Hochschild Cohomologies of the Algebra of Smooth Functions

Based on the previously developed technique using the Laplace transformation of distributions with compact support, we calculate the Hochschild cohomologies of the algebra of smooth functions on a finite-dimensional real vector space with coefficients in the adjoint representation.     

Hamiltonian Operators with Zero-Divergence Constraints

Theoretical and Mathematical Physics - Using previously proposed techniques, we derive the defining system for a differential algebra associated with zero-divergence constraints. We study this...     

Focused array transducer for two-dimensional optoacoustic tomography

Optoacoustic (OA) imaging utilizes short laser pulses to create acoustic sources in tissue and time resolved detection of generated pressure profiles for image reconstruction. The ultrasonic transients provide information on the distribution of optical absorption coefficient that can be useful for early cancer diagnostics. In this work a new design of wide-band array transducer is developed and tested. The array consists of 32 focused piezo-elements made of PVDF slabs imposed on a cylindrical surface. A single array element response to an OA signal coming from arbitrarily located point source is investigated theoretically and experimentally. The measured signals correspond well to numerically calculated ones. Focal zone maps of the elements with aperture angles 30 degrees and 60 degrees are presented and discussed; the resolution in direction perpendicular to the imaging plane is determined. Point spread function of the whole array is calculated using experimentally obtained signals from the sources located at different distances from the array. Backprojection algorithm is employed for reconstruction of the optoacoustic images. It is shown that the spatial resolution of the images yielded by the proposed array increases significantly compared to previous transducer designs.     

Green’s formula for difference operators

We construct an analogue of the classic Green’s formula for linear partial differential operators for difference operators on a multidimensional integer lattice.     

Cohomologies of the Lie Algebra of Vector Fields on a Line

Providing adequate mathematical tools, we find cohomologies of the Lie algebra of smooth vector fields on a line with coefficients in the trivial, natural, and adjoint representations. We construct the generalized series of complexes and calculate the corresponding cohomologies.     

A model of relativistic dynamics

A model of relativistic dynamics is proposed for classical (nonquantum) multiparticle systems within the Lagrangian formalism on the space of world lines.     

Navier–Stokes equations,the algebraic aspect

Theoretical and Mathematical Physics - We present an analysis of the Navier–Stokes equations in the framework of an algebraic approach to systems of partial differential equations (the formal...     

Determinating the Volume Content of a Polymeric Matrix in CFRP Structures Using a Laser-Ultrasonic Method

Mechanics of Composite Materials - An acoustic method for a quantitative assessment of the volume content of a polymeric matrix in CFRPs is proposed and realized experimentally. For this purpose, a...