We start with a special case. Consider an irreducible quintic polynomial f(X) = X + a1X + a2X + a3X + a4X + a5 with rational coefficients and with three real roots and one pair of complex conjugate roots. For example, f(X) could be X − 10X + 5. Question. If α is a root of f , then how many roots of f lie in the field Q(α)? The field Q(α) is obtained by adjoining the root α to Q. Thus Q(α) conta...

Given a polynomial with all real roots, the Polynomial Root Squeezing Theorem states that moving two roots an equal distance toward each other, without passing other roots, will cause each critical point to move toward (ri + rj)/2, or remain fixed. In this note, we extend the Polynomial Root Squeezing Theorem to the case where two roots are squeezed together a nonuniform distance.

Flooding induced several physiological and morphological changes in Fraxinus pennsylvanica seedlings, with stomatal closure among the earliest responses. Subsequent changes included: reduction in dry weight increment of roots, stems, and leaves; formation of hypertrophied lenticels and production of adventitious roots on submerged portions of the stem above the soil line; leaf necrosis; and lea...

Despite growing underground, largely in darkness, roots emerge to be very sensitive to light. Recently, several important papers have been published which reveal that plant roots not only express all known light receptors but also that their growth, physiology and adaptive stress responses are light-sensitive. In Arabidopsis, illumination of roots speeds-up root growth via reactive oxygen speci...

Roots are the frontier of plant body to perceive underground environmental change. Endoplasmic reticulum (ER) stress response represents circumvention of cellular stress caused by various environmental changes; however, a limited number of studies are available on the ER stress responses in roots. Here, we report the tunicamycin (TM) -induced ER stress response in Arabidopsis roots by monitorin...

Root turnover is fastest in the finest roots of the root system (first root order). Additionally, tissue chemistry varies among even the finest root orders and between white roots and older, pigmented roots. Yet the effects of pigmentation and order on root decomposition have rarely been examined. We separated the first four root orders (all,1 mm) of four temperate tree species into three class...

A total of 139 extracted mandibular second molars were injected with India ink and demineralized. They were made clear and transparent with methyl salicylate, and the anatomy of their canals was studied. It was found that 86.3% of mandibular second molars had two roots, 9.3% had one root, and 4.3% had three roots. Ninety percent of the mesial roots of the mandibular second molars with two roots...

We introduce the concept of a morphism from the set of Butson Hadamard matrices over k th roots of unity to the set of Butson matrices over l roots of unity. As concrete examples of such morphisms, we describe tensor-product-like maps which reduce the order of the roots of unity appearing in a Butson matrix at the cost of increasing the dimension. Such maps can be constructed from Butson matric...