On the Schrodinger equation involving a critical Sobolev exponent and magnetic field

We consider the semilinear Schrodinger equation -Delta(A)u + V(x)u = Q(x)vertical bar u vertical bar(2* -2) u. Assuming that V changes sign, we establish the existence of a solution u not equal 0 in the Sobolev space H-A,V(1) + (R-N). The solution is obtained by a min-max type argument based on a topological linking. We also establish certain regularity properties of solutions for a rather general class of equations involving the operator -Delta(A).

Sharp Sobolev inequality involving a critical nonlinearity on a boundary

We consider the solvability of the Neumann problem for the equation -Delta u + lambda u = 0, partial derivative u/partial derivative v = Q(x)vertical bar u vertical bar(q-2)u on partial derivative Omega, where Q is a positive and continuous coefficient on partial derivative Omega, lambda is a parameter and q = 2(N - 1)/(N - 2) is a critical Sobolev exponent for the trace embedding of H-1(Omega) into L-q(partial derivative Omega). We investigate the joint effect of the mean curvature of partial derivative Omega and the shape of the graph of Q on the existence of solutions. As a by product we establish a sharp Sobolev inequality for the trace embedding. In Section 6 we establish the existence of solutions when a parameter lambda interferes with the spectrum of -Delta with the Neumann boundary conditions. We apply a min-max principle based on the topological linking.

Structural model of the CopA copper ATPase of Enterococcus hirae based on chemical cross-linking

The CopA copper ATPase of Enterococcus hirae belongs to the family of heavy metal pumping CPx-type ATPases and shares 43% sequence similarity with the human Menkes and Wilson copper ATPases. Due to a lack of suitable protein crystals, only partial three-dimensional structures have so far been obtained for this family of ion pumps. We present a structural model of CopA derived by combining topological information obtained by intramolecular cross-linking with molecular modeling. Purified CopA was cross-linked with different bivalent reagents, followed by tryptic digestion and identification of cross-linked peptides by mass spectrometry. The structural proximity of tryptic fragments provided information about the structural arrangement of the hydrophilic protein domains, which was integrated into a three-dimensional model of CopA. Comparative modeling of CopA was guided by the sequence similarity to the calcium ATPase of the sarcoplasmic reticulum, Serca1, for which detailed structures are available. In addition, known partial structures of CPx-ATPase homologous to CopA were used as modeling templates. A docking approach was used to predict the orientation of the heavy metal binding domain of CopA relative to the core structure, which was verified by distance constraints derived from cross-links. The overall structural model of CopA resembles the Serca1 structure, but reveals distinctive features of CPx-type ATPases. A prominent feature is the positioning of the heavy metal binding domain. It features an orientation of the Cu binding ligands which is appropriate for the interaction with Cu-loaded metallochaperones in solution. Moreover, a novel model of the architecture of the intramembranous Cu binding sites could be derived.

Equilibrium distributions of topological states in circular DNA: Interplay of supercoiling and knotting

Two variables define the topological state of closed double-stranded DNA: the knot type, K, and ΔLk, the linking number difference from relaxed DNA. The equilibrium distribution of probabilities of these states, P(ΔLk, K), is related to two conditional distributions: P(ΔLk|K), the distribution of ΔLk for a particular K, and P(K|ΔLk) and also to two simple distributions: P(ΔLk), the distribution of ΔLk irrespective of K, and P(K). We explored the relationships between these distributions. P(ΔLk, K), P(ΔLk), and P(K|ΔLk) were calculated from the simulated distributions of P(ΔLk|K) and of P(K). The calculated distributions agreed with previous experimental and theoretical results and greatly advanced on them. Our major focus was on P(K|ΔLk), the distribution of knot types for a particular value of ΔLk, which had not been evaluated previously. We found that unknotted circular DNA is not the most probable state beyond small values of ΔLk. Highly chiral knotted DNA has a lower free energy because it has less torsional deformation. Surprisingly, even at |ΔLk| > 12, only one or two knot types dominate the P(K|ΔLk) distribution despite the huge number of knots of comparable complexity. A large fraction of the knots found belong to the small family of torus knots. The relationship between supercoiling and knotting in vivo is discussed.

Topological challenges to DNA replication: Conformations at the fork

The unwinding of the parental DNA duplex during replication causes a positive linking number difference, or superhelical strain, to build up around the elongating replication fork. The branching at the fork and this strain bring about different conformations from that of (−) supercoiled DNA that is not being replicated. The replicating DNA can form (+) precatenanes, in which the daughter DNAs are intertwined, and (+) supercoils. Topoisomerases have the essential role of relieving the superhelical strain by removing these structures. Stalled replication forks of molecules with a (+) superhelical strain have the additional option of regressing, forming a four-way junction at the replication fork. This four-way junction can be acted on by recombination enzymes to restart replication. Replication and chromosome folding are made easier by topological domain barriers, which sequester the substrates for topoisomerases into defined and concentrated regions. Domain barriers also allow replicated DNA to be (−) supercoiled. We discuss the importance of replicating DNA conformations and the roles of topoisomerases, focusing on recent work from our laboratory.

The mechanical strength of phosphates under friction-induced cross-linking

Purpose: In the present study, we consider mechanical properties of phosphate glasses under high temperatureinduced and under friction-induced cross-linking, which enhance the modulus of elasticity. Design/methodology/approach: Two nanomechanical properties are evaluated, the first parameter is the modulus of elasticity (E) (or Young's modulus) and the second parameter is the hardness (H). Zinc meta-, pyro - and orthophosphates were recognized as amorphous-colloidal nanoparticles were synthesized under laboratory conditions and showed antiwear properties in engine oil. Findings: Young's modulus of the phosphate glasses formed under high temperature was in the 60-89 GPa range. For phosphate tribofilm formed under friction hardness and the Young's modulus were in the range of 2-10 GPa and 40-215 GPa, respectively. The degree of cross-linking during friction is provided by internal pressure of about 600 MPa and temperature close to 1000°C enhancing mechanical properties by factor of 3 (see Fig 1). Research limitations/implications: The addition of iron or aluminum ions to phosphate glasses under high temperature - and friction-induced amorphization of zinc metaphosphate and pyrophosphate tends to provide more cross-linking and mechanically stronger structures. Iron and aluminum (FeO4 or AlO4 units), incorporated into phosphate structure as network formers, contribute to the anion network bonding by converting the P=O bonds into bridging oxygen. Future work should consider on development of new of materials prepared by solgel processes, eg., zinc (II)-silicic acid. Originality/value: This paper analyses the friction pressure-induced and temperature–induced the two factors lead phosphate tribofilm glasses to chemically advanced glass structures, which may enhance the wear inhibition. Adding the coordinating ions alters the pressure at which cross-linking occurs and increases the antiwear properties of the surface material significantly.

Linking Theory and Practice: Performing a Reality Check on a Model of IS Success

The issue of ‘rigour vs. relevance’ in IS research has generated an intense, heated debate for over a decade. It is possible to identify, however, only a limited number of contributions on how to increase the relevance of IS research without compromising its rigour. Based on a lifecycle view of IS research, we propose the notion of ‘reality checks’ in order to review IS research outcomes in the light of actual industry demands. We assume that five barriers impact the efficient transfer of IS research outcomes; they are lack of awareness, lack of understandability, lack of relevance, lack of timeliness, and lack of applicability. In seeking to understand the effect of these barriers on the transfer of mature IS research into practice, we used focus groups. We chose DeLone and McLean’s IS success model as our stimulus because it is one of the more widely researched areas of IS.

Linking resource acquisition and development processes to resource-based advantage : bricolage and the resource-based view

We investigate the relationship between bricolage – an approach to a firm’s resource development – and the firm’s strategic resource position as depicted by the resource-based view (RBV). The RBV is concerned with the resource characteristics of firms that lead to sustainable competitive advantage. Alternatively, bricolage is a process of resource use and development characterised by using resources at hand, recombining resources and making do. Based on a sample of approximately 700 nascent and 700 young firms we find that higher levels of bricolage behaviour tend to lead to more advantageous strategic resource positions.

Linking resource acquisition and development processes to resource-based advantage : bricolage and the resource-based view

We investigate the relationship between bricolage – an approach to a firm’s resource development – and the firm’s strategic resource position as depicted by the resource-based view (RBV). The RBV is concerned with the resource characteristics of firms that lead to sustainable competitive advantage. Alternatively, bricolage is a process of resource use and development characterised by using resources at hand, recombining resources and making do. Based on a sample of 1,329 entrepreneurial start-ups we find that higher levels of bricolage behaviour tend to lead to more advantageous strategic resource positions.

Topological SLAM Using Fast Vision Techniques

In this paper we propose a method for vision only topological simultaneous localisation and mapping (SLAM). Our approach does not use motion or odometric information but a sequence of colour histograms from visited places. In particular, we address the perceptual aliasing problem which occurs using external observations only in topological navigation. We propose a Bayesian inference method to incrementally build a topological map by inferring spatial relations from the sequence of observations while simultaneously estimating the robot's location. The algorithm aims to build a small map which is consistent with local adjacency information extracted from the sequence measurements. Local adjacency information is incorporated to disambiguate places which otherwise would appear to be the same. Experiments in an indoor environment show that the proposed technique is capable of dealing with perceptual aliasing using visual observations only and successfully performs topological SLAM.

Topological SLAM using neighbourhood information of places

Perceptual aliasing makes topological navigation a difficult task. In this paper we present a general approach for topological SLAM~(simultaneous localisation and mapping) which does not require motion or odometry information but only a sequence of noisy measurements from visited places. We propose a particle filtering technique for topological SLAM which relies on a method for disambiguating places which appear indistinguishable using neighbourhood information extracted from the sequence of observations. The algorithm aims to induce a small topological map which is consistent with the observations and simultaneously estimate the location of the robot. The proposed approach is evaluated using a data set of sonar measurements from an indoor environment which contains several similar places. It is demonstrated that our approach is capable of dealing with severe ambiguities and, and that it infers a small map in terms of vertices which is consistent with the sequence of observations.

A multi-hypothesis topological SLAM approach for loop closing on edge-ordered graphs

We present a method for topological SLAM that specifically targets loop closing for edge-ordered graphs. Instead of using a heuristic approach to accept or reject loop closing, we propose a probabilistically grounded multi-hypothesis technique that relies on the incremental construction of a map/state hypothesis tree. Loop closing is introduced automatically within the tree expansion, and likely hypotheses are chosen based on their posterior probability after a sequence of sensor measurements. Careful pruning of the hypothesis tree keeps the growing number of hypotheses under control and a recursive formulation reduces storage and computational costs. Experiments are used to validate the approach.