Analytical Properties Research Articles

Chemically Modified Electrodes Based on 4-((5-Isopropyl-3,8-dimethylazulen-1-yl)methylene)-2-phenyloxazol-5(4H)-one

Novel chemically modified electrodes (CMEs) based on azulene were prepared by electrooxidation of guaiazulene derivative 4-((5-isopropyl-3,8-dimethylazulen-1-yl)methylene)-2-phenyloxazol-5(4H)-one (G). G is based on guaiazulene non-alternating aromatic hydrocarbon exhibiting a less symmetrical structure compared to naphthalene skeletal derivative. Therefore, it can be used as a building block for the preparation of novel materials. To evaluate the chemical structure and surface images, the CMEs based on G (G-CMEs) were characterized by ferrocene redox probe, X-ray photon spectroscopy (XPS), and scanning electron microscopy (SEM). They were also tested for the analysis of synthetic samples of heavy metal (HM) ions. The influence of preparation conditions (electric charge and potential) on the properties of these CMEs was examined. This paper highlights the importance of electropolymerization conditions on electrodeposited film surfaces, especially on their analytical properties vs. Cd(II), Pb(II), Cu(II), and Hg(II) investigated ions. This study is relevant for further design and development of advanced materials based on azulenyl-phenyloxazolone for the HM analysis in water. A linear dependence of the peak currents for Pb(II) ion on the concentration in test aqueous solutions was obtained between 10−7 M and 5·10−5 M. The detection limits of 5·10−6 M; 10−7 M; 5·10−6 M; and 10−5 M were estimated for Cd(II), Pb(II), Cu(II), and Hg(II), respectively, for G-CMEs.

Generating arbitrary analytically solvable two-level systems

We present a new approach for generating arbitrary analytically solvable two-level systems. This method offers the ability to completely derive all analytically solvable Hamiltonians for any analytical evolutions of two-level systems. To demonstrate the effectiveness of this approach, we reconstruct the Rosen–Zener model and generate several new exact solutions. Using this approach, we present the exact evolution of the semi-classical Rabi model with new analytical properties. The parameters used to generate Hamiltonians have direct physical interpretations within the Bloch sphere, the quantum speed limit, and the geometric phase. As a result, the physical properties of the generated Hamiltonian are highly controllable, which plays a significant role in the fields of quantum control, quantum computing, and quantum information.

Dielectric Detection of Single Nanoparticles Using a Microwave Resonator Integrated with a Nanopore.

The characterization of individual nanoparticles in a liquid constitutes a critical challenge for the environmental, material, and biological sciences. To detect nanoparticles, electronic approaches are especially desirable owing to their compactness and lower costs. While electronic detection in the form of resistive-pulse sensing has enabled the acquisition of geometric properties of various analytes, impedimetric measurements to obtain dielectric signatures of nanoparticles have scarcely been reported. To explore this orthogonal sensing modality, we developed an impedimetric sensor based on a microwave resonator with a nanoscale sensing gap surrounding a nanopore built on a 220 nm silicon nitride membrane. The microwave resonator has a coplanar waveguide configuration with a resonance frequency of approximately 6.6 GHz. The approach of single nanoparticles near the sensing region and their translocation through the nanopores induced sudden changes in the impedance of the structure. The impedance changes, in turn, were picked up by the phase response of the microwave resonator. We worked with 100 and 50 nm polystyrene nanoparticles to observe single-particle events. Our current implementation was limited by the nonuniform electric field at the sensing region. This work provides a complementary sensing modality for nanoparticle characterization, where the dielectric response, rather than ionic current, determines the signal.

Development of a New Amperometric Biosensor for Measurement of Plasma Galactose Levels.

Galactosemia is an inherited disease that occurs as a result of insufficient or no synthesis of some enzymes (GALT, GALK, and GALE) in galactose metabolism. Failure to make an early diagnosis, especially in newborns, can lead to severe clinical and even fatal consequences. The aim of this study is to develop a biosensor for measuring free galactose in plasma. The immobilization components of the developed free galactose biosensor are screen printed carbon electrode (SCPE), Prussian blue (PB), chitosan (CHIT), Nafion (NAF), gold nanoparticle (GNP), and galactose oxidase (GaOX). The CHIT/GaOX/NAF-GNP/GaOX/CHIT-GNP/SCPE-PB electrode showed a sensitive amperometric response to detect galactose. While the surface characterization of the biosensor was performed with cyclic voltammetry and scanning electron microscopy, the optimization and performance characterizations were made by applying an amperometry technique. The amperometric operating potential for the free galactose biosensor was determined as -0.05 V. The linear detection range for the free galactose biosensor is between 0.025 and 10 mM. This range includes galactose levels in plasma of both healthy and patients. The percent coefficient of variation values calculated for intraday and interday repeatability of the developed biosensor are below 10%. The practical use of the biosensor, for which optimization and characterization studies were carried out, was tested in 10 healthy 11 patients with galactosemia, and the results were compared with the colorimetric method. In conclusion, the unique analytical properties and effortless preparation of the new galactose biosensor developed in this study make them serious candidates for point-of-care diagnostic testing.

Multi‐soliton solutions of the three‐level coupled Schrödinger Maxwell‐Bloch equations via the Riemann‐Hilbert approach

In this paper, a study of the coupled Schrödinger Maxwell‐Bloch equations, which described the propagation of two optical pulses in an optical medium with coherent three‐level atoms, is presented via the Riemann‐Hilbert approach. First, we performed a spectral analysis on the basis of Lax pair with the negative flow, and then the Jost function, scattering matrix, and their analytic and symmetric properties are given. Second, the Riemann‐Hilbert problem is established successfully through a standard dressing procedure via the Riemann‐Hilbert approach, and then the potential function related to the solution of the Riemann‐Hilbert problem is reconstructed. By introducing the special matrix functions, we can transform the irregular Riemann‐Hilbert problem into the regular one, which can be solved by the Plemelj formula. Finally, some applications are given to solve the Riemann‐Hilbert problem without reflection for the coupled Schrödinger Maxwell‐Bloch equation, and the multi‐soliton solutions are obtained explicitly. Moreover, the dynamic behaviors of some soliton solutions are discussed graphically by choosing appropriate parameters.

Recent Advances in Real-Time Label-Free Detection of Small Molecules.

The detection and analysis of small molecules, typically defined as molecules under 1000 Da, is of growing interest ranging from the development of small-molecule drugs and inhibitors to the sensing of toxins and biomarkers. However, due to challenges such as their small size and low mass, many biosensing technologies struggle to have the sensitivity and selectivity for the detection of small molecules. Notably, their small size limits the usage of labeled techniques that can change the properties of small-molecule analytes. Furthermore, the capability of real-time detection is highly desired for small-molecule biosensors' application in diagnostics or screening. This review highlights recent advances in label-free real-time biosensing technologies utilizing different types of transducers to meet the growing demand for small-molecule detection.

On the geometric and analytical properties of the anharmonic oscillator

Here we consider the anharmonic oscillator that is a dynamical system given by yxx+δyn=0. We demonstrate that to this equation corresponds a new example of a superintegrable two-dimensional metric with a linear and a transcendental first integrals. Moreover, we show that for particular values of n the transcendental first integral degenerates into a polynomial one, which provides an example of a superintegrable metric with additional polynomial first integral of an arbitrary even degree. We also discuss a general procedure of how to construct a superintegrable metric with one linear first integral from an autonomous nonlinear oscillator that is cubic with respect to the first derivative. We classify all cubic oscillators that can be used in this construction. Furthermore, we study the Liénard equations that are equivalent to the anharmonic oscillator with respect to the point transformations. We show that there are nontrivial examples of the Liénard equations that belong to this equivalence class, like the generalized Duffing oscillator or the generalized Duffing–Van der Pol oscillator.

RANSBox: A zero-dimensional modular software package for Reynolds-averaged Navier-Stokes modeling

RANSBox is a zero-dimensional software package for Reynolds-averaged Navier-Stokes (RANS) modeling developed at Lawrence Livermore National Laboratory to support common implementation of RANS models across a variety of host codes with different numerical schemes and code bases. This work describes the key features of RANSBox including “model-agnostic integration,” which allows new models to be implemented in RANSBox and quickly deployed to host codes without additional changes to the host code base. Three one-dimensional test problems with analytical asymptotic properties are described which can be used to verify correctness of RANSBox integration. Results for these problems are then compared across different RANS models in a single code and across different codes with a common RANS model. By using a common model implementation in RANSBox, host codes with different numerical schemes and formal orders of accuracy are demonstrated to predict the expected behavior for the three test problems.

Electrosynthesis of toluidine blue on Fe3O4 nanoparticles modified electrodes in a deep eutectic solvent for the electrochemical determination of neurotransmitter epinephrine

The electrochemical methodology is important and challenging for rapid, simple, low-cost, sensitive, selective and reliable determination of biomolecules to diagnose and treat diseases. Our work presents the combination of the catalytic ability of a toluidine blue (TB) redox polymer and the important physical and chemical properties of Fe3O4 nanoparticles (Fe3O4NPs) to develop a new disposable sensor with advanced analytical performancecharacteristics for the determination of EP. Fe3O4NPs combined with poly(toluidine blue) (PTB) redox polymer film on a PGE support have been developed involving electropolymerization of TB in deep eutectic solvents (DES), which is a green solvent. Scanning electron microscopy (SEM) was used to evaluate the effect of the electrode composition on the surface morphology of the nanostructured PTB films, being correlated with the electrochemical characteristics observed by cyclic voltammetry (CV), electrochemical impedance spectroscopy (EIS), and differential pulse voltammetry (DPV). It has been shown that combining Fe3O4NPs with PTB synthesized in DES improves the analytical properties of the sensor more than using each modifier individually due to synergistic effects. The analytical performance of PTBethaline-HCl/Fe3O4/PGE was evaluated for epinephrine (EP) reduction in the presence of an excess dopamine (DA) by DPV. The proposed sensor was used to determine EP using the reduction peak as a voltammetric signal instead of the oxidation peak usually employed to minimize possible interfering effects in biological samples. The developed sensor showed good response with high sensitivity (9.26 µA µM−1 cm−2), low detection limit (0.05 µM), wide linear range (0.19–20 µM), and excellent reproducibility (RSD 1.7 %) and repeatability (RSD 2.9 %). The practical applicability of the proposed sensor has been successfully tested for the quantification of EP in human serum and injection ampoule samples. This is a very promising analytical method for monitoring the level of EP in real samples.

Accurate Quantum States for a 2D-Dipole.

Edge dislocations are crucial in understanding both mechanical and electrical transport in solid and are modeled as line distributions of dipole moments. The calculation of the electronic spectrum for the two dimensional dipole, represented by the potential energy V(r,θ)=pcosθ/r, has been the topic of several studies that show significant difficulties in obtaining accurate results. In this work, we demonstrate that the source of these difficulties is a logarithmic contribution to the behavior of the wave function at the origin that was neglected by previous authors. By taking into account this non-analytic deviation of the solution of Schrödinger's equation, superior results, with the expected rate of convergence, are obtained. This goal is accomplished by "adapting" general algorithms for solving partial derivative differential equations to include the desired asymptotic behavior. We illustrate this principle for the variational principle and finite difference methods. Accurate energies and wave functions are obtained not only for the ground state but also for the first eleven excited states and are useful for designing nanoelectronic devices. This paper demonstrates that augmentary knowledge about analytic properties of the solutions leads to the improved convergence and stability of numerical methods.

Von Neumann equivalence and properly proximal groups

We introduce a new equivalence relation on groups, which we call von Neumann equivalence, that is coarser than both measure equivalence and W⁎-equivalence. We introduce a general procedure for inducing actions in this setting and use this to show that many analytic properties, such as amenability, property (T), and the Haagerup property, are preserved under von Neumann equivalence. We also show that proper proximality, which was defined recently in [9] using dynamics, is also preserved under von Neumann equivalence. In particular, proper proximality is preserved under both measure equivalence and W⁎-equivalence, and from this we obtain examples of non-inner amenable groups that are not properly proximal.

Hankel transform, [formula omitted]-Bessel functions and zeta distributions in the Dunkl setting

We study analytic properties of a Hankel transform for the type A Dunkl setting with arbitrary multiplicity parameter k≥0 which goes back to Baker and Forrester and, in an earlier symmetrized version, to Macdonald. Moreover, we introduce a Dunkl analogue of the Bessel functions and K-Bessel functions, generalizing those of a symmetric cone which occur when the multiplicity parameter k is chosen to be twice the Peirce dimension constant of the cone. In particular, we show that our K-Bessel function is a solution of a type B system of Dunkl operators which is a generalization of the Bessel system on a symmetric cone. Furthermore, we define zeta distributions and prove a functional equation relating them with their type B Dunkl transform. In the case of symmetric cones the aforementioned functional equation reduces to the known functional equation between zeta distributions and their Fourier transform. For the proof of this functional equation, the K-Bessel function and its analytic properties turn out to be crucial. Finally, we examine which of the zeta distributions are given by a positive measure.

Strong user rights in fisheries: An editorial note

This is an editorial note for the special issue: Strong User Rights in Fisheries (SURFs). SURFs are rights that constitute a subset of the wider category of rights in fisheries. Being held by the existing operators in the fishery, SURFs may be more acceptable than other fisheries rights. The special issue contains eight (8) papers addressing various issues concerning SURFs such as the theoretical and analytical properties of SURFs, empirical verification of SURF theory, case studies of the impacts of SURFs and challenges to achieve agreements in international fisheries required for the establishment of SURFs.

Nonequilibrium Schwinger-Keldysh formalism for density matrix states: Analytic properties and implications in cosmology

Motivated by cosmological Hartle-Hawking and microcanonical density matrix prescriptions for the quantum state of the Universe we develop a Schwinger-Keldysh in-in formalism for generic nonequilibrium dynamical systems with the initial density matrix. We build the generating functional of in-in Green’s functions and expectation values for a generic density matrix of the Gaussian type and show that the requirement of particle interpretation selects a distinguished set of positive/negative frequency basis functions of the wave operator of the theory, which is determined by the density matrix parameters. Then we consider a special case of the density matrix determined by the Euclidean path integral of the theory, which in the cosmological context can be considered as a generalization of the no-boundary pure state to the case of the microcanonical ensemble, and show that in view of a special reflection symmetry its Wightman Green’s functions satisfy Kubo-Martin-Schwinger periodicity conditions which hold despite the nonequilibrium and nonstationary nature of the physical setup. Rich analyticity structure in the complex plane of the time variable reveals the combined Euclidean-Lorentzian evolution of the theory, which depending on the properties of the initial density matrix can be interpreted as a decay of a classically forbidden quantum state. Published by the American Physical Society 2024

Central factorial numbers are Pólya frequency sequences

The central factorial numbers are closely related to the central difference operator, and have received increasing attention from combinatorialists recently. Known properties of the central factorial numbers include their generating functions, recurrence relation and combinatorial interpretations. The purpose of this work is to adjoin to the list the analytical property that the generating functions of central factorial numbers of odd, and even, indices, are simply real-rooted, thus establishing the numbers being Pólya frequency sequences.

Global properties of generic real–analytic nearly–integrable Hamiltonian systems

We introduce a new class Gsn of generic real analytic potentials on Tn and study global analytic properties of natural nearly–integrable Hamiltonians 12|y|2+εf(x), with potential f∈Gsn, on the phase space M=B×Tn with B a given ball in Rn. The phase space M can be covered by three sets: a ‘non–resonant’ set, which is filled up to an exponentially small set of measure e−cK (where K is the maximal size of resonances considered) by primary maximal KAM tori; a ‘simply resonant set’ of measure εKa and a third set of measure εKb which is ‘non perturbative’, in the sense that the H–dynamics on it can be described by a natural system which is not nearly–integrable. We then focus on the simply resonant set – the dynamics of which is particularly interesting (e.g., for Arnol'd diffusion, or the existence of secondary tori) – and show that on such a set the secular (averaged) 1 degree–of–freedom Hamiltonians (labeled by the resonance index k∈Zn) can be put into a universal form (which we call ‘Generic Standard Form’), whose main analytic properties are controlled by only one parameter, which is uniform in the resonance label k.

Multiplicative topological indices: Analytical properties and application to random networks

<abstract><p>We consider two general classes of multiplicative degree-based topological indices (MTIs), denoted by $ X_{\Pi, F_V}(G) = \prod_{u \in V(G)} F_V(d_u) $ and $ X_{\Pi, F_E}(G) = \prod_{uv \in E(G)} F_E(d_u, d_v) $, where $ uv $ indicates the edge of $ G $ connecting the vertices $ u $ and $ v $, $ d_u $ is the degree of the vertex $ u $, and $ F_V(x) $ and $ F_E(x, y) $ are functions of the vertex degrees. This work has three objectives: First, we follow an analytical approach to deal with a classical topic in the study of topological indices: to find inequalities that relate two MTIs between them, but also to their additive versions $ X_\Sigma(G) $. Second, we propose some statistical analysis of MTIs as a generic tool for studying average properties of random networks, extending these techniques for the first time to the context of MTIs. Finally, we perform an innovative scaling analysis of MTIs which allows us to state a scaling law that relates different random graph models.</p></abstract>

A NOTE ON FRACTAL DIMENSION OF RIEMANN–LIOUVILLE FRACTIONAL INTEGRAL

This paper intends to study the analytical properties of the Riemann–Liouville fractional integral and fractal dimensions of its graph on [Formula: see text]. We show that the Riemann–Liouville fractional integral preserves some analytical properties such as boundedness, continuity and bounded variation in the Arzelá sense. We also deduce the upper bound of the box dimension and the Hausdorff dimension of the graph of the Riemann–Liouville fractional integral of Hölder continuous functions. Furthermore, we prove that the box dimension and the Hausdorff dimension of the graph of the Riemann–Liouville fractional integral of a function, which is continuous and of bounded variation in Arzelá sense, are [Formula: see text].

Molecularly imprinted polymer-based electrochemical sensors for monitoring the persistent organic pollutants chlorophenols.

Because of the serious risks they pose to the environment and public health, chlorophenols (CPs), a typical class of the most persistent organic pollutants, have drawn increasing attention. Monitoring CPs effectively has become a pressing and difficult problem. The rapidly increasing need for onsite and real-time CP detection has led to the consideration of electrochemical sensing as a workable solution. Molecularly imprinted polymer (MIP)-based electrochemical sensing has emerged as a promising area for environmental monitoring in response to this analytical problem. MIPs, in conjunction with miniature electrochemical transducers, provide the opportunity to detect target analytes in situ. These devices have the advantages of great chemical and physical stability, cheap production costs, good selectivity, and quick response times. Most studies suggest that these sensors use nanoparticles to improve their analytical properties, especially sensitivity. Furthermore, these sensors have successfully used real water samples without the need for time-consuming pretreatment procedures. This article provides an overview of electrochemical MIP-based sensors reported to detect CPs in water samples. To obtain the highest sensitivity, special consideration is given to the fabrication of the sensors, which includes the use of various functional monomers, sensing platforms, and materials. Several other parameters are also discussed, including the linear concentration range, limit of detection, and the types of water samples that were examined.

The Multi-Index Mittag-Leffler-Le Roy Functions as I- and H¯-Functions and New Fractional Calculus Operators

In the last decade, the interest in a special function named after the French mathematician Le Roy has provoked several authors to introduce and study its various extensions. Historically, the Le Roy function appeared almost in same time and in similar way of goals like the Mittag-Leffler function that has important role in Fractional Calculus. The Le Roy type functions are also “fractional exponentials” but the fractionalizing parameters appear as power indices of the involved Gamma functions. In our recent works, we have introduced rather general multi-index Le Roy type functions, studied their analytical properties and proposed their association to the class of Special Functions of Fractional Calculus.A newly developed idea is to show that the Le Roy type functions can be represented in terms of the I-functions of Rathie and H-functions of Inayat-Hussain that are further extensions of the Fox H¯-functions and Fox-Wright pΨq-functions. It happens that other important mathematical functions as the polylogarithms, Riemann Zeta function and its extensions, also belong to this more general class of special functions. We have solved, at least in some simpler case, the problem to find integral and differential-like operators for which the Le Roy type functions are eigenfunctions. This lead us to a new class of operators with I-functions kernels that can be considered as further extensions of the operators of generalized fractional calculus.