In this paper we investigate the sub-channel assignment and power control to maximize the total sum rate in the uplink of two-cell network. It is assumed that there are some sub-channels in each cell which should be allocated among some users. Also, each user is subjected to a power constraint. The underlying problem is a non-convex mixed integer non-linear optimization problem which does not h...

For any k ∈ N, the k-subdivision of a graph G is a simple graph G 1 k , which is constructed by replacing each edge of G with a path of length k. In [Moharram N. Iradmusa, On colorings of graph fractional powers, Discrete Math., (310) 2010, No. 10-11, 1551-1556] the mth power of the n-subdivision of G has been introduced as a fractional power of G, denoted by G m n . In this regard, we investig...

An unsteady problem is considered for a space-fractional diffusion equation in a bounded domain. A first-order evolutionary equation containing a fractional power of an elliptic operator of second order is studied for general boundary conditions of Robin type. Finite element approximation in space is employed. To construct approximation in time, regularized twolevel schemes are used. The numeri...

The models that are based of fractional derivatives should be highlighted among promising new models to describe turbulent fluid flows. In the present work, a steadystate flow in a duct is considered under the condition that the turbulent diffusion is governed by a fractional power of the Laplace operator. To study numerically flows in rectangular channels, finite-difference approximations are ...

We state the fractional Fourier transform and the continuous fractional wave packet transform as ways for analyzing persistent signals such as almost periodic functions and strong limit power signals. We construct frame decompositions for almost periodic functions using these two transforms. Also a norm equality of this signal is given using the continuous fractional wave packet transform.

Numerical approximations of fractional PDEs in unbounded domains are considered in this paper. Since their solutions decay slowly with power laws at infinity, a domain truncation approach is not effective as no transparent boundary condition is available. We develop efficient Hermite-collocation and Hermite–Galerkin methods for solving a class of fractional PDEs in unbounded domains directly, a...

We study the first passage time (FPT) problem in Levy type of anomalous diffusion. Using the recently formulated fractional Fokker-Planck equation, we obtain an analytic expression for the FPT distribution which, in the large passage time limit, is characterized by a universal power law. Contrasting this power law with the asymptotic FPT distribution from another type of anomalous diffusion exe...

The traditional conservation of mass equation is derived using a first-order Taylor series to represent flux change in a control volume, which is valid strictly for cases of linear changes in flux through the control volume. We show that using higher-order Taylor series approximations for the mass flux results in mass conservation equations that are intractable. We then show that a fractional T...

In their article Cheung and Lai (1993), propose a test for cointegration against fractional alternatives. The test is based on the GPH estimator by Geweke and Porter-Hudak (1983). This test uses only the Tα smallest frequencies, where α usually is set between 0.5 and 0.6. The choice of α has impact on the power of the test. In this paper we argue that using larger α increases the power against ...