Related papers: Generalizations on a Problem of Saffari

We find an explicit closed form for the subword complexity of the infinite fixed point of the morphism sending $a \rightarrow aab$ and $b \rightarrow b$. This morphism is then generalized in three different ways, and we find similar…

We present a proof of a conjecture of Goh and Wildberger on the factorization of the spread polynomials. We indicate how the factors can be effectively calculated and exhibit a connection to the factorization of Fibonacci numbers into…

The recent proposal by Ben-Zvi, Sakellaridis and Venkatesh of a duality in the relative Langlands program, leads, via the process of quantization of Hamiltonian varieties, to a duality theory of branching problems. This often unexpectedly…

We introduce semicontinuous summation methods for series of fuzzy numbers and give Tauberian conditions under which summation of a series of fuzzy numbers via generalized Dirichlet series and via generalized factorial series implies its…

In their study of the Yamabe problem in the presence of isometry group, Hebey and Vaugon announced a conjecture. This conjecture generalizes Aubin's conjecture, which has already been proven and is sufficient to solve the Yamabe problem. In…

General solutions of nonlinear ordinary differential equations (ODEs) are in general difficult to find although powerful integrability techniques exist in the literature for this purpose. It has been shown that in some scalar cases…

In this work we look at the original fractional calculus of variations problem in a somewhat different way. As a simple consequence, we show that a fractional generalization of a classical problem has a solution without any restrictions on…

We consider a zero-surface-tension two-dimensional Hele-Shaw flow in an infinite wedge. There exists a self-similar interface evolution in this wedge, an analogue of the famous Saffman-Taylor finger in a channel, exact shape of which has…

A general method for solving nonlinear ill-posed problems is developed. The method consists of solving a Cauchy problem with a regularized operator and proving that the solution of this problem tends, as time grows, to a solution of the…

We prove the universality of the regular realizability problems for several classes of filters. The filters are encodings of finite relations on the set of non-negative integers in the format proposed by P. Wolf and H. Fernau. The…

Frobenius built a representation theory of finite groups in the process of obtaining the irreducible factorization of the group determinant. Here, we give a generalization of Frobenius' theorem. The generalization leads to a corollary on…

We give a decomposition of the jacobian variety of a generalized Fermat curve. This extends a result obtained by Auffarth, Lucchini-Arteche and Rojas on Humbert-Edge curves, which are a particular case of generalized Fermat curves. (A…

A new generalization of Dawson's integral function based on the link between a Riccati nonlinear differential equation and a second-order ordinary differential equation is reported. The MacLaurin expansion of this generalized function is…

We prove Banach, Newton-Raphson and Brouwer fixed point theorems in the framework of generalized smooth functions, a minimal extension of Colombeau's theory (and hence of classical distribution theory) which makes it possible to model…

Under certain mild assumption, we establish a one-to-one correspondence between solutions of the Nehari-Takagi problem and solutions of some Takagi-Sarason interpolation problem. The resolvent matrix of the Nehari-Takagi problem is shown to…

The purpose of this paper is to introduce the notion of a generalized derivation which derivates a prescribed family of smooth vector-valued functions of several variables. The basic calculus rules are established and then a result derived…

A Fano problem consists of enumerating linear spaces of a fixed dimension on a variety, generalizing the classical problem of 27 lines on a cubic surface. Those Fano problems with finitely many linear spaces have an associated Galois group…

In this PhD thesis we introduce a generalized fractional calculus of variations. We consider variational problems containing generalized fractional integrals and derivatives, and study them using standard (indirect) and direct methods. In…

In this paper we present a complete proof of I.R.Safarevic's famous theorem that every finite solvable group occurs as a Galois group over Q.

We study operators that are generalizations of the classical Riemann-Liouville fractional integral, and of the Riemann-Liouville and Caputo fractional derivatives. A useful formula relating the generalized fractional derivatives is proved,…