Nanometric positioning accuracy in the presence of presliding and sliding friction: Modelling,identification and compensation

Presliding and sliding frictional effects, limiting the performances of ultrahigh precision mechatronics devices, are studied in this work. The state-of-the-art related to frictional behavior in both motion regimes is, hence, considered, and the generalized Maxwell-slip (GMS) friction model is adopted to characterize frictional disturbances present in a micromanipulation device. All the parameters of the model are identified via experimental set-ups and included in the overall MATLAB/SIMULINK model. With the aim of compensating frictional effects, the modelled response of the system is thus compared to experimental results when using proportional-integral-derivative (PID) control, feed-forward model-based compensation and a self-tuning adaptive regulator. The adaptive regulator proves to be the most efficient and is, hence, used in the final repetitive point-to-point positioning tests allowing to achieve nanometric precision and accuracy.     

A note on the maximum number of triangles in a C5-free graph

We prove that the maximum number of triangles in a -free graph on vertices is at most , improving an estimate of Alon and Shikhelman.     

Orthogonal exponentials, translations, and Bohr completions

We are concerned with an harmonic analysis in Hilbert spaces L²(μ), where μ is a probability measure on . The unifying question is the presence of families of orthogonal (complex) exponentials e_λ(x)=exp(2πiλx) in L²(μ). This question in turn is connected to the existence of a natural embedding of L²(μ) into an L²-space of Bohr almost periodic functions on . In particular we explore when L²(μ) contains an orthogonal basis of e_λ functions, for λ in a suitable discrete subset in ; i.e, when the measure μ is spectral. We give a new characterization of finite spectral sets in terms of the existence of a group of local translation. We also consider measures μ that arise as fixed points (in the sense of Hutchinson) of iterated function systems (IFSs), and we specialize to the case when the function system in the IFS consists of affine and contractive mappings in . We show in this case that if μ is then assumed spectral then its partitions induced by the IFS at hand have zero overlap measured in μ. This solves part of the Łaba–Wang conjecture. As an application of the new non-overlap result, we solve the spectral-pair problem for Bernoulli convolutions advancing in this way a theorem of Ka-Sing Lau. In addition we present a new perspective on spectral measures and orthogonal Fourier exponentials via the Bohr compactification.     

Ionic conductivity of the aqueous layer separating a lipid bilayer membrane and a glass support

The in-plane ionic conductivity of the approximately 1-nm-thick aqueous layer separating a 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) bilayer membrane and a glass support was investigated. The aqueous layer conductivity was measured by tip-dip deposition of a POPC bilayer onto the surface of a 20- to 75-microm-thick glass membrane containing a single conical-shaped nanopore and recording the current-voltage (i-V) behavior of the glass membrane nanopore/POPC bilayer structure. The steady-state current across the glass membrane passes through the nanopore (45-480 nm radius) and spreads radially outward within the aqueous layer between the glass support and bilayer. This aqueous layer corresponds to the dominant resistance of the glass membrane nanopore/POPC bilayer structure. Fluorescence recovery after photobleaching measurements using dye-labeled lipids verified that the POPC bilayer maintains a significant degree of fluidity on the glass membrane. The slopes of ohmic i-V curves yield an aqueous layer conductivity of (3 +/- 1) x 10(-3) Omega(-1) cm(-1) assuming a layer thickness of 1.0 nm. This conductivity is essentially independent of the concentration of KCl in the bulk solution (10-4 to 1 M) in contact with the membrane. The results indicate that the concentration and mobility of charge carriers in the aqueous layer between the glass support and bilayer are largely determined by the local structure of the glass/water/bilayer interface.     

Synthesis of 2-phosphonopyrrolidine and its substitution for proline in an inhibitor of angiotensin-converting enzyme

The title compound was synthesized $\text{via}$ its diethyl ester from 1-pyrroline trimer and diethyl phosphite. The 3-mercaptopropanoyl derivative inhibited angiotensin converting enzyme with I₅₀ = 1.7 μM.     

Partition conditions and vertex-connectivity of graphs

It was proved ([5], [6]) that ifG is ann-vertex-connected graph then for any vertex sequencev ₁, ...,v _n ≠V(G) and for any sequence of positive integersk ₁, ...,k _n such thatk ₁+...+k _n =|V(G)|, there exists ann-partition ofV(G) such that this partition separates the verticesv ₁, ...,v(n), and the class of the partition containingv _i induces a connected subgraph consisting ofk _i vertices, fori=1, 2, ...,n. Now fix the integersk ₁, ...,k _n . In this paper we study what can we say about the vertex-connectivity ofG if there exists such a partition ofV(G) for any sequence of verticesv ₁, ...,v _n ≠V(G). We find some interesting cases when the existence of such partitions implies then-vertex-connectivity ofG, in the other cases we give sharp lower bounds for the vertex-connectivity ofG.     

Analysis of orthogonality and of orbits in affine iterated function systems

We introduce a duality for affine iterated function systems (AIFS) which is naturally motivated by group duality in the context of traditional harmonic analysis. Our affine systems yield fractals defined by iteration of contractive affine mappings. We build a duality for such systems by scaling in two directions: fractals in the small by contractive iterations, and fractals in the large by recursion involving iteration of an expansive matrix. By a fractal in the small we mean a compact attractor X supporting Hutchinson’s canonical measure μ, and we ask when μ is a spectral measure, i.e., when the Hilbert space has an orthonormal basis (ONB) of exponentials . We further introduce a Fourier duality using a matched pair of such affine systems. Using next certain extreme cycles, and positive powers of the expansive matrix we build fractals in the large which are modeled on lacunary Fourier series and which serve as spectra for X. Our two main results offer simple geometric conditions allowing us to decide when the fractal in the large is a spectrum for X. Our results in turn are illustrated with concrete Sierpinski like fractals in dimensions 2 and 3. Research supported in part by the National Science Foundation DMS 0457491.