Summability Methods Research Articles

Comparative analysis of SPI and SPEI drought indices for Montenegro and the impact of teleconnections

ABSTRACT After 2000, Montenegro has been hit by several severe droughts. The results presented in this study were based on the analysis of the standardized precipitation index (SPI) and the standardized precipitation evapotranspiration index (SPEI) for the period 1961–2020. They showed the prevalence of a negative trend in both indices and a significantly higher frequency of drought in the second half of the observed period (1991–2020). The SPEI index is a more representative indicator of drought, because in addition to precipitation, it also takes into account potential evapotranspiration. Using the rescaled adjusted partial sums (RAPS) method, it was determined that the tipping point when the SPEI suddenly fell was the mid-1980s. Out of the 15 analyzed teleconnection variation indicators (atmospheric and oceanic oscillations), 11 oscillations have a significant impact on one or more of the 24 analyzed SPEI time series. The consequences of the drought in Montenegro, as part of the Mediterranean, are most noticeable in the summer, primarily in the form of water shortages, dried vegetation, and frequent fires. Decision-makers in Montenegro should pay attention to this extreme, as drought could pose a serious problem under the projected warmer climate conditions.

Preliminary Validation of Measures of Experienced, Perceived, and Internalized Stigma Among Adults Who Are d/Deaf or Hard of Hearing in the United States and Ghana.

In this article, we examine the psychometric performance of 3 scales measuring experienced, perceived, and internalized d/Deaf or hard of hearing (d/DHH) stigma among adult (18 and older) populations of individuals who are d/DHH, including those who have been d/DHH since before they developed language (lifelong) and those who became d/DHH after they developed language (acquired) in the United States and Ghana. The preliminary validation study took place in the Greater Accra and Eastern regions of Ghana and across the United States. In the United States, all data were collected online via self-administered surveys in English. In Ghana, trained interviewers who are d/DHH and fluent in Ghanaian Sign Language conducted interviews with participants who are lifelong d/DHH using a video survey. Ghanaian participants with acquired d/DHH status were surveyed by trained hearing interviewers. We calculated polychoric correlation matrices between the measures to remove redundant and unrelated items and used exploratory factor analysis to create the final scales. We also tested the association between the factor scores and a simple summing method for calculating the scale. The study sample included people who have been d/DHH since before they developed language (Ghana: n = 171, United States n = 100) and people who became d/DHH after they developed language (Ghana: n = 174, United States: n = 219). The final experienced, perceived, and internalized scales included six, seven, and five items, respectively. All three scales performed well as unidimensional measures across all four samples. Across the four samples, the experienced, perceived, and internalized stigma scales yielded ordinal αs ranging from 0.725 to 0.947, 0.856 to 0.935, and 0.856 to 0.935, respectively. It would be acceptable to operationalize all stigma scales as sum-of-item scores. The scales performed well and appear to provide a valid means of measuring different types of stigma among diverse groups of people who are d/DHH. Future work should refine and validate these scales in additional contexts.

On Statistical Riemann-Stieltjes Integrablility and Deferred Cesàro Summabilit

In this paper, we first introduce and study the notion of statistical Riemann-Stieltjes sum for the sequence of functions and establish some elementary results based on this notion. Subsequently, we extend this notion to the probability space and demonstrate some new results for sequence of distribution functions. Furthermore, we suggest the deferred Cesàro summability method for Riemann-Stieltjes sum. We then establish various inclusion theorems based on our proposed methods in association with the Riemann-Stieltjes sum for the sequence of usual functions as well as distribution functions in Rn.

Parallel Brownian dynamics implementation of the Angular Averaged Ewald sums in Coulombic fluids

In nature, Coulombic fluids are present in many different forms, for instance, as aqueous electrolytes dissolving charged biomolecules (such as the DNA or lipid bilayers), macroion or nanoparticle solutions, molten salts, ionic liquids, plasmas, etc. One important characteristic of charged fluids is the long-range electrostatic interaction, which must be incorporated adequately in computer simulations in order to avoid artifacts. In this work, an MPI-Fortran 90 parallel implementation of Coulombic interactions using the Angular Averaged Ewald sums in Brownian dynamics is reported. This computational implementation is considerably faster than the corresponding serial version for a small to a sizable number of particles (tens of thousands). The accuracy of the parallelized Angular Averaged Ewald sums is compared regarding the Ewald sums method at the level of structural and electrostatic properties of a size- and valence-asymmetric electrolyte.

Almost everywhere convergence of two-dimensional Walsh-Nörlund means

The present paper the almost everywhere convergence of two-dimensional Walsh-Nörlund means is studied, when the given function belongs to the hybrid Hardy space $H_{\natural}$. Because the Nörlund means are a generalization of several known classical summability methods, previously known classical theorems are derived from the main theorem. In addition some new results follow in particular cases as well.

Applications of martingale Hardy Orlicz–Lorentz–Karamata theory in Fourier analysis

In this article, we discuss the applications of martingale Hardy Orlicz–Lorentz–Karamata spaces in Fourier analysis. More precisely, we show that the partial sums of the Walsh–Fourier series converge to the function in norm if f∈LΦ,q,b\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f\\in L_{\\Phi ,q,b}$$\\end{document} with 1<p-≤p+<∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1<p_-\\le p_+<\\infty $$\\end{document}. The equivalence of maximal operators on martingale Hardy Orlicz–Lorentz–Karamata spaces is presented. The Fejér summability method is also studied and it is proved that the maximal Fejér operator is bounded from martingale Hardy Orlicz–Lorentz–Karamata spaces to Orlicz–Lorentz–Karamata spaces. As a consequence, we obtain conclusions about almost everywhere and norm convergence of Fejér means.

On the divergence of Taylor series in de Branges–Rovnyak spaces

It is known that there exist functions in certain de Branges–Rovnyak spaces whose Taylor series diverge in norm, even though polynomials are dense in the space. This is often proved by showing that the sequence of Taylor partial sums is unbounded in norm. In this note we show that it can even happen that the Taylor partial sums tend to infinity in norm. We also establish similar results for lower-triangular summability methods such as the Cesàro means.

Optimization of Stock Investments in Indonesia Stock Exchange: Comparing the Method of Dollar Cost Averaging (DCA) and Lump Sum (LS)

The aim of this research is to find out how to optimize stock investment using the dollar cost averaging method and the lump sum method and also to compare the performance between the dollar cost averaging method and the lump sum method based on return results. This research uses a descriptive method with a quantitative approach. This research uses 2 companies with the largest market cap listed on the Indonesian Stock Exchange for the 2021-2023 period. The results of this research found that the lump sum method return in 2022 on BBCA shares reached 22.85% and on BBRI shares 18.19% higher than the return on the dollar cost averaging method on BBCA shares which was only 13.70% and on shares BBRI is only 10.86%. The lump sum method return in 2022 is the highest return between 2021 and 2023. These results prove that the lump sum method is more optimal than the dollar cost averaging method.

Sustainable energy production and resilience towards floods by using hydro and solar photovoltaic energy

Unexpected and intense floods have become more frequent recently; this is related to extreme weather events that are difficult to predict accurately. This necessitates new solutions to decrease the risk of flooding urban and rural areas. Moreover, such solutions should have negligible impact on the environment. There are several concepts, tools, and technical measures for preventing floods, one of which is the ‘monkey cheek’ concept for flood protection, used in Thailand for protection from river and sea floods. Monkeys collect food in their mouths and eat subsequently in stages. In a similar manner, excess water from floods could be collected and stored in reservoirs, sags, canals, floodplain forests, and unused space. Collected water could then be used for irrigation. In most cases, collected water must be pumped to distant or higher locations compared to the location where the water was collected. This requires electric energy for the pumps. This paper analyses a case study for the presented concept for the town of Ludbreg in Croatia, currently undergoing real-site measurements and calculations. A rescaled adjusted partial sums method is applied for the analysis. It has been shown that the energy potential of the local, small river Bednja in the observed location could be approximated using the “monkey cheek’’ concept. Within this, using the produced electricity from small hydropower plants and solar photovoltaic systems has been proven promising. The solution avoids building dams for flood protection, satisfying the environmental aspects.

Sustainable Energy Development and Sustainable Economic Development in EU Countries

Sustainable development is the subject of many economic analyses, but so far no attempt has been made to identify the main mechanism of interdependence between sustainable energy development and sustainable economic development in the second decade of the 21st century. The particular role of energy in achieving the Sustainable Development Goals is due to the fact that the production, supply and use of energy underpin economic growth. The article fills this research gap and spawns both a better understanding of the essence of sustainable development as well as practical conclusions. The aim is to assess sustainable energy development and sustainable economic development in EU member states and to determine the correlation between the two in the EU. Substantive and formal methods were used to select diagnostic variables, including: the parametric method, the standardized sums method, and correlation analysis. The analysis period covers the years 2014–2021. The conducted research demonstrated a significant variation in the level of sustainable energy development and sustainable economic development among EU countries.

Some summability methods for Dunkl–Gamma‐type operators including Appell polynomials

In this paper, we give some properties of the Dunkl–Gamma‐type operators including Appell polynomials, using into consideration the generalized power summability method. In the first section are given moments of the new defined operators. In second section are given some direct estimation related to the Dunkl–Gamma‐type operators, including Korovkin‐type theorem. In the third section, we give some results related to the weighted spaces of continuous functions, and in the last section, we give some properties in the sense of ‐statistically convergence, including Voronovskaya and Grüss–Voronovskaya‐type theorem.

Kantorovich Version of Vector-Valued Shepard Operators

In the present work, in order to approximate integrable vector-valued functions, we study the Kantorovich version of vector-valued Shepard operators. We also display some applications supporting our results by using parametric plots of a surface and a space curve. Finally, we also investigate how nonnegative regular (matrix) summability methods affect the approximation.

Trigonometric approximation of signals (functions) belonging to certain Lipschitz spaces using C δ.C operator

Abstract In 2015, Srivastava and Singh [S. K. Srivastava and U. Singh, Trigonometric approximation of periodic functions belonging to weighted Lipschitz class W ⁢ ( L p , Ψ ⁢ ( t ) , β ) W(L^{p},\Psi(t),\beta) , Function Spaces in Analysis, Contemp. Math. 645, American Mathematical Society, Providence 2015, 283–291] determined the order of approximation of periodic functions belonging to W ⁢ ( L p , Ψ ⁢ ( u ) , β ) {W(L^{p},\Psi(u),\beta)} -class, which is a weighted version of Lip ⁢ ( ω ⁢ ( u ) , p ) {\mathrm{Lip}(\omega(u),p)} -class with weight function sin β ⁢ p ⁡ ( y 2 ) {\sin^{\beta p}(\frac{y}{2})} through matrix means of their trigonometric Fourier series. It is a well-known fact that the product summability methods are stronger than the single summability methods, and they can approximate a wider class of functions. Therefore, in this article, an effort is made to determine the degree of approximation for periodic functions from the same weighted Lipschitz class W ⁢ ( L p , Ψ ⁢ ( u ) , β ) {W(L^{p},\Psi(u),\beta)} , p ≥ 1 {p\geq 1} , using C δ . T {C^{\delta}.T} -means of their trigonometric Fourier series.

An analytical approach to deduce loading rate-sensitivity of fracture mode of concrete and mortar

The fracture of two-component solids is considered in order to study the sensitivity of the failure mode to the loading rate. The incubation time approach, supplemented by the randomized Sign-Perturbed Sums (SPS) method, is applied to develop an analytical model to predict the difference in the fracture pattern under dynamic and static conditions. To verify and validate the model, experimental data of dynamic tests on concrete, mortar and granite aggregate are analyzed. It was demonstrated that the model indicates the change in the failure mode for inhomogeneous material such as concrete, while the analysis results for pure granite do not predict the same phenomenon. The results obtained are in agreement with the experimentally observed change in the fracture mechanism of concrete from transgranular to intergranular as the loading rate decreases. Thus, it was shown that the developed model is able to predict the change of the fracture mechanism with the increase of the loading rate.

Some Tauberian Theorems for the Weighted Mean Method of Summability of Double Sequences

Some Tauberian Theorems for the Weighted Mean Method of Summability of Double Sequences

On Gradual Borel Summability Method of Rough Convergence of Triple Sequences of Beta Stancu Operators

We define the concept of rough limit set of a triple sequence space of beta Stancu operators of Borel summability of gradual real numbers and obtain the relation between the set of rough limit and the extreme limit points of a triple sequence space of beta Stancu operators of Borel summability method of gradual real numbers. Finally, we investigate some properties of the rough limit set of beta Stancu operators under which Borel summable sequence of gradual real numbers are convergent. Also, we give the results for Borel summability method of series of gradual real numbers.

General logarithmic control modulo and Tauberian remainder theorems

Let $\lambda=(\lambda_n)$ be a nondecreasing sequence of positive numbers such that $\lambda_n\to\infty$. A sequence $(\xi_n)$ is called $\lambda$-bounded if \begin{equation*} \lambda_n(\xi_n-\alpha)=O(1)\end{equation*} with the limit $\displaystyle{\lim_{n\rightarrow \infty}\xi_n=\alpha}$. In this work, we obtain several Tauberian remainder theorems on $\lambda$-bounded sequences for the logarithmic summability method with help of general logarithmic control modulo of the oscillatory behavior. Tauber conditions in our main results are on the generator sequence and the general logarithmic control modulo.

Estimation of errors of signals (functions) by (C,2)(E,δ) product means of Fourier series

In this paper, we establish a new theorem to estimate the errors of signals (functions) class by new product summability method.

Equivalence Theorem for Absolute Matrix Summability Methods

Equivalence Theorem for Absolute Matrix Summability Methods

The method of Haar sums for numerical solution of kinematic Poisson equations system that determine an evolution of a spacecraft position

In the present paper the method for the numerical solution of Poisson kinematic equations system that determine the evolution of the spacecraft position is proposed. The system of Poisson kinematic equations is used to determine the transition matrix from the coordinate system associated with the spacecraft at the selected time t1 to the coordinate system associated with the spacecraft at the current time t2. This matrix is used in the process of solving problems of determining a three-axis orientation of the spacecraft from the readings of the magnetometer using information about its angular velocities. The proposed method is based on replacing the derivatives of the desired functions in the Poisson kinematic equations by partial sums of series in the scaled Haar system. The partial sums of these series are generalized polynomials in the scaled Haar system. Hence these sums are step (piecewise constant) functions. The estimates of the proposed method error are derived, which reveal that in the case of the coefficients of the equations which are functions matching the Lipschitz condition, the absolute error in calculating each of the elements of the transition matrix from one coordinate system to another is the value O(N–1) at N ® ¥, where N is the number of partitions of the segment [t1, t2] when constructing a grid of nodes involved in this method. It is proved that the complexity of constructing an algorithm for approximating the system of Poisson kinematic properties insignificantly exceeds the complexity of solving this system by Euler method, which has the first order of accuracy. The results of numerical experiments are presented, showing that in certain cases the Haar sums method gives an error that is much smaller than the Euler method, and is almost identical to the errors of the Euler – Cauchy and Runge – Kutta methods of the 2nd order, the complexity of which is approximately two times greater than the complexity of the Haar sums method.