CNL社内製本用.PDF
|
|
|
- せぴあ こしの
- 5 years ago
- Views:
Transcription
1 VERSION 6.0 C Numerical Library Function Catalog
2 IMSL TM C IMSL C Math / Library IMSL C / Stat / Library 1
3 IMSL TM C IMSL C IMSL C IMSL C IMSL C IMSL C IMSL C C IMSL C UNIX/Linux Windows
4 3 IMSL C IMSL C IMSL C SMP IMSL Fortran (SMP) Fourier SMP IMSL C IMSL 30
5 IMSL C C/ C Hermite 3 2 Gauss Adams-GearRunge-Kutta 1 2 Fourier Laplace Bessel 50 CPU -
6 13 Wilcoxon 2 Shapiro-Wilk - - Yates lattice split-plot strip-plot split-split plot strip-split plot Wilcoxon Cochran 2 Kolmogorov/ Smirnov ARMA GARCH (Generalized Autoregressive Conditional Heteroscedasticity) kalman K-means 2 2 Cox Kaplan-Meier 2 2 Poisson Faure 5
7 IMSL TM JMSL TM - Java TM JMSL Java J2SE JSEE 100 Java Java Java Java 100 JMSL Java JMSL JMSL 100 Java JMSL JMSL Java PC Java system latency IMSL TM C# IMSL C# Microsoft.Net Framework 100%C# IMSL C# Visual Studio.NET C#Visual Basic.NET (VB.NET) Visual Studio.NET Framework C# IMSL C# IMSL TM Fortran IMSL TM Fortran IMSL Fortran IMSL Fortran IMSL IMSL Fortran Fortran IMSL Fortran IMSL Fortran 100 IMSL Fortran IMSL Fortran IMSL F90 IMSL Fortran 77 IMSL IMSL, JMSL Visual Numerics.Inc. Visual Numerics.Inc.Visual Numerics.Inc. Java Java Sun Microsystems,Inc
8 IMSL C : Math / Library lin_sol_gen Ax = b lin_sol_gen ( ) Ax = b lin_sol_posdef Ax = b lin_sol_ posdef ( ) Hermitian Ax = b lin_sol_gen_band Ax = b lin_sol_gen_band ( ) Ax = b lin_sol_posdef _band Ax = b lin_sol_posdef _band ( ) Hermitian Ax = b lin_sol_gen_coordinate Ax = b lin_sol_gen_coordinate ( ) A Hermitian Ax = b lin_sol_posdef_coordinate Ax = b lin_sol_posdef_coordinate ( ) Hermitian Ax = b lin_sol_gen_min_residual lin_sol_def_cg (GMRES) Ax = b lin_least_squares_gen 2 Ax = b lin_lsq_lin_constraints 2 lin_svd_gen ASVD A = USV T lin_svd_gen ( ) ASVD A = USV T lin_sol_nonnegdef Ax = b eig_gen A eig_gen ( ) A eig_sym A eig_herm ( ) Hermitian A eig_symgen geneig A B B Ax = Bx A B Ax =Bx 7
9 geneig ( ) A B Ax =Bx 3 cub_spline_interp_e_cnd cub_spline_interp_shape cub_spline_value cub_spline_integral spline_interp spline_knots spline_2d_interp spline_value spline_integral spline_2d_value spline_2d_integral user_fcn_least_squares spline_least_squares spline_2d_least_squares cub_spline_smooth spline_lsq_constrained smooth_1d_data scattered_2d_interp radial_scattered_fit radial_evaluate n 1 R n
10 int_fcn_sing int_fcn int_fcn_sing_pts int_fcn_alg_log int_fcn_inf int_fcn_trig int_fcn_fourier int_fcn_cauchy int_fcn_smooth int_fcn_2d int_fcn_hyper_rect int_fcn_qmc gauss_quad_rule fcn_derivative Gauss-Kronrod Gauss-Kronrod - Fourier b f ( x) Cauchy dx x c a 2 b0 bn 1... ( x0,..., xn 1) dxn 1... dx a0 an 1 Monte-Carlo Gauss Gauss-Radau RUNGE-KUTTA ode_runge_kutta ADAM GEAR ode_adams_gear Runge-Kutta-Verner 5 6 Adams-Gear Petzold-Gear dea_petzold_gear Petzold Gear BDF 1 g(t, y, y ) = 0 pde_1d_mg 1 pde_method_of_lines ut = f(x, t, u, ux, uxx) 9
11 bvp_finite_difference POISSON fast_poisson_2d 1 HODIE Poisson 2 Poisson Helmholtz fft_real fft_real_init fft_complex fft_complex_init fft_cosine fft_cosine_init fft_sine fft_sine_init imsl_f_fft_real imsl_c_fft_complex imsl_f_fft_cosine imsl_f_fft_sine 2 fft_2d_complex 2 2 convolution 2 convolution ( ) 2 LAPLACE inverse_laplace Laplace zeros_poly Jenkins-Traub 3 zeros_poly ( ) Jenkins-Traub 3 zeros_fcn Muller zeros_sys_eqn Powell n f (x) = 0
12 min_uncon min_uncon_deriv min_uncon_multivar nonlin_least_squares read_mps linear_programming lin_prog quadratic_prog min_con_gen_lin bounded_least_squares 1 f(x) 1 1 f(x) Newton n f(x) Levenberg-Marquardt 2 2 MPS / 2 / Levenberg-Marquardt 2 Constrained_nlp GAMMA erf erfc erf_inverse erfce erfe erfc_inverse beta log_beta beta_incomplete gamma log_gamma gamma_incomplete BESSEL bessel_j0 bessel_j1 bessel_jx bessel_y0 bessel_y1 bessel_yx erf(x) erf(x) erf(x)-1 erfc(z) erfc-1(x) beta (x, y) beta ln(x, y) beta Ix = x(a,b)/(a,b) gamma (x) gamma log (x) gamma (a, x) 1 0 Bessel J0(x) 1 1 Bessel J1(x) 1 Bessel 2 0 Bessel Y0(x) 2 1 Bessel Y1(x) 2 Bessel 11
13 bessel_i0 bessel_exp_i0 bessel_i1 bessel_exp_i1 bessel_ix bessel_k0 bessel_exp_k0 bessel_k1 bessel_exp_k1 bessel_kx elliptic_integral_k elliptic_integral_e elliptic_integral_rf elliptic_integral_rd elliptic_integral_rj elliptic_integral_rc FRESNEL fresnel_integral_c fresnel_integral_s AIRY airy_ai airy_bi airy_ai_derivative airy_bi_derivative KELVIN kelvin_ber0 kelvin_bei0 kelvin_ker0 kelvin_kei0 kelvin_ber0_derivative kelvin_bei0_derivative kelvin_ker0_derivative kelvin_kei0_derivative normal_cdf normal_inverse_cdf chi_squared_cdf chi_squared_inverse_cdf F_cdf F_inverse_cdf t_cdf t_inverse_cdf gamma_cdf binomial_cdf hypergeometric_cdf poisson_cdf beta_cdf beta_inverse_cdf 1 0 Bessel I0(x) 1 0 Bessel 1 1 Bessel I1(x) 1 1 Bessel 1 Bessel 3 1 Bessel K0(x) 3 0 Bessel 3 1 Bessel K1(x) 3 1 Bessel 3 Bessel 1 K(x) 2 E(x) 1 Carlson RF(x, y, z) 2 Carlson RD(x, y, z) 3 Carlson RJ(x, y, z) Fresnel Fresnel Airy 2 Airy Airy 2 Airy 0 1 Kelvin ber 0 1 Kelvin bei 0 2 Kelvin ker 0 2 Kelvin kei 0 1 Kelvin ber 0 1 Kelvin bei 0 2 Kelvin ker 0 2 Kelvin kei (Gaussian) (Gaussian) 2 2 F F Student t Student t gamma 2 Poisson beta beta
14 13 bivariate_normal_cdf 2 cumulative_interest 2 cumulative_principal 2 depreciation_db depreciation_ddb depreciation_sln depreciation_syd depreciation_vdb dollar_decimal dollar_fraction effective_rate future_value future_value_schedule interest_payment interest_rate_annuity 1 internal_rate_of_return internal_rate_schedule modified_internal_rate net_present_value nominal_rate number_of_periods payment present_value present_value_schedule principal_payment accr_interest_maturity accr_interest_periodic bond_equivalent_yield convexity coupon_days coupon_number days_before_settlement days_to_next_coupon depreciation_amordegrc depreciation_amorlinc depreciation_amordegrc depreciation_amordegrc discount_price 100 discount_rate discount_yield duration
15 interest_rate_security modified_duration next_coupon_date previous_coupon_date price price_maturity received_maturity treasury_bill_price treasury_bill_yield year_fraction yield_maturity yield_periodic Macauley simple_statistics table_oneway chi_squared_test covariances regression poly_regression ranks random_seed_get random_seed_set random_option random_uniform random_normal random_poisson random_gamma random_beta random_exponential faure_next_point IMSL IMSL (0, 1) (0, 1) CDF Poisson gamma beta Faure
16 write_matrix page write_options output_file version ctime date_to_days days_to_date error_options error_code constant machine (integer) machine (float) sort sort (integer) vector_norm. CPU mat_mul_rect, 1 3 mat_mul_rect ( ),,1 3 mat_mul_rect_band mat_mul_rect_band ( ) mat_mul_rect_coordinate 15
17 mat_mul_rect_coordinate ( ) mat_add_band 2 C A B mat_add_band ( ) 2 C A B mat_add_coordinate 2 C A B mat_add_coordinate ( ) 2 C A B matrix_norm matrix_norm_band matrix_norm_coordinate generate_test_band E (n,c) generate_test_band ( ) E (n,c) generate_test_coordinate D(n,c)E(n,c) generate_test_coordinate ( ) D(n,c)E(n,c) c_neg c_add c_sub c_mul c_div c_eq cz_convert zc_convert cf_convert c_conjg c_abs c_arg c_sqrt c_cos c_sin c_exp c_log cf_power cc_power fi_power ii_power 2 2 2
18 IMSL C: Stat / Library simple_statistics normal_one_sample normal_two_sample table_oneway table_twoway sort_data ranks regressors_for_glm regression - regression_summary regression_prediction hypothesis_partial hypothesis_scph hypothesis_test regression_selection regression_stepwise poly_regression poly_prediction nonlinear_regression nonlinear_optimization 2 Lnorm_regression 2 2 Powell 2 Lp 17
19 covariances - partial_covariances pooled_covariances - robust_covariances anova_oneway 1 anova_factorial anova_nested anova_balanced crd_factorial rcbd_factorial latin_square lattice split_plot split-plot split_split_plot split-split-plot strip_plot strip-plot strip_split_plot strip-split-plot homogeneity Bartlett Levene multiple_comparisons SNK LSD TukeyDuncan Bonferroni Yates Yate contingency_table 2 2 exact_enumeration 2 exact_network 2 categorical_glm Probit Poisson
20 - sign_test wilcoxon_sign_rank noether_cyclical_trend cox_stuart_trends_test tie_statistics wilcoxon_rank_sum kruskal_wallis_test friedmans_test cochran_q_test k_trends_test Wilcoxon Noether Cox Stuarts 1 Wilcoxon Kruskal Wallis Friedman Cochran Q K chi_squared_test normality_test kolmogorov_one kolmogorov_two multivar_normality_test randomness_test 2 Kolmogorov-Smirnov 1 Kolmogorov-Smirnov 2 Mardia ARIMA arma max_arma auto_uni_ar ts_outlier_identification ts_outlier_forecast ARMA 2 ARMA: ARMA (AIC) AIC ψ 19
21 auto_arima arma_forecast difference seasonal_fit ARIMA ( p,0, q) (0, d,0) s ARMA AR(p) box_cox_transform Box-Cox autocorrelation crosscorrelation 2 multi_crosscorrelation 2 partial_autocorrelation lack_of_fit estimate_missing GARCH garch kalman GARCH (p, q) dissimilarities cluster_hierarchical cluster_number k-means cluster_k_means principal_components factor_analysis discriminant_analysis K-means
22 aplan_meier_estimates rop_hazards_gen_lin survival_glm survival_estimates nonparam_hazard_rate Kaplan-Meier Cox life_tables binomial_cdf binomial_pdf hypergeometric_cdf hypergeometric_pdf poisson_cdf poisson_pdf Poisson beta_cdf beta_inverse_cdf bivariate_normal_cdf chi_squared_cdf chi_squared_inverse_cdf non_central_chi_sq non_central_chi_sq_inv F_cdf F_inverse_cdf gamma_cdf normal_cdf normal_inverse_cdf t_cdf t_inverse_cdf non_central_t_cdf non_central_t_inv_cdf 2 2 Poisson F F Gauss Gauss Student t Student t Student t Student t random_binomial random_geometric random_hypergeometric random_logarithmic 2 21
23 random_neg_binomial 2 random_poisson Poisson random_uniform_discrete random_general_discrete random_beta random_cauchy Chaucy random_chi_squared 2 random_exponential random_exponential_mix random_gamma random_lognormal random_normal CDF random_stable random_student_t student-t random_triangular random_uniform 0, 1 random_von_mises Von Mises random_weibull Weibull random_general_continuous continuous_table_setup random_normal_multivariate random_orthogonal_matrix random_mvar_from_data random_multinomial random_sphere K random_table_twoway 2 random_order_normal random_order_uniform (0, 1) random_arma ARMA random_npp random_permutation random_sample_indices random_sample random_option 0, 1 random_option_get 0, 1 random_seed_get IMSL random_substream_seed_get 100,000 random_seed_set IMSL random_table_set
24 23 random_table_get random_gfsr_table_set GFSR random_gfsr_table_get GFSR random_mt32_init 32 random_mt32_table_get 32 random_mt32_table_set 32 random_mt64_init 64 random_mt64_table_get 64 random_mt64_table_set 64 faure_next_point Faure mlff_network mlff_network_trainer mlff_network_forecast scale_filter time_series_filter time_series_class_filter unsupervised_nominal_filter 2 2 unsupervised_ordinal_filter write_matrix
25 page write_options output_file version error_options error_code machine (integer) machine (float) data_sets mat_mul_rect permute_vector permute_matrix binomial_coefficient 2 beta beta_incomplete log_beta gamma gamma_incomplete log_gamma ctime CPU
imslfunction1.qxd
VERSION 5.5 C Numerical Library Function Catalog IMSL TM C Numerical Library Function Catalog IMSL C 3 6 7 IMSL Java TM Fortran 8 IMSL C Math / Library 9 10 10 12 13 13 14 15 15 21 22 22 IMSL C / Stat
fortranfunction2.qxd
Fortran Numerical Library Function Catalog IMSL TM Fortran Numerical Library Function Catalog IMSL Fortran 4 8 9 10 IMSL Java TM C 12 IMSL Math / Library 13 13 21 23 27 28 29 31 32 34 40 41 IMSL Math /
JMSL 3.0 FC_日_ .doc
V E R S I O N 3. 0 JMSL Numerical Library Function Catalog JMSL Numerical Library Function Catalog Java 4 7 IMSLC C# Fortran 8 com.imsl Package 9 com.imsl.math Package 10 10 10 10 11 11 11 12 12 12 12
1 1 1.1...................................... 1 1.2................................... 5 1.3................................... 7 1.4............................. 9 1.5....................................
PowerPoint プレゼンテーション
40 6 Fischer 2 McNemar 2 No Yes No Yes Mann Whitney s U Wilcoxon 1 Kruskal Wallis 2 Friedman No Yes 2 Yes No Yes Bonferroni ANOVA No Scheffe Yes Student s T No Paired T Welch s T 40 6 Fischer 2 McNemar
V E R S I O N C# Numerical Library Function Catalog
V E R S I O N 4.0. 2 C# Numerical Library Function Catalog 目次 1 IMSL C# ライブラリ4.02 概要 2 Imsl.Math Package 5 基本関数 5 線形代数 5 固有値解析 5 補間と近似 5 積分 5 微分方程式 6 変換 6 非線形方程式 6 最適化 6 特殊関数 6 その他 7 印刷関数 7 Imsl.Stat Package
18 ( ) I II III A B C(100 ) 1, 2, 3, 5 I II A B (100 ) 1, 2, 3 I II A B (80 ) 6 8 I II III A B C(80 ) 1 n (1 + x) n (1) n C 1 + n C
8 ( ) 8 5 4 I II III A B C( ),,, 5 I II A B ( ),, I II A B (8 ) 6 8 I II III A B C(8 ) n ( + x) n () n C + n C + + n C n = 7 n () 7 9 C : y = x x A(, 6) () A C () C P AP Q () () () 4 A(,, ) B(,, ) C(,,
Bessel ( 06/11/21) Bessel 1 ( ) 1.1 0, 1,..., n n J 0 (x), J 1 (x),..., J n (x) I 0 (x), I 1 (x),..., I n (x) Miller (Miller algorithm) Bess
Bessel 5 3 11 ( 6/11/1) Bessel 1 ( ) 1.1, 1,..., n n J (x), J 1 (x),..., J n (x) I (x), I 1 (x),..., I n (x) Miller (Miller algorithm) Bessel (6 ) ( ) [1] n n d j J n (x), d j I n (x) Deuflhard j= j=.1
: 1g99p038-8
16 17 : 1g99p038-8 1 3 1.1....................................... 4 1................................... 5 1.3.................................. 5 6.1..................................... 7....................................
Introduction to Numerical Analysis of Differential Equations Naoya Enomoto (Kyoto.univ.Dept.Science(math))
Introduction to Numerical Analysis of Differential Equations Naoya Enomoto (Kyoto.univ.Dept.Science(math)) 2001 1 e-mail:s00x0427@ip.media.kyoto-u.ac.jp 1 1 Van der Pol 1 1 2 2 Bergers 2 KdV 2 1 5 1.1........................................
Microsoft Word - 触ってみよう、Maximaに2.doc
i i e! ( x +1) 2 3 ( 2x + 3)! ( x + 1) 3 ( a + b) 5 2 2 2 2! 3! 5! 7 2 x! 3x! 1 = 0 ",! " >!!! # 2x + 4y = 30 "! x + y = 12 sin x lim x!0 x x n! # $ & 1 lim 1 + ('% " n 1 1 lim lim x!+0 x x"!0 x log x
1 4 1 ( ) ( ) ( ) ( ) () 1 4 2
7 1995, 2017 7 21 1 2 2 3 3 4 4 6 (1).................................... 6 (2)..................................... 6 (3) t................. 9 5 11 (1)......................................... 11 (2)
-1-1 1 1 1 1 12 31 2 2 3 4
2007 -1-1 1 1 1 1 12 31 2 2 3 4 -2-5 6 CPU 3 Windows98 1 -3-2. 3. -4-4 2 5 1 1 1 -5- 50000 50000 50000 50000 50000 50000 50000 50000 50000 50000-6- -7-1 Windows 2 -8-1 2 3 4 - - 100,000 200,000 500,000
確率論と統計学の資料
5 June 015 ii........................ 1 1 1.1...................... 1 1........................... 3 1.3... 4 6.1........................... 6................... 7 ii ii.3.................. 8.4..........................
Stata 11 Stata ts (ARMA) ARCH/GARCH whitepaper mwp 3 mwp-083 arch ARCH 11 mwp-051 arch postestimation 27 mwp-056 arima ARMA 35 mwp-003 arima postestim
TS001 Stata 11 Stata ts (ARMA) ARCH/GARCH whitepaper mwp 3 mwp-083 arch ARCH 11 mwp-051 arch postestimation 27 mwp-056 arima ARMA 35 mwp-003 arima postestimation 49 mwp-055 corrgram/ac/pac 56 mwp-009 dfgls
1.2 y + P (x)y + Q(x)y = 0 (1) y 1 (x), y 2 (x) y 1 (x), y 2 (x) (1) y(x) c 1, c 2 y(x) = c 1 y 1 (x) + c 2 y 2 (x) 3 y 1 (x) y 1 (x) e R P (x)dx y 2
1 1.1 R(x) = 0 y + P (x)y + Q(x)y = R(x)...(1) y + P (x)y + Q(x)y = 0...(2) 1 2 u(x) v(x) c 1 u(x)+ c 2 v(x) = 0 c 1 = c 2 = 0 c 1 = c 2 = 0 2 0 2 u(x) v(x) u(x) u (x) W (u, v)(x) = v(x) v (x) 0 1 1.2
( ) p.2/70
p.1/70 ( ) p.2/70 ( p.3/70 (1)20 1970 cf.box and Jenkins(1970) (2)1980 p.4/70 Kolmogorov(1940),(1941) Granger(1966) Hurst(1951) Hurst p.5/70 Beveridge Wheat Prices Index p.6/70 Nile River Water Level p.7/70
5 Armitage x 1,, x n y i = 10x i + 3 y i = log x i {x i } {y i } 1.2 n i i x ij i j y ij, z ij i j 2 1 y = a x + b ( cm) x ij (i j )
5 Armitage. x,, x n y i = 0x i + 3 y i = log x i x i y i.2 n i i x ij i j y ij, z ij i j 2 y = a x + b 2 2. ( cm) x ij (i j ) (i) x, x 2 σ 2 x,, σ 2 x,2 σ x,, σ x,2 t t x * (ii) (i) m y ij = x ij /00 y
36 3 D f(z) D z f(z) z Taylor z D C f(z) z C C f (z) C f(z) f (z) f(z) D C D D z C C 3.: f(z) 3. f (z) f 2 (z) D D D D D f (z) f 2 (z) D D f (z) f 2 (
3 3. D f(z) D D D D D D D D f(z) D f (z) f (z) f(z) D (i) (ii) (iii) f(z) = ( ) n z n = z + z 2 z 3 + n= z < z < z > f (z) = e t(+z) dt Re z> Re z> [ ] f (z) = e t(+z) = (Rez> ) +z +z t= z < f(z) Taylor
総合薬学講座 生物統計の基礎
2013 10 22 ( ) 2013 10 22 1 / 40 p.682 1. 2. 3 2 t Mann Whitney U ). 4 χ 2. 5. 6 Dunnett Tukey. 7. 8 Kaplan Meier.. U. ( ) 2013 10 22 2 / 40 1 93 ( 20 ) 230. a t b c χ 2 d 1.0 +1.0 e, b ( ) e ( ) ( ) 2013
n Y 1 (x),..., Y n (x) 1 W (Y 1 (x),..., Y n (x)) 0 W (Y 1 (x),..., Y n (x)) = Y 1 (x)... Y n (x) Y 1(x)... Y n(x) (x)... Y n (n 1) (x) Y (n 1)
D d dx 1 1.1 n d n y a 0 dx n + a d n 1 y 1 dx n 1 +... + a dy n 1 dx + a ny = f(x)...(1) dk y dx k = y (k) a 0 y (n) + a 1 y (n 1) +... + a n 1 y + a n y = f(x)...(2) (2) (2) f(x) 0 a 0 y (n) + a 1 y
b3e2003.dvi
15 II 5 5.1 (1) p, q p = (x + 2y, xy, 1), q = (x 2 + 3y 2, xyz, ) (i) p rotq (ii) p gradq D (2) a, b rot(a b) div [11, p.75] (3) (i) f f grad f = 1 2 grad( f 2) (ii) f f gradf 1 2 grad ( f 2) rotf 5.2
(pdf) (cdf) Matlab χ ( ) F t
(, ) (univariate) (bivariate) (multi-variate) Matlab Octave Matlab Matlab/Octave --...............3. (pdf) (cdf)...3.4....4.5....4.6....7.7. Matlab...8.7.....9.7.. χ ( )...0.7.3.....7.4. F....7.5. t-...3.8....4.8.....4.8.....5.8.3....6.8.4....8.8.5....8.8.6....8.9....9.9.....9.9.....0.9.3....0.9.4.....9.5.....0....3
FD 2 ( )..................... 3 FD 14 ( )..................... 15 FD 39 ( ).................... 40................. 54................................
14 15 3 FD 2 ( )..................... 3 FD 14 ( )..................... 15 FD 39 ( ).................... 40................. 54.......................................... 66..........................................
106 4 4.1 1 25.1 25.4 20.4 17.9 21.2 23.1 26.2 1 24 12 14 18 36 42 24 10 5 15 120 30 15 20 10 25 35 20 18 30 12 4.1 7 min. z = 602.5x 1 + 305.0x 2 + 2
105 4 0 1? 1 LP 0 1 4.1 4.1.1 (intger programming problem) 1 0.5 x 1 = 447.7 448 / / 2 1.1.2 1. 2. 1000 3. 40 4. 20 106 4 4.1 1 25.1 25.4 20.4 17.9 21.2 23.1 26.2 1 24 12 14 18 36 42 24 10 5 15 120 30
time2print4.dvi
iii 2 P. J. Brockwell and R.A. Davis, Introduction to Time Series and Forecasting, 2nd edition (Springer, 2002) 1 2 ITSM2000(version 7) 6 10 7 2 2 2 ITSM2000 student version professional version CD-ROM
p12.dvi
301 12 (2) : 1 (1) dx dt = f(x,t) ( (t 0,t 1,...,t N ) ) h k = t k+1 t k. h k k h. x(t k ) x k. : 2 (2) :1. step. 1 : explicit( ) : ξ k+1 = ξ k +h k Ψ(t k,ξ k,h k ) implicit( ) : ξ k+1 = ξ k +h k Ψ(t k,t
−g”U›ß™ö‡Æ…X…y…N…g…‰
1 / 74 ( ) 2019 3 8 URL: http://www.math.kyoto-u.ac.jp/ ichiro/ 2 / 74 Contents 1 Pearson 2 3 Doob h- 4 (I) 5 (II) 6 (III-1) - 7 (III-2-a) 8 (III-2-b) - 9 (III-3) Pearson 3 / 74 Pearson Definition 1 ρ
1 filename=mathformula tex 1 ax 2 + bx + c = 0, x = b ± b 2 4ac, (1.1) 2a x 1 + x 2 = b a, x 1x 2 = c a, (1.2) ax 2 + 2b x + c = 0, x = b ± b 2
filename=mathformula58.tex ax + bx + c =, x = b ± b 4ac, (.) a x + x = b a, x x = c a, (.) ax + b x + c =, x = b ± b ac. a (.3). sin(a ± B) = sin A cos B ± cos A sin B, (.) cos(a ± B) = cos A cos B sin
( ) C 2 f(x) = 0 (1) x (1) x 3 3x 2 + 9x 8 = 0 (2) 1
2004 8 25 1 1.1 ( ) 4 2 1.2 4 C 2 f(x) = 0 (1) x (1) x 3 3x 2 + 9x 8 = 0 (2) 1 [ ] 1/3 [ 2 1 ( x 1 = 1 2 1 + + 1 + ) ] 1/3 33 33 2 x 2 = 1 + (1 + [ ] 1/3 2 3i) 1 + 1 33 2 (1 [ 1 3i) 2 x 2 = 1 + (1 [ ]
takei.dvi
0 Newton Leibniz ( ) α1 ( ) αn (1) a α1,...,α n (x) u(x) = f(x) x 1 x n α 1 + +α n m 1957 Hans Lewy Lewy 1970 1 1.1 Example 1.1. (2) d 2 u dx 2 Q(x)u = f(x), u(0) = a, 1 du (0) = b. dx Q(x), f(x) x = 0
x h = (b a)/n [x i, x i+1 ] = [a+i h, a+ (i + 1) h] A(x i ) A(x i ) = h 2 {f(x i) + f(x i+1 ) = h {f(a + i h) + f(a + (i + 1) h), (2) 2 a b n A(x i )
![x h = (b a)/n [x i, x i+1 ] = [a+i h, a+ (i + 1) h] A(x i ) A(x i ) = h 2 {f(x i) + f(x i+1 ) = h {f(a + i h) + f(a + (i + 1) h), (2) 2 a b n A(x i )](/thumbs/92/107866678.jpg "x h = (b a)/n [x i, x i+1 ] = [a+i h, a+ (i + 1) h] A(x i ) A(x i ) = h 2 {f(x i) + f(x i+1 ) = h {f(a + i h) + f(a + (i + 1) h), (2) 2 a b n A(x i )")
1 f(x) a b f(x)dx = n A(x i ) (1) ix [a, b] n i A(x i ) x i 1 f(x) [a, b] n h = (b a)/n y h = (b-a)/n y = f (x) h h a a+h a+2h a+(n-1)h b x 1: 1 x h = (b a)/n [x i, x i+1 ] = [a+i h, a+ (i + 1) h] A(x
seminar0220a.dvi
1 Hi-Stat 2 16 2 20 16:30-18:00 2 2 217 1 COE 4 COE RA E-MAIL: ged0104@srv.cc.hit-u.ac.jp 2004 2 25 S-PLUS S-PLUS S-PLUS S-code 2 [8] [8] [8] 1 2 ARFIMA(p, d, q) FI(d) φ(l)(1 L) d x t = θ(l)ε t ({ε t }
( 30 ) 30 4 5 1 4 1.1............................................... 4 1.............................................. 4 1..1.................................. 4 1.......................................
6. Euler x
...............................................................................3......................................... 4.4................................... 5.5......................................
68 A mm 1/10 A. (a) (b) A.: (a) A.3 A.4 1 1
67 A Section A.1 0 1 0 1 Balmer 7 9 1 0.1 0.01 1 9 3 10:09 6 A.1: A.1 1 10 9 68 A 10 9 10 9 1 10 9 10 1 mm 1/10 A. (a) (b) A.: (a) A.3 A.4 1 1 A.1. 69 5 1 10 15 3 40 0 0 ¾ ¾ É f Á ½ j 30 A.3: A.4: 1/10
一般演題（ポスター）
6 5 13 : 00 14 : 00 A μ 13 : 00 14 : 00 A β β β 13 : 00 14 : 00 A 13 : 00 14 : 00 A 13 : 00 14 : 00 A β 13 : 00 14 : 00 A β 13 : 00 14 : 00 A 13 : 00 14 : 00 A β 13 : 00 14 : 00 A 13 : 00 14 : 00 A
Release Notes for JMP book
8.0.2 JMP, A Business Unit of SAS SAS Campus Drive Cary, NC 27513 SAS Institute Inc. 2009.JMP 8.0.2, Cary, NC: SAS Institute Inc. JMP 8.0.2 Copyright 2009, SAS Institute Inc., Cary, NC, USA All rights
i
i 3 4 4 7 5 6 3 ( ).. () 3 () (3) (4) /. 3. 4/3 7. /e 8. a > a, a = /, > a >. () a >, a =, > a > () a > b, a = b, a < b. c c n a n + b n + c n 3c n..... () /3 () + (3) / (4) /4 (5) m > n, a b >, m > n,
ax 2 + bx + c = n 8 (n ) a n x n + a n 1 x n a 1 x + a 0 = 0 ( a n, a n 1,, a 1, a 0 a n 0) n n ( ) ( ) ax 3 + bx 2 + cx + d = 0 4
20 20.0 ( ) 8 y = ax 2 + bx + c 443 ax 2 + bx + c = 0 20.1 20.1.1 n 8 (n ) a n x n + a n 1 x n 1 + + a 1 x + a 0 = 0 ( a n, a n 1,, a 1, a 0 a n 0) n n ( ) ( ) ax 3 + bx 2 + cx + d = 0 444 ( a, b, c, d
u = u(t, x 1,..., x d ) : R R d C λ i = 1 := x 2 1 x 2 d d Euclid Laplace Schrödinger N := {1, 2, 3,... } Z := {..., 3, 2, 1,, 1, 2, 3
2 2 1 5 5 Schrödinger i u t + u = λ u 2 u. u = u(t, x 1,..., x d ) : R R d C λ i = 1 := 2 + + 2 x 2 1 x 2 d d Euclid Laplace Schrödinger 3 1 1.1 N := {1, 2, 3,... } Z := {..., 3, 2, 1,, 1, 2, 3,... } Q
arma dvi
ARMA 007/05/0 Rev.0 007/05/ Rev.0 007/07/7 3. : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 3. : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 3.3 : : : :
2.2 ( y = y(x ( (x 0, y 0 y (x 0 (y 0 = y(x 0 y = y(x ( y (x 0 = F (x 0, y(x 0 = F (x 0, y 0 (x 0, y 0 ( (x 0, y 0 F (x 0, y 0 xy (x, y (, F (x, y ( (
(. x y y x f y = f(x y x y = y(x y x y dx = d dx y(x = y (x = f (x y = y(x x ( (differential equation ( + y 2 dx + xy = 0 dx = xy + y 2 2 2 x y 2 F (x, y = xy + y 2 y = y(x x x xy(x = F (x, y(x + y(x 2
2S III IV K A4 12:00-13:30 Cafe David 1 2 TA 1 appointment Cafe David K2-2S04-00 : C
2S III IV K200 : April 16, 2004 Version : 1.1 TA M2 TA 1 10 2 n 1 ɛ-δ 5 15 20 20 45 K2-2S04-00 : C 2S III IV K200 60 60 74 75 89 90 1 email 3 4 30 A4 12:00-13:30 Cafe David 1 2 TA 1 email appointment Cafe
June 2016 i (statistics) F Excel Numbers, OpenOffice/LibreOffice Calc ii *1 VAR STDEV 1 SPSS SAS R *2 R R R R *1 Excel, Numbers, Microsoft Office, Apple iwork, *2 R GNU GNU R iii URL http://ruby.kyoto-wu.ac.jp/statistics/training/
1 Edward Waring Lagrange n {(x i, y i )} n i=1 x i p i p i (x j ) = δ ij P (x) = p i p i (x) = n y i p i (x) (1) i=1 n j=1 j i x x j x i x j (2) Runge
Edwrd Wring Lgrnge n {(x i, y i )} n x i p i p i (x j ) = δ ij P (x) = p i p i (x) = n y i p i (x) () n j= x x j x i x j (2) Runge [] [2] = ξ 0 < ξ < ξ n = b [, b] [ξ i, ξ i ] y = /( + 25x 2 ) 5 2,, 0,,
A
A 2563 15 4 21 1 3 1.1................................................ 3 1.2............................................. 3 2 3 2.1......................................... 3 2.2............................................
18 2 F 12 r 2 r 1 (3) Coulomb km Coulomb M = kg F G = ( ) ( ) ( ) 2 = [N]. Coulomb
![18 2 F 12 r 2 r 1 (3) Coulomb km Coulomb M = kg F G = ( ) ( ) ( ) 2 = [N]. Coulomb](/thumbs/93/114079295.jpg "18 2 F 12 r 2 r 1 (3) Coulomb km Coulomb M = kg F G = ( ) ( ) ( ) 2 = [N]. Coulomb")
r 1 r 2 r 1 r 2 2 Coulomb Gauss Coulomb 2.1 Coulomb 1 2 r 1 r 2 1 2 F 12 2 1 F 21 F 12 = F 21 = 1 4πε 0 1 2 r 1 r 2 2 r 1 r 2 r 1 r 2 (2.1) Coulomb ε 0 = 107 4πc 2 =8.854 187 817 10 12 C 2 N 1 m 2 (2.2)
d dt A B C = A B C d dt x = Ax, A 0 B 0 C 0 = mm 0 mm 0 mm AP = PΛ P AP = Λ P A = ΛP P d dt x = P Ax d dt (P x) = Λ(P x) d dt P x =
3 MATLAB Runge-Kutta Butcher 3. Taylor Taylor y(x 0 + h) = y(x 0 ) + h y (x 0 ) + h! y (x 0 ) + Taylor 3. Euler, Runge-Kutta Adams Implicit Euler, Implicit Runge-Kutta Gear y n+ y n (n+ ) y n+ y n+ y n+
7 27 7.1........................................ 27 7.2.......................................... 28 1 ( a 3 = 3 = 3 a a > 0(a a a a < 0(a a a -1 1 6
26 11 5 1 ( 2 2 2 3 5 3.1...................................... 5 3.2....................................... 5 3.3....................................... 6 3.4....................................... 7
I L01( Wed) : Time-stamp: Wed 07:38 JST hig e, ( ) L01 I(2017) 1 / 19
I L01(2017-09-20 Wed) : Time-stamp: 2017-09-20 Wed 07:38 JST hig e, http://hig3.net ( ) L01 I(2017) 1 / 19 ? 1? 2? ( ) L01 I(2017) 2 / 19 ?,,.,., 1..,. 1,2,.,.,. ( ) L01 I(2017) 3 / 19 ? I. M (3 ) II,
0201
2018 10 17 2019 9 19 SI J cal 1mL 1ºC 1999 cal nutrition facts label calories cal kcal 1 cal = 4.184 J heat capacity 1 K 1 J K 1 mol molar heat capacity J K mol (specific heat specific heat capacity) 1
ランダムウォークの境界条件・偏微分方程式の数値計算
B L06(2018-05-22 Tue) : Time-stamp: 2018-05-22 Tue 21:53 JST hig,, 2, multiply transf http://hig3.net L06 B(2018) 1 / 38 L05-Q1 Quiz : 1 M λ 1 = 1 u 1 ( ). M u 1 = u 1, u 1 = ( 3 4 ) s (s 0)., u 1 = 1
P1-1 P1-2 P1-3 P1-4 P1-5 P1-6 P3-1 P3-2 P3-3 P3-4 P3-5 P3-6 P5-1 P5-2 P5-3 P5-4 P5-5 P5-6 P7-1 P7-2 P7-3 P7-4 P7-5 P7-6 P9-1 P9-2 P9-3 P9-4 P9-5 P9-6 P11-1 P11-2 P11-3 P11-4 P13-1 P13-2 P13-3 P13-4 P13-5
…K…E…X„^…x…C…W…A…fi…l…b…g…‘†[…N‡Ì“‚¢−w‘K‡Ì‹ê™v’«‡É‡Â‡¢‡Ä
2009 8 26 1 2 3 ARMA 4 BN 5 BN 6 (Ω, F, µ) Ω: F Ω σ 1 Ω, ϕ F 2 A, B F = A B, A B, A\B F F µ F 1 µ(ϕ) = 0 2 A F = µ(a) 0 3 A, B F, A B = ϕ = µ(a B) = µ(a) + µ(b) µ(ω) = 1 X : µ X : X x 1,, x n X (Ω) x 1,,
webkaitou.dvi
( c Akir KANEKO) ).. m. l s = lθ m d s dt = mg sin θ d θ dt = g l sinθ θ l θ mg. d s dt xy t ( d x dt, d y dt ) t ( mg sin θ cos θ, sin θ sin θ). (.) m t ( d x dt, d y dt ) = t ( mg sin θ cos θ, mg sin
C による数値計算法入門 ( 第 2 版 ) 新装版 サンプルページ この本の定価 判型などは, 以下の URL からご覧いただけます. このサンプルページの内容は, 新装版 1 刷発行時のものです.
C による数値計算法入門 ( 第 2 版 ) 新装版 サンプルページ この本の定価 判型などは, 以下の URL からご覧いただけます. http://www.morikita.co.jp/books/mid/009383 このサンプルページの内容は, 新装版 1 刷発行時のものです. i 2 22 2 13 ( ) 2 (1) ANSI (2) 2 (3) Web http://www.morikita.co.jp/books/mid/009383
2 1 Introduction (1.1.2) Logistic ث Malthus (1.1.3) (( ) ث)( ) α = ( ) ( + ) [Verhulst 1845] 0 ( ) ( + ) lim ( ) = 0 t (1.1.4) (( ) ث)( ) α = ( ) Logi
![2 1 Introduction (1.1.2) Logistic ث Malthus (1.1.3) (( ) ث)( ) α = ( ) ( + ) [Verhulst 1845] 0 ( ) ( + ) lim ( ) = 0 t (1.1.4) (( ) ث)( ) α = ( ) Logi](/thumbs/81/82814896.jpg "2 1 Introduction (1.1.2) Logistic ث Malthus (1.1.3) (( ) ث)( ) α = ( ) ( + ) [Verhulst 1845] 0 ( ) ( + ) lim ( ) = 0 t (1.1.4) (( ) ث)( ) α = ( ) Logi")
1 1 Introduction 1.1 ( ) ( ) Malthus ( ) (1.1.1) ( ) α = ( ) ( + ) 0 ( ) ( + ) lim ( ) = 0 t ( ) α = ( ) αt م = ( ) ( ) = ( 0 ) 0 (1.1.2) αt م 0 = ( ) (1.1.1) ( ) ( α + (1 = ( + ) = 0 1 ( ( ) 2... ) geometric
Trapezoidal Rule θ = 1/ x n x n 1 t = 1 [f(t n 1, x n 1 ) + f(t n, x n )] (6) 1. dx dt = f(t, x), x(t 0) = x 0 (7) t [t 0, t 1 ] f t [t 0, t 1 ], x x
![Trapezoidal Rule θ = 1/ x n x n 1 t = 1 [f(t n 1, x n 1 ) + f(t n, x n )] (6) 1. dx dt = f(t, x), x(t 0) = x 0 (7) t [t 0, t 1 ] f t [t 0, t 1 ], x x](/thumbs/92/107866474.jpg "Trapezoidal Rule θ = 1/ x n x n 1 t = 1 [f(t n 1, x n 1 ) + f(t n, x n )] (6) 1. dx dt = f(t, x), x(t 0) = x 0 (7) t [t 0, t 1 ] f t [t 0, t 1 ], x x")
University of Hyogo 8 8 1 d x(t) =f(t, x(t)), dt (1) x(t 0 ) =x 0 () t n = t 0 + n t x x n n x n x 0 x i i = 0,..., n 1 x n x(t) 1 1.1 1 1 1 0 θ 1 θ x n x n 1 t = θf(t n 1, x n 1 ) + (1 θ)f(t n, x n )
関数のグラフを描こう
L05(2010-05-07) 1 2 hig3.net ( ) L05(2010-05-07) 1 / 16 #i n c l u d e double f ( double x ) ; i n t main ( void ){ i n t n ; i n t nmax=10; double x ; double s =0.0; } x = 1.0; s=s+x ;
untitled
* 10 100 1 ( ) ( ) 20 2 X f( ) (pdf: probability density function) F( ) X (cdf: cumulative distribution function) (2.1) X ( ) p ( ) W( ) 1 F( ) p p 1(p) W( p) ( p) X 1/T T ( ) T p T T T p 1 1/T p F( )
( ) kadai4, kadai4.zip.,. 3 cos x [ π, π] Python. ( 100 ), x cos x ( ). (, ). def print cos(): print cos()
![( ) kadai4, kadai4.zip.,. 3 cos x [ π, π] Python. ( 100 ), x cos x ( ). (, ). def print cos(): print cos()](/thumbs/91/105030926.jpg "( ) kadai4, kadai4.zip.,. 3 cos x [ π, π] Python. ( 100 ), x cos x ( ). (, ). def print cos(): print cos()")
4 2010.6 1 :, HP.. HP 4 (, PGM/PPM )., python,,, 2, kadai4,.,,, ( )., ( ) N, exn.py ( 3 ex3.py ). N 3.., ( )., ( ) N, (exn.txt).. 1 ( ) kadai4, kadai4.zip.,. 3 cos x [ π, π] Python. ( 100 ), x cos x (
1. A0 A B A0 A : A1,...,A5 B : B1,...,B
1. A0 A B A0 A : A1,...,A5 B : B1,...,B12 2. 3. 4. 5. A0 A B f : A B 4 (i) f (ii) f (iii) C 2 g, h: C A f g = f h g = h (iv) C 2 g, h: B C g f = h f g = h 4 (1) (i) (iii) (2) (iii) (i) (3) (ii) (iv) (4)
1 (bit ) ( ) PC WS CPU IEEE754 standard ( 24bit) ( 53bit)
GNU MP BNCpack tkouya@cs.sist.ac.jp 2002 9 20 ( ) Linux Conference 2002 1 1 (bit ) ( ) PC WS CPU IEEE754 standard ( 24bit) ( 53bit) 10 2 2 3 4 5768:9:; = %? @BADCEGFH-I:JLKNMNOQP R )TSVU!" # %$ & " #
1 1 [1] ( 2,625 [2] ( 2, ( ) /
![1 1 [1] ( 2,625 [2] ( 2, ( ) /](/thumbs/95/122470987.jpg "1 1 [1] ( 2,625 [2] ( 2, ( ) /")
[] (,65 [] (,3 ( ) 67 84 76 7 8 6 7 65 68 7 75 73 68 7 73 7 7 59 67 68 65 75 56 6 58 /=45 /=45 6 65 63 3 4 3/=36 4/=8 66 7 68 7 7/=38 /=5 7 75 73 8 9 8/=364 9/=864 76 8 78 /=45 /=99 8 85 83 /=9 /= ( )
S I. dy fx x fx y fx + C 3 C dy fx 4 x, y dy v C xt y C v e kt k > xt yt gt [ v dt dt v e kt xt v e kt + C k x v + C C k xt v k 3 r r + dr e kt S dt d
S I.. http://ayapin.film.s.dendai.ac.jp/~matuda /TeX/lecture.html PDF PS.................................... 3.3.................... 9.4................5.............. 3 5. Laplace................. 5....
untitled
1 2 3 4 5 6 7 8 9 10 11 12 13 13,996t 0% 2,379.3t 17.0% 4,630t 0% 532.4t 11.5% 72.9% 96.6% 3,000t 2.9% 3,000t 100.0% 20t BDF 75.0% 18t 90.0% 1,053t 1,053t 100.0% 1,068t 19.9% 854t 80.2% 670t 21.8% 670t
Design of highly accurate formulas for numerical integration in weighted Hardy spaces with the aid of potential theory 1 Ken ichiro Tanaka 1 Ω R m F I = F (t) dt (1.1) Ω m m 1 m = 1 1 Newton-Cotes Gauss
p = mv p x > h/4π λ = h p m v Ψ 2 Ψ
II p = mv p x > h/4π λ = h p m v Ψ 2 Ψ Ψ Ψ 2 0 x P'(x) m d 2 x = mω 2 x = kx = F(x) dt 2 x = cos(ωt + φ) mω 2 = k ω = m k v = dx = -ωsin(ωt + φ) dt = d 2 x dt 2 0 y v θ P(x,y) θ = ωt + φ ν = ω [Hz] 2π
DVIOUT
A. A. A-- [ ] f(x) x = f 00 (x) f 0 () =0 f 00 () > 0= f(x) x = f 00 () < 0= f(x) x = A--2 [ ] f(x) D f 00 (x) > 0= y = f(x) f 00 (x) < 0= y = f(x) P (, f()) f 00 () =0 A--3 [ ] y = f(x) [, b] x = f (y)
I , : ~/math/functional-analysis/functional-analysis-1.tex
I 1 2004 8 16, 2017 4 30 1 : ~/math/functional-analysis/functional-analysis-1.tex 1 3 1.1................................... 3 1.2................................... 3 1.3.....................................
FX ) 2
(FX) 1 1 2009 12 12 13 2009 1 FX ) 2 1 (FX) 2 1 2 1 2 3 2010 8 FX 1998 1 FX FX 4 1 1 (FX) () () 1998 4 1 100 120 1 100 120 120 100 20 FX 100 100 100 1 100 100 100 1 100 1 100 100 1 100 101 101 100 100
A11 (1993,1994) 29 A12 (1994) 29 A13 Trefethen and Bau Numerical Linear Algebra (1997) 29 A14 (1999) 30 A15 (2003) 30 A16 (2004) 30 A17 (2007) 30 A18
2013 8 29y, 2016 10 29 1 2 2 Jordan 3 21 3 3 Jordan (1) 3 31 Jordan 4 32 Jordan 4 33 Jordan 6 34 Jordan 8 35 9 4 Jordan (2) 10 41 x 11 42 x 12 43 16 44 19 441 19 442 20 443 25 45 25 5 Jordan 26 A 26 A1
I ( ) 1 de Broglie 1 (de Broglie) p λ k h Planck ( Js) p = h λ = k (1) h 2π : Dirac k B Boltzmann ( J/K) T U = 3 2 k BT
I (008 4 0 de Broglie (de Broglie p λ k h Planck ( 6.63 0 34 Js p = h λ = k ( h π : Dirac k B Boltzmann (.38 0 3 J/K T U = 3 k BT ( = λ m k B T h m = 0.067m 0 m 0 = 9. 0 3 kg GaAs( a T = 300 K 3 fg 07345
Fuchs Fuchs Laplace Katz [Kz] middle convolution addition Gauss Airy Fuchs addition middle convolution Fuchs 5 Fuchs Riemann, rigidity
![Fuchs Fuchs Laplace Katz [Kz] middle convolution addition Gauss Airy Fuchs addition middle convolution Fuchs 5 Fuchs Riemann, rigidity](/thumbs/91/106755634.jpg "Fuchs Fuchs Laplace Katz [Kz] middle convolution addition Gauss Airy Fuchs addition middle convolution Fuchs 5 Fuchs Riemann, rigidity")
2010 4 8 7 22 2 Fuchs Fuchs Laplace Katz [Kz] middle convolution addition Gauss Airy Fuchs addition middle convolution Fuchs 5 Fuchs Riemann, rigidity 0 Fuchs addition middle convolution Riemann Fuchs
Risk Simulator 2012 User Manual (Japanese)
Johnathan Mun, Ph.D., MBA, MS, CFC, CRM, FRM, MIFC RISK SIMULATOR 2012 CEO, Admin@RealOptionsValuation.com www.realoptionsvaluation.com 2005-2012 Microsoft 1.... 7 2011/2012... 13... 13 2.... 19?... 19...
IA hara@math.kyushu-u.ac.jp Last updated: January,......................................................................................................................................................................................
( ) a, b c a 2 + b 2 = c 2. 2 1 2 2 : 2 2 = p q, p, q 2q 2 = p 2. p 2 p 2 2 2 q 2 p, q (QED)
rational number p, p, (q ) q ratio 3.14 = 3 + 1 10 + 4 100 ( ) a, b c a 2 + b 2 = c 2. 2 1 2 2 : 2 2 = p q, p, q 2q 2 = p 2. p 2 p 2 2 2 q 2 p, q (QED) ( a) ( b) a > b > 0 a < nb n A A B B A A, B B A =
インテル® VTune™ パフォーマンス・アナライザー 9.1 Windows* 版
VTune 9.1 Windows* ................................. 3...................... 3.................................................. 3............................................ 4 :.........................4................................................
all.dvi
5,, Euclid.,..,... Euclid,.,.,, e i (i =,, ). 6 x a x e e e x.:,,. a,,. a a = a e + a e + a e = {e, e, e } a (.) = a i e i = a i e i (.) i= {a,a,a } T ( T ),.,,,,. (.),.,...,,. a 0 0 a = a 0 + a + a 0
会津若松市民の運動行動における変化ステージの評価
2 Bandura1977 2000 Bandura 50 36 3 4 MarcusSimkin1993 2002 6 6 6 6 1995 2000.81 1998 1995 2000.91 2000 5 .65 1986.83 Marcus et al1992 2002 Pros.81 Cons.80 Pros Cons Pros Cons 6 7 8 9 10 11 12 13 5 Tukey
橡表紙参照.PDF
CIRJE-J-58 X-12-ARIMA 2000 : 2001 6 How to use X-12-ARIMA2000 when you must: A Case Study of Hojinkigyo-Tokei Naoto Kunitomo Faculty of Economics, The University of Tokyo Abstract: We illustrate how to
,. Black-Scholes u t t, x c u 0 t, x x u t t, x c u t, x x u t t, x + σ x u t, x + rx ut, x rux, t 0 x x,,.,. Step 3, 7,,, Step 6., Step 4,. Step 5,,.
9 α ν β Ξ ξ Γ γ o δ Π π ε ρ ζ Σ σ η τ Θ θ Υ υ ι Φ φ κ χ Λ λ Ψ ψ µ Ω ω Def, Prop, Th, Lem, Note, Remark, Ex,, Proof, R, N, Q, C [a, b {x R : a x b} : a, b {x R : a < x < b} : [a, b {x R : a x < b} : a,
2/50 Auction: Theory and Practice 3 / 50 (WTO) 10 SDR ,600 Auction: Theory and Practice 4 / 50 2
stakagi@econ.hokudai.ac.jp June 24, 2011 2.... 3... 4... 7 8... 9.... 10... 11... 12 IPV 13 SPSB... 15 SPSB.... 17 SPSB.... 19 FPSB... 20 FPSB.... 22 FPSB.... 23... 24 Low Price Auction.... 27 APV 29...
II Brown Brown
II 16 12 5 1 Brown 3 1.1..................................... 3 1.2 Brown............................... 5 1.3................................... 8 1.4 Markov.................................... 1 1.5