If g, g are complex rational functions, we say that g ∼ g if g = ( ax+b cx+d )−1 ◦ g ◦ (ax+b cx+d ) , where ∣∣∣∣ a b c d ∣∣∣∣ 6= 0. For practical purposes, the general problem of finding a collection of rational invariants that are sufficient to partition ∼ into equivalency classes may be intractable for arbitrary degree rational functions. In this paper, we first outline a simple and naive met...

Pulse period of earthquake records has been known as a key parameter in seismology and earthquake engineering. This paper presents a detailed characterization of this parameter for a special class of earthquake records called pulse-like ground motions. This type of motions often resulting from directivity effects is characterized by a strong pulse in the velocity time history of motion, in norm...

In this paper, we explore the theory of tensor invariants as a mathematical framework for computing new biomarkers for HARDI. We present and explain the integrity basis, basic invariants and principal invariants of 2nd & 4th order tensors to expand on a recently proposed paper on 4th order tensor invariants. We present the mathematical results and compute the basic and principal invariants on a...

double- unsymmetric-plan medium-rise buildings subjected to bi-directional seismic excitation are complex structures where higher-mode effects in plan and elevation are important in estimating the seismic responses using nonlinear static or pushover analysis. considering two horizontal components of the ground motions makes the problem more intricate. this paper presents a method for nonlinear ...

This paper aims to present a survey of object recognition/classification methods based on image moments. We review various types of moments (geometric moments, complex moments) and moment-based invariants with respect to various image degradations and distortions (rotation, scaling, affine transform, image blurring, etc.) which can be used as shape descriptors for classification. We explain a g...

We study the eta-invariants of links and show that in many cases they form link concordance invariants, in particular that many eta-invariants vanish for slice links. This result contains and generalizes previous invariants by Smolinsky and Cha–Ko. We give a formula for the eta-invariant for boundary links. In several intersting cases this allows us to show that a given link is not slice. We sh...

Chirality plays an important role in physics, chemistry, biology, and other fields. It describes an essential symmetry in structure. However, chirality invariants are usually complicated in expression or difficult to evaluate. In this paper, we present five general three-dimensional chirality invariants based on the generating functions which are called ShapeDNA. And the five chiral invariants ...

In this paper, we propose integral invariants based on group invariant parameterisation. The new invariants do not suuer from occlusion problems, do not require any correspondence of image features unlike existing algebraic invariants, and are less sensitive to noise than diier-ential invariants. Our framework applies aane diierential geometry to derive novel aane integral invariants. The new i...