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Article
Open AccessProbabilistic Degenerate Fubini Polynomials Associated with Random Variables
Let Y be a random variable such that the moment generating function of Y exists in a neighborhood of the origin. The aim of this paper is to study probabilistic versions of the degenerate Fubini polynomials and t...
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Article
A case study on the impact of real-time land cover changes in the intertidal zone on coastal meteorological predictions using a coupled atmosphere–ocean model
The effect of time-varying land cover within the intertidal zone on meteorological predictions was evaluated on the west coast of South Korea during the summer of 2020 (July 3–8). Time-varying spatial distribu...
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Article
Some identities and properties on degenerate Stirling numbers
The aim of this paper is by using generating functions to further study some identities and properties on the degenerate Stirling numbers of the second kind, the degenerate r-Stirling numbers of the second kind, ...
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Article
Open AccessA process-based assessment of the sea-level rise in the northwestern Pacific marginal seas
Because regional sea-level rise can threaten coastal communities, understanding and quantifying the underlying process contributing to reginal sea-level budget are essential. Here, we assessed whether the regi...
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Article
Open AccessImpact of surgical factors on delayed hyponatremia in patients with nonfunctioning pituitary adenoma after endonasal endoscopic transsphenoidal procedure
Delayed hyponatremia can occur after pituitary surgery, resulting in prolonged hospitalization. However, the influence of surgical factors after such a procedure has not been well established. The impact of su...
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Article
Open AccessPoly-central factorial sequences and poly-central-Bell polynomials
In this paper, we introduce poly-central factorial sequences and poly-central Bell polynomials arising from the polyexponential functions, reducing them to central factorials and central Bell polynomials of th...
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Article
Open AccessOn λ-linear functionals arising from p-adic integrals on \(\mathbb{Z}_{p}\)
The aim of this paper is to determine the λ-linear functionals sending any given polynomial p ( ...
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Article
Open AccessA note on degenerate generalized Laguerre polynomials and Lah numbers
The aim of this paper is to introduce the degenerate generalized Laguerre polynomials as the degenerate version of the generalized Laguerre polynomials and to derive some properties related to those polynomial...
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Article
Open AccessMulti-Lah numbers and multi-Stirling numbers of the first kind
In this paper, we introduce multi-Lah numbers and multi-Stirling numbers of the first kind and recall multi-Bernoulli numbers, all of whose generating functions are given with the help of multiple logarithm. T...
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Article
Open AccessDegenerate poly-Bell polynomials and numbers
Numerous mathematicians have studied ‘poly’ as one of the generalizations to special polynomials, such as Bernoulli, Euler, Cauchy, and Genocchi polynomials. In relation to this, in this paper, we introduce th...
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Article
Open AccessSome new formulas of complete and incomplete degenerate Bell polynomials
The aim of this paper is to study the complete and incomplete degenerate Bell polynomials, which are degenerate versions of the complete and incomplete Bell polynomials, and to derive some properties and ident...
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Article
Open AccessSome properties of degenerate complete and partial Bell polynomials
In this paper, we study degenerate complete and partial Bell polynomials and establish some new identities for those polynomials. In addition, we investigate the connections between modified degenerate complet...
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Article
Differential Equations Associated with Higher-order Frobenius–Euler Numbers Revisited
In this paper, we derive differential equations from the generating function of higher-order Frobenius–Euler numbers. In addition, we give some new and explicit identities for higher-order Frobenius–Euler numb...
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Article
Ocular blood flow by laser speckle flowgraphy to detect cerebral ischemia during carotid endarterectomy
Laser speckle flowgraphy (LSFG) is a noninvasive technique that can measure relative blood flow velocity in the optic fundus contributed by the ophthalmic artery, the main first branch originating from the int...
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Article
Open AccessRepresentations of degenerate poly-Bernoulli polynomials
As is well known, poly-Bernoulli polynomials are defined in terms of polylogarithm functions. Recently, as degenerate versions of such functions and polynomials, degenerate polylogarithm functions were introdu...
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Article
Open AccessGeneralized degenerate Bernoulli numbers and polynomials arising from Gauss hypergeometric function
A new family of p-Bernoulli numbers and polynomials was introduced by Rahmani (J. Number Theory 157:350–366, 2015) with the help of the Gauss hypergeometric function. Motivated by that paper and in the light of t...
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Article
Open AccessComplete and incomplete Bell polynomials associated with Lah–Bell numbers and polynomials
The nth r-extended Lah–Bell number is defined as the number of ways a set with n + r ...
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Article
Open AccessReciprocity of poly-Dedekind-type DC sums involving poly-Euler functions
The classical Dedekind sums appear in the transformation behavior of the logarithm of the Dedekind eta-function under substitutions from the modular group. The Dedekind sums and their generalizations are defin...
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Chapter
Correction to: Optimal Control
The original version of the book was inadvertently published with errors. Some are errors in the Mathematical Equations (such as on Preface, Part I from pages 4 to 7, Part II from pages 21 to 105 and Part III ...
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Chapter
Small Increments of a Trajectory
With the aid of «small» variations of a fixed basis process we construct and describe the family of «close» processes by means of linear approximation. We clarify the concept of small variations and close proc...
