Obituary Ferenc Móricz (1939–2021)

Analysis Mathematica -     

Extensions of Szegö's theory of orthogonal polynomials,II

Let {? _n (dμ)} be a system of orthonormal polynomials on the unit circle with respect to a measuredμ. Szegö's theory is concerned with the asymptotic behavior of? _n (dμ) when logμ'∈L ¹. In what follows we will discuss the asymptotic behavior of the ratio φ_n(dμ ₁)/φ_n(dμ ₂) off the unit circle in casedμ ₁ anddμ ₂ are close in a sense (e.g.,dμ ₂=g dμ ₁ whereg≥0 is such thatQ(e ^it )g(t) andQ(e ^it )/g(t) are bounded for a suitable polynomialQ) and μ ₁ ^′ >0 almost everywhere or (a somewhat weaker requirement) lim _n→∞Φ _n (dμ ₁,0)=0, for the monic polynomials Φ _n . The consequences for orthogonal polynomials on the real line are also discussed.     

A simplified multidimensional integral

We present a simplified integral of functions of several variables. Although less general than the Riemann integral, most functions of practical interest are still integrable. On the other hand, the basic integral theorems can be obtained more quickly. We also give a characterization of the integrable functions and their primitives.     

Combining transmission geometry laser ablation and a non‐contact continuous flow surface sampling probe/electrospray emitter for mass spectrometry based chemical imaging

This paper describes the coupling of ambient pressure transmission geometry laser ablation with a liquid‐phase sample collection into a continuous flow surface sampling probe/electrospray emitter for mass spectrometry based chemical imaging. The flow probe/emitter device was placed in close proximity to the surface to collect the sample plume produced by laser ablation. The sample collected was immediately aspirated into the probe and onto the electrospray emitter, ionized and detected with the mass spectrometer. Freehand drawn ink lines and letters and an inked fingerprint on microscope slides were analyzed. The circular laser ablation area was about 210 µm in diameter and under the conditions used in these experiments the spatial resolution, as determined by the size of the surface features distinguished in the chemical images, was about 100 µm. Published in 2011 by John Wiley & Sons, Ltd.     

Ingham-Beurling type theorems with weakened gap conditions

Completing a series of works begun by Wiener [34], Paley and Wiener [28] and Ingham [9], a far-reaching generalization of Parseval"s identity was obtained by Beurling [4] for nonharmonic Fourier series whose exponents satisfy a uniform gap condition. Later this gap condition was weakened by Ullrich [33], Castro and Zuazua [5], Jaffard, Tucsnak and Zuazua [11] and then in [2] in some particular cases. In this paper we prove a general theorem which contains all previous results. Furthermore, applying a different method, we prove a variant of this theorem for nonharmonic Fourier series with vector coefficients. This result, partly motivated by control-theoretical applications, extends several earlier results obtained in [15] and [2]. Finally, applying these results we obtain an optimal simultaneous observability theorem concerning a system of vibrating strings. This revised version was published online in June 2006 with corrections to the Cover Date.     

Minimizing analyte electrolysis in an electrospray emitter

The electrospray (ES) ion source is a controlled-current electrolytic flow cell. Electrolytic reactions in the ES emitter capillary are continually ongoing to sustain the production of charged droplets and ultimately gas-phase ions from this device. Under certain circumstances, the analytes under study may be directly involved in these electrolytic processes. It is demonstrated that a simple means to minimize analyte electrolysis is to exchange the normal metal emitter capillary of commercial ES sources with one made of fused silica. This change is shown to provide an ES mass spectrometric system of similar performance in terms of gas-phase ion signal generated for non-electroactive analytes and also assures minimal oxidation of electroactive analytes even at low (2.0 microl x min(-1)) solution flow-rates and high (millimolar) solution electrolyte concentrations.     

Spin crossover of spiro-biphenalenyl neutral radical molecular conductors

We present ab initio molecular and solid-state calculations at the level of density functional theory (DFT) for the ethyl-substituted spiro-biphenalenyl neutral radical organic conductor. We find that the phase transition of this material is accompanied by a spin crossover (low-spin, LS, to high-spin, HS), and consequently a different band becomes the conduction band. The energy gap (Eg) increases from 0.12 eV of the low-temperature polymorph to 0.23 eV of the high-temperature polymorph corresponding to a different occupancy causing a change in the number of the available charge carriers, explaining the change of conductivity by 2 orders of magnitude at the phase transition. These gap values are also consistent with structural, IR, electrical conductivity, and magnetic susceptibility data of Itkis et al. The proximity of the monomers in the stacking dimers is closely related to the spin crossover in this material.