The cohomology ring of the GKM graph of a flag manifold of classical type

If a closed smooth manifold $M$ with an action of a torus $T$ satisfies certain conditions, then a labeled graph \mG_M with labeling in $H^2(BT)$ is associated with $M$, which encodes a lot of geometrical information on $M$. For instance, the "graph cohomology" ring \mHT^*(\mG_M) of \mG_M is defined to be a subring of \bigoplus_{v\in V(\mG_M)}H^*(BT), where V(\mG_M) is the set of vertices of \mG_M, and is known to be often isomorphic to the equivariant cohomology $H^*_T(M)$ of $M$. In this paper, we determine the ring structure of \mHT^*(\mG_M) with $\Z$ (resp. $\Z[1/2]$) coefficients when $M$ is a flag manifold of type A, B or D (resp. C) in an elementary way.Comment: 22 page

A New Simple Equation for Obtaining The Strain Distribution of a Granular Bed

A new simple equation to estimate the strain distribution of a granular bed is derived based on the mechanics of an elastic body and the hydrodynamics. A new assumption introduced is that stresses caused by strains depend on both the strains and the average stress in the granular bed. As a simple but typical example to verify the new theory, the strain distribution of a powder bed sandwiched between two parallel plates is discussed. The distribution caused by the slow movement of the upper or lower plate is represented not by a straight line, but a curved line. The simple equation based on the new theory gives a good estimation for the strain distribution

Todd genera of complex torus manifolds

In this paper, we prove that the Todd genus of a compact complex manifold $X$ of complex dimension $n$ with vanishing odd degree cohomology is one if the automorphism group of $X$ contains a compact $n$-dimensional torus \Tn as a subgroup. This implies that if a quasitoric manifold admits an invariant complex structure, then it is equivariantly homeomorphic to a compact smooth toric variety, which gives a negative answer to a problem posed by Buchstaber-Panov.Comment: 12 pages, Remark 1.2 is adde

Mean Particle Diameter in an Analysis of a Particulate Process

In the study of a participate process, one of the most important subjects to consider is what mean particle diameter to employ. In this study, an experimental value is divided into two terms, one with some interaction between particles and the other without such interaction (the linear term). The mean particle diameter is defined only in terms of the latter, that is the linear term. It is shown that the scattering in previously published data for the particulate process, is attributable to the fact that the mean diameter is not determined correctly. Further, if such a diameter as determined in this study is used, a satisfactory result with little scattering in the data is achieved. In connection with the definition, the practical method for determining the mean particle diameter and suggestions as to its use are given, and the relation between the process variables observed when the distribution is log-normal, is also discussed

Perturbative path-integral of string field and the A∞A_{\infty } structure of the BV master equation

The perturbative path-integral gives a morphism of the (quantum) $A_{\infty }$ structure intrinsic to each quantum field theory, which we show explicitly on the basis of the homological perturbation. As is known, in the BV formalism, any effective action also solves the BV master equation, which implies that the path-integral can be understood as a morphism of the BV differential. Since each solution of the BV master equation is in one-to-one correspondence with a (quantum) $A_{\infty }$ structure, the path-integral preserves this intrinsic $A_{\infty }$ structure of quantum field theory, where $A_{\infty }$ reduces to $L_{\infty }$ whenever multiplications of space-time fields are graded commutative. We apply these ideas to string field theory and (re-)derive some quantities based on the perturbative path-integral, such as effective theories with finite $\alpha ^{\prime }$, reduction of gauge and unphysical degrees, $S$-matrix and gauge invariant observables.Comment: 41 pages, appendix adde

Topological toric manifolds

We introduce the notion of a topological toric manifold and a topological fan and show that there is a bijection between omnioriented topological toric manifolds and complete non-singular topological fans. A topological toric manifold is a topological analogue of a toric manifold and the family of topological toric manifolds is much larger than that of toric manifolds. A topological fan is a combinatorial object generalizing the notion of a simplicial fan in toric geometry. Prior to this paper, two topological analogues of a toric manifold have been introduced. One is a quasitoric manifold and the other is a torus manifold. One major difference between the previous notions and topological toric manifolds is that the former support a smooth action of an $S^1$-torus while the latter support a smooth action of a \C^*-torus. We also discuss their relation in details.Comment: 42 pages, 4 figure

An efficient early-pooling protocol for environmental DNA metabarcoding

Environmental DNA (eDNA) metabarcoding, a method that applies high-throughput sequencing and universal primer sets to eDNA analysis, has been a promising approach for efficient, comprehensive biodiversity monitoring. However, significant money-, labor-, and time-costs are still required for performing eDNA metabarcoding. In this study, we assessed the performance of an “early-pooling” protocol (a protocol based on 1st PCR tagging) to reduce the experimental costs of library preparation for eDNA metabarcoding. Specifically, we performed three experiments to investigate the effects of 1st PCR-tagging and 2nd PCR-indexing protocols on the community composition revealed by eDNA metabarcoding, the effects of post-1st PCR exonuclease purification on tag jumping (corresponds to index hopping in 2nd PCR indexing), and the effects of the number of PCR replicates and the eDNA template volume on the number of detected OTUs. Analyses of 204 eDNA libraries from three natural aquatic ecosystems and one mock eDNA sample showed that (i) 1st PCR tagging does not cause clear biases in the outcomes of eDNA metabarcoding, (ii) post-1st PCR exonuclease purification reduces the risk of tag jumping, and (iii) increasing the eDNA template volume may increase the number of detected OTUs and reduce variations in the detected community compositions, similar to increasing the number of 1st PCR replicates. Our results show that an early-pooling protocol with post-1st PCR exonuclease purification and an increased amount of the DNA template reduces the risk of tag jumping, the costs for consumables and reagents (except for many tagged 1st PCR primers), and the handling time in library preparation, and produces similar results to a 2nd PCR-indexing protocol. Therefore, once a target metabarcoding region is selected and a set of tagged-1st PCR primers is prepared, the early-pooling protocol provides a cost, labor, and time-efficient approach for processing a large number of samples