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Moduli Space of Vector Bundles
In this chapter, we recall Mumford’s construction of a moduli space of semistable holomorphic vector bundles over Riemann surfaces by using geometric...
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Symmetry of the B-J Orthogonality
While working with the usual orthogonality relation in Hilbert spaces, little do we realize that the symmetry of the orthogonality is a precious...
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Virasoro constraints for moduli of sheaves and vertex algebras
In enumerative geometry, Virasoro constraints were first conjectured in Gromov-Witten theory with many new recent developments in the sheaf theoretic...
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Implementation of Numerical Experiments
The last chapter is dedicated to the numerical experiments to verify our theoretical results obtained in this monograph, particularly in Chaps....
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On Extension of the Markov Chain Approximation Method for Computing Feynman–Kac Type Expectations
An efficient discrete time and space Markov chain approximation employing a Brownian bridge correction for computing curvilinear boundary crossing...
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Overconvergent Eichler-Shimura isomorphisms for unitary Shimura curves over totally real fields
We compare two different cohomology groups on unitary Shimura curves over totally real number fields; these groups are used in the construction of p -a...
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A High-Order Velocity-Based Discontinuous Galerkin Scheme for the Shallow Water Equations: Local Conservation, Entropy Stability, Well-Balanced Property, and Positivity Preservation
The nonlinear shallow water equations (SWEs) are widely used to model the unsteady water flows in rivers and coastal areas. In this work, we present...
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A Third Order Exponential Time Differencing Numerical Scheme for No-Slope-Selection Epitaxial Thin Film Model with Energy Stability
In this paper we propose and analyze a (temporally) third order accurate exponential time differencing (ETD) numerical scheme for the...
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A property of meets in slim semimodular lattices and its application to retracts
Slim semimodular lattices were introduced by G. Grätzer and E. Knapp in 2007, and they have intensively been studied since then. These lattices can...
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Study of Fuzzy Fractional Caputo Order Approach to Diabetes Model
An understanding of the mathematical explanation of different global environmental challenges is the current mathematical model. The modeling of...
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Statistical inference in the partial functional linear expectile regression model
As extensions of means, expectiles embrace all the distribution information of a random variable. The expectile regression is computationally...
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Numerical Modeling of Heat Diffusion
This chapter contains all the necessary information to determine the desired approximated solutions. Firstly, the numerical discretization...
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Formal Factorization of Higher Order Irregular Linear Differential Operators
We study the problem of formal decomposition (non-commutative factorization) of linear ordinary differential operators over the field
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Gevrey Formal Power Series
As it is already the case when working with ordinary differential equations, it appears soon that the Poincaré asymptotics is not sufficient to study...
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Toral Diffeomorphisms Induce Quantum Superoperators via TAQS
We propose a new method for adapting (perturbing) models of quantum observables. The method is dubbed TAQS as it is based on toral automorphisms...
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An Exactly Curl-Free Staggered Semi-Implicit Finite Volume Scheme for a First Order Hyperbolic Model of Viscous Two-Phase Flows with Surface Tension
In this paper, we present a pressure-based semi-implicit numerical scheme for a first order hyperbolic formulation of compressible two-phase flow...
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Parameter Sensitivity for Wave-Breaking Closures in Boussinesq-Type Models
We consider the issue of wave-breaking closure for the well-known Green–Naghdi model and attempt at providing some more understanding of the...
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An Operator Version of the Jensen Inequality for s-Convex Functions
The objective of this paper is to reveal an operator version of the Jensen inequality and its reverse one for s -convex functions and self-adjoint...
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A journey through the mathematical world of Karen Uhlenbeck
In this article we discuss some of Karen Uhlenbeck’s most prominent mathematical results. Uhlenbeck’s publications range across many mathematical...