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We consider the problem of creating locally supersymmetric theories in signature (10,2). The most natural algebraic starting point is the F-algebra, which is the de Sitter-type (10,2) extension of the super-Poincare algebra. We derive the…
A manifestly N=2 supersymmetric completion of the four-dimensional Nambu-Goto-Born-Infeld action, which is self-dual with respect to electric-magnetic duality, is constructed in terms of the abelian N=2 superfield strength W in the…
We associate a $C^*$-algebra to a partial action of the integers acting on the base space of a vector bundle, using the framework of Cuntz--Pimsner algebras. We investigate the structure of the fixed point algebra under the canonical gauge…
A Weyl structure is a bundle over space-time, whose fiber at each space-time point is a space of maximally isotropic complex tangent planes. We develop the theory of Weyl connections for Weyl structures and show that the requirement that…
We present a model for introducing dynamics into a space-time geometry. This space-time structure is constructed from a C*-algebra defined in terms of the generators of an irreducible unitary representation of a finite-dimensional Lie…
The use in the action integral of a volume element of the form $\Phi d^{D}x$, where $\Phi$ is a metric-independent measure density, can yield new interesting results in all types of known generally coordinate-invariant theories: (1) 4-D…
New algebraic structure on electronic Fock space is studied in detail. This structure is defined in terms of a certain multiplication of many electron wave functions and has close interrelation with coupled cluster and similar approaches.…
D-string action is constructed from IIB matrices, a spacetime commutator is essential in this construction. This hints at the central role of the spacetime uncertainty relation in a unified formulation of strings. Vertex operators of…
A novel mathematical model for fiber-reinforced materials is proposed. It is based on a 1-dimensional beam model for the thin fiber structures, a flexible and general 3-dimensional elasticity model for the matrix and an overlapping domain…
In a space-time $M$ with a Killing vector field $\xi^a$ which is either everywhere timelike or everywhere spacelike, the collection of all trajectories of $\xi^a$ gives a 3-dimension space $S$. Besides the symmetry-reduced action from that…
We address the problem of action detection in videos. Driven by the latest progress in object detection from 2D images, we build action models using rich feature hierarchies derived from shape and kinematic cues. We incorporate appearance…
For a fibration with the fiber $K(\pi,n)$-space, the algebraic model as a twisted tensor product of chains of the base with standard chains of $K(\pi,n)$-complex is given which preserves multiplicative structure as well. In terms of this…
In this paper, we analyze and provide numerical illustrations for a moving finite element method applied to convection-dominated, time-dependent partial differential equations. We follow a method of lines approach and utilize an underlying…
Linear algebra's main concerns are sets of vectors, linear functions, subspaces, linear systems, matrices and concepts about those, such as whether the solution of linear system exists or is unique; a set of vectors is linearly independent…
We consider a general fibre of given length in a generic projection of a va- riety. Under the assumption that the fibre is of local embedding dimension 2 or less, an assumption which can be checked in many cases, we prove that the fibre is…
Around 1920, Kaluza and Klein had the idea to add a fifth dimension to the classical 4-dimensional spacetime of general relativity to create a geometric theory of gravitation and electromagnetism. Today, theoretical evidences, like string…
A finite element simulation of the mechanical behaviour of woven textile materials at the scale of individual fibers is proposed in this paper. The aim of the simulation is to understand and identify phenomena involved at different scales…
We show that singular Riemannian foliations, or, more generally, manifold submetries, defined on a compact normal homogeneous space, have algebraic nature. Moreover, in this case there exists a one-to-one correspondence between algebras of…
We propose a unified theoretical framework, Measurement-Induced Temporal Geometry (MTG), in which time, causality, and spacetime geometry emerge from quantum measurement acting on a fiber-valued internal time field. Each spacetime point…
The Invariant Subset Problem on the Hilbert space is to know whether there exists a bounded linear operator $T$ on a separable infinite-dimensional Hilbert space $H$ such that the orbit $\{T^{n}x;\ n\ge 0\}$ of every non-zero vector $x\in…