Global solution of nonlinear mixed-integer bilevel programs

An algorithm for the global optimization of nonlinear bilevel mixed-integer programs is presented, based on a recent proposal for continuous bilevel programs by Mitsos et al. (J Glob Optim 42(4):475–513, 2008). The algorithm relies on a convergent lower bound and an optional upper bound. No branching is required or performed. The lower bound is obtained by solving a mixed-integer nonlinear program, containing the constraints of the lower-level and upper-level programs; its convergence is achieved by also including a parametric upper bound to the optimal solution function of the lower-level program. This lower-level parametric upper bound is based on Slater-points of the lower-level program and subsets of the upper-level host sets for which this point remains lower-level feasible. Under suitable assumptions the KKT necessary conditions of the lower-level program can be used to tighten the lower bounding problem. The optional upper bound to the optimal solution of the bilevel program is obtained by solving an augmented upper-level problem for fixed upper-level variables. A convergence proof is given along with illustrative examples. An implementation is described and applied to a test set comprising original and literature problems. The main complication relative to the continuous case is the construction of the parametric upper bound to the lower-level optimal objective value, in particular due to the presence of upper-level integer variables. This challenge is resolved by performing interval analysis over the convex hull of the upper-level integer variables.     

Development of a time-resolved white-light interference microscope for optical phase measurements during fs-laser material processing

A modified Mach–Zehnder interferometer set-up combined with microscope objectives has been developed for the measurement of phase changes in the processed material sample, like modification and melting of glass. The white light is generated by focusing ultrafast laser radiation (t _p=80 fs) in a sapphire crystal using a micro-lens array to minimize temporal and spatial fluctuations in the white-light continuum. Lateral and coaxial pump-probe measurements of the phase changes during material processing are performed using two coupled ultrafast laser sources at different repetition rates (f _rep=1 Hz–1 MHz). The optical phase shift and therefore the refractive index of the material are calculated from the interference images using two approaches. The knowledge of the refractive index during the laser processing with a temporal resolution in the ps-range and a spatial resolution of several microns leads to a better understanding of the initial processes for the permanent material modifications.     

Minimalistic Ditopic Ligands: An α‐S,N‐Donor‐Substituted Alkyne as Effective Intermetallic Conjugation Linker

The capability of donor‐substituted alkynes to link different metal ions in a side‐on carbon donor‐chelate coordination mode is extended from the donor centers S and P to the second period element N. The complex [Tp′W(CO)₂{η²‐C₂(S)(NHBn)}] (Tp′=hydrido‐tris(3,5‐dimethylpyrazolyl)borate, Bn=benzyl) bearing a terminal sulfur atom and a secondary amine substituent is accessible by a metal‐template synthesis. Subsequent deprotonation allowed the formation of remarkably stable heterobimetallic complexes with the [(η⁵‐C₅H₅)Ru(PPh₃)] and the [Ir(ppy)₂] moiety. Electrochemical and spectroscopic investigations (cyclic voltammetry, IR, UV/Vis, luminescence, EPR), as well as DFT calculations, and X‐ray structure determinations of the W–Ru complex in two oxidation states reveal a strong metal–metal coupling but also a limited delocalization of excited states.     

氟胺氰菊酯的定性定量分析

氟胺氰菊酯是一种用于蜜峰的高效杀螨剂。从20%商品氟胺氰菊酯粉剂中通过硅胶柱层板分离得到了96.6%的纯品并用FTIR和GC/MC进行定性量测定。采用GC/MS定量分析的方法，氟胺氰菊酯的浓度在0.05-10mg/L范围为线性响应，最低检测极限为 0.01mg/L。采用R（-）N-3，5-二硝基苯甲酰-苯基甘氨酸和长链烃的硅胶微粒手性柱，可成功地分离氟胺氰菊酯的二种旋光异构体，它们在商品氟胺氰菊酯中的比例近似为1：1。     

Small Periodic Solutions Generated by Sublinear Terms

The paper is concerned with Hopf bifurcations in systems of autonomous ordinary differential equations with a parameter. The principal distinction between usual theorems on Hopf bifurcations and our results is that here the linearized equation is degenerate and independent of the parameter. We present sufficient conditions for a parameter value to be a bifurcation point and analyze properties of small cycles arising in the vicinity of the equilibrium. Sublinear nonlinearities play the main role in the results obtained.     

The Proalgebraic Completion of Rigid Groups

A finitely generated group is called representation rigid (briefly, rigid) if for every n, has only finitely many classes of simple representations in dimension n. Examples include higher rank S-arithmetic groups. By Margulis super rigidity, the latter have a stronger property: they are representation super rigid; i.e., their proalgebraic completion is finite dimensional. We construct examples of nonlinear rigid groups which are not super rigid, and which exhibit every possible type of infinite dimensionality. Whether linear representation rigid groups are super rigid remains an open question.     

Liouville Theorems for Generalized Harmonic Functions

Each nonzero solution of the stationary Schrödinger equation u(x)–c(r)u(x)=0 in R ⁿ with a nonnegative radial potential c(r) must have certain minimal growth at infinity. If r ² c(r)=O(1), r, then a solution having power growth at infinity, is a generalized harmonic polynomial.