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Table Of Integrals Series And Products

The term photonic crystals appears because of the analogy between electron waves in crystals and the light waves in artificial periodic dielectric structures. During the recent years the investigation of one-, two-and three-dimensional periodic structures has attracted a widespread attention of the world optics community because of great potentiality of such structures in advanced applied optical fields. The interest in periodic structures has been stimulated by the fast development of semiconductor technology that now allows the fabrication of artificial structures, whose period is comparable with the wavelength of light in the visible and infrared ranges.

http://ieeexplore.ieee.org/iel5/6354/16969/00781867.pdf

Photonic crystals

Photoacoustic (PA) imaging, also called optoacoustic imaging, is a new biomedical imaging modality based on the use of laser-generated ultrasound that has emerged over the last decade. It is a hybrid modality, combining the high-contrast and spectroscopic-based specificity of optical imaging with the high spatial resolution of ultrasound imaging. In essence, a PA image can be regarded as an ultrasound image in which the contrast depends not on the mechanical and elastic properties of the tissue, but its optical properties, specifically optical absorption. As a consequence, it offers greater specificity than conventional ultrasound imaging with the ability to detect haemoglobin, lipids, water and other light-absorbing chomophores, but with greater penetration depth than purely optical imaging modalities that rely on ballistic photons. As well as visualizing anatomical structures such as the microvasculature, it can also provide functional information in the form of blood oxygenation, blood flow and temperature. All of this can be achieved over a wide range of length scales from micrometres to centimetres with scalable spatial resolution. These attributes lend PA imaging to a wide variety of applications in clinical medicine, preclinical research and basic biology for studying cancer, cardiovascular disease, abnormalities of the microcirculation and other conditions. With the emergence of a variety of truly compelling in vivo images obtained by a number of groups around the world in the last 2–3 years, the technique has come of age and the promise of PA imaging is now beginning to be realized. Recent highlights include the demonstration of whole-body small-animal imaging, the first demonstrations of molecular imaging, the introduction of new microscopy modes and the first steps towards clinical breast imaging being taken as well as a myriad of in vivo preclinical imaging studies. In this article, the underlying physical principles of the technique, its practical implementation, and a range of clinical and preclinical applications are reviewed.

/pdf/biomedical-photoacoustic-imaging-4s982wv96j.pdf

Biomedical photoacoustic imaging

A quantum graph is a graph equipped with a self-adjoint differential or pseudo-differential Hamiltonian. Such graphs have been studied recently in relation to some problems of mathematics, physics and chemistry. The paper has a survey nature and is devoted to the description of some basic notions concerning quantum graphs, including the boundary conditions, self-adjointness, quadratic forms, and relations between quantum and combinatorial graph models.

/pdf/quantum-graphs-i-some-basic-structures-2sf0fhd9ca.pdf

Quantum graphs: I. Some basic structures

Photoacoustic imaging is a promising method for visualizing biological tissues with optical absorbers. This article provides an overview of the rapidly developing field of photoacoustic imaging. Photoacoustics, the physical basis of photoacoustic imaging, is analyzed briefly. The merits of photoacoustic technology, compared with optical imaging and ultrasonic imaging, are described. Various imaging techniques are also discussed, including scanning tomography, computed tomography and original detection of photoacoustic imaging. Finally, some biomedical applications of photoacoustic imaging are summarized.

Photoacoustic imaging in biomedicine

The paper presents a survey of mathematical problems, techniques, and challenges arising in the Thermoacoustic (also called Photoacoustic or Optoacoustic) Tomography.

/pdf/mathematics-of-thermoacoustic-tomography-4454wdhd1p.pdf

Mathematics of thermoacoustic tomography

http://math.arizona.edu/~leonk/papers/JCP-PUB.PDF

A fast, high-order algorithm for the solution of surface scattering problems: basic implementation, tests, and applications

The paper presents a survey of mathematical problems, techniques, and challenges arising in the Thermoacoustic and Photoacoustic Tomography.

We derive explicit formulae for the reconstruction of a function from its integrals over a family of spheres, or for the inversion of the spherical mean Radon transform. Such formulae are important for problems of thermo- and photo-acoustic tomography. A closed-form inversion formula of a filtrationbackprojection type is found for the case when the centres of the integration spheres lie on a sphere in R n surrounding the support of the unknown function.

/pdf/explicit-inversion-formulae-for-the-spherical-mean-radon-1jr1bnfqpd.pdf

Explicit inversion formulae for the spherical mean Radon transform

We derive explicit formulas for the reconstruction of a function from its integrals over a family of spheres, or for the inversion of the spherical mean Radon transform. Such formulas are important for problems of thermo- and photo- acoustic tomography. A closed-form inversion formula of a filtration-backprojection type is found for the case when the centers of the integration spheres lie on a sphere in Rn surrounding the support of the unknown function. An explicit series solution is presented for the case when the centers of the integration spheres lie on a general closed surface.

Leonid Kunyansky

Papers

Mathematics of thermoacoustic tomography

A fast, high-order algorithm for the solution of surface scattering problems: basic implementation, tests, and applications

Mathematics of thermoacoustic tomography

Explicit inversion formulae for the spherical mean Radon transform

Explicit inversion formulas for the spherical mean Radon transform