On d- and D-separability

In this article we study relationships between d-separability and D-separability and present conditions under which these concepts are equivalent. We also study their relationship with D+-separability and define a generalization of discrete generability. (C) 2012 Elsevier B.V. All rights reserved.

Differential calculus and integration of generalized functions over membranes

In this paper we continue the development of the differential calculus started in Aragona et al. (Monatsh. Math. 144: 13-29, 2005). Guided by the so-called sharp topology and the interpretation of Colombeau generalized functions as point functions on generalized point sets, we introduce the notion of membranes and extend the definition of integrals, given in Aragona et al. (Monatsh. Math. 144: 13-29, 2005), to integrals defined on membranes. We use this to prove a generalized version of the Cauchy formula and to obtain the Goursat Theorem for generalized holomorphic functions. A number of results from classical differential and integral calculus, like the inverse and implicit function theorems and Green's theorem, are transferred to the generalized setting. Further, we indicate that solution formulas for transport and wave equations with generalized initial data can be obtained as well.

GROUND STATE AND NON-GROUND STATE SOLUTIONS OF SOME STRONGLY COUPLED ELLIPTIC SYSTEMS

We study an elliptic system of the form Lu = vertical bar v vertical bar(p-1) v and Lv = vertical bar u vertical bar(q-1) u in Omega with homogeneous Dirichlet boundary condition, where Lu := -Delta u in the case of a bounded domain and Lu := -Delta u + u in the cases of an exterior domain or the whole space R-N. We analyze the existence, uniqueness, sign and radial symmetry of ground state solutions and also look for sign changing solutions of the system. More general non-linearities are also considered.

MAXIMAL PSEUDOCOMPACT AND MAXIMAL R-CLOSED SPACES

In this paper a space X is pseudocompact if it is Tychonoff and every real-valued continuous function on X is bounded. We obtain conditions under which a Tychonoff space is maximal pseudocompact and study conditions under which a regular space is maximal R-closed.

Homogeneous structures and rigidity of isoparametric submanifolds in Hilbert space

We study isoparametric submanifolds of rank at least two in a separable Hilbert space, which are known to be homogeneous by the main result in [E. Heintze and X. Liu, Ann. of Math. (2), 149 (1999), 149-181], and with such a submanifold M and a point x in M we associate a canonical homogeneous structure I" (x) (a certain bilinear map defined on a subspace of T (x) M x T (x) M). We prove that I" (x) , together with the second fundamental form alpha (x) , encodes all the information about M, and we deduce from this the rigidity result that M is completely determined by alpha (x) and (Delta alpha) (x) , thereby making such submanifolds accessible to classification. As an essential step, we show that the one-parameter groups of isometries constructed in [E. Heintze and X. Liu, Ann. of Math. (2), 149 (1999), 149-181] to prove their homogeneity induce smooth and hence everywhere defined Killing fields, implying the continuity of I" (this result also seems to close a gap in [U. Christ, J. Differential Geom., 62 (2002), 1-15]). Here an important tool is the introduction of affine root systems of isoparametric submanifolds.

Polar foliations and isoparametric maps

A singular Riemannian foliation F on a complete Riemannian manifold M is called a polar foliation if, for each regular point p, there is an immersed submanifold Sigma, called section, that passes through p and that meets all the leaves and always perpendicularly. A typical example of a polar foliation is the partition of M into the orbits of a polar action, i.e., an isometric action with sections. In this article we prove that the leaves of H : M -> Sigma, coincide with the level sets of a smooth map H: M -> Sigma, if M is simply connected. In particular, the orbits of a polar action on a simply connected space are level sets of an isoparametric map. This result extends previous results due to the author and Gorodski, Heintze, Liu and Olmos, Carter and West, and Terng.

Pain in preterm infants: effects of sex, gestational age, and neonatal illness severity

Neonates hospitalized in a neonatal intensive care unit are exposed to many painful and stressful procedures. Biobehavioral pain reactivity in preterm infants during the neonatal period may reflect the capacity of the central nervous system to regulate arousal and neurobiological organization. We review empirical studies on the effects of sex, gestational age, and neonatal illness severity on pain reactivity in children born preterm. A literature search was conducted using PubMed, Institute of Scientific Information Web of Science, PsycINFO, Latin American and Caribbean Health Sciences Literature, and Scientific Electronic Library Online databases. Additionally, a special search was performed in online journals that publish pain studies including Pain, Early Human Development, European Journal of Pain, and Pain Management Nursing. The literature search covered the period from 2004 to 2009. Data were extracted according to predefined inclusion and exclusion criteria. Of the 18 studies reviewed, 16 analyzed gestational age, 13 examined neonatal illness severity, and eight focused on sex. Most of the studies analyzed more than one of these three variables. The majority of the studies found effects of gestational age (n = 14) and neonatal illness severity (n = 11) on pain responses. Only two studies found an influence of sex on infant pain responses. In conclusion, gestational age and neonatal illness severity influence pain responses in infants born preterm. Further studies should be conducted to examine the influence of sex on pain responses.

Factorization method and inclusions of mixed type in an inverse elliptic boundary value problem

In various imaging problems the task is to use the Cauchy data of the solutions to an elliptic boundary value problem to reconstruct the coefficients of the corresponding partial differential equation. Often the examined object has known background properties but is contaminated by inhomogeneities that cause perturbations of the coefficient functions. The factorization method of Kirsch provides a tool for locating such inclusions. In this paper, the factorization technique is studied in the framework of coercive elliptic partial differential equations of the divergence type: Earlier it has been demonstrated that the factorization algorithm can reconstruct the support of a strictly positive (or negative) definite perturbation of the leading order coefficient, or if that remains unperturbed, the support of a strictly positive (or negative) perturbation of the zeroth order coefficient. In this work we show that these two types of inhomogeneities can, in fact, be located simultaneously. Unlike in the earlier articles on the factorization method, our inclusions may have disconnected complements and we also weaken some other a priori assumptions of the method. Our theoretical findings are complemented by two-dimensional numerical experiments that are presented in the framework of the diffusion approximation of optical tomography.

Factorization method and irregular inclusions in electrical impedance tomography

In electrical impedance tomography, one tries to recover the conductivity inside a physical body from boundary measurements of current and voltage. In many practically important situations, the investigated object has known background conductivity but it is contaminated by inhomogeneities. The factorization method of Andreas Kirsch provides a tool for locating such inclusions. Earlier, it has been shown that under suitable regularity conditions positive (or negative) inhomogeneities can be characterized by the factorization technique if the conductivity or one of its higher normal derivatives jumps on the boundaries of the inclusions. In this work, we use a monotonicity argument to generalize these results: We show that the factorization method provides a characterization of an open inclusion (modulo its boundary) if each point inside the inhomogeneity has an open neighbourhood where the perturbation of the conductivity is strictly positive (or negative) definite. In particular, we do not assume any regularity of the inclusion boundary or set any conditions on the behaviour of the perturbed conductivity at the inclusion boundary. Our theoretical findings are verified by two-dimensional numerical experiments.

Fontaine modules and F-T-crystals, a dévissage

Das Hauptziel der Arbeit ist es, die Beziehung zwischen Fontaine Modulen und F-T-Kristall zu studieren. Im ersten Kapitel wird die Definition von Fontaine Modulen, die auf die inversen Cartier Transform setzt erinnern wir von Ogus und Vologodsky errichtet. Neben der Erinnerung an die urspruengliche Konstruktion des inversen Cartier Transform, eine direktere Konstruktion, die wir auch vorstellen von G.T. Lan, M. Sheng und K. Zuo. Darueber hinaus beweisen wir diernGleichwertigkeit der beiden Konstruktion.rnrnrnIm zweiten Kapitel werden wir uns daran erinnern, den Konstruktion von inversen Cartier Transform in der Log Einstellung von D. Schepler und verallgemeinern die Lan-Sheng-Zuo Konstruktion an dieser Einstellung. Darueber hinaus geben wir eine Definition von Log FontainernModulen. Im dritten Kapitel werden wir erinnern an die Definition von F-T-Kristall und beweisen das wichtigste Ergebnis dieser Arbeit: Sei $Y$ eine glatte $S_{nu}$-Schema, wobei $S_{nu}$ ist eine flache $W_{nu+1}(k)$-Schema, $nugeq1$, und $X/S_0$ seine Reduction modulo $p$ sein. Bei einem F-T-Kristall $(E,Phi,B)$ auf $Y$ der Breite von weniger als $p$ und let $(E_Y ,B_Y ,nabla_Y)$ die entsprechende gefilterte $O_Y$-modulen mit einer integrierbar Zusammenhang ausgestattet. Anschliesend wird die Reduktion dieses Objekt modulo $p$ definiert eine Fontaine Modulen auf $X/S_0$ im dem Sinnernder Ogus und Vologodsky.

Shimura subvarieties and the Torelli locus

We investigate the Torelli locus of abelian and cyclic covers of the projective line for occurrence of Shimura subvarieties. Amon other things, we show that under some conditions there are no Shimura subvarieties in this locus.

The plasmin-antiplasmin system: structural and functional aspects

The plasmin-antiplasmin system plays a key role in blood coagulation and fibrinolysis. Plasmin and (2)-antiplasmin are primarily responsible for a controlled and regulated dissolution of the fibrin polymers into soluble fragments. However, besides plasmin(ogen) and (2)-antiplasmin the system contains a series of specific activators and inhibitors. The main physiological activators of plasminogen are tissue-type plasminogen activator, which is mainly involved in the dissolution of the fibrin polymers by plasmin, and urokinase-type plasminogen activator, which is primarily responsible for the generation of plasmin activity in the intercellular space. Both activators are multidomain serine proteases. Besides the main physiological inhibitor (2)-antiplasmin, the plasmin-antiplasmin system is also regulated by the general protease inhibitor (2)-macroglobulin, a member of the protease inhibitor I39 family. The activity of the plasminogen activators is primarily regulated by the plasminogen activator inhibitors 1 and 2, members of the serine protease inhibitor superfamily.

T-cell recognition of chemicals, protein allergens and drugs: towards the development of in vitro assays

Chemicals can elicit T-cell-mediated diseases such as allergic contact dermatitis and adverse drug reactions. Therefore, testing of chemicals, drugs and protein allergens for hazard identification and risk assessment is essential in regulatory toxicology. The seventh amendment of the EU Cosmetics Directive now prohibits the testing of cosmetic ingredients in mice, guinea pigs and other animal species to assess their sensitizing potential. In addition, the EU Chemicals Directive REACh requires the retesting of more than 30,000 chemicals for different toxicological endpoints, including sensitization, requiring vast numbers of animals. Therefore, alternative methods are urgently needed to eventually replace animal testing. Here, we summarize the outcome of an expert meeting in Rome on 7 November 2009 on the development of T-cell-based in vitro assays as tools in immunotoxicology to identify hazardous chemicals and drugs. In addition, we provide an overview of the development of the field over the last two decades.

Attacks on German public figures, 1968-2004: warning behaviors, potentially lethal and non-lethal acts, psychiatric status, and motivations

Fourteen non-terrorist attackers of public figures in Germany between 1968 and 2004 were intensively studied, with a particular focus on warning behaviors, attack behaviors, and the relationship between psychiatric diagnosis, symptoms, and motivations for the assault. A large proportion of the attackers were severely mentally ill, and most likely to be in the potentially lethal rather than the non-lethal group. A new typology of seven warning behaviors was applied to the data, and all were present, most frequently fixation and pathway warning behavior, and least frequently a direct threat. Psychiatric diagnosis could be closely linked to motivation when analyzed at the level of symptom and content of thought, often delusional. Most of the attacks were directed at political figures, and the majority occurred after 1995.

Extensive clonal spread and extreme longevity in saw palmetto, a foundation clonal plant

The lack of effective tools have hampered our ability to assess the size, growth and ages of clonal plants. With Serenoa repens (saw palmetto) as a model, we introduce a novel analytical framework that integrates DNA fingerprinting and mathematical modelling to simulate growth and estimate ages of clonal plants. We also demonstrate the application of such life-history information of clonal plants to provide insight into management plans. Serenoa is an ecologically important foundation species in many Southeastern United States ecosystems; yet, many land managers consider Serenoa a troublesome invasive plant. Accordingly, management plans have been developed to reduce or eliminate Serenoa with little understanding of its life history. Using Amplified Fragment Length Polymorphisms, we genotyped 263 Serenoa and 134 Sabal etonia (a sympatric non-clonal palmetto) samples collected from a 20 X 20 m study plot in Florida scrub. Sabal samples were used to assign small field-unidentifiable palmettos to Serenoa or Sabal and also as a negative control for clone detection. We then mathematically modelled clonal networks to estimate genet ages. Our results suggest that Serenoa predominantly propagate via vegetative sprouts and 10000-year-old genets may be common, while showing no evidence of clone formation by Sabal. The results of this and our previous studies suggest that: (i) Serenoa has been part of scrub associations for thousands of years, (ii) Serenoa invasion are unlikely and (ii) once Serenoa is eliminated from local communities, its restoration will be difficult. Reevaluation of the current management tools and plans is an urgent task.