We examine a nonlinear initial value problem both singularly perturbed in a complex parameter and singular in complex time at the origin. The study undertaken in this paper is the continuation of a joined work with A. Lastra published in 2015. A change of balance between the leading and a critical subdominant term of the problem considered in our previous work is performed. It leads to a phenomenon of coalescing singularities to the origin in the Borel plane w.r.t time for a finite set of holomorphic solutions constructed as Fourier series in space on horizontal complex strips. In comparison to our former study, an enlargement of the Gevrey order of the asymptotic expansion for these solutions relatively to the complex parameter is induced.

We investigate a singularly perturbed q-difference differential Cauchy problem with polynomial coefficients in complex time and space with quadratic nonlinearity. We construct local holomorphic solutions on sectors in the complex plane with respect to the perturbation parameter with values in some Banach space of formal power series in space with analytic coefficients on shrinking domains in time. Two aspects of these solutions are addressed. One feature concerns asymptotic expansions in the parameter for which a Gevrey type structure is unveiled. The other fact deals with confluence properties as q tends to 1. In particular the built up Banach valued solutions are shown to merge in norm to a fully bounded holomorphic map in all its arguments that solves a nonlinear partial differential Cauchy problem.

We examine a family of nonlinear q-difference-differential Cauchy problems obtained as a coupling of linear Cauchy problems containing dilation q-difference operators, recently investigated by the author, and quasi-linear Kowalevski type problems that involve contraction q-difference operators. We build up local holomorphic solutions to these problems. Two aspects of these solutions are explored. One facet deals with asymptotic expansions in the complex time variable for which a mixed type Gevrey and q-Gevrey structure is exhibited. The other feature concerns the problem of confluence of these solutions as q tends to 1.

A linear Cauchy problem with polynomial coefficients wich combines q-difference operators for q>1 and differential operators of irregular type is examined. A finite set of sectorial holomorphic solutions w.r.t the complex time is constructed by means of classical Laplace transforms. These functions share a common asymptotic expansion in the time variable which turns out to carry a double layers structure which couples q-Gevrey and Gevrey bounds. In the last part of the work, the problem of confluence of these solutions as q tends to 1 is investigated.

We examine a linear q-difference differential equation which is singular in complex time t at the origin. Its coefficients are polynomial in time and bounded holomorphic on horizontal strips in one complex space variable. The equation under study represents a q-analog of a singular partial differential equation, recently investigated by the author, which comprises Fuchsian operators and entails a forcing term that combines polynomial and logarithmic type functions in time. A sectorial holomorphic solution to the equation is constructed as a double complete Laplace transform in both time t and its complex logarithm log t and Fourier inverse integral in space. For a particular choice of the forcing term, this solution turns out to solve some specific nonlinear q-difference differential equation with polynomial coefficients in some positive rational power of t. Asymptotic expansions of the solution relatively to time t are investigated. A Gevrey type expansion is exhibited in a logarithmic scale. Furthermore, a formal asymptotic expansion in power scale is displayed, revealing a new fine structure involving remainders with both Gevrey and q-Gevrey type growth.

The available direct gas dynamic tables provide the area ratio and the Prandtl-Meyer(P-M) angle of isentropic expansion of gas as functions of the Mach number. But finding the value of the Mach number in terms of area ratio or P-M angle requires an inverse function. Currently, the Mach number is determined by either interpolation from the direct gas dynamics tables, or the application of non-linear equation solvers using numerical methods. Both methods are approximate. In this paper inverse functions for Mach number in the form of Taylor’s series expansions are reported to develop the so-called inverse tables. The advantage of this approach is that the Mach number with a greater accuracy, referred to as nearly exact can be obtained by reading from the inverse table. In the presentation, the necessary equations and new tables that can be used by the scientific community will be disseminated. The data and computer programs are made available on GitHub through https://github.com/anillals/Inverse-gas-dynamic-tables- and-codes. A paper describing the complete mathematical steps in the derivation of the equations can be found at https://rdcu.be/dgrlf

Long-range interactions are relevant for a large variety of quantum systems in quantum optics and condensed matter physics. In particular, the control of quantum-optical platforms promises to gain deep insights in quantum-critical properties induced by the long-range nature of interactions. From a theoretical perspective, long-range interactions are notoriously complicated to treat. Here, we give an overview of recent advancements to investigate quantum magnets with long-range interactions focusing on two techniques based on Monte Carlo integration. First, the method of perturbative continuous unitary transformations where classical Monte Carlo integration is applied within the embedding scheme of white graphs. This linked-cluster expansion allows to extract high-order series expansions of energies and observables in the thermodynamic limit. Second, stochastic series expansion quantum Monte Carlo which enables calculations on large finite systems. Finite-size scaling can then be used to determine physical properties of the infinite system. In recent years, both techniques have been applied successfully to one- and two-dimensional quantum magnets involving long-range Ising, XY, and Heisenberg interactions on various bipartite and non-bipartite lattices. Here, we summarise the obtained quantum-critical properties including critical exponents for all these systems in a coherent way. Further, we review how long-range interactions are used to study quantum phase transitions above the upper critical dimension and the scaling techniques to extract these quantum critical properties from the numerical calculations.

We examine a family of linear partial differential equations both singularly perturbed in a complex parameter and singular in complex time at the origin. These equations entail forcing terms which combine polynomial and logarithmic type functions in time and that are bounded holomorphic on horizontal strips in one complex space variable. A set of sectorial holomorphic solutions are built up by means of complete and truncated Laplace transforms w.r.t time and parameter and Fourier inverse integral in space. Asymptotic expansions of these solutions relatively to time and parameter are investigated and two distinguished Gevrey type expansions in monomial and logarithmic scales are exhibited.

We investigate a family of nonlinear partial differential equations which are singularly perturbed in a complex parameter and singular in a complex time variable at the origin. These equations combine differential operators of Fuchsian type in time and space derivatives on horizontal strips in the complex plane with a nonlocal operator acting on the complex parameter known as the formal monodromy around 0. Their coefficients and forcing terms comprise polynomial and logarithmic type functions in time and are bounded holomorphic in space. A set of logarithmic type solutions are shaped by means of Laplace transforms relatively to time and parameter and Fourier integrals in space. Furthermore, a formal logarithmic type solution is modeled which represents the common asymptotic expansion of Gevrey type of the genuine solutions with respect to the complex parameter on bounded sectors at the origin.

Different values of the Hubble constant for extragalactic objects are not considered here. We give a number of examples of the extreme accordance of expansion rates of different fields of knowledge with the cosmological expansion rate. The coincidence of the expansion rates means that a common cause is almost inevitable. All these examples are gravitationally bound in themselves and in this case are subject to cosmological expansion. According to standard theory, this should not happen. We therefore question the common boundary of gravity and expansion for both theoretical and observational reasons and conclude that all gravitationally dominated objects participate in cosmological expansion or scale drift, contrary to general doctrine. The space expands with its contents while numerically maintaining distance, radius, rotation time and density. What is generally interpreted as an expansion is obviously a scale drift with a drift rate that corresponds to the size of the Hubble constant. The Earth is subject to expansion and scale drift. This results in numerically constant measured values. This drift apparently also applies to distant galaxies and other objects. The cosmological red shift is not interpreted here as a Doppler effect and numerical increase in distances, but in accordance with standard theory as an expansion or drift of the space-time scale. The expansion of the radii of galaxies makes the assumption of dark matter superfluous. The continents and our everyday environment are not subject to expansion or scale drift.

We introduce and analyze conceptual approximations of the Boussinesq equation for horizontal unconfined aquifers during the pure drainage phase, without any reharge and zero-inflow conditions. We employ a variety of methods, which include wave solution, variable separation and series expansion to constract a new model and explore its behavior and performance against the Boussinesq equation and its exact (non-closed form) solution, at early and later times. The modeled non-linear forms are finally linearized concluding with explicit analytical expressions that incorporate most of the basic characteristics regarding the evolution of the water table and the outflow from the exact Boussinesq equation under different initial conditions. The endeavors of this work might be useful for theoretical and modeling purposes related to this problem.

A family of linear singularly perturbed Cauchy problems is studied. The equations defining the problem combine both partial differential operators together with the action of linear fractional transforms. The exotic geometry of the problem in the Borel plane, involving both sectorial regions and strip-like sets, gives rise to asymptotic results relating the analytic solution and the formal one through Gevrey asymptotic expansions. The main results lean on the appearance of domains in the complex plane which remain intimately related to Lambert W function, which turns out to be crucial in the construction of the analytic solutions. On the way, an accurate description of the deformation of the integration paths defining the analytic solutions and the knowledge of Lambert W function are needed in order to provide the asymptotic behavior of the solution near the origin, regarding the perturbation parameter. Such deformation varies depending on the analytic solution considered, which lies in two families with different geometric features.

The work is devoted to the study of a family of linear initial value problems of partial differential equations in the complex domain, dealing with two complex time variables. The use of a truncated Laplace-like transformation in the construction of the analytic solution allows to overcome a small divisor phenomenon arising from the geometry of the problem and represents an alternative approach to the one proposed in a recent work by the first two authors. The result leans on the application of a fixed point argument and the classical Ramis-Sibuya theorem.

A nonlinear singularly perturbed Cauchy problem with confluent fuchsian singularities is examined. This problem involves coefficients with polynomial dependence in time. A similar initial value problem with logarithmic reliance in time has been investigated by the author in a recent work, for which sets of holomorphic inner and outer solutions were built up and expressed as a Laplace transform with logarithmic kernel. Here, a family of holomorphic inner solutions are constructed by means of exponential transseries expansions containing infinitely many Laplace transforms with special kernel. Furthermore, asymptotic expansions of Gevrey type for these solutions relatively to the perturbation parameter are established.

Four methods in two different families have been constructed to derive the exact solutions to Benjamin-Bona-Mahony equation in two space dimensions. Simply defined hyperbolic tangent, hyperbolic secant and hyperbolic cosecant ansatzes and the expansion method based on the Sine-Gordon equation in two dimensions are directly substituted into the governing ODE reduced from the two dimensional BBM equation. Classical algebraic method is used to find the relations among the target parameters representing the nonzero coefficients in the predicted solutions and the wave transform parameters. Some complex and real solutions have been constructed in explicit forms.

This paper is a slightly modified, abridged version of a previous work ``Parametric Gevrey asymptotics in two complex time variables through truncated Laplace transforms'' motivated by our contribution in the conference ``Formal and Analytic Solutions of Diff. (differential, partial differential, difference, q-difference, q-difference-differential) Equations on the Internet'' (FASnet20). It aims to clarify and give further detail at some crucial points concerning the asymptotic behavior of the solutions of the problems studied in that work.

This paper is a slightly modified, abridged version of a previous work "Parametric Gevrey asymptotics in two complex time variables through truncated Laplace transforms'' motivated by our contribution in the conference "Formal and Analytic Solutions of Diff. (differential, partial differential, difference, q-difference, q-difference-differential) Equations on the Internet'' (FASnet20). It aims to clarify and give further detail at some crucial points concerning the asymptotic behavior of the solutions of the problems studied in that work.

Significant efforts are being made across academia and industry to better characterize lithium-ion battery cells as reliance on the technology for applications ranging from green energy storage to electric mobility increases. The measurement of short-term and long-term volume expansion in lithium-ion battery cells is relevant for several reasons. For instance, it provides information about the quality and homogeneity of battery cells during charge and discharge cycles, as well as aging over it’s lifetime. The expansion measurements are useful for the evaluation of new materials and the improvement of end-of-line quality tests during cell production. These measurements may also indicate the safety of battery cells by aiding in predicting state of charge and state of health over the lifetime of the cell. Expansion measurements can also assess inhomogeneities on the electrodes and defects such as gas accumulation and lithium plating. In this review, we first establish the known mechanisms through which short term and long term volume expansion in lithium-ion battery cells occurs. We then explore the current state-of-the-art for both contact and non-contact measurements of volume expansion. This review compiles existing literature to outline the various options available to researchers aiming to make ex situ volume expansion measurements by doing post mortem analyses on individual components and in operando measurements on entire battery cells. Finally, we discuss the different considerations when selecting an appropriate measurement technique. The selection of the optimal method for measuring battery cell expansion depends on the objective of the characterization, duration, required resolution, and repeatability of results. Costs and required space for the measurement equipment are also considered.

An experimental investigation on the heat pump performance improvement equipped with the two-phase ejector called “an ejector-expansion heat pump (EEHP)” is proposed. The system performance of the EEHP is compared with a vapour-compression heat pump (VCHP). The improvement potential is determined and discussed. The heat pump test system is constructed which is based on a water-to-water heat pump. It can be experimented with both EEHP and VCHP. The two-phase ejector with the cooling load up to 2500 W is installed for experiment. The results show that the EEHP always produces a higher heating rate and COP than the VCHP throughout the specified working conditions. The heating COP is increased by 5.7-12.2% depending on the working conditions. It is also that under the same heat sink and heat source temperature, the EEHP can produce lower compressor discharge temperature and lower compressor pressure ratio than the VCHP. This is evidence that the two-phase ejector can provide better compressor working characteristics which yields a longer compressor lifetime. It is demonstrated that a key to the performance of the EEHP is the expansion pressure ratio. A larger expansion pressure ratio yields a higher improvement potential when compared with the VCHP.

Hydrogen powered vehicles use high-pressure reservoirs from which the gas is transferred to the low-pressure fuel-cell via a classical pressure reduction valve. In these systems no expansion work is recovered and the question is addressed of the potential to increase the global efficiency by using an expansion machine between the reservoir and the electrochemical reactor. This paper investigates the feasibility of such an expansion machine, evaluates the mechanical constraints in terms of forces, torques and produced power by numeric simulation. It further evaluates the energetic contribution to the whole conversion chain from the hydrogen reservoir to the common electrical network on board. A low energy contribution of the expansion system addresses the question of the real benefit of such an investment.

We consider a family of nonlinear singularly perturbed PDEs whose coefficients involve a logarithmic dependence in time with confluent Fuchsian singularities that unfold an irregular singularity at the origin and rely on a single perturbation parameter. We exhibit two distinguished finite sets of holomorphic solutions, so-called outer and inner solutions, by means of a Laplace transform with special kernel and Fourier integral. We analyze the asymptotic expansions of these solutions relatively to the perturbation parameter and show that they are (at most) of Gevrey order 1 for the first set of solutions and of some Gevrey order that hinges on the unfolding of the irregular singularity for the second.

We study and describe possibilities for arities of elementary theories and of their expansions. Links for arities with respect to Boolean algebras, to disjoint unions and to compositions of structures are shown. Arities and aritizabilities are semantically characterized. The dynamics for arities of theories is described.

In this article, we discuss the concept of infinity (∞), infinitesimals □ , and a new mathematical operation that expands calculations into the realm of the infinite. This breakthrough allows for the computation of infinite numbers, leading to new possibilities for mathematical research and practical applications. By introducing infinite numbers, numerous advantages arise, such as accurately representing limits, divergences in integrals and infinite series, and extending calculations to infinity. This mathematical advancement opens doors to exploring uncharted territories, offering valuable insights and breakthroughs.

Expansion of the universal space was never directly observed. It is an unproven assumption. Measurement of the gravitational redshift proves only gravitational redshift and nothing more. Gravitational redshift is proven by the Mössbauer experiment. Claiming that gravitational redshift proves universal space expansion is false because there is no causality between gravitational redshift and hypothetical expansion. Even if universal space would expand, gravitational redshift could not be taken as proof of expansion. The Doppler effect was never observed in an expanding space and claiming that cosmological redshift is partially caused by the Doppler effect caused by the expanding of space is an unproved assumption. The discovery of CMB proves only that the entire universal space radiates CMB. CMB is not proof of the existence of the recombination period.

China’s rural e-commerce has been developing rapidly. Taobao Villages are combination of e-commerce and rural industries. When rural e-commerce coverage evolves from Taobao village to Taobao town, the scale of industrial clusters has been expanding synchronously. This paper investigates flower and seedling industrial cluster in Xinhe Town, Yanji Town and Miaotou Town of Shuyang County, China, and conducts the econometric analysis of the expansive determinants of flower and seedling industrial cluster of Taobao Villages. An effective sample of 263 was obtained through a face-to-face survey of e-merchants of flower and seedling in the Shuyang County of Jiangsu Province. Bases on the structural equation modeling, series of test results show that the data can be used to calculate the path regression. The outcomes shows that creation of e-merchants of flower and seedling, integration of e-commerce platform, supply chain friendliness, involvement of e-commerce service providers, and governmental policy guidance are driving expansion of flower and seedling industrial cluster together, moreover, the five forces interact with each other. This implies that expansion of flower and seedling industrial cluster is a systematic process, each stakeholder needs to pay attention to the role of other forces, and five forces achieve a balanced situation in the cluster.

This paper aims to investigate the rate of expansion and extraction within the solar system. We carried out the Solar system expansion calculations to do such a review. The Universe is expected to look the same from every point in it. After the big bang, Universe is expanding at some speed. Astrophysicists have been in a race to measure precisely how fast the Universe is expanding since Hubble announced that galaxies were systematically moving away from Milky Way Galaxy with a current speed in 1929. Hubble’s observations came after Einstein’s general relativity, which inspired the big bang theory. According to the Big Bang theory, the Universe has created billions of years ago with an explosion and started to expand until today. The expansion of the Universe mostly happens in vast spaces, so clusters of galaxies move away from each other. For example, raising bread during baking will expand, but the raisings will stay the same size while moving each other to expand the bread. Observers have proven that an object (galaxies, a cluster of planets) held together by gravity has a patch of nonexpanding space produced by a gravitational field. However, some observers claimed the solar system is not expanding, while others claimed it is expanding. Does our solar system expand in an expanding Universe? The cosmological expansion of local systems is reviewed in the modern cosmological models. We showed answers related to this question with the help of literature. This review article revisited the proof of the Solar System’s expansion and its speed with about 0.32 nm/s in an expanding Universe.

This study explores the changes in the landmass bounded by the coast of India during 1975-2005 by using on-screen visual interpretation technique (with 100m resolution and 1:50,000 scale) from NASA Landsat Imagery in three different time periods viz. 1975, 1990, and 2005. The result indicated an overall expansion of 130 sq. km area of the landmass that surrounded by the Indian coast during 1975-2005 (74 sq. km during 1975-1990 and 56 sq. km during 1991-2005). These estimations are based on the preliminary analysis and may be estimated more accurately by reducing the scale and using further higher resolution images.

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 introduce hybrid algorithm named novel matrix profile (NMP) to solve the all-pairs similarity search problem for time series data. The proposed NMP inherits the features from two state-of-the art algorithms: similarity time-series automatic multivariate prediction (STAMP), and short text online microblogging protocol (STOMP). The proposed algorithm caches the output in an easy-to-access fashion for single- and multidimensional data. The proposed NMP algorithm can be used on large data sets and generates approximate solutions of high quality in a reasonable time. The proposed NMP can also handle several data mining tasks. It is implemented on a Python platform. To determine its effectiveness, it is compared with the state-of-the-art matrix profile algorithms i.e., STAMP and STOMP. The results confirm that the proposed NMP provides higher accuracy than the compared algorithms.

In this work, Gd-filled skutterudite GdxCo4Sb12 has been prepared in one-step method under high-pressure conditions in a piston-cylinder press at 3.5 GPa and moderate temperature of 800 °C. A detailed structural characterization was performed using synchrotron X-ray diffraction (SXRD), revealing a filling fraction of x = 0.066(4) and an average <Gd–Sb> bond length of 3.3499(3) Å. The lattice thermal expansion accessed via temperature-dependent SXRD led to a precise determination of a Debye temperature of 322(3) K, from the fitting of the unit-cell volume expansion using the second order Grüneisen approximation. Such parameter, when evaluated from the mean square displacements of Co and Sb, displayed a value of 265(2) K, meaning that the application of the harmonic Debye theory underestimates the Debye temperature in skutterudites. Regarding the Gd atom, its intrinsic disorder value is ~5× and ~25× higher than those of Co and Sb, respectively, denoting that Gd has a strong rattling behavior with an Einstein temperature of θE = 67(2) K. As a result, an ultra-low thermal conductivity of ~0.89 W/m·K at 773 K was obtained, leading to a thermoelectric efficiency zT of ~0.5 at 673 K.

The unicellular eukaryote S. cerevisiae is an invaluable resource for the study of basic eukaryotic cellular and molecular processes. However, due to its small size compared to other eukaryotic organisms the study of subcellular structures is challenging. Expansion microscopy (ExM) holds great potential to study the intracellular architecture of yeast, especially when paired with pan-labelling techniques visualising the full protein content inside cells. ExM allows to increase imaging resolution by physically enlarging a fixed sample that is embedded and cross- linked to a swellable gel followed by isotropic expansion in water. The cell wall present in fungi – including yeast – and Gram-positive bacteria is a resilient structure that resists denaturation and conventional digestion processes usually used in ExM protocols, resulting in uneven expansion. Thus, the digestion of the cell wall while maintaining the structure of the resulting protoplasts are crucial steps to ensure isotropic expansion. For this reason, specific experimental strategies are needed, and only a few protocols are currently available. We have developed a modified ExM protocol for S. cerevisiae, with 4x expansion factor, which allows the visualisation of the ultrastructure of the cells. Here, we describe the experimental procedure in detail, focusing on the most critical steps required to achieve isotropic expansion for ExM of S. cerevisiae.

The recent Planck Legacy release confirmed the existence of an enhanced lensing amplitude in the cosmic microwave background (CMB) power spectra, which endorses the positive curvature of the early Universe with a confidence level exceeding 99%. In this study, the pre-existing curvature is incorporated to extend the field equations where the derived wave function of the Universe is utilized to model Universe evolution with reference to the scale factor of the early Universe and its radius of curvature upon the emission of the CMB. The wave function reveals both positive and negative solutions, implying that matter and antimatter of early Universe plasma evolve in opposite directions as distinct Universe sides. The wave function indicates that a nascent hyperbolic expansion is followed by a first phase of decelerating expansion away from early plasma during the first 10 Gyr, and then, a second phase of accelerating expansion in reverse directions, whereby both Universe sides free-fall towards each other under gravitational acceleration. Simulations of the predicted conformal curvature evolution demonstrate the fast orbital speed of outer stars owing to the external fields exerted on galaxies as they travel through conformally curved space-time. Finally, the wave function predicts an eventual time-reversal phase comprising rapid spatial contraction that culminates in a Big Crunch, signalling a cyclic Universe. These findings reveal that early plasma could have separated and evolved into distinct sides that collectively and geometrically influencing the Universe evolution, physically explanting the effects attributed to dark matter and energy.

As the coproduct of steelmaking, steelmaking slag, volumetrically expansive-prone without treatment, has been satisfactorily used as an aggregate base course material in highway construction. Although numerous technical reports and papers have revealed that steel slag aggreged using in rigid matrixes, the end product, paving block, non-structural concrete, for example, possesses superb strength and durability properties, the application of steel slag aggregate as a concrete aggregate is currently prohibited in highway construction. Naturally, researchers explore the practicality of use of steel slag, how to connect the laboratory experiment results to the end-product behavior, and further convert the research results into real construction? For all nontraditional or secondary materials utilization, the procedure of laboratory material examination, lab and field trial test are critical. To generalize the utilization, usability criteria establishment is necessary. This paper tries to use step-by-step method and plain language to explain how the volumetrically expansion can be simulated in lab testing apparatus, and based on the model, the mathematical deduction can result in a numerical usability criterion for steel slag use as a coarse aggregate in concrete (a rigid material). Therefore the paper is composed four main parts, laboratory test methods to examine the expansion force resulted from steel slag; converting the measured expansion force in a given volume of mass aggregate to the expansion (body) force of a single particle; modeling of slag and end material disruption; and a usability criterion from numerical deduction for the use of expansive-prone coarse slag in concrete or other rigid matrices. The paper provides the solutions to answer the above questions. Through the mathematical and mechanical modeling, provides the potential criteria that could result in specifications and guidance establishment for broad volumetric expansive-prone slags.

The anomaly detection task is very important in computer science. And there are a lot of anomaly detection methods. Different from some thresholding methods, some unsupervised methods could make us get more accurate and faster result, which is the object of the project. In this paper, I tried to use EWMA and some other methods in two datasets: Webank time consuming indicators dataset and AIOps Challenge dataset. The paper consists nine parts: background of the project, related work, description of algorithms, implementation details, experimental setup and data sets used, experimental results and discussion, future directions, reference and meeting notes.

Divergences have become a very useful tool for measuring similarity (or dissimilarity) between probability distributions. Depending on the field of application a more appropriate measure may be necessary. In this paper we introduce a family of divergences we call gamma-divergences. They are based on the convexity property of the functions that generate them. We demonstrate that these divergences verify all the usually required properties, and we extend them to weighted probability distribution. We investigate their properties in the context of kernel theory. Finally, we apply our findings to the analysis of simulated and real time series.

The Bessel function of the first kind J_N(kx) is expanded in a Fourier-Legendre series, as is the modified Bessel functions of the first kind I_N(kx) . Known polynomial approximations for the range −3≤x≤3 (having five-digit accuracy) are compared with those arising from this Legendre series and substitute versions are given with twice the number of terms and range (with five-digit accuracy or having fifteen-digit accuracy over −3≤x≤3). It is shown that infinite series of like-powered contributors (involving _2F_3 hypergeometric functions) extracted from the Fourier-Legendre series may be summed, having values that are inverse powers of the first five primes 1/(2^i 3^j 5^k 7^l 11^mm) for powers of order x24.

Industrial data scarcity is one of the largest factors holding back the widespread use of machine learning in manufacturing. To overcome this problem, the concept of transfer learning was developed and it achieved high attention in recent industrial research. Our paper focuses on the problem of time series segmentation and presents the first in-depth research about transfer learning for deep-learning based time series segmentation on the example of industrial end-of-line pump testing. In particularly, we investigate if the performance of deep learning models can be increased by pretraining the network with data from other domains. Three different scenarios are analyzed: source and target data being closely related, source and target data being distantly related, and source and target data being non-related. The results demonstrate that transfer learning can enhance the performance of time series segmentation models in respect to accuracy and training speed. The benefit is most clearly seen in scenarios where source and training data are closely related and the number of target training data samples is lowest. However, in the scenario of non-related datasets, cases of negative Transfer Learning were observed as well. Thus, the research emphasizes the potential, but also the challenges of industrial Transfer Learning.

While increasing empirical evidence suggests that global time series forecasting models can achieve better forecasting performance than local ones, there is a research void regarding when and why the global models fail to provide a good forecast. This paper uses anomaly detection algorithms and Explainable Artificial Intelligence (XAI) to answer when and why a forecast should not be trusted. To address this issue, a dashboard was built to inform the user regarding (i) the relevance of the features for that particular forecast, (ii) which training samples most likely influenced the forecast outcome, (iii) why the forecast is considered an outlier, and (iv) provide a range of counterfactual examples to understand value changes, in the feature vector or the predicted value, can lead to a different outcome. Moreover, a modular architecture and a methodology were developed to iteratively remove noisy data instances from the train set, to enhance the overall global time series forecasting model performance. Finally, to test the effectiveness of the proposed approach, it was validated on two publicly available real-world datasets.

Recently, Gohar et al. introduced a novel, local, and well-behaved fractional calculus. It possesses all the classical properties, and Its locality imposes simplicity and accuracy in modeling fractional order systems. In this article, we further develop the definitions and extend the classical properties of Gohar fractional calculus to address some of the open problems in Calculus. The fractional Gronwall's integral inequality, Taylor power series expansion, and Laplace transform are defined and applied to overcome some of the limitations in the classical integer-order calculus. The fractional Laplace transform is applied to solve Bernoulli-type logistic and Bertalanffy nonlinear fractional differential equations, and the criteria under which it can be applied to solve linear differential equations are investigated.

Background: Our previous study revealed that the addition of pentavalent cations, such as niobium (Nb), to zirconia stabilized with trivalent cations, such as yttrium (Y), increased fracture toughness. However, the coefficient of thermal expansion (CTE) and opacity also increased undesirably. Thus, a novel surface treatment is required to enhance fracture toughness without changing the CTE and the translucency. Methods: The surfaces of pre-sintered 3-mol% yttria-stabilized tetragonal zirconia polycrystal (3Y-TZP) and 4.2-mol% yttria-stabilized partially stabilized zirconia (4.2Y-PSZ) were treated with an Nb sol solution containing Nb2O5 nanoparticles. After drying and final sintering, a surface layer with high Nb content formed to a depth of approximately 1 mm. Results: Nb was equivalent to that of the bulk uniformly containing 1 mol% Nb2O5. The tetragonality of tetragonal zirconia near the surface increased with the addition of Nb, leading to improve fracture toughness in the surface layer and enhancing the fracture toughness of the entire specimen. However, the CTE and the translucency remained unchanged. Conclusions: The addition of pentavalent cations such as Nb, confined to the surface vicinity, improved fracture toughness without affecting the CTE and the translucency. By selectively adding Nb to the surface of weak parts of zirconia prosthesis, the overall strength can be improved, making it possible to produce highly reliable dental restorations.

It is generally assumed that the universe expands only on large scales. For some time now, there has also been a well-founded assumption in the literature that cosmic expansion also exists in gravitationally bound systems. In this article we attempt to establish whether cosmic expansion also takes place on scales such as the Earth's sphere of influence. In the examples presented, we find the expansion rate of the size required by the "constant" found by Hubble and Lemaître. This is supported by other examples that also contradict the general assumption mentioned at the beginning. However, this leads to conclusions that also call other cosmological assumptions into question.

Motivated by the intriguing discovery of $X(6900)$ by LHCb Collaboration, we undertake a comprehensive study of the $s\bar{s}s\bar{s}$ tetraquark system in positive parity, employing the Gaussian expansion within the chiral quark model method. We consider two structures, diquark-antidiquark ($ss$-$\bar{s}\bar{s}$) structure and meson-meson ($s\bar{s}$-$s\bar{s}$)strcuture, encompassing all conceivable color and spin configurations. Despite the absence of bound states in our calculations, we have identified potential resonant states with $J^P=0^{+}$, namely $R(0,2150)$ and $R(0,2915)$, as well as a resonant state with $J^P=1^{+}$ denoted as $R(1,2950)$, and a resonant state with $J^P=2^{+}$ denoted as $R(2,2850)$, utilizing the real-scaling method. Through a comparison of their energies and widths, we propose that $R(0,2915)$ and $R(1,2950)$ may share characteristics with $X(6900)$, while $R(0,2150)$ could be a promising experimental candidate for $f_0(2100)$. We strongly advocate for experimental investigations to shed light on the existence and properties of these resonant states.

We prove that the Legendre coefficients associated with a function f(x) can be represented as the Fourier coefficients of a suitable Abel-type transform of the function itself. Thus, the computation of N Legendre coefficients can be performed efficiently in O(NlogN) operations by means of a single Fast Fourier Transform of the Abel-type transform of f(x). We also show how the symmetries associated with the Abel-type transform can be exploited to further reduce the computational complexity. The dual problem of calculating the sum of Legendre expansions is also considered. We prove that a Legendre series can be written as the Abel transform of a suitable Fourier series. This fact allows us to state an efficient algorithm for the evaluation of Legendre expansions. Finally, numerical tests are presented to exemplify and confirm the theoretical results.

Genetic code expansion has emerged as an enabling tool to provide insight into functions of understudied proteinogenic species such as small proteins and peptides, and to probe protein biophysics in the cellular context. Here we discuss recent technical advances and applications of genetic code expansion in cellular imaging of complex mammalian protein species, along with considerations and challenges upon using the method.

The post-2007 crisis-induced an agricultural expansion across Africa, but local level production and marketing experiences remain understudied. This study assesses the dynamics of agricultural expansion and small-scale farmers’ experiences in rural Zambia. Using a mixed research design, data were drawn from surveys, multi-level interviews, group discussions policy reviews and observations. Results show an agriculture expansion among small-scale farmers is underway due to favourable climatic conditions, land, and water availability, enabled by state subsidies, and an emerging market in commercial and supermarket outlets. However, farmers encounter production and marketing challenges related to poor tenure security, late delivery of inputs, and low financing. They face low and fluctuating prices, poor infrastructure, including low levels of mechanisation necessary to expand the production. Overall, despite an agricultural and land-use expansion taking shape, actual benefits for real transformation are largely missing – and currently over their heads. An argument is made that whilst policy actors continue to impress farmers to organise themselves to maximise benefits of an agricultural expansion, actual processes on how farmers can achieve this are missing in policy and practice. This necessitates a focus on multi-level processes aimed at addressing production, storage and marketing dynamics within a progressive coordination arrangement that centralizes small producers. Until that is addressed, the prospects for local development and poverty reduction for small-scale farmers under an agricultural expansion will be slender but continue to centrally reside in the state efforts to create enabling local and community environment that addresses real challenges. Overall, this study helps to extend the debate on diverse processes shaping rural transformation in Zambia and across sub-Saharan Africa, including the role and importance of agricultural expansion.

This enquiry follows the investigation into a propulsion system purportedly utilising the QED vacuum as reactive momenergy. The QFT vacuum is contentious because the “naïve” value for it is extraordinarily large, yet on the cosmic scale it is hardly present. This begs the question as to whether it is really real and further highlights the problem between General Relativity on very large scales, with Quantum Mechanics on very small scales. We find a mathematical procedure that: to the 1^st order removes the “embarrassing” QFT vacuum constant from the Einstein tensor and then covers nearly all of the 120 orders of magnitude difference between the Cosmological Constant and Vacuum Energy by introducing it as an higher order correction in (G/c⁴)³. There is a proviso for further work, that the difference of a few orders we calculate, might be made up by considering fluctuations or running constants in the QFT vacuum and Cosmic Inflation.

The expansion of concrete subjected to extreme elevated temperature is linked with intricate micro-structural variations, such as the transformation of the constituent phases. This study proposes a model to predict the thermal expansion of cement paste and concrete considering micro-structural changes under elevated temperatures ranging from 20°C to 800°C. The model presented can consider characteristics of various aggregates in the calculation of thermal expansion for concrete. The model is a combination of a multi-scale stoichiometric model and a multi-scale composite model. At the cement paste level, the model satisfactorily predicted a test result. At concrete level, upper bounds from the model were matched relatively well with test results by previous researcher. If the mechanical properties, such as elastic modulus (E), Poisson’s ratio (ν), and thermal deformation, of the aggregates used in concrete are given, it is likely that the model will reasonably predict experimental results.

Based on historical facts, revisited from a present-day perspective, and on the documented opinions of the scientists involved in the discovery themselves, strong arguments are given in favor of a proposal to include prominent astronomer Vesto Slipher to the suggested addition of Georges Lemaître's name to Hubble's law on the expansion of the Universe, and thus eventually call it Hubble-Lemaître-Slipher's (HLS) law.

SLEUTH Model (slope, landuse, exclusion, urban extent, transportation and hillshade) is an important tool for landuse planning and land policy. To evaluate the performance of SLEUTH model, implementation of Sensitivity Analysis (SA) is essential. The main limitation of SA in SLEUTH application is a lack of insight into model input self-modification parameters (SMPs) variation, namely, uncertainty involved in the model transfer metrics and model presumptions, which often misled the decision makers and model users. To address this issue, this study divided the forward process into two stages. Firstly, during the transfer process ①, the contribution scores of five SMPs were drawn, and parameters highly sensitive to model output were given. Apart from that, the recommended initial value for SMPs of 0.11, 0.2, 0.87, 1.13, 15, 1.01, 0.49 were found to be subordinated to such a heterogeneous urban area simulation. Secondly, during the transfer process ②, SMP caused imagery metrics indicated the disparity between parameters with Fixed Reference and with Successive Reference. Reversely, it derives reasonable threshold for the best fit values of five prediction coefficients’ initialization by comparing the real image with the predicted one. The framework of SLEUTH model transfer mechanism not only could distinguish highly sensitive SMPs with higher contribution scores, but also could give parametric analysis for simulation imagery based on metrics. The study was found to be a practical tool for quantization response of model input variables for modelling complex urban systems. So, this insight can help geographic information scientists decide how to find out the inner forward transfer mechanism of SLEUTH model for further make good use of it and improve the model.

The concept of graphs with clique-width at most was first introduced by Courcelle et al.to be the graphs that can be characterized using -expressions derived from graph operations that use labels of vertices. If the clique-width for some graph is bounded then a grand number of algorithmic problems, in general NP-hard, can be solved in polynomial time when restricted to this graph. This important fact motivated the researchers to prove that the clique-width of certain graphs is bounded. Following this research direction, we prove in this paper that the clique-width of series-parallel digraphs is at most 6 and we present an time algorithm to construct a 6-expression for this class of digraphs. In another part, we present a linear time recognition algorithm for a similar class of series-parallel digraphs and prove that the clique-width of this class is at most 3.

Fractal analysis of time series aims to extract the hidden or complex structures issued from the associated real data, such as scaling laws, non-stationary, dynamics, and so on. In the present work, the air quality index and its components are considered as time series owing fractal structures. To understand their underlying dynamics, wavelet multifractal approach is applied starting with a wavelet multifractal spectrum test to confirm the multifractality of the underlying data. Next, a new model is introduced improving the classical minmax one, provided with a statistical measure for the adequacy of the new model. The theoretical findings are applied to the north west Tabuk region of Saudi Arabia for environmental and climate data related to pollutants and factors involved in the estimation of the air quality index.

This article presents the results of reviewing the predictive capacity of Google trends for national elections in Chile. The electoral results of the elections between Michelle Bachelet and Sebastián Piñera in 2006, Sebastián Piñera and Eduardo Frei in 2010, Michelle Bachelet and Evelyn Matthei in 2013, Sebastián Piñera and Alejandro Guillier in 2017, and Gabriel Boric and José Antonio Kast in 2021 were reviewed. The time series analysed were organised on the basis of relative searches between the candidacies, assisted by R software, mainly with the gtrendsR and forecast libraries. With the series constructed, forecasts were made using the ARIMA technique to check the weight of one presidential option over the other. The ARIMA analyses were performed on 3 ways of organising the data: the linear series, the series transformed by moving average and the series transformed by Hodrick-Prescott. The result indicates that the method offers optimal pre-dictive ability.

Landslide is a sliding movement of rock mass, debris and soil along the slope under the action of gravity. Small Baseline Subset (SBAS) is an established method for the investigation and monitoring of landslide moments. This study focuses on monitoring the long-temporal displacement of mountainous terrain in Danba County, Sichuan Province via SBAS technique, based on 31 scenes of L-band ALOS/PALSAR data from Feb. 2007 to Oct. 2010.The results show that the largest velocity rates in LOS direction are ±120 mm/yr and maximum accumulated displacement is up to -300, which indicates fast movement of the mountainous terrain during the observation time. These results get good consistency against the results of previous study. This demonstrates the strong potential of SBAS technique for monitoring the landslides geohazard.

The principal aim of a spectral observer is twofold: the reconstruction of a signal of time via state estimation and the decomposition of such a signal into the frequencies that make it up. A spectral observer can be catalogued as an online algorithm for time-frequency analysis because is a method that can compute on the fly the Fourier transform (FT) of a signal, without having the entire signal available from the start. In this regard, this paper presents a novel spectral observer with an adjustable constant gain for reconstructing a given signal by means of the recursive identification of the coefficients of a Fourier series. The reconstruction or estimation of a signal in the context of this work means to find the coefficients of a linear combination of sines a cosines that fits a signal such that it can be reproduced. The design procedure of the spectral observer is presented along with the following applications: (1) the reconstruction of a simple periodical signal, (2) the approximation of both a square and a triangular signal, (3) the edge detection in signals by using the Fourier coefficients, (4) the fitting of the historical Bitcoin market data from 2014-12-01 to 2018-01-08 and (5) the estimation of a input force acting upon a Duffing oscillator. To round out this paper, we present a detailed discussion about the results of the applications as well as a comparative analysis of the proposed spectral observer vis-à-vis the Short Time Fourier Transform (STFT), which is a well-known method for time-frequency analysis.

Today, there is a time series analysis that has gained significant popularity across various industries to provide effective solutions for any specific challenges. Artificial intelligence logic is generally used to solve time-series problems with the help of various frameworks that are available for the development of AI-based applications. Currently, there is a significant framework in Python that is driven by its comprehensive libraries and their practical implementations. Time series analysis can be built with the help of some specific models that give results to differentiate the efficiency and domains of great work. This paper focuses on three diverse libraries of Python to predict the Gulf stock exchange market. These libraries are prediction models that are helpful in predicting future values. These models utilized include SARIMA (Seasonal Auto-Regressive Integrated Moving Average), Neural Prophet Model, and Fb Prophet model. Each model is trained using the provided datasets, which are followed by evaluation parameters such as MSE, RMSE, recall, MDAPE, accuracy, precision, etc. The main purpose of using these three models for stock market prediction is to find the better-suited models. In the past few decades, the stock market industry has seemed to have promising growth after 2022 onwards. This paper will help us make a significant decision about model usage for addressing such complex challenges. Especially, the research findings indicate that all three models demonstrate in different domains. SARIMA can perform well in overall prediction tasks, while the Prophet model works great with smaller datasets that contain seasonality trends.

We present a new theory to explain the expansion of the universe that augments general relativity to create a container within which quantum effects can be explained by treating time as an artefact of a fourth spatial dimension. The theory is tested by accurately modelling against stellar luminosity data that is available for redshifts, z

The growing importance of hydrogen as an energy carrier in a future decarbonized energy system has led to a surge in its production plans. However, the development of infrastructure for hydrogen delivery, particularly in the hard-to-abate sectors, remains a significant challenge. While the construction of new pipelines entails substantial investment, repurposing existing pipelines offers a cost-effective approach to jump-starting hydrogen networks. Many European countries are exploring the possibility of utilizing their current pipeline infrastructure for hydrogen transport. Yet, a critical aspect requiring extensive research is the expansion planning of these networks to accommodate increased capacity in the future. This study investigates the utilization of existing natural gas pipeline infrastructure for hydrogen transportation as a cost-saving measure. It explores two expansion strategies, namely pipeline looping and compression, for repurposing a segment of a 342 km x 36inch existing pipeline, from the Escravos – Lagos gas pipeline system (ELPS) in Nigeria, for hydrogen transport. Employing the Promax® process simulator tool, the study assesses compliance with the API RP 14E and ASME B31.12 standards for hydrogen and hydrogen-methane blends. Both expansion strategies demonstrate acceptable velocity and pressure drop characteristics for hydrogen blends of up to 40%. Additionally, the increase in hydrogen content leads to heightened compression power requirements until approximately 80% hydrogen in the blends for compression, and a corresponding extension in looping length until around 80% hydrogen in the blend for looping. Moreover, the compression option proves to be more economically viable for all investigated proportions of hydrogen blends for the PS1-PS5 segment of the Escravos – Lagos gas pipeline case study. The percentage price differentials between the two expansion strategies reach as high as 495% for a 20% hydrogen proportion in the blend. This study offers valuable insights into the technical and economic implications of repurposing existing natural gas infrastructure for hydrogen transportation.

This contribution shows the possibilities of a low-cost multipurpose data logger that was built around an Arduino Mega 2560 single board computer. To transform the Arduino Mega into such a data logger, a sensor shield was designed that contains an SD-card, real-time clock, and different kinds of connectors so that sensors can easily be attached to the device. The software considers a wide range of predefined sensors from which a user can choose. To assess the performance of such a device, short-term monitoring campaigns in relation to outdoor air quality, human activity in an office, motion of a journey on a bike, and exhaust gas monitoring of a diesel generator were realized. Besides the possibilities to apply the data logger in different kinds of applications, a method is proposed to assess the credibility of such a system. The assessment based on the various short-term campaigns showed that the system scores positively on most of the performance indicators, but that unexpected (black swan) events affect the assessment over the longer term. This makes the development of low-cost scientific instruments harder than expected. The stability and long-term performance of this type of design requires continuous evaluation and engineering correction.

The Roman economy of the Iberian Peninsula has habitually been characterised in terms of prestige goods and economic activities such as trade, mining and metallurgy. The analysis of plant-based foods –less prestigious but more essential in everyday life– has commonly been marginalised in state-of-the-art reviews. The O Areal saltworks is exceptional in terms of the large number of organic materials it preserves, and the excellent state of that preservation. After its abandonment (end of the 3rd/4th century AD), the saltworks was briefly used as a dumping ground for the surrounding area. The site's archaeobotanical remains, preserved under anoxic, waterlogged conditions, consist of the building materials used at the saltworks, tools and other artefacts, organic objects employed in activities such as fishing, and refuse. The assemblage suggests a wide diversity of species to have been introduced into northwestern Iberia during the Roman Period, including the mulberry, peach, fig, plum, grapevine, and melon. The notable presence of other edible fruit species that normally grew wild during this period, such as chestnut, walnut, stone pine, and cherry trees, might be related to the start of their cultivation.

In the present paper, a measure of the influence of irregularities of the underlying surface (for instance, the real terrain profile) on the dynamics of air flow is estimated. It is shown that these irregularities significantly perturbing the pressure, density, velocity and temperature of air flow; for perturbed pressure, density, velocity and temperature of air flow the closed formulas in the Fourier integral form are obtained. In addition, in the present paper, it is proved that due to these perturbations, at a certain altitude of the atmosphere some surface of the "sturdy wall" form appears, on which the vertical and horizontal components of the air flow velocity become infinitesimal and infinitely large, respectively.

Expansive soil shows dual swell-shrink which is not suitable for the construction. Several mitigating techniques exist to counteract the problem promulgate by expansive clayey soils. This paper explored the penitential mecho-chemical reinforcement of expansive clayey soil to mitigate the effect of upward swelling pressure and heave. The polypropylene fiber is randomly distributed in the soil for mechanical stabilization, and the industrial residual silica fume is used as a chemical stabilizer. The experimental analysis is made in three phases which involved the tests on mechanical reinforced expansive soil using randomly distributed polypropylene fibers with different percentages (0.25%, 0.50%, and 1.00%), and 12mm length. The second phase of experiments carried out on chemical stabilized expansive soil with different percentages (2%, 4% and 8%) of silica and next phase of the experimental focused in the combination of mecho-chemical stabilization of the expansive soil with different combination of silica (i.e., 2%, 4% and 8%) and polypropylene fibers (i.e., 0.25%, 0.50% and 1.00%). Maximum dry density (MDD), optimum moisture content (OMC), liquid limit (LL), plastic limit (PL), plastic index (PI) grain size, and constant volume swelling pressure test were performed on unreinforced and reinforced expansive soil to investigate the effect of polypropylene fiber and silica fume on the engineering properties of expansive clayey soil. The experimental results illustrate that the inclusion of polypropylene fiber has a significant effect on the upward swelling pressure and expansion property of expansive soil. The reduction in the upward swelling pressure and expansion is a function of fiber content. These results also indicated that the use of silica fume caused a reduction in upward swelling potential, and its effect was considerably more than the influence of fiber.

Climate change and the overall increase of seawater temperature is causing a poleward shift in species distribution, which includes a phenomenon described as tropicalization of temperate regions. This work aims at reporting the first records of four species off the southwestern Iberian Peninsula, namely oceanic puffer Lagocephalus lagocephalus Linnaeus, 1758, Madeira rockfish Scorpaena maderensis Valenciennes, 1833, ornate wrasse Thalassoma pavo Linnaeus, 1758, and bearded fireworm Hermodice carunculata Pallas, 1766. These last three species, along with other occurrences of aquatic fauna and flora along the Portuguese coast, reveal an ongoing process of poleward expansion of several species for which a comprehensive survey along the entire Iberian Peninsula is urgent. The putative origins of these subtropical and tropical species off continental Portugal are discussed, as well as the urgent need of public awareness due to potential health risks resulting from the toxicity of two of the four species reported in this paper.

We describe the effect of the expansion of space on the wavelength of the light beam in a Fabry-Pérot interferometer. For an instrument such as the Laser Interferometer Gravitational-Wave Observatory (LIGO), which has high sensitivity and a long period of light storage, the wavelength ${\lambda }_L$ of laser photons are redshifted due to the expansion of space in each cavity by an amount $\delta \lambda$ given by $\delta \lambda /{\lambda }_L=H_0{\tau }_s\approx 8.8\times {10}^{-21}$ , where $H_0\approx 2.2\times {10}^{-18}{\mathrm{s}}^{-1}$ is the Hubble constant and ${\tau }_s\approx 4\mathrm{ms}$ is the light storage time for the cavity. Since ${\tau }_s$ is based on the cavity finesse $\mathcal{F}$ which depends on the laser beam full width at half maximum (FWHM) $\delta \omega$ of each cavity, we show that a difference in finesses between the LIGO arm cavities produces a signal $h_H\left(t\right)$ at the anti-symmetric output port given by $h_H\left(t\right)=2a_1{H}_0\left(\frac{1}{\delta {\omega }_X\left(t\right)}-\frac{1}{\delta {\omega }_Y\left(t\right)}\right),$ where $\delta {\omega }_X\left(t\right)$ and $\delta {\omega }_Y\left(t\right)$ are the beam FWHM at time t, respectively, for the X and Y arm cavities and $a_1$ is a beam proportionality constant to be determined expermentally. Assuming $a_1\approx 1$ , then for cavity beams FWHM of $\delta \omega \left(t\right)\approx (523.2\pm 31)\mathrm{rad}.{\mathrm{s}}^{-1}$ the output signal has the range $\mid h_H\left(t\right)\mid \le 1\times {10}^{-21}$ , which is detectable by advanced LIGO.

The energy transition towards renewable and more decentral power production triggers the need for grid and storage expansion on all voltage levels. Today's power system planning focuses on certain voltage levels or spatial resolutions. In this work we present an open source software tool eGo which is able to optimize grid and storage expansion throughout all voltage levels in a developed top-down approach. System costs are minimized by applying a linear optimal power flow considering the grid infrastructure of the extra-high and high-voltage (380 to 110 kV) level. Hence, the common differentiation of transmission and distribution grid is partly dissolved, integrating the high-voltage level into the optimization problem. Consecutively, optimized curtailment and storage units are allocated in the medium voltage grid in order to lower medium and low voltage grid expansion needs, that are consequently determined. Here, heuristic optimization methods using the non-linear power flow were developed. Applying the tool on future scenarios we derived cost-efficient grid and storage expansion for all voltage levels in Germany. Due to the integrated approach storage expansion and curtailment can significantly lower grid expansion costs in medium and low voltage grids and at the same time serve the optimal functioning of the overall system. Nevertheless, the cost-reducing effect for the whole of Germany was marginal. Instead, the consideration of realistic, spatially differentiated time series lead to substantial overall savings.

The obtention of simple formulae for the Lebesgue constants arising in the the classical Fourier series approximation is presented. Both even and odd cases are treated enlarging Fejér result. Asymptotic formulae are also obtained.

The assessment of photovoltaic devices, which convert light energy into electricity, becomes significantly relevant due to the aspiration to reduce pollution on a global scale. In this context, the pursuit of optimizing the efficiency in converting light energy into electrical energy involves exhaustive studies and structural analyses of solar cells, all directed toward achieving this goal. This study introduces a research proposal aimed at analyzing the losses associated with series resistance (Rs). The analysis takes into account each component comprising this resistance, pro-posing a network of resistances that precisely models each of these elements. The aforementioned research focused on simple-structured crystalline silicon cells. During this investigation, the junction depth (xj) of n-p materials was varied with the aim of achieving efficiencies in the range of 12%. However, in the pursuit of this desired efficiency, a significant impact on series resistance was observed when analyzing the I-V curves of the cells obtained in each manufacturing process.

Reservoir computing is a machine learning method that uses the response of a dynamical system to a certain input in order to solve a task. As the training scheme only involves optimising the weights of the responses of the dynamical system, this method is particularly suited for hardware implementation. Furthermore, the inherent memory of dynamical systems which are suitable for use as reservoirs mean that this method has the potential to perform well on time series prediction tasks, as well as other tasks with time dependence. However, reservoir computing still requires extensive task dependent parameter optimisation in order to achieve good performance. We demonstrate that by including a time-delayed version of the input for various time series prediction tasks, good performance can be achieved with an unoptimised reservoir. Furthermore, we show that by including the appropriate time-delayed input, one unaltered reservoir can perform well on six different time series prediction tasks at a very low computational expense. Our approach is of particular relevance to hardware implemented reservoirs, as one does not necessarily have access to pertinent optimisation parameters in physical systems but the inclusion of an additional input is generally possible.

We evaluate various sums involving the powers of Fibonacci and Lucas numbers.

Traditional applications of Interferometric Synthetic Aperture Radar (InSAR) data involved inverting an interferogram stack to determine the average displacement velocity. While this approach has useful applications in continuously deforming regions, much information is lost by simply fitting a line through the time series. Thanks to regular acquisitions across most of the the world by the ESA Sentinel-1 satellite constellation, we are now in a position to explore opportunities for near-real time deformation monitoring. In this paper we present a simple statistical approach for detecting offsets and gradient changes in InSAR time series. Our key assumption is that 5 years of Sentinel-1 data is sufficient to calculate the population standard deviation of the detection variables. Our offset detector identifies statistically significant peaks in the first, second and third difference series. The gradient change detector identifies statistically significant movements in the second derivative series. We exploit the high spatial resolution of Sentinel-1 data and the spatial continuity of geophysical deformation signals to filter out false positive detections that arise due to signal noise. When combined with near-real time processing of InSAR data these detectors, particularly the gradient change, could be used to detect incipient ground deformation associated with geophysical phenomena, for example from landslides or volcanic eruptions.

The semi-nonparametric (SNP) modeling of the return distribution has been proved to be a flexible and accurate methodology for portfolio risk management that allows two-step estimation of the dynamic conditional correlation (DCC) matrix. For this SNP-DCC model, we propose a stepwise procedure to compute pairwise conditional correlations under bivariate marginal SNP distributions, overcoming the curse of dimensionality. The procedure is compared to the assumption of Dynamic Equicorrelation (DECO), which is a parsimonious model when correlations among the assets are not significantly different but requires joint estimation of the multivariate SNP model. The risk assessment of both methodologies is tested for a portfolio on cryptocurrencies by implementing backtesting techniques and for different risk measures: Value-at-Risk, Expected Shortfall and Median Shortfall. The results support our proposal showing that the SNP-DCC model has better performance for a smaller confidence level than the SNP-DECO model, although both models perform similarly for higher confidence levels.

The study of order patterns of three equally spaced values $x_t,x_{t+d},x_{t+2d}$ in a time series is a powerful tool. The lag $d$ is changed in a wide range so that differences of frequencies of order patterns become autocorrelation functions. Similar to a spectrogram in speech analysis, four ordinal autocorrelation functions are used to visualize big data series, as for instance heart and brain activity over many hours. The method applies to real data without preprocessing, outliers and missing data do not matter. On the theoretical side, we study properties of order correlation functions and show that the four autocorrelation functions are orthogonal in a certain sense. An analysis of variance of a modified permutation entropy can be performed with four variance components associated with the functions.

New q-series in the spirit of Jacobi have been found in a publication rst published in 1884 written in Russian and translated into English in 1928. This work was found by chance and appears to be almost totally unknown. From these entirely new q-series, fresh lattice sums have been discovered and are presented here.

Thermal expansion of four alkaline-earth borates, namely Ca3B2O6 (0D), CaB2O4 (1D), Sr3B14O24 (2D) and CaB4O7 (3D), have been studied by in situ high-temperature powder X-ray diffraction (HTXRD). Strong anisotropy of thermal expansion is observed for the structures of Ca3B2O6 (0D) and CaB2O4 (1D) built up from BO3 triangles only: these borates exhibit the maximal expansion perpendicular to the BO3 plane, i.e. along the direction of weaker bonding in the crystal structure. Layered Sr3B14O24 (2D) and framework CaB4O7 (3D) built up from various B-O groups expand less anisotropically. Thermal properties of the studied compounds compared to the other alka-line-earth borates are summarized depending on the selected structural characteristics like anion dimensionality, residual charge per one polyhedron (BO3 BO4), cationic size, and structural com-plexity. For the first time these dependencies were established as an average for both types of polyhedra (triangle and tetrahedron) occurring in the same structure at the same time. The most common trends were identified for : (i) Melting temperature decreases as the dimensionality of the borate polyanion, and more precisely, as the residual charge per one polyhedron (triangle or tetrahedron) decreases; (ii) volumetric expansion decreases while the degree of anisotropy in-creases weakly when the residual charge decreases; (iii)both trends (i) and (ii) are most steady within borates built by the triangles only, while the borates built by both triangles and tetrahedra show a larger scatter in values.

The holographic principle states that the information about the volume of space is stored on its boundary. Assuming this holds, we can explain the aspects of gravity. The spacetime needs to be extended to 5D to explain gravity in this context. This naturally explains the four classical tests of gravity namely the gravitational redshift, the perihelion precession, the bending of light, and the gravitational time delay. We also show a novel way in which the universe expands in an accelerated manner at late times without the need for any form of dark energy.

Unlike trees, shrubs (i.e., multiple-stemmed woody plants) do not need evenly spaced large diameter structural roots and thus can spread further per unit belowground biomass. We therefore hypothesized that compared to trees, shrubs respond more to asymmetric distributions of nutrients and reach nutrient-rich patches of soil faster and with less below-ground biomass. To test these hypotheses we planted individual seedlings of shrubs (Cornus racemosa, Rhus glabra, and Viburnum dentatum) and trees (Acer rubrum, Betula populifera, and Fraxinus americana) in the centers of sand-filled rectangular boxes. In one direction we created stepwise gradients of increasing soil nutrients with slow-release fertilizer; in the other direction no fertilizer was added. Seedlings were harvested when their first root reached the plexiglass-covered fertilized end of their box; time taken as well as above- and below-ground biomass by nutrient segment were determined. There were no consistent differences between the shrubs and trees in belowground architectural plasticity (= ratio of biomass in fertilized and unfertilized volumes of soil) or in the rate and efficiency of lateral growth. Interspecific variation appeared more related to edaphic characteristics of the native habitats than to growth form. The fastest and most efficient roots were produced by the shrub (R. glabra) and the tree (B. populifolia) that are characteristic of poor soils. Root foraging by R. glabra was also facilitated by rapid rhizomatous expansion. The tested shrubs and trees did not consistently differ in nutrient foraging efficiencies or rates but further study is warranted with larger plants and more species.

Energy storage systems (ESSs) are the key elements to improve the operation of power systems. On the other hand, these elements challenge the power system planners. The difficulties arise as a result of the ESSs' economic and technological features. The cycle life of ESSs is a critical aspect that influences the choices made during expansion planning processes. In this manuscript, we have focused on a new model for the expansion planning of ESSs considering the impacts of technical properties, such as the cycle life and depth of discharge. For this purpose, the proposed model consists of the hourly operation planning of ESSs in the sample days of year. A new indicator is proposed to determine the daily charging/discharging cycles of ESSs. Numerical results show the ability of the proposed model to determine the optimal technology and capacity of ESSs.

Apple (Malus x domestica) fruit size is dependent on cell division and cell expansion, processes which are subsequently regulated by plant hormones such as auxins, gibberellins, and cytokinins. In this study, we investigated the role of cell division and cell expansion in apple growth and identified which of the two was more deterministic to final fruit size. Three cultivars of different sizes were selected, namely, ‘Twenty Ounce’ (large-sized), ‘Royal Gala’ (medium-sized), and ‘Crabapple’ (small-sized). Gene expression and cell size analyses were conducted over the course of two consecutive seasons. The expression patterns of three classes of genes were markedly similar across all cultivars. Two cell division markers, namely, MdCDKB2;2 and MdANT2, were discovered to be correlatively expressed as both displayed initially high expression levels, which gradually declined from the early to late stages of growth time course. For cell expansion markers, MdEXP3 was upregulated as the cells expanded, while MdARF106 was expressed in both the cell division and expansion stages. Meanwhile, the ripening related gene MdACO1 was expectedly expressed only during the ending stages associated with ripening. Interestingly, the cell measurements taken regularly from each cultivar throughout the same eperimental timespan showed that cell sizes were unaltered and remained constant from initial pollination at the zeroth Days After Pollination (DAP), to ripening at 120 Days After Full Bloom (DAFB).

Genus Clematis is one of the largest within Ranunculaceae. Here we report the chloroplast genome of two Clematis species, C. brachyura and C. trichotoma endemic to Korea. The chloroplast genome lengths of C. brachyura and C. trichotoma are 159,532 bp and 159,170 bp, respectively. Gene contents in the complete chloroplast genomes of these two Clematis species are identical to that of most Ranunculaceae and other angiosperms. However, our data results demonstrated that genus Clematis has inversion and rearrangement events concerning gene rps4 gene, rps16 to trnH region, and trnL to ndhC region, and IR regions expansion. Comparison of IR regions among Ranunculaceae species revealed that Clematis species contained six protein coding genes (infA, rps8, rpl14, rpl16, rps3, and rpl22) usually found in the long single copy (LSC) region of other species. Phylogenetic analysis demonstrated that genus Clematis is closely related to genus Ranunculus. Differences in repeat structure, substitution rates, and IR expansion in genera Clematis and Ranunculus, explained their relationship. Clematis species showed slightly higher tandem repeats content than Ranunculus species. The six protein-coding genes showed lower synonymous substitution rates in the IR of Clematis species than in the LSC of Ranunculus species. Overall, the chloroplast genomes and results presented here provide important information on the evolution of Ranunculaceae.

The quasi-two-dimensional organic charge-transfer salt κ-(BEDT-TTF)₂Cu₂(CN)₃ is one of the prime candidates for a quantum spin-liquid due the strong spin frustration of its anisotropic triangular lattice in combination with its proximity to the Mott transition. Despite intensive investigations of the material's low-temperature properties, several important questions remain to be answered. Particularly puzzling are the 6 K anomaly and the enigmatic effects observed in magnetic fields. Here we report on low-temperature measurements of lattice effects which were shown to be particularly strongly pronounced in this material (R. S. Manna et al., Phys. Rev. Lett. 104, 016403 (2010)). A special focus of our study lies on sample-to-sample variations of these effects and their implications on the interpretation of experimental data. By investigating overall nine single crystals from two different batches, we can state that there are considerable differences in the size of the second-order phase transition anomaly around 6 K, varying within a factor of 3. In addition, we find field-induced anomalies giving rise to pronounced features in the sample length for two out of these nine crystals for temperatures T < 9 K. We tentatively assign the latter effects to B-induced magnetic clusters suspected to nucleate around crystal imperfections. These B-induced effects are absent for the crystals where the 6 K anomaly is most strongly pronounced. The large lattice effects observed at 6 K are consistent with proposed pairing instabilities of fermionic excitations breaking the lattice symmetry. The strong sample-to-sample variation in the size of the phase transition anomaly suggests that the conversion of the fermions to bosons at the instability is only partial and to some extent influenced by not yet identified sample-specific parameters.

In analogy with entanglement in physics, the concept of entanglement has been developed in mathematics as a symmetry to build upon as a tool to study 'proximity' relations between different number sequences and series in a unifying way. Examples of entanglement are shown. A general algorithm for detecting entangled sequences/series is given in the appendix. The novelty of this paper is to propose the concept of entanglement as a tool to study different sequences and se-ries-series phenomena. To enable useful treatment suggested by Poincaré.

The ability of thermoresponsive polymers to respond to temperature with a reversible conformational change makes them promising ‘smart’ materials for solutions in medical and biotechnological applications. In this work, two such polymers and structural isomers were studied: poly(N-isopropyl acrylamide) (PNiPAm) and poly(2-isopropyl-2-oxazoline) (PiPOx). We compare the critical solution temperatures (CST) of these polymers in D2O and H2O in the presence of Hofmeister series salts, as results obtained under these different solvent conditions are often compared. D2O has a higher dipole moment and electronegativity than H2O, which could significantly alter the CST transition. We used two complementary methods to measure the CST, dynamic light scattering (DLS) and differential scanning calorimetry (DSC), and found that the CST decreased significantly in D2O compared to H2O. In the presence of highly concentrated kosmotropes, the CST of both polymers decreased in both solvents. The influence of the kosmotropic anions was smaller than the water isotope effect at low ionic strengths but considerably higher at physiological ionic strengths. However, the Hofmeister anion effect was quantitatively different in H2O than in D2O, with the largest relative differences observed for Cl-, where the CSTs in D2O decreased more than in H2O measured by DLS but less by DSC. PiPOx was more sensitive than PNiPAm to the presence of chaotropes. It exhibited much higher transition enthalpies and multistep transitions, especially in aqueous solutions. Our results highlight that measurements of thermoresponsive polymer properties in D2O cannot be compared directly or quantitatively to application conditions or even measurements performed in H2O.

This paper draws upon the theory of turbulence in physics to explore the similarities and differences between volatility in financial markets and turbulent phenomena at a statistical physics level. By analogizing the dynamics of financial markets with fluid turbulence, we have developed an innovative analytical framework aimed at deepening the understanding of the complexity inherent in financial markets. Our research methodology includes a comparative analysis of simulated time series data for the Standard & Poor's 500 Index and fully developed turbulent velocity time series. We focus on the similarities in key statistical physical properties, including probability distributions, correlation structures, and power spectral densities. Furthermore, we have established a model of capital flow in financial markets and proposed corresponding solutions. Through computational simulations and data analysis, we find that while financial market volatility shares some statistical characteristics with turbulent phenomena, significant differences exist in the shapes of probability distributions and the temporal scales of correlations. This suggests that although financial markets exhibit patterns akin to turbulence, the behavior of this complex, multi-variable driven system does not completely correspond to natural turbulence, highlighting the limitations of directly applying turbulence theory to financial market analysis. Our study offers a new perspective for the theories of financial markets and the field of econophysics, providing fresh insights into the complexity of financial markets and contributing to the prevention and management of financial risk.

The distribution laws of various natural and anthropogenic processes in the world around us are stochastic in nature. The development of mathematics and, in particular, of stochastic modelling allows us to study regularities in such processes. In practice, stochastic modelling finds a huge number of applications in various fields, including finance and economics. In this work, some particular applications of stochastic processes in finance are examined in the conditions of financial crisis. More specifically, Autoregressive Integrated Moving Average (ARIMA) models and Modified Ordinary Differential Equations (ODE) models, which have been previously developed by the authors to predict assets’ prices of four Bulgarian companies, are validated on a time period during the crisis. Estimated rates of return are calculated from the models for one period ahead. The errors are estimated and the models are compared. The predicted return values with each of the two approaches are used to derive optimal risk portfolios based on the Markowitz Model. The resulting portfolios are compared in terms of distribution (weights of the stocks), risk and rate of return.

Landsat and Sentinel-2 data archives provide ever-increasing amounts of satellite data for studying land cover and land use change (LCLUC) over the past four decades. However, the availability of cloud-, shadow-, and snow-free observations varies spatially and temporally due to climate and satellite data acquisition schemes. Spatio-temporal heterogeneity poses a major issue for some time-series analysis approaches, but can be addressed with pixel-based compositing that generates temporally equidistant cloud-free or near-cloud free synthetic images. Although much consideration is given to methods identifying the ‘best’ pixel value for each composite, determining the aggregation period receives less attention and is often done arbitrary, or based on expert intuition. Here, we evaluated data compositing windows ranging from five days to one year for 1984-2021 Landsat and 2015-2021 Sentinel‑2 time series across Europe. We considered separate and joint use of both data archives and analyzed spatio-temporal availability of composites during each calendar year and pixel-specific growing season. We reported mean annual composites’ availability investigating differences among biogeographical regions, checked feasibility of pan‑European analyses for three LCLUC applications based on annual, monthly and 10-day composites, and analyzed the shortest feasible compositing window ensuring ≥50% temporal data availability and interpolation of the remaining composites for individual years and across a variety of medium- and long‑term time windows. Our results highlighted low data coverage in the 1980s, 1990s, and in 2012, as well as spatial variability in data availability driven by climate and orbit overlaps, which altogether impact spatio-temporal consistency of medium- and long-term time series, limiting feasibility of some LCLUC analyses. We demonstrated that prior to 2011 monthly composites ensured overall 50-62% data coverage for each calendar year, and ~75% afterwards, with further increase to ~82% when Landsat and Sentinel-2 were combined. Temporal consistency of monthly composites was overall low and temporal interpolation augmenting up to 50% missing data each year and across a time window of interest, ensured feasibility of analyses. Applications based on shorter than monthly composites were challenging without joining Landsat and Sentinel‑2 archives after 2015, and beyond the Mediterranean biogeographical region. Using pixel-specific growing season data typically boosted data availability in most geographies and diminished most of the latitudinal differences, but feasibility of complete time series with sub-monthly compositing windows was still restricted to the most recent years, and required data interpolation. Overall, our analyses provided a detailed assessment of Landsat and Sentinel-2 data availability over Europe, and based on selected application examples, highlighted often lacking spatio-temporal consistency of time series with sub-monthly compositing windows and long-time periods, which might hinder feasibility of some LCLUC applications.

Retailers must have accurate sales forecasts to operate their businesses efficiently and effectively and to remain competitive in the marketplace. Global forecasting models like RNNs can be a powerful tool for forecasting in retail settings, where multiple time series are often interrelated and influenced by a variety of external factors. By including covariates in a forecasting model, we can better capture the various factors that can influence sales in a retail setting. This can help improve the accuracy of our forecasts and enable better decision-making for inventory management, purchasing, and other operational decisions. In this study we investigate how the accuracy of global forecasting models is affected by the inclusion of different potential demand covariates. To ensure the significance of the study's findings, we used the M5 forecasting competition's openly accessible and well-established dataset. The results obtained from the DeepAR models, which were trained on various combinations of features including time, price, events, and IDs, suggest that individually only the features corresponding to IDs improve the baseline model. However, when all the features are used together, the best performance is achieved, indicating that the individual relevance of each feature is emphasized when the information is given jointly. Comparing the model with features to the model without features, there is an improvement of 1.76\% for MRMSSE and 6.47\% for MMASE.

We study the divisibility properties of the constant terms of certain meromorphic modular forms for Hecke groups. We relate those properties to those of some sequences that have already appeared in the literature. For possible use in later drafts, we show how to invert the map taking a Laurent series $f(x) = 1/x + \sum_{n=0}^{\infty}a_{n+1} x^n$ to the sequence of constant terms of its positive powers. At the end of the article, we construct from elementary arithmetic functions some meromorphic but not necessarily modular functions and study their constant terms.

GNSS time series prediction plays a significant role in monitoring crustal plate motion, landslide detection, and maintenance of the global coordinate framework. Long Short-Term Memory (LSTM), a deep learning model has been widely applied in the field of high-precision time series prediction especially when combined with Variational Mode Decomposition (VMD) to form the VMD-LSTM hybrid model. To further improve the prediction accuracy of the VMD-LSTM model, this paper proposes a dual variational modal decomposition long short-term memory (DVMD-LSTM) model to effectively handle the noise in GNSS time series prediction. This model extracts fluctuation features from the residual terms obtained after VMD decomposition to reduce the prediction errors associated with residual terms in the VMD-LSTM model. Daily E, N, and U coordinate data recorded at multiple GNSS stations between 2000 and 2022 are used to validate the performance of the proposed DVMD-LSTM model. The experimental results demonstrate that compared to the VMD-LSTM model, the DVMD-LSTM model achieves significant improvements in prediction performance across all measurement stations. The average RMSE is reduced by 9.86%, and the average MAE is reduced by 9.44%. Furthermore, the average accuracy of the optimal noise model for the predicted results is improved by 36.50%, and the average speed accuracy of the predicted results is enhanced by 33.02%. These findings collectively attest to the superior predictive capabilities of the DVMD-LSTM model, thereby enhancing the reliability of the predicted results.

Time series (TS)-based predictions are made by examining the behaviour of historical data to forecast future values. Multiple industries; such as stock market trading, power load forecasting, medical monitoring, and intrusion detection; frequently use it. Several variables; such as the performance of other markets as well as the economic situation of a country which affect its market performance; significantly affect the prediction of stock market prices. Therefore, this present study uses numerous variables; such as the opening, lowest, highest, and closing prices; to predict the indices of the stock market of the Kingdom of Saudi Arabia (KSA). Successfully accomplishing an investment goal largely depends on choosing the right stocks to buy, sell, or maintain. The project's output is the projected closing prices (regression) over the next seven days, which helps investors make the best decisions. This present study used exponential smoothing (ES) to remove noise from the input data obtained from the Saudi Stock Exchange, or Tadawul, before using a multivariate long short-term memory (LSTM) deep learning (DL) algorithm to forecast stock market prices. The proposed multivariate LSTMDL model had satisfactory prediction rates of 97.49% and 92.19% for the univariate model. Therefore, it can be used to effectively predict stock market prices. The results also indicate that DL as well as multiple sources of information can be used to accurately predict stock markets.

Machine learning methods have widely been applied to detect anomalies in machine and cutting tool behavior during lathe or milling. However, detecting anomalies in the workpiece itself did not get the same attention by researchers. That is why in this article, the authors present a pub-licly available multivariate time series dataset which was recorded during milling of 16MnCr5. Due to artificially introduced, though realistic anomalies in the workpiece the dataset can be ap-plied for anomaly detection. By using a convolutional autoencoder as a first model good results in detecting the location of the anomalies in the workpiece were achieved. Furthermore, milling tools with two different diameters where used which led to a dataset eligible for transfer learn-ing. The objective of this article is to provide researchers with a real-world time series dataset of the milling process which is suitable for modern machine learning research topics like anomaly detection and transfer learning.

The removal of non-climatic biases, so-called inhomogeneities, from long climatic records needs sophistically developed statistical methods. One principle is that usually the differences between a candidate series and its neighbour series are analysed instead of directly the candidate series, in order to neutralize the possible impacts of regionally common natural climate variation on the detection of inhomogeneities. In most homogenization methods, two main kinds of time series comparisons are applied, i.e. composite reference series or pairwise comparisons. In composite reference series the inhomogeneities of neighbour series are attenuated by averaging the individual series, and the accuracy of homogenization can be improved by the iterative improvement of composite reference series. By contrast, pairwise comparisons have the advantage that coincidental inhomogeneities affecting several station series in a similar way can be identified with higher certainty than with composite reference series. In addition, homogenization with pairwise comparisons tends to facilitate the most accurate regional trend estimations. A new time series comparison method is presented here, which combines the use of pairwise comparisons and composite reference series in a way that their advantages are unified. This time series comparison method is embedded into the ACMANT homogenization method, and tested in large, commonly available monthly temperature test datasets.

We study the problem of predicting time series data using the autoregressive integrated moving average (ARIMA) model in an online manner. Existing algorithms require model selection, which is time consuming and inapt for the setting of online learning. Using adaptive online learning techniques, we develop algorithms for fitting ARIMA models with fewest possible hyperparameters. We analyse the regret bound of the proposed algorithms and examine their performance using experiments on both synthetic and real world datasets

The present study analyzed light emitting diodes (LEDs) as an output load and used a Taylor series to describe the characteristic curve based on the exponential characteristic of voltage and current. A prototype circuit of a flyback LED driver system was established to verify whether the theory is consistent with actual results. This study focused on the exponential relationship of LED voltage and current. Conventional simulations usually used linear models to present LED loads. However, the linear model resulted in considerable error between simulation and actual characteristics. Therefore, this study employed a Taylor series to describe the nonlinear characteristic of an LED load. Through precise calculations with Mathcad computation software, the error was effectively reduced. Moreover, the process clarified the influence of temperature on LEDs, which benefited the characteristic analysis of the entire system. Finally, a realized circuit of 120-W flyback LED drivers was established for conducting theory verification, including theoretic analysis and evaluation of the system design process of the flyback converter. The circuit simulation software SIMPLIS was used to demonstrate the system model, which enabled quick understanding of the system framework established in this study. Regarding LEDs, a commercially available aluminum luminaire was used as the output load. The measured results of the actual circuit and the simulation results were remarkably consistent. For the same system at the same temperature, the error between the simulation and actual results was less than 3%, which proved the reliability of the Taylor series simulation.

A method for measuring the mechanical parameters of viscoelastic polymers by nanoindentation technology was proposed and verified. Through the mechanical response of load-displacement curves at different loading rates, then creep compliances and relaxation modulus were fitted. Polyimide thin film was employed in this research and experiments for five different loading rates were conducted. The fitting load-displacement loading curves obtained by the inversion method were identical to the experimental curves at five different loading rates，confirming the validity of the method. Moreover, with the loading rates increased，the fitting curves were more consistent commensurately with the nanoindentation experiment. DMA experiments were tested, and the generalized Kelvin/ Maxwell model were used for fitting experiment data. Results from DMA tests generally agree well with data from nanoindentation method, thereby verifying the feasibility of the method. The Prony series obtained by the two methods were used to simulate the creep experiments, which further verified the method.

This study compared the performance of five Family Generalized Auto-Regressive Conditional Heteroscedastic (fGARCH) models (sGARCH, gjrGARCH, iGARCH, TGARCH and NGARCH) in the presence of high positive autocorrelation. To achieve this, financial time series was simulated with autocorrelated coefficients as ρ = (0.8, 0.85, 0.9, 0.95, 0.99), at different time series lengths (as 250, 500, 750, 1000, 1250, 1500) and each trial was repeated 1000 times carried out in R environment using rugarch package. And the performance of the preferred model was judged using Root Mean Squared Error (RMSE) and Mean Absolute Error (MAE). Results from the simulation revealed that these GARCH models performances varies with the different autocorrelation values and at different time series lengths. But in the overall, NGARCH model dominates with 62.5% and 59.3% using RMSE and MAE respectively. We therefore recommended that investors, financial analysts and researchers interested in stock prices and asset return should adapt NGARCH model when there is high positive autocorrelation in the financial time series data.

In this paper, we study the usage of machine learning models for sales time series forecasting. The effect of machine learning generalization has been considered. A stacking approach for building regression ensemble of single models has been studied. The results show that using stacking technics, we can improve the performance of predictive models for sales time series forecasting.

In this paper, we investigate an analytical solution of a class of nonlinear fractional integro-differential equation base on a generalized fractional power series expansion. The fractional derivatives are described in the conformable's type. The new approach is a modified form of the well-known Taylor series expansion. The illustrative examples are presented to demonstrate the accuracy and effectiveness of the proposed method

The morphology and the activity of a submarine caldera, Avyssos, at the northern part of Nisyros volcano in the South Aegean Sea (Greece), has been studied by means of remotely operated underwater vehicle dives. The recorded time series of temperature and conductivity over the submarine volcano have been analyzed in terms of the Generalized Moments Method. The findings of the mathematical analysis shed light on the volcanic activity, but also on the morphology (shape) of the submarine volcano. The conductivity time series indicates the volcano is at rest in agreement with other types of observations. On the other hand, temperature fluctuations, which in general describe a multifractal process, show that the submarine caldera operates as an open system that interacts with its surroundings. This type of analysis can be used as an indicator for the state of activity and the morphological structure (closed or open system) of a submarine volcano.

We define a new seasonal forecasting method based on fuzzy transforms. We use the best interpolating polynomial for extracting the trend of the time series and generate the inverse fuzzy transform on each seasonal subset of the universe of discourse for predicting the value of a an assigned output. Like first example, we use the daily weather dataset of the municipality of Naples (Italy) starting from data collected from 2003 till to 2015 making predictions on the following outputs: mean temperature, max temperature and min temperature, all considered daily. Like second example, we use the daily mean temperature measured at the weather station “Chiavari Caperana” in the Liguria Italian Region. We compare the results with our method, the average seasonal variation, ARIMA and the usual fuzzy transforms concluding that the best results are obtained under our approach in both examples.

In this paper, we study the asymptotic behavior of the sequential empirical process and the sequential empirical copula process, both constructed from residuals of multivariate stochastic volatility models. Applications for the detection of structural changes and specification tests of the distribution of innovations are discussed. It is also shown that if the stochastic volatility matrices are diagonal, which is the case if the univariate time series are estimated separately instead of being jointly estimated, then the empirical copula process behaves as if the innovations were observed; a remarkable property. As a by-product, one also obtains the asymptotic behavior of rank-based measures of dependence applied to residuals of these time series models.

According to the fact that the low convergence level on the complete elliptic integral of the first kind for the modulus which having values approach to one. In this paper we propose novelty of the complete elliptic integral consists of the new infinite series. We apply the scheme of iteration by substituting the common modulus with own modulus function into the new infinite series. We obtained so many new exact formulas of the complete elliptic integral derived from this method correspond to the number of iteration order. On the other hand, it has been also obtained a lot of new modulus functions rather than common used previously. The calculation results show that the number of significant figures of the new infinite series of the complete elliptic integral of the first kind is increased more and more. It means more fastly convergent would be obtained comparison values with the previous infinite series.

Signal approximation, is the basic idea of signal processing and mathematical analysis where complex signals can be represented with simpler ones. This paper explores unifying two mathematical fundamentals, Dirichlet-type problems, and hyperbolic series identities, into signal approximation. In this paper, we address a well-known classic topic in mathematical analysis - the Dirichlet problem - to improve (the approximation of) signal using Fourier series. We also discuss using hyperbolic series representations to increase signal modeling flexibility. In this way, we hope to create new links that span some distance along this dimension and result in a somewhat theoretical view of signal behavior - present with the mathematical rigor needed for speculation but absent from an understanding capable of appropriately handling real-world complexity. This paper provides a theoretical investigation of the mechanics at play and reveals by analogy how these mathematical tools can potentially advance signal processing techniques and understanding. This paper illustrates Fourier series and fuzzy logic methods by two case studies on signal processing, satellite communication and financial risk measurement. The first case study performs signal approximation using the Fourier series and hyperbolic function identities to provide insight into how signals behave and are modeled. The second case study deals with applying fuzzy logic for risk evaluation of investment portfolios, emphasizing the utility in evasion systems solving uncertainty and imprecision problems related to financial decisions.