,3.09808,3.09831,3.09853,3.09875,3.09897,3. 09919,3.0994,3.09961,3.09982,3.10002,3.10023,3.10043,3.10063,3.10082,3.10102,3. 10121,3.1014,3.10159,3.10178,3.10197,3.10215,3.10234,3.10252,3.1027,3.10288,3.1 0306,3.10324,3.10342,3.1036,3.10377,3.10395,3.10412,3.1043,3.10447,3.10464,3.10 482,3.10499,3.10516,3.10533,3.10551,3.10568,3.10585,3.10602,3.10619,3.10637,3.1 0654,3.10671,3.10688,3.10706,3.10723,3.1074,3.10758,3.10775,3.10793,3.1081,3.10 828,3.10846,3.10863,3.10881,3.10899,3.10917,3.10935,3.10953,3.10971,3.10989,3.1 1007,3.11025,3.11044,3.11062,3.1108,3.11099,3.11118,3.11136,3.11155,3.11174,3.1 1193,3.11212,3.11231,3.1125,3.11269,3.11288,3.11308,3.11327,3.11347,3.11366,3.1 1386,3.11406,3.11426,3.11446,3.11466,3.11486,3.11506,3.11526,3.11547,3.11567,3. 11588,3.11609,3.1163,3.11651,3.11672,3.11693,3.11714,3.11736,3.11758,3.11779,3. 11801,3.11824,3.11846,3.11868,3.11891,3.11914,3.11937,3.1196,3.11984,3.12008,3. 12032,3.12056,3.1208,3.12105,3.1213,3.12156,3.12181,3.12207,3.12233,3.1226,3.12 287,3.12314,3.12342,3.1237,3.12398,3.12427,3.12456,3.12486,3.12516,3.12546,3.12 577,3.12608,3.1264,3.12672,3.12705,3.12738,3.12771,3.12805,3.12839,3.12874,3.12 909,3.12945,3.12981,3.13018,3.13054,3.13092,3.13129,3.13167,3.13205,3.13244,3.1 3283,3.13322,3.13361,3.134,3.13439,3.13479,3.13518,3.13557,3.13596,3.13635,3.13 673,3.13711,3.13749,3.13786,3.13822,3.13858,3.13892,3.13925,3.13958,3.13988,3.1 4018,3.14045,3.14071,3.14095}（这便是拟合函数数值化后，再取对数的结果，将大括号中的数字复制到word中，使用查找替换命令，将逗号换成^p（^p这是代表回车的意思，就可以把数据转换成一列）。把这一列数据导入origin中，画图，再取微分，如下图）

200300400500600700800

2.2

2.4

2.6

2.8

3.0

3.2

Y A x i s T i t l e X Axis Title

（此为对数的曲线图）

0.00

0.01

0.02

0.030.04

0.05

Y A x i s T i t l e X Axis Title

（此为取微分的曲线图）

将origin 中得到的对数曲线的微分曲线的数据导入excel 中又可得微分后的一一对应数据点。需要强调一点，在excel 中，需要把导入的数据表示成mathematice 认识的形式，即正常的我们人书写使用的格式。可以在excel 中，选中数据，右键，“单元格格式”中更改数据表示格式。

2再打开“先取对数,再微分的200-2500数据拟合.nb”，这个小程序可以得到需要积分的函数表达式。如下：

f={{200.0000000000,0.0390700000},{201.0000000000,0.0347400000},{202.0000000000,0.027*******},{203.0000000000,0.021*******},{204.0000000000,0.0175700000},{205.0000000000,0.0145500000},{206.0000000000,0.0123400000},{207.0000000000,0.010*******},{208.0000000000,0.0096100000},{209.0000000000,0.0088200000},{210.0000000000,0.0083100000},{211.0000000000,0.0079600000},{212.0000000000,0.0077500000},{213.0000000000,0.0076400000},{214.0000000000,0.0075800000},{215.0000000000,0.0075500000},{216.0000000000,0.0075500000},{217.

0000000000,0.0075500000},{218.0000000000,0.0075400000},{219.0000000000,0.0 075200000},{220.0000000000,0.0074800000},{221.0000000000,0.0074300000},{2 22.0000000000,0.0073700000},{223.0000000000,0.0072700000},{224.0000000000, 0.0071700000},{225.0000000000,0.0070600000},{226.0000000000,0.0069300000}, {227.0000000000,0.0068000000},{228.0000000000,0.0066500000},{229.00000000 00,0.0065000000},{230.0000000000,0.0063500000},{231.0000000000,0.006190000 0},{232.0000000000,0.0060400000},{233.0000000000,0.0058800000},{234.000000 0000,0.0057400000},{235.0000000000,0.0056000000},{236.0000000000,0.0054500 000},{237.0000000000,0.0053200000},{238.0000000000,0.0051800000},{239.0000 000000,0.0050600000},{240.0000000000,0.0049400000},{241.0000000000,0.00483 00000},{242.0000000000,0.0047300000},{243.0000000000,0.0046300000},{244.00 00000000,0.0045400000},{245.0000000000,0.0044600000},{246.0000000000,0.004 3800000},{247.0000000000,0.0043100000},{248.0000000000,0.0042400000},{249. 0000000000,0.0041800000},{250.0000000000,0.0041300000},{251.0000000000,0.0 040800000},{252.0000000000,0.0040400000},{253.0000000000,0.0039800000},{2 54.0000000000,0.0039500000},{255.0000000000,0.0039200000},{256.0000000000, 0.0038800000},{257.0000000000,0.0038500000},{258.0000000000,0.0038300000}, {259.0000000000,0.0038000000},{260.0000000000,0.0037700000},{261.00000000 00,0.0037600000},{262.0000000000,0.0037400000},{263.0000000000,0.003710000 0},{264.0000000000,0.0037000000},{265.0000000000,0.0036800000},{266.000000 0000,0.0036600000},{267.0000000000,0.0036400000},{268.0000000000,0.0036200 000},{269.0000000000,0.0036100000},{270.0000000000,0.0035900000},{271.0000 000000,0.0035700000},{272.0000000000,0.0035500000},{273.0000000000,0.00353 00000},{274.0000000000,0.0035100000},{275.0000000000,0.0034900000},{276.00 00000000,0.0034600000},{277.0000000000,0.0034500000},{278.0000000000,0.003 4300000},{279.0000000000,0.0034000000},{280.0000000000,0.0033800000},{281. 0000000000,0.0033500000},{282.0000000000,0.0033300000},{283.0000000000,0.0 033000000},{284.0000000000,0.0032700000},{285.0000000000,0.0032500000},{2 86.0000000000,0.0032200000},{287.0000000000,0.0031900000},{288.0000000000, 0.0031600000},{289.0000000000,0.0031400000},{290.0000000000,0.0031000000}, {291.0000000000,0.0030700000},{292.0000000000,0.0030400000},{293.00000000 00,0.0030100000},{294.0000000000,0.0029800000},{295.0000000000,0.002950000 0},{296.0000000000,0.0029200000},{297.0000000000,0.0028900000},{298.000000 0000,0.0028500000},{299.0000000000,0.0028200000},{300.0000000000,0.0027900 000},{301.0000000000,0.0027600000},{302.0000000000,0.0027300000},{303.0000 000000,0.0026900000},{304.0000000000,0.0026500000},{305.0000000000,0.00263 00000},{306.0000000000,0.0026000000},{307.0000000000,0.0025600000},{308.00 00000000,0.0025200000},{309.0000000000,0.0025000000},{310.0000000000,0.002 4700000},{311.0000000000,0.0024300000},{312.0000000000,0.0024000000},{313. 0000000000,0.0023700000},{314.0000000000,0.0023400000},{315.0000000000,0.0 023100000},{316.0000000000,0.0022800000},{317.0000000000,0.0022500000},{3 18.0000000000,0.0022100000},{319.0000000000,0.0021900000},{320.0000000000, 0.0021600000},{321.0000000000,0.0021300000},{322.0000000000,0.0021000000}, {323.0000000000,0.0020700000},{324.0000000000,0.0020400000},{325.00000000

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495},{521.,0.00049},{522.,0.00049},{523.,0.00049},{524.,0.000485},{525.,0.00048 5},{526.,0.000485},{527.,0.000475},{528.,0.000475},{529.,0.000475},{530.,0.0004 7},{531.,0.00047},{532.,0.00047},{533.,0.000465},{534.,0.00046},{535.,0.00046},{ 536.,0.000455},{537.,0.000455},{538.,0.000455},{539.,0.000445},{540.,0.000445}, {541.,0.000445},{542.,0.00044},{543.,0.00044},{544.,0.000435},{545.,0.00043},{5 46.,0.00043},{547.,0.00043},{548.,0.000425},{549.,0.00042},{550.,0.00042},{551., 0.000415},{552.,0.000415},{553.,0.00041},{554.,0.000405},{555.,0.000405},{556., 0.0004},{557.,0.0004},{558.,0.000395},{559.,0.000395},{560.,0.00039},{561.,0.000 385},{562.,0.000385},{563.,0.00038},{564.,0.00038},{565.,0.000375},{566.,0.0003 7},{567.,0.00037},{568.,0.00037},{569.,0.000365},{570.,0.00036},{571.,0.000355}, {572.,0.000355},{573.,0.000355},{574.,0.00035},{575.,0.000345},{576.,0.00034},{ 577.,0.00034},{578.,0.00034},{579.,0.000335},{580.,0.00033},{581.,0.00033},{582. ,0.000325},{583.,0.00032},{584.,0.00032},{585.,0.00032},{586.,0.000315},{587.,0. 000315},{588.,0.00031},{589.,0.000305},{590.,0.000305},{591.,0.0003},{592.,0.00 03},{593.,0.0003},{594.,0.000295},{595.,0.00029},{596.,0.00029},{597.,0.000285}, {598.,0.00028},{599.,0.00028},{600.,0.00028},{601.,0.00028},{602.,0.000275},{60 3.,0.00027},{604.,0.00027},{605.,0.00027},{606.,0.000265},{607.,0.00026},{608.,0. 00026},{609.,0.00026},{610.,0.000255},{611.,0.000255},{612.,0.000255},{613.,0.0 0025},{614.,0.00025},{615.,0.000245},{616.,0.000245},{617.,0.000245},{618.,0.00 024},{619.,0.00024},{620.,0.000235},{621.,0.000235},{622.,0.000235},{623.,0.000 23},{624.,0.00023},{625.,0.00023},{626.,0.00023},{627.,0.00023},{628.,0.000225}, {629.,0.00022},{630.,0.00022},{631.,0.00022},{632.,0.00022},{633.,0.00022},{634. ,0.00022},{635.,0.000215},{636.,0.000215},{637.,0.000215},{638.,0.00021},{639.,0 .000215},{640.,0.000215},{641.,0.00021},{642.,0.000205},{643.,0.000205},{644.,0. 00021},{645.,0.00021},{646.,0.000205},{647.,0.000205},{648.,0.000205},{649.,0.0 00205},{650.,0.000205},{651.,0.0002},{652.,0.0002},{653.,0.000205},{654.,0.0002 05},{655.,0.0002},{656.,0.0002},{657.,0.0002},{658.,0.0002},{659.,0.0002},{660.,0 .0002},{661.,0.0002},{662.,0.0002},{663.,0.0002},{664.,0.0002},{665.,0.0002},{66 6.,0.0002},{667.,0.000205},{668.,0.000205},{669.,0.0002},{670.,0.0002},{671.,0.00 02},{672.,0.0002},{673.,0.0002},{674.,0.0002},{675.,0.000205},{676.,0.000205},{6 77.,0.0002},{678.,0.000205},{679.,0.000205},{680.,0.0002},{681.,0.000205},{682., 0.00021},{683.,0.000205},{684.,0.000205},{685.,0.00021},{686.,0.00021},{687.,0.0 00205},{688.,0.000205},{689.,0.00021},{690.,0.000215},{691.,0.000215},{692.,0.0 0021},{693.,0.000215},{694.,0.000215},{695.,0.000215},{696.,0.000215},{697.,0.0 00215},{698.,0.00022},{699.,0.00022},{700.,0.00022},{701.,0.00022},{702.,0.0002 2},{703.,0.00022},{704.,0.000225},{705.,0.000225},{706.,0.000225},{707.,0.00023 },{708.,0.00023},{709.,0.00023},{710.,0.00023},{711.,0.00023},{712.,0.00023},{71 3.,0.000235},{714.,0.000235},{715.,0.000235},{716.,0.00024},{717.,0.00024},{718. ,0.00024},{719.,0.00024},{720.,0.00024},{721.,0.000245},{722.,0.000245},{723.,0. 000245},{724.,0.000245},{725.,0.000245},{726.,0.00025},{727.,0.00025},{728.,0.0 00255},{729.,0.000255},{730.,0.00025},{731.,0.000255},{732.,0.00026},{733.,0.00 026},{734.,0.00026},{735.,0.00026},{736.,0.00026},{737.,0.00026},{738.,0.000265 },{739.,0.000265},{740.,0.000265},{741.,0.00027},{742.,0.000265},{743.,0.000265 },{744.,0.000275},{745.,0.000275},{746.,0.00027},{747.,0.000275},{748.,0.000275

},{749.,0.000275},{750.,0.00028},{751.,0.000275},{752.,0.000275},{753.,0.00028}, {754.,0.000285},{755.,0.000285},{756.,0.00028},{757.,0.000285},{758.,0.000285}, {759.,0.000285},{760.,0.00029},{761.,0.000285},{762.,0.000285},{763.,0.00029},{ 764.,0.00029},{765.,0.00029},{766.,0.000295},{767.,0.000295},{768.,0.00029},{76 9.,0.000295},{770.,0.000295},{771.,0.000295},{772.,0.000295},{773.,0.000295},{7 74.,0.0003},{775.,0.0003},{776.,0.000295},{777.,0.000295},{778.,0.0003},{779.,0.0 003},{780.,0.0003},{781.,0.0003},{782.,0.000305},{783.,0.000305},{784.,0.0003},{ 785.,0.0003},{786.,0.0003},{787.,0.000305},{788.,0.000305},{789.,0.0003},{790.,0. 0003},{791.,0.000305},{792.,0.000305},{793.,0.0003},{794.,0.000305},{795.,0.000 305},{796.,0.0003},{797.,0.000305},{798.,0.000305},{799.,0.0003},{800.,0.000305 }}

{T-10→-9.3586 1028,T-9→4.20404 1027,T-8→-8.58229 1025,T-7→1.04756 1024,T-6→-8.42324 1021,T-5→4.58249 1019,T-4→-1.60976 1017,T-3→2.64818 1014,T-2→6 .2827 1011,T-1→-5.82359 109,T0→2.04799 107,T1→-43646.2,T2→54.0737,T3→-0 .0119145,T4→-0.000100414,T5→2.31208 10-7,T6→-2.86402 10-10,T7→2.28159 1 0-13,T8→-1.17248 10-16,T9→3.56601 10-20,T10→-4.90328 10-24}

2.04799 107-9.3586 1028/x10+4.20404 1027/x9-8.58229 1025/x8+1.04756 1024/x7-8.42324 1021/x6+4.58249 1019/x5-1.60976 1017/x4+2.64818 1014/x3+6.2827 1011 /x2-5.82359 109/x-43646.2 x+54.0737 x2-0.0119145 x3-0.000100414

x4+2.31208 10-7 x5-2.86402 10-10 x6+2.28159 10-13 x7-1.17248 10-16

x8+3.56601 10-20 x9-4.90328 10-24 x10（此函数表达式即为需要用来积分的表达式）

3．积分

打开“积分结果”文件夹，打开任一个文件，说明如下：

（1）被积函数

（2）此命令为积分选择积分区间。因为积分时间较长，容易死机。如：y=Table[200+u,{u,0,50}]表示从200积到250，一次积50个点。200表示起始点，u 为0到50，即表示从200积到250，如果{u,51,100}，即表示从251积到300。在这里，你可以根据你的电脑配置来选择一次积分多少个点，如果你的电脑不行，我建议一次50个点，比较合理。第一次积分：{u,0,50}，第二次{u,51,100}，第三次{u,101,150}。。。一直积到你的数据结束，以本例说明，范围是200－800，最后一个积分为{u,551,600}

（3）积分命令。图中为我原始数据200－2500，根据你的数据，200改为你的数据的开始波长，2500改为你的数据的结束波长。式中f为被积函数，在第（1）步中已经定义，可以不管它。

（4）此结果告诉你是从哪里积到哪里的，即输入你的积分区间。

（5）这是积分结果，把它复制到word中，把逗号替换成回车，再复制到excel中保存起来。把所有的积分都积出来之后，即得到你的数据所有积分结果。保存起来，到这里，你的工作已经完成了2/3了。其中，你积分得到的这个数组为w2（后面会用到的。）

4解析延拓

（1）小于你的数据的开始点的数据延拓。

打开“解析延拓(小于200nm).nb”

A＝6.00639/210^4

B=D[Log[A*x^4],x]

其实，不管A如何变，B都等于4/x，所以，只需要计算一次小于你的开始点的解析延拓即可，即，只需要对4/x积分就行了。

y=Table[200+u,{u,0,2300}]，这一步同样是为了设定积分区间，2300是我的数据，即从200到2500，有2300个点，你的数据，你自己更改。

W1即是为了求小于开始点的解析延拓。W1的式中，200表示开始点（根据你的数据，自己设定），这里面，你只需要改200就行了。

积出的结果为数组w1,保存起来。w1的值都是一样的，你每个样品都可以用这个值。这个积分比较快，可以一次积完。

（2）大于你的数据的结束点的数据延拓。

打开“g100解析延拓(大于2500nm).nb”

这里，你只需改f的表达式，f=25-(25-24.57144)*2500/x。这里，24.57144为你原始数据的最后一个数据点的y值，25为略大于最后一个数据点y值的整数。

y=Table[200+u,{u,0,2300}],200为开始点。2300为一共多少个数据点。

W3需要改动的地方为2500，即改为你的数据结束点。

其它的不用更改。

得到的数组为w3.保存起来。

5 w1+w2+w3,拟合。

打开“w1+w2+w3拟合.nb”

钻柱分析

钻柱 一、钻柱的作用与组成 二、钻柱的工作状态与受力分析 三、钻柱设计 一、钻柱的组成与功用 （一）钻柱的组成 钻柱(Drilling String)是钻头以上，水龙头以下部分的钢管柱的总称. 它包括方钻杆(Square Kelly)、钻杆(Drill Pipe)、钻挺(Drill Collar)、各种接头(Joint)及稳定器(Stabilizer)等井下工具。 （二）钻柱的功用 (1)提供钻井液流动通道； (2)给钻头提供钻压； (3)传递扭矩； (4)起下钻头； (5)计量井深。 (6)观察和了解井下情况（钻头工作情况、井眼状况、地层情况）； (7)进行其它特殊作业（取芯、挤水泥、打捞等）； (8)钻杆测试 ( Drill-Stem Testing),又称中途测试。 1. 钻杆 （1）作用：传递扭矩和输送钻井液，延长钻柱。 （2）结构：管体+接头 （3）规范： 壁厚：9 ～ 11mm 外径： 长度： 根据美国石油学会(American Petroleum Institute,简称API)的规定，钻杆按长度分为三类： 第一类 5.486～ 6.706米(18～22英尺)； 第二类 8.230～ 9.144米(27～30英尺); 第三类 11.582～13.716米(38～45英尺)。 常用钻杆规范（内径、外径、壁厚、线密度等）见表2-12 ?丝扣连接条件：尺寸相等，丝扣类型相同，公母扣相匹配。 ?钻杆接头特点：壁厚较大，外径较大，强度较高。 ?钻杆接头类型：内平（IF）、贯眼（FH）、正规（REG）； NC系列 ?

内平式：主要用于外加厚钻杆。特 点是钻杆通体内径相同，钻井液 流动阻力小；但外径较大，容易 磨损。 贯眼式：主要用于内加厚钻杆。其 特点是钻杆有两个内径，钻井液 流动阻力大于内平式，但其外径 小于内平式。 正规式：主要用于内加厚钻杆及钻 头、打捞工具。其特点是接头内 径<加厚处内径<管体内径，钻井 液流动阻力大，但外径最小，强 度较大。 三种类型接头均采用V型螺纹， 但扣型、扣距、锥度及尺寸等都 有很大的差别。 NC型系列接头NC23，NC26，NC31，NC35，NC38，NC40，NC44，NC46，NC50，NC56，NC61，NC70，NC77 NC—National Coarse Thread，（美国）国家标准粗牙螺纹。 xx—表示基面丝扣节圆直径，用英寸表示的前两位数字乘以10。 如：NC26表示的节圆直径为2.668英寸。 NC螺纹也为V型螺纹, 表2-17所列的几种NC型接头与旧API标准接头有相同的节圆直 2. 钻铤 结构特点：管体两端直接车制丝扣，无专门接头；壁厚大(38-53毫米）， 重量大，刚度大。 主要作用：(1)给钻头施加钻压; (2)保证压缩应力条件下的必要强度; (3)减轻钻头的振动、摆动和跳动等，使钻头工作平稳； (4)控制井斜。 类型：光钻铤、螺旋钻铤、扁钻铤。 常用尺寸：6-1/4〃，7 〃，8 〃，9 〃 3.方钻杆 类型：四方形、六方形 特点：壁厚较大，强度较高 主要作用：传递扭矩和承受钻柱的全部重量。 常用尺寸：89mm(3.5英寸)，108mm (4.5英寸)，133.4mm (5.5英寸)。 4.稳定器 类型：刚性稳定器、不转动橡胶套稳定器、滚轮稳定器。

小学数学常见数量关系和计算公式

小学数学常见数量关系 和计算公式 集团档案编码：[YTTR-YTPT28-YTNTL98-UYTYNN08]

1.一般关系式 路程=速度×时间速度=路程÷时间 时间=路程÷速度 工作总量=工作效率×工作时间 工作效率=工作总量÷工作时间 工作时间=工作总量÷工作效率 总产量=单产量×数量 单产量=总产量÷数量 数量=总产量÷单产量 总价=单价×数量单价=总价÷数量 数量=总价÷单价 利息=本金×年利率×年数 利息=本金×月利率×月数 税后利息=本金×年利率×年数×（1-税率）税后利息=本金×月利率×月数×（1-税率） 个人所得税=（收入-基数）×税率 2.四则运算中的关系式 加数+加数=和 一个加数=和—另一加数 被减数—减数=差被减数=差+减数

减数=被减数—差 因数×因数=积 一个因数=积÷另一个因数 被除数÷除数=商被除数=商×除数 除数=被除数÷商 3.计算公式 (1)周长 长方形周长=（长+宽）×2 正方形周长=边长×4 圆的周长：C=2Лr或C=Лd （2）面积 长方形的面积=长×宽 正方形的面积=边长×边长 三角形的面积=底×高÷2 平行四边形的面积=底×高 梯形的面积=（上底+下底）×高÷2 圆面积；S=Лr2 （3）表面积 正方体表面积=棱长×棱长×6 长方体的表面积=（长×宽+长×高+宽×高）×2 圆柱的表面积=侧面积=底面积×2

（4）柱体的侧面积 圆柱的侧面积=底面周长×高 （5）体积 正方体体积=棱长×棱长×棱长或V=a3 长方体的体积=长×宽×高或V=abh 圆柱的体积=底面积×高或v=sh 圆锥的体积=底面积×高÷3 或v=1/3sh （6）圆的相关计算公式（直径d,半径r，大圆半径R，圆周率Л，周长C） r=d÷2r=c÷Л÷2 d=2rd=c÷Л 环形面积=Л（R2-r2） (7)比例尺 图上距离：实际距离=比例尺 实际距离=图上距离÷比例尺 图上距离=实际距离×比例尺

数量关系及面积体积的计算(教师版)

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的激光位敏传感器安装在传感器座内，传感器座的头部与定心套连接，尾部与推杆连接。通过手动推动推杆可以使位置检测单元在炮管内孔内移动。 激光器定心去 工作时激光器发射1束激光射向激光位敏传感器，传感器内的PSD 芯片监测接收到的激光能量中心位置。定心套用来保证传感器一直处于炮管内孔的中心位置。当炮管在检测位置出现弯曲时，PSD芯片上的激光能量中心坐标值将发生变化。位置检测单元的电源线和数据线通过推杆中心孔与控制柜连接。

小学数学常用数量关系计算公式

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1公顷=10000平方米。1亩=666.666平方米。 1升=1立方分米=1000毫升1毫升=1立方厘米 7、什么叫比：两个数相除就叫做两个数的比。如：2÷5或3:6或1/3 比的前项和后项同时乘以或除以一个相同的数(0除外)，比值不变。 8、什么叫比例：表示两个比相等的式子叫做比例。如3:6=9:18 9、比例的基本性质：在比例里，两外项之积等于两内项之积。 要练说，得练听。听是说的前提，听得准确，才有条件正确模仿，才能不断地掌握高一级水平的语言。我在教学中，注意听说结合，训练幼儿听的能力，课堂上，我特别重视教师的语言，我对幼儿说话，注意声音清楚，高低起伏，抑扬有致，富有吸引力，这样能引起幼儿的注意。当我发现有的幼儿不专心听别人发言时，就随时表扬那些静听的幼儿，或是让他重复别人说过的内容，抓住教育时机，要求他们专心听，用心记。平时我还通过各种趣味活动，培养幼儿边听边记，边听边想，边听边说的能力，如听词对词，听词句说意思，听句子辩正误，听故事讲述故事，听谜语猜谜底，听智力故事，动脑筋，出主意，听儿歌上句，接儿歌下句等，这样幼儿学得生动活泼，轻松愉快，既训练了听的能力，强化了记忆，又发展了思维，为说打下了基础。10、解比例：求比例

数学图形计算公式

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用两种方式实现表达式自动计算培训资料

用两种方式实现表达式自动计算

数据结构（双语） ——项目文档报告用两种方式实现表达式自动计算 专业：计算机科学与技术应用 班级： 指导教师：吴亚峰 姓名： 学号：

目录 一、设计思想 (01) 二、算法流程图 (01) 三、源代码 (03) 四、运行结果 (15) 五、遇到的问题及解决 (16) 六、心得体会 (17)

一、设计思想 A: 中缀表达式转后缀表达式的设计思想： 我们借助计算机计算一个算数表达式的值，而在计算机中，算术表达式是由常量，变量，运算符和括号组成。由于运算符的优先级不同又要考虑括号。所以表达式不可能严格的从左到右进行，因此我们借助栈和数组来实现表达式的求值。栈分别用来存储操作数和运算符。 在计算表达式的值之前，首先要把有括号的表达式转换成与其等值的无括号的表达式，也就是通常说的中缀表达式转后缀表达式。在这个过程中，要设计两个栈，一个浮点型的存储操作数，用以对无符号的表达式进行求值。另一个字符型的用来存储运算符，用以将算术表达式变成无括号的表达式；我们要假设运算符的优先级：( ) , * /, + - 。首先将一标识号‘#’入栈，作为栈底元素；接着从左到右对算术表达式进行扫描。每次读一个字符，若遇到左括号‘（’，则进栈；若遇到的是操作数，则立即输出；若又遇到运算符，如果它的优先级比栈顶元素的优先级数高的话，则直接进栈，否则输出栈顶元素，直到新的栈顶元素的优先级数比它低的，然后将它压栈；若遇到是右括号‘）’，则将栈顶的运算符输出，直到栈顶的元素为‘（’，然后，左右括号互相底消；如果我们设计扫描到‘#’的时候表示表达式已经扫描完毕，表达式已经全部输入，将栈中的运算符全部输出，删除栈底的标识号。以上完成了中缀表达式转后缀表达式，输出无括号的表达式，若遇数值，操作数进栈；若遇运算符，让操作数栈的栈顶和次栈顶依次出栈并与此运算符进行运算，运算结果入操作数栈；重复以上的步

数量关系计算公式方面

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直线度测量计算方法

1引言 在工程实际中，评定导轨直线度误差的方法常用两端点连线法和最小条件法。两端点连线法，是将误差曲线首尾相连，再通过曲线的最高和最低点，分别作两条平行于首尾相连的直线，两平行线间沿纵坐标测量的数值，通过数据处理后，即为导轨的直线度误差值;最小条件法，是将误差曲线的“高、高”(或“低、低”)两点相连，过低(高)点作一直线与之相平行，两平行线间沿纵标坐测量的数值，通过数据处理后，即为导轨的直线误差值。 最小条件法是仲裁性评定。两端点连线法不是仲裁性评定，只是在评定时简单方便，所以在生产实际中常采用，但有时会产生较大的误差。本文讨论这两种评定方法之间产生误差的极限值。 2误差曲线在首尾连线的同侧 测量某一型号液压滑台导轨的直线度误差，得到直线度误差曲线，如图1所示。由图可知，该误差曲线在其首尾连线的同侧。下面分别采用最小条件法和两端点连线法，评定该导轨直线度误差值。 (1)最小条件法评定直线度误差 根据最小条件法，图1曲线的首尾分别是低点1和低点2(低点1与坐标原点重合)，用直a1a1线相连，如图2所示。通过最高点3作a1a1直线的平行线a2a2。

在a1a1和a2a2两平行线包容的区域，沿y轴测量的数值，经数据处理，即为该导轨的直线度误差值

δ最小法。 (2)两端点连线法评定直线度误差 根据两端点连线法，图1曲线的首尾也分别是曲线的两端点1和2，如图3所示。将曲线端点1和端点2，用直线b1b1相连，再通过高点作b1b1的平行线b2b2。在b1b1和b2b2两平行线包容的区域，沿y轴测量的数值，经数据处理，即为该导轨的直线度误差值δ两端点。 (3)求解两种评定方法产生的误差极限 由于是对同一导轨误差曲线求解直线度误差，图2中的“低点1”、“低点2”和“高点3”分别对应图3中的“端点1”、“端点2”和“高点3”，即直线 a1a1与直线b1b1重合，直线a2a2与直线b2b2重合，因此两种评定方法产生的误差值为零

钻柱强度计算新方法

钻柱强度计算新方法 韩志勇 （石油大学石油工程系，山东东营257062） 摘要 提出了一种钻柱强度计算新方法。可用于钻柱的强度设计和强度校核。新方法和传统方法相比，有以下五个特点：（1）对钻柱每一个断面都进行强度校核；（2）对管的内壁和外壁分别进行强度校核；（3）利用计算机进行断面上有关内力的计算；（4）用“液压系数”处理液压环境对钻柱轴向力的影响；（5）考虑液压环境引起的附加剪应力的影响。作者认为，“浮力系数”一次不甚恰当，应该用“液压系数”。详细地给出了各种液压环境下钻柱液压系数的计算公式及算例。并指出了新方法所属概念和共识的适用范围。 主题词 钻柱力学；钻井设计；强度；计算 0 引言 对钻柱在垂直井眼、倾斜井眼、弯曲井眼内，以及在循环条件下的轴向力计算问题，以有详细的论述和相关计算公式[1 ～4] 。但对一些问题的论述和钻柱强度计算公式的推导，还 有不完善的地方，本文对此作进一步阐述。文中给出的所有公式，均可按法定计量单位运算。使用常用单位时，应进行换算。 1 钻柱强度计算公式 1．1 安全系数和相当应力计算公式 微段的上断面的内缘处： N i =σs/σei )(3)(2 22ni mi bi a ei ττσσσ+++= 微段的上断面的外缘处： N o =σs/σeo )(3)(222no mo bo a eo ττσσσ+++= 式中，Ni 和No —分别为钻柱计算断面内缘、外缘处的强度安全数；

σs —钻柱钢材的最小屈服极限； σei 和σeo —分别为钻柱计算断面内、外缘处的相当应力； σa —钻柱计算断面上的轴向应力； σbi 和σbo —分别为钻柱计算断面内、外缘处的弯曲应力； τmi 和τni —分别为钻柱计算断面内缘处的扭应力和附加剪应力； τmO 和τnO —分别为钻柱计算断面外缘处的扭应力和附加剪应力； 1．2 轴向应力σa 的计算 σa =σz +σf +σp 式中，σz —由重力和液压力引起的轴向力； σf —钻柱轴向运动摩阻力引起的轴向应力； σp —钻压引起的轴向应力； 1．3 弯曲应力σbo 和σbi 的计算 若已知断面上的弯矩，可用下式计算： )(324 4i o i b bi D D D M ?=πσ ) (3244i o o b bo D D D M ?= πσ 若已知井眼曲率，可用下式计算： K ED i bi 21 =σ K ED o bo 2 1 =σ 若考虑接头影响，可用下式计算： )tanh(2U U K ED i bi =σ ) tanh(2U U K ED o bo =σ 其中，ρ??= L U 2 1 EI F z = ρ 式中，M b —计算断面的弯矩；

数量关系计算方法

一、 直接代入法 二、 数字特性法 1、有一个三位数，其百位数是个位数的2倍，十位数等于百位数和个位数之和，那么这个三位数是( ) A ．211 B ．432 C ．693 D ．824 解析：C 2、下列可以分解为三个不同质数相乘的三位数是( ) A ．100 B ．102 C ．104 D ．125 解析：100是4的倍数，104也是4的倍数，125=53 ，所以此题选择B 。 3、两根同样长的蜡烛，点完粗蜡烛要3个小时，点完细蜡烛要1个小时，同时点燃两根蜡烛，一段时间后，同时熄火，发现粗蜡烛长度是细蜡烛长度的3倍，问两根蜡烛燃烧了多长时间？ A??30分钟 B??35分钟 C??40分钟 D??45分钟 解析：假设两根蜡烛长度都是1， 燃烧同样时间之后，长蜡烛剩余长度 不到1，因为长蜡烛长度剩余部分是 细蜡烛长度的3倍，所以细蜡烛长度 剩余不到13 ，也就是说细蜡烛燃烧长 度超过23 ，也就是说时间超过23 ，即大于40 分钟，选D 。 1、某汽车厂生产甲、乙、丙三种车型， 其中乙型产量的3倍与丙型产量的6倍之和等于甲型产量的4倍，甲型产量与乙型的2倍之和等于丙型产量的7倍。则甲、乙、丙三型产量之比为（）。 A. 5:4:3 B. 4:3:2 C. 4:2:1 D. 3:2:1 解析：乙×3+丙×6=甲×4，等式的左边是3的倍数，等式的右边4不是3的倍数，则甲一定是3的倍数，所以用选D 。 2、产一批零件原计划每天产100个，实际每天生产120个。提前4天完成任务，还多生产80个。则工厂原计划生产零件（ ）个。 A. 2520 B. 2600 C.2800 D.2880 解析：120个/天×天数=原来计划+80，等号右侧应能被120整除，即(答案数+80)能被120整除，也就是能被3整除，选C 。 3、学校组织学生举行献爱心捐款活动，某年级共有三个班，甲班捐款数是另外两个班捐款总数的2/5，乙班捐款学是丙班的1.2

石油钻采设备及工艺处理在线作业任务(第二次在线作业任务)

第二次在线作业 单选题 (共40道题) 1.（ 2.5分）作用在钻头上的压力简称钻压。钻压大小由司钻控制（）进行调节。 ? A、钻具高度 ? B、钻井泵排量 ? C、钻具悬重 ? D、钻井泵压力 我的答案：C 此题得分：2.5分 2.（2.5分）钻头转速，对转盘钻而言，即（）转速。 ? A、水龙头 ? B、大钩 ? C、转盘 ? D、井下动力钻具的转子 我的答案：C 此题得分：2.5分

3.（2.5分）钻井液性能通常用（）表示 ? A、比重、粘度和切力 ? B、比重、温度和切力 ? C、比重、粘度和拉力 ? D、比重、温度和拉力 我的答案：A 此题得分：2.5分 4.（2.5分）平衡压力钻井是指钻井过程中保持井内（）相等。 ? A、钻井液动压力与地层孔隙压力 ? B、钻井液静压力与钻井液动压力 ? C、钻井液静压力与地层孔隙压力 ? D、地层膨胀压力与地层孔隙压力 我的答案：A 此题得分：2.5分 5.（2.5分）钻机有（）项主要参数。 ? A、2 ? B、4 ? C、6 ? D、8 我的答案：D 此题得分：2.5分

6.（2.5分）方钻杆由（ )悬持。 ? A、控制系统 ? B、循环系统 ? C、传动系统 ? D、起升系统 ? E、辅助系统 我的答案：D 此题得分：2.5分 7.（2.5分）以下说法，（）正确。 ? A、转盘旋转钻井法中，起升系统由井架、天车及游车组成，以悬持、提升和下放钻柱。 ? B、转盘旋转钻井法中，起升系统由井架、天车、游车、大钩及绞车组成，以悬持、提升和下放钻柱。 ? C、转盘旋转钻井法中，起升系统由天车、游车、大钩及绞车组成，以悬持、提升和下放钻柱。 ? D、转盘旋转钻井法中，起升系统由天车、游车、大钩及水龙头组成，以悬持、提升和下放钻柱。 我的答案：B 此题得分：2.5分 8.（2.5分）以下说法，（）正确。 ? A、转盘旋转钻井法中，工作时，动力机驱动绞车，通过水龙头带动井中钻杆柱，从而带动钻头旋转。 ? B、转盘旋转钻井法中，工作时，动力机驱动水龙头带动井中钻杆柱，从而带动钻头旋转。

小学一至四年级数学公式及定义(人教版)常用数量关系及计算公式

小学一至四年级数学公式及定义(人教版)常用数量关系及计算公式 1.每份数×份数=总数总数÷每份数=份数总数÷份数=每份数 2. 1倍数×倍数=几倍数几倍数÷1倍数=倍数几倍数÷倍数=1倍数 3.速度×时间=路程路程÷速度=时间路程÷时间=速度 4、单价×数量=总价总价÷单价=数量总价÷数量=单价 5、工作效率×工作时间=工作总量 工作总量÷工作效率=工作时间工作总量÷工作时间=工作效率 6、加数+加数=和和一一个加数=另一个加数 7、被减数-减数=差被减数一差=减数差+诚数=被减数 8、因数×因数=积积÷一个因数=另一个因数 9、被除数÷除数=商被除数÷商=除数商×除数=被除数 10、单产量×面积=总产量总产量÷面积=单产量总产量÷单产量=面积图形计算公式: 1、正方形周长=边长×4 字母公式:C=4a 面积=边长×边长 S=a×a 2.长方形周长=（长+宽)×2 C=2(a+b) 面积=长×宽 S=a×b 三角形面积=底×高÷2 S=ah÷2 三角形高=面积×2÷底 h=S×2÷a 三角形底=面积×2÷高 a=S×2÷h 3.平行四边形面积=底×高 S=ah 4.梯形面积=（上底+下底)×高÷2 S=(a+b)×h÷2 单位换算: 长度单位： 一公里=1千米=1000米 1分米=10厘米 1米=10分米 1厘米=10毫米 面积单位: 1平方千米=100公顷 1公顷=100公亩 1公亩=100平方米 1平方千米=10000方米 1公顷=1000平方米 1平方米=100平方分米 1平方分米=100平方厘米 1平方厘米=100平方毫米 重量单位: 1吨=1000千克 1千克=1000克

用两种方法实现表达式求值

一、设计思想 一．中缀式计算结果的设计思想： 此种算法最主要是用了两个栈：用两个栈来实现算符优先，一个栈用来保存需要计算的数据numStack（操作数栈）,一个用来保存计算优先符priStack（操作符栈）。从字符串中获取元素，如果是操作数，则直接进操作数栈，但如果获取的是操作符，则要分情况讨论，如下：（这里讨论优先级时暂不包括“（”和“）”的优先级） 1.如果获取的操作符a的优先级高于操作符栈栈顶元素b的优先级，则a直接入操作符栈; 2.如果获取的操作符a的优先级低于操作符栈栈顶元素b的优先级，则b出栈，a进栈，并且取出操作数栈的栈顶元素m，再取出操作数栈新的栈顶元素n，如果b为+，则用n+m，若为减号，则n-m，依此类推，并将所得结果入操作数栈； 3.如果获取的是“（”，则直接进操作符栈； 4.如果获取的是“）”，则操作符栈的栈顶元素出栈,做类似于情况2的计算，之后把计算结果入操作数栈，再取操作符栈顶元素，如果不是“（”，则出栈，重复操作，直到操作符栈顶元素为“（”，然后“（”出栈； 5.当表达式中的所有元素都入栈后，看操作符栈中是否还有元素，如果有，则做类似于情况2 的计算，并将结果存入操作数栈，则操作数栈中最终的栈顶元素就是所要求的结果。 二．中缀转后缀及对后缀表达式计算的设计思想： 中缀转后缀时主要用了一个操作符栈和一个用来存放后缀表达式的栈，从表达式中依次获取元素，如果获取的是操作数，则直接存入s3栈中，如果获取的是操作符也需分情况讨论，如下：（这里讨论优先级时暂不包括“（”和“）”的优先级） 1. 如果获取的操作符a的优先级高于操作符栈栈顶元素b的优先级，则a直接入操作符栈; 2. 如果获取的操作符a的优先级低于操作符栈栈顶元素b的优先级，则b出栈，a进栈，并且将b存入到操作符栈中； 3.如果获取的是“（”，则直接进操作符栈； 4.如果获取的是“）”，则操作符栈的栈顶元素出栈,并依次存入到操作符栈中，直到操作符栈栈顶元素为“（”，然后将“（”出栈； 5.当表达式中的所有元素都入栈或存入到操作符栈之后，看操作符栈中是否还有元素，如果有，则依次出栈，并且依次存入到操作符栈中，最后打印操作符栈中的字符串，则此字符串即为要求的后缀表达式。 对后缀表达式的计算方法：主要用到了一个操作数栈，从操作符栈中依次取出元素，如果是操作数，则进栈，如果是操作符，则从操作数栈中依次取出两个栈顶元素a1和a2,如果操作符是“/”,则计算a2/a1,将计算结果再次进栈，依此类推，最终栈顶元素即为计算的最终结果。 在这两种算法中，应该特别注意一点：人的习惯，用户在输入表达式时，容易这样输入，如：3*4（3+2），这样是不可取的，应必须要用户输入3*4*（3+2），这是在设计思想上错误提示的很重要一点，否则计算不全面！ 二、算法流程图 第一个图是直接计算的流程图，图中反应除了这种方法的大致设计思路，但是有些细节没有反映出来，比如说，怎样把字符型数据转换为浮点型数据，就没有反映出来。特别说明

导轨直线度误差检测方法介绍

导轨直线度误差检测方法介绍

一、直经度的定义 限制实际直线对理想直线变动量的一种形状公差。由形状（理想包容形状）、大小（公差值）、方向、位置四个要素组成。用于限制一个平面内的直线形状偏差，限制空间直线在某一方向上的形状偏差，限制空间直线在任一方向上的形状偏差。 几何误差是指零件加工后的实际形状、方向和相互位置与理想形状、方向和相互位置的差异。在形状上的差异称形状误差，在方向上的差异称方向误差，在相互位置上的差异称位置误差。直线度在几何公差中是最基础的部分，按检测关系分直线度属于被测要素中的单一要素——指对要素本身提出形状公差要求的被测要素。 二、导轨直线度误差检测方法 直线度误差的检测方法很多。工件较小时，常以刀口尺、检验平尺作为模拟理想直线，用光隙法或间隙法确定被测实际要素的直线度误差。当工件较大时，则常按国标规定的测量坐标值原则进行测量，取得必要的一组数据，经作图法或计算法得到直线度误差，还有种高效的测量方法就是直接利用太友科技的数据采集仪连接百分表来测量，无需人工读数、作图、分析，采集仪会自动读数数据并进行数据分析，一旦测量结果不合格还会自动产生报警功能。 测量直线度误差常用的仪器有：框式水平仪、合象水平仪、电感式水平仪、自准直仪以及数据采集分析仪等。这类仪器的特点是：测定微小角度的变化，换算为线值误差。本实验用合象水平仪和数据采集分析仪来进行直线度测量。 1、利用合象水平仪测量直线度法 1）合象水平仪的介绍 合象水平仪采用光学放大，并以对称棱镜使双象重合来提高读数精度，利用杠杆和微动螺杆传动机构来提高测量精度和增大测量范围。将合象水平仪置于被测工件表面上，当被测两点相对水平线不等高时，将引起两气泡象不重合，转动度盘，使两气泡重合，度盘转过格数代表被测两点相对水平线的高度差，见图2-3。

第5章钻柱

第五章 钻柱 第一节 钻柱的工作状态及受力分析 一、工作状态 起下钻时： 钻柱处于悬持状态－－受拉伸(自重)，直线稳定状态 正常钻进： Ｐ＜Ｐ1 直线稳定 Ｐ1≤Ｐ＜Ｐ2 一次弯曲 Ｐ2≤Ｐ＜Ｐ3 二次弯曲 钻柱旋转→扭矩 离心力→下部弯曲半波缩短 上部弯曲半波增长（上部受拉） 结论：变节距的空间螺旋弯曲曲线形状 钻柱在井内可能有4种旋转形式：(P96) a.自转： b.公转：沿井壁滑动。 c.自转和公转的结合：沿井壁滚动。 d.整个钻柱作无规则的摆动： 二、钻柱在井下的受力分析 (1) 轴向拉应力与压应力 拉应力：由钻柱自重产生，井口最大，起钻和卡钻时产生附加拉力。 压应力：由钻压产生，井底最大。应力分布(P97，图3-2) 轴向力零点：钻柱上即不受拉也不受压的一点。 中和点：该点以下钻柱在液体中的重量等于钻压。 (2) 剪应力(扭矩)：旋转钻柱和钻头所需的力，井口最大。 (3) 弯曲应力：钻柱弯曲并自转时产生交变的拉压应力。 井眼弯曲→钻柱弯曲 1 32

(4) 纵向、横向、扭转振动 (5) 其他外力：起下钻动载（惯性）,井壁磨擦力，钻柱旋转时因离心力引起的弯曲。 综合以上分析：工况不同，应力作用不同，需根据实际工况确定应力状态。 (1) 钻进时钻柱下部：轴向压力、扭矩、弯曲力矩、交变应力； (2) 钻进和起下钻时井口钻柱：拉力、扭力最大＋动载 (3) 钻压、地层岩性变化引起中和点位移产生交变载荷。 第二节 钻井过程中各种应力的计算 一、轴向应力计算 （一）上部拉应力计算 1、钻柱在泥浆中空悬 浮力：αρ????=F L g B m α——考虑钻杆接头和加厚影响的重量修正系数，1.05～1.10 钻柱在空气中的重力：αρ????=F L g Q s a 井口拉力：B Q Q a -= a f Q K Q ?= 浮力系数：)1(s m f K ρρ-= ρs －－钢的密度，7.85 g/cm 3 拉应力：F Q t =σ 注意计算井口以下任一截面上的拉力不能直接用浮力系数法计算。 2、钻进时 F P B Q a t --=σ

小学数学常用公式大全数量关系计算公式

小学数学常用公式大全（数量关系计算公式） 1、单价×数量＝总价 2、单产量×数量＝总产量 3、速度×时间＝路程 4、工效×时间＝工作总量 5、加数+加数＝和一个加数＝和＋另一个加数 被减数－减数＝差减数＝被减数－差被减数＝减数＋差 因数×因数＝积一个因数＝积÷另一个因数 被除数÷除数＝商除数＝被除数÷商被除数＝商×除数 有余数的除法：被除数＝商×除数+余数 一个数连续用两个数除，可以先把后两个数相乘，再用它们的积去除这个数，结果不变。例：90÷5÷6＝90÷（5×6） 6、1公里＝1千米 1千米＝1000米 1米＝10分米 1分米＝10厘米 1厘米＝10毫米 1平方米＝100平方分米 1平方分米＝100平方厘米 1平方厘米＝100平方毫米 1立方米＝1000立方分米 1立方分米＝1000立方厘米 1立方厘米＝1000立方毫米 1吨＝1000千克 1千克= 1000克= 1公斤= 1市斤 1公顷＝10000平方米。 1亩＝平方米。 1升＝1立方分米＝1000毫升 1毫升＝1立方厘米 7、什么叫比：两个数相除就叫做两个数的比。如：2÷5或3:6或1/3 比的前项和后项同时乘以或除以一个相同的数（0除外），比值不变。 8、什么叫比例：表示两个比相等的式子叫做比例。如3:6＝9:18 9、比例的基本性质：在比例里，两外项之积等于两内项之积。 10、解比例：求比例中的未知项，叫做解比例。如3:χ＝9:18 11、正比例：两种相关联的量，一种量变化，另一种量也随着化，如果这两种量中相对应的的比值（也就是商k）一定，这两种量就叫做成正比例的量，它们的关系就叫做正比例关系。如：y/x=k( k一定)或kx=y 12、反比例：两种相关联的量，一种量变化，另一种量也随着变化，如果这两种量中相对应的两个数的积一定，这两种量就叫做成反比例的量，它们的关系就叫做反比例关系。如：x×y = k( k一定)或k / x = y 百分数：表示一个数是另一个数的百分之几的数，叫做百分数。百分数也叫做百分率或百分比。

数据结构表达式的两种计算方法

一、设计思想 （一）先将输入的中缀表达式转为后缀再计算的设计思想 我们所熟知的计算表达式为中缀表达式，这之中包含运算符的优先级还有括号，这对我们来说已经习以为常了，但是在计算机看来，这是非常复杂的一种表达式。因此我们需要有一种更能使计算机理解的不用考虑优先级也不包括括号的表达式，也就是后缀表达式。我们可以借助栈将其实现。 首先，我们需要将中缀表达式转换为后缀表达式，这也是这个算法的关键之处。我们将创建两个栈，一个是字符型的，用来存放操作符；另一个是浮点型的，存放操作数。 接着，开始扫描输入的表达式，如果是操作数直接进入一个存放后缀表达式的数组，而操作符则按照优先级push进栈（加减为1，乘除为2），若当前操作符优先级大于栈顶操作符优先级或栈为空，push进栈，而当其优先级小于等于栈顶操作符优先级，则从栈内不断pop出操作符并进入后缀表达式数组，直到满足条件，当前操作符才能push 进栈。左括号无条件入栈，右括号不入栈，而不断从栈顶pop出操作符进入后缀表达式数组，直到遇到左括号后，将其pop出栈。这样当扫描完输入表达式并从操作符栈pop 出残余操作符后并push进栈，后缀表达式数组中存放的就是我们所需要的后缀表达式了。 扫描后缀表达式数组，若是操作数，将其转换为浮点型push进数栈；若是操作符，则连续从数栈中pop出两个数做相应运算，将结果push进数栈。当扫描完数组后，数栈顶便为最终结果，将其pop出，输出结果。 （二）一边扫描一边计算的设计思想 由于第一种算法需要进行两遍扫描，因此在性能上不会十分优秀。而此种算法只用扫描一遍，当扫描完输入的表达式后便可以直接输出最终结果。是第一种算法的改进版，性能上也得到提升，与第一种算法所不同的是其需要同时使用两个栈，一个操作符栈，一个数栈。 当扫描表达式时，若是操作数则将其转换为浮点型后直接push进数栈，而若是操作符则按照优先级规则push进操作符栈（加减为1，乘除为2），若当前操作符优先级大于栈顶操作符优先级或栈为空，push进栈，而当其优先级小于等于栈顶操作符优先级，则从栈内不断pop出操作符，直到满足条件，当前操作符才能push进栈。左括号无条件入栈，右括号不入栈，而不断从栈顶pop出操作符，直到遇到左括号后，将其pop出栈。这中间pop出操作符后直接从数栈中pop出两个数并计算，将结果push进数栈。括号的处理与第一个算法相同。 扫描完成后，从操作符栈pop出残余操作符，从数栈中pop出两个数并计算并进行计算，将结果push进数栈。数栈顶便为最终结果，将其pop出，输出结果。 两种算法各有各的优缺点，第一种算法过程比较清晰，使我们能够更加容易理解栈的使用规则，但是其性能不如第二种。第二种算法相比第一种来说性能提高了，但是理解起来就不如第一种那么清晰了。

直线度-形位公差之一

一)、直线度误差的测量和评定方法 1、直线度——表示零件被测的线要素直不直的程度。 2、直线度公差：指实际被测直线对理想直线的允许变动量。 3、直线度公差带： 包容实际直线且距离为最小的两平行直线（或平面）之间的距离?或圆柱体的直径??。 1）、给定平面内的直线度 包容实际直线且距离为最小的 两平行直线之间的距离?。 2）、给定方向上的直线度误差 当给定一个方向时，是包容实际直线且距离为最 小的两平行平面之间的区域。 当给定相互垂直的两个方向时，是包容实际直 线且距离为最小的两组平行平面之间的区域。 3）、任意方向上的直线度误差： 包容实际直线且距离为最小的 圆柱体的直径??。

4、直线度误差的检测方法 按照测量原理、测量器具及测量基准等可将直线度误差的检测方法分为四类：直接方法、间接方法、组合方法和量规检验法。1）、直接方法：此类方法一般是首先确定一条测量基线，然后通过测量得到实际被测直线上的各点相对测量基线的偏差，再按规 定进行数据处理得到直线度值。（素线的测量） （1）、光隙法：将被测实际素线与其理想直线相比较来测量给定平面内直线度误差的测量方法。 是将刀口尺置于被测实际线上并使与被测线紧密 接触，转动刀口尺使它的位置符合最小条件，然后 观察刀口尺与被测线之间的最大光隙，此最大光隙 即为直线度误差。当光隙较大时，可用量块和塞尺测量其值，光隙较小时，可通过与标准光隙比较，估读出光 隙量大小。 该方法适合于磨削或研磨加工的小平面及短园柱（锥）面的直线度误差的测量。 标准光隙：标准光隙由1级量块、0级刀口尺 和1级平面平晶组成。 光隙尺寸的大小借助于光线通过狭缝时呈现的不同颜色来鉴别。光隙 >2.5um时，光线呈白光：间隙在 1.25—1.17um时，呈红

数量关系计算公式方面

3、速度＞＜0寸间=路程 4、工效＞时间=工作总量 6、1 公里=1 千米= 1000 米 米=10分米1分米= 10厘米1厘米= 10毫米 平方米= 100平方分米1 平方分米= 100平方厘米 平方厘米= 100 平方毫米立方米= 1000立方分米1立方分米= 1000 立方厘米立方厘米= 1000 立方毫米吨= 1000千克1千克= 1000克= 1公斤= 1市斤 1 公顷= 100 平方米。1 亩= 666.666 平方米。 1 升= 1 立方分米= 1000 毫升1 毫升= 1 立方厘米 8、什么叫比例： 表示两个比相等的式子叫做比例。如3:6= 9:18 9、比例的基本性质： 在比例里，两外项之积等于两内项之积。 10、解比例： 求比例中的未知项，叫做解比例。女口3: = 9:18 11、正比例： 两种相关联的量，一种量变化，另一种量也随着化，如果这两种量中相对应的的比值（也就是商k）一定，这两种量就叫做成正比例的量，它们的关系就叫做正比例关 定， 系。如： y/x=k（ k 一定）或kx=y 12、反比例：

两种相关联的量，一种量变化，另一种量也随着变化，如果这两种量中相对应的两个数的积一定，这两种量就叫做成反比例的量，它们的关系就叫做反比例关系。如： x X y = k（一定）或k / x = y 16、最大公约数： 几个数都能被同一个数一次性整除，这个数就叫做这几个数的最大公约数。（或几个数公有的约数，叫做这几个数的公约数。其中最大的一个，叫做最大公约数。） 17、互质数： 公约数只有1 的两个数，叫做互质数。 18、最小公倍数： 几个数公有的倍数，叫做这几个数的公倍数，其中最小的一个叫做这几个数的最小公倍数。 19、通分： 把异分母分数的分别化成和原来分数相等的同分母的分数，叫做通分。通分用最小公倍数） 20、约分： 把一个分数化成同它相等，但分子、分母都比较小的分数，叫做约分。约分用最大公约数） 28、利息=本金＞利率X寸间（时间一般以年或月为单位，应与利率的单位相对应） 29、利率： 利息与本金的比值叫做利率。一年的利息与本金的比值叫做年利率。一月的利息与本金的比值叫做月利率。 30、自然数：