A necessary flexibility condition of a nondegenerate suspension in Lobachevsky 3-space

We show that some combination of the lengths of all edges of the equator of a flexible suspension in Lobachevsky 3-space is equal to zero (each length is taken either positive or negative in this combination).Comment: 20 pages, 13 figure

Amenable actions, free products and a fixed point property

We investigate the class of groups admitting an action on a set with an invariant mean. It turns out that many free products admit such an action. We give a complete characterisation of such free products in terms of a strong fixed point property.Comment: 12 page

Towards concolic testing for hybrid systems

Hybrid systems exhibit both continuous and discrete behavior. Analyzing hybrid systems is known to be hard. Inspired by the idea of concolic testing (of programs), we investigate whether we can combine random sampling and symbolic execution in order to effectively verify hybrid systems. We identify a sufficient condition under which such a combination is more effective than random sampling. Furthermore, we analyze different strategies of combining random sampling and symbolic execution and propose an algorithm which allows us to dynamically switch between them so as to reduce the overall cost. Our method has been implemented as a web-based checker named HYCHECKER. HYCHECKER has been evaluated with benchmark hybrid systems and a water treatment system in order to test its effectiveness.CPCI-S(ISTP)[email protected]; [email protected]

On the loss of continuity for super-critical drift-diffusion equations

We show that there exist solutions of drift-diffusion equations in two dimensions with divergence-free super-critical drifts, that become discontinuous in finite time. We consider classical as well as fractional diffusion. However, in the case of classical diffusion and time-independent drifts we prove that solutions satisfy a modulus of continuity depending only on the local $L^1$ norm of the drift, which is a super-critical quantity.Comment: Minor edit

Effective-Range Expansion of the Neutron-Deuteron Scattering Studied by a Quark-Model Nonlocal Gaussian Potential

The S-wave effective range parameters of the neutron-deuteron (nd) scattering are derived in the Faddeev formalism, using a nonlocal Gaussian potential based on the quark-model baryon-baryon interaction fss2. The spin-doublet low-energy eigenphase shift is sufficiently attractive to reproduce predictions by the AV18 plus Urbana three-nucleon force, yielding the observed value of the doublet scattering length and the correct differential cross sections below the deuteron breakup threshold. This conclusion is consistent with the previous result for the triton binding energy, which is nearly reproduced by fss2 without reinforcing it with the three-nucleon force.Comment: 21 pages, 6 figures and 6 tables, submitted to Prog. Theor. Phy

Regularity Properties and Pathologies of Position-Space Renormalization-Group Transformations

We reconsider the conceptual foundations of the renormalization-group (RG) formalism, and prove some rigorous theorems on the regularity properties and possible pathologies of the RG map. Regarding regularity, we show that the RG map, defined on a suitable space of interactions (= formal Hamiltonians), is always single-valued and Lipschitz continuous on its domain of definition. This rules out a recently proposed scenario for the RG description of first-order phase transitions. On the pathological side, we make rigorous some arguments of Griffiths, Pearce and Israel, and prove in several cases that the renormalized measure is not a Gibbs measure for any reasonable interaction. This means that the RG map is ill-defined, and that the conventional RG description of first-order phase transitions is not universally valid. For decimation or Kadanoff transformations applied to the Ising model in dimension $d \ge 3$, these pathologies occur in a full neighborhood $\{ \beta > \beta_0 ,\, |h| < \epsilon(\beta) \}$ of the low-temperature part of the first-order phase-transition surface. For block-averaging transformations applied to the Ising model in dimension $d \ge 2$, the pathologies occur at low temperatures for arbitrary magnetic-field strength. Pathologies may also occur in the critical region for Ising models in dimension $d \ge 4$. We discuss in detail the distinction between Gibbsian and non-Gibbsian measures, and give a rather complete catalogue of the known examples. Finally, we discuss the heuristic and numerical evidence on RG pathologies in the light of our rigorous theorems.Comment: 273 pages including 14 figures, Postscript, See also ftp.scri.fsu.edu:hep-lat/papers/9210/9210032.ps.

Lineability and algebrability of pathological phenomena in analysis

We show that, in analysis, many pathological phenomena occur more often than one could expect, that is, in a linear or algebraic way. We show this by means of the construction of large algebraic structures (infinite dimensional vector spaces or infinitely generated algebras) enjoying some special or pathological properties

Release of bradykinin and expression of kinin B2 receptors in the brain: role for cell death and brain edema formation after focal cerebral ischemia in mice

Pharmacological studies using bradykinin B2 receptor antagonists suggest that bradykinin, an early mediator of inflammation and the main metabolite of the kallikrein-kinin system, is involved in secondary brain damage after cerebral ischemia. However, the time-course of bradykinin production and kinin receptor expression as well as the conclusive role of bradykinin B2 receptors for brain damage after experimental stroke have not been elucidated so far. C57/Bl6 mice were subjected to 45 mins of middle cerebral artery occlusion (MCAO) and 2, 4, 8, 24, and 48 h later brains were removed for the analysis of tissue bradykinin concentration and kinin B2 receptor mRNA and protein expression. Brain edema, infarct volume, functional outcome, and long-term survival were assessed in WT and B2-/- mice 24 h or 7 days after MCAO. Tissue bradykinin was maximally increased 12 h after ischemia (three-fold), while kinin B2 receptor mRNA upregulation peaked 24 to 48 h after MCAO (10- to 12-fold versus naive brain tissue). Immunohistochemistry revealed that kinin B2 receptors were constitutively and widely expressed in mouse brain, were upregulated 2 h after ischemia in cells showing signs of ischemic damage, and remained upregulated in the penumbra up to 24 h after ischemia. B2-/- mice had improved motor function (P&lt;0.05), smaller infarct volumes (-38%; P&lt;0.01), developed less brain edema (-87%; P&lt;0.05), and survived longer (P&lt;0.01) as compared with wild-type controls. The current results show that bradykinin is produced in the brain, kinin B2 receptors are upregulated on dying cells, and B2 receptors are involved in cell death and brain edema formation after experimental stroke