Full O(alpha) corrections to e+e- -> sf_i sf_j

We present a complete precision analysis of the sfermion pair production process e+e- -> sf_i sf_j (f = t, b, tau, nu_tau) in the Minimal Supersymmetric Standard Model. Our results extend the previously calculated weak corrections by including all one-loop corrections together with higher order QED corrections. We present the details of the analytical calculation and discuss the renormalization scheme. The numerical analysis shows the results for total cross-sections, forward-backward and left-right asymmetries. It is based on the SPS1a' point from the SPA project. The complete corrections are about 10% and have to be taken into account in a high precision analysis.Comment: 32 pages, 24 figures, RevTeX

Two dimensional Berezin-Li-Yau inequalities with a correction term

We improve the Berezin-Li-Yau inequality in dimension two by adding a positive correction term to its right-hand side. It is also shown that the asymptotical behaviour of the correction term is almost optimal. This improves a previous result by Melas.Comment: 6 figure

On the lowest eigenvalue of Laplace operators with mixed boundary conditions

In this paper we consider a Robin-type Laplace operator on bounded domains. We study the dependence of its lowest eigenvalue on the boundary conditions and its asymptotic behavior in shrinking and expanding domains. For convex domains we establish two-sided estimates on the lowest eigenvalues in terms of the inradius and of the boundary conditions

Scorpions of Iran (Arachnida: Scorpiones). Part VI. Lorestan Province

Ten species of scorpions belonging to three families are reported from the Lorestan Province of Iran. Of these, five species are recorded from the province for the first time: Hottentotta zagrosensis Kovařík, 1997; Mesobuthus eupeus phillipsii (Pocock, 1889); Orthochirus iranus Kovařík, 2004; Razianus zarudnyi (Birula, 1903); and Scorpio maurus townsendi (Pocock, 1900). One new species is described, Hottentotta lorestanus sp. n.; it can be easily distinguished from the other four species of the genus known from Iran by its coloration; it is the only Iranian species which has the entire pedipalps yellow and the metasomal segments I to IV greenish gray. Also presented is a key to all species of scorpions found in the province

Scorpions of Iran (Arachnida: Scorpiones). Part VI. Lorestan Province

Ten species of scorpions belonging to three families are reported from the Lorestan Province of Iran. Of these, five species are recorded from the province for the first time: Hottentotta zagrosensis Kovařík, 1997; Mesobuthus eupeus phillipsii (Pocock, 1889); Orthochirus iranus Kovařík, 2004; Razianus zarudnyi (Birula, 1903) ; and Scorpio maurus townsendi (Pocock, 1900). One new species is described, Hottentotta lorestanus sp. n.; it can be easily distinguished from the other four species of the genus known from Iran by its coloration; it is the only Iranian species which has the entire pedipalps yellow and the metasomal segments I to IV greenish gray. Also presented is a key to all species of scorpions found in the province

Spectrum of the Schr\"odinger operator in a perturbed periodically twisted tube

We study Dirichlet Laplacian in a screw-shaped region, i.e. a straight twisted tube of a non-circular cross section. It is shown that a local perturbation which consists of "slowing down" the twisting in the mean gives rise to a non-empty discrete spectrum.Comment: LaTeX2e, 10 page

A Hardy inequality in twisted waveguides

We show that twisting of an infinite straight three-dimensional tube with non-circular cross-section gives rise to a Hardy-type inequality for the associated Dirichlet Laplacian. As an application we prove certain stability of the spectrum of the Dirichlet Laplacian in locally and mildly bent tubes. Namely, it is known that any local bending, no matter how small, generates eigenvalues below the essential spectrum of the Laplacian in the tubes with arbitrary cross-sections rotated along a reference curve in an appropriate way. In the present paper we show that for any other rotation some critical strength of the bending is needed in order to induce a non-empty discrete spectrum.Comment: LaTeX, 20 page

A simple proof of Hardy-Lieb-Thirring inequalities

We give a short and unified proof of Hardy-Lieb-Thirring inequalities for moments of eigenvalues of fractional Schroedinger operators. The proof covers the optimal parameter range. It is based on a recent inequality by Solovej, Soerensen, and Spitzer. Moreover, we prove that any non-magnetic Lieb-Thirring inequality implies a magnetic Lieb-Thirring inequality (with possibly a larger constant).Comment: 12 page

Weakly coupled bound states of Pauli operators

We consider the two-dimensional Pauli operator perturbed by a weakly coupled, attractive potential. We show that besides the eigenvalues arising from the Aharonov-Casher zero modes there are two or one (depending on whether the flux of the magnetic field is integer or not) additional eigenvalues for arbitrarily small coupling and we calculate their asymptotics in the weak coupling limit.Comment: 19 page

Resonances in Models of Spin Dependent Point Interactions

In dimension $d=1,2,3$ we define a family of two-channel Hamiltonians obtained as point perturbations of the generator of the free decoupled dynamics. Within the family we choose two Hamiltonians, $\hat H_0$ and \hat H_\ve, giving rise respectively to the unperturbed and to the perturbed evolution. The Hamiltonian $\hat H_0$ does not couple the channels and has an eigenvalue embedded in the continuous spectrum. The Hamiltonian \hat H_\ve is a small perturbation, in resolvent sense, of $\hat H_0$ and exhibits a small coupling between the channels. We take advantage of the complete solvability of our model to prove with simple arguments that the embedded eigenvalue of $\hat H_0$ shifts into a resonance for \hat H_\ve. In dimension three we analyze details of the time behavior of the projection onto the region of the spectrum close to the resonance.Comment: Changes in the proof of theorem 3, few misprints corrected, 21 page