On the average volume of sections of convex bodies

The average section functional as(K) of a star body in Rn is the average volume of its central hyperplane sections: \(as\left( k \right) = \int_{{S^{n - 1}}} {\left| {K \cap {\xi ^ \bot }} \right|} d\sigma \left( \xi \right)\). We study the question whether there exists an absolute constantC > 0 such that for every n, for every centered convex body K in R ⁿ and for every 1 ≤ k ≤ n ? 2,

$$as\left( K \right) \leqslant {C^k}{\left| K \right|^{\frac{k}{n}}}\mathop {\max }\limits_{|E \in G{r_{n - k}}} {\kern 1pt} as\left( {K \cap E} \right)$$

. We observe that the case k = 1 is equivalent to the hyperplane conjecture. We show that this inequality holds true in full generality if one replaces C by CL _K orCd_ovr(K, BP _k ⁿ ), where L _K is the isotropic constant of K and dovr(K, BP _k ⁿ ) is the outer volume ratio distance of K to the class BP _k ⁿ of generalized k-intersection bodies. We also compare as(K) to the average of as(K ∩ E) over all k-codimensional sections of K. We examine separately the dependence of the constants on the dimension when K is in some classical position. Moreover, we study the natural lower dimensional analogue of the average section functional.

     

An ab initio study of the E 3Πg state of the iodine molecule

The E (3)Π(g) state of the iodine molecule is studied by ab initio multireference methods coupled with effective core potentials and large basis sets. Two potential minima are found, a global featuring an ion-pair character, and a local presenting a purely Rydberg nature. Four avoided crossings along the dissociation coordinate attribute an interesting topology to its potential energy curve, and their effect on the vibrational levels of I(2) is discussed.     

Specializations of Multigradings and the Arithmetical Rank of Lattice Ideals

In this article, we study specializations of multigradings and apply them to the problem of the computation of the arithmetical rank of a lattice ideal I _{L 𝒢}  ? K[x ₁,…, x _n ]. The arithmetical rank of I _{L 𝒢} equals the ?-homogeneous arithmetical rank of I _{L 𝒢} , for an appropriate specialization ? of 𝒢. To the lattice ideal I _{L 𝒢} and every specialization ? of 𝒢, we associate a simplicial complex. We prove that combinatorial invariants of the simplicial complex provide lower bounds for the ?-homogeneous arithmetical rank of I _{L 𝒢} .     

Grothendieck groups arising from contravariantly finite subcategories

The subject of the paper is the study of the relative homological properties of a given additive category C in relation to a given contravariantly finite subcategory X in C under the assumption that any X-epic has a kernel in C. We introduce the notion of the Grothendieck group relative to the pair (C, X) and also that of the Cartan map cx relative to (C, X) and we show that the cokernel of cx is isomorphic to the corresponding Grothendieck group of the stable category C/Jx We also show that if the right x-dimension of C is finite, then cx is an isomorphism. In case C is a finite dimensional k-additive Krull-Schmidt category, we introduce the notion of the x-dimension vector of an object of C. We give criteria for when an indecomposable object is determined, up to isomorphism, by its x-dimension vector.     

Identification and quantification of glutathione adducts of clozapine using ultra-high-performance liquid chromatography with orthogonal acceleration time-of-flight mass spectrometry and inductively coupled plasma mass spectrometry

The application of sulphur-specific detection via ultra-performance liquid chromatography coupled to inductively coupled plasma mass spectrometry (UPLC/ICPMS) to detect and quantify the glutathione (GSH)-adducts produced via the in vitro formation of reactive metabolites is demonstrated. The adducts were formed in human liver microsomes supplemented with unlabelled GSH for clozapine. The calculation of adduct concentration was performed via comparison of the peak areas to calibration curves constructed from omeprazole, a sulphur-containing compound over the range of 0.156 to 15.62 μM of sulphur with a detection limit of 1.02 ng of sulphur on-column. Identification of the adducts was performed using conventional UPLC/time-of-flight (TOF)-MS with the calculation of clozapine intrinsic clearance carried out by high-performance liquid chromatography/tandem mass spectrometry (HPLC/MS/MS). The use of ICPMS in this way appears to offer a novel, rapid and sensitive means of determining the quantity of GSH conjugates with the combined adducts producing 0.9 μM of reactive metabolite out of a total of 3.5 μM of metabolites. The GSH adduct therefore represents 26% of this total produced as a result of the metabolism of drug to reactive species.     

Ultrasensitive Determination of Vitamin B12 Using Disposable Graphite Screen‐Printed Electrodes and Anodic Adsorptive Voltammetry

A facile, rapid and ultra‐sensitive method for the determination of vitamin B₁₂ (cyanocobalamin) at the sub‐nanomolar concentration range by using low‐cost, disposable graphite screen‐printed electrodes is described. The method is based on the cathodic preconcentration of square planar vitamin B_12s, as occurred due to the electro reduction of Co(III) center in vitamin B_12a to Co(I), at ?1.3 V versus Ag/AgCl/3 M KCl for 40 s. Then, an anodic square wave scan was applied and the height of the peak appeared at ca. ?0.73 V versus Ag/AgCl/3 M KCl, due to the oxidation of Co(I) to Co(II) in the adsorbed molecule, was related to the concentration of the vitamin B₁₂ in the sample. EDTA was found to serve as a key‐component of the electrolyte by eliminating the background signal caused by metal cations impurities contained in the electrolyte (0.1 M phosphate buffer in 0.1 M KCl, pH 3). It also blocks trace metals contained in real samples, thus eliminating their interference effect. The method was optimized to various working parameters and under the selected conditions the calibration curve was linear over the range 1×10^?10–8×10^?9 mol L^?1 vitamin B₁₂ (R²=0.994), while the limit of detection for a signal‐to‐noise ratio of 3 (7×10^?11 mol L^?1 vitamin B₁₂) is the lowest value of any reported in the literature for the electrochemical determination of vitamin B₁₂. The sensors were successfully applied to the determination of vitamin B₁₂ in pharmaceutical products.     

Facile and Low-Cost SPE Modification Towards Ultra-Sensitive Organophosphorus and Carbamate Pesticide Detection in Olive Oil

Despite the fact that a considerable amount of effort has been invested in the development of biosensors for the detection of pesticides, there is still a lack of a simple and low-cost platform that can reliably and sensitively detect their presence in real samples. Herein, an enzyme-based biosensor for the determination of both carbamate and organophosphorus pesticides is presented that is based on acetylcholinesterase (AChE) immobilized on commercially available screen-printed carbon electrodes (SPEs) modified with carbon black (CB), as a means to enhance their conductivity. Most interestingly, two different methodologies to deposit the enzyme onto the sensor surfaces were followed; strikingly different results were obtained depending on the family of pesticides under investigation. Furthermore, and towards the uniform application of the functionalization layer onto the SPEs’ surfaces, the laser induced forward transfer (LIFT) technique was employed in conjunction with CB functionalization, which allowed a considerable improvement of the sensor’s performance. Under the optimized conditions, the fabricated sensors can effectively detect carbofuran in a linear range from 1.1 × 10^?9 to 2.3 × 10^?8 mol/L, with a limit of detection equal to 0.6 × 10^?9 mol/L and chlorpyrifos in a linear range from 0.7 × 10^?9 up to 1.4 × 10^?8 mol/L and a limit of detection 0.4 × 10^?9 mol/L in buffer. The developed biosensor was also interrogated with olive oil samples, and was able to detect both pesticides at concentrations below 10 ppb, which is the maximum residue limit permitted by the European Food Safety Authority.     

Rapid Microwave-Assisted Synthesis of CdS/Graphene/MoSx Tunable Heterojunctions and Their Application in Photocatalysis

Nanoscale two-dimensional nanostructures have shown great potential as functional components in photocatalysis. Here, investigations on the synthesis of heterostructured hybrids, comprised of 0D CdS nanoparticles as semiconductor and 2D/2D graphene/MoS_x as co-catalyst, are reported. The approach involves a rapid microwave-assisted reaction in autoclave conditions, by adopting either a one-step or a two-step protocol. The chemical speciation of the nanocomposites was found to depend strongly on the compounding conditions of the precursor substances. The photocatalytic activity was assessed by monitoring the photodegradation rate of 4-nitrophenol in solution using simulated solar light irradiation. The photocatalytic activity of the hybrids may be attributed to a combination of beneficial characteristics, strongly related to the chemical speciation of the composite components. Moreover, intimate contacts of the latter result in efficient heterojunctions. Overall, the present study provides valuable insight into the development of functional heterostructured photocatalysts comprised of two-dimensional nanomaterials.