In this paper we consider the properties of moduli of smoothness of fractional order. The main result of the paper describes the equivalence of the modulus of smoothness and a function from some class.

The definition of lacunary strong convergence with respect to a modulus is extended to a definition of lacunary strong A-convergence with respect to a modulus when A = (aik) is an infinite matrix of complex numbers. We study some connections between lacunary strong A-convergence with respect to a modulus and lacunary A-statistical convergence.

Introduction: Early diagnosis of disc degeneration is critical for the success of treatment strategies. Several MR parameters, including T2 and T1-rho maps, have been proposed as markers to quantitatively evaluate the progression of disc degeneration [1, 2]. Although MR parameters are correlated with degeneration grade and the decrease of glycosaminoglycan content, they represent the dynamics o...

The paper describes a program of mechanical testing on donated human eye bank lenses. The principal purpose of the tests was to obtain experimental data on the shear modulus of the lens for use in future computational models of the accommodation process. Testing was conducted using a procedure in which deformations are induced in the lens by spinning it about its polar axis. Shear modulus data ...

Iterative constant modulus algorithms such as Godard and CMA have been used to blindly separate a superposition of co-channel constant modulus (CM) signals impinging on an antenna array. These algorithms have certain deficiencies in the context of convergence to local minima and the retrieval of all individual CM signals that are present in the channel. In this paper, we show that the underlyin...

Let X be a completely regular Hausdorff space, E a Banach lattice, and μ an E-valued countably additive, regular Borel measure on X. Some results about the countable additivity and regularity of the modulus |μ| are proved. Also in special cases, it is proved that L1(μ) = L1(|μ|).

In 1999, the 512-bit number of 155 digits taken from the RSA Challenge list was first factored by the General Number Field Sieve. This work was done on a supercomputer and about 300 PCs or workstations by 17 experts all over the world. The calendar time for the factorization was over 6 months. Based on the open source GGNFS, we improved its algorithms and implementations. Now the 512-bit RSA mo...

The scaled-particle theory equation of state for the two-dimensional hard-disk fluid on a curved surface is proposed and used to determine the saddle-splay modulus of a particle-laden fluid interface. The resulting contribution to saddle-splay modulus, which is caused by thermal motion of the adsorbed particles, is comparable in magnitude with the saddlesplay modulus of a simple fluid interface.

A uniqueness theorem is proven for the problem of the recovery of a complex valued compactly supported 2-D function from the modulus of its Fourier transform. An application to the phase problem in optics is discussed.

We explore the phenomenology of a stabilized modulus field in the RandallSundrum scenario. It is found that if the large separation between branes arises from a small bulk scalar mass then the modulus (i.e. radion) is likely to be lighter than the lowest Kaluza-Klein excitations of bulk fields, and consequently may be the first direct signature of the model. Four-dimensional general covariance ...