Symmetry of zeros of Lerch zeta-function for equal parameters

For most values of parameters λ and α, the zeros of the Lerch zeta-function L(λ, α, s) are distributed very chaotically. In this paper, we consider the particular case of equal parameters L(λ, λ, s) and show by calculations that the nontrivial zeros either lie extremely close to the critical line σ = 1/2 or are distributed almost symmetrically with respect to the critical line. We also investigate this phenomenon theoretically.     

Nonhomogeneous Hemivariational Inequalities with Indefinite Potential and Robin Boundary Condition

We consider a nonlinear, nonhomogeneous Robin problem with an indefinite potential and a nonsmooth primitive in the reaction term. In fact, the right-hand side of the problem (reaction term) is the Clarke subdifferential of a locally Lipschitz integrand. We assume that asymptotically this term is resonant with respect the principal eigenvalue (from the left). We prove the existence of three nontrivial smooth solutions, two of constant sign and the third nodal. We also show the existence of extremal constant sign solutions. The tools come from nonsmooth critical point theory and from global optimization (direct method).     

On categories associated to a Quasi-Hopf algebra

A quasi-Hopf algebra H can be seen as a commutative algebra A in the center 𝒵(H-Mod) of H-Mod. We show that the category of A-modules in 𝒵(H-Mod) is equivalent (as a monoidal category) to H-Mod. This can be regarded as a generalization of the structure theorem of Hopf bimodules of a Hopf algebra to the quasi-Hopf setting.     

AIFS—A Tool for Biomorphic Fractal Modeling

A considerable class of fractal sets can be represented by using the attractors of Iterated Function Systems (Barnsley, 1988), with affine contractive mappings of a metric space . The modeling capabilities of such systems are heavily limited however. For example, it is not easy to predict the location of the attractor nor its global shape. Then, Iterated Systems are not affinely invariant (affine mappings of the elements of the system do not result in affine image of its attractor). In this paper a new setting, the affine invariant Iterated Function System is described in such a way that it removes the mentioned shortcomings and can be used for shape-predictable modeling of fractal based forms. The stress is put on modeling of biological forms and their atributes such as: continuous deformation of the attractor in desired way (like in growing), branching (plants, vascular or alveolar network), gradual changing of fractal dimension from smooth to space-filling fractals. The last is useful for creating images of tissues in different stages of development, symmetry, gradual transformation from one to another form, etc. The fractal images obtained by AIFS are merely to gain resemblance to bio-forms.     

Circular punch on the unstretchable Westergaard-type subgrade

Summary Horizontally unstretchable continuum of the Westergaard's type is modelled by elastic layers of finite thicknesses interconnected with very thin, flexible but unstretchable sheets. For the regular layered structure, the finite difference equations are formulated and their closed solutions is presented. The resulting formulase are used when the contact problem solution is sought in a form of series of spherical functions. The unknown series coefficients are determined via Galerkine method, the formulae for punch settlement and inclination are presented and a numerical procedure is developed and used to study the influence of the Westergaard's subgrade material parameters (subgrade reinforcement intensity) and (Poisson's ratio of the basic material).

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Kreisförmiger Stempel auf unausdehnbarer Unterlage Westergaard'schen Typs

Übersicht Horizontal unausdehnbares Kontinuum Westergaard'schen Typs wird über elastische Schichten endlicher Dicke, die mittels sehr dünner und biegsamer, aber nichtdehnbarer Membranen verbunden sind, modelliert. Für den Fall regulärer Schichtstrukturen werden die Finite-Differenzen-Gleichungen aufgestellt und die geschlossene Lösung formuliert. Diese Lösung wird dann benutzt, wenn das Kontaktproblem in der Form von sphärischen Funktionenreihen dargestellt wird; die unbekannten Koeffizienten der Reihe werden über die Galerkin-Methode bestimmt. Für den Fall einer senkrechten Belastung und einer Momentenbelastung werden die Setzung und Verdrehung bestimmt. Dafür wird ein numerisches Verfahren entwickelt und verwendet, um den Einfluß der Materialparameter und des Westergaard'schen Kontinuum zu untersuchen.

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Presented at the GAMM Seminar Kontakt fester Körper, Stuttgart 18.–19. March 1993

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Dedicated to Prof. H. Bufler upon the occasion of his 65th birthday anniversary     

Multivalued penalty method for evolution variational inequalities with <Emphasis Type="Italic">λ</Emphasis><Subscript>0</Subscript>-pseudomonotone multivalued maps

We consider evolution variational inequalities with λ ₀-pseudomonotone maps. The main properties of these maps are investigated. By using the finite-difference method, we prove the property of strong solvability for the class of evolution variational inequalities with λ ₀-pseudomonotone maps. Using the penalty method for multivalued maps, we show the existence of weak solutions of evolution variational inequalities on closed convex sets. The class of multivalued penalty operators is constructed. We also consider a model example to illustrate this theory.     

The existence of light‐like homogeneous geodesics in homogeneous Lorentzian manifolds

In previous papers, a fundamental affine method for studying homogeneous geodesics was developed. Using this method and elementary differential topology it was proved that any homogeneous affine manifold and in particular any homogeneous pseudo‐Riemannian manifold admits a homogeneous geodesic through arbitrary point. In the present paper this affine method is refined and adapted to the pseudo‐Riemannian case. Using this method and elementary topology it is proved that any homogeneous Lorentzian manifold of even dimension admits a light‐like homogeneous geodesic. The method is illustrated in detail with an example of the Lie group of dimension 3 with an invariant metric, which does not admit any light‐like homogeneous geodesic.     

Monitoring of the <Superscript>14</Superscript>C concentration in the stack air of the nuclear power plant VVER Jaslovske Bohunice

¹⁴C releases in the stack air of the NPPs V1 and V2, Jaslovske Bohunice was determined during the year 2004–2010. Radioactivity concentration of ¹⁴C in the stack air was determined in the forms of inorganic ¹⁴CO₂ and ¹⁴C _n H _m . The annual average activity concentration in the stacks air samples varies between 12 and 121 Bq m⁻³. NPP V1, starting with 45 Bq m⁻³ in 2005 is decreasing due to the shutting down of the reactors (the first reactor was shut down in December 2006 and the second reactor in December 2008). The average value of radioactivity concentration for power unit V2 was 32 Bq m⁻³ in 2004 and reached the value of 102 Bq m⁻³ in the first-quarter of the 2010. The average normalized yearly discharge rates were between 0.39 and 0.64 TBq GW_e⁻¹ year⁻¹ (2005–2008), NPP V1 and 0.19–0.61 TBq GW_e⁻¹ year⁻¹ (2004–first-quarter 2010) for NPP V2, Jaslovske Bohunice. Most of the discharged ¹⁴C is in a hydrocarbon form, (95% for Jaslovske Bohunice NPP V2), but the CO₂ fraction may reach 37% in the air stack for Jaslovske Bohunice V1.