Regularity of optimal sets for some functional involving eigenvalues of an operator in divergence form

In this paper we consider minimizers of the functional$\min \{{\lambda }_1(\mathrm{\Omega })+\cdots +{\lambda }_k(\mathrm{\Omega })+\mathrm{\Lambda }|\mathrm{\Omega }|,:\mathrm{\Omega }\subset D\text{ open}\}$ where $D\subset {\mathbb{R}}^d$ is a bounded open set and where $0<{\lambda }_1(\mathrm{\Omega })\le \cdots \le {\lambda }_k(\mathrm{\Omega })$ are the first k eigenvalues on Ω of an operator in divergence form with Dirichlet boundary condition and with Hölder continuous coefficients. We prove that the optimal sets ${\mathrm{\Omega }}^{⁎}$ have finite perimeter and that their free boundary $\partial {\mathrm{\Omega }}^{⁎}\cap D$ is composed of a regular part, which is locally the graph of a $C^{1,\alpha }$-regular function, and a singular part, which is empty if $d<d^{⁎}$, discrete if $d=d^{⁎}$ and of Hausdorff dimension at most $d-d^{⁎}$ if $d>d^{⁎}$, for some $d^{⁎}\in \{5,6,7\}$.     

Explicit breather solution of the nonlinear Schrödinger equation

Theoretical and Mathematical Physics - We present a one-line closed-form expression for the three-parameter breather of the nonlinear Schrödinger equation. This provides an analytic proof of...     

Strain effects on multiferroic BiFeO3 films

The field of multiferroics has experienced a rapid progress resulting in the discovery of many new physical phenomena. BiFeO₃ (BFO) compound, which is one of the few room-temperature single-phase multiferroics, has contributed subsequently to this progress. As a result, significant review articles have been devoted specifically to this famous system. This chapter is dedicated to the strain effects on the structure stability and property changes of BFO thin films. It is a short and non-exhaustive topical overview that may be seen as an invitation for interested readers to go beyond. There is a very active and prolific research in this field and we apologize to the authors whose relevant work is not cited here. After a short introduction, we will thus review the effect of strain on BFO films by describing the consequences on the structure and the phase transitions as well as on polar, magnetic and magnetoelectric properties.     

Non-contact measurement of the electric field shielding performance and the resistivity of layer materials

An approach is described to measure the electric field shielding performance of materials as a function of frequency. This provides a broader appreciation of the performance of materials than is available from standard energy transfer type measurements. Materials that include metallic conducting components show little variation of shielding performance with frequency, whereas the performance of resistive materials falls away with increasing frequency. It is shown that the variation of attenuation with frequency relates to the resistivity on or within the material. This has particular practical relevance to the risk of occurrence of damaging or incendive electrostatic discharges from charged material surfaces.     

Asymmetric palladium-catalyzed benzylic nucleophilic substitution: high enantioselectivity with the DUPHOS family ligands

The asymmetric palladium-catalyzed benzylic reaction of 1-(2-naphthyl)ethyl acetate and its 6-methoxy substituted analogue with dimethyl malonate anion led to substitution products with up to 90% ee when the iPr-DUPHOS chiral ligand was used.     

Automated linkage of proteins and payloads producing monodisperse conjugates

Controlled protein functionalization holds great promise for a wide variety of applications. However, despite intensive research, the stoichiometry of the functionalization reaction remains difficult to control due to the inherent stochasticity of the conjugation process. Classical approaches that exploit peculiar structural features of specific protein substrates, or introduce reactive handles via mutagenesis, are by essence limited in scope or require substantial protein reengineering. We herein present equimolar native chemical tagging (ENACT), which precisely controls the stoichiometry of inherently random conjugation reactions by combining iterative low-conversion chemical modification, process automation, and bioorthogonal trans-tagging. We discuss the broad applicability of this conjugation process to a variety of protein substrates and payloads.

Controlled protein functionalization holds great promise for a wide variety of applications.

Applications of protein conjugates are limitless, including imaging, diagnostics, drug delivery, and sensing.^1–4 In many of these applications, it is crucial that the conjugates are homogeneous.⁵ The site-selectivity of the conjugation process and the number of functional labels per biomolecule, known as the degree of conjugation (DoC), are crucial parameters that define the composition of the obtained products and are often the limiting factors to achieving adequate performance of the conjugates. For instance, immuno-PCR, an extremely sensitive detection technique, requires rigorous control of the average number of oligonucleotide labels per biomolecule (its DoC) in order to achieve high sensitivity.⁶ In optical imaging, the performance of many super-resolution microscopy techniques is directly defined by the DoC of fluorescent tags.⁷ For therapeutics, an even more striking example is provided by antibody–drug conjugates, which are prescribed for the treatment of an increasing range of cancer indications.⁸ A growing body of evidence from clinical trials indicates that bioconjugation parameters, DoC and DoC distribution, directly influence the therapeutic index of these targeted agents and hence must be tightly controlled.⁹Standard bioconjugation techniques, which rely on nucleophile–electrophile reactions, result in a broad distribution of different DoC species (Fig. 1a), which have different biophysical parameters, and consequently different functional properties.¹⁰Open in a separate windowFig. 1Schematic representation of the types of protein conjugates.To address this key issue and achieve better DoC selectivity, a number of site-specific conjugation approaches have been developed (Fig. 1b). These techniques rely on protein engineering for the introduction of specific motifs (e.g., free cysteines,¹¹ selenocysteines,¹² non-natural amino acids,^13,14 peptide tags recognized by specific enzymes^15,16) with distinct reactivity compared to the reactivity of the amino acids present in the native protein. These motifs are used to simultaneously control the DoC (via chemo-selective reactions) and the site of payload attachment. Both parameters are known to influence the biological and biophysical parameters of the conjugates,¹¹ but so far there has been no way of evaluating their impact separately.The influence of DoC is more straightforward, with a lower DoC allowing the minimization of the influence of payload conjugation on the properties of the protein substrate. The lowest DoC that can be achieved for an individual conjugate is 1 (corresponding to one payload attached per biomolecule). It is noteworthy that DoC 1 is often difficult to achieve through site-specific conjugation techniques due to the symmetry of many protein substrates (e.g., antibodies). Site selection is a more intricate process, which usually relies on a systematic screening of conjugation sites for some specific criteria, such as stability or reactivity.¹⁷Herein, we introduce a method of accessing an entirely new class of protein conjugates with multiple conjugation sites but strictly homogenous DoCs (Fig. 1c). To achieve this, we combined (a) iterative low conversion chemical modification, (b) process automation, and (c) bioorthogonal trans-tagging in one workflow.The method has been exemplified for protein substrates, but it is applicable to virtually any native bio-macromolecule and payload. Importantly, this method allows for the first time the disentangling of the effects of homogeneous DoC and site-specificity on conjugate properties, which is especially intriguing in the light of recent publications revealing the complexity of the interplay between payload conjugation sites and DoC for in vivo efficacy of therapeutic bioconjugates.¹⁸ Finally, it is noteworthy that this method can be readily combined with an emerging class of site-selective bioconjugation reagents to produce site-specific DoC 1 conjugates, thus further expanding their potential for biotechnology applications.¹⁹     

Appointment-driven queueing systems with non-punctual customers

Queueing Systems - We consider a single-server queueing system where a finite number of customers arrive over time to receive service. Arrivals are driven by appointments, with a scheduled...     

Corona discharge secondary ionization of laser desorbed neutral molecules from a liquid matrix at atmospheric pressure

Matrix assisted laser desorption/ionization (MALDI) is studied at atmospheric pressure using liquid sampling methods. A time-of-flight mass spectrometer couples to an open sample stage accessed by a UV laser for desorption and ionization. Also coupled to the sampling state is a corona discharge for auxiliary ionization of desorbed neutral molecules. The interaction of the laser desorption and corona ionization is studied for a range of desorption conditions, showing enhanced analyte ionization, but the effect is analytically advantageous only at low desorption rates. The effect of corona discharge voltage was also explored. The decoupling of neutral molecule formation and subsequent ionization provides an opportunity to study each process separately.     

Adaptation of a commercial total reflection X-ray fluorescence system for wafer surface analysis equipped with a new generation of silicon drift detector

Within the framework of a collaborative project, it is shown that commercial total reflection X-ray fluorescence (TXRF) systems used in laboratories can easily be upgraded with a silicon drift detector (SDD). SDDs have advantages when used with fully automatized wafer analyzers working under cleanroom conditions, because no liquid nitrogen is required as they are electrically cooled. The goal of this work was the integration of a KETEK 10 mm² SDD in an ATOMIKA 8030W wafer analyzer with special attention to maintain the high degree of automation of the system. An electronic device was designed to establish communication between the SDD and the TXRF electronic control system. The adapted system was tested and compared with the original setup using an 80 mm² Si(Li) detector. Multielement droplet samples on silicon wafers were analyzed and the results showed two times better detection limits for the Si(Li) detector for 1000 pg Ni in comparison to the SDD. Additionally, a RADIANT 50 mm² SDD (VORTEX) was tested which showed identical detection limits compared to the 80 mm² Si(Li) detector.