 sinx x if x 6= 0 1 otherwise This function is important in many areas of computing science, approximation theory, and numerical analysis. For example, it is used in interpolation and approximation of functions, approximate evaluation of transforms (e.g. Hilbert, Fourier, Laplace, Hankel, and Mellon transforms as well as the fast Fourier transform). It is used in finding approximate solutions ...

We consider the transform from sequences to triangular arrays defined in terms of generating functions by f(x) → 1−x 1−xyf (x(1−x) 1−xy ) . We establish a criterion for the transform of a nonnegative sequence to be nonnegative, and we show the transform counts certain classes of lattice paths by number of so-called pyramid ascents and certain classes of partitions into sets of lists (blocks) by...

The technique of direct and inverse fuzzy (F-)transforms of three different types is introduced and approximating properties of the inverse F-transforms are described. A method of lossy image compression and reconstruction on the basis of the F-transform is presented.

The technique of the direct and inverse fuzzy (F-) transform is introduced and approximating properties of the inverse F-transforms are described. A method of lossy image compression and reconstruction on the basis of F-transforms is illustrated on examples of pictures and music.

We give some characterizations of self-adjointness and symmetricity of operator monotone functions by using the Barbour transform f → t+f 1+f and show that there are many non-symmetric operator means between the harmonic mean ! and the arithmetic mean ∇. Indeed, we show that there exists a non-symmetric operator mean between any two symmetric operator means.

Let D be a nonnegative integer and Θ ⊂ S1 be a lacunary set of directions of order D. We show that the Lp norms, 1 < p < ∞, of the maximal directional Hilbert transform in the plane HΘ f (x ) B sup v ∈Θ p.v. ∫ R f (x + tv ) dt t , x ∈ R 2, are comparable to (log #Θ) 2 . For vector elds vD with range in a lacunary set of of order D and generated using suitable combinations of truncations of Lips...

F. Shakeri and M. Dehghan in [13] presented the variational iteration method for solving the model describing biological species living together. Here we suggest the differential transform (DT) method for finding the numerical solution of this problem. To this end, we give some preliminary results of the DT and by proving some theorems, we show that the DT method can be easily applied to mentio...

and Applied Analysis 3 fractional order to distributed order fractional. In Section 4, we introduce the distributed order fractional evolution systems C doD α t x t A C doD β t x t Bu t , x 0 x0, 0 < β < α ≤ 1, 1.5 where u t is control vector, and generalize the results obtained in Section 3 for this case. Finally, the conclusions are given in the last section. 2. Elementary Definitions and The...

We show that requiring diffeomorphic equivalence for one-dimensional stationary states implies that the reduced action S0 satisfies the quantum Hamilton-Jacobi equation with the Planck constant playing the role of a covariantizing parameter. The construction shows the existence of a fundamental initial condition which is strictly related to the Möbius symmetry of the Legendre transform and to i...