We calculate some infinite sums containing the digamma function in closed form. These sums are related either to the incomplete beta function or to the Bessel functions. The calculations yield interesting new results as by-products, such as parameter...
We derive new reduction formulas for the incomplete beta function
Herein, we calculate reduction formulas for some generalized hypergeometric functions
Generalization of the ordinary hyperbolic functions called hyperbolic Ateb-functions is considered. They are the inverse of incomplete Beta-function. These functions are solutions of differential equations, which describe the aperiodic vibration moti...
Asymmetric functional-order (variable-order) fractional diffusion–wave equations (FO-FDWEs) introduce considerable computational challenges, as the fractional order of the derivatives can vary spatially or temporally. To overcome these challeng...
This paper presents an improved swarming algorithm that enhances low-illumination images. The algorithm combines a hybrid Harris Eagle algorithm with double gamma (IHHO-BIGA) and incomplete beta (IHHO-NBeta) functions. This paper integrates the conce...
Enhancement is a crucial step in the field of image processing, as it significantly improves image analysis and understanding. One of the most commonly used methods for image contrast enhancement is the incomplete beta function (IBF). However, the ke...
In this article, we consider a unified generalized version of extended Euler’s Beta function’s integral form a involving Macdonald function in the kernel. Moreover, we establish functional upper and lower bounds for this extended Beta fun...
We systematically exploit a new generalized hypergeometric identity to obtain new hypergeometric summation formulas. As a consistency test, alternative proofs for some special cases are also provided. As a byproduct, new summation formulas with finit...
In this article, a new four-parameter lifetime model called the beta generalized inverse Rayleigh distribution (BGIRD) is defined and studied. Mixture representation of this model is derived. Curve’s behavior of probability density function, reliabil...
This manuscript concerns two definite integrals that could be connected to the Bose-Einstein and the Fermi-Dirac functions in the integrands, separately, with numerators slightly modified with a difference in two expressions that contain the Fourier...
This paper studies a two-dimensional P-wave model in a fractal-continuum setting, where the classical Laplacian is replaced by the Hausdorff Laplacian. Using a Galerkin finite-element formulation on the reference triangle, we derive exact element-lev...
Very recently, the incomplete Pochhammer ratios were defined in terms of the incomplete beta function
Nor1, the third member of the Nr4a subfamily of nuclear receptor, is garnering increased interest in view of its role in the regulation of glucose homeostasis. Our previous study highlighted a proapoptotic role of Nor1 in pancreatic beta cells and sh...
Background: Since the most well-known function of thyroid hormone receptors (TRs) relies on their ability to act as ligand-activated transcription factors, their subcellular localization has been recognized to be relevant for their biological meaning...
In this paper, we introduce a new continuous probability distribution with five parameters called the modified beta Gompertz distribution. It is derived from the modified beta generator proposed by Nadarajah, Teimouri and Shih (2014) and the Gompertz...
Traditional path planning is mainly utilized for path planning in discrete action space, which results in incomplete ship navigation power propulsion strategies during the path search process. Moreover, reinforcement learning experiences low success...
The determination of the distributions of the eigenvalues associated with matrix-variate gamma and beta random variables of either type proves to be a challenging problem. Several of the approaches utilized so far yield unwieldy representations that,...
The Carlson–Shaffer operator plays an important role in the geometric theory of analytic functions. It is associated with the hypergeometric function and the incomplete beta function. The Carlson–Shaffer operator generalizes various other...
In this paper, the modeling of the liberation of scheelite is presented. A pattern of concentration experiments was performed to investigate the scheelite liberation and distribution density calculation procedure. In this work, one sample from a Mitt...
In this paper, the very fundamental geometrical characteristics of the Mylar balloon like the profile curve, height, volume, arclength, surface area, crimping factor, etc. are recognized as geometrical moments
In this article, a structural modification of the Kumaraswamy distribution yields a new two-parameter distribution defined on
In this paper, algorithms for calculating different types of generalized trigonometric and hyperbolic functions are developed and presented. The main attention is focused on the Ateb-functions, which are the inverse functions to incomplete Beta-funct...
Skeletal muscle mitochondrial dysfunction, evidenced by incomplete beta oxidation and accumulation of fatty acid intermediates in the form of long and medium chain acylcarnitines, may contribute to ectopic lipid deposition and insulin resistance duri...
Bounded continuous data arise in many areas of applied probability and statistics, particularly when the underlying variable is restricted to a finite interval and the density is expected to vanish at the endpoints. This paper studies a parsimonious...
In this paper, we solve Riccati equations by using the fractional-order hybrid function of block-pulse functions and Bernoulli polynomials (FOHBPB), obtained by replacing x with
In multiple sclerosis (MS) patients with a progressive form of the disease, spinal cord (SC) functions slowly deteriorate beyond age 40. We previously showed that in the SC of these patients, large areas of incomplete demyelination extend distance aw...
In rats, the time of birth is characterized by a transient rise in beta cell replication, as well as beta cell neogenesis and the functional maturation of the endocrine pancreas. However, the knowledge of the gene expression during this period of bet...
Background: Heterozygous, large-scale deletions at 14q24.3-31.1 affecting the neurexin-3 gene have been associated with neurodevelopmental disorders such as autism. Both “de novo” occurrences and inheritance from a healthy parent suggest...
In this study, we propose a new flexible two-parameter continuous distribution with support on the unit interval. It can be identified as a special member of the so-called type I half-logistic-G family of distributions, defined with the Topp–Le...
Background: Spinal cord injury (SCI) frequently leads to pain, leading to significant disability. Pain sensitization, a key feature of SCI, is commonly assessed via quantitative sensory testing like the Pressure Pain Threshold (PPT), though the facto...
Sarcopenia is an age-related condition characterized by a decline in skeletal muscle mass and function, leading to impaired mobility and an increased risk of adverse health outcomes. However, the neuromuscular mechanisms underlying gait dysfunction i...
In this article, we intend to introduce and study a new two-parameter distribution as a new extension of the power Topp–Leone (PTL) distribution called the Kavya–Manoharan PTL (KMPTL) distribution. Several mathematical and statistical fea...
The β-site Amyloid precursor protein Cleaving Enzyme 1 (BACE1) is an extensively studied therapeutic target for Alzheimer’s disease (AD), owing to its role in the production of neurotoxic amyloid beta (Aβ) peptides. However, despite n...
Given the high prevalence of cutaneous genus beta human papillomavirus (β-HPV) infections, it is important to understand how they manipulate their host cells. This is particularly true for cellular responses to UV damage, since our skin is conti...
We consider a lossy transmission line with a nonlinear voltage–charge relation. We derive an equation for a traveling front with the charge approaching constant asymptotic values on both sides of the front and solve the inverse problem for this...
The unit-Rayleigh distribution is a one-parameter distribution with support on the unit interval. It is defined as the so-called unit-Weibull distribution with a shape parameter equal to two. As a particular case among others, it seems that it has no...
Regulatory B cells (Bregs) participate in auto-tolerance maintenance and immune homeostasis. Despite their impact on many diseases and due to the difficulty to define them, knowledge about their origin and their physiological inducers is still unclea...
Interferon Regulatory Factors (IRFs) are critical modulators of immune and inflammatory responses, yet their roles in Alzheimer’s disease (AD) and other neurodegenerative disorders remain incompletely understood. While IRFs are recognized for t...
Alzheimer’s disease (AD) is a neurodegenerative disease impacting over 6 million Americans, with cases projected to increase to over 14 million by 2060. The AD pathology leads to difficulty completing everyday tasks or conversations, and ultima...
The quantitative description of growth rings is yet incomplete, including the functional division into earlywood and latewood. Methods developed to date, such as the Mork criterion for conifers, can be biased and arbitrary depending on species and gr...
Background/Objectives: Developing and implementing clinical trials for rare diseases is complicated by the incomplete understanding of the varied genotype and subsequent phenotypic differences of a condition, particularly when low numbers of subjects...
Gut microbiota dysbiosis is implicated in metabolic disorders, yet taxonomic and functional alterations in canine diabetes remain incompletely defined. Here, we performed shotgun metagenomic sequencing of fecal samples from 38 diabetic dogs and 37 he...
Cirrhotic cardiomyopathy is a syndrome of blunted cardiac systolic and diastolic function in patients with cirrhosis. However, the mechanisms remain incompletely known. Since contractility and relaxation depend on cardiomyocyte calcium transients, an...
Cellular responses to DNA damage and other stresses are important determinants of mutagenesis and impact the development of a wide range of human diseases. TP53 is highly mutated in human cancers and plays an essential role in stress responses and ce...
Background: In advanced Parkinson’s disease, the pedunculopontine nucleus region is thought to be abnormally inhibited by gamma-aminobutyric acid (GABA) ergic inputs from the over-active globus pallidus internus. Recent attempts to boost pedunc...
Porto-sinusoidal vascular disorder (PSVD) is an umbrella term proposed by the Vascular Liver Disease Interest Group (VALDIG) in 2019. It refers to a group of non-cirrhotic vascular liver diseases that cause portal hypertension. These were previously...
Dental caries is a prevalent global health issue characterized by the progressive demineralization of dental tissues, which occurs when the balance between demineralization and remineralization processes is disrupted at the tooth level. Silver diamin...
In this paper, a novel approximate triangular fuzzy finite element method (FEM) is proposed to solve the one-dimensional second-order unsteady nonlinear fuzzy partial differential Boussinesq equation. The physical problem concerns the case of the dro...
Poly(butylene adipate-co-terephthalate) (PBAT) is widely used in biodegradable agricultural mulch films, yet its degradation may remain incomplete under field conditions, leading to persistent residues in soil. To investigate microbial processes pote...
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