RIGIDITY OF HOLOMORPHIC MAPS BETWEEN FIBER SPACES

In the study of holomorphic maps, the term ``rigidity'' refers to certain types of results that give us very specific information about a general class of holomorphic maps owing to the geometry of their domains or target spaces. Under this theme, we begin by studying when, given two compact connected complex manifolds X and Y, a degree-one holomorphic map f :Y -> X is a biholomorphism. Given that the real manifolds underlying X and Y are diffeomorphic, we provide a condition under which f is a biholomorphism. Using this result, we deduce a rigidity result for holomorphic self-maps of the total space of a holomorphic fiber space. Lastly, we consider products X = X-1 x X-2 and Y = Y-1 x Y-2 of compact connected complex manifolds. When X-1 is a Riemann surface of genus >= 2, we show that any non-constant holomorphic map F:Y -> X is of a special form.

Arithmetic Algorithms in a Negative Base

Algorithms are described for the basic arithmetic operations and square rooting in a negative base. A new operation called polarization that reverses the sign of a number facilitates subtraction, using addition. Some special features of the negative-base arithmetic are also mentioned.

A constraint Jacobian based approach for static analysis of pantograph masts

This paper presents a constraint Jacobian matrix based approach to obtain the stiffness matrix of widely used deployable pantograph masts with scissor-like elements (SLE). The stiffness matrix is obtained in symbolic form and the results obtained agree with those obtained with the force and displacement methods available in literature. Additional advantages of this approach are that the mobility of a mast can be evaluated, redundant links and joints in the mast can be identified and practical masts with revolute joints can be analysed. Simulations for a hexagonal mast and an assembly with four hexagonal masts is presented as illustrations.

Karyotype instability in the ponerine ant genus Diacamma

The queenless ponerine ant Diacamma ceylonense and a population of Diacamma from the Nilgiri hills which we refer to as `nilgiri', exhibit interesting similarities as well as dissimilarities. Molecular phylogenetic study of these morphologically almost similar taxa has shown that D ceylonense is closely related to `nilgiri' and indicates that `nilgiri' is a recent diversion in the Diacamma phylogenetic tree. However, there is a striking behavioural difference in the way reproductive monopoly is maintained by the respective gamergates (mated egg laying workers), and there is evidence that they are genetically differentiated, suggesting a lack of gene flow To develop a better understanding of the mechanism involved in speciation of Diacamma, we have analysed karyotypes of D. ceylonense and `nilgiri' In both, we found surprising inter-individual and intra-individual karyotypic mosaicism. The observed numerical variability, both at intra-individual and inter-individual levels, does not appear to have hampered the sustainability of the chromosomal diversity in each population under study Since the related D. indicum, displays no such intra-individual or inter-Individual variability whatsoever under identical experimental conditions, these results are unlikely to he artifacts. Although no known mechanisms can account for the observed karyotypic variability of this nature, we believe that the present findings on the ants under study would provide opportunities for exciting new discoveries concerning the origin, maintenance and significance of intra-individual and inter-individual karyotypic mosaicism.

The diatom genus Gomphonema Ehrenberg in India: Checklist and description of three new species

We have compiled a checklist of Gomphonema Ehrenberg taxa reported previously from India. From forty-nine references, over 100 Gomphonema taxa have been reported, including 39 new taxon descriptions. In addition to these previous reports of Gomphonema taxa, we describe three new species. G. gandhii Karthick & Kociolek, sp. nov., G. difformum Karthick & Kociolek, sp. nov. and G. diminutum Karthick & Kociolek, sp. nov., all from hill streams of Western Ghats, India. Frustule morphology, as studied in light and scanning electron microscopy, is compared with that of other recently described Gomphonema species from Africa and Asia. All three Indian species have distinctly dilated proximal raphe ends, in addition to differentiated apical pore fields, septa, pseudosepta and a round external stigma! opening. Gomphonema gandhii is linear-lanceolate-clavate, has a wide axial area, and is 19-51 mu m long, 3-7 mu m broad. Gomphonema difformum is smaller than G. gandhii, and has a hyaline area around the headpole. Gomphonema diminuta is much smaller and narrower than the other two species. These species are distinct from their closest congeners by their sizes, shape and structure of the head pole, and striae densities. All these species were described from low nutrient, neutral, low ionic content streams of Western Ghats. As most other species described from tropical region these three species appear to be endemic to India. Moreover, within India they have hitherto only been found in Western Ghats, one of the twelve biodiversity hotspots of the World.

Testing concordance in species boundaries using acoustic, morphological, and molecular data in the field cricket genus Itaropsis (Orthoptera: Grylloidea, Gryllidae: Gryllinae)

In most taxa, species boundaries are inferred based on differences in morphology or DNA sequences revealed by taxonomic or phylogenetic analyses. In crickets, acoustic mating signals or calling songs have species-specific structures and provide a third data set to infer species boundaries. We examined the concordance in species boundaries obtained using acoustic, morphological, and molecular data sets in the field cricket genus Itaropsis. This genus is currently described by only one valid species, Itaropsis tenella, with a broad distribution in western peninsular India and Sri Lanka. Calling songs of males sampled from four sites in peninsular India exhibited significant differences in a number of call features, suggesting the existence of multiple species. Cluster analysis of the acoustic data, molecular phylogenetic analyses, and phylogenetic analyses combining all data sets suggested the existence of three clades. Whatever the differences in calling signals, no full congruence was obtained between all the data sets, even though the resultant lineages were largely concordant with the acoustic clusters. The genus Itaropsis could thus be represented by three morphologically cryptic incipient species in peninsular India; their distributions are congruent with usual patterns of endemism in the Western Ghats, India. Song evolution is analysed through the divergence in syllable period, syllable and call duration, and dominant frequency.

Modified Newton, rank-1 Broyden update and rank-2 BFGS update methods in helicopter trim: A comparative study

Nonlinear equations in mathematical physics and engineering are solved by linearizing the equations and forming various iterative procedures, then executing the numerical simulation. For strongly nonlinear problems, the solution obtained in the iterative process can diverge due to numerical instability. As a result, the application of numerical simulation for strongly nonlinear problems is limited. Helicopter aeroelasticity involves the solution of systems of nonlinear equations in a computationally expensive environment. Reliable solution methods which do not need Jacobian calculation at each iteration are needed for this problem. In this paper, a comparative study is done by incorporating different methods for solving the nonlinear equations in helicopter trim. Three different methods based on calculating the Jacobian at the initial guess are investigated. (C) 2011 Elsevier Masson SAS. All rights reserved.

Nodal length fluctuations for arithmetic random waves

Using the spectral multiplicities of the standard torus, we endow the Laplace eigenspaces with Gaussian probability measures. This induces a notion of random Gaussian Laplace eigenfunctions on the torus (''arithmetic random waves''). We study the distribution of the nodal length of random eigenfunctions for large eigenvalues, and our primary result is that the asymptotics for the variance is nonuniversal. Our result is intimately related to the arithmetic of lattice points lying on a circle with radius corresponding to the energy.

Revalidation of Natrix clerki Wall, 1925, an overlooked species in the genus Amphiesma Dumeril, Bibron & Dumeril, 1854 (Squamata: Natricidae)

Natrix clerki Wall, 1925, previously known from its sole holotype and considered a synonym of Amphiesma parallelum (Boulenger, 1890), is resurrected in the genus Amphiesma on the basis of the analysis of morphological variation in 28 specimens of ``Amphiesma parallelum'' auctorum, plus six living, unvouchered specimens discovered in Arunachal Pradesh and Nagaland, India, and one vouchered specimen from Talle Valley in Arunachal Pradesh. Specimens from northeast India (Nagaland), northern Myanmar, and China (Yunnan), previously identified as Amphiesma parallelum either in the literature or in museum's catalogues, are also here referred to A. clerki. The holotype of Amphiesma clerki is redescribed. As a consequence, the definition of Amphiesma parallelum is modified. A. parallelum inhabits the Khasi Hills and Naga Hills in Northeast India, whereas A. clerki has a wider range in the Eastern Himalayas, northern Myanmar and Yunnan (China). Amphiesma clerki differs from A. parallelum by its longer tail, dorsal scales more strongly keeled, scales of the first dorsal scale row strongly keeled vs. smooth, a postocular streak not interrupted at the level of the neck, and a much more vivid pattern on a darker background colour. Characters of species of the Amphiesma parallelum group, i.e. A. clerki, A. parallelum, A. bitaeniatum, A. platyceps and A. sieboldii are compared. A key to this group is provided.

An Exponential Lower Bound for Homogeneous Depth Four Arithmetic Formulas

We show here a 2(Omega(root d.log N)) size lower bound for homogeneous depth four arithmetic formulas. That is, we give an explicit family of polynomials of degree d on N variables (with N = d(3) in our case) with 0, 1-coefficients such that for any representation of a polynomial f in this family of the form f = Sigma(i) Pi(j) Q(ij), where the Q(ij)'s are homogeneous polynomials (recall that a polynomial is said to be homogeneous if all its monomials have the same degree), it must hold that Sigma(i,j) (Number of monomials of Q(ij)) >= 2(Omega(root d.log N)). The above mentioned family, which we refer to as the Nisan-Wigderson design-based family of polynomials, is in the complexity class VNP. Our work builds on the recent lower bound results 1], 2], 3], 4], 5] and yields an improved quantitative bound as compared to the quasi-polynomial lower bound of 6] and the N-Omega(log log (N)) lower bound in the independent work of 7].

Molecular phylogeny of Glyphochloa (Poaceae, Panicoideae), an endemic grass genus from the Western Ghats, India

The genus Glyphochloa (Poaceae: Panicoideae: Andropogoneae: Rottboellinae) is endemic to peninsular India and is distributed on lateritic plateaus of low and high altitude in and around Western Ghats and the Malabar Coast. The genus presumably originated and diversified in the Western Ghats. Species relationships in the genus Glyphochloa were deduced here based on molecular phylogenies inferred using nuclear ribosomal ITS sequences and plastid intergenic spacer regions (atpB-rbcL, trnT-trnL, trnL-trnF), and new observations were made of spikelet morphology, caryopsis morphology and meiotic chromosome counts. We observed two distinct clades of Glyphochloa s.l. One of these (group I') includes Ophiuros bombaiensis, and is characterized by a single-awned lower glume and a base chromosome number of 6; it grows in low elevation coastal areas. The other clade (group II') has a double-awned lower glume, a base chromosome number of 7, and is restricted to higher elevation lateritic plateaus; G. ratnagirica may belong to the group II clade, or may be a third distinct lineage in the genus. A sister-group relationship between group I and II taxa (with or without G. ratnagirica) is not well supported, although the genus is recovered as monophyletic in shortest trees inferred using ITS or concatenated plastid data. We present a key to species of Glyphochloa and make a new combination for O. bombaiensis.