Article
Computer Science, Theory & Methods
Michael Kupper, Jose M. Zapata
Summary: This paper introduces a weaker form of maximality and shows that under this assumption, the Shilkret integral is still determined by its possibility distribution for sufficiently regular functions. Inspired by large deviation theory, a Laplace principle for maximative integrals is provided and the possibility distribution is characterized under certain separation and convexity assumptions. Moreover, a maximative integral representation result for weakly maximative non-linear expectations is shown. The theoretical results are illustrated by providing large deviations bounds for sequences of capacities and deriving a monotone analogue of Cramer's theorem.
FUZZY SETS AND SYSTEMS
(2023)
Article
Mathematics, Applied
Fatih Aylikci, Nese Dernek, Gulesin Balaban
Summary: In this paper, the authors provide iteration identities for the generalized Laplace transform L2n and the generalized Glasser transform G2n. Based on these identities, a Parseval-Goldstein type theorem for the L2n-transform and G2n-transform is presented, leading to new identities for these and other integral transforms. These proven identities have useful corollaries for evaluating infinite integrals of special functions. Several examples are provided.
Article
Mathematics, Applied
Alireza Ansari
Summary: In this paper, it is demonstrated that certain logarithmic functions are eigenfunctions of integral operators with M-Wright kernels using Buschman's theorem for the Laplace transform. Connections between Mittag-Leffler functions and these logarithmic functions are also established through various identities.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2021)
Article
Mathematics
Lev B. B. Klebanov, Yulia V. V. Kuvaeva-Gudoshnikova, Svetlozar T. T. Rachev
Summary: This paragraph provides two examples of heavy-tailed distributions in social sciences applications, including the laws of Pareto and Lotka and some new ones. The examples are illustrated through the construction of suitable toy models.
Article
Plant Sciences
Benedikt Schrofner-Brunner, James G. Hagan, Laura Cappelatti, Jesper Hassellov, Merle Wissmann, Lars Gamfeldt
Summary: The spatial insurance hypothesis posits that biodiversity increases ecosystem functioning in landscapes with environmental variability, assuming that species maintain high functioning only in places where they dominate. We tested this prediction in a marine macroalgae system and found limited responses to transplanting species, suggesting that spatial insurance may play a minor role in sustaining landscape ecosystem functioning.
JOURNAL OF ECOLOGY
(2023)
Review
Ecology
Renata M. Diaz, Hao Ye, S. K. Morgan Ernest
Summary: Exploring and accounting for emergent properties of ecosystems as complex systems is a promising horizon in understanding common ecological patterns. While the ubiquitous hollow-curve form of species abundance distribution may arise as a statistical phenomenon, deviations between empirical distributions and statistical baselines can reflect biological processes and offer new avenues for advancing ecological theory. Empirical abundance distributions are often uneven and dominated by rare species, demonstrating the potential of leveraging complexity to understand ecological processes, but limitations may arise in studying small communities due to poorly resolved statistical baselines.
Article
Mathematics, Applied
Trinh Tuan
Summary: The paper introduces the concept of polyconvolution for Fourier-cosine and Laplace integral operators and explores its applications. It investigates the structure of this polyconvolution operator and associated integral transforms. The paper establishes necessary and sufficient conditions for the operator to be an isometric isomorphism and provides its inverse in the conjugate symmetric form. It also shows the correlation between the existence of polyconvolution and weighted spaces, and obtains Young's type theorem and norm inequalities in weighted space. Additionally, the paper investigates the solvability of certain integral equations with the help of factorization identities of polyconvolution and provides illustrative examples of the obtained results.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Business, Finance
Florian Gerth, Grigory Temnov
Summary: This research analyzes the effects of recently introduced macroprudential policies on the financial stability of the Irish economy. The study found that borrowing limits improve financial stability risks for First Time Buyers, but actually worsen financial stability for Second Subsequent Buyers, challenging the one size fits all approach of policy makers in Ireland.
INTERNATIONAL REVIEW OF ECONOMICS & FINANCE
(2021)
Article
Statistics & Probability
Hansjoerg Albrecher, Martin Bladt, Mogens Bladt
Summary: This study extends the construction principle of multivariate phase-type distributions to establish a class of heavy-tailed multivariate random variables with Marginal distributions of Mittag-Leffler type. These distributions are shown to be dense among all multivariate positive random variables, making them versatile candidates for modeling tail-independent risks in various fields.
ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS
(2021)
Article
Mathematics, Interdisciplinary Applications
Evangelos Bakalis, Francesca Lugli, Francesco Zerbetto
Summary: White noise, with flat power spectral density and delta-correlated autocorrelation, can be transformed into colored noise through operator manipulation in either time or frequency domain. This study investigates whether any white noise properties remain in colored noises generated by operators and provides evidence to infer the mother process from which a colored noise originated. The study demonstrates kurtosis and codifference as two indices that categorize colored noises based on their mother processes, such as Gaussian, Laplace, Cauchy, and Uniform white noise distributions. The results show that different mother processes determine the kurtosis values of colored noises, while codifference function remains constant around the corresponding white noise value.
FRACTAL AND FRACTIONAL
(2023)
Article
Genetics & Heredity
Carolina A. Martinez-Gutierrez, Frank O. Aylward
Summary: The evolutionary forces determining genome size in bacteria and archaea have been debated for decades. This study suggests that there is a strong phylogenetic signal in genome size distributions at broad phylogenetic scales, despite the ability of bacteria and archaea to exchange genes rapidly.
Article
Statistics & Probability
Pierre Druilhet, Erwan Saint Loubert Bie
Summary: In this paper, the comparison between improper distributions and diffuse FAPs as limits of proper distribution sequences is discussed. Improper distributions characterize the behavior of the sequence inside the domain, while diffuse FAPs characterize how the mass concentrates on the boundary of the domain. Therefore, a diffuse FAP cannot be seen as the counterpart of an improper distribution.
ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS
(2021)
Article
Statistics & Probability
A. M. Mathai, Nicy Sebastian
Summary: This paper discusses the distribution of covariance structures in real-world scalar/vector/matrix variables, using bilinear forms and Laplace transforms or moment generating functions. The results show that the density function can be expressed as a linear function of double gamma densities or double exponential or Laplace densities when alpha is a positive integer, and in terms of double Mittag-Leffler functions or double confluent hypergeometric functions for the general value of alpha.
COMMUNICATIONS IN STATISTICS-THEORY AND METHODS
(2023)
Article
Acoustics
Rohit Singla, Ricky Hu, Cailin Ringstrom, Victoria Lessoway, Janice Reid, Christopher Nguan, Robert Rohling
Summary: Modelling ultrasound speckle to characterise tissue properties has generated interest, particularly for investigating dysfunction in transplanted kidneys. It is unclear which statistical distribution best characterises such speckle or how these distributions vary by patient variables. This study aims to investigate these questions.
ULTRASOUND IN MEDICINE AND BIOLOGY
(2023)
Article
Mathematics, Applied
Feng Qi
Summary: In this paper, the author investigates the complete monotonicity or monotonicity of two functions defined by the derivatives of a function involving the trigamma function. The conditions for these functions to be completely monotonic or monotonic are obtained using the convolution theorem for Laplace transforms, the monotonicity and logarithmic concavity of a function involving exponential function, and analytic techniques.
TWMS JOURNAL OF PURE AND APPLIED MATHEMATICS
(2022)
