Hallux valgus (HV), one of the most common forefoot pediatric pathologies, is characterized by lateral deviation of the big toe and medial displacement of the first metatarsal bone. Different surgical techniques have been described to correct the def...
By employing the bisection series approach, two classes of nonterminating 3
The practical usefulness of Levin-type nonlinear sequence transformations as numerical tools for the summation of divergent series or for the convergence acceleration of slowly converging series is nowadays beyond dispute. The Weniger transformation,...
The author’s research devoted to the Hilbert’s double series theorem and its various further extensions are the focus of a recent survey article. The sharp version of double series inequality result is extended in the case of a not exhaustively inves...
By utilizing the modified Abel lemma on summation by parts, we examine a class of quintic q-series, that have close connections to the “twisted cubic q-series”. Several remarkable summation and transformation formulae are established. The related rev...
B-series were defined to unify the formalism of solutions for ordinary differential equations defined by series. Runge–Kutta schemes can be seen as truncated B-series, similar to Taylor series. In the prolific domain of reachability analysis, i...
We study the convergence of the parameter family of series:
In this paper, function approximation is utilized to establish functional series approximations to integrals. The starting point is the definition of a dual Taylor series, which is a natural extension of a Taylor series, and spline based series appro...
Summation of infinite series has played a significant role in a broad range of problems in the physical sciences and is of interest in a purely mathematical context. In a prior paper, we found that the Fourier–Legendre series of a Bessel functi...
The main contribution of this paper is to propose a closed expression for the Ramanujan constant of alternating series, based on the Euler–Boole summation formula. Such an expression is not present in the literature. We also highlight the only choice...
This paper reviews the basics of series compensation in transmission systems through a literature survey. The benefits that this technology brings to enhance the steady state and dynamic operation of power systems are analyzed. The review outlines th...
Two distances based on permutations are considered to measure the similarity of two time series according to their strength of dependency. The distance measures are used together with different linkages to get hierarchical clustering methods of time...
Utilizing a temperature time-series prediction model to achieve good results can help us to accurately sense the changes occurring in temperature levels in advance, which is important for human life. However, the random fluctuations occurring in a te...
The earliest and simplest impedance compensation technique used in inductive wireless power transfer (WPT) design is the series-series (SS) compensation circuit, which uses capacitors in series with both primary and secondary coils of an air-gapped t...
Binomial series involving harmonic polynomials are expressed in terms of parametric integrals. By evaluating these parametric integrals, we establish several remarkable closed formulae for the infinite series containing both central binomial coeffici...
Shapelet-based time series classification methods are widely adopted models for time series classification tasks. However, the high computational cost greatly limits the practicability of the Shapelet-based methods. What is more, traditional Shapelet...
A very recent article delved into and expanded the four parametric linear Euler sums, revealing that two well-established subjects—Euler sums and series involving the zeta functions—display particular correlations. In this study, we prese...
This paper investigates D-finite discrete generating series and their sections. The concept of D-finiteness is extended to multidimensional discrete generating series and its equivalence to p-recursive sequences is rigorously established. It is furth...
The Bessel function of the first kind
Padé approximants are computational tools customarily employed for resumming divergent Stieltjes series. However, they become ineffective or even fail when applied to Stieltjes series whose moments do not satisfy the Carleman condition. Differ...
In this part of a series of two papers, we extend the theorems discussed in Part I for infinite series. We then use these theorems to develop distinct novel results involving the Hurwitz zeta function, Riemann zeta function, polylogarithms and Fibona...
This research introduces a novel high-accuracy time-series forecasting method, namely the Time Neural Network (TNN), which is based on a kernel filter and time attention mechanism. Taking into account the complex characteristics of time-series data,...
Nowadays, climate change and atmospheric pollution are two of humanity's most significant challenges. Greenhouse gases (GHGs) are responsible for climate change, and they create effects that are mostly irreversible. Therefore, monitoring and reducing...
By making use of the linearization method, we examine a class of nonterminating
Flood frequency analysis using partial series data has been shown to provide better estimates of small to medium magnitude flood events than the annual series, but the annual series is more often employed due to its simplicity. Where partial series a...
In this paper, a novel data augmentation method for time-series classification is proposed. In the introduced method, a new time-series is obtained in warped space between suboptimally aligned input examples of different lengths. Specifically, the al...
By examining Fourier–Legendre series pairs
The DC arc is the main cause of fire in photovoltaic (PV) systems. This is due to the fact that the DC arc has no zero-crossing point and is prone to stable combustion. Failure to detect it in a timely manner can seriously endanger the PV system. Thi...
The article presents a novel method of fractal time series classification by meta-algorithms based on decision trees. The classification objects are fractal time series. For modeling, binomial stochastic cascade processes are chosen. Each class that...
Time series of financial data are both frequent and important in everyday practice. Numerous applications are based, for example, on time series of asset prices or market indices. In this article, the application of fractal interpolation functions in...
Several q-series identities were obtained using the telescoping method. These identities were then used to derive double series expressions for well-known zeta-value constants.
Time series anomaly detection through unsupervised methods has been an active research area in recent years due to its enormous potential for networks management. The representation and reconstruction of time series have made extraordinary progress i...
A new comprehensive approach to nonlinear time series analysis and modeling is developed in the present paper. We introduce novel data-specific mid-distribution-based Legendre Polynomial (LP)-like nonlinear transformations of the original time series...
The removal of non-climatic biases, so-called inhomogeneities, from long climatic records needs sophistically developed statistical methods. One principle is that the differences between a candidate series and its neighbor series are usually analyzed...
High-quality Normalized Difference Vegetation Index (NDVI) time series are essential in studying vegetation phenology, dynamic monitoring, and global change. Gap filling is the most important issue in reconstructing NDVI time series from satellites w...
The Padua temperature series is one of the longest in the world, as daily observations started in 1725 and have continued almost unbroken to the present. Previous works recovered readings from the original logs, and digitalized and corrected observat...
Monitoring vegetation changes over time is very important in dry areas such as Iran, given its pronounced drought-prone agricultural system. Vegetation indices derived from remotely sensed satellite imageries are successfully used to monitor vegetati...
In order to investigate the effect of different loading models on the nonlinear variations in Global Positioning System (GPS) height time series, the characteristics of annual signals (amplitude and phase) of GPS time series, loading series from Deut...
In this paper, we consider parallel-series and series-parallel systems comprising dependent components that are drawn from a heterogeneous population consisting of m different subpopulations, and each subsystem is equipped with a starter device. We a...
Time series data are significant, and are derived from temporal data, which involve real numbers representing values collected regularly over time. Time series have a great impact on many types of data. However, time series have anomalies. We introdu...
The paper concerns the solution of the ordinary differential equation
Rotary kiln temperature forecasting plays a significant part of the automatic control of the sintering process. However, accurate forecasts are difficult owing to the complex nonlinear characteristics of rotary kiln temperature time series. With the...
In this paper, a nonlinear time series model is developed for the case when the underlying time series data are reported by
We examine a large class of infinite triple series and establish a general summation formula. This is done by expressing the triple series in terms of definite integrals involving arctangent function that are evaluated in turn in closed forms. Numero...
This paper reviews the application of artificial neural network (ANN) models to time series prediction tasks. We begin by briefly introducing some basic concepts and terms related to time series analysis, and by outlining some of the most popular ANN...
It is hard for current time series reconstruction methods to achieve the balance of high-precision time series reconstruction and explanation of the model mechanism. The goal of this paper is to improve the reconstruction accuracy with a well-explain...
Time-series data are widespread and have inspired numerous research works in machine learning and data analysis fields for the classification and clustering of temporal data. While there are several clustering methods for univariate time series and a...
Floods typically occur due to ice jams in the winter or extended periods of precipitation in the spring and summer seasons. An increase in the rate of water discharge in the river coincides with a flood event. This research combines the time series d...
The Key Laboratory of Integrated Microsystems (IMS) of Peking University Shenzhen Graduate School has deployed a self-developed acoustic and electromagnetics to artificial intelligence (AETA) system on a large scale and at a high density in China to...
We derive some series related to the polylogarithmic function, and we also give a new proof to the existing series. Our approach is based on using the summation and integral representation methods. We obtain various interesting series as a consequence.
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