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On Certain Algebraic Structures Associated with Lie (Super)Algebras
In this paper we exhibit a survey of constructions of Lie (super)algebras associated with certain triple systems, several examples and a historical...
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On BV supermanifolds and the super Atiyah class
We study global and local geometry of forms on odd symplectic BV supermanifolds, constructed from the total space of the bundle of 1-forms on a base...
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Cohomology in Algebraic Geometry
We shall now look more closely at how cohomology is used in algebraic geometry. This will include exploring additional structure present on the...
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A super-localized generalized finite element method
This paper presents a novel multi-scale method for elliptic partial differential equations with arbitrarily rough coefficients. In the spirit of...
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On the Symmetry Reduction of the (1+3)-Dimensional Inhomogeneous Monge–Ampère Equation to Algebraic Equations
We perform the procedure of symmetry reduction of (1+3)-dimensional inhomogeneous Monge–Ampère equation to algebraic equations. Some results obtained...
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Algebra, Geometry and Topology of ERK Kinetics
The MEK/ERK signalling pathway is involved in cell division, cell specialisation, survival and cell death (Shaul and Seger in Biochim Biophys Acta...
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Geometry on the Finite Time Collapsing for Continuity Method
This paper is concerned about a class of finite time collapsing along continuity method over a compact Kähler manifold. It is shown that along the...
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Stokes, Gibbs, and Volume Computation of Semi-Algebraic Sets
We consider the problem of computing the Lebesgue volume of compact basic semi-algebraic sets. In full generality, it can be approximated as closely...
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Super-localization of spatial network models
Spatial network models are used as a simplified discrete representation in a wide range of applications, e.g., flow in blood vessels, elasticity of...
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Counting intrinsic Diophantine approximations in simple algebraic groups
We establish an explicit asymptotic formula for the number of rational solutions of intrinsic Diophantine inequalities on simply-connected simple...
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Towards Massively Parallel Computations in Algebraic Geometry
Introducing parallelism and exploring its use is still a fundamental challenge for the computer algebra community. In high-performance numerical...
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Noncommutative Geometry of Random Surfaces
AbstractWe associate a noncommutative curve to a periodic, bipartite, planar dimer model with polygonal boundary. It determines the inverse...
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On super Plücker embedding and cluster algebras
We define a super analog of the classical Plücker embedding of the Grassmannian into a projective space. One of the difficulties of the problem is...
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Hofer geometry via toric degeneration
The main theme of this paper is to use toric degeneration to study Hofer geometry by producing distinct homogeneous quasimorphisms on the group of...
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A Universal Algebraic Set Theory Built on Mereology with Applications
Category theory is often treated as an algebraic foundation for mathematics, and the widely known algebraization of ZF set theory in terms of this...
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Non-boundedness of the number of super level domains of eigenfunctions
Generalizing Courant’s nodal domain theorem, the “Extended Courant property” is the statement that a linear combination of the first n eigenfunctions...
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Quantization of Geometry
The low energy effective behavior of \(\mathcal {N} = 2\)...