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Р Š Ԡ Š Р

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, D . D. 1.

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ߠ .

, :

ì 0, t < -x,

u(t) = í 0.5(t/x+1), -x £ t £ x, (1)

î 1, t > x.

.

2x. x , . :

ì 0, t < 0,

s(t) = í 0.5, t = 0, (2)

î 1, t > 0.

t0. :

ì 0, t < t0,

s(t - t0) = í 0.5, t = t0, (3)

î 1, t > t0.

Š Π ɠ .

S(t), , S(t)=0 t<0. {D,2D,3D,...} - {S1,S2,S3,...} - . S0=S(0), t :

¥

s(t)s0s(t)+(s1-s0)s(t-D)+...=s0s(t)+å(sk-sk-1)s(t-kD).

k=1

     D . kD t. ds=(ds/dt)dt ,

¥

ó ds

S(t)=s0 s(t) + ô s(t-t) dt (4)

õ dt

0

, , - -.

- .

, :

1 é x x ù

u(t;x) = ----- ê s (t + ---- ) - s (t - ---- ) ÷ (5)

x ë 2 2 û

x

:

¥

Ϡ = ò u dt = 1

- ¥

, u - , = 1 *.

x . , , , . x 0 - , [1] :

d(t) = lim u (t;x)

x0

- . , 堠 t = 0 [2] - . - :

 

Š Š ̠ -.

⠠ (. 2) . - u (t) . Sk - k - , k :

hk(t) = Sk [ s(t - tk) - s(t - tk - D) ] (6)

S (t) :

¥

S(t) = å h (t) (7)

k= - ¥ k

, , t :

tk < t < tk+1

, (6) (7) D,

¥ 1

S(t) = å Sk --- [ s(t - tk) - s(t - tk - D) ] D

k=- ¥ D

D 0 , t, dt , D .

1

lim [ s(t - tk) - s(t - tk - D) ] ---

D0 D

¥

S (t) = ò s (t) d(t - t) dt

- ¥

, - , , d - . , -.[3]

- (3) . , - - ¥ t , - :

d(t) = 1 (t) ;

d(t-t0) = 1 (t-t0) .

.

, S(t) - t . d(t) - 蠠 t = 0 , . . .

. - , , . (t) , ,

¥

ò (t) j(t) dt (8)

- ¥

j(t) , .

j(t) , , . , (8) j(t). , ,

(, aj1 + bj2) = a(,j1) + b(,j2).

, , j(t) (t) [4]. , -, .

, , . , .

, . , .

:

1. . . , . . ⠠ Š

ޠ   Ƞ .

2. . . ⠠ Š

Ƞ .



[1] ,

[2] , - .

[3] , 頠 S(t). : .

[4] .


Р Š Ԡ Š Р ࠠ : 堠 : .. : .. .

 

 

 

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