Using the Stickelberger-Swan theorem, the parity of the number of irreducible factors of a self-reciprocal even-degree polynomial over a finite field will be hereby characterized. It will be shown that in the case of binary fields such a characterization can be presented in terms of the exponents of the monomials of the self-reciprocal polynomial.

A chemical invariant of graphical structure Z is a unique value characteristic that remains unchanged under graph automorphisms. In the study QSAR/QSPR, like many other invariants, reciprocal degree distance has played significant role to estimate bioactivity several compounds in chemistry. Reciproca...

By synergistically combining modeling, simulation and experiments, we show that there exists a regime of self-propulsion in which the inertia fluid dynamics can be separated from swimmer. This is demonstrated by motion an asymmetric dumbbell that, despite deforming reciprocal fashion, self-propagates due to non-reciprocal Stokesian flow field. The latter arises difference coasting times two con...

The only primitive trinomials of degree 6972593 over GF(2) are x6972593 + x3037958 + 1 and its reciprocal.

The achievement of a ‘consensual’ solution in a group decision making problem depends on experts’ ideas, principles, knowledge, experience, etc. The measurement of consensus has been widely studied from the point of view of different research areas, and consequently different consensus measures have been formulated, although a common characteristic of most of them is that they are driven by the...

Heterostyly (i.e., reciprocal placement of anthers and stigmas between two or three floral morphs) is hypothesized to enhance outcrossing and reduce selfing. However, few studies have documented reciprocity among individual plants; instead, mean anther and stigma heights for floral morphs are usually reported, masking interindividual variation. We measured eight floral dimensions for individual...

We developed an algorithm that improves upon the common procedure of taking reciprocal best blast hits(rbh) in the identification of orthologs. The method-reciprocal smallest distance algorithm (rsd)-relies on global sequence alignment and maximum likelihood estimation of evolutionary distances to detect orthologs between two genomes. rsd finds many putative orthologs missed by rbh because it i...

A polynomial is called unimodular if each of its coefficients is a complex number of modulus 1. A polynomial P of the form P (z) = ∑n j=0 ajz j is called conjugate reciprocal if an−j = aj , aj ∈ C for each j = 0, 1, . . . , n. Let ∂D be the unit circle of the complex plane. We prove that there is an absolute constant ε > 0 such that max z∈∂D |f(z)| ≥ (1 + ε) √ 4/3m , for every conjugate recipro...

This paper provides evidence about the determinants of trust and reciprocal inclinations, that is, a tendency for people to respond in kind to hostile or kind actions, in a representative setting. We investigate the prevalence of reciprocity in the population, the correlation between trust and positive and negative reciprocal inclinations within person, the individual determinants of reciprocit...