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&RPSXWLQJ /DSODFH 7UDQVIRUPV ( YDOXDWLQJ WKH /DSODFH , QWHJU DO 6 LQ F H W K H / D S OD F H W U D Q V IR U P LV G H p Q H G E \ D Q LQ W H J U D O LW LV F OH D U W K D W LW V H oH F W LYH F R P S X W D W LR Q ZLOO U H TX LU H V R P H S U R p F LH Q F \ LQ W K H E D V LF LQ W H J U D W LR Q V NLOOV R I W K H V W D Q G D U G F D OF X OX V � : H ZLOO LOOX V W U D W H ZLW K D Q X P E H U R I H [D P S OH V � ( [DPSOH � / H W I � [� [� [ � >� ��� � 7K H Q � / I � V = � � HbV[[G[� ,Q W H J U D OV R I W K LV W \S H F D Q E H H YD OX D W H G X V LQ J LQWHJUDWLRQ E\ SDUWV� IR U ZK LF K W K H V W D Q G D U G IR U P X OD LV = J � [� K� [� G[ *� [� K� [� b = *� [� K � � [� G[� ZK H U H *� [� G H Q R W H V D Q D Q W LG H U LYD W LYH R I J � [� � 7D NLQ J J � [� HbV[� K� [� [ D Q G X V LQ J W K H V W D Q G D U G OLP LW V IR U W K H / D S OD F H LQ W H J U D O ZH K D YH � / [� V = � � HbV[[G[ b H bV[ V [ ppp� � � � V = � � HbV[ � G[� ,W LV F OH D U IU R P W K LV W K D W W K H LQ W H J U D O LV G H p Q H G IR U V ! � D Q G � IR U V X F K YD OX H V R I V ZH K D YH � / [� V � � � � � V� v b OLP [�� HbV[ � HbVc� w � V� � � � � � � V� � )R U I � [� [� W K H LQ W H J U D W LR Q E \ S D U W V S U R F H V V LV X V H G W ZLF H � G LoH U H Q W LD W LQ J [� W R J H W � [ D Q G W K H Q G LoH U H Q W LD W LQ J W K D W D J D LQ W R J H W � ZLW K W K H U H V X OW W K D W t / [� u V � V� � � ,Q J H Q H U D O� Q D S S OLF D W LR Q V R I LQ W H J U D W LR Q E \ S D U W V V K R Z W K D W � / [Q � V Q� VQ�� � + R ZH YH U W K LV LV W K H K D U G ZD \ W R R E W D LQ W K LV U H V X OW � D Q H D V LH U ZD \ ZLOO E H G H V F U LE H G X Q G H U 3 U RSHU WLHV RI WKH /DSODFH 7 U DQVIRU P� 8VH RI &RPSOH[ ( [WHQVLRQV RI 5HDO )XQFWLRQV 7K H / D S OD F H 7U D Q V � IR U P U H P D LQ V YD OLG IR U &RPSOH[ ( [WHQVLRQV R I W K H V W D Q G D U G U H D O�YD OX H G H OH P H Q W D U \ IX Q F W LR Q V � 8 V H R I W K LV ID F W W R J H W K H U ZLW K W K H ID F W W K D W D Q W LG LoH U � H Q W LD W LR Q IR U P X OD V YD OLG IR U U H D O H OH P H Q W D U \ IX Q F W LR Q V U H P D LQ YD OLG IR U W K H LU F R P S OH [ H V W H Q V LR Q V � R IW H Q D OOR ZV W K H G H V LU H G � U H D O� / D S OD F H LQ W H J U D O W R E H LG H Q W Lp H G D V W K H U H D O R U LP D J LQ D U \ S D U W R I D F R P S OH [ LQ W H J U D O ZK LF K LV P R U H H D V LO\ H YD OX D W H G � ( [DPSOH � 7K H / D S OD F H W U D Q V IR U P V R I F R V D[ D Q G V LQ D[ F D Q E H R E W D LQ H G G LU H F W O\ E \ H YD OX D W LQ J W K H / D S OD F H LQ W H J U D OV 5 � � HbV[ F R V D[ G[ D Q G 5 � � HbV[ V LQ D[ G[� U H V S H F W LYH O\� + R ZH YH U � V X F K H YD OX D W LR Q ZLW K LQ D Q H [F OX V LYH O\ U H D O Q X P E H U F R Q W H [W U H TX LU H V D G R X E OH D S S OLF D W LR Q R I LQ W H J U D W LR Q E \ S D U W V � $ F R Q V LG H U � D E O\ V LP S OH U U R X W H W D NH V D G YD Q W D J H R I W K H LG H Q W LW \ � HL D[ F R V D[ � L V LQ D[� U H OD W LQ J W K H F R P S OH [ H [S R Q H Q W LD O IX Q F W LR Q W R W K H V H W U LJ R Q R P H W U LF IX Q F W LR Q V � )U R P W K D W LG H Q W LW \ ZH K D YH F R V D[ 5 H HL D[� ZK H U H ? 5 H � P H D Q V ? U H D O S D U W � � $ V D F R Q V H TX H Q F H ZH K D YH � / F R V D[� � V� 5 H = � � HbV[ � F R V D[� L V LQ D[� G[ 5 H = � � HbV[ HL D[ G[ 5 H = � � H�L DbV�[ G[ 5 H � Vb LD 5 H V� LD � Vb LD� � V� LD � 5 H V� LD V� � D� V V� � D� � � 7R R E W D LQ W K H / D S OD F H W U D Q V IR U P R I V LQ D[ ZH V LP S O\ W D NH W K H F R U U H V S R Q G LQ J LP D J LQ D U \ S D U W � U H V X OW LQ J LQ � / V LQ D[� � V� ,P V� LD V� � D� D V� � D� � 8VH RI WKH /LQHDU LW\ RI WKH 7 U DQVIRU P )R U F R Q V W D Q W V F � F � D Q G IX Q F � W LR Q V I � � [� � I � � [� ZH K D YH � S U R YLG LQ J D OO LQ W H J U D OV LQ G LF D W H G D U H ZH OO G H p Q H G � � � / F � I � � F � I � � � V� = � � HbV[ � F � I � � [� � F � I � � [� � G[ F � = � � HbV[ I � � [� G[ � F � = � � HbV[ I � � [� G[ F � � / I � � � V� � F � � / I � � � V� � ,Q W K LV ZD \ ZH V H H W K D W W K H OLQHDULW\ SURSHUW\ � / F � I � � F � I � � � V� F � � / I � � � V� � F � � / I � � � V� R I W K H / D S OD F H W U D Q V IR U P LV D V LP S OH F R Q V H TX H Q F H R I W K H F R U U H � V S R Q G LQ J OLQ H D U LW \ S U R S H U W \ R I LQ W H J U D W LR Q � 7K LV P D \ V H H P D E LW W U LYLD O E X W X V H R I W K LV S U R S H U W \ LV D Q LP S R U W D Q W W R R O LQ LG H Q W LI\LQ J F H U W D LQ / D S OD F H W U D Q V � IR U P V � ( [DPSOH � 7K H K\SHUEROLF FRVLQH D Q G K\SHUEROLF VLQH IX Q F W LR Q V D U H G H � p Q H G LQ W H U P V R I W K H H [S R Q H Q W LD O IX Q F W LR Q V E \ P H D Q V R I W K H OLQ H D U F R P E LQ D � W LR Q V F R V K D[ HD[ � HbD[ � � V LQ K D[ HD[ b HbD[ � � U H V S H F W LYH O\� 6 LQ F H W K H H [S R Q H Q W LD O IX Q F W LR Q V HD[ D Q G D Q G HbD[ K D YH / D S OD F H W U D Q V IR U P V � VbD D Q G � V�D � U H V S H F W LYH O\� W K H OLQ H D U LW \ S U R S H U W \ V K R ZV W K D W � / F R V K D[� � V� � � � Vb D � � � � V� D V V� b D� � � / V LQ K D[� � V� � � � Vb D b � � � V� D D V� b D� � �
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