Spectral theory of differential operators on finite metric graphs and on bounded domains

Die vorliegende Arbeit widmet sich der Spektraltheorie von Differentialoperatoren auf metrischen Graphen und von indefiniten Differentialoperatoren auf beschränkten Gebieten. Sie besteht aus zwei Teilen. Im Ersten werden endliche, nicht notwendigerweise kompakte, metrische Graphen und die Hilberträume von quadratintegrierbaren Funktionen auf diesen betrachtet. Alle quasi-m-akkretiven Laplaceoperatoren auf solchen Graphen werden charakterisiert, und Abschätzungen an die negativen Eigenwerte selbstadjungierter Laplaceoperatoren werden hergeleitet. Weiterhin wird die Wohlgestelltheit eines gemischten Diffusions- und Transportproblems auf kompakten Graphen durch die Anwendung von Halbgruppenmethoden untersucht. Eine Verallgemeinerung des indefiniten Operators $-tfrac{d}{dx}sgn(x)tfrac{d}{dx}$ von Intervallen auf metrische Graphen wird eingeführt. Die Spektral- und Streutheorie der selbstadjungierten Realisierungen wird detailliert besprochen. Im zweiten Teil der Arbeit werden Operatoren untersucht, die mit indefiniten Formen der Art $langlegrad v, A(cdot)grad urangle$ mit $u,vin H_0^1(Omega)subset L^2(Omega)$ und $OmegasubsetR^d$ beschränkt, assoziiert sind. Das Eigenwertverhalten entspricht in Dimension $d=1$ einer verallgemeinerten Weylschen Asymptotik und für $dgeq 2$ werden Abschätzungen an die Eigenwerte bewiesen. Die Frage, wann indefinite Formmethoden für Dimensionen $dgeq 2$ anwendbar sind, bleibt offen und wird diskutiert.

Specific Activation of Leukocyte β2 Integrins Lymphocyte Function–associated Antigen-1 and Mac-1 by Chemokines Mediated by Distinct Pathways via the α Subunit Cytoplasmic Domains

We show that CC chemokines induced a sustained increase in monocyte adhesion to intercellular adhesion molecule-1 that was mediated by Mac-1 (αMβ2) but not lymphocyte function–associated antigen-1 (LFA-1; αLβ2). In contrast, staining for an activation epitope revealed a rapid and transient up-regulation of LFA-1 activity by monocyte chemotactic protein-1 (MCP-1) in monocytes and Jurkat CCR2 chemokine receptor transfectants or by stromal-derived factor-1α in Jurkat cells. Differential kinetics for activation of Mac-1 (sustained) and LFA-1 (transient) avidity in response to stromal-derived factor-1α were confirmed by expression of αM or αL in αL-deficient Jurkat cells. Moreover, expression of chimeras containing αL and αM cytoplasmic domain exchanges indicated that α cytoplasmic tails conferred the specific mode of regulation. Coexpressing αM or chimeras in mutant Jurkat cells with a “gain of function” phenotype that results in constitutively active LFA-1 demonstrated that Mac-1 was not constitutively active, whereas constitutive activity was mediated via the αL cytoplasmic tail, implying the presence of distinct signaling pathways for LFA-1 and Mac-1. Transendothelial chemotaxis of monocytes in response to MCP-1 was dependent on LFA-1; however, Mac-1 was involved at MCP-1 concentrations stimulating its avidity, showing differential contributions of β2 integrins. Our data suggest that a specific regulation of β2 integrin avidity by chemokines may be important in leukocyte extravasation and may be triggered by distinct activation pathways transduced via the α subunit cytoplasmic domains.

Reversibly locking a protein fold in an active conformation with a disulfide bond: Integrin αL I domains with high affinity and antagonist activity in vivo

The integrin αLβ2 has three different domains in its headpiece that have been suggested to either bind ligand or to regulate ligand binding. One of these, the inserted or I domain, has a fold similar to that of small G proteins. The I domain of the αM and α2 subunits has been crystallized in both open and closed conformations; however, the αL I domain has been crystallized in only the closed conformation. We hypothesized that the αL domain also would have an open conformation, and that this would be the ligand binding conformation. Therefore, we introduced pairs of cysteine residues to form disulfides that would lock the αL I domain in either the open or closed conformation. Locking the I domain open resulted in a 9,000-fold increase in affinity to intercellular adhesion molecule-1 (ICAM-1), which was reversed by disulfide reduction. By contrast, the affinity of the locked closed conformer was similar to wild type. Binding completely depended on Mg2+. Orders of affinity were ICAM-1 > ICAM-2 > ICAM-3. The kon, koff, and KD values for the locked open I domain were within 1.5-fold of values previously determined for the αLβ2 complex, showing that the I domain is sufficient for full affinity binding to ICAM-1. The locked open I domain antagonized αLβ2-dependent adhesion in vitro, lymphocyte homing in vivo, and firm adhesion but not rolling on high endothelial venules. The ability to reversibly lock a protein fold in an active conformation with dramatically increased affinity opens vistas in therapeutics and proteomics.

Genera et species Curculionidum, cum synonymia hujus familae species novæ / a C.J. Schoenherr ; species novae aut hactenus minus cognitae, descriptionibus a L. Gyllenhal, C. H. Boheman entomologis aliis illustratæ.

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Fe III in a low-spin state in caesium bis[3-ethoxysalicylaldehyde 4-methylthiosemicarbazonato(2–)-κ3O2,N1,S]ferrate(III) methanol monosolvate

The synthesis and crystal structure (at 100K) of the title compound, Cs[Fe(C11H13N3O2S2) 2] CH3OH, is reported. The asymmetric unit consists of an octahedral [FeIII(L)2]- fragment, where L 2- is 3-ethoxysalicylaldehyde 4-methylthiosemicarbazonate(2-) {systematic name: [2-(3-ethoxy-2-oxidobenzylidene)hydrazin-1-ylidene] (methylamino)methanethiolate}, a caesium cation and a methanol solvent molecule. Each L2- ligand binds through the thiolate S, the imine N and the phenolate O atoms as donors, resulting in an FeIIIS2N 2O2 chromophore. The O,N,S-coordinating ligands are orientated in two perpendicular planes, with the O and S atoms in cis positions and the N atoms in trans positions. The FeIII cation is in the low-spin state at 100K. © 2014 International Union of Crystallography.

Studies on the relative stabilities of Mn(II) and Mn(III) in complexes with N4O2 donor environments:crystal structures of [Mn(pybzhz)2] and [Mn(Ophsal)(imzH)2] ClO4 (pybzhz = N-(benzoyl)-N-(picolinylidene) hydrazine, Ophsal = N,N-o-phenylenebis(salicylideneimine), imzH = imidazole)

Five manganese complexes in an N 4O 2 donor environment have been prepared. Four of the compounds involve aroyl hydrazone as ligands and manganese is in a +2 oxidation state. The fifth compound was prepared using N,Nprime-o-phenylenebis(salicylideneimine) and imidazole as ligands where manganese is present in +3 oxidation state. X-ray crystal structure of one Mn +2 compound and the Mn +3 compound was determined. The relative stabilities of the Mn +2 and Mn +3 oxidation states were analyzed using the structural data and MO calculations. Manganese(II) complexes of four aroyl hydrazone ligands were prepared and characterized by different physicochemical techniques. The complexes are of the type Mn(L) 2, where L stands for the deprotonated hydrazone ligand. One of the compounds, Mn(pybzhz) 2, was also characterized by single crystal structure determination. In all these complexes, the Mn(II) is in an N 4O 2 donor environment and the Mn(II) center cannot be oxidized either chemically or electrochemically. However, when another ligand Ophsal is used to give the compound [Mn(Ophsal)(imzH) 2]ClO 4, which was also characterized by X-ray crystal structure determination, manganese can easily avail the +3 oxidation state. The relative stabilities of the +2 and +3 oxidation states of manganese were analyzed and it was concluded that the extent of distortion from the perfect octahedral geometry is the main controlling factor in these cases. © 2004 Elsevier B.V. All rights reserved.

On the Hyperbolicity Domain of the Polynomial x^n + a1x^(n-1) + 1/4+ an

∗ Partially supported by INTAS grant 97-1644

Embeddings of α-Modulation Spaces

2010 Mathematics Subject Classification: 42B35, 46E35.

Síntesis, caracterización y estudio de compuestos de coordinación con el ligando N,N¿dimetil-N-N-bis(2-hidroxi-3-metoxi-5-metilbencil) etilendiamina (H2L)

257 p.

Second-order elliptic PDE with discontinuous boundary data

We shall consider the weak formulation of a linear elliptic model problem with discontinuous Dirichlet boundary conditions. Since such problems are typically not well-defined in the standard H^1-H^1 setting, we will introduce a suitable saddle point formulation in terms of weighted Sobolev spaces. Furthermore, we will discuss the numerical solution of such problems. Specifically, we employ an hp-discontinuous Galerkin method and derive an L^2-norm a posteriori error estimate. Numerical experiments demonstrate the effectiveness of the proposed error indicator in both the h- and hp-version setting. Indeed, in the latter case exponential convergence of the error is attained as the mesh is adaptively refined.

Problema di Cauchy-Dirichlet per l'equazione del calore

In quest'elaborato si risolve il problema di Cauchy-Dirichlet per l'equazione del calore, prendendo come oggetto d'esame una sbarra omogenea. Nel primo capitolo si studiano le serie di Fourier reali a partire dalle serie trigonometriche; vengono dati, poi, i principali risultati di convergenza puntuale, uniforme ed in L^2 e si discute l'integrabilità termine a termine di una serie di Fourier. Il secondo capitolo tratta la convergenza secondo Cesàro, le serie di Fejèr ed i principali risultati di convergenza di queste ultime. Nel terzo, ed ultimo, capitolo si risolve il Problema di Cauchy-Dirichlet, distinguendo i casi in cui il dato iniziale sia di classe C^1 o solo continuo; nel secondo caso si propone una risoluzione basata sulle serie di Fejér e sul concetto di barriera ed una utilizzando il nucleo di Green per l'equazione del calore.

Somatic embryogenesis, organogenesis and plant regeneration in taro (Colocasia esculenta var. esculenta)

Callus was initiated in three different ‘‘esculenta’’ taro cultivars by culturing corm slices in the dark on half-strength MS medium supplemented with 2.0 mg/l 2,4- dichlorophenoxyacetic acid (2,4-D) for 20 days followed by subculture of all corm slices to half-strength MS medium containing 1.0 mg/l thidiazuron (TDZ). Depending on the cultivar, 20–30% of corm slices produced compact, yellow, nodular callus on media containing TDZ. Histological studies revealed the presence of typical embryogenic cells which were small, isodiametric with dense cytoplasms. Somatic embryos formed when callus was transferred to hormone-free medium and *72% of the embryos germinated into plantlets on this medium. Simultaneous formation of roots and shoots during germination, and the presence of shoot and root poles revealed by histology, confirmed that these structures were true somatic embryos. Plants derived from somatic embryos appeared phenotypically normal following 2 months growth in a glasshouse. This method is a significant advance on those previously reported for the esculenta cultivars of taro due to its efficiency and reproducibility.

Initiation of embryogenic cell suspensions of taro (Colocasia esculenta var. esculenta) and plant regeneration

Embryogenic callus was initiated by culturing in vitro taro corm slices on agar-solidified half-strength MS medium containing 2.0 mg/L 2,4-dichlorophenoxyacetic acid (2,4-D) for 20 days followed by transfer to 1.0 mg/L thidiazuron (TDZ). Callus was subsequently proliferated on solid medium containing 1.0 mg/L TDZ, 0.5 mg/L 2,4- D and 800 mg/L glutamine before transfer to liquid medium containing the same components but with reduced glutamine (100 mg/L). After 3 months in liquid culture on an orbital shaker, cytoplasmically dense cell aggregates began to form. Somatic embryogenesis was induced by plating suspension cells onto solid media containing reduced levels of hormones (0.1 mg/L TDZ, 0.05 mg/L 2,4-D), high concentrations of sucrose (40–50 g/L) and biotin (1.0 mg/L). Embryo maturation and germination was then induced on media containing 0.05 mg/L benzyladenine (BA) and 0.1 mg/L indole-3-acetic acid (IAA). Histological studies of the developing embryos revealed the presence of typical shoot and root poles suggesting that these structures were true somatic embryos. The rate of somatic embryos formation was 500–3,000 per mL settledcell volume while approximately 60% of the embryos regenerated into plants.