Automatic locking of a parametrically resonating,base-excited,nonlinear beam

Nonlinear Dynamics - Described is a closed-loop control scheme capable of stabilizing a parametrically excited nonlinear structure in several vibration modes. By setting the relative phase between...     

Obtaining fast error rates in nonconvex situations

We show that under mild assumptions on the learning problem, one can obtain a fast error rate for every reasonable fixed target function even if the base class is not convex. To that end, we show that in such cases the excess loss class satisfies a Bernstein type condition.     

Mixing of all orders of Lie groups actions

Summary We show that for Lie groups whose adjoint representation reflects their topology, mixing implies mixing of all orders. In particular we prove that mixing actions of a semisimple Lie group are mixing of all orders, answering a conjecture of B. Marcus.Oblatum 6-VIII-1990 & 4-IV-1991Sponsored in part by the Edmund Landau Center for research in Mathematical Analysis supported by the Minerva Foundation (Federal Republic of Germany)     

Scheduling precedence graphs of bounded height

The existence of a schedule for a partially ordered set of unit length tasks on m identical processors is known to be NP-complete (J. D. Ullman, NP-complete scheduling problems, J. Comput. System Sci., 10 (1975), 384–393). The problem remains NP-complete even if we restrict the precedence graph to be of height bounded by a constant. (J. K. Lenkstra and A. H. G. Rinnooy Kan, Complexity of scheduling under precedence constraints, Operations Res., 26 (1978), 22–35; D. Dolev and M. K. Warmuth, “Scheduling Flat Graphs,” IBM Research Report RJ 3398, 1982). In these NP-completeness proofs the upper bound on the number of available processors varies with the problem instance. We present a polynomial algorithm for the case where the upper bound on the number of available processors and the height of the precedence graph are both constants.     

Automata and Square Complexes

We introduce a new geometric tool for analyzing groups of finite automata. To each finite automaton we associate a square complex. The square complex is covered by a product of two trees iff the automaton is bi-reversible. Using this method we give examples of free groups and of Kazhdan groups which are generated by the different states of one finite (bi-reversible) automaton. We also reprove the theorem of Macedońska, Nekrashevych, Sushchansky, on the connection between bi-reversible automata and the commensurator of a regular tree.     

Empirical Processes with a Bounded Ψ 1 Diameter

We study the empirical process ${{\rm sup}_{f \in F}|N^{-1}\sum_{i=1}^{N}\,f^{2}(X_i)-\mathbb{E}f^{2}|}We study the empirical process sup_{f ? F}|N^-1?_i=1^N f²(X_i)-\mathbbEf²|{{\rm sup}_{f \in F}|N^{-1}\sum_{i=1}^{N}\,f^{2}(X_i)-\mathbb{E}f^{2}|}, where F is a class of mean-zero functions on a probability space (Ω, μ), and (X_i)_{i = 1}^N{(X_{i})_{i =1}^N} are selected independently according to μ.     

Computational design, synthesis and biological evaluation of para-quinone-based inhibitors for redox regulation of the dual-specificity phosphatase Cdc25B

Quinoid inhibitors of Cdc25B were designed based on the Linear Combination of Atomic Potentials (LCAP) methodology. In contrast to a published hypothesis, the biological activities and hydrogen peroxide generation in reducing media of three synthetic models did not correlate with the quinone half-wave potential, E(1/2).     

Dvoretzky Type Theorems for Subgaussian Coordinate Projections

Given a class of functions F on a probability space \((\Omega ,\mu )\), we study the structure of a typical coordinate projection of the class, defined by \(\{(f(X_i))_{i=1}^N : f \in F\}\), where \(X_1,\ldots ,X_N\) are independent, selected according to \(\mu \). We show that when F is a subgaussian class, a typical coordinate projection satisfies a Dvoretzky type theorem.     

Laser desorption fast gas chromatography–Mass spectrometry in supersonic molecular beams

A novel method for fast analysis is presented. It is based on laser desorption injection followed by fast gas chromatography-mass spectrometry (GC-MS) in supersonic molecular beams. The sample was placed in an open air or purged laser desorption compartment, held at atmospheric pressure and near room temperature conditions. Desorption was performed with a XeCl Excimer pulsed laser with pulse energy of typically 3 mJ on the surface. About 20 pulses at 50 Hz were applied for sample injection, resulting in about 0.4 s injection time and one or a few micrograms sample vapor or small particles. The laser desorbed sample was further thermally vaporized at a heated frit glass filter located at the fast GC inlet. Ultrafast GC separation and quantification was achieved with a 50-cm-long megabore column operated with a high carrier gas flow rate of up to 240 mL/min. The high carrier gas flow rate provided effective and efficient entrainment of the laser desorbed species in the sweeping gas. Following the fast GC separation, the sample was analyzed by mass spectrometry in supersonic molecular beams. Both electron ionization and hyperthermal surface ionization were employed for enhanced selectivity and sensitivity. Typical laser desorption analysis time was under 10 s. The laser desorption fast GC-MS was studied and demonstrated with the following sample/matrices combinations, all without sample preparation or extraction: (a) traces of dioctylphthalate plasticizer oil on stainless steel surface and the efficiency of its cleaning; (b) the detection of methylparathion and aldicarb pesticides on orange leaves; (c) water surface analysis for the presence of methylparathion pesticide; (d) caffeine analysis in regular and decaffeinated coffee powder; (e) paracetamol and codeine drug analysis in pain relieving drug tablets; (f) caffeine trace analysis in raw urine; (g) blood analysis for the presence of 1 ppm lidocaine drug. The features and advantages of the laser desorption fast GC-MS are demonstrated and discussed.