Analytical Properties Research Articles

Electrochemiluminescence Microscopy.

Electrochemiluminescence (ECL) is rapidly evolving from an analytical method into an optical microscopy. The orthogonality of the electrochemical trigger and the optical readout distinguishes it from classic microscopy and electrochemical techniques, owing to its near-zero background, remarkable sensitivity, and absence of photobleaching and phototoxicity. In this minireview, we summarize the recent advances in ECL imaging technology, emphasizing original configurations which enable the imaging of biological entities and the improvement of the analytical properties by increasing the complexity and multiplexing of bioassays. Additionally, mapping the (electro)chemical reactivity in space provides valuable information on nanomaterials and facilitates deciphering ECL mechanisms for improving their performances in diagnostics and (electro)catalysis. Finally, we highlight the recent achievements in imaging at the ultimate limits of single molecules, single photons or single chemical reactions, and the current challenges to translate the ECL imaging advances to other fields such as material science, catalysis and biology.

Electrochemiluminescence Microscopy

AbstractElectrochemiluminescence (ECL) is rapidly evolving from an analytical method into an optical microscopy. The orthogonality of the electrochemical trigger and the optical readout distinguishes it from classic microscopy and electrochemical techniques, owing to its near‐zero background, remarkable sensitivity, and absence of photobleaching and phototoxicity. In this minireview, we summarize the recent advances in ECL imaging technology, emphasizing original configurations which enable the imaging of biological entities and the improvement of the analytical properties by increasing the complexity and multiplexing of bioassays. Additionally, mapping the (electro)chemical reactivity in space provides valuable information on nanomaterials and facilitates deciphering ECL mechanisms for improving their performances in diagnostics and (electro)catalysis. Finally, we highlight the recent achievements in imaging at the ultimate limits of single molecules, single photons or single chemical reactions, and the current challenges to translate the ECL imaging advances to other fields such as material science, catalysis and biology.

Monkeypox obeys the (Benford) law: a dynamic analysis of daily case counts in the United States of America

We analyze, for the first time, the first-digit distribution of the monkeypox daily cases in the United States of America, from May 17 to September 21, 2022. The overall data follow Benford’s law, a conclusion substantiated by eight different statistical tests, including the “Euclidean distance test”, which has been designed to specifically check Benford’s distribution in data. This result aligns with those of other infectious diseases, such as COVID 19, whose Benfordness has already been confirmed in the literature. Daily counts of monkeypox cases, like any other disease evolve in time. For this reason, we analyzed the temporal deviation of monkeypox counts from Benford’s law to check for possible anomalies in the temporal series of cases. The dynamic analysis was performed by means of the Euclidean distance test. This is because, to our best knowledge, that is the only statistically valid, Benford-specific test whose underlying estimator has a cumulative distribution function with known analytical properties, and is applicable to small and large samples. This is the case in dynamic analyses, where the number of data points usually starts from small values and then increases in time. No anomalies were detected, which indicates that no (fraudulent) alterations or errors in data gathering took place.

Analytical Properties and Numerical Preservation of an Age-Group Susceptible-Infected-Recovered Model: Application to the Diffusion of Information

Abstract This paper analyzes an age-group susceptible-infected-recovered (SIR) model. Theoretical results concerning the conservation of the total population, the positivity of the analytical solution, and the final size of the epidemic are derived. Since the model is a nonlinear system of ordinary differential equations (ODEs), a numerical approximation is considered, based on Standard and non-Standard Finite Difference methods, and on a Modified Patankar-Runge–Kutta (MPRK) method. The numerical preservation of the qualitative properties of the analytical solution is studied. The obtained results are applied to the diffusion of information in social networks, and the effectiveness of the different numerical approaches is shown through several numerical tests on real data.

REAL ANALYTIC DISCRETE CHOICE MODELS OF DEMAND: THEORY AND IMPLICATIONS

We demonstrate that a large class of discrete choice models of demand can be approximated by real analytic demand models. We obtain this result by combining (i) a novel real analytic property of the mixed logit and the mixed probit models with any distribution of random coefficients and (ii) an approximation property of finite mixtures of Gumbel and Gaussian distributions. To illustrate some of the implications of this result, we discuss how real analyticity facilitates nonparametric and semi-nonparametric identification, extrapolation to hypothetical counterfactuals, numerical implementation of demand inverses, and numerical implementation of the maximum likelihood estimator.

Improvement of Qualitative Analyses of Aliphatic Alcohols Using Direct Catalytic Fuel Cell and Chemometric Analysis Format.

Direct catalytic methanol fuel cells (DCMFCs) have been studied for several years for energy conversion. Less extensive is the investigation of their analytical properties. In this paper, we demonstrate that the behavior of both the discharge and charger curves of DCMFCs depends on the chemical composition of the solution injected in the fuel cell. Their discharge and charge curves, analyzed using a chemometric data fusion method named ComDim, enable the identification of various types of aliphatic alcohols diluted in water. The results also show that the identification of alcohols can be obtained from the first portion of the discharge and charge curves. To this end, the curves have been described by a set of features related to the slope and intercept of the initial portion of the curves. The ComDim analysis of this set of features shows that the identification of alcohols can be obtained in a time that is about thirty times shorter than the time taken to achieve steady-state voltage.

Riemann-Hilbert approach and double-pole solutions for the third-order flow equation of DNLS-type equation with nonzero boundary conditions

In this paper, the Riemann-Hilbert approach is applied to study a third-order flow equation of derivative nonlinear Schrödinger-type equation with nonzero boundary conditions. By utilizing the analytical, symmetric, and asymptotic properties of eigenfunctions, a generalized Riemann-Hilbert problem is formulated for the third-order flow equation of derivative nonlinear Schrödinger-type equation with nonzero boundary conditions. The formulas of N-soliton solutions for cases of single pole and double poles are given. We present some kinds of soliton solutions of these two cases according to different distributions of spectral parameters to study the dynamical behavior of them.

Analysis of the ψ(3770)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\psi (3770)}$$\\end{document} resonance in line with unitarity and analyticity constraints

We study the inclusive and exclusive cross sections of e+e-→hadrons\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$e^+e^-\\rightarrow \ ext {hadrons}$$\\end{document} for center-of-mass energies between 3.70 and 3.83GeV\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$3.83\\,\\,\ extrm{GeV} $$\\end{document} to infer the mass, width, and couplings of the ψ(3770)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\psi (3770)$$\\end{document} resonance. By using a coupled-channel K-matrix approach, we setup our analysis to respect unitarity and the analyticity properties of the underlying scattering amplitudes. We fit several models to the full dataset and identify our nominal results through a statistical model comparison. We find that, accounting for the interplay between the ψ(2S)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\psi (2S)$$\\end{document} and the ψ(3770)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\psi (3770)$$\\end{document}, no further pole is required to describe the ψ(3770)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\psi (3770)$$\\end{document} line shape. In particular we derive from the pole location Mψ(3770)=3778.8±0.3MeV\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$M_{\\psi (3770)}~=~3778.8~\\pm ~0.3~\\,\ extrm{MeV} $$\\end{document} and Γψ(3770)=25.0±0.5MeV\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varGamma _{\\psi (3770)}~=~25.0~\\pm ~0.5~\\,\ extrm{MeV} $$\\end{document}. Moreover, we find the decay to D+D-\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$D^+D^-$$\\end{document} and D0D¯0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$D^0\\bar{D}^0$$\\end{document} to be consistent with isospin symmetry and derive an upper bound on the branching ratio B(ψ(3770)→non-DD¯)<6%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {B}}(\\psi (3770) \\rightarrow \ ext {non-}D\\bar{D}) < 6\\%$$\\end{document} at 90%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$90\\%$$\\end{document} probability.

Quasiconformal almost parametrizations of metric surfaces

We look for minimal conditions on a two-dimensional metric surface X of locally finite Hausdorff 2-measure under which X admits an (almost) parametrization with good geometric and analytic properties. Only assuming that X is locally geodesic, we show that Jordan domains in X of finite boundary length admit a quasiconformal almost parametrization. If X satisfies some further conditions, then such an almost parametrization can be upgraded to a geometrically quasiconformal homeomorphism or a quasisymmetric homeomorphism. In particular, we recover Rajala’s recent quasiconformal uniformization theorem in the special case that X is locally geodesic as well as Bonk–Kleiner’s quasisymmetric uniformization theorem. On the way, we establish the existence of Sobolev discs spanning a given Jordan curve in X under nearly minimal assumptions on X and prove the continuity of energy minimizers.

A statistical framework for a new Kavya-Manoharan Bilal distribution using ranked set sampling and simple random sampling

In survival and stochastic lifespan modeling, numerous families of distributions are sometimes considered unnatural, unjustifiable theoretically, and occasionally superfluous. Here, a novel parsimonious survival model is developed using the Bilal distribution (BD) and the Kavya-Manoharan (KM) parsimonious transformation family. In addition to other analytical properties, the forms of probability density function (PDF) and behavior of the distributions' hazard rates are analyzed. The insights are theoretical as well as practical. Theoretically, we offer explicit equations for the single and product moments of order statistics from Kavya-Manoharan Bilal Distribution. Practically, maximum likelihood (ML) technique, which is based on simple random sampling (SRS) and ranked set sampling (RSS) sample schemes, is employed to estimate the parameters. Numerical simulations are used as the primary methodology to compare the various sampling techniques.

Analytical properties, fractal dimensions and related inequalities of [formula omitted]-Riemann–Liouville fractional integrals

In this paper, we rigorously explore (k,h)-Riemann–Liouville fractional integrals applied to continuous functions defined on closed real intervals. Firstly, we delve into the analytical properties of (k,h)-Riemann–Liouville fractional integrals for continuous functions, examining aspects like boundedness, continuity, and bounded variation. Secondly, we derive an upper bound for the upper box dimensions of (k,h)-Riemann–Liouville fractional integral graphs for continuous functions defined on real closed intervals. Finally, we present several applications of (k,h)-Riemann–Liouville fractional integral operators, including the reverse analog Hölder inequality, the reverse analog Minkowski inequality, and Hermite–Hadamard-type inequalities.

The Small-N Series in the Zero-Dimensional O(N) Model: Constructive Expansions and Transseries

AbstractWe consider the zero-dimensional quartic O(N) vector model and present a complete study of the partition function Z(g, N) and its logarithm, the free energy W(g, N), seen as functions of the coupling g on a Riemann surface. We are, in particular, interested in the study of the transseries expansions of these quantities. The point of this paper is to recover such results using constructive field theory techniques with the aim to use them in the future for a rigorous analysis of resurgence in genuine quantum field theoretical models in higher dimensions. Using constructive field theory techniques, we prove that both Z(g, N) and W(g, N) are Borel summable functions along all the rays in the cut complex plane $$\mathbb {C}_{\pi } =\mathbb {C}{\setminus } \mathbb {R}_-$$ C π = C \ R - . We recover the transseries expansion of Z(g, N) using the intermediate field representation. We furthermore study the small-N expansions of Z(g, N) and W(g, N). For any $$g=|g| e^{\imath \varphi }$$ g = | g | e ı φ on the sector of the Riemann surface with $$|\varphi |&lt;3\pi /2$$ | φ | &lt; 3 π / 2 , the small-N expansion of Z(g, N) has infinite radius of convergence in N, while the expansion of W(g, N) has a finite radius of convergence in N for g in a subdomain of the same sector. The Taylor coefficients of these expansions, $$Z_n(g)$$ Z n ( g ) and $$W_n(g)$$ W n ( g ) , exhibit analytic properties similar to Z(g, N) and W(g, N) and have transseries expansions. The transseries expansion of $$Z_n(g)$$ Z n ( g ) is readily accessible: much like Z(g, N), for any n, $$Z_n(g)$$ Z n ( g ) has a zero- and a one-instanton contribution. The transseries of $$W_n(g)$$ W n ( g ) is obtained using Möbius inversion, and summing these transseries yields the transseries expansion of W(g, N). The transseries of $$W_n(g)$$ W n ( g ) and W(g, N) are markedly different: while W(g, N) displays contributions from arbitrarily many multi-instantons, $$W_n(g)$$ W n ( g ) exhibits contributions of only up to n-instanton sectors.

Black hole perturbation theory meets CFT2 : Kerr-Compton amplitudes from Nekrasov-Shatashvili functions

We present a novel study of Kerr Compton amplitudes in a partial wave basis in terms of the Nekrasov-Shatashvili (NS) function of the confluent Heun equation (CHE). Remarkably, NS-functions enjoy analytic properties and symmetries that are naturally inherited by the Compton amplitudes. Based on this, we characterize the analytic dependence of the Compton phase shift in the Kerr spin parameter and provide a direct comparison to the standard post-Minkowskian (PM) perturbative approach within general relativity (GR). We also analyze the universal large frequency behavior of the relevant characteristic exponent of the CHE—also known as the renormalized angular momentum—and find agreement with numerical computations. Moreover, we discuss the analytic continuation in the harmonics quantum number ℓ of the partial wave, and show that the limit to the physical integer values commutes with the PM expansion of the observables. Finally, we obtain the contributions to the tree-level, point-particle, gravitational Compton amplitude in a covariant basis through O(aBH8), without the need to take the superextremal limit for Kerr spin. Published by the American Physical Society 2024

A serendipity fully discrete div-div complex on polygonal meshes

In this work we address the reduction of face degrees of freedom (DOFs) for discrete elasticity complexes. Specifically, using serendipity techniques, we develop a reduced version of a recently introduced two-dimensional complex arising from traces of the three-dimensional elasticity complex. The keystone of the reduction process is a new estimate of symmetric tensor-valued polynomial fields in terms of boundary values, completed with suitable projections of internal values for higher degrees. We prove an extensive set of new results for the original complex and show that the reduced complex has the same homological and analytical properties as the original one. This paper also contains an appendix with proofs of general Poincaré–Korn-type inequalities for hybrid fields.

Feynman Diagrams beyond Physics: From Biology to Economy

Feynman diagrams represent one of the most powerful and fascinating tools developed in theoretical physics in the last century. Introduced within the framework of quantum electrodynamics as a suitable method for computing the amplitude of a physical process, they rapidly became a fundamental mathematical object in quantum field theory. However, their abstract nature seems to suggest a wider usage, which actually exceeds the physical context. Indeed, as mathematical objects, they could simply be considered graphs that depict not only physical quantities but also biological or economic entities. We survey the analytical and algebraic properties of such diagrams to understand their utility in several areas of science, eventually providing some examples of recent applications.

Fuzzy bounces

We observe that the energy and the enthalpy densities can be smeared by two fudge factors that are constrained by the contracted Bianchi identities. Depending on the analytic properties of the smearing functions the underlying cosmological solutions belong to two physically different classes, namely the bounces of the scale factor and the curvature bounces. While the curvature bounces are naturally compatible with a stage of accelerated expansion, the bounces of the scale factor demand an early phase of accelerated contraction even if a short inflationary stage may arise prior to the decelerated regime. Despite the regularity of the underlying solutions, gradient instabilities and singularities do occasionally appear in the evolution of curvature inhomogeneities. After deducing the specific criteria behind these occurrences, the background-independent conclusions are corroborated by a series of concrete examples associated with different forms of the smearing functions. The evolution of the curvature inhomogeneities restricts the ranges of the solutions that turn out to be unsuitable even for a limited description of the pre-inflationary initial data. The same observation holds in the case of the gauge-invariant evolution of the matter density contrast. It is however not excluded that a class of scenarios (mainly associated with the curvature bounces) could indeed avoid the potential instabilities. All in all the present analysis explore a general approach whose results are relevant in all the contexts where bouncing solutions are invoked either as complementary or as alternative to the conventional inflationary scenarios.

On the properties of the anisotropic multivariate Hermite-Gauss functions

The Hermite-Gauss basis functions have been extensively employed in classical and quantum optics due to their convenient analytic properties. A class of multivariate Hermite-Gauss functions, the anisotropic Hermite-Gauss functions, arise by endowing the standard univariate Hermite-Gauss functions with a positive definite quadratic form. These multivariate functions admit useful applications in optics, signal analysis and probability theory, however they have received little attention in literature. In this paper, we examine the properties of these functions, with an emphasis on applications in computational optics.

A New Planar Potentiometric Sensor for In Situ Measurements.

A new construction of a potentiometric sensor was introduced for the first time. It relies on the use of two membranes instead of one, as in the well-known coated-disc electrode. For this purpose, a new electrode body was constructed, including not one, but two glassy carbon discs covered with an ion-selective membrane. This solution allows for the sensor properties to be enhanced without using additional materials (layers or additives) on the membrane. The new construction is particularly useful for in situ measurements in environmental samples. Two ion-selective polymeric membranes were used, namely H+ and K+-selective membranes, to confirm the universality of the idea. The tests conducted included chronopotentiometric tests, electrochemical impedance spectroscopy, and potentiometric measurements. The electrical and analytical parameters of the sensors were evaluated and compared for all tested electrodes to evaluate the properties of the planar electrode versus previously known constructions. Research has shown that the application of two membranes instead of one allows for the resistance of an electrode to be lowered and for the electrical capacitance to be elevated. Improving the electrical properties of an electrode resulted in the enhancement of its analytical properties. The pH measurement range of the planar electrode is 2-11, which is much wider in contrast to that of the single-membrane electrode. The linear range of the K+-selective planar electrode is wider than that of the coated-disc electrode and equals 10-6 to 10-1 M. The response time turned out to be a few seconds shorter, and the potential drift was smaller due to the application of an additional membrane in the electrode construction. This research creates a new opportunity to design robust potentiometric sensors, as the presented construction is universal and can be used to obtain electrodes selective to various ions.

The Impact of the Limit q-Durrmeyer Operator on Continuous Functions

AbstractThe limit q-Durrmeyer operator, $$D_{\infty ,q}$$ D ∞ , q , was introduced and its approximation properties were investigated by Gupta (Appl. Math. Comput. 197(1):172–178, 2008) during a study of q-analogues for the Bernstein–Durrmeyer operator. In the present work, this operator is investigated from a different perspective. More precisely, the growth estimates are derived for the entire functions comprising the range of $$D_{\infty ,q}$$ D ∞ , q . The interrelation between the analytic properties of a function f and the rate of growth for $$D_{\infty ,q}f$$ D ∞ , q f are established, and the sharpness of the obtained results are demonstrated.

Geometric and Analytic Properties Associated With Extension Operators

Geometric and Analytic Properties Associated With Extension Operators