Analytical Properties Research Articles

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 $$|\varphi |<3\pi /2$$ | φ | < 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.

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

Resurgence and self-completion in renormalized gauge theories

Under certain assumptions and independent of the instantons, we show that the logarithm expansion of dimensional regularization in quantum field theory needs a nonperturbative completion to have a renormalization group flow valid at all energies. Then, we show that such nonperturbative completion has the analytic properties of the renormalons, which we find with only a marginal reference to diagrammatic calculations. We demonstrate that renormalon corrections necessarily lead to analyzable functions, namely, resurgent transseries. A detailed analysis of the resurgent properties of the renormalons is provided. The self-consistency of the theory requires these nonperturbative contributions to render the running coupling well defined at any energy, thus with no Landau pole. We illustrate the point within the case of quantum electrodynamics (QED). This way, we explicitly realize the correspondence between the nonperturbative Landau pole scale and the renormalons. What is seen as a Landau pole in perturbation theory is cured by the nonperturbative, resurgent contributions.

Evaluation of survival weighted Pareto distribution: Analytical properties and applications to industrial and aeronautics data

In statistical modeling, lifetime datasets play an important and significant role. Weighted distributions can be useful to attain the essential purposes relating to the developed distributions’ flexibility and to improve further compliances in data forming; they provide the extension of distributions. The current study suggests a new best-fit probability distribution model based on Pareto distribution. The new model is called Survival Weighted Pareto (SWP) distribution model. Furthermore, the statistical expressions for different properties, which include moments, inverse moments, quantile function, and order statistics, are reported. Moreover, to check the performance and the behavior of different estimators using different sample sizes, a simulation study, which is based on SWP distribution, is performed. According to the simulation results, it is established that the proposed model is a most useful fitted probability model. In addition, an application of the SWP model for three datasets is provided to check the goodness of fit measures of the model.

Graphical Representation of Quaternions and Their Concomitant Functions

In this particular paper we will demonstrate that, by invoking the concept of a ‘quaternionic quasicomplex component’, it is possible to graphically represent all quaternions and their concomitant functions with the aid of specific quaternionic analogues of the Argand diagram from complex variable analysis, bearing in mind that the algebraic and analytic properties of the aforesaid numbers and functions have been comprehensively elucidated in the author’s antecedent papers [2]; [3]; [4] & [5]

Geometric realization of the Sasa-Satsuma equation on the symmetric space SU(3)/U(2)

The analytic property of the Sasa-Satsuma equation has been well-explored via using an array of mathematical tools (such as the inverse scattering transformation, the Hirota bilinear method and the Darboux transformation). This paper devotes to exploring geometric properties of this equation via the zero curvature representation in terms of the language in Yang-Mills theory. The generalized Landau-Lifshitz type model of Sym-Pohlmeyer moving curves evolving in the symmetric Lie algebra g=k⊕m with initial data being suitably restricted is gauge equivalent to the Sasa-Satsuma equation. This gives a geometric realization of the Sasa-Satsuma equation.

New methods for quasi-interpolation approximations: Resolution of odd-degree singularities

In this paper, we study functional approximations where we choose the so-called radial basis function method and more specifically, quasi-interpolation. From the various available approaches to the latter, we form new quasi-Lagrange functions when the orders of the singularities of the radial function’s Fourier transforms at zero do not match the parity of the dimension of the space, and therefore new expansions and coefficients are needed to overcome this problem. We develop explicit constructions of infinite Fourier expansions that provide these coefficients and make an extensive comparison of the approximation qualities and - with a particular focus - polynomial reproduction and uniform approximation order of the various formulae. One of the interesting observations concerns the link between algebraic conditions of expansion coefficients and analytic properties of localness and convergence.

Performance evaluation of biodegradable polymer PHBV and PBAT blends with adjustable melt flow behaviour, heat deflection temperature, and morphological transition

AbstractMelt blending is a reliable and well‐demonstrated strategy for improving the mechanical, thermal, rheological, and surface properties of biopolymers. Poly(hydroxy‐3‐butyrate‐co‐3‐hydroxyvalerate) (PHBV) and poly(butylene adipate‐co‐terephthalate) (PBAT) are the two popular choices for blending polymers due to their diverse properties and complementary soil biodegradable behaviour. Due to their immiscibility, however, blending with the help of processing additives is necessary to reap the most significant benefits from this process and to avoid immiscibility issues. This study utilized the additives (peroxides and epoxy‐based chain extender) to compatibilize the biodegradable polymers PHBV and PBAT in a 60:40 blending ratio. The tensile strength and Young's modulus of the PHBV/PBAT(60/40) blend were improved by 32% and 64%, respectively, after adding a combination of peroxide (0.02 phr) and chain extender (0.3 phr) due to the formation of a complex network structure with increased chain length. The positive effect of an additive addition was also reflected by a 30°C increment in heat deflection temperature of biodegradable blend due to its high modulus value as supported by mechanical properties. The combined action of a peroxide and chain extender demonstrated a significantly higher complex viscosity of the PHBV/PBAT(60/40) blend due to the formation of a crosslinked polymer network as analyzed by rheological analysis. Our research demonstrated the effect of additives and their combined impact on analytical properties of PHBV/PBAT(60/40) blend to guide future work in improving their candidature to serve as a drop‐in solution in replacing non‐biodegradable petro‐based plastic products.

The modularity of Siegel’s zeta functions

Siegel defined zeta functions associated with indefinite quadratic forms, and proved their analytic properties such as analytic continuations and functional equations. Coefficients of these zeta functions are called measures of representations, and play an important role in the arithmetic theory of quadratic forms. In a 1938 paper, Siegel made a comment to the effect that the modularity of his zeta functions would be proved with the help of a suitable converse theorem. In the present paper, we accomplish Siegel’s original plan by using a Weil-type converse theorem for Maass forms, which has appeared recently. It is also shown that “half” of Siegel’s zeta functions correspond to holomorphic modular forms.

Quantum–classical correspondence and dissipative to dissipationless crossover in magnetotransport phenomena

The three-dimensional magneto-conductivity tensor was derived in a gauge invariant form based on the Kubo formula considering quantum effects under a magnetic field, such as the Landau quantization and quantum oscillations. We analytically demonstrated that the quantum formula of the magneto-conductivity can be obtained by adding a quantum oscillation factor to the classical formula. This result establishes the quantum–classical correspondence, which has long been missing in magnetotransport phenomena. Moreover, we found dissipative-to-dissipationless crossover in the Hall conductivity by paying special attention to the analytic properties of the thermal Green’s function. Finally, by calculating the magnetoresistance of semimetals, we identified a phase shift in quantum oscillation originating from the dissipationless transport predominant at high fields.

Revisiting loop quantum gravity with selfdual variables: classical theory

We review the classical formulation of general relativity as an SL(2,C) gauge theory in terms of Ashtekar’s self-dual variables and reality conditions for the spatial metric (first reality condition) and its evolution (second reality condition), and we add some new observations and results. We first explain in detail how a connection taking values in the Lie algebra of the complex Lorentz group yields two spin(3,1) connections, one self-dual and one anti-self-dual, without the need for a spin structure. We then demonstrate that the self-dual part of the complexified Palatini action in Ashtekar variables requires a holomorphic phase space description in order to obtain a non-degenerate symplectic structure. The holomorphic phase space does not allow for the implementation of the reality conditions as additional constraints, so they have to be taken care of ‘by hand’ during the quantisation. We also observe that, due to the action being complex, there is an overall complex phase that can be chosen at will. We then review the canonical formulation and the consequences of the implementation of the reality conditions. We pay close attention to the transformation behaviour of the various fields under (complex) basis changes, as well as to complex analytic properties of the relevant functions on phase space.

Availability and maintenance strategy under time-varying environments for redundant repairable systems with PH distributions

Systems commonly operate in time-varying environments which have essential impact on system performance, thus reliability modeling and maintenance strategy are faced with new challenges. In this study, a cold standby repairable system in a time-varying environment is investigated based on different operational levels and maintenance strategies, in which repairman's vacation and maintenance rules vary with environments. The evolution of dynamic environments is governed by a Markov process, and the successive vacation time is governed by Markovian arrival processes (MAPs). Using Phase-type (PH) distribution not only increases the flexibility of analytical properties because it can approximate to any probability distribution defined on a nonnegative real line, but also could effectively ensure the applicability of the model in engineering practice, specially all the lifetimes of components and maintenance time are subject to disparate PH distributions in diverse environments. By employing the matrix-analytic method, Kronecker operator theory and aggregated stochastic processes, some reliability indexes and the system average benefit are obtained respectively. Finally, an example of a redundant power supply is given to illustrate the validity and applicability of the proposed model.

Fundamental absorption bandwidth to thickness limit for transparent homogeneous layers

Abstract Past work has considered the analytic properties of the reflection coefficient for a metal-backed slab. The primary result established a fundamental relationship for the minimal layer thickness to bandwidth ratio achievable for an absorber. There has yet to be establishment of a similar relationship for non-metal-backed layers, and here we present the universal result based on the Kramers–Kronig relations. Our theory is validated with transfer matrix calculations of homogeneous materials, and full-wave numerical simulations of electromagnetic metamaterials. Our results place more general fundamental limits on absorbers and thus will be important for both fundamental and applied studies.

Moments of the central L-values of the Asai lifts

Abstract We study some analytic properties of the Asai lifts associated with cuspidal Hilbert modular forms, and prove sharp bounds for the second moment of their central L-values.

Chemiluminescence and electrochemiluminescence of water-soluble iridium(III) complexes containing a tetraethylene-glycol functionalised triazolylpyridine ligand

BackgroundIridium(III) complexes, exhibiting high luminescence quantum yields and a wide range of emission colours, are promising alternatives to tris(2,2ʹ-bipyridine)ruthenium(II) for chemiluminescence (CL) and electrochemiluminescence (ECL) detection. This emerging class of reagent, however, is limited by the poor solubility of many iridium(III) complexes in aqueous solution, and lack of understanding of their remarkably variable selectivities towards different analytes. ResultsSeven [Ir(CˆN)2(pt-TEG)]+ complexes, exhibiting a wide range of reduction potentials and emission energies, were examined with six model analytes. For CL, cerium(IV) was used as the oxidant. The alkylamine analytes generally produced greater CL and ECL with the more readily oxidised Ir(III) complexes (CˆN = piq, bt, ppy), predominantly through the ‘direct’ pathway requiring oxidation of both metal complex and analyte. Aniline derivatives that did not also contain secondary or tertiary alkylamines elicited CL from the less readily oxidised complexes (CˆN = df-ppy-CF3, df-ppy) via energy transfer. The most difficult to oxidise complexes (CˆN = df(CF3)-ppy-Me, df(CN)-ppy) gave poor responses due to the limited potential window of the solvent and inefficiency of energy transfer to their high energy excited states. Greater CL and/or ECL intensities were generally obtained for each analyte with at least one Ir(III) complex than with [Ru(bpy)3]2+; superior limits of detection for two analytes were demonstrated. SignificanceThis exploration of CL/ECL in which the properties of luminophore, analyte and oxidant are all varied provides a new understanding of the influence of the metal-complex potentials and excited state energy on the light-producing and quenching pathways, and consequently, their distinct selectivity towards different analytes. These findings will guide the development of water-soluble Ir(III) complexes as CL and ECL reagents.

Exact tunneling solutions in multi-field potentials

The tunneling potential formalism makes it easy to construct exact solutions to the vacuum decay problem in potentials with multiple fields. While some exact solutions for single-field decays were known, we present the first nontrivial analytic examples with two and three scalar fields, and show how the method can be generalized to include gravitational corrections. Our results illuminate some analytic properties of the tunneling potential functions and can have a number of uses, among others: to serve as simple approximations to realistic potentials; to learn about parametric dependencies of decay rates; to check conjectures on vacuum decay; as benchmarks for multi-field numerical codes; or to study holographic interpretations of vacuum decay.

On the Efficiency Impacts of Berthing Priority Provision

Facing intensified interport competition in the global container shipping market, an increasing number of ports choose to offer berthing priority for carriers to increase their attractiveness. This study is the first to theoretically analyze the efficiency impacts of such prioritization. Specifically, this study models the steady-state dynamics for each terminal in a biterminal port as a prioritized queuing system. We explore the equilibrated shipping flow distribution and resulting total system cost (i.e., bunker consumption cost and waiting time cost) with and without priority provision, along with their major analytical properties. Then, we examine the “second-order” effects of these priority schemes on just-in-time (JIT) arrivals, an increasingly popular green port management tool. Specifically, we investigate how the equilibrium state associated with JIT arrivals could change with priority berthing. These analyses generate some interesting results, including (1) the total system cost increases or remains unchanged when a priority scheme is implemented under a symmetric port with equal service capacities for both terminals; (2) under the asymmetric biterminal case, however, it is also possible that berth prioritization could reduce the total system cost, and such phenomenon occurs only if the terminal which offers prioritization owns larger service capacity; (3) the results indicate that the “price of prioritization” could reach [Formula: see text] in port operation when the berth loading is heavy, implying that priority provision may significantly harm the operational efficiency; and (4) lastly, priority provision has a negative second-order effect on JIT strategies in a symmetric port, and such negative effect may neutralize the positive ones. Those theoretical results are validated by numerical experiments, and some of them are also supported by empirical data. The results provide important practical implications for the decision making of the port (or terminal) agencies. Funding: This work was supported by the National Natural Science Foundation of China [Grants 72371143 and 72188101]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2022.0411 .

Autocombustion Route Derived Zinc Ferrite Nanoparticles as Chemiresistive Sensor for Detection of Alcohol Vapors.

Prolonged exposure to alcohol vapors can have detrimental effects on human health, potentially leading to eye irritation, dizziness, and in some cases, damage to the nervous system. The present article aims to provide a comprehensive understanding on the synthesis and characterization of zinc ferrite (ZnFe2O4) nanoparticles, as well as their interactions with a range of alcohol vapors, including methanol, ethanol, n-propanol, and isopropanol. These alcohols differ in their molecular weight, boiling points, diffusivity, and other properties. The study reveals the semiconducting ZnFe2O4 nanoparticulate sensor's capability for reversible, repeatable, and sensitive detection of alcohol vapors. The sensor exhibits the highest response to ethanol within operating temperature range (225-300°C). An attempt is made to establish a correlation between the properties of the target analytes and the observed sensing signals. Additionally, the response conductance transients of ZnFe2O4 under the exposure to the studied alcohol vapors are modeled based on the Langmuir-Hinshelwood adsorption mechanism. The characteristic time constants obtained from this modeling are justified with respect to the properties of the analytes.

Edman Degradation Reveals Unequivocal Analysis of the Disulfide Connectivity in Peptides and Proteins.

Disulfide bridges in peptides and proteins play an essential role in maintaining their conformation, structural integrity, and consequently function. Despite ongoing efforts, it is still not possible to detect disulfide bonds and the connectivity of multiply bridged peptides directly through a simple and sufficiently validated protein sequencing or peptide mapping method. Partial or complete reduction and chemical cysteine modification are required as initial steps, followed by the application of a proper detection method. Edman degradation (ED) has been used for primary sequence determination but is largely neglected since the establishment of mass spectrometry (MS)-based protein sequencing. Here, we evaluated and thoroughly characterized the phenyl thiohydantoin (PTH) cysteine derivatives PTH-S-methyl cysteine and PTH-S-carbamidomethyl cysteine as bioanalytical standards for cysteine detection and quantification as well as for the elucidation of the disulfide connectivity in peptides by ED. Validation of the established derivatives was performed according to the guidelines of the International Committee of Harmonization on bioanalytical method validation, and their analytical properties were confirmed as reference standards. A series of model peptides was sequenced to test the usability of the PTH-Cys-derivatives as standards, whereas the native disulfide-bonded peptides CCAP-vil, μ-conotoxin KIIIA, and human insulin were used as case studies to determine their disulfide bond connectivity completely independent of MS analysis.