# the Theorem of existence of mutual influence of innovations

Let there are two innovative products and? And ujв structure of portfolio U, ready to start on market E and for which it is executed M? ∩ Mj ≠ 0, where E - theoretically possible sales volumes of a product, M?, Mj∈Е - predicted sales volumes of products and? And and: disregarding mutual influence.

Then degree of influence of one innovative product and? On other and: it is possible to express through factor and?::

t J

Where f (t) - function of sales of a product;

- Actual sales volume of a product;

! - time moment when the product has been introduced from the market

- Predicted sales volumes of products and? And uj-disregarding

Mutual influence by time moment t;

> °.

Nonempty crossing mnozhestvjavljaetsja the necessary

Condition that expression (2.9) became fair.

The algorithm of complete search of variants will allow to define a sufficient condition mutual influences (table 2.3). In total probably eight variants of mutual influence of innovative products against each other. We will enter following designations:

Having substituted significance of the formula (2.10) in the formula (2.11), we will receive following expression:

First eight variants will designate mutual influence. The ninth variant is indicated according to algorithm of complete search, however the necessary condition in that case is not satisfied.

If aij 1 two innovative products make against each other positive impact. If aij - = 1 it is possible to speak about the mixed influence (see cases 6, 7 and 8 of table 2.3) or about absence of mutual influence (see the case 9 of table 2.3).

Then current factor of interaction at the moment of time T we name

MU and Mjy - a predicted sales volume of products and? And without mutual influence by time moment!.

Table 2.3 - the Direction of influence of innovative products against each other

2.2.2