393c00a0-d26d-470b-a5f1-cba0190760e1 42 4 5 decimal

&[DATE] &[TIME] - &[FILENAME]

e 100 :

λ 20 :

h 1 :

c 0.125 :

x λ u e λ c x * - (2^-^e λ c x * + (2^-^+ :

x λ U h 0 x λ u < 0 cases :

x λ U

λ 0.5 :

c 0.025 :

n 10 :

x λ U λ c x * - (n^- exp λ c x * + (n^- exp + :

x λ U

λ 5 :

c 0.125 :

n 10 :

x λ U λ c x * - (2^- exp λ c x * + (2^- exp + :

x λ U

α 0.5 :

x β f α β * x β 1 -^* α x β^* - exp * :

f x 0.75 f x 1 f x 1.25 f x 1.5 f x 2 f 51 sys :

x n Naja x 0.5 x n^+ / :

N x 0.5 Naja x 0.75 Naja x 1.01 Naja x 1.25 Naja x 1.5 Naja x 1.75 Naja 61 sys :

a x Bicorne 1110 x a - / abs exp + / :

x NOTasymptotic x 1.8^1 x 1.75^+ / :

B 0 x Bicorne 5 x Bicorne 10 x Bicorne 15 x Bicorne 41 sys :

B x NOTasymptotic

L 10 : b 0.0025 : T.L 1200 : T.o 300 : 14 mat

x Thermal 1 b / b T.o * - exp x L / b T.o * - exp b T.L * - exp - (* - ln * - :

x Thermal 0 x ≤ ( * T.o 2 1 sys

==================================================

x λ HolySpirit x 1 x - (* (λ^:

Golden 15 sqrt + 2 / : 1.618

H x 0.25 HolySpirit x 0.5 HolySpirit x 0.75 HolySpirit x 1 HolySpirit x 2 HolySpirit x 4 HolySpirit x 6 HolySpirit 71 sys :

H Golden 1 + 20 black 1 5 mat 2 1 sys

x k LongHorn 0.01 x 2^(* (k^:

x β f x 1 β x * /^:

x 1 f x 5 f x 20 f 3 1 sys

LH x 0.25 LongHorn x 0.5 LongHorn x 0.75 LongHorn x 1 LongHorn x 1.25 LongHorn x 1.5 LongHorn x 1.75 LongHorn 71 sys :

x α W x α 1 x - (* exp * :

W x 0.25 W x 0.5 W x 0.75 W x 1 W x 1.25 W x 1.5 W x 2 W 71 sys :

x D x 4^x exp * x exp 1 - (2^/ :

x D

x p q Diffusion 1 p q + (x * - exp - 1 q p / (p q + (x * - exp * + / :

x 0.125 1 Diffusion x 1 0.25 Diffusion 2 1 sys

x δ n Unknown δ x n^/ - exp x 1 n +^/ :

Uk x 14 Unknown x 24 Unknown x 34 Unknown 31 sys :

x λ °C 12 λ * 2 λ * x - / ln / :

°C x 1 °C x 2 °C x 3 °C 31 sys :

°C

x m S m m x - / :

S x 10 S x 20 S x 30 S x 40 S 41 sys :

a 1 : b 0.5 : 12 mat

x m Sm b m x * + a b m x * + (* x - / :

Sm x 0.5 Sm x 0.75 Sm x 1 Sm x 1.25 Sm x 1.5 Sm 51 sys :

x n Peacock x n^1 x - (* sqrt :

Pea x 0.5 Peacock x 1 Peacock x 1.5 Peacock x 2 Peacock x 2.5 Peacock x 3 Peacock x 3.5 Peacock 71 sys :

x n Peacock x n^1 x - (* sqrt :

Peacock x 0.5 Peacock x 1 Peacock x 1.5 Peacock x 2 Peacock x 2.5 Peacock x 3 Peacock x 3.5 Peacock x 4 Peacock 81 sys :

Peacock

x ν Chi x 2 k * 1 +^2 k * 1 + (ν^/ k 020 sum :

x 0 Chi x 1 Chi x 2 Chi 3 1 sys

x m EnglishHat_1 113 x m^* + / :

x n EnglishHat_2 113 x n^* + / :

EnglishHat_1 x 2 EnglishHat_1 x 4 EnglishHat_1 x 6 EnglishHat_1 x 8 EnglishHat_1 41 sys :

EnglishHat_2 x 0.5 EnglishHat_2 x 1.5 EnglishHat_2 x 2.5 EnglishHat_2 x 3.5 EnglishHat_2 41 sys :

EnglishHat_1 EnglishHat_2

x erfc 1 x erf - :

yo α n m D x Dopant yo α x n^D / (m^erfc * + :

yo 3.847 : α 98.291 : n 0.966 : m 0.503 : D 1818 : 15 mat

Parameters wrt a data set fit

yo α n m D x Dopant

Rich model wrt [m, n, xo] ... try xo = -0.5 m n xo x MomentsQuadratic x xo - (2^x xo - (- (n^(m^:

m 14 : n 0.08 : xo 1 - : 13 mat

m 14 : n 0.0625 : xo 1 - : 13 mat

m 14 : n 0.075 : xo 1 - : 13 mat

m n xo x MomentsQuadratic m n xo x MomentsQuadratic x / 2 1 sys

Two families of continued fraction

x q xo T1 11 x xo + q 11 x xo + q 11 x xo + q 11 x + xo + / + / + / + / + / + / + / :

x q T2 1 q x q 1 q x q 1 q x q 1 q x + / + / + / + / + / + / + / :

xo 2 - :

T1 x 0.25 xo T1 x 0.5 xo T1 x 0.75 xo T1 x 1 xo T1 x 1.25 xo T1 x 1.5 xo T1 61 sys :

T2 x 0.25 T2 x 0.5 T2 x 0.75 T2 x 1 T2 x 1.25 T2 x 1.5 T2 61 sys :

T1 T2

yo 0 : A 1 : xo 0 : n 0.125 : w 0.75 : 15 mat

x z x xo - w / :

x yo xo A w n E yo A x z - exp - x z n^- 1 + exp * + :

x yo xo A w n E

CCE: Chesler-Cram

yo 0 : A 1 : B 1 : W 1 : x1 1.1 : x2 2 : k2 0.75 : k3 1.5 : 18 mat

x x3 Q yo A x x1 - (2^- 2 W * / exp 1 0.6 1 0.75 k2 x x2 - (* tanh * - (* - (B 0.5 k3 x x3 - abs x x3 - (+ (* * - exp * * + (* + :

x c 11 - x ≤ cases :

x 2 Q x c * x 3 Q x c * x 4 Q x c * x 5 Q x c * 4 1 sys

x f 11 i! / x ln i^* x i^* i 130 sum + :

x c 13 - x ≤ cases :

x f Re x c * x f Im x c * x f abs x c * 3 1 sys

data char size clr plot k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 31 line for data r3 r4 r5 augment 21 line :

XY 020406080100120140160180200 210.3 113.2 63.7 39 27.6 24.3 27.6 39 63.7 113.2 210.3 211 mat transpose :

A 200 : B 200 : C 10 : D 30 : E 30 : F 0 : G 200 : 17 mat

x BathTub A x F - (D / - exp * B x G - E / exp * + C + :

x c 10 x ≤ (x 200 ≤ (& cases :

pts XY o 5 black plot :

x BathTub x c * 200 pts 3 1 sys

x b n F 1 x b / - (n^exp - :

(b≤1)|(b≥1) b 0.75 :

b 1 ≤ (b 1 ≥ (|

b - b 0.125 F 1.7183 -

F x b 0.125 F x b 0.15 F x b 0.175 F x b 0.201 F x b 0.225 F x b 0.25 F 61 sys :

F b - b - b 0.125 F + 30 black 1 5 mat 2 1 sys

F x b 0.125 F Im x b 0.15 F Im x b 0.175 F Im x b 0.201 F Im x b 0.225 F Im x b 0.25 F Im 61 sys :

<= b => ω 1 :

1 ω / 1 x ω * - exp - ( * ω 1 - x ω * - exp + / - 2 1 sys

x b n Ω n x n 1 - (^b n^/ * x b / - (n^exp * :

Ωim x b 0.125 Ω Im x b 0.15 Ω Im x b 0.175 Ω Im x b 0.201 Ω Im x b 0.225 Ω Im x b 0.25 Ω Im 61 sys :

Ωre x b 0.125 Ω Re x b 0.15 Ω Re x b 0.175 Ω Re x b 0.201 Ω Re x b 0.225 Ω Re x b 0.25 Ω Re 61 sys :

Ωim Ωre

n 3 : m 2.5 : Q 1 : xo 0 : 14 mat

The very rich Psi 2/3
get lot more from 'm'
... PDF "a la carte" x λ Psi Q n 2^* x xo - (* 1 n 3^x xo - (m^* + / (λ^:

max from Golden ratio
specific for m = 2.5 mid 0.228 :

Psi x 0.5 Psi x 1.5 Psi x 2.5 Psi x 3.5 Psi 41 sys :

Psi mid 5 mid 1 - 2 2 mat 3 1 sys x 1 Psi