Functional Principles of Morphological and Anatomical Structures in Pinecones

In order to better understand the functions of plants, it is important to analyze the internal structure of plants with a complex structure, as well as to efficiently monitor the morphology of plants altered by their external environment. This anatomical study investigated structural characteristics of pinecones to provide detailed descriptions of morphological specifications of complex cone scales. We analyzed cross-sectional image data and internal movement patterns in the opening and closing motions of pinecones, which change according to the moisture content of its external environment. It is possible to propose a scientific system for the deformation of complex pinecone for the variable structures due to changes in relative humidity, as well as the application of technology. This study provided a functional principle for a multidisciplinary approach by exploring the morphological properties and anatomical structures of pinecones. Therefore, the results suggest a potential application for use in energy-efficient materials by incorporating hygroscopic principles into engineering technology and also providing basic data for biomimicry research.

Curvature and the c-projective mobility of Kähler metrics with hamiltonian 2-forms

The mobility of a Kähler metric is the dimension of the space of metrics with which it is c-projectively equivalent. The mobility is at least two if and only if the Kähler metric admits a nontrivial hamiltonian 2-form. After summarizing this relationship, we present necessary conditions for a Kähler metric to have mobility at least three: its curvature must have nontrivial nullity at every point. Using the local classification of Kähler metrics with hamiltonian 2-forms, we describe explicitly the Kähler metrics with mobility at least three and hence show that the nullity condition on the curvature is also sufficient, up to some degenerate exceptions. In an appendix, we explain how the classification may be related, generically, to the holonomy of a complex cone metric.

Singular Levi-flat hypersurfaces in complex projective space induced by curves in the Grassmannian

Let H ⊂ ℙn be a real-analytic subvariety of codimension one induced by a real-analytic curve in the Grassmannian G(n + 1, n). Assuming H has a global defining function, we prove H is Levi-flat, the closure of its smooth points of top dimension is a union of complex hyperplanes, and its singular set is either of dimension 2n - 2 or dimension 2n - 4. If the singular set is of dimension 2n - 4, then we show the hypersurface is algebraic and the Levi-foliation extends to a singular holomorphic foliation of ℙn with a meromorphic (rational of degree 1) first integral. In this case, H is in some sense simply a complex cone over an algebraic curve in ℙ1. Similarly if H has a degenerate singularity, then H is also algebraic. If the dimension of the singular set is 2n - 2 and is nondegenerate, we show by construction that the hypersurface need not be algebraic nor semialgebraic. We construct a Levi-flat real-analytic subvariety in ℙ2 of real codimension 1 with compact leaves that is not contained in any proper real-algebraic subvariety of ℙ2. Therefore a straightforward analogue of Chow's theorem for Levi-flat hypersurfaces does not hold.

AN ANALYTIC APPROACH TO THE STRATIFIED MORSE INEQUALITIES FOR COMPLEX CONES

In a previous paper the author extended the Witten deformation to singular spaces with cone-like singularities and to a class of Morse functions called admissible Morse functions. The method applies in particular to complex cones and stratified Morse functions in the sense of the theory developed by Goresky and MacPherson. It is well-known from stratified Morse theory that the singular points of the complex cone contribute to the stratified Morse inequalities in middle degree only. In this paper, an analytic proof of this fact is given.

Photoreceptors and visual pigments in the red-eared turtle, Trachemys scripta elegans

Absorbance spectra of cone outer segments and oil droplets were recorded microspectrophotometrically in the retina of the red-eared turtle, Trachemys scripta elegans. There are four cone visual pigments, with λmax = 617 nm (red sensitive), 515 nm (green sensitive), 458 nm (blue sensitive), and 372 nm (UV-sensitive). The red-sensitive pigment resides in single cones with red or orange oil droplets, and in both members of double cones. The principal member of the double cone contains an orange oil droplet, and the accessory member is droplet free. The green-sensitive pigment is situated in single cones with orange/dark yellow droplets. The blue-sensitive pigment is combined with the UV-absorbing oil droplet in single cones. The UV-sensitive pigment resides in single cones with clear oil droplets that exhibited virtually no absorbance down to 325 nm. Thus, seven types of cones can be identified based on their morphology, oil droplet color, and the visual pigment absorbance. At the moment, this is the most complex cone system described for vertebrates.