Journal articles: 'Absolutely Monotonic Functions'

1

Morillas, Mariela. "A characterization of absolutely monotonic (Δ) functions." Publications de l'Institut Math?matique (Belgrade) 78, no. 92 (2005): 93–105. http://dx.doi.org/10.2298/pim0578093m.

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2

Bilodeau, G. G. "Extensions of Bernstein's theorem on absolutely monotonic functions." Journal of Mathematical Analysis and Applications 116, no. 2 (June 1986): 489–96. http://dx.doi.org/10.1016/s0022-247x(86)80013-0.

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3

Koumandos, Stamatis, and Henrik L. Pedersen. "On the Laplace Transform of Absolutely Monotonic Functions." Results in Mathematics 72, no. 3 (December 21, 2016): 1041–53. http://dx.doi.org/10.1007/s00025-016-0638-4.

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4

Bilodeau, G. G. "Absolutely monotonic functions and connection coefficients for polynomials." Journal of Mathematical Analysis and Applications 131, no. 2 (May 1988): 517–29. http://dx.doi.org/10.1016/0022-247x(88)90222-3.

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5

Yang, Shijun. "Absolutely (completely) monotonic functions and Jordan-type inequalities." Applied Mathematics Letters 25, no. 3 (March 2012): 571–74. http://dx.doi.org/10.1016/j.aml.2011.09.061.

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6

Novitskii, M., and D. Sacchetti. "On the functions whose inverse is jet-absolutely monotonic." Applicable Analysis 77, no. 3-4 (April 2001): 297–304. http://dx.doi.org/10.1080/00036810108840909.

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7

Gol'dberg, A. A., and I. V. Ostrovskii. "Indicators of entire absolutely monotonic functions of finite order." Siberian Mathematical Journal 27, no. 6 (1987): 811–25. http://dx.doi.org/10.1007/bf00970000.

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8

Skorokhodov, D. S. "On Landau-Kolmogorov problem on the interval for absolutely monotonic functions." Researches in Mathematics 17 (January 29, 2021): 120. http://dx.doi.org/10.15421/240918.

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9

Yang, Zhen-Hang, and Jing-Feng Tian. "Absolutely monotonic functions involving the complete elliptic integrals of the first kind with applications." Journal of Mathematical Inequalities, no. 3 (2021): 1299–310. http://dx.doi.org/10.7153/jmi-2021-15-87.

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10

Koumandos, Stamatis, and Henrik L. Pedersen. "Absolutely monotonic functions related to Euler’s gamma function and Barnes’ double and triple gamma function." Monatshefte für Mathematik 163, no. 1 (February 14, 2010): 51–69. http://dx.doi.org/10.1007/s00605-010-0197-9.

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11

Wang, Miao-Kun, Hong-Hu Chu, Yong-Min Li, and Yu-Ming Chu. "Answers to three conjectures on convexity of three functions involving complete elliptic integrals of the first kind." Applicable Analysis and Discrete Mathematics 14, no. 1 (2020): 255–71. http://dx.doi.org/10.2298/aadm190924020w.

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In the article, we prove that the function x ? (1-x)pK(?x) is logarithmically concave on (0,1) if and only if p ? 7/32, the function x ? K(?x)/log(1+4/?1-x) is convex on (0,1) and the function x ? d2/dx2 [K(?x)- log (1+4/?1-x) is absolutely monotonic on (0,1), where K(x) = ??/20 (1-x2 sin2t)-1/2 dt (0 < x < 1) is the complete elliptic integral of the first kind.

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12

Góra, P., and A. Boyarsky. "Compactness of Invariant Densities for Families of Expanding, Piecewise Monotonic Transformations." Canadian Journal of Mathematics 41, no. 5 (October 1, 1989): 855–69. http://dx.doi.org/10.4153/cjm-1989-039-8.

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Let I = [0,1] and let be the space of all integrable functions on I, where m denotes Lebesque measure on I. Let ∥ ∥1 be the ℒ-1-norm and let be a measurable, nonsingular transformation on I. Let denote the space of densities. The probability measure μ is invariant under τ if for all measurable sets A, The measure μ is absolutely continuous if there exists an such that for any measurable set A We refer to ƒ* as the invariant density of τ (with respect to m). It is well-known that ƒ * is a fixed point of the Frobenius-Perron operator defined by

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13

Smajdor, Andrzej. "On absolutely monotone set-valued functions." Annales Polonici Mathematici 88, no. 2 (2006): 113–18. http://dx.doi.org/10.4064/ap88-2-2.

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14

Lapidot, E. "On Singular Generalized Absolutely Monotone Functions." Journal of Approximation Theory 79, no. 2 (November 1994): 199–221. http://dx.doi.org/10.1006/jath.1994.1125.

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15

Mihailović, Biljana, and Endre Pap. "Sugeno integral based on absolutely monotone real set functions." Fuzzy Sets and Systems 161, no. 22 (November 2010): 2857–69. http://dx.doi.org/10.1016/j.fss.2010.03.004.

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16

Mihailović, Biljana, Martin Kalina, and Mirjana Štrboja. "On the generalized k-order additivity for absolutely monotone set functions." Soft Computing 23, no. 15 (November 1, 2018): 6043–50. http://dx.doi.org/10.1007/s00500-018-3605-z.

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17

Goswami, Angshuman R., and Zsolt Páles. "On approximately monotone and approximately Hölder functions." Periodica Mathematica Hungarica 81, no. 1 (June 11, 2020): 65–87. http://dx.doi.org/10.1007/s10998-020-00351-0.

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Abstract A real valued function f defined on a real open interval I is called $$\Phi $$ Φ -monotone if, for all $$x,y\in I$$ x , y ∈ I with $$x\le y$$ x ≤ y it satisfies $$\begin{aligned} f(x)\le f(y)+\Phi (y-x), \end{aligned}$$ f ( x ) ≤ f ( y ) + Φ ( y - x ) , where $$ \Phi :[0,\ell (I) [ \rightarrow \mathbb {R}_+$$ Φ : [ 0 , ℓ ( I ) [ → R + is a given nonnegative error function, where $$\ell (I)$$ ℓ ( I ) denotes the length of the interval I. If f and $$-f$$ - f are simultaneously $$\Phi $$ Φ -monotone, then f is said to be a $$\Phi $$ Φ -Hölder function. In the main results of the paper, we describe structural properties of these function classes, determine the error function which is the most optimal one. We show that optimal error functions for $$\Phi $$ Φ -monotonicity and $$\Phi $$ Φ -Hölder property must be subadditive and absolutely subadditive, respectively. Then we offer a precise formula for the lower and upper $$\Phi $$ Φ -monotone and $$\Phi $$ Φ -Hölder envelopes. We also introduce a generalization of the classical notion of total variation and we prove an extension of the Jordan Decomposition Theorem known for functions of bounded total variations.

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18

Skorokhodov, D. S. "Landau–Kolmogorov problem for a class of functions absolutely monotone on a finite interval." Ukrainian Mathematical Journal 63, no. 4 (September 2011): 617–37. http://dx.doi.org/10.1007/s11253-011-0529-5.

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19

Li, Jun. "Absolute Continuity of Fuzzy Measures and Convergence of Sequence of Measurable Functions." Mathematics 8, no. 5 (May 5, 2020): 726. http://dx.doi.org/10.3390/math8050726.

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In this note, the convergence of the sum of two convergent sequences of measurable functions is studied by means of two types of absolute continuity of fuzzy measures, i.e., strong absolute continuity of Type I, and Type VI. The discussions of convergence a.e. and convergence in measure are done in the general framework relating to a pair of monotone measures, and general results are shown. The previous related results are generalized.

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20

Babenko, V. F., Yu V. Babenko, and O. V. Kovalenko. "Kolmogorov's problem about the existence of absolute monotone and multiply monotone functions with given norms of derivatives." Reports of the National Academy of Sciences of Ukraine, no. 10 (October 20, 2015): 7–11. http://dx.doi.org/10.15407/dopovidi2015.10.007.

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21

Mihailović, Biljana, and Endre Pap. "Asymmetric integral as a limit of generated Choquet integrals based on absolutely monotone real set functions." Fuzzy Sets and Systems 181, no. 1 (October 2011): 39–49. http://dx.doi.org/10.1016/j.fss.2011.05.007.

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22

Alexeev, Ivan A., and Alexey A. Khartov. "On convergence and compactness in variation with shift of discrete probability laws." Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy 8, no. 3 (2021): 385–93. http://dx.doi.org/10.21638/spbu01.2021.301.

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We consider a class of discrete distribution functions, whose characteristic functions are separated from zero, i. e. their absolute values are greater than positive constant on the real line. The class is rather wide, because it contains discrete infinitely divisible distribution functions, functions of lattice distributions, whose characteristic functions have no zeroes on the real line, and also distribution functions with a jump greater than 1/2. Recently the authors showed that characteristic functions of elements of this class admit the Lévy-Khinchine type representations with non-monotonic spectral function. Thus our class is included in the set of so called quasi-infinitely divisible distribution functions. Using these representation the authors also obtained limit and compactness theorems with convergence in variation for the sequences from this class. This note is devoted to similar results concerning convergence and compactness but with weakened convergence in variation. Replacing of type of convergence notably expands applicability of the results.

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23

Li, Yixia, Muhammad Samraiz, Ayesha Gul, Miguel Vivas-Cortez, and Gauhar Rahman. "Hermite-Hadamard Fractional Integral Inequalities via Abel-Gontscharoff Green’s Function." Fractal and Fractional 6, no. 3 (February 23, 2022): 126. http://dx.doi.org/10.3390/fractalfract6030126.

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The Hermite-Hadamard inequalities for κ-Riemann-Liouville fractional integrals (R-LFI) are presented in this study using a relatively novel approach based on Abel-Gontscharoff Green’s function. In this new technique, we first established some integral identities. Such identities are used to obtain new results for monotonic functions whose second derivative is convex (concave) in absolute value. Some previously published inequalities are obtained as special cases of our main results. Various applications of our main consequences are also explored to special means and trapezoid-type formulae.

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24

Sedding, Helmut A. "Scheduling jobs with a V-shaped time-dependent processing time." Journal of Scheduling 23, no. 6 (September 8, 2020): 751–68. http://dx.doi.org/10.1007/s10951-020-00665-4.

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AbstractIn the field of time-dependent scheduling, a job’s processing time is specified by a function of its start time. While monotonic processing time functions are well-known in the literature, this paper introduces non-monotonic functions with a convex, piecewise-linear V-shape similar to the absolute value function. They are minimum at an ideal start time, which is the same for all given jobs. Then, the processing time equals the job’s basic processing time. Earlier or later, it increases linearly with slopes that can be asymmetric and job-specific. The objective is to sequence the given jobs on a single machine and minimize the makespan. This is motivated by production planning of moving car assembly lines, in particular, to sequence a worker’s assembly operations such that the time-dependent walking times to gather materials from the line-side is minimized. This paper characterizes the problem’s computational complexity in several angles. NP-hardness is observed even if the two slopes are the same for all jobs. A fully polynomial time approximation scheme is devised for the more generic case of agreeable ratios of basic processing time and slopes. In the most generic case with job-specific slopes, several polynomial cases are identified.

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25

Oehring, Charles. "Spectral decay for definite kernels and functions." Mathematical Proceedings of the Cambridge Philosophical Society 105, no. 1 (January 1989): 161–63. http://dx.doi.org/10.1017/s0305004100001481.

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A classical theorem of Weyl [7] guarantees that the eigenvalues, ordered according to decreasing absolute values, of a symmetric kernel of class Cm (m ≥ 0) satisfy λn = o(n−m−½). Reade [5, 6] recently proved that if K is, in addition, positive definite, then λn = o(n−m−1;). He has also in [4] made similar improvements of classical spectral estimates for kernels of class Lip α. James Cochran pointed out to me that allied theorems for trigonometric Fourier coefficients seem to have been neglected in the literature. The trigonometric versions turn out to be elementary; nevertheless, in their conclusions concerning the decreasing rearrangement {f^*(n)} they generalize known results about the behaviour of monotone trigonometric transforms. Furthermore they suggest that the Cm hypothesis of Reade's theorem could be relaxed.

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26

Khan, Sundas, Huseyin Budak, and Yuming Chu. "New quantum inequalities of Hermite-Hadamard type via Green function." MATHEMATICA 64 (87), no. 2 (December 15, 2022): 233–46. http://dx.doi.org/10.24193/mathcluj.2022.2.08.

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In this study, the Hermite-Hadamard inequality for q^{kappa_2}-integrals is demonstrated by a new method called the Green Function Technique. For this purpose, we first obtain certain identities. Then, by using these identities, we establish many new inequalities for functions whose second derivative is convex, monotone and concave in absolute value.

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27

Soravia, Pierpaolo. "The Aronsson Equation, Lyapunov Functions, and Local Lipschitz Regularity of the Minimum Time Function." Abstract and Applied Analysis 2019 (December 25, 2019): 1–9. http://dx.doi.org/10.1155/2019/6417074.

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We define and study C1-solutions of the Aronsson equation (AE), a second order quasi linear equation. We show that such super/subsolutions make the Hamiltonian monotone on the trajectories of the closed loop Hamiltonian dynamics. We give a short, general proof that C1-solutions are absolutely minimizing functions. We discuss how C1-supersolutions of (AE) become special Lyapunov functions of symmetric control systems, and allow to find continuous feedbacks driving the system to a target in finite time, except on a singular manifold. A consequence is a simple proof that the corresponding minimum time function is locally Lipschitz continuous away from the singular manifold, despite classical results showing that it should only be Hölder continuous unless appropriate conditions hold. We provide two examples for Hörmander and Grushin families of vector fields where we construct C1-solutions (even classical) explicitly.

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28

STOCCHINO, ALESSANDRO, GIOVANNI BESIO, SONIA ANGIOLANI, and MAURIZIO BROCCHINI. "Lagrangian mixing in straight compound channels." Journal of Fluid Mechanics 675 (March 29, 2011): 168–98. http://dx.doi.org/10.1017/s0022112011000127.

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Recently Stocchino & Brocchini (J. Fluid Mech., vol. 643, 2010, p. 425 have studied the dynamics of two-dimensional (2D) large-scale vortices with vertical axis evolving in a straight compound channel under quasi-uniform flow conditions. The mixing processes associated with such vortical structures are here analysed through the results of a dedicated experimental campaign. Time-resolved Eulerian surface velocity fields, measured using a 2D particle-image velocimetry system, form the basis for a Lagrangian analysis of the dispersive processes that occur in compound channels when the controlling physical parameters, i.e. the flow depth ratio (rh) and the Froude number (Fr) are changed. Lagrangian mixing is studied by means of various approaches based either on single-particle or multiple-particle statistics (relative and absolute statistics, probability density functions (p.d.f.s) of relative displacements and finite-scale Lyapunov exponents). Absolute statistics reveal that transitional macrovortices, typical of shallow flow conditions, strongly influence the growth in time of the total absolute dispersion, after the initial ballistic regime, leading to a non-monotonic behaviour. In deep flow conditions, on the contrary, the absolute dispersion displays a monotonic growth because the generation of transitional macrovortices does not take place. In all cases an asymptotic diffusive regime is reached.Multiple-particle dynamics is controlled by rh and Fr. Different growth regimes of the relative diffusivity have been found depending on the flow conditions. This behaviour can be associated with different energy transfer processes and it is further confirmed by the p.d.f.s of relative displacements, which show a different asymptotical shape depending on the separation scales and the Froude number. Finally, an equilibrium regime is observed for all the experiments by analysing the decay of the finite-scale Lyapunov exponents with the particle separations.

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29

Schmidtchen, Franz P. "Synthese und Bindungsverhalten eines künstlichen Rezeptors für biogene Amine /Synthesis and Complexing Features of an Artificial Receptor for Biogenic Amines." Zeitschrift für Naturforschung C 42, no. 4 (April 1, 1987): 476–85. http://dx.doi.org/10.1515/znc-1987-0425.

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Abstract The synthesis of a ditopic linear receptor 3 consisting of an azacrown ether moiety for binding prim, ammonium functions and a macrotricyclic tetrahedral moiety for binding hydrophobic guest species is described. The covalent interconnection of these subunits was supposed to constitute a receptor with enhanced specificity towards dopamine-type biogenic amines. Host-guest complexation was studied in a competition method with potassium ion using ion selective electrodes. The binding features of 3 with a series of biogenic amines reveal that neither the absolute binding strength nor the selectivity is enhanced in relation to the monotopic receptor 4. It is concluded that 3 does not simultaneously utilize both receptor subunits in binding the biogenic amine substrates.

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30

Ali, Muhammad, Dost Muhammad Khan, Huda M. Alshanbari, and Abd Al-Aziz Hosni El-Bagoury. "Prediction of Complex Stock Market Data Using an Improved Hybrid EMD-LSTM Model." Applied Sciences 13, no. 3 (January 21, 2023): 1429. http://dx.doi.org/10.3390/app13031429.

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Because of the complexity, nonlinearity, and volatility, stock market forecasting is either highly difficult or yields very unsatisfactory outcomes when utilizing traditional time series or machine learning techniques. To cope with this problem and improve the complex stock market’s prediction accuracy, we propose a new hybrid novel method that is based on a new version of EMD and a deep learning technique known as long-short memory (LSTM) network. The forecasting precision of the proposed hybrid ensemble method is evaluated using the KSE-100 index of the Pakistan Stock Exchange. Using a new version of EMD that uses the Akima spline interpolation technique instead of cubic spline interpolation, the noisy stock data are first divided into multiple components technically known as intrinsic mode functions (IMFs) varying from high to low frequency and a single monotone residue. The highly correlated sub-components are then used to build the LSTM network. By comparing the proposed hybrid model with a single LSTM and other ensemble models such as the support vector machine (SVM), Random Forest, and Decision Tree, its prediction performance is thoroughly evaluated. Three alternative statistical metrics, namely root means square error (RMSE), mean absolute error (MAE) and mean absolute percentage error (MAPE), are used to compare the aforementioned techniques. The empirical results show that the suggested hybrid Akima-EMD-LSTM model beats all other models taken into consideration for this study and is therefore recommended as an effective model for the prediction of non-stationary and nonlinear complex financial time series data.

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31

Riley, Jonathan. "On the Possibility of Liberal Democracy." American Political Science Review 79, no. 4 (December 1985): 1135–51. http://dx.doi.org/10.2307/1956252.

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A complex liberal version of utilitarianism is introduced which bears similarities to John Stuart Mill's moral and political philosophy and offers a promising approach to liberal democratic theory. Formally, liberal utilitarianism is represented as a type of generalized social welfare functional which maps any given set of individual vector-valued utility functions into a social ordering. The generalized social welfare functional in question relies on the experienced members of society to classify ond compare the different kinds of utilities found in individual vectors; to grant and protect libertarian rights with respect to a well-defined private kind of individual utilities; and to make the interpersonal comparisons required to aggregate over each of the public kinds of individual utilities. At the same time, it is dynamic in that it implicitly comprehends many different levels of a society's moral development from a liberal perspective.An axiomatization of the ideal liberal utilitarian social welfare functional is provided such that, on the one hand, each person has an absolute right to individual liberty over the issues within his private sphere, and, on the other hand, has an equal voice in a liberty-respecting, strongly monotonk, anonymous and neutral public choice rule operating in a distinct public sphere. The harmony of these private and public components implies the possibility of an ideal liberal democracy.

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32

Tian, Jing-Feng, and Zhen-Hang Yang. "Several Absolutely Monotonic Functions Related to the Complete Elliptic Integral of the First Kind." Results in Mathematics 77, no. 3 (April 6, 2022). http://dx.doi.org/10.1007/s00025-022-01641-4.

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33

Vinogradov, O. L. "Logarithmically Absolutely Monotone Trigonometric Functions." Journal of Mathematical Sciences, December 3, 2022. http://dx.doi.org/10.1007/s10958-022-06217-9.

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34

Möhle, M. "A Particular Family of Absolutely Monotone Functions and Relations to Branching Processes." Analysis Mathematica, February 28, 2023. http://dx.doi.org/10.1007/s10476-023-0211-9.

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35

Vinogradov, Vladimir Vladimirovich, and Richard Bruce Paris. "On two extensions of the canonical Feller–Spitzer distribution." Journal of Statistical Distributions and Applications 8, no. 1 (March 4, 2021). http://dx.doi.org/10.1186/s40488-021-00113-4.

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AbstractWe introduce two extensions of the canonical Feller–Spitzer distribution from the class of Bessel densities, which comprise two distinct stochastically decreasing one-parameter families of positive absolutely continuous infinitely divisible distributions with monotone densities, whose upper tails exhibit a power decay. The densities of the members of the first class are expressed in terms of the modified Bessel function of the first kind, whereas the members of the second class have the densities of their Lévy measure given by virtue of the same function. The Laplace transforms for both these families possess closed–form representations in terms of specific hypergeometric functions. We obtain the explicit expressions by virtue of the particular parameter value for the moments of the distributions considered and establish the monotonicity of the mean, variance, skewness and excess kurtosis within the families. We derive numerous properties of members of these classes by employing both new and previously known properties of the special functions involved and determine the variance function for the natural exponential family generated by a member of the second class.

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36

Khan, Dost Muhammad, Muhammad Ali, Nadeem Iqbal, Umair Khalil, Hassan M. Aljohani, Amirah Saeed Alharthi, and Ahmed Z. Afify. "Short-Term Prediction of COVID-19 Using Novel Hybrid Ensemble Empirical Mode Decomposition and Error Trend Seasonal Model." Frontiers in Public Health 10 (July 29, 2022). http://dx.doi.org/10.3389/fpubh.2022.922795.

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In this article, a new hybrid time series model is proposed to predict COVID-19 daily confirmed cases and deaths. Due to the variations and complexity in the data, it is very difficult to predict its future trajectory using linear time series or mathematical models. In this research article, a novel hybrid ensemble empirical mode decomposition and error trend seasonal (EEMD-ETS) model has been developed to forecast the COVID-19 pandemic. The proposed hybrid model decomposes the complex, nonlinear, and nonstationary data into different intrinsic mode functions (IMFs) from low to high frequencies, and a single monotone residue by applying EEMD. The stationarity of each IMF component is checked with the help of the augmented Dicky–Fuller (ADF) test and is then used to build up the EEMD-ETS model, and finally, future predictions have been obtained from the proposed hybrid model. For illustration purposes and to check the performance of the proposed model, four datasets of daily confirmed cases and deaths from COVID-19 in Italy, Germany, the United Kingdom (UK), and France have been used. Similarly, four different statistical metrics, i.e., root mean square error (RMSE), symmetric mean absolute parentage error (sMAPE), mean absolute error (MAE), and mean absolute percentage error (MAPE) have been used for a comparison of different time series models. It is evident from the results that the proposed hybrid EEMD-ETS model outperforms the other time series and machine learning models. Hence, it is worthy to be used as an effective model for the prediction of COVID-19.

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Journal articles on the topic 'Absolutely Monotonic Functions'

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