We prove that a general miraculous cancellation formula, the divisibility of certain characteristic numbers, and some other topological results related to the generalized Rochlin invariant, the η-invariant and the holonomies of certain determinant line bundles, are consequences of the modular invariance of elliptic operators on loop space. 1. Motivations In [AW], a gravitational anomaly cancell...

A soil-water characteristic (SWC) curve describes the amount of water retained in a soil (expressed as mass or volume water content, m or v) under equilibrium at a given matric potential. An SWC is an important hydraulic property, related to size and connectedness of pore spaces, hence strongly affected by soil texture and structure, and by other constituents, including organic matter. Modeling...

In this article we introduce and study the concept of characteristic degree of a subgroup in a finite group. We define the characteristic degree of a subgroup H in a finite group G as the ratio of the number of all pairs (h,α) ∈ H×Aut(G) such that h^α∈H, by the order of H × Aut(G), where Aut(G) is the automorphisms group of G. This quantity measures the probability that H can be characteristic ...

We derive simple explicit formula for the character of a cycle in the Connes’ (b, B)-bicomplex of cyclic cohomology and apply it to write formulas for the equivariant Chern character and characters of finitely-summable bounded Fredholm modules.

In this paper we survey various constructions and properties of genera and characteristic numbers of singular complex algebraic varieties. In particular, we discuss genera for the singular varieties appearing in the minimal model program, as well as those defined by Hodge theory and functorial characteristic classes.

We explore the relation between the positive dimensional irreducible components of the characteristic varieties of rank one local systems on a smooth surface and the associated (rational or irrational) pencils. Our study, which may viewed as a continuation of D. Arapura’s paper [1], yields new geometric insight into the translated components relating them to the multiplicities of curves in the ...

A new causal power-normalized waveguide equivalent-circuit theory determines uniquely both the magnitude and phase of the characteristic impedance of a waveguide.

Let £ be a partially ordered linear normed space over the field of real numbers whose positive cone K has nonempty interior K0.1 A functional / in E*, the conjugate space of E, is called positive if f(K)^0 and/5^0. A semi-group V of linear operators on E is called positive if r(A7) QK. It will be assumed that T contains the identity operator. This note is concerned with the properties of positi...

A [ An−1 + p1A n−2 + · · ·+ pn−1 In ] = −pn In . Since A is nonsingular, pn = (−1)n det(A) 6= 0; thus the result follows. Newton’s Identity. Let λ1, λ2, . . . , λn be the roots of the polynomial K(λ) = λ + p1λ n−1 + p2λ n−2 + · · · · · ·+ pn−1λ+ pn. If sk = λ k 1 + λ k 2 + · · ·+ λn, then pk = − 1 k (sk + sk−1 p1 + sk−2 p2 + · · ·+ s2 pk−2p1 + s1 pk−1) . Proof. From K(λ) = (λ − λ1)(λ − λ2) . . ...

3D modeling of Pd/α-Al2O3 hollow fiber membrane by using computational fluid dynamic for hydrogen separation from H2/N2 mixture was considered in steady and unsteady states by using the concept of characteristic time. Characteristic time concept could help us to design and calculate surface to volume ratio and membrane thickness, and adjust the feed conditions. The contribution of resistance be...