Bilinear optimality constraints for the cone of positive polynomials

For a proper cone \({{\mathcal K}\subset\mathbb{R}^n}\) and its dual cone \({{\mathcal K}^*}\) the complementary slackness condition \({\langle{\rm {\bf x}},{\rm {\bf s}}\rangle=0}\) defines an n-dimensional manifold \({C({\mathcal K})}\) in the space \({{\mathbb R}^{2n}}\) . When \({{\mathcal K}}\) is a symmetric cone, points in \({C({\mathcal K})}\) must satisfy at least n linearly independent bilinear identities. This fact proves to be useful when optimizing over such cones, therefore it is natural to look for similar bilinear relations for non-symmetric cones. In this paper we define the bilinearity rank of a cone, which is the number of linearly independent bilinear identities valid for points in \({C({\mathcal K})}\) . We examine several well-known cones, in particular the cone of positive polynomials \({{\mathcal P}_{2n+1}}\) and its dual, and show that there are exactly four linearly independent bilinear identities which hold for all \({({\rm {\bf x}},{\rm {\bf s}})\in C({\mathcal P}_{2n+1})}\), regardless of the dimension of the cones. For nonnegative polynomials over an interval or half-line there are only two linearly independent bilinear identities. These results are extended to trigonometric and exponential polynomials. We prove similar results for Müntz polynomials.     

Comparative electrochemical study of new self-assembled monolayers of 2-{[(Z)-1-(3-furyl)methylidene]amino}-1-benzenethiol and 2-{[(2-sulfanylphenyl)imino]methyl}phenol for determination of dopamine in the presence of high concentration of ascorbic acid and uric acid

The comparative electrochemical behavior of self-assembled monolayers of two Schiff's bases, 2-{[(Z)-1-(3-furyl)methylidene]amino}-1-benzenethiol (FMAB) and 2-{[(2-sulfanylphenyl)imino]methyl}phenol (SIMP) on a bare gold electrode (Au FMAB SAM-modified electrode and Au SIMP SAM-modified electrode, respectively), was investigated by means of cyclic voltammetry and electrochemical impedance spectroscopy in a 0.1 mol L(-1) KCl solution that contains 5.0 × 10(-3) mol L(-1) [Fe(CN)(6)](3-/4-). The results revealed that the modified electrodes showed an electrocatalytic activity toward the anodic oxidation of dopamine by a marked enhancement in the current response and lower overpotential (60 and 90 mV for the Au FMAB and Au SIMP SAM-modified electrodes, respectively) in phosphate buffer solution at pH 6.0. The Au SIMP SAM-modified electrode was applied successfully to the determination of dopamine in the presence of a high concentration of ascorbic acid. Selective detection was realized in total elimination of ascorbic acid response-a method different from the ones based on the potential separations. The detection limit of dopamine was 5.0 × 10(-8) mol L(-1) in a linear range from 1.0 × 10(-6) to 1.2 × 10(-4) mol L(-1) in the presence of 1.0 × 10(-3) mol L(-1) ascorbic acid. The interference studies also showed that the Au SIMP SAM-modified electrode exhibited good selectivity in the presence of a large excess of uric acid and could be employed for the determination of dopamine in pharmaceutical formulations, plasma samples and human urine with adequate selectivity and precision.     

A new solid phase micro extraction for simultaneous head space extraction of ultra traces of polar and non-polar compounds

The results of the innovative study on a new stationary phase with high efficiency based on ZnO nano and micro rod coating on fused silica are reported in this paper. ZnO nanorods with a diameter in the range of 70–300 nm and the length of about 500 nm, have been grown on fused silica fibers using a hydrothermal process. The extraction properties of the fiber were investigated using headspace solid-phase microextraction (HS-SPME) mode coupled with gas chromatography–mass spectrometry detection (GC–MS) for 1,4-dichloro-nitrobenzene, biphenyl and acenaphthene. The calibration curves were linear up to 10²–10⁷ ng L⁻¹ (R² > 0.995) with detection limits of 10⁻³ ng L⁻¹ for biphenyl and acenaphthene and 10 ng L⁻¹ for 1,4-dichloro-nitrobenzene. The RSD for single fiber and fiber-to-fiber were less than 7.0 and 11.5%, respectively. The high stability of the ZnO coating is proved at relatively high temperatures (up to 300 °C) with a high extraction capacity and long lifespan (more than 100 times). Promising recoveries (91–102%) were obtained in environmental water samples analysis by applying the proposed technique.     

Rapid and Facile Access to Indeno[1,2‐d]imidazoles via a Tandem Addition?Cyclization Reaction

A novel and tandem synthesis of highly functionalized tetrahydroindeno[1,2‐d]imidazole is described. A one‐pot reaction between a primary amine, an aryl isothiocyanate, and ninhydrin leads to highly substituted indeno[1,2‐d]imidazoles under solvent‐free conditions in excellent yields (Scheme). Their structures were corroborated spectroscopically (IR, ¹H‐ and ¹³C‐NMR, and EI‐MS) and by elemental analyses.     

Isocyanide-based multicomponent reactions: synthesis of alkyl-2-(1-(alkylcarbamoyl)-2,2-dicyanoethyl)benzoate and isochromeno[3,4-b]pyrrole derivatives

A novel four-component reaction between 2-formylbenzoic acids, malononitrile, isocyanides, and alcohols has been developed for a highly efficient preparation of alkyl-2-(1-(alkylcarbamoyl)-2,2-dicyanoethyl)benzoate derivatives. This high atom economy reaction led to the construction of two carbon-carbon bonds, one amide, and one ester group in a single synthetic step. Furthermore, a three-component reaction between 2-formylbenzoic acids, malononitrile, and isocyanides in dichloromethane for the preparation of isochromeno[3,4-b]pyrroles has been reported.     

Study binding of Al-curcumin complex to ds-DNA, monitoring by multispectroscopic and voltammetric techniques

In this work a complex of Al3+ with curcumin ([Al(curcumin) (EtOH)2](NO3)2) was synthesized and characterized by UV-vis, FT-IR, elemental analysis and spectrophotometric titration techniques. The mole ratio plot revealed a 1:1 complex between Al3+ and curcumin in solution. For binding studies of this complex to calf thymus-DNA various methods such as: UV-vis, fluorescence, circular dichroism (CD), FT-IR spectroscopy and cyclic voltammetry were used. The intrinsic binding constant of ACC with DNA at 25°C was calculated by UV-vis and cyclic voltammetry as 2.1×10(4) and 2.6×10(4), respectively. The thermodynamic studies showed that the reaction is enthalpy and entropy favored. The CD results showed that only the Δ-ACC interacts with DNA and the Δ-ACC form has not any tendency to interact with DNA, also the pure curcumin has not any stereoselective interaction with CT-DNA. Fluorimetric studies showed that fluorescence enhancement was initiated by a static process in the ground state. The cyclic voltammetry showed that ACC interact with DNA with a binding site size of 2. From the FT-IR we concluded that the Δ-ACC interacts with DNA via partial electrostatic and minor groove binding. In comparison with previous works it was concluded that curcumin significantly reduced the affinity of Al3+ to the DNA.     

Mixed mode axisymmetric annular cracks in a finite layer: Off angle crack initiation

The solutions of axisymmetric Volterra type climb and glide edge dislocations are obtained in a layer by means of the Hankel transforms. Utilizing the same procedure, Green’s function solution is obtained for a layer under self-equilibration normal ring traction. The distributed dislocation technique is used to construct integral equations for a system of co-axial annular cracks where the layer is under axisymmetric normal loads. These equations are solved numerically to obtain dislocation density on the cracks surfaces. The results are employed to determine stress intensity factors for annular and penny-shaped cracks and the interaction between two co-axial penny-shaped cracks is studied. Moreover, the stress intensity factors of the interacting cracks are determined such that they can be further used in conjunction with strain energy density (SED) failure criterion to obtain the possible direction of crack initiation that may not be apparent under mixed mode conditions.     

Continuous and discrete flows over time

Network flows over time form a fascinating area of research. They model the temporal dynamics of network flow problems occurring in a wide variety of applications. Research in this area has been pursued in two different and mainly independent directions with respect to time modeling: discrete and continuous time models. In this paper we deploy measure theory in order to introduce a general model of network flows over time combining both discrete and continuous aspects into a single model. Here, the flow on each arc is modeled as a Borel measure on the real line (time axis) which assigns to each suitable subset a real value, interpreted as the amount of flow entering the arc over the subset. We focus on the maximum flow problem formulated in a network where capacities on arcs are also given as Borel measures and storage might be allowed at the nodes of the network. We generalize the concept of cuts to the case of these Borel Flows and extend the famous MaxFlow-MinCut Theorem.     

On fail‐safe systems under random shocks

In practical situations, systems often suffer shocks from external stressing environments, stressing the system at random. These random shocks may have non‐ignorable effects on the system's reliability. In this paper, we provide sufficient (and necessary) conditions on components' lifetimes and their surviving probabilities from random shocks for comparing the lifetimes of two fail‐safe systems by means of the usual stochastic, hazard rate, and likelihood ratio orderings. Numerical examples are presented to highlight these theoretical results as well.     

On the Schröder–Bernstein property for modules

The well known Schröder–Bernstein Theorem states that any two sets with one to one maps into each other are isomorphic. The question of whether any two (subisomorphic or) direct summand subisomorphic algebraic structures are isomorphic, has long been of interest. Kaplansky asked whether direct summands subisomorphic abelian groups are always isomorphic? The question generated a great deal of interest. The study of this question for the general class of modules has been somewhat limited. We extend the study of this question for modules in this paper. We say that a module Msatisfies the Schröder–Bernstein property (S-B property) if any two direct summands of M which are subisomorphic to direct summands of each other, are isomorphic. We show that a large number of classes of modules satisfy the S-B property. These include the classes of quasi-continuous, directly finite, quasi-discrete and modules with ACC on direct summands. It is also shown that over a Noetherian ring R, every extending module satisfies the S-B property. Among applications, it is proved that the class of rings R for which every R-module satisfies the S-B property is precisely that of pure-semisimple rings. We show that over a commutative domain R, any two quasi-continuous subisomorphic R-modules are isomorphic if and only if R is a PID. We study other conditions related to the S-B property and obtain characterizations of certain classes of rings via those conditions. Examples which delimit and illustrate our results are provided.