50 Results Found

Let F be the normalized Hecke-eigen cusp form for the full modular group and $\zeta (s,F)$ be the corresponding zeta-function. In the paper, the joint universality theorem on the approximation of a collection of analytic functions by shifts $(\zeta (s+i{h}_1\tau ,F),\dots ,\zeta$...

Let $\Gamma$ be a non-uniform lattice in $SL(2,\mathbb{R})$. In this paper, we study various $L^2$-norms of automorphic representations of $SL(2,\mathbb{R})$. We bound these norms with intrinsic norms defined on the representation. Comparison of these norms can help us unders...

Waddington envisioned stem cell differentiation as a marble rolling down a hill, passing through hierarchically branched valleys representing the cell’s temporal state. The terminal valleys at the bottom of the hill indicate the possible commit...

In optics, light rays emitted from a light source form a wavefront (orthotomic) upon reflection by a mirror. The mirror is referred to as an antiorthotomic of the orthotomic. The investigation of the relationship between orthotomics and antiorthotomi...

Background: Glioblastoma represents the most common primary brain tumor in adults. Despite technological advances, patients with this disease typically die within 1–2 years after diagnosis. In the search for novel therapeutics, drug repurposing...

This work takes up the task of the determination of the rate of pointwise and uniform convergences to the unit operator of the “normalized cusp neural network operators”. The cusp is a compact support activation function, which is the com...

This paper proposes a classification of all non-isomorphic anatomies of an orthogonal metamorphic manipulator according to the topology of workspace considering cusps and nodes. Using symbolic algebra, a general kinematics polynomial equation is form...

In this study, we examine sphere contact for a cuspidal edge–cusp pair $(X,B)$, where $X\subset {\mathbb{R}}^3$ is a cuspidal edge and $B\subset X$ is a distinguished curve whose germ at the singular point is a $(2,3)$-type cuspidal space curve. Let $f:({\mathbb{R}}^2,0)\to ({\mathbb{R}}^3,0)$...

The flow characteristics of a 30P30N three-element high-lift airfoil at low Reynolds numbers $\left[\mathrm{O}\left({10}^4\right)\right]$ are examined through three-dimensional simulations using a high-order spectral element method. This study primarily investigates the flow structures of...

In this study, we analyzed a large number of vertical sounding ionograms, obtained by the mid-latitude Cyclone ionosonde (55.85° N; 48.8° E) of Kazan (Volga Region) Federal University, which operates in a rapid-run mode of ionograms (1 ionogram per m...

In this paper, we study two-dimensional divisor problems of the Fourier coefficients of some automorphic product L-functions attached to the primitive holomorphic cusp form $f\left(z\right)$ with weight k for the full modular group $S{L}_2\left(\mathbb{Z}\right)$. Additionally, we establ...

The structure of the winter noon ionosphere of the southern hemisphere was studied. This structure includes the dayside cusp, associated high-latitude ionospheric trough (HLT), main ionospheric trough (MIT), electron density (Ne) peak at latitudes ab...

The Autobiography of Saint Marguerite-Marie Alacoque recounts her many visions, ecstasies, and sufferings as she became God’s messenger, initiating the highly successful modern form of devotion to the Sacred Heart. Reading the Autobiography tod...

In this paper, we consider the influence of a nonlinear contact rate caused by multiple contacts in classical SIR model. In this paper, we unversal unfolding a nilpotent cusp singularity in such systems through normal form theory, we reveal that the...

Background and Objectives: The aim of this study was to evaluate the correlation between the mandibular arch shape and the vertical skeletal pattern in growing patients. Materials and Methods: A total of 73 Caucasian patients (33 males and 40 females...

In this paper, we analyze planar parametric sextic curves to determine conditions for Pythagorean hodograph (PH) curves. By expressing the curves to be analyzed in the complex form, the analysis is conducted in algebraic form. Since sextic PH curves...

This study quantitatively approximates the unit operator using three types of multivariate, overactivated, and spiked convolution operators. The core of these operators is a multivariate “cusp” kernel, which acts as a novel, compact-suppo...

Thermal inflation was proposed as a mechanism to dilute the density of cosmological moduli. Thermal inflation is driven by a complex scalar field possessing a large vacuum expectation value and a very flat potential, called a “flaton”. Su...

The roll equation of a port–starboard symmetric ship is a clean physical realization of an order-two reflection (${\mathbb{Z}}_2$)-equivariant nonlinear oscillator: odd restoring and damping make the upright state a symmetric equilibrium whose two angles of...

In this paper, we consider the fractional ion sound and Langmuir waves (FISALWs) equation. We apply the unified solver technique in order to extract some new solutions for the FISALWs equation. The fractional derivative is defined in the sense of a c...

The expectation that the physical expansion of space occurs smoothly may be expressed mathematically as a requirement for continuity in the time derivative of the metric scale factor of the Friedmann–Robertson–Walker cosmology. We explore...

We apply a very simple procedure to construct non-singular cosmological models for flat Friedmann universes filled with minimally coupled scalar fields or by tachyon Born–Infeld-type fields. Remarkably, for the minimally coupled scalar field an...

We describe a series of parallel lenses with constant proportions packed in a circle. To construct n lenses, a regular 2(n + 1)-gon is drawn with a central diagonal of 2r length, followed by an array of n parallel diagonals perpendicular to the forme...

The effects of surface roughness, presence of nitrided diffusion regions, and magnetron sputtering of Cr₂N–6Ag thin films on the toughness of Cr–V ledeburitic Vanadis 6 die steel were investigated by using the flexural strength measuremen...

In this note, we propose a new construction of cyclotomic p-adic L-functions that are attached to classical modular cuspidal eigenforms. This allows for us to cover most known cases to date and provides a method which is amenable to generalizations t...

This article argues that animism in the Japanese context is more fruitfully understood as animation, a technique that imbues man-made things with life. Two forms of animation are at work in so-called animist beliefs: one is the docile animation of in...

Mesenchymal stem cells (MSCs) are on the cusp of regenerative medicine due to their differentiation capacity, favorable culture conditions, ability to be manipulated in vitro, and strong immunomodulatory activity. Recent studies indicate that the ple...

I review the connection between dynamics and the baryonic mass distribution in rotationally-supported galaxies. The enclosed dynamical mass-to-light ratio increases with decreasing galaxy luminosity and surface brightness. The correlation with surfac...

When catastrophe theory is applied to the experimental modeling of catastrophe phenomena, it is impossible to know in advance the corresponding relationship and mapping form between the parameters of the actual catastrophe mathematical model and the...

The present paper studies the fatigue delamination behaviour of an epoxy/carbon composite material under mode III loading using a longitudinal half fixed beam (LHFB) device initially designed for mode III static tests of composite materials formed by...

Mixtures of hydrogen with common hydrocarbon fuels are considered viable for reducing carbon footprint in modern industry, power production, and transportation. The addition of hydrogen alters the kinetics and thermophysical properties of the mixture...

Coherent neuronal activity is believed to underlie the transfer and processing of information in the brain. Coherent activity in the form of synchronous firing and oscillations has been measured in many brain regions and has been correlated with enha...

A type of specially designed pin model of Mg-Zn alloy was implanted into the full thickness of lesions of New Zealand rabbits’ femoral condyles. The recovery progress, outer surface healing and in vivo degradation were characterized by various method...

Among the aortic valve diseases, the bicuspid aortic valve (BAV) occurs when the aortic valve has two leaflets (cusps), rather than three, and represents the most common form of congenital cardiac malformation, affecting 1–2% of the population....

Featured observations of high frequency (HF) heating experiments are first introduced; the uniqueness of each observation is presented; the likely cause and physical process of each observed phenomenon instigated by the HF heating are discussed. A sp...

Let ${\mathbb{P}}_c\left(x\right)=\{p\le x|p,\left[p^c\right]\mathrm{are}\mathrm{primes}\},c\in {\mathbb{R}}^{+}\setminus \mathbb{N}$ and ${\lambda }_{sy{m}^{2}f}\left(n\right)$ be the n-th Fourier coefficient associated with the symmetric square L-function $L(s,sy{m}^{2}f)$. For any $A>0$, we prove that the mean value of ${\lambda }_{sy{m}^{2}f}\left(n\right)$ over ${\mathbb{P}}_c\left(x\right)$ is $\ll x{log}^{-A-2}x$ for almost all $c\in \left(\epsilon ,(\sqrt{5}+\right)$...

The world of energy is on the cusp of profound transformation. Hydrogen or hydrogen-containing fuel mixtures in the form of synthesis gas, as carriers of clean energy, will be in the short term among the most efficient solutions to pressing environme...

Background: Enamel knots and Hertwig epithelial root sheath (HERS) regulate the growth and folding of the dental epithelium, which subsequently determines the final form of tooth crown and roots. We would like to investigate the genetic etiology of s...

Background—Bicuspid aortic valve (BAV) disease is the most prevalent congenital heart disease in the world. Knowledge about its subtypes origin, development, and evolution is poor despite the frequency and the potential gravity of this conditio...

(1) Background: to propose a new approach for crown veneers, with the use of an aesthetic porcelain coating, only in part of the zirconia infrastructure, and to analyze its biomechanical behavior to minimize chipping failures. (2) Methods: a maxillar...

Understanding how geometry governs interfacial contact and material removal is central to designing efficient bioinspired surface systems. Gastropod radular teeth form natural arrays of microscale cutting elements optimized for repeated interaction w...

Aortic root aneurysms are a heterogeneous form of thoracic aortic disease in which wall pathology, root geometry, valve function, and patient phenotype jointly determine clinical risk and surgical strategy. PubMed/MEDLINE was searched for publication...

The closedness of solution trajectories around singular points is a central question in the qualitative analysis of nonlinear oscillators, but it is rarely established rigorously when the restoring force has a finite-distance singularity. This work a...

Ocean circulation plays an important role in the formation and occurrence of extreme climate events. The study shows that the periodic variation of ocean circulation under strong wind stress is closely related to climate oscillation. Ocean circulatio...

Background: Different methods are established for the changes in aortic valve stenosis with cardiac computed tomography angiography (CCTA), but the effect of the grade of stenosis on contrast densities around the valve has not been investigated. Aims...

In the recent years a considerable effort has been devoted to foster the understanding of the basic mechanisms underlying the dynamical arrest that is involved in glass forming in supercooled liquids and in the sol-gel transition. The elucidation of...

Dwarf galaxies, although intrinsically faint and containing only modest stellar populations, provide an unusually sensitive testing ground for understanding how structure emerges in a cosmological context. Their shallow gravitational potentials make...

Sparse matrix-vector (SpMV) multiplication is a vital building block for numerous scientific and engineering applications. This paper proposes SURAA (translates to speed in arabic), a novel method for SpMV computations on graphics processing units (G...

Promoting technological innovation in the natural gas industry is a feasible means of achieving energy transition. Guided by the geographic innovation theory, this article carries out research on the scale, technical fields, capabilities, and influen...

Background and Objectives: The long face type is associated with excessive vertical facial growth and most often with anterior open bite. In many cases of anterior open bite of high severity associated with bimaxillary dento-alveolar protrusion, lips...