Second solution: We proceed by induction on the degree of p, with base case where p has degree 0. As in the first solution, we may reduce to a smaller degree in case p has any real roots, so assume it has none. Then p(x)> 0 for all real x, and since p(x)→∞ for x→±∞, p has a minimum value c. Now p(x)− c has real roots, so as above, we deduce that p(x)−c is a sum of squares. Now add one more squa...

Algorithmic skeletons in conjunction with list homomorphisms play an important role in formal development of parallel algorithms. We have designed a notion of homomorphism dedicated to bulk synchronous parallelism. In this paper we derive two application using this theory: sparse matrix vector multiplication and the all nearest smaller values problem. We implement a support for BSP homomorphism...

In this paper, I investigate when an algebraic number can be expressed in terms of algebraic numbers of smaller degree. First, I describe an algorithm to decide, given an irreducible polynomial P in Q[x], whether one of its roots α can be expressed as β + γ , where β and γ are roots of polynomials in Q[x] of degree strictly less than the degree of α. Then, I turn to generalizations such as when...

We propose new Las Vegas randomized algorithms for the solution of a square nonde-generate system of equations, with well-separated roots. The algorithms use O(δ 3 n D 2 log(D) log(b)) arithmetic operations (in addition to the operations required to compute the normal form of the boundary monomials modulo the ideal) to approximate all real roots of the system as well as all roots lying in a fix...

Downward redistribution of soil water through plant roots has important consequences for water and nutrient balance of arid and semi-arid ecosystems. Nevertheless, information on the seasonal patterns and magnitudes of redistribution is lacking for all but a few plant species. We measured sap flow in the taproot and three main lateral roots of a 10-year-old Juglans major Torr. tree, on an ephem...

There is lot of anatomical variation in the mandibular canine. A clinical case report is presented to illustrate anatomical variation in the human mandibular canine. Endodontic treatment may sometimes fail because morphological features of the tooth adversely affect the treatment procedures. Many investigators have reported the anatomical variations associated with mandibular canines. Mandibula...

This paper presents a general method, based on Galois Theory, for establishing that a problem can not be solved by a ‘machine’ that is capable of the standard arithmetic operations, extraction of radicals (that is, m-th roots for any m) and Singular Value Decomposition, as well as extraction of roots of polynomials of degree smaller than n, but no other numerical operations. The method is appli...

Sugar metabolism and the oxidative pentose phosphate pathway (OPPP) are strongly implicated in N assimilation, although the relationship between them and the roles of the plastidial and cytosolic OPPP have not been established genetically. We studied a knock-down mutant of the plastid-localized OPPP enzyme 6-phosphogluconolactonase 3 (PGL3). pgl3-1 plants exhibited relatively greater resource a...

Cytokinin flow from roots to shoots can serve as a long-distance signal important for root-to-shoot communication. In the past, changes in cytokinin flow from roots to shoots have been mainly attributed to changes in the rate of synthesis or breakdown in the roots. The present research tested the possibility that active uptake of cytokinin by root cells may also influence its export to shoots. ...

Increased soil strength due to soil compaction or soil drying is a major limitation to root growth and crop productivity. Roots need to exert higher penetration force, resulting in increased penetration stress when elongating in soils of greater strength. This study aimed to quantify how the genotypic diversity of root tip geometry and root diameter influences root elongation under different le...