❆❜str❛❝t ✕ ❆ss❡ss✐♥❣ s♦❢t✇❛r❡ q✉❛❧✐t2 ❛ttr✐❜✉t❡s ✭s✉❝❤ ❛s ♣❡r❢♦r♠❛♥❝❡✱ r❡❧✐❛❜✐❧✐t2✱ ❛♥❞ s❡❝✉r✐t2✮ ❢r♦♠ s♦✉r❝❡ ❝♦❞❡ ✐s ♦❢ t❤❡ ✉t♠♦st ✐♠♣♦rt❛♥❝❡✳ ❚❤❡ ♣❡r❢♦r♠❛♥❝❡ ♦❢ ❛ s♦❢t✇❛r❡ s2st❡♠ ❝❛♥ ❜❡ ✐♠♣r♦✈❡❞ ❜2 ✐ts ♣❛r❛❧❧❡❧ ❛♥❞ ❞✐str✐❜✉t❡❞ ❡1❡❝✉t✐♦♥✳ ❚❤❡ ❛✐♠ ♦❢ t❤❡ ♣❛r❛❧❧❡❧ ❛♥❞ ❞✐str✐❜✉t❡❞ ❡1❡❝✉t✐♦♥ ✐s t♦ s♣❡❡❞ ✉♣ ❜2 ♣r♦✈✐❞✐♥❣ t❤❡ ♠❛1✐♠✉♠ ♣♦ss✐❜❧❡ ❝♦♥❝✉rr❡♥❝2 ✐♥ ❡1❡❝✉t✐♥❣ t❤❡ ❞✐str✐❜✉t❡❞ s❡❣♠❡♥ts✳ ■t ✐s ❛...

❆❜str❛❝t ✕ ❆ss❡ss✐♥❣ s♦❢t✇❛r❡ q✉❛❧✐t2 ❛ttr✐❜✉t❡s ✭s✉❝❤ ❛s ♣❡r❢♦r♠❛♥❝❡✱ r❡❧✐❛❜✐❧✐t2✱ ❛♥❞ s❡❝✉r✐t2✮ ❢r♦♠ s♦✉r❝❡ ❝♦❞❡ ✐s ♦❢ t❤❡ ✉t♠♦st ✐♠♣♦rt❛♥❝❡✳ ❚❤❡ ♣❡r❢♦r♠❛♥❝❡ ♦❢ ❛ s♦❢t✇❛r❡ s2st❡♠ ❝❛♥ ❜❡ ✐♠♣r♦✈❡❞ ❜2 ✐ts ♣❛r❛❧❧❡❧ ❛♥❞ ❞✐str✐❜✉t❡❞ ❡1❡❝✉t✐♦♥✳ ❚❤❡ ❛✐♠ ♦❢ t❤❡ ♣❛r❛❧❧❡❧ ❛♥❞ ❞✐str✐❜✉t❡❞ ❡1❡❝✉t✐♦♥ ✐s t♦ s♣❡❡❞ ✉♣ ❜2 ♣r♦✈✐❞✐♥❣ t❤❡ ♠❛1✐♠✉♠ ♣♦ss✐❜❧❡ ❝♦♥❝✉rr❡♥❝2 ✐♥ ❡1❡❝✉t✐♥❣ t❤❡ ❞✐str✐❜✉t❡❞ s❡❣♠❡♥ts✳ ■t ✐s ❛...

❆❜str❛❝t ✕ ❆ss❡ss✐♥❣ s♦❢t✇❛r❡ q✉❛❧✐t2 ❛ttr✐❜✉t❡s ✭s✉❝❤ ❛s ♣❡r❢♦r♠❛♥❝❡✱ r❡❧✐❛❜✐❧✐t2✱ ❛♥❞ s❡❝✉r✐t2✮ ❢r♦♠ s♦✉r❝❡ ❝♦❞❡ ✐s ♦❢ t❤❡ ✉t♠♦st ✐♠♣♦rt❛♥❝❡✳ ❚❤❡ ♣❡r❢♦r♠❛♥❝❡ ♦❢ ❛ s♦❢t✇❛r❡ s2st❡♠ ❝❛♥ ❜❡ ✐♠♣r♦✈❡❞ ❜2 ✐ts ♣❛r❛❧❧❡❧ ❛♥❞ ❞✐str✐❜✉t❡❞ ❡1❡❝✉t✐♦♥✳ ❚❤❡ ❛✐♠ ♦❢ t❤❡ ♣❛r❛❧❧❡❧ ❛♥❞ ❞✐str✐❜✉t❡❞ ❡1❡❝✉t✐♦♥ ✐s t♦ s♣❡❡❞ ✉♣ ❜2 ♣r♦✈✐❞✐♥❣ t❤❡ ♠❛1✐♠✉♠ ♣♦ss✐❜❧❡ ❝♦♥❝✉rr❡♥❝2 ✐♥ ❡1❡❝✉t✐♥❣ t❤❡ ❞✐str✐❜✉t❡❞ s❡❣♠❡♥ts✳ ■t ✐s ❛...

❆❜str❛❝t ✕ ❆ss❡ss✐♥❣ s♦❢t✇❛r❡ q✉❛❧✐t2 ❛ttr✐❜✉t❡s ✭s✉❝❤ ❛s ♣❡r❢♦r♠❛♥❝❡✱ r❡❧✐❛❜✐❧✐t2✱ ❛♥❞ s❡❝✉r✐t2✮ ❢r♦♠ s♦✉r❝❡ ❝♦❞❡ ✐s ♦❢ t❤❡ ✉t♠♦st ✐♠♣♦rt❛♥❝❡✳ ❚❤❡ ♣❡r❢♦r♠❛♥❝❡ ♦❢ ❛ s♦❢t✇❛r❡ s2st❡♠ ❝❛♥ ❜❡ ✐♠♣r♦✈❡❞ ❜2 ✐ts ♣❛r❛❧❧❡❧ ❛♥❞ ❞✐str✐❜✉t❡❞ ❡1❡❝✉t✐♦♥✳ ❚❤❡ ❛✐♠ ♦❢ t❤❡ ♣❛r❛❧❧❡❧ ❛♥❞ ❞✐str✐❜✉t❡❞ ❡1❡❝✉t✐♦♥ ✐s t♦ s♣❡❡❞ ✉♣ ❜2 ♣r♦✈✐❞✐♥❣ t❤❡ ♠❛1✐♠✉♠ ♣♦ss✐❜❧❡ ❝♦♥❝✉rr❡♥❝2 ✐♥ ❡1❡❝✉t✐♥❣ t❤❡ ❞✐str✐❜✉t❡❞ s❡❣♠❡♥ts✳ ■t ✐s ❛...

❆❜str❛❝t ✕ ❆ss❡ss✐♥❣ s♦❢t✇❛r❡ q✉❛❧✐t2 ❛ttr✐❜✉t❡s ✭s✉❝❤ ❛s ♣❡r❢♦r♠❛♥❝❡✱ r❡❧✐❛❜✐❧✐t2✱ ❛♥❞ s❡❝✉r✐t2✮ ❢r♦♠ s♦✉r❝❡ ❝♦❞❡ ✐s ♦❢ t❤❡ ✉t♠♦st ✐♠♣♦rt❛♥❝❡✳ ❚❤❡ ♣❡r❢♦r♠❛♥❝❡ ♦❢ ❛ s♦❢t✇❛r❡ s2st❡♠ ❝❛♥ ❜❡ ✐♠♣r♦✈❡❞ ❜2 ✐ts ♣❛r❛❧❧❡❧ ❛♥❞ ❞✐str✐❜✉t❡❞ ❡1❡❝✉t✐♦♥✳ ❚❤❡ ❛✐♠ ♦❢ t❤❡ ♣❛r❛❧❧❡❧ ❛♥❞ ❞✐str✐❜✉t❡❞ ❡1❡❝✉t✐♦♥ ✐s t♦ s♣❡❡❞ ✉♣ ❜2 ♣r♦✈✐❞✐♥❣ t❤❡ ♠❛1✐♠✉♠ ♣♦ss✐❜❧❡ ❝♦♥❝✉rr❡♥❝2 ✐♥ ❡1❡❝✉t✐♥❣ t❤❡ ❞✐str✐❜✉t❡❞ s❡❣♠❡♥ts✳ ■t ✐s ❛...

g l o b a l c o m p e t i t i v e n e s s h a s r e c e n t l y b e c o m e a b i g c h a l l e n g e f o r m a n y c o m p a n i e s a r o u n d t h e w o r l d, w h i c h a r e f o r c e d t o s e e k l o w e r c o s t s a n d h i g h e r q u a l i t y f o r w h a t t h e y p r o d u c e. t h e p r o s p e r i t y o f m a n u f a c t u r i n g f i r m s d e p e n d s o n s e l e c t i n g a n...

and Applied Analysis 3 Lemma 3. Let q ∈ E. Then for any V > 0, r < s ∈ R such that q(t) ∉ B ε (V) and |q(t)| ⩽ V for any t ∈ [r, s], I (q) ⩾ √2σ ε,V 󵄨󵄨󵄨󵄨q (r) − q (s) 󵄨󵄨󵄨󵄨 . (16) In particular, if σ ε > 0, then for any r < s ∈ R such that q(t) ∉ B ε (V) for any t ∈ [r, s], I (q) ⩾ √2σ ε 󵄨󵄨󵄨󵄨q (r) − q (s) 󵄨󵄨󵄨󵄨 . (17) Proof. Denote l = |q(r) − q(s)| and τ = |r − s|. Then l = 󵄨󵄨󵄨󵄨󵄨󵄨󵄨 ∫ s r q 󸀠 (t)...

▼❛t❡r✐❛❧✐3❡❞ ✈✐❡✇s ❛r❡ ♦♥❡ ♦❢ t❤❡ ♠♦st ♣♦♣✉❧❛r ♦♣t✐♠✐3❛✲ t✐♦♥ t❡❝❤♥✐q✉❡s s❡❧❡❝t❡❞ ❞✉r✐♥❣ t❤❡ ♣❤2s✐❝❛❧ ♣❤❛s❡ t♦ s♣❡❡❞ ✉♣ q✉❡r2 ♣r♦❝❡ss✐♥❣ ✐♥ tr❛❞✐t✐♦♥❛❧ ❛♥❞ ❛❞✈❛♥❝❡❞ ❞❛t❛❜❛s❡s✳ ❚❤❡✐r s❡❧❡❝t✐♦♥ ❤❛s ❜❡❡♥ ♣r♦✈❡♥ t♦ ❜❡ ◆P✲❤❛r❞✳ ❆s ❛ ❝♦♥✲ s❡q✉❡♥❝❡ ❧❛r❣❡ ♣❛♥♦♣❧2 ♦❢ ❤❡✉r✐st✐❝s ❤❛s ❜❡❡♥ ♣r♦♣♦s❡❞ t♦ ✜♥❞ ♥❡❛r ♦♣t✐♠❛❧ s♦❧✉t✐♦♥s✳ ❯s✉❛❧❧2✱ t❤❡ s❡❧❡❝t❡❞ ♠❛t❡r✐❛❧✲ ✐3❡❞ ✈✐❡✇s ❛r❡ ✇❤♦❧❡ ❧✐❢❡ ❞✐s❦ r❡s✐❞❡♥t ❛♥❞ t❤...