Exponential Estimates Research Articles

Lyapunov functionals for linear continuous-time difference systems: A single delay case

This paper focuses on the Lyapunov stability problem of linear continuous-time difference systems. We show that although the stability of these systems has been extensively investigated, the problem of determining suitable quadratic Lyapunov functionals is not completely solved yet, even for the simplest system with a single delay. Herein, using the single delay case as an example, we construct new quadratic Lyapunov functionals. The functionals, which depend on a matrix-valued function strongly related to the discrete-time Lyapunov matrix equation, allow deriving a converse Lyapunov functional result. We show how the functionals can be used to solve problems such as the computation of exponential estimates for solutions and robustness bounds of perturbed systems.

An analytical solution for heat and mass transfer in falling film absorption with arbitrary thermal boundary conditions

Absorption, the process of capturing the absorptive component in the volume of the absorbent, is essential for various industrial applications. Several analytical solutions exist for falling film absorbers, which is the most common absorber used in industrial applications. However, in existing models, the temperature of the heat transfer fluid has been assumed to be constant, while the design of falling film absorbers for absorption heat pumps requires an analytical model accounting for the variation in the heat transfer fluid temperature changes. This study presents a new and comprehensive analytical solution for non-volatile absorbents using the Laplace transform method, where an arbitrary heat flux is applied to the heat exchanger wall in contact with the heat transfer fluid. For the first time, this study provides analytical solutions for various wall boundary conditions, including arbitrary heat flux, isothermal, as well as mean, linear, and exponential temperature variation of the heat transfer fluid. The present model is validated with experimental data available in the literature with a relative difference of 11% for several absorber configurations. Considering a case study of an absorber with a length of 1 m, it is shown that assuming an average temperature for the heat transfer fluid overestimates the optimal length of the absorber and results in up to 3 times the absorption rate at the outlet region of the absorber compared to a linear and an exponential temperature estimation.

A “lifting” method for exponential large deviation estimates and an application to certain non-stationary 1D lattice Anderson models

Proofs of localization for random Schrödinger operators with sufficiently regular distribution of the potential can take advantage of the fractional moment method introduced by Aizenman–Molchanov [Commun. Math. Phys. 157(2), 245–278 (1993)] or use the classical Wegner estimate as part of another method, e.g., the multi-scale analysis introduced by Fröhlich–Spencer [Commun. Math. Phys. 88, 151–184 (1983)] and significantly developed by Klein and his collaborators. When the potential distribution is singular, most proofs rely crucially on exponential estimates of events corresponding to finite truncations of the operator in question; these estimates in some sense substitute for the classical Wegner estimate. We introduce a method to “lift” such estimates, which have been obtained for many stationary models, to certain closely related non-stationary models. As an application, we use this method to derive Anderson localization on the 1D lattice for certain non-stationary potentials along the lines of the non-perturbative approach developed by Jitomirskaya–Zhu [Commun. Math. Physics 370, 311–324 (2019)] in 2019.

Free Energy and Equilibrium States for Families of Interval Maps

We study continuity, and lack thereof, of thermodynamical properties for one-dimensional dynamical systems. Under quite general hypotheses, the free energy is shown to be almost upper-semicontinuous: some normalised component of a limit measure will have free energy at least that of the limit of the free energies. From this, we deduce results concerning existence and continuity of equilibrium states (including statistical stability). Metric entropy, not semicontinuous as a general multimodal map varies, is shown to be upper semicontinuous under an appropriate hypothesis on critical orbits. Equilibrium states vary continuously, under mild hypotheses, as one varies the parameter and the map. We give a general method for constructing induced maps which automatically give strong exponential tail estimates. This also allows us to recover, and further generalise, recent results concerning statistical properties (decay of correlations, etc.). Counterexamples to statistical stability are given which also show sharpness of the main results.

Evolution of Esthetic Publications in Dentistry, Research Trends, and Global Productivity: A Bibliometric Analysis.

To perform a bibliometric study in the literature about the increasing number of global studies on dental esthetics in recent years. Articles on dental esthetics published between 1980 and 2021 were pulled from the Web of Science (WoS) database. In this comprehensive bibliometric study on dental esthetics, a summary of 2,858 articles published in the last 41 years was shared. Network visualization maps were used to identify citation analyses and trending topics. Spearman correlation coefficient was used for correlation studies. The exponential smoothing estimator was used to estimate the number of articles to be published in the coming years. Of the 3,666 publications, 2,858 (77.9%) were articles. The top three contributing countries to the literature were the USA (816, 28.5%), Brazil (286, 10%), and Italy (246, 8.6%). The most active institution was the University of Bern (n = 55). The journal with the highest number of articles was Journal of Prosthetic Dentistry (n = 178). According to the average number of citations per article, the most influential journal was Journal of Periodontology (citations: 55.6). Keywords of the trending topics related to dental esthetics are perception, bleaching, cleft lip, connective tissue graft, smile esthetics, adolescent, esthetic region, soft tissue augmentation, and clinical studies. In regard to the global output in dental esthetics, this article is a useful resource for clinicians, scientists, and dental students.

A Time-Varying Coefficient Double Threshold GARCH Model with Explanatory Variables

In this article, we consider the nonparametric inference for the time-varying coefficient double-threshold generalized autoregressive conditional heteroscedastic models. The quasi-maximum exponential likelihood estimators (QMELEs) of the model’s parameters and the asymptotic properties of the estimators are obtained. The simulation study implies that the distribution of the estimators is asymptotically normal. A real data application to stock returns is given. Both the simulations and real data example imply that the model and the QMELE are proper, compatible and accurately fit the financial time series data of the Nikkei 225.

Initial boundary value problem for a Kirchhoff wave model with strong nonlinear damping

This work is concerned with a Kirchhoff wave equation with strong nonlinear damping. We establish the local existence of the solution and provide some sufficient conditions for the global existence and finite time blow‐up of the solution. Moreover, we derive the exponential decay estimation of the energy functional and the upper and lower bounds of the blow‐up time.

An Improved Estimation of Population Mean Using Auxiliary Attribute in Stratified Sampling

Stratification improves the efficiency when the variance between strata is much larger than the variances within strata. An exponential estimator for stratified random sampling was proposed. Data sets on the amount of Apple production taken at three different occasions in Turkey in 1999 were used to validate the proposed estimator. The data sets were stratified by regions of Turkey and from each region; we randomly selected the samples by using the Neyman allocation method. Expressions for MSE of the proposed estimators were derived, up to first order of approximation. The suggested estimator families' bias and MSE equations were computed, the MSE for the proposed estimators is unbiased and efficient. The results of the theoretical comparison and numerical analysis shows that the suggested estimator outperformed the existing estimator. Moreover, the derived exponential estimator performed better than existing estimators for estimating population mean in stratified random sampling with an auxiliary attribute.

The Carathéodory approximation scheme for stochastic differential equations with G‐Lévy process

This article investigates the Carathéodory approximation scheme for stochastic differential equations (SDEs) in the G‐Lévy process framework. In the context of the G‐Lévy process, the possibility of SDE solutions has been developed. The solution's boundedness and uniqueness have been discussed. The convergence of approximate Carathéodory solutions to the unique solution of the given SDEs has been determined. The G‐Lévy framework is used to obtain exponential estimates for solutions to SDEs. An example has been provided to validate the results.

A class of multilinear bounded oscillation operators on measure spaces and applications

In this paper, we develop a comprehensive weighted theory for a class of Banach-valued multilinear bounded oscillation operators on measure spaces, which merges multilinear Calder\'{o}n-Zygmund operators with a quantity of operators beyond the multilinear Calder\'{o}n-Zygmund theory. We prove that such multilinear operators and corresponding commutators are locally pointwise dominated by two sparse dyadic operators, respectively. We also establish three kinds of typical estimates: local exponential decay estimates, mixed weak type estimates, and sharp weighted norm inequalities. Beyond that, based on Rubio de Francia extrapolation for abstract multilinear compact operators, we obtain weighted compactness for commutators of specific multilinear operators on spaces of homogeneous type. A compact extrapolation allows us to get full range of exponents, while weighted interpolation for multilinear compact operators is crucial to the compact extrapolation. These are due to a weighted Fr\'{e}chet-Kolmogorov theorem in the quasi-Banach range, which gives a characterization of relative compactness of subsets in weighted Lebesgue spaces. As applications, we illustrate multilinear bounded oscillation operators with examples including multilinear Hardy-Littlewood maximal operators on measure spaces, multilinear $\omega$-Calder\'{o}n-Zygmund operators on spaces of homogeneous type, multilinear Littlewood-Paley square operators, multilinear Fourier integral operators, higher order Calder\'{o}n commutators, maximally modulated multilinear singular integrals, and $q$-variation of $\omega$-Calder\'{o}n-Zygmund operators.

On asymptotic properties of solutions for differential equations of neutral type

The stability of systems of linear autonomous functional differential equations of neutral type is studied. The study is based on the well-known representation of the solution in the form of an integral operator, the kernel of which is the Cauchy function of the equation under study. The definitions of Lyapunov, asymptotic, and exponential stability are formulated in terms of the corresponding properties of the Cauchy function, which allows us to clarify a number of traditional concepts without loss of generality. Along with the concept of asymptotic stability, a new concept of strong asymptotic stability is introduced. The main results are related to the stability with respect to the initial function from the spaces of summable functions. In particular, it is established that strong asymptotic stability with initial data from the space \(L_1\) is equivalent to the exponential estimate of the Cauchy function and, moreover, exponential stability with respect to initial data from the spaces \(L_p\) for any \(p\ge1.\)

Exponential stability estimates for an axially travelling string damped at one end

We study the small vibrations of an axially travelling string with a dashpot damping at one end. The string is modelled by a wave equation in a time-dependent interval with two endpoints moving at a constant speed . For the undamped case, we obtain a conserved functional equivalent to the energy of the solution. We derive precise upper and lower exponentially decaying estimates for the energy with explicit constants. These estimates do not seem to be reported in the literature even for the non-travelling case .

Exponential state estimate of positive systems with time-varying delays: a Lyapunov–Razumikhin approach

AbstractIn this paper, for the first time, a linear Lyapunov–Razumikhin function is introduced to find an $\alpha$-exponential state estimate for positive systems with time delays. A new set of conditions for the existence of exponential state boundedness of positive systems with bounded time-varying delays is established. Two procedures are then proposed to find the factor vector of $\alpha$-exponential state estimate, in which some techniques of optimization are applied to find the smallest possible factor vector. Numerical experiments are presented to demonstrate the effectiveness of the linear Lyapunov–Razumikhin function as well as of the optimization techniques.

Exponential stability of linear discrete systems with multiple delays by degenerated Lyapunov–Krasovskii functionals

The problem of exponential stability of delayed discrete systems with multiple delays x(n+1)=(I+A)x(n)+∑i=1sBix(n−i),n=0,1,…is studied, where x=(x1x2…xm)T is an unknown vector, m and s are fixed positive integers, A, Bi are square constant matrices and I is a unit matrix. A new degenerated Lyapunov–Krasovskii functional is used to derive sufficient conditions for exponential stability and to derive an exponential estimate of the norm of solutions. Though often used in the study of stability, the assumption that the spectral radius of the matrix of linear terms is less than 1 is not applied here. The criterion derived is illustrated by an example and compared with previously known results.

Global productivity and research trends of colorectal carcinoma: A scientometric analysis of studies published between 1980 and 2021.

Although colorectal cancer (CRC) is a serious cause of death and has a significant impact on patients' quality of life and incidence rate of CRC has increased among the younger populations, bibliometric research of CRC has not been conducted yet. To perform a comprehensive analysis of scientific publications on CRC using various statistical and bibliometric techniques. Publications on CRC published between 1980 and 2021 were downloaded from the Web of Science database and analyzed using statistical methods. The trending topics, collaborations among countries, and citation relationships were analyzed using bibliometric network visualization mapping. The number of articles to be probably published in the next 5 years was estimated using the exponential smoothing estimator. The Spearman's correlation rank correlation coefficient was used to analyze the correlations among the variables. A total of 122,717 publications were found in the fields of oncology, gastroenterology, hepatology, and surgery. Of the published articles, 64,774 publications were research articles. The top five countries that contributed the most to the literature were the USA (16,604; 25.6%), China (10,567; 16.3%), Japan (7932; 12.2%), the UK (5009; 7.1%), and Italy (4287; 6.6%). The most prolific author, institution, and journal in the field of CRC were Zhang Y (n = 331), University of Texas System (n = 1646), and Diseases of the Colon and Rectum (n = 2090), respectively. The most influential journal based on the average number of citations received per article was CA-A Cancer Journal for Clinicians (citations per article; 286). There was a significant positive correlation between the number of articles produced by the countries on CRC and gross domestic product and human development index (r = 0.726, P < .001; r = 0.658, P < .001, respectively). Additionally, a significant moderate correlation of CRC was found with gross domestic product per capita (r = 0.711, P < .001). Keywords like overall survival, neoadjuvant chemoradiotherapy, locally advanced rectal cancer, robotic surgery, anastomotic leakage, chemoradiotherapy, metastatic colorectal cancer, KRAS, meta-analysis, colorectal surgery, and laparoscopic surgery were studied.

Increase in chlorophyll-a concentration in Lake Taihu from 1984 to 2021 based on Landsat observations

Lake Taihu, located in a densely populated and highly industrialized area in eastern China, has experienced dramatic changes in water quality since the reform and opening-up in the 1980s. Landsat data can be used to trace water quality changes over approximately 40 years. However, chlorophyll-a (Chla) estimation, which characterizes the trophic status, has not been thoroughly explored (especially in turbid water using wide bandwidth Landsat) due to the interference of suspended particulate matter (SPM) to Chla. In this study, we used Landsat TM/OLI for turbid water Chla inversion and to analyze the spatiotemporal variation of Chla in Lake Taihu for 38 years and its influencing factors. An optical classification algorithm based on Rrs(green)/Rrs(red) was used to exclude highly turbid waters dominated by SPM; Chla was estimated only in waters with low SPM. We constructed an exponential estimation model based on Rrs(NIR)/Rrs(red), and verified the accuracy of the model using the measured Chla synchronized with satellite data. The model was applied to Landsat images to calculate the Chla concentration in Lake Taihu during 1984–2021, and its spatiotemporal distribution patterns were further analyzed. Spatially, the Chla concentrations in the western and northern regions of Lake Taihu were higher than those in other regions, probably because these areas are estuaries with large exogenous pollutant discharge and more nutrients are imported from exogenous sources. Chla showed an overall significant upward trend from 1984 to 2021 probably because of temperature rise, wind speed reduction, and nutrient increase. The results of the spatial and temporal variation of Chla and the influencing factors in this study provide supporting data for eutrophication monitoring and management in Lake Taihu. The proposed Chla estimation method can be extended to assess the spatial and temporal distribution of eutrophication in other inland waters with similar optical properties.

Clubfoot from past to the present: A bibliometric analysis with global productivity and research trends.

Clubfoot, a common congenital abnormality, affects the lower extremities; however, the literature search revealed no bibliometric research on this subject. Thus, we aimed to holistically analyze scientific articles and reveal global productivity and trend issues. This study statistically analyzed 1417 published articles on clubfoot (1980-2021) from the Web of Science database. Bibliometric network visualization maps were created to reveal trend topics, citation analysis, and cross-country collaborations. The analysis was conducted using Spearman correlation analysis. An exponential smoothing estimator was used to predict article productivity. The United States of America (433, 30.5%), the United Kingdom (166, 11.7%), and India (107, 7.5%) are the top 3 countries contributing to the literature. The Journal of Pediatric Orthopedics (220 articles), the Journal of Pediatric Orthopedics-Part B (147 articles), and Clinical Orthopedics and Related Research (69 articles) are the top 3 most productive journals. Dobbs MB (34 articles) is the most active author, and Shriners Hospital Children (44 articles) is the most active institution. Bibliometric analysis revealed that recently studied trend topics included Pirani score, Dimeglio score, Ponseti method, Ponseti casting, tenotomy, recurrence, neglected, tendon transfer, bracing, gait, risk factors, pedobarography, complex clubfoot, and polymorphism. The most studied subjects included Ponseti technique, treatment/casting, recurrent/relapsed clubfoot, Pirani score, pediatrics/children, foot deformities, surgery, ultrasound, Achilles tendon/tenotomy, gait analysis, casting, outcomes, neglected clubfoot, and tenotomy. Research leadership was determined in the western and European countries and Canada in studies and scientific collaborations on clubfoot; its impact was remarkable in India, China, and Turkey.

Decoupling inequalities for quadratic forms

We prove sharp $\ell^q L^p$ decoupling inequalities for $p,q \in [2,\infty)$ and arbitrary tuples of quadratic forms. Connections to prior results on decoupling inequalities for quadratic forms are also explained. We also include some applications of our results to exponential sum estimates and to Fourier restriction estimates. The proof of our main result is based on scale-dependent Brascamp--Lieb inequalities.

АДАПТИВНІ СПОСТЕРІГАЧІ ЧАСТОТИ ДВОФАЗНИХ ТА ОДНОФАЗНИХ ГАРМОНІЧНИХ СИГНАЛІВ

An adaptive observer for frequency and magnitude of two-phase symmetrical sinusoidal signal is presented. It is de-signed based on control concept of internal model approach. The observer guarantees global exponential estimation and high performance. If the information about one of the two-phase signal components is missing, a modified structure of the observer is proposed. This case is equivalent to the measurement of a single-phase sinusoidal signal. The proper-ties of local exponential stability of single-phase signal observer are proved using Lyapunov’s conversion theorem for disturbed systems. The robustness of the two-phase signal observer with respect to additive disturbances (high-frequency noise, varying frequency) is confirmed by simulation results. It is shown that the observer estimation speed can be arbitrarily increased by increasing the feedback gains. A method for single-phase harmonic signal frequency observer tuning is developed, which ensures the expansion of the stability region. References 14, figures 7.

Exponential ratio estimator of the median: An alternative to the regression estimator of the median under stratified sampling

This article develops statistical inference about the population median under the stratified sampling method. An exponential class of ratio estimators of the median was suggested using the combination of scalars and known supplementary information on the population median. Mean square error and bias expressions were derived theoretically and also the AOE (asymptotic optimum estimator) conditions were obtained with its mean square error and bias expressions. From both the empirical evidence and analytical approach evaluations of the AOE with other obtainable members of the suggested class of estimators show that the AOE performs better than its competitors in the literature and is also the alternative to the regression estimator of the median under a stratified random sampling scheme.