A minimal area problem imposing different length conditions on open and closed curves is shown to define a one parameter family of covariant open-closed quantum string field theories. These interpolate from a recently proposed factorizable open-closed theory up to an extended version of Witten’s open string field theory capable of incorporating on shell closed strings. The string diagrams of th...

This article describes a formula for second variation of energy for twodimensional parametrized minimal surfaces, in which the conformal structure on the two-dimensional domain is allowed to vary. Moreover, it shows that minimal surfaces with branch points have tangential Jacobi fields which are not visible via the standard formulae for second variation of area which is commonly used to study s...

Minimal immersions of a compact Riemannian homogeneous manifold into round spheres, or spherical minimal immersions for short, or “spherical soap bubbles,” belong to a fast growing and fascinating area between algebra and geometry. This theory has rich interconnections with a variety of mathematical disciplines such as representation theory, convex geometry, harmonic maps, minimal surfaces, and...

due to the notable role of different land uses in carbon sequestration and emission, four treatments including rangeland as control, haloxylon plantation area, olea plantation (olive garden), and residential lands, were selected to study the effects of land use change on soil carbon sequestration and emissions in eivanakei rangelands, semnan province. carbon stocks in vegetation and soil of eac...

In this paper, we prove that any BL-general fuzzy automaton (BL-GFA) and its quotient have the same behavior. In addition, we obtain the minimal quotient BL-GFA and minimal quotient transformation of the BL-GFA, considering the notion of maximal admissible partition. Furthermore, we show that the number of input symbols and time complexity of the minimal quotient transformation of a BL-GFA are ...

We show that a practical translation of MRS descriptions into normal dominance constraints is feasible. We start from a recent theoretical translation and verify its assumptions on the outputs of the English Resource Grammar (ERG) on the Redwoods corpus. The main assumption of the translation— that all relevant underspecified descriptions are nets—is validated for a large majority of cases; all...