Monotone path systems in simple regions

A monotone path system (MPS) is a finite set of pairwise disjoint paths (polygonal areas) in thexy-plane such that every horizontal line intersects each of the paths in at most one point. A MPS naturally determines a pairing of its top points with its bottom points. We consider a simple polygon in thexy-plane wich bounds the simple polygonal (closed) regionD. LetT andB be two finite, disjoint, equicardinal sets of points ofD. We give a good characterization for the existence of a MPS inD which pairsT withB, and a good algorithm for finding such a MPS, and we solve the problem of finding all MPSs inD which pairT withB. We also give sufficient conditions for any such pairing to be the same.The first author's research is supported by the Natural Sciences and Engineering Research Council of Canada     

Amphiphilic treelike rods at interfaces: layered stems and circular aggregation

Amphiphilic dendron-rod molecules with three hydrophilic poly(ethylene oxide) (PEO) branches attached to a hydrophobic octa-p-phenylene rod stem were investigated for their ability to form two-dimensional micellar structures on a solid surface. A treelike shape of the molecules was reported to be a major factor in the formation of nonplanar micellar structures in solution and in the bulk state (cylindrical and spherical). We observed that in these treelike amphiphilic molecules the hydrophilic terminated dendron branches assemble themselves in surface monolayers with the formation of two-dimensional layered or circular micellar structures. We suggested the formation of the planar ribbon-like structures with interdigitated layering within the loosely packed monolayers and circular, ringlike structures (2D circular aggregates) in the precollapsed state.     

Major histocompatibility complex (MHC) protein analysis by optimised two-dimensional electrophoretic methods

Human histocompatibility molecules HLA-Class I and Class II (DR, DQ, DP) were analysed using three two-dimensional protocols: nonequilibrium pH gradient electrophoresis (NEPHGE), isoelectric focusing-acidic gradient (IEF-AG) and isoelectric focusing-basic gradient (IEF-BG). The three methods differ in their carrier ampholyte combinations and electrophoretic conditions. They provide different pH gradients and therefore different electrofocusing profiles. The NEPHGE protocol was adequate for separating proteins across a broad range of pI mobilities, i.e. 4.4 pH units between the acidic and the basic end. In contrast, the IEF-AG and the IEF-BG protocols gave a separation power across a narrow pH range, 1.9 and 1.7 pH units respectively. Thus, whereas the NEPHGE protocol provides a tool for a global major histocompatibility complex (MHC) antigen profile analysis, the IEF-AG and -BG allows one to investigate subcomponents of the individual MHC chains. For example, NEPHGE analysis of the HLA Class I heavy chain revealed a single spot. However, IEF-BG revealed the presence of six equidistantly spaced spots spanning a short pH gradient with identical molecular weight. Similar improved resolution was seen for the HLA-DR, DQ, and DP molecules. The IEF acidic gradient was adequate for separating the alpha chain; the IEF basic gradient gave better resolution of the beta chains. This data provides a baseline set of conditions for both analytical and preparative MHC protein studies prior to amino acid sequencing.     

Surprising selectivity in the transformation of dimethoxy azaindoles

Transformation of 4,7-dimethoxy-6-azaindole into 4-hydroxy-7-methoxy-6-azaindole or 7-hydroxy-4-methoxy-6-azaindole can be readily controlled by careful selection of a reagent. Treatment with concentrated HCl results in hydrolysis at the 4-position exclusively, while TMS-I provides demethylation at the 7-position only. Products were unambiguously identified by single crystal X-ray crystallography.     

Autonomous intelligent agents for accelerated materials discovery

We present an end-to-end computational system for autonomous materials discovery. The system aims for cost-effective optimization in large, high-dimensional search spaces of materials by adopting a sequential, agent-based approach to deciding which experiments to carry out. In choosing next experiments, agents can make use of past knowledge, surrogate models, logic, thermodynamic or other physical constructs, heuristic rules, and different exploration–exploitation strategies. We show a series of examples for (i) how the discovery campaigns for finding materials satisfying a relative stability objective can be simulated to design new agents, and (ii) how those agents can be deployed in real discovery campaigns to control experiments run externally, such as the cloud-based density functional theory simulations in this work. In a sample set of 16 campaigns covering a range of binary and ternary chemistries including metal oxides, phosphides, sulfides and alloys, this autonomous platform found 383 new stable or nearly stable materials with no intervention by the researchers.

We present an end-to-end computational system for autonomous materials discovery.     

A new look at electromagnetic field theory

The most general expression of electromagnetic theory is examined in the light of (1) Faraday's interpretation of the field as a potentiality for the force of charged matter to act upon a test body, and (2) Einstein's view of the field equations as an example of a covariant expression of special relativity. Faraday's original interpretation, in which all physical variables must be expressible as nonsingular fields, implies a particular generalization of the standard forms of the conservation equations and leads to a removal of the problem of the infinite self-energy of point sources. A further generalization of the mathematical expression of electromagnetism occurs when it is asserted that the form of the laws must be compatible with the symmetry requirements of the irreducible representations of the Poincaré group. This yields a factorization of the vector field equations, giving a set of two uncoupled two-component spinor equations. It is shown that the latter lead to twice as many conservation equations for electromagnetism, compared with the vector formalism, thus making extra predictions that are not made in the latter formalism. It is shown that the extra conservation equations reveal themselves only when incorporating the requirements of Faraday's interpretation of the field solutions.     

From a monomer to a protein-sized, doughnut-shaped coordination oligomer-the influence of side chains of C3-symmetric ligands in supramolecular chemistry

Herein we describe the importance of side chains in C3-symmetric ligands in supramolecular chemistry. The reaction of the new ligand tris(5-bromo-2-methoxybenzylidene)triaminoguanidinium chloride [H3Me3Br3L]Cl (1) with ZnCl2 results in the formation of the monomeric complex (Et3NH)2[(ZnCl2)3Me3Br3L] (2), in which the ligand remains in a conformation less favourable for the coordination of metal centres. The use of the related tris(5-bromo-2-hydroxybenzylidene)triaminoguanidinium chloride, [H6Br3L]Cl, under similar conditions, results in the formation of two different dimeric compounds (NH4)[{[Zn(NH3)]3Br3L}2{mu-(OH)}3]1/4MeOH (3) and [Zn{Zn2(OH2)3(NH3)Br3L}2] (4), depending on the solvent mixture used. The comparable reaction of the ligand tris(5-bromo-2-hydroxy-3-methoxybenzylidene)triaminoguanidinium chloride [H6(OMe)3Br3L]Cl (5), leads to the formation of a doughnut-shaped, protein-sized coordination oligomer (Et3NH)18[{Zn[Zn2Cl{(OMe)3Br3L}]2}6(mu-Cl)6(OH2)6]x CH3CN (6), which comprises six dimeric [Zn5{(OMe)3Br3L}2] units. Whereas 3 and 4 decompose in DMSO solution, 6 is surprisingly stable in the same solvent.     

Die Strommer-Zykliden des Flaggenraumes

According to H. BRAUNER a flag space is a three-dimensional affine space with an absolute {,f,F}, wheref is a line in the plane of infinity andF a point onf. A cyclide is a surface of order 4 that intersects only atf. A STROMMER-cyclide is a cyclide generated by translation of a circle in an isotropic plane. In this paper we proof that all STROMMER-cyclides can be generated by translation of an isotropic circle along a divergent Newton-parabola or a conic in a full isotropic plane. We give normal-forms and CAD-pictures of these surfaces. Finaly some geometrical results about STROMMER-cyclides are developed.

---

---

Herrn o.Prof. Dr. Gy. Strommer zum 70. Geburtstag gewidmet.