Some existence results on nonlinear fractional differential equations.

In this paper, by using fixed-point methods, we study the existence and uniqueness of a solution for the nonlinear fractional differential equation boundary-value problem D(α)u(t)=f(t,u(t)) with a Riemann-Liouville fractional derivative via the different boundary-value problems u(0)=u(T), and the three-point boundary condition u(0)=β(1)u(η) and u(T)=β(2)u(η), where T>0, t∈I=[0,T], 0<α<1, 0<η View Article and Find Full Text PDF

Equivalence of structure constants in non-Kolmogorov and Kolmogorov spectra.

We find the equivalence of the structure constants in non-Kolmogorov and Kolmogorov spectra in a turbulent atmosphere. As the reference point, the spherical wave scintillation index in a non-Kolmogorov medium is used. Relations of the structure constants are found to be functions of the power law of the turbulence spectrum and the Fresnel zone.

Mining MEDLINE for the treatment of osteoporosis.

In this paper, we consider the importance of osteoporosis disease in terms of medical research and pharmaceutical industry and we introduce a knowledge discovery approach regarding the treatment of osteoporosis from a historical perspective. Osteoporosis is a systemic skeletal disease in which osteoporotic fractures are associated with substantial morbidity and mortality and impaired quality of life. Osteoporosis has also higher costs, for example, longer hospital stays than many other diseases such as diabetes and heart attack and it is an attractive market for pharmaceutical companies.

Physical optics theory for the diffraction of waves by impedance surfaces.

The solution of the scattering problem of waves by a half-screen with equal face impedances, which was introduced by Malyughinetz, is transformed into a physical optics integral by using the inverse edge point method. The obtained integral is applied to the diffraction problem of plane waves by an impedance truncated circular cylinder and the scattered waves are derived asymptotically. The results are examined numerically.

Prediction of similarities among rheumatic diseases.

We introduce a method for extracting hidden patterns seen in rheumatic diseases by using articles from the widely used biomedical database MEDLINE. Rheumatic diseases affect hundreds of millions of people worldwide and lead to substantial loss of functioning and mobility. Diagnosing rheumatic diseases can be difficult because some symptoms are common to many of them.

Scattered fields of conducting half-plane between two dielectric media.

We investigate the scattering process of plane waves by a conducting half-plane between two dielectric media by introducing novel boundary conditions, in terms of soft and hard surfaces. The cases of soft and hard half-planes are studied independently. The scattered waves are examined numerically.

Uniform boundary diffraction wave theory of Rubinowicz.

Rubinowicz introduced a uniform asymptotic evaluation of the boundary diffraction wave at the transition region [Ann. Phys. (Leipzig) 378, 339 (1924)].

Apertured paraxial Bessel beams.

The paraxial Bessel beam is obtained by applying an approximation in the wavenumbers. The scattering of the beams by a circular aperture in an absorbing screen is investigated. The scattered fields are expressed in terms of the Fresnel integrals by evaluating the Kirchhoff diffraction integral in the paraxial approximation.

Fictitious diffracted waves in the diffraction theory of Kirchhoff.

The diffraction theory of Kirchhoff is applied to the semi-infinite aperture of a black half-screen. The derivative of the spherical Green's function is taken into account without any approximation. The uniformly evaluated scattering integral is compared with the physical optics solution.

Effect of the shadow geometry in wedge diffraction.

The surface integrals of the modified theory of physical optics are divided into two parts for diffraction by a wedge. Each integral represents the incident or reflected field scattered by one of the faces of the wedge. The results are investigated numerically and compared with the uniform theory of diffraction.

Improved equivalent source theory.

The equivalent source theorem, which is an important technique in the study of radiation and scattering by apertures, is improved by using the two axioms of the modified theory of physical optics. The method is applied to the problem of radiation of electromagnetic waves by a parallel plate waveguide. The results are investigated numerically.

Scintillations of partially coherent multiple Gaussian beams in turbulence.

For an incidence composed of partially coherent multiple Gaussian beams, Huygens-Fresnel principle-based on-axis scintillation index is formulated in a weakly turbulent homogeneous horizontal atmospheric path. Our general formulation is applied to two examples of partially coherent annular and partially coherent flat-topped Gaussian beams. Compared to partially coherent single Gaussian beam scintillations, annular beam scintillations seem to possess higher values for all partial coherence levels, whereas flat-topped Gaussian beam intensity fluctuations are slightly larger, especially at lower coherence levels and at larger source sizes.

Removal of ammonium and phosphate from the supernatant of anaerobically digested waste activated sludge by chemical precipitation.

The removal of ammonium (NH(4)(+)) and phosphate (PO(4)(3-)) from supernatant of anaerobic digestion by magnesium ammonium phosphate (MAP) formation was studied. To be able to find out the loss of NH(4)(+) by its transformation to NH(3), rates of NH(4)(+) removal by aeration and by MAP formation combined with aeration were compared. NH(4)(+) removal by aeration was found to be insignificant.

Scintillation index of modified Bessel-Gaussian beams propagating in turbulent media.

The scintillation index is formulated for modified Bessel-Gaussian beams propagating in weakly turbulent media. Numerical calculations applied directly to the derived triple integral show that, for off-axis positions, the modified Bessel-Gaussian beams of higher than zero order scintillate less than Gaussian beams at large input beam sizes and low beam orders with the increasing width parameter initially contributing positively to this phenomenon of less scintillation. As the beam order exceeds two, this advantage is diminished.

Effect of the shadow geometry on diffraction.

The effect of the scatterer surface on the shadow region is examined by using the surface integrals of the modified theory of physical optics. It is shown that the shadow geometry has a considerable effect on the structure of the edge diffracted waves. The diffracted fields for the illuminated and shadowed surface of a half-plane are evaluated in terms of Fresnel integrals and plotted numerically.

Bit error rates for general beams.

In order to analyze the effect of beam type on free space optical communication systems, bit error rate (BER) values versus signal-to-noise ratio (SNR) are calculated for zero order and higher order general beam types, namely for Gaussian, cos-Gaussian, cosh-Gaussian, and annular beams. BER analysis is based on optical scintillation using log-normal distribution for the intensity, which is valid in weak atmospheric turbulence. BERs for these beams are plotted under variations of propagation length, source size, wavelength of operation, and order of the beam.

Young-Kirchhoff-Rubinowicz theory of diffraction in the light of Sommerfeld's solution.

Kirchhoff's theory of diffraction is derived by transforming the exact solution of Sommerfeld into surface integrals for the half-plane problem. It is shown that the exact solution directly yields the integral theorem of Kirchhoff in the context of the modified diffraction theory of Kirchhoff. The line integrals of Young-Rubinowicz are also derived by considering the rigorous solution of the reflected scattered fields for grazing incidence.

Integral representation of the edge diffracted waves along the ray path of the transition region.

The expression of the edge diffracted fields, in terms of the Fresnel integral, is transformed into a path integral. The obtained integral considers the integration of the incident field along the ray path of the transition region. The similarities of the path integral with Kirchhoff's theory of diffraction and the modified theory of physical optics are examined.

Modified diffraction theory of Kirchhoff.

The diffraction theory of Kirchhoff is reinterpreted and a new form of a surface diffraction integral is developed by using the axioms of the modified theory of physical optics, which leads to the exact scattered fields by conducting bodies. The new integral is arranged according to the interpretation of Young, and the diffracted waves are expressed in terms of a line integral. The method is applied to the diffraction problem by a semi-infinite edge contour.

Scattering of a line source by a cylindrical parabolic impedance surface.

The scattering of the radiated fields of a line source by a cylindrical parabolic reflector, which has impedance boundary conditions on its surface, is obtained by using the surface integrals of the modified theory of physical optics. The reflected geometrical optics and edge diffracted fields are evaluated by using the asymptotic methods. The scattered fields are plotted numerically for various parameters such as surface impedance and angles of the edges.

Alternative interpretation of the edge-diffraction phenomenon.

An alternative interpretation of the phenomenon of edge diffraction is proposed according to a new separation of the Fresnel function. The subfields are investigated in the problem of diffraction of a plane wave by a perfectly conducting half-plane, and the results are compared numerically with other interpretations.

Uniform line integral representation of edge-diffracted fields.

A uniform line integral representation is derived for edge-diffracted fields by using the modified theory of physical optics and uniform asymptotic evaluation methods. The method is applied to the problem of diffraction of plane waves by a semi-infinite edge, which creates tip-diffracted fields with edge-diffracted waves. The uniform diffracted fields are plotted and examined numerically.

Diffraction of evanescent plane waves by a resistive half-plane.

Diffraction of evanescent plane waves by a resistive half-plane is examined. The scattering integrals are constructed with the modified theory of physical optics. These integrals are evaluated uniformly by using an unusual method.

Scattering of a Gaussian beam by an impedance half-plane.

The diffraction of a Gaussian beam by an impedance half-plane is studied through the method of the modified theory of physical optics. An electric line source, which is defined in the complex space, is used to represent the Gaussian beam. The uniform evaluation of the diffraction integral is performed and the scattering patterns of the field are investigated for various numerical parameters of the incident wave.

Complex degree of coherence for partially coherent general beams in atmospheric turbulence.

With the use of the general beam formulation, the modulus of the complex degree of coherence for partially coherent cosh-Gaussian, cos-Gaussian, Gaussian, annular and higher-order Gaussian optical beams is evaluated in atmospheric turbulence. For different propagation lengths in horizontal atmospheric links, the moduli of the complex degree of coherence at the source and receiver planes are examined when reference points are taken on the receiver axis and off-axis. In the on-axis case, it is observed that in propagation, the moduli of the complex degree of coherence are symmetrical and look like the intensity profile of the related coherent beam propagating in a turbulent atmosphere.