104 Results Found

Let X be a compact Riemann surface of genus $g\ge 2$ and $M\left(G_2\right)$ be the moduli space of polystable principal bundles over X, the structure group of which is the simple complex Lie group of exceptional type $G_2$. In this work, it is proved that the only aut...

Let X be a compact Riemann surface of genus $g\ge 2$, G be a complex semisimple Lie group, and ${\mathcal{M}}_G\left(X\right)$ be the moduli space of stable principal G-bundles. This paper studies the fixed point set of involutions on ${\mathcal{M}}_G\left(X\right)$ induced by an anti-holomorphic involu...

In this paper, the fixed points of involutions on the moduli space of principal $E_6$-bundles over a compact Riemann surface X are investigated. In particular, it is proved that the combined action of a representative $\sigma$ of the outer involution of...

We discuss the complex-analytic subsets of the moduli spaces of rank 2 vector bundles on a classical Hopf surface formed by irregular bundles. We stratify the set of irregular bundles by weight (and irregular profiles). We provide the topological res...

The number of planted trees per hectare influences individual volume growth, which in turn can affect wood properties. The objective of this study was to assess the effect of six different plantation spacings of jack pine (Pinus banksiana Lamb.) 25 y...

In this paper, we propose using quiver representations as a tool for understanding artificial neural network algorithms. Specifically, we construct these algorithms by utilizing the group algebra of a finite cyclic group as vertices and convolution t...

We find an application in quantum finite automata for the ideas and results of [JL21] and [JL22]. We reformulate quantum finite automata with multiple-time measurements using the algebraic notion of a near-ring. This gives a unified understanding tow...

In this paper, the solution to a spatially colored stochastic heat equation (SHE) is studied. This solution is a random function of time and space. For a fixed point in space, the resulting random function of time has exact, dimension-dependent, glob...

Our goal is to describe superconformal structures on super Riemann surfaces (SRSs) based on data assigned to a fatgraph. We start from the complex structures on punctured $(1|1)$-supermanifolds, characterizing the corresponding moduli and the deformati...

Quivers are oriented graphs that have profound connections to various areas of mathematics, including representation theory and geometry. Quiver representations correspond to a vast generalization of classical linear algebra problems. The geometry of...

In this paper, we mainly discuss the angle modulus of convexity ${\delta }_X^a\left(ϵ\right)$ and the angle modulus of smoothness ${\rho }_X^a\left(ϵ\right)$ in a real normed linear space X, which are closely related to the classical modulus of convexity ${\delta }_X\left(ϵ\right)$...

We propose a new method to compare between the essential skeleton of Berkovich analytification of $({\overline{\mathsf{M}}}_{0,n},{\overline{\mathsf{M}}}_{0,n}\setminus {\mathsf{M}}_{0,n})$ and faithful tropicalization of ${\mathsf{M}}_{0,n}$ over a complete discrete valued field. In particular, we proved the two combinat...

IN MEMORIAM OF ALEXANDER GROTHENDIECK. THE MAN.

We investigate spatial moduli of non-differentiability for the fourth-order linearized Kuramoto–Sivashinsky (L-KS) SPDEs and their gradient, driven by the space-time white noise in one-to-three dimensional spaces. We use the underlying explicit kerne...

The Swampland Program aims to address the question, “when does an effective field theory model of quantum gravity have an ultraviolet complete embedding in string theory?”, and can be regarded as a bottom-up approach for investigations of...

High order and fractional PDEs have become prominent in theory and in modeling many phenomena. In this paper, we study spatial moduli of non-differentiability for the fourth order time fractional stochastic partial integro-differential equations (SPI...

In this paper, we study ${\mathrm{Spin}}^{*}\left(8\right)$-Higgs bundles over compact Riemann surfaces, extending the work of Bradlow, García-Prada, and Gothen on ${\mathrm{SO}}^{*}\left(8\right)$. The group ${\mathrm{Spin}}^{*}\left(8\right)$ is exceptional among classical real forms, as its complexification $\mathrm{Spin}(8,\mathbb{C})$ ad...

Woven composites and natural fiber-reinforced composites both have widespread applications in various industries due to their appealing load-carrying capacity and performance compared to conventionally manufactured composites, such as polymeric compo...

Let $\mathcal{M}(Spin(8,\mathbb{C}\left)\right)$ be the moduli space of $Spin(8,\mathbb{C})$-Higgs bundles over a compact Riemann surface X of genus $g\ge 2$. This admits a system called the Hitchin integrable system, induced by the Hitchin map, the fibers of which are Prym varieties. Moreover,...

In the first part of this paper, we give generalizations of the Fekete–Szegö inequalities for quasiconvex mappings F of type B and the first elements F of g-Loewner chains on the unit ball of a complex Banach space, recently obtained by H....

We consider the twistor descriptions of harmonic maps of the Riemann sphere into Kähler manifolds and Yang–Mills fields on four-dimensional Euclidean space. The motivation to study twistor interpretations of these objects comes from the harmonic sphe...

Mirror symmetry was first observed in worldsheet string constructions, and was shown to have profound implications in the Effective Field Theory (EFT) limit of string compactifications, and for the properties of Calabi–Yau manifolds. It opened...

We address the reasons why the “Wick-rotated”, positive-definite, space-time metric obeys the Pythagorean theorem. An answer is proposed based on the convexity and smoothness properties of the functional spaces purporting to provide the kinematic fra...

(1) Significance of geometry for bio-inspired hygroscopically actuated bilayer structures is well studied and can be used to fine-tune curvatures in many existent material systems. We developed a material design space to find new material combination...

Numerous experimental and theoretical studies undertaken to determine the effective stress coefficient for seismic velocities in rocks stem from the importance of this geomechanical parameter both for monitoring changes in rock saturation and pore pr...

We review Poisson–Lie groups and their applications in gauge theory and integrable systems from a mathematical physics perspective. We also comment on recent results and developments and their applications. In particular, we discuss the role of quasi...

Fractional and high-order PDEs have become prominent in theory and in the modeling of many phenomena. In this article, we study the temporal fractal nature for fourth-order time-fractional stochastic partial integro-differential equations (TFSPIDEs)...

Porous titanium (Ti) offers several key attributes as a biomedical material. Among the known characteristics of Ti relevant to biomedical applications, the mechanical performance and effects of a pore structure on the deformation characteristics unde...

There is a family of vector bundles over the moduli space of stable curves that, while first appearing in theoretical physics, has been an active topic of study for algebraic geometers since the 1990s. By computing the rank of the exceptional Lie alg...

In this paper, we construct two deformations of the Godeaux surface with ${\pi }_1\cong {\mathbb{Z}}_4$, such that each central fibre contains a family of conics. We show that surfaces that are birational to these Godeaux surfaces exist in two connected components of...

We review that in no-scale models in perturbative string theory, flat, homogeneous and isotropic cosmological evolutions found at the quantum level can enter into “quantum no-scale regimes” (QNSRs). When this is the case, the quantum effe...

The purpose of the article is to highlight the role of binomial polynomials in the construction of classes of positive linear approximation sequences on Banach spaces. Our results aim to introduce and study an integral extension in Kantorovich sense...

Mechanical stress governs the dynamics of viscoelastic polymer systems and supercooled glass-forming fluids. It was recently established that liquids with long terminal relaxation times are characterized by transiently frozen stress fields, which, mo...

Let $U=U(t,x)$ for $(t,x)\in {\mathbb{R}}_{+}\times {\mathbb{R}}^d$ and ${\partial }_{x}U={\partial }_{x}U(t,x)$ for $(t,x)\in {\mathbb{R}}_{+}\times \mathbb{R}$ be the solution and gradient solution of the fourth order linearized Kuramoto–Sivashinsky (L-KS) SPDE driven by the space-time white noise in one-to-three dimensional spaces, respectively....

Suffusion erosion may occur in sandy gravel dam foundations that use suspended cutoff walls. This erosion causes a loss of fine particles, degrades the soil strength and deformation moduli, and adversely impacts the cutoff walls of the dam foundation...

In this paper, we study asymptotic bounds on the m-th derivatives of general algebraic polynomials in weighted Bergman spaces. We consider regions in the complex plane defined by bounded, piecewise, asymptotically conformal curves with strictly posit...

The review is devoted to exact solutions with hidden symmetries arising in a multidimensional gravitational model containing scalar fields and antisymmetric forms. These solutions are defined on a manifold of the form M = M₀ x M₁ x . . . x M_n , where...

In this paper, zero modes of fluctuation are dissected around the two species of BPS vortices existing in the critical Higgs phase, where the scalar and vector meson masses are equal, of a gauged $\mathbb{U}\left(1\right)$ nonlinear ${\mathbb{CP}}^1$ -model. If $2$...

Mock modular forms, first invented by Ramanujan, provide a beautiful generalization of the usual modular forms. In recent years, it was found that they capture the generating functions of the number of microstates of BPS black holes appearing in comp...

The IDEAL IMPLANT^® Structured Breast Implant is a dual lumen saline-filled implant with capsular contracture and deflation/rupture rates much lower than single-lumen silicone gel-filled implants. To better understand the implant’s mechanica...

Textile-reinforced concrete (TRC) has many advantages, including corrosion resistance, but TRC is a novel composite material and there is limited experimental research on the flexural behavior of TRC members. This paper aims to experimentally evaluat...

With the advancement of the construction of urban underground spaces, it is inevitable that new tunnels will pass through existing pipelines. To ensure the safety and stability of these pipelines, it is essential to strictly control the impact of shi...

The impact of contact between two elastic–plastic bodies is highly complex, with no established theoretical contact model currently available. This study investigates the problem of an elastic–plastic sphere impacting an elastic–pla...

The contribution of this article is quadruple. It (1) unifies various schemes of premodels/models including situations such as presheaves/sheaves, sheaves/flabby sheaves, prespectra/ $\Omega$ -spectra, simplicial topological spaces/(complete) Segal spac...

Sodium hydroxide was used as a base catalyst to reduce the flammability of poly(vinyl alcohol) (PVA) aerogels. The base-modified aerogels exhibited significantly enhanced compressive moduli, likely resulting in decreased gallery spacing and increased...

The synergistic preparation of geopolymer from lithium slag, fly ash, and slag for underground construction can facilitate the extensive recycling of lithium slag. The effects of different activator moduli and water–binder ratios on the mechani...

The influence of carbon black (CB) structure and surface area on key rubber properties such as monotonic stress-strain, cyclic stress–strain, and dynamic mechanical behaviors are investigated in this paper. Natural rubber compounds containing e...

A reproducing kernel Hilbert space (RKHS) approximation problem arising from learning theory is investigated. Some K-functionals and moduli of smoothness with respect to RKHSs are defined with Fourier–Bessel series and Fourier–Bessel tran...

The microscopic origin of the de Sitter entropy remains a central puzzle in quantum gravity that is related to the cosmological constant problem. Within the paradigm of $\mathcal{H}$olographic $\mathcal{N}$aturalness, we propose that this entropy is carried by a vast number...

Polymerizable microspheres are introduced into acrylamide to prepare the high mechanical strength hydrogels with a novel three-dimensional pore structure. Rheological properties, compressive stress–strain, tensile property, and compression stre...