A Topological Approach to Indices of Geometric Operators on Manifolds with Fibered Boundaries

In this paper, we investigate topological aspects of indices of twisted geometric operators on manifolds equipped with fibered boundaries. We define K-groups relative to the pushforward for boundary fibration, and show that indices of twisted geometric operators, defined by complete $$\Phi $$Φ or edge metrics, can be regarded as the index pairing over these K-groups. We also prove various properties of these indices using groupoid deformation techniques. Using these properties, we give an application to the localization problem of signature operators for singular fiber bundles.

Quantum Computing, Seifert Surfaces, and Singular Fibers

The fundamental group π 1 ( L ) of a knot or link L may be used to generate magic states appropriate for performing universal quantum computation and simultaneously for retrieving complete information about the processed quantum states. In this paper, one defines braids whose closure is the L of such a quantum computer model and computes their braid-induced Seifert surfaces and the corresponding Alexander polynomial. In particular, some d-fold coverings of the trefoil knot, with d = 3 , 4, 6, or 12, define appropriate links L, and the latter two cases connect to the Dynkin diagrams of E 6 and D 4 , respectively. In this new context, one finds that this correspondence continues with Kodaira’s classification of elliptic singular fibers. The Seifert fibered toroidal manifold Σ ′ , at the boundary of the singular fiber E 8 ˜ , allows possible models of quantum computing.

Kajian Sifat Tarik Serat Pelepah Lontar dengan Singular Fiber Tensile Testing Methode

Penggunaan serat alam sebagai filler pada komposit mulai banyak digunakan. Salah satu yang memiliki prospek cukup baik adalah serat pelepah pohon lontar (Borassus Flabellifer), yang penggunaannya masih terbatas pada bahan bakar atau komponen tertentu dalam pembangunan rumah. Serat pelepah lontar yang dikombinasikan dengan polyester sebagai matriks dapat bermanfaat untuk alternatif pembuatan body kapal ikan. Akan tetapi data dan informasi ilmiah tentang sifat mekanis kekuatan tarik serat tunggal pelepah pohon lontar ini masih belum tersedia sehingga pemanfaatan serat pelepah lontar ini masih sangat terbatas khususnya dalam penggunaan sebagai penguat pada komposit. Penelitian ini bertujuan untuk mengetahui seberapa besar nilai kekuatan tarik yang dihasilkan serat pelepah lontar tanpa perlakuan alkali maupun melalui perlakuan alkali dengan menggunakan singular fiber tensile testing methode. Nilai kekuatan tarik yang dihasilkan serat lontar tanpa perlakuan alkali adalah 364,32 MPa, dan kekuatan tarik maksimal serat yang diberi perlakuan alkali adalah serat dengan waktu perlakuan 4 jam (240 menit) sebesar 496,75 MPa, The use of natural fiber as a filler of composite is commonly used. One of the natural fibers that has quite good prospect is the fiber from the midrib of palm tree (Borassus Flabellifer), which its usage is limited on fuel or certain components in constructing houses. Fiber from midrib of palm tree that combined with polyester as matrix can be beneficial to be an alternative in constructing the body of boat for fishing. However, data and scientific information about the mechanic system of the tensile strenght of the singular fiber of palm tree is very limited in particular in the utilization as strengthener on composite. This research is to find out how strong the tensile strenght created by palm fiber without treatment either with alkali or alkali with singular fiber tensile testing method. The value of tensile strenght generated by palm fiber without alkali treatment is 364.32 Mpa, and the maximum tensile strenght of the fiber with alkali treatment is the fiber with 4 hours (240 minutes) treatment amounts 496.74 Mpa.

­Comparative spigot ontogeny across the spider tree of life

Spiders are well known for their silk and its varying use across taxa. Very few studies have examined the silk spigot ontogeny of the entire spinning field of a spider. Historically the spider phylogeny was based on morphological data and behavioral data associated with silk. Recent phylogenomics studies have shifted major paradigms in our understanding of silk use evolution, reordering phylogenetic relationships that were once thought to be monophyletic. Considering this, we explored spigot ontogeny in 22 species, including Dolomedes tenebrosus and Hogna carolinensis, reported here for the first time. This is the first study of its kind and the first to incorporate the Araneae Tree of Life. After rigorous testing for phylogenetic signal and model fit, we performed 60 phylogenetic generalized least squares analyses on adult female and second instar spigot morphology. Six analyses had significant correlation coefficients, suggesting that instar, strategy, and spigot variety are good predictors of spigot number in spiders, after correcting for bias of shared evolutionary history. We performed ancestral character estimation of singular, fiber producing spigots on the posterior lateral spinneret whose potential homology has long been debated. We found that the ancestral root of our phylogram of 22 species, with the addition of five additional cribellate and ecribellate lineages, was more likely to have either none or a modified spigot rather than a pseudoflagelliform gland spigot or a flagelliform spigot. This spigot ontogeny approach is novel and we can build on our efforts from this study by growing the dataset to include deeper taxon sampling and working towards the capability to incorporate full ontogeny in the analysis.