Nonperturbative treatment of open strings in less than 1-dimension

We investigate nonperturbative aspects of the open strings, using matrix models containing vectors. First considering the double scaling limit of the model, we obtain the differential equation for the nonperturbative free energy of open strings. Second, we study the asymptotic behaviour of the free energy and we see that the terms corresponding to closed surfaces agree with those of the ordinary matrix model. Using the results which we have obtained, we further give some consideration on the contribution for the free energy from the surfaces with fixed number of boundaries. Next, we make one kind of extension of our model, which is a model with two kinds of boundaries. Finally, we consider the correlation functions of some operators and derive the differential equation for the generating function of them. (author)