Georgi Nikolov Georgiev

Effect of the dielectric filling on the phase behaviour of the circular waveguide with azimuthally magnetized ferrite toroid and dielectric cylinder

The phase characteristics of the circular waveguide, comprising an azimuthally magnetized ferrite toroid and a dielectric cylinder of relative permittivity, larger than that of the ferrite, under normal TE01 mode excitation, are figured. The analysis reveals that they are finite for both directions of magnetization, limited by the cut-off frequencies and by specific envelope lines, depending on certain positive real numbers ( L numbers), related to the roots of the characteristic equation of the structure. The expansion of the region, occupied by dielectric and the increase of its relative permittivity entails a moving of the position and a shortening of the length of the curves mentioned (a shrinking of the areas of wave propagation), as well as a change of the sign of the differential phase shift provided.

Monitoring the establishment and prevalence of the fungal entomopathogen Entomophaga maimaiga in two Lymantria dispar L. populations in Bulgaria

The establishment and prevalence of the entomopathogenic fungus Entomophaga maimaiga, (Zygomycetes, Entomophthorales), introduced into two gypsy moth populations in Bulgaria, was monitored during 2000–2004. In the Karlovo Region population, where E. maimaiga was introduced in 1999, the fungus was recovered every year and the prevalence of infection varied from 6.1% to 15.9%. A microsporidian infection caused by an Endoreticulatus sp. (Protista, Microsporidia) was also recorded every year and the prevalence varied from 2.1% and 5.0%. In the Svoge Region population, where E. maimaiga was introduced in late 2000 and first found in 2002, the prevalence of infection varied from 8.8% to 13.8%. Larval parasitism caused by Cotesia melanoscela, Protapanteles liparidis (Hymenoptera, Braconidae) and species of tachinids (Diptera, Tachinidae) was also recorded in the larvae of both populations. We provide a rationale as to why other countries should consider introducing E. maimaiga for biological control of Lymantria dispar populations.

Analysis of the differential phase shift in the circular ferrite-dielectric waveguide with azimuthal magnetization

Employing an iterative approach, the differential phase shift provided by the circular waveguide, containing an azimuthally magnetized coaxial ferrite cylinder, surrounded by a dielectric toroid, is computed in normalized form for normal TE01 mode. The method uses the positive purely imaginary roots of the complex characteristic equation of the structure, derived in terms of the complex Kummer and the real cylindrical functions, determined, varying the imaginary part of the first complex parameter of the Kummer function. The results are presented in tabular and numerical form and discussed.

An application of the complex Tricomi function

The logarithmic form of complex Tricomi function Ψ(a,c;x), holding for c - a positive integer, is used in case a =c/2-jk - complex, k - real, -∞ < k < +∞, x = jz, z -real, positive, to develop a special iterative technique for exact computation of the differential phase shift provided by the circular waveguide with coaxially positioned dielectric cylinder and azimuthally magnetized latching ferrite toroid that sustains normal TE0n modes. An original form of the structures characteristic equation, constructed by the function mentioned and its complex conjugate, and real Bessel functions, valid for equal values of the relative permittivities of the media, is harnessed for the purpose. A highlight of the method makes up the numerical study of Ψ(a,c;x), the results of which are illustrated graphically. The effect of parameters of configuration on the differential phase shift for the TE01 mode is explored, too.

Entomophaga maimaiga – New entomopathogenic fungus in the Republic of Serbia

The higher mortality rate of the older gypsy moth larval instars was reported in the forest complexes of Belgrade and Valjevo region, in the culmination phase of the new outbreak of the gypsy moth in Serbia. By field and laboratory studies of the causes of their death, the presence of conidia and resting spores of the entomopathogenic fungus Entomophaga maimaiga was reported in the dead caterpillars. This has been the first report of occurrence of this species in Serbia, that is, Serbia is the third European country in which this fungus has been reported. It showed to be a powerful reducer of the population size of the gypsy moth, and in both regions it caused the collapse of the outbreak in 2011. Keywords: Entomophaga maimaiga , Lymantria dispar , gypsy moth, biological control, epizootics

Theory of the L 3 numbers: Definition, computational modeling, properties and application

The theory of the L numbers - the positive real limits of certain sequences of numbers, constructed through the positive purely imaginary zeros of the complex Kummer or of definite special functions, composed of several complex Kummer and Tricomi confluent hypergeometric and eventually also of some real cylindrical ones of suitably chosen parameters, is formulated. The limits are attained, when the imaginary part of the complex first parameter(s) of the confluent function(s) tends to minus infinity (to minus and plus infinity, if cylindrical functions are involved). The discussion is confined to the subclasses L1 (c,n) and L2 (c,ρ,n) , (c - arbitrary real, n - natural and ρ - positive real number, less than unity) of the general family of L numbers, linked with the zeros of the Kummer function and of a function, formed as a combination of two Kummer and two Tricomi ones, resp. Definitions of the numbers are given, procedures for their computational modeling are devised and some of their properties are found. The cases c - different from and c - equal to a negative integer or zero (when the Kummer function has no sense), are considered. Tables of values of L1 (c,n) and L2 (c,ρ,n) are compiled. Graphs illustrate the numerical results. The application of quantities examined in the analysis of the normal TE0n modes propagation in the azimuthally magnetized circular and coaxial ferrite waveguide, is debated.

Iterative Method for Differential Phase Shift Computation in the Azimuthally Magnetized Circular Ferrite Waveguide

A reiterative technique is developed for flnding in normalized form the difierential phase shift provided by the circular waveguide, completely fllled with azimuthally magnetized ferrite which propagates normal TE01 mode. It consists in a repeated numerical solution of the structures characteristic equation, derived in terms of a deflnite complex Kummer con∞uent hypergeometric function, followed by a computation of the normalized guide radius and phase constant at a flxed value of the ofi-diagonal ferrite permeability tensor element. The idea of the method is to vary arbitrarily or according to a certain scheme the imaginary part of the flrst complex parameter of wave function until the counted numerical equivalent of the guide radius coincides with a chosen one of the same with a prescribed accuracy. The relevant value of the phase constant is accepted as the one, looked for. Calculations are performed for both signs of the imaginary part (of the ferrite magnetization), yielding the phase shift sought. The numerically presented results are discussed.

On the A, B, C Numbers and Their Application in the Theory of Circular Waveguide with Azimuthally Magnetized Ferrite

An iterative method is worked out and applied to calculate the A, B, C numbers | positive real numbers, connected with the normalized difierential phase shift, produced by the circular waveguide, containing azimuthally magnetized ferrite which sustains normal TE01 mode. It is based on the recently formulated deflnition of the quantities in question and uses the positive purely imaginary zeros of a certain complex Kummer con∞uent hypergeometric function, deter- mined for a varying imaginary part of its flrst complex parameter. The results of investigation are presented graphically. The in∞uence of the normalized guide radius and of the magnitude of ofi-diagonal ferrite permeability tensor element on the numbers is analyzed. A numerical example is presented, demonstrating the way of flguring out the phase shift with their help.

An application of the zeros of Laguerre polynomials

A theorem is formulated and substantiated numerically, stating that if λ<inf>m, n</inf>^(v) is the n th zero of the generalized Laguerre polynomial L<inf>m</inf>^(v)(X) (x and λ<inf>m, n</inf>^(v) — real, positive, v =0,1,2,…, m =0,1,2,…, n =1,2,3…) and L(c, n) (c =1,2,3,…) is a positive real number, defined by means of the relation: L(c, n) =<inf>k_→−∞</inf>^lim K_(c, n, k_) = <inf>k_→−∞</inf>^lim M_(c, n, k_) in which K_(c, n, k_) = |k_|ζ^(c)<inf>k_, n</inf>, M_(c, n, k_) = |a_|ζ^(c)<inf>k_, n</inf>, and ζ^(c)<inf>k_, n</inf> is the n th positive purely imaginary zero in x of the Kummer confluent hypergeometric function Φ(a_, c; x) with a_= c/2−jk_ — complex, x =jz, z — real, positive and k_ — real, negative, (c, n — fixed), in case v =c −1 and m is large, it holds: λ<inf>m, n</inf>^(v) ≈L(c, n). The result obtained is used to develop a simple approximate method for computation of the differential phase shift, provided by the azimuthally magnetized circular ferrite waveguide for the normal TE<inf>01</inf> mode.

On a Class of Electromagnetic Wave Functions for Propagation Along the Circular Gyrotropic Waveguide

The properties of confluent hypergeometric functions as exact electromagnetic wave fnnctions for propagation in a circular waveguide containing azimuthally magnetized remanent ferrite are investigated. Two different forms of solutions of the propagation problem for angular symmetric transverse electric modes are constructed-one in terms of Kummer and Tricomi confluent hypergeometric functions of complex parameter and variable and a second in terms of Whittaker functions. An evaluation of this class of wave functions is performed to sufficient extent, followed by tabulation of their imaginary zeros, providing computation of eigenvalue spectrum and phase characteristics of the gyrotropic guide.