A characterization of the non-Baer lines of a Hermitian surface

We give a characterization of the set of the lines which either belong to or are tangent to a non-singular Hermitian surface in the projective space of dimension 3 and order q ².     

(1,2,3,4,7-Pentamethylindenyl)rhodium complexes with arene ligands

The reaction of (η⁵-C₉H₂Me₅)Rh(1,5-C₈H₁₂) (1) with I₂ gives the iodide complex [(η⁵-C₉H₂Me₅)RhI₂]₂ (2). The solvate complex [(η⁵- C₉H₂Me₅)Rh(MeNO₂)₃]²⁺ (generated in situ by treatment of 2 with Ag⁺ in nitromethane) reacts with benzene and its derivatives giving the dicationic arene complexes [(η⁵-₉H₂Me₅)Rh(arene)]²⁺ [arene = C₆H₆ (3a), C₆Me₆ (3b), C₆H₅OMe (3c)]. Similar reaction with the borole sandwich compound CpRh(η⁵-C₄H₄BPh) results in the arene-type complex [CpRh(μ-η⁵:η⁶-C₄H₄BPh)Rh(η⁵-C₉H₂Me₅)]²⁺ (4). Treatment of 2 with CpTl in acetonitrile affords cation [(η⁵-C₉H₂Me₅)RhCp]⁺ (5). The structure of [3c](BF₄)₂ was determined by X-ray diffraction. The electrochemical behaviour of complexes prepared was studied. The rhodium-benzene bonding in series of the related complexes [(ring)Rh(C₆H₆)]²⁺ (ring = Cp, Cp^∗, C₉H₇, C₉H₂Me₅) was analyzed using energy and charge decomposition schemes.     

Heisenberg-Pauli-Weyl uncertainty inequalities and polynomial volume growth

In its simpler form, the Heisenberg-Pauli-Weyl inequality says that

     

Stability-based biomarker selection

Biomarker identification, i.e., finding those variables that indicate true differences between two or more populations, is an ever more important topic in the omics sciences. In most cases, the number of variables far exceeds the number of samples, making biomarker identification extremely difficult. We present a strategy based on the stability of putative biomarkers under perturbation of the data, and show that in several cases important gains can be achieved. The strategy is very general and can be applied with all common biomarker identification methods; it also has the advantage that it does not rely on error estimates from crossvalidation, that in this setting tend to be highly variable.     

Challenges in thermal noise for 3rd generation of gravitational wave detectors

Various noise sources limit the sensitivity of current interferometric gravitational wave detectors, including seismic noise, thermal noise of the optical components and suspension elements and photon shot noise. Plans are in place for a suite of hardware upgrades which should increase the sensitivity of these detectors by reducing the various noise sources. With these designs for 2nd generation detectors mature, techniques for further improvement of detector sensitivity by a factor of approximately 10 are under study. A particular challenge is the reduction of the thermal noise associated with the interferometer mirrors and their suspensions. We review the current status of research on thermal noise in interferometric gravitational wave detectors. Aspects of possible techniques for use in future ‘3rd generation detectors’ such as cryogenics and diffractive optics are discussed.     

Retention prediction of a set of amino acids under gradient elution conditions in hydrophilic interaction liquid chromatography

The analysis of amino acids presents significant challenges to contemporary analytical separations. The present paper investigates the possibility of retention prediction in hydrophilic interaction chromatography (HILIC) gradient elution based on the analytical solution of the fundamental equation of the multilinear gradient elution derived for reversed‐phase systems. A simple linear dependence of the logarithm of the solute retention (ln k) upon the volume fraction of organic modifier (φ) in a binary aqueous‐organic mobile is adopted. Utility of the developed methodology was tested on the separation of a mixture of 21 amino acids carried out with 14 different gradient elution programs (from simple linear to multilinear and curved shaped) using ternary eluents in which a mixture of methanol and water (1:1, v/v) was the strong eluting member and acetonitrile was the weak solvent. Starting from at least two gradient runs, the prediction of solute retention obtained under all the rest gradients was excellent, even when curved gradient profiles were used. Development of such methodologies can be of great interest for a wide range of applications.     

D-optimal design of an untargeted HS-SPME-GC-TOF metabolite profiling method

In recent times we have seen the development of many "-omics" technologies. One of the youngest is undoubtedly metabolomics, which aims to define the whole chemical fingerprint unique to each specific organism. The development and optimisation of an untargeted high-throughput method capable of investigating the volatile fraction of a biological system represents a crucial step for the success of such holistic approaches, and specific optimisation criteria must be developed in connection with suitable experimental designs. In this paper experimental designs (D-optimal) were applied for the first time as an automatic optimisation tool to an untargeted HS-SPME-GC-TOF method. In this case, optimal conditions correspond to a maximal number of detected features, in order to provide a fingerprint that is as complete as possible. The system under study is the grape berry. Four variables were considered: the type of fibre, extraction time, equilibration time and temperature. The results show that the D-optimal design methodology provides an easily interpretable assessment of experimental settings. This and other specific properties of the D-optimal design, such as the possibility to explicitly exclude certain experimental conditions, make it an extremely suitable strategy for method optimisation in untargeted metabolomics.     

Population branching in the conical intersection of the retinal chromophore revealed by multipulse ultrafast optical spectroscopy

The branching ratio of the excited-state population at the conical intersection between the S(1) and S(0) energy surfaces (Φ(CI)) of a protonated Schiff base of all-trans retinal in protic and aprotic solvents was studied by multipulse ultrafast transient absorption spectroscopy. In particular, pump-dump-probe experiments allowed to isolate the S(1) reactive state and to measure the photoisomerization time constant with unprecedented precision. Starting from these results, we demonstrate that the polarity of the solvent is the key factor influencing the Φ(CI) and the photoisomerization yield.