SHORT NOTE ON THE m-COMPARTMENT MODEL UNDER THE ONE-PARAMETER HYPOTHESIS

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TRU Mathematics 24−1 〔1988）

SHORT NO理qN、］ZHE・pa−、（蹴銀㎜M凪田田R

THE oNE・・PARAMETER HYPoTH正…sIS MbtosabUro MASUYAMA ． ’． ’ （Received February 29，1988〕 In・the③PPendix of．the Previgus paper ［1］，we．have used a cmPbersQme apProach to prove that under the one−parameter．hyp6thesis， only・one root of the

characters itic equation of the difference equation ” ． −

（A．1）

_{@∵「t＋ mhノ；lk・ll・1−；。㌶；，1驚1「＃．m、；㌶。7，；’：。}

is individuality−dependent’，“rhere we omit the sul）script i as befbre． In this short note， we will avoid this round−about route． We will use the same s）mbols and the salne nulnbering as those fbr the fo㎝ulas in the previous paper． Let （A・4）「Sh・i−A7／・・一「Sh2i−A、〃・2−…一一 r・hrm−、」i 一 Am−、〃・m。、＝ShMi−Am rαm＝ヱノ be the l ine under this hypothesis． We set

〔A・5）㌃R・う＝・ノ・Fゴ・砲ereる一・ブαみf・r j−・・・・…．

m一ヱ， and F ＝ 0． Then the characteristic equations for any two different individuals are given by

（A・・） gM−Sh、㌶一1・Sh、i・M−2−…・・一・・m”Sh，、、、・・・一・・栩5励一・、

for i＝1and 2， say． Taking the difference between these twt）equations， we have

：1警蔑1；繧：’浩、㌶彫三；、弛・〉 r

Since R・＝R2卿1ies th・t 3厄・一％、 f・r a・・」．by（・・5）…m・y・assum・ th・t R、声2・The・w・h・v・

〔…2）・，zM’1 一・㌶一2・・・…一．・・㌦・・．

99

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100 M．MASUYAMA

This being mu江土iplied by R』とnd“． s’Ubttadt’i ’9 ffo㎡（A．2），・we．6btain finally 〔…3） ♂−F！−2子一・、・加一2−・∴・’・一：・・惚．ヱー−t・・ Consequently， co叩paring （A．12） and 〔A．13〕，we get the relation 〔A．9） Fゴ＝αゴチ1／al’ 」＝ヱ⊃ 23 ・．・， m一ヱ・

REFERENCE

［1］ Masuyamal M．（1987）．：On the three−compart血ent m6del in phannacokinetiqs fr㎝the vie卿int qf、the a1JrK）st．っne，parameter㎞othesis，蜘 Mathematics，『23−2， 273−277・』 ’」 DEPARIMiNT OF APPLIED MATHHMAITICS sclEN（］UNIVERslTY oF T（）KYo

SHORT NOTE ON THE m-COMPARTMENT MODEL UNDER THE ONE-PARAMETER HYPOTHESIS

SHORT NO理qN、］ZHE・pa−、（蹴銀㎜M凪田田R

characters itic equation of the difference equation ” ． −

@∵「t＋ mhノ；lk・ll・1−；。㌶；，1驚1「＃．m、；㌶。7，；’：。

〔A・5） ㌃R・う＝・ノ・Fゴ・砲ereる一・ブαみf・r j−・・・・…．

（A・・） gM−Sh、㌶一1・Sh、i・M−2−…・・一・・m”Sh， 、、、・・・一・・栩5励一・、