Based on the notions of locality and recognizability for n-dimensional languages n-dimensionally colorable 1-dimensional languages are introduced. It is shown: A language L is in NP if and only if L is n-dimensionally colorable for some n. An analogous characterization in terms of deterministic n-dimensional colorability is obtained for P. The addition of one unbounded dimension for coloring le...

The angle defect, which is the standard way to measure the curvatures at the vertices of polyhedral surfaces, goes back at least as far as Descartes. Although the angle defect has been widely studied, there does not appear to be in the literature an axiomatic characterization of the angle defect. In this paper a characterization of the angle defect for simplicial surfaces is given, and it is sh...

The angle defect, which is the standard way to measure curvature at the vertices of polyhedral surfaces, goes back at least as far as Descartes. Although the angle defect has been widely studied, there does not appear to be in the literature an axiomatic characterization of the angle defect. We give a characterization of the angle defect for simplicial surfaces, and we show that variants of the...

One of unsolved problems in quantum measurement theory is to characterize coexistence of quantum effects. In this paper, applying positive operator matrix theory, we give a mathematical characterization of the witness set of coexistence of quantum effects and obtain a series of properties of coexistence. We also devote to characterizing bijective morphisms on quantum effects leaving the witness...

In this paper, a numerical study of barrier characterization effects on the high-temperature internal performance of an InGaAsP multi-quantum well laser is presented. The softwareused for this purpose self-consistently combines the three-dimensional simulation of carrier transports, self-heating, and optical waveguiding. The laser model calculates all relevant physical mechanisms, including the...

Three-dimensional Computed Tomography (3-DCT)was performed in 2l patients for characterization of 29 aneurysms of va rious sizes and locations. and determining the relationsrup between the vascular and bony structures. These findings are com· pared with results ofaxial CT. digital subtraction angiography and

In this paper, we generalize a result by Ball, Hill, Landjev and Ward on plane arcs to arcs with multiple points in spaces of arbitrary dimension. This result is further applied to the characterization of some non-Griesmer arcs in the 3-dimensional projective geometry over F4.

We investigate factor maps of higher-dimensional subshifts of finite type. In particular, we are interested in how the number of ergodic measures of maximal entropy behaves under such factor maps. We show that this number is preserved under almost invertible maps, but not in general under finite to one factor maps. One of our tools, which is of independent interest, is a higher-dimensional char...

Based on the notions of locality and recognizability for n-dimensional languages ndimensionally colorable 1-dimensional languages are introduced. It is shown: A language L is in NP if and only if L is n-dimensionally colorable for some n. An analogous characterization in terms of deterministic n-dimensional colorability is obtained for P. The addition of one unbounded dimension for coloring lea...

– The relation between fracture surface morphology and the three-dimensional structure of crack fronts is investigated through direct observation of brittle cracks in gels. A key notion in this investigation is the discontinuity of the crack front, whose advancement creates the fracture surface. We discuss the significance of our findings in the studies of general three-dimensional brittle frac...