There do not exist context–free languages of intermediate growth. The function γ whose value at each non–negative integer n is the number of words on length n in a fixed formal language L is called the growth function of L. Flajolet [3] asked if there are context–free languages of intermediate growth; that is, such that γ is not bounded above by a polynomial, but lim sup γ(n)/r = 0 for all r > ...

this paper is devoted to the study of establishing sufficient conditions forexistence and uniqueness of positive solution to a class ofnon-linear problems of fractional differential equations. the boundary conditionsinvolved riemann-liouville fractional order derivative and integral. further, the non-linear function $f$ containfractional order derivative which produce extra complexity. thank to...

in this paper, we prove the existence of the solution for boundary value prob-lem(bvp) of fractional dierential equations of order q 2 (2; 3]. the kras-noselskii's xed point theorem is applied to establish the results. in addition,we give an detailed example to demonstrate the main result.

‎the subject of this paper is the solution of the fredholm integral equation with toeplitz, hankel and the toeplitz plus hankel kernel. the mean value theorem for integrals is applied and then extended for solving high dimensional problems and finally, some example and graph of error function are presented to show the ability and simplicity of the ‎method.

in this paper, we study a coupled system of nonlinear fractional differential equations with multi-point boundary condi- tions. the differential operator is taken in the riemann-liouville sense. applying the schauder fixed-point theorem and the contrac- tion mapping principle, two existence results are obtained for the following system d^{alpha}_{0+}x(t)=fleft(t,y(t),d^{p}_{0+}y(t)right), t in (0,...

G. Darbo [Rend. Sem. Math. Univ. Padova, 24 (1955) 84--92] used the measure of noncompactness to investigate operators whose properties can be characterized as being intermediate between those of contraction and compact operators. In this paper, we apply the Darbo's fixed point theorem for solving infinite system of linear equations in some sequence spaces.  

Then, f (x) = 0 has a solution in Ω. For n = 1, Theorem 1.1 reduces to the well-known intermediate-value theorem. Miranda proved his theorem using the Brouwer fixed point theorem. Using the Brouwer degree of a mapping, Vrahatis gave another short proof of Theorem 1.1 (see [2]). Following this proof it is easy to see that Theorem 1.1 is also true, if L is dependent of i; that is, Ω can also be a...

We present a new proof and extension of the classical Sylvester Inertia Theorem to a pair of non-Hermitian matrices which satisfies the property that any real linear combination of the pair has only real eigenvalues. In the proof, we embed the given problem in a one-parameter family of related problems and examine the eigencurves of the family. The proof requires only elementary matrix theory a...

In this paper, we concerned with positive solutions for higher order m-point nonlinear fractional boundary value problems with integral boundary conditions. We establish the criteria for the existence of at least one, two and three positive solutions for higher order m-point nonlinear fractional boundary value problems with integral boundary conditions by using a result from the theory of fixed...

Convergence under various topologies and analytical properties of power series on Levi-Civita fields are studied. A radius of convergence is established that asserts convergence under a weak topology and reduces to the conventional radius of convergence for real power series. It also asserts strong (order) convergence for points the distance of which from the center is infinitely smaller than t...