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.     

Sets that force recurrence

We characterize those subsets of the positive integers with the property that, whenever a point in a dynamical system enters a compact set along , contains a recurrent point. We do the same for uniform recurrence.

     

New weighted Rogers-Ramanujan partition theorems and their implications

This paper has a two-fold purpose. First, by considering a reformulation of a deep theorem of Göllnitz, we obtain a new weighted partition identity involving the Rogers-Ramanujan partitions, namely, partitions into parts differing by at least two. Consequences of this include Jacobi's celebrated triple product identity for theta functions, Sylvester's famous refinement of Euler's theorem, as well as certain weighted partition identities. Next, by studying partitions with prescribed bounds on successive ranks and replacing these with weighted Rogers-Ramanujan partitions, we obtain two new sets of theorems - a set of three theorems involving partitions into parts (mod 6), and a set of three theorems involving partitions into parts (mod 7), .