Let G be a graph, and k a positive integer. A fractional k-factor is a way of assigning weights to the edges of a graph G (with all weights between 0 and 1) such that for each vertex the sum of the weights of the edges incident with that vertex is k. A graph G is a fractional k-deleted graph if G − e has a fractional k-factor for each e ∈ E(G). In this paper, we obtain some sufficient condition...

Tempered fractional Brownian motion is obtained when the power law kernel in the moving average representation of a fractional Brownian motion is multiplied by an exponential tempering factor. This paper develops the theory of stochastic integrals for tempered fractional Brownian motion. Along the way, we develop some basic results on tempered fractional calculus.

the complex-step derivative approximation is applied to compute numerical derivatives. in this study, we propose a new formula of fractional complex-step method utilizing jumarie definition. based on this method, we illustrated an approximate analytic solution for the fractional cauchy-euler equations. application in image denoising is imposed by introducing a new fractional mask depending on s...

Let k ≥ 3 be an integer, and let G be a graph of order n with n ≥ 9k + 3− 4 √ 2(k − 1)2 + 2. Then a spanning subgraph F of G is called a k-factor if dF (x) = k for each x ∈ V (G). A fractional k-factor is a way of assigning weights to the edges of a graph G (with all weights between 0 and 1) such that for each vertex the sum of the weights of the edges incident with that vertex is k. A graph G ...

A graph G is called a fractional (g, f)-deleted graph if G - {e} admits a fractional (g, f)-factor for any e ∈ E(G). A graph G is called a fractional (g, f, n)-critical deleted graph if, after deleting any n vertices from G, the resulting graph is still a fractional (g, f)-deleted graph. The toughness, as the parameter for measuring the vulnerability of communication networks, has received sign...

The various proposals for FQHE quasi-electron trial wave functions are reconsidered. In a short-range model for the electronic interaction, the energy expectation values of four different trial wave functions are calculated at filling factor 1 3 for up to ten electrons in the disk geometry. Jain's trial wave function displays the lowest energy expectation value.

The non-Fermi liquid physics at the edge of fractional quantum Hall systems is described by specific chiral Conformal Field Theories with central charge c = 1. The charged quasi-particles in these theories have fractional charge and obey a form of fractional statistics. In this paper we study form factors, which are matrix elements of physical (conformal) operators, evaluated in a quasi-particl...