This study presents a novel numerical framework for simulating glucose-insulin regulatory dynamics using the Caputo-Fabrizio (CF) fractal-fractional operator with both constant and variable fractional orders. The model incorporates an exponential decay kernel to capture memory and hereditary effects in metabolic regulation. A Newton interpolation-based numerical scheme is developed to approximate the CF-FF derivatives, ensuring computational stability and accuracy. For the variable-order formulation, the fractional order dynamically evolves with time, reflecting physiological variability typically observed during intravenous glucose tolerance tests (IVGTT). Numerical experiments reproduce physiologically realistic glucose-insulin oscillations and demonstrate how feedback control stabilizes chaotic metabolic behavior. The results are based entirely on simulation evidence calibrated within clinically reported parameter ranges, providing conceptual validation rather than direct patient-data comparison. The proposed approach bridges mathematical fractional calculus with biomedical applications, offering new insights for personalized diabetes management and adaptive glucose control strategies.•Fractal-fractional model formulation capturing glucose-insulin memory and adaptation•Stable numerical scheme using Newton interpolation for accurate fractional integration•Linear feedback control applied to regulate chaotic glucose-insulin dynamics•Numerical Methodology for glucose-insulin dynamics. Our investigation of the fractal-fractional glucose-insulin system employs the following analytical framework:•Model Development: We formulate a fractal-fractional-order extension of the minimal glucose insulin model, incorporating an exponential decay type kernel to capture the system's memory effects and anomalous diffusion characteristics inherent in metabolic processes. The model accounts for both insulin-dependent and independent glucose utilization dynamics.•Computational Implementation: We develop a novel numerical solver based on Newton's interpolation polynomials, implementing the Atangana-Seda fractal-fractional derivative formulation. This method provides an efficient computational framework for solving the coupled nonlinear fractional differential equations while maintaining numerical stability across different fractional orders.•The purpose of this section is to define a mathematical model to study the dynamic behavior of glucose-insulin physiology.•With the Adams-Bashforth-Moulton numerical scheme, we compute the Lyapunov exponent of the system, which is useful for studying dissipative.•In a generalized numerical method, we simulate the solutions of the system using the time-fractal fractional derivative of Atangana-Seda.

We explore slowly rotating traversable wormholes placed inside realistic cosmic voids, focusing on three types: compensated voids, top-hat voids, and exponential voids. Using the standard Teo-type rotating wormhole metric, we build the wormhole geometry from the void density, looking at features like the throat shape, how sharply it flares out, and where the usual energy conditions are violated. We then follow how light moves in these spacetimes. Photon paths, circular orbits, and the small twisting caused by rotation (Lense-Thirring (LT) effect) all change depending on the void. Steep, concentrated voids such as compensated ones tend to pull photons closer and create asymmetry, while smoother voids like top-hat and exponential types allow photons to move more evenly, forming nearly circular paths. Finally, we look at the shadows these wormholes would cast. Wormholes in compensated voids produce smaller, slightly distorted shadows, while smoother voids give larger, rounder, and more symmetric silhouettes. Altogether, this shows how the void’s structure, combined with slow rotation, shapes both photon motion and the appearance of the wormhole shadow from a distance.

Originally developed for bioanalytical assays such as quantitative polymerase chain reaction, dark quenchers have been adapted in other areas, from gene sequencing to ultra-sensitive chemical detection. Most applications require that the dark quenchers' presumed properties be ideal; however, it is not obvious if such assumptions are always valid. One such issue is photoblinking, whereby a quencher intermittently enters a non-absorbing state for a short period of time. Here, we investigated the role of quencher photoblinking, if detectable, by interrogating a freely diffusing QSY9-tagged single-stranded DNA (ssDNA) that stochastically binds to an immobilized complementary ssDNA tagged with Cy3B. The resulting single-molecule trajectories exhibited two-state emission levels arising from molecular binding/unbinding events, quencher photoblinking, or both. The dwell-time distributions were found to be of the exponential type and dependent on excitation power, suggesting time-independent rate parameters for the quencher. In contrast, population-level time traces resembled those arising from power-law blinking reported for other systems. To reconcile these observations, we developed an analytical theory model based on the premises that both photoblinking and DNA binding can be expressed in terms of elementary chemical steps and that the experimental observations resulted from a temporal overlap of these random and independent events. This model was able to quantitatively explain the experimental results. QSY9 photoblinking dynamics were dependent on photoexcitation power and followed first-order chemical kinetics-not power law-with a thermal recovery rate of ∼3.3×10-2 s-1 at room temperature. In addition to advancing dark quencher photophysics, this study demonstrates a quantitative understanding based on simple underlying dynamical processes for an apparent power-law photoblinking observation.

We consider the asymptotic evaluation of the integral transform ∫ 0 ∞ f ( x ) sin n ⁡ ( λx ) / x n d x of an exponential type function f ( x ) of type 0 $ ]]> τ > 0 , for large values of the parameter λ, where n is a positive integer. We refer to this integral as the Sinc transform. Under the condition that f ( x ) is even with respect to x, we derive a terminating asymptotic expansion of the Sinc transform which behave as a polynomial in positive powers of λ as λ grows large provided that the conditions \ au /2 $ ]]> λ > τ / 2 for even n and \ au $ ]]> λ > τ for odd n are satisfied.

Abstract The solutions of an indeterminate Hamburger moment problem can be parameterised using the Nevanlinna matrix of the problem. The entries of this matrix are entire functions of minimal exponential type, and any growth less than that can occur. An indeterminate moment problem can be considered as a canonical system in limit circle case by rewriting the three-term recurrence of the problem into a discrete vector-valued differential equation. We give a bound for the growth of the Nevanlinna matrix in terms of the parameters of this canonical system. In most situations this bound can be evaluated explicitly. It is sharp in the sense that for well-behaved parameters it coincides with the actual growth of the Nevanlinna matrix up to multiplicative constants.

ABSTRACT Here, we propose an efficient exponential type estimator of population mean of a quantitative sensitive study variable using scrambled response model in Ranked Set Sampling ( RSS ) in case of missing data. It is assumed that information on non-sensitive auxiliary variable is known. The expressions of biases and Mean Square Errors ( MSE ) of the proposed and other estimators are derived upto first order approximation. The conditions are derived under which proposed estimator will become more efficient as compared to other estimators. To validate the theoretical results, we perform a thorough simulation study. The effects of variance of scrambling variable, responding probabilities and varying correlation coefficient between study and auxiliary variable on MSE s of the proposed and other estimators have been studied in the simulation process. The analysis clearly signifies the superior performance of our proposed estimator as compared to other estimators in the context of Ranked Set Sampling (RSS).

There are microwave sensors where the predictive variable (X) and the response variable (Y) present nonlinear and exponential type relationships, performing regressions where they do not establish compliance with the corresponding assumptions and do not make a fair comparison between regressions. This paper presents a methodology for evaluating nonlinear regression assumptions, which include outliers, normality, homoscedasticity, and independence. Additionally, the dynamic range, the maximum sensitivity, the resolution, and the accuracy are considered parameters for evaluating the quality of the regression. To implement the methodology, the snl_regression_quality package was developed, which runs in Python. Regressions for ring resonator and complementary split-ring sensors were considered. Both met the assumptions and, considering the dynamic range, resolution, and accuracy, the Split ring complementary resonator sensor regression was the one that showed the best performance. This methodology aims to make a fairer comparison between exponential nonlinear regressions of microwave sensors.

This work investigates the global well-posedness and long-term dynamics of two-component reaction-diffusion systems on bounded domains under homogeneous Dirichlet boundary conditions. We introduce a weaker dissipative condition that enables us to prove the global existence and uniqueness of classical solutions to the associated Cauchy problem, without imposing any growth constraints on the nonlinear terms. The admissible nonlinearities include, but are not limited to, polynomial and exponential growth types. Furthermore, we demonstrate that such systems admit both global and exponential attractors, which exhibit finite-dimensional characteristics in appropriate continuous function spaces.

In this work, we highlight two remarkable phenomena related to the action of a single family of Non-Iterative Functions (FFNI). The first result concerns the fundamental spectral distributions of Random Matrix Theory: GUE, GOE, GSE. We show that a simple Nonlinear Transformation (NLT), controlled by an exponent, establishes a direct bridge between these distributions. Each spectral distribution can be transformed into another and then retrieved by applying inverse transformation. All six possible conversions: GUE ↔ GOE, GUE ↔ GSE, GOE ↔ GSE, are obtained within the same framework. The second result concerns the convergence of numerous unimodal distributions toward a Limiting Distribution LD. By applying the same NLT, we observe that diverse distributions, bell-shaped, triangular, exponential, trapezoidal, spectral, and many synthetic types, all converge to a LD characterized by: σ/μ=1 Both phenomena, spectral distribution conversion and unimodal distribution convergence toward LD, are based on the same NIF family, revealing an unexpected functional unification between seemingly independent domains: random matrices, classical distributions, synthetic laws, and asymptotic behaviors. This forms a simple, accessible, and powerful framework for generating, transforming, and connecting numerous probability distributions. In addition, the same functional structure can analytically generate a wide variety of multimodal distributions (with multiple peaks), revealing that complex shapes can emerge without iteration, solely through parameter variation. Taken together, these results suggest the existence of a unified mathematical architecture linking: spectral distributions, the LD attractor, and a structural generator of multimodal forms.

In this work, we concern the existence and concentration of positive ground state solutions for the following $ (p, q) $-Kirchhoff type problem <p class="disp_formula">$ \left\{\begin{array}{ll} \quad-(1+a\int_{\mathbb{R}^N}|\nabla u|^pdx)\Delta_p u-(1+b\int_{\mathbb{R}^N}|\nabla u|^qdx)\Delta_q u+V(\varepsilon x)(|u|^{p-2}u+|u|^{q-2}u)\ \\ =f(u) \quad \text{in}\, \mathbb{R}^N, \, u\in W^{1, p}(\mathbb{R}^N)\cap W^{1, q}(\mathbb{R}^N), \quad u&gt;0 \, \, \text{in}\, \, \mathbb{R}^N, \end{array}\right. $ where $ \varepsilon&gt;0 $ is a small parameter, $ a, b&gt;0, 1&lt;p&lt;q=N, $ $ \Delta_m u=\mathrm{div}(|\nabla u|^{m-2}\nabla u) $ with $ m\in \{p, q\} $ is the <i>m</i>-Laplacian operator, the potential $ V: \mathbb{R}^N\rightarrow \mathbb{R} $ is a positive continuous function and $ f: \mathbb{R}\rightarrow \mathbb{R} $ is a continuous nonlinearity involving critical exponential growth and not satisfying usual Ambrosetti-Rabinowitz condition. The existence and concentration behavior of positive ground state solutions are established by variational methods combined with some sharp exponential type inequalities.

In this paper, we study the existence of the solution to the 3D modified critical homogeneous convective Brinkman-Forchheimer equation where the initial data belongs to the non-homogeneous Sobolev-Gevrey spaces. Moreover, we give an exponential type explosion in Sobolev-Gevrey spaces with less regularity on the initial condition. Correction: The author’s affiliation has been corrected from “Department of Mathematics and Statistics College, Science Imam Mohammad Ibn Saud Islamic University (IMSIU)” to “Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU)”. We apologize for any inconvenience this may cause.

In this paper, we study the well-posedness of a problem with two multiple nodes with respect to a distinguished variable $t$ and periodicity conditions with respect to the remaining coordinates $x_1,\ldots, x_p$ for linear pseudodifferential equations. Conditions for the existence and uniqueness of a solution to the problem under consideration in spaces of exponential type on the torus are established. By means of a metric approach, theorems providing lower bounds for small denominators arising in the construction of the solution are proved.

This study proposes a generalized difference–cum–exponential type estimator for estimating the finite population mean under simple random sampling without replacement in the presence of measurement error and non-response. Auxiliary information is incorporated to improve estimation efficiency under a specific non-response scenario. Using first-order approximations, expressions for the bias and mean square error (MSE) of the proposed estimator are derived. The optimum values of the involved constants are obtained by minimizing the MSE. Theoretical efficiency conditions are established to assess the performance of the estimator. The proposed estimator is analytically compared with existing estimators, including those of Hansen and Hurwitz (1946), Cochran (1977), Rao (1986), Bahl and Tuteja (1991), and Kumar and Bhougal (2011). Results based on MSE comparisons show that the proposed estimator outperforms the competing estimators under realistic survey conditions. The findings indicate that the proposed estimator is a reliable and efficient alternative for practical survey applications affected by measurement error and non-response.

The article describes the tensor products of approximation spaces associated with regular elliptic operators on tensor products of Lebesgue spaces $L_2(\partial\Omega)$, where $\partial \Omega$ considers as smooth manifold that describes in the usual way by local system of local coordinates. We use the quasi-normed approximation spaces and subspaces of exponential type functions associated with such operators.} A connection between the tensor products of approximation spaces and interpolation spaces obtained by the real method of interpolation is showed. We prove the direct and inverse approximation theorems for Bernstein–Jackson type inequalities as well as we give the explicit dependence of constants on parameters of approximation spaces. Such constants are expressed via some normalization factor. Application to spectral approximations on tensor products of interpolation spaces associated with regular elliptic operators on compact manifolds is shown. In the article also consider the spectral approximations (Theorem 2), since the subspaces of entire functions of exponential type of regular elliptic operators on compact manifolds coincide with their spectral subspaces (Lemma 3).

In this paper, we introduce a new three-parameter distribution, the New Exponentiated Burr Type III distribution (NEBIII), which is a member of the Generalized (G)-family of continuous distributions. The mathematical features that are derived include the mode, actuarial measures, order statistics, the analytical forms of the density and hazard functions, and explicit formulations for the moment generating function (MGF). The Maximum Likelihood Estimation (MLE) approach is used to estimate the model parameters. A simulated research with different sample sizes is used to evaluate the estimation's efficacy. The versatility and adaptability of the proposed distribution family are demonstrated on four real-world data sets. Additionally, we examine a Mixture of the Exponential and Exponentiated Burr Type III Distributions, identifying various mathematical characteristics and demonstrating their application to actual data.

We show the existence and uniqueness of a continuous solution to a path-dependent volatility model introduced by Guyon &amp; Lekeufack [(2023) Volatility is (mostly) path-dependent, Quantitative Finance 23 (9), 1221–1258] to model the price of an equity index and its spot volatility. The considered model for the trend and activity features can be written as a Stochastic Volterra Equation (SVE) with non-convolutional and non-bounded kernels as well as non-Lipschitz coefficients. We first prove the existence and uniqueness of a solution to the SVE under integrability and regularity assumptions on the two kernels and under a condition on the second kernel weighting the past squared returns which ensures that the activity feature is bounded from below by a positive constant. Then, assuming in addition that the kernel weighting the past returns is of exponential type and that an inequality relating the logarithmic derivatives of the two kernels with respect to their second variables is satisfied, we show the positivity of the volatility process which is obtained as a nonlinear function of the SVE’s solution. We show numerically that the choice of an exponential kernel for the kernel weighting the past returns has little impact on the quality of model calibration compared to other choices and the inequality involving the logarithmic derivatives is satisfied by the calibrated kernels. These results extend those of Nutz &amp; Riveros Valdevenito [(2024) On the Guyon–Lekeufack volatility model, Finance and Stochastics 28 (4), 1203–1223].

INVERSE THEOREM OF APPROXIMATION BY ENTIRE FUNCTIONS OF EXPONENTIAL TYPE

This work investigates the global well-posedness and long-term dynamics of two-component reaction-diffusion systems on bounded domains under homogeneous Dirichlet boundary conditions. We introduce a weaker dissipative condition that enables us to prove the global existence and uniqueness of classical solutions to the associated Cauchy problem, without imposing any growth constraints on the nonlinear terms. The admissible nonlinearities include, but are not limited to, polynomial and exponential growth types. Furthermore, we demonstrate that such systems admit both global and exponential attractors, which exhibit finite-dimensional characteristics in appropriate continuous function spaces.

The proper measurement of natural radionuclides by gamma-ray spectrometry is very important because of their multiple applications in environmental radioactivity. The self-attenuation effect correction factor, f a , is essential to calculate the full-energy peak efficiency for a wide range of sample mass attenuation coefficients, η , and apparent densities, ρ . Using experimental procedures, the accurate f a obtention is complicated for significant differences between the calibration and problem samples regarding their η and ρ , especially true at 46 keV ( 210 Pb) and 63 keV ( 234 Th). The software LabSOCS is widely used but it has important limitations regarding the chemical composition that is possible to be specified for each sample. This is the first study aims to develop a robust methodology for the f a obtention achieving a general and analytical f a function at 46 keV and 63 keV, f a 46 , 63 ( ρ , η 46 , 63 ) , using LabSOCS for a wide η and ρ range. For this, justified intervals for η (0.23–8.00 cm 2 g −1 and 0.19–3.55 cm 2 g −1 at 46 keV and 63 keV, respectively) and ρ (0.5–5 g cm −3 ) were selected for the problem samples, using water as the calibration sample and a cylindrical geometry with 25 mm of sample thickness. For the previous η and ρ ranges, the f a obtained by LabSOCS was fitted versus ρ fixing η , where its behaviour was found to be of exponential type. Then, the resulting parameters were fitted in turn varying η , where exponential and polynomial fits were used, achieving f a 46 , 63 ( ρ , η 46 , 63 ) . The residuals obtained from fitting the parameters involved in f a 46 , 63 ( ρ , η 46 , 63 ) were generally very good, less than 10 %. In addition, f a 46 , 63 ( ρ , η 46 , 63 ) was validated for a wide η and ρ range obtaining satisfactory z score values for all cases. • A novel and robust methodology for self-attenuation effect corrections was developed using LabSOCS. • A general and analytical function of f a was obtained for the most complicated cases like 46 keV ( 210 Pb) and 63 keV ( 234 Th). • A multiple fit procedure of the f a obtained using LabSOCS was developed for a very wide range of the η and ρ. • Very good residual values were generally obtained from the multiple fit procedure. • The general f a function was validated for a very wide range of η and ρ using certified and non-certified reference materials.

Weighted kappa and kappa-like coefficients are used for the calculation of inter-rater agreement in cases where raters classify objects into ordinal categories. Weighted kappa coefficients are extended for use in studies with multiple raters. It is crucial to select appropriate weighting schemes as they can significantly impact the value of the coefficient. In this study, the accuracy of weighted kappa coefficients and the effects of linear, quadratic, ridit type, and exponential type weighting schemes on these coefficients are discussed in the multi-rater agreement studies with ordinal categories. The accuracy of the coefficients is investigated by an illustrative data and a simulation study.