Iterated Differential Forms IV: C-Spectral Sequence

For the multiple differential algebra of iterated differential forms (see math.DG/0605113 and math.DG/0609287) on a diffiety (O,C) an analogue of C-spectral sequence is constructed. The first term of it is naturally interpreted as the algebra of secondary iterated differential forms on (O,C). This allows to develop secondary tensor analysis on generic diffieties, some simplest elements of which are sketched here. The presented here general theory will be specified to infinite jet spaces and infinitely prolonged PDEs in subsequent notes.Comment: 8 pages, submitted to Math. Dok

Endocide-Induced Abnormal Growth Forms of Invasive Giant Salvinia (Salvinia molesta)

Giant salvinia (Salvinia molesta) is one of the most noxious invasive species in the world. The fern is known to have primary, secondary, and tertiary growth forms, which are also commonly hypothesized as growth stages. The identification of these forms is primarily based on the size and folding status of the floating leaves. However, we identified 12 forms in the greenhouse and the field. Our experiments showed that the folding of floating leaves is a reversible trait dependent on water access. The floating leaves quickly fold in response to water shortage, reducing water loss and needs, decreasing growth, and avoiding trichome damage. The leaves re-open to allow trichomes repel water and enhance growth when having adequate water supply. Larger secondary or tertiary forms do not produce small-leaf primary forms without high intensity stress. These results do not support the hypothesis that three growth forms represent sequential growth stages. The abnormal small-leaf forms are the result of endocide-induced autotoxicity and some of them never grow into other forms. The development of abnormal forms and reversible leaf folding strategy in response to high stress along with rapid asexual reproduction are major adaptive traits contributing to the invasiveness of S. molesta

Differential geometry construction of anomalies and topological invariants in various dimensions

In the model of extended non-Abelian tensor gauge fields we have found new metric-independent densities: the exact (2n+3)-forms and their secondary characteristics, the (2n+2)-forms as well as the exact 6n-forms and the corresponding secondary (6n-1)-forms. These forms are the analogs of the Pontryagin densities: the exact 2n-forms and Chern-Simons secondary characteristics, the (2n-1)-forms. The (2n+3)- and 6n-forms are gauge invariant densities, while the (2n+2)- and (6n-1)-forms transform non-trivially under gauge transformations, that we compare with the corresponding transformations of the Chern-Simons secondary characteristics. This construction allows to identify new potential gauge anomalies in various dimensions.Comment: 27 pages, references added, matches published versio

Physiographic Features of Faulting in Southern California

The abundance and variety of faults in southern California provide good opportunity for study of landforms created directly by faulting or indirectly by other processes acting upon faulted materials. High-angle gravity faults, high- and low-angle thrusts, and faults with large strike-slip displacement are present (see Chapter IV). Furthermore, all degrees and dates of activity are represented. Landforms created by faulting can be classed as primary and secondary, or as original and subsequent (Lahee, 1952, p. 248). Primary features are those formed by actual fault displacement. They are nearly always modified by erosion, but should be classed as primary until completely effaced. Secondary or fault-line features are those formed solely by other processes acting upon faulted materials. Further subdivision into initial and modified primary forms and into erosional and depositional secondary forms would be possible, but it is not urged

Analytic torsion of Hirzebruch surfaces

Using different forms of the arithmetic Riemann-Roch theorem and the computations of Bott-Chern secondary classes, we compute the analytic torsion and the height of Hirzebruch surfaces