Measurement of distribution anisotropy of X-ray yield from a pyroelectric crystal surface

A technique for measuring the spatial distribution of X-rays generated by a pyroelectric source is developed and tested. Anisotropy in the spatial distribution of X-rays from the surface perpendicular to the pyroelectric axis of the lithium niobate crystal depending on the piezoelectric crystal axis orientation was detected. The result obtained shows the necessity of considering the effect of piezoelectric properties of pyroelectric crystals on X-ray generation processes.     

Lyapunov‐type inequalities for a class of fractional boundary value problems with integral boundary conditions

In this paper, Lyapunov‐type inequalities are derived for a class of fractional boundary value problems with integral boundary conditions. As an application, we obtain a lower bound for the eigenvalues of corresponding equations.     

On the classical solution of SO(3) gauge theory and ’t Hooft-Polyakov monopole

It is shown that the ansatz for the asymptotic (r → ∞) gauge fields used by ’t Hooft in the study of monopoles in SO(3) electroweak theory is not unique.     

Parametric X-ray radiation from powders

Parametric X-ray Radiation (PXR) produced in powders has been observed for the first time. PXR spectra were measured under observation angles of 150° and 180° during the interaction of relativistic 7 MeV electrons with a tungsten powder. All the PXR peaks that theoretically can be produced in the studied energy region were registered. The performed absolute comparison of the experiment with the PXR kinematical theory from randomly oriented crystallites showed a good accordance.     

Investigation of Neutron Generation upon Irradiation of Deuterated Crystalline Structures with an Electron Beam

Physics of Atomic Nuclei - The possibility of neutron generation by irradiating deuterated crystalline structures with an electron beam with an energy of 20–40 keV was studied. As targets,...     

On a quadratic integral equation with supremum involving Erdélyi‐Kober fractional order

We introduce Erdélyi‐Kober fractional quadratic integral equation with supremum, namely . This equation contains as special cases numerous integral equations studied by other authors. We show that there exists at least one monotonic solution belonging to C[0, 1] of our equation. The main tools in our analysis are Darbo fixed point theorem and the measure of noncompactness related to monotonicity which was introduced by Bana? and Olszowy. Finally, we present an example for illustrating the natural realizations of our abstract results.     

Dynamical symmetries in mechanics

The object of this review is to discuss methods that enable one to trace the origin of symmetries and conservation laws in mechanics to geometrical symmetries of space-time. Starting with the basic Newtonian assumptions on absolute space and time classical mechanics is developed in configuration space and phase space independently together with the related structures such as force-less mechanics. Heuristic considerations on geometric symmetries in configuration space reveal their intimate relation to conservation laws. Using the methods of differential geometry this relationship is put on a formal footing and symmetry groups of all spherically symmetric single term potentials are classified. The method of infinitesimal canonical transformations is presented as an alternative method of deducing dynamical symmetries of an arbitrary system in phase space. These methods also apply to non-relativistic quantum theory. Possible extension to special and general relatively is also discussed.     

A note on “Some inequalities in inner product spaces related to the generalized triangle inequality” by S.S. Dragomir et al.

In this note, we present an affirmative answer to a question presented in the paper “Some inequalities in inner product spaces related to the generalized triangle inequality” by S.S. Dragomir et al. [Appl. Math. Comput. 217 (18) (2011) 7462-7468].