Nowadays the tenor of reports on applications of digital photogrammetric procedures consists of a unison message: processing modules of automatic image orientation are available in digital photogrammetric systems and with them the productivity is much higher than with all existing conventional photogrammetric plotters. In fact, interior and relative orientation procedures as well as automated a...

the contraposition (musāmita) argument is among the arguments for proving the finitude of dimensions that has received attention in discussing physics and has yielded some philosophical consequences. contraposition argument is based on the two concepts of motion and contraposition, and by proving the impossibility of the motion of circle in case of the infinitude of dimensions, it deals with th...

Given a digraph G = (V,E) with the set of vertices V and the set of edges E, let d : F → Ω be the exterior derivative map from the space of complex-valued functions on V to the complex vector space spanned by E. We introduce the Laplacian ∆ : F → F and the label difference map d̂ : F → (Ω1)∗ of F into the dual space (Ω1)∗ of Ω and establish their connections with d. In particular, we prove that,...

Spatial relations is a key component of Geographical information science (GIS). Efforts have been made on formal definition of spatial relations and the 9-intersection model developed by Egenhofer and his collaborators is the most popular framework for the topological spatial relations. In that model, the topological relationships between two simple spatial entities A and B is transformed into ...

Magnetic edge states are responsible for various phenomena of magneto-transport. Their importance is due to the fact that, unlike the bulk of the eigenstates in a magnetic system, they carry electric current along the boundary of a confined domain. Edge states can exist both as interior (quantum dot) and exterior (anti-dot) states. In the present report we develop a consistent and practical spe...

This paper will prove the generalized Stokes Theorem over kdimensional manifolds. We will begin from the definition of a k-dimensional manifold as well as introduce the notion of boundaries of manifolds. Using these, we will construct the necessary machinery, namely tensors, wedge products, differential forms, exterior derivatives, and integrals over manifolds, in order to prove the main result...

We discuss the algebraic way of solving the descent equations corresponding to the BRST consistency condition for the gauge anomalies and the Chern–Simons terms on a nontrivial bundle. The method of decomposing the exterior derivative as a BRST commutator is extended to the present case.

We show how the high order finite element spaces of differential forms due to Raviart-Thomas-Nédelec-Hiptmair fit into the framework of finite element systems, in an elaboration of the finite element exterior calculus of Arnold-Falk-Winther. Based on observations by Bossavit, we provide new low order degrees of freedom. As an alternative to existing choices of bases, we provide canonical resolu...

Connections on principal bundles play a fundamental role in expressing the equations of motion for mechanical systems with symmetry in an intrinsic fashion. A discrete theory of connections on principal bundles is constructed by introducing the discrete analogue of the Atiyah sequence, with a connection corresponding to the choice of a splitting of the short exact sequence. Equivalent represent...