scholarly journals Differential bud activation by a net positive root signal explains branching phenotype in prostrate clonal herbs: a model

2014 ◽  
Vol 65 (2) ◽  
pp. 673-682 ◽  
Author(s):  
R. G. Thomas ◽  
F. Y. Li ◽  
M. J. M. Hay
Keyword(s):  
Positive Root ◽  
Root Signal

scholarly journals Time Decay for Nonlinear Dissipative Schrödinger Equations in Optical Fields

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Nakao Hayashi ◽  
Chunhua Li ◽  
Pavel I. Naumkin
Keyword(s):  
Lower Bound ◽  
Positive Root ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Time Decay ◽  
Large Initial Data ◽  
Initial Value ◽  
Optical Fields ◽  
Gauge Invariant ◽  
Dissipative Condition

We consider the initial value problem for the nonlinear dissipative Schrödinger equations with a gauge invariant nonlinearityλup-1uof orderpn<p≤1+2/nfor arbitrarily large initial data, where the lower boundpnis a positive root ofn+2p2-6p-n=0forn≥2andp1=1+2forn=1.Our purpose is to extend the previous results for higher space dimensions concerningL2-time decay and to improve the lower bound ofpunder the same dissipative condition onλ∈C:Im⁡ λ<0andIm⁡ λ>p-1/2pRe λas in the previous works.

scholarly journals Partitioning the positive integers with higher order recurrences

1991 ◽  
Vol 14 (3) ◽  
pp. 457-462 ◽  
Author(s):  
Clark Kimberling
Keyword(s):  
Positive Integer ◽  
Positive Root ◽  
Irrational Number ◽  
Higher Order ◽  
Typical Result ◽  
Algebraic Integers ◽  
Positive Integers

Associated with any irrational numberα>1and the functiong(n)=[αn+12]is an array{s(i,j)}of positive integers defined inductively as follows:s(1,1)=1,s(1,j)=g(s(1,j−1))for allj≥2,s(i,1)=the least positive integer not amongs(h,j)forh≤i−1fori≥2, ands(i,j)=g(s(i,j−1))forj≥2. This work considers algebraic integersαof degree≥3for which the rows of the arrays(i,j)partition the set of positive integers. Such an array is called a Stolarsky array. A typical result is the following (Corollary 2): ifαis the positive root ofxk−xk−1−…−x−1fork≥3, thens(i,j)is a Stolarsky array.

Interspecific root interactions enhance photosynthesis and biomass of intercropped millet and peanut plants

2019 ◽  
Vol 70 (3) ◽  
pp. 234
Author(s):  
Xiaojin Zou ◽  
Zhanxiang Sun ◽  
Ning Yang ◽  
Lizhen Zhang ◽  
Wentao Sun ◽  
...  
Keyword(s):  
Crop Yields ◽  
Positive Root ◽  
Foxtail Millet ◽  
Phosphoglycerate Kinase ◽  
Plant Productivity ◽  
Photosynthetic Rates ◽  
Interspecific Facilitation ◽  
Growing Seasons ◽  
Root Interactions ◽  
Root Barrier

Intercropping is commonly practiced worldwide because of its benefits to plant productivity and resource-use efficiency. Belowground interactions in these species-diverse agro-ecosystems can greatly contribute to enhancing crop yields; however, our understanding remains quite limited of how plant roots might interact to influence crop biomass, photosynthetic rates, and the regulation of different proteins involved in CO2 fixation and photosynthesis. We address this research gap by using a pot experiment that included three root-barrier treatments with full, partial and no root interactions between foxtail millet (Setaria italica (L.) P.Beauv.) and peanut (Arachis hypogaea L.) across two growing seasons. Biomass of millet and peanut plants in the treatment with full root interaction was 3.4 and 3.0 times higher, respectively, than in the treatment with no root interaction. Net photosynthetic rates also significantly increased by 112–127% and 275–306% in millet and peanut, respectively, with full root interaction compared with no root interaction. Root interactions (without barriers) contributed to the upregulation of key proteins in millet plants (i.e. ribulose 1,5-biphosphate carboxylase; chloroplast β-carbonic anhydrase; phosphoglucomutase, cytoplasmic 2; and phosphoenolpyruvate carboxylase) and in peanut plants (i.e. ribulose 1,5-biphosphate carboxylase; glyceraldehyde-3-phosphate dehydrogenase; and phosphoglycerate kinase). Our results provide experimental evidence of a molecular basis that interspecific facilitation driven by positive root interactions can contribute to enhancing plant productivity and photosynthesis.

Double-bosonization of braided groups and the construction of Uq(g)

1999 ◽  
Vol 125 (1) ◽  
pp. 151-192 ◽  
Author(s):  
S. MAJID
Keyword(s):  
Hopf Algebra ◽  
Quantum Groups ◽  
Cartan Subalgebra ◽  
Positive Root ◽  
Point Of View ◽  
Root Space ◽  
Quantum Double ◽  
Braided Group ◽  
Negative Root ◽  
Quasitriangular Hopf Algebra

We introduce a quasitriangular Hopf algebra or ‘quantum group’ U(B), the double-bosonization, associated to every braided group B in the category of H-modules over a quasitriangular Hopf algebra H, such that B appears as the ‘positive root space’, H as the ‘Cartan subalgebra’ and the dual braided group B* as the ‘negative root space’ of U(B). The choice B=Uq(n+) recovers Lusztig's construction of Uq(g); other choices give more novel quantum groups. As an application, our construction provides a canonical way of building up quantum groups from smaller ones by repeatedly extending their positive and negative root spaces by linear braided groups; we explicitly construct Uq(sl3) from Uq(sl2) by this method, extending it by the quantum-braided plane. We provide a fundamental representation of U(B) in B. A projection from the quantum double, a theory of double biproducts and a Tannaka–Krein reconstruction point of view are also provided.

scholarly journals On the Roots of the Modified Orbit Polynomial of a Graph

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 972
Author(s):  
Modjtaba Ghorbani ◽  
Matthias Dehmer
Keyword(s):  
Positive Root ◽  
Current Work ◽  
Positive Zero ◽  
Unique Positive Root ◽  
Definition Of

The definition of orbit polynomial is based on the size of orbits of a graph which is OG(x)=∑ix|Oi|, where O1,…,Ok are all orbits of graph G. It is a well-known fact that according to Descartes’ rule of signs, the new polynomial 1−OG(x) has a positive root in (0,1), which is unique and it is a relevant measure of the symmetry of a graph. In the current work, several bounds for the unique and positive zero of modified orbit polynomial 1−OG(x) are investigated. Besides, the relation between the unique positive root of OG in terms of the structure of G is presented.

A computationally efficient non-linear beamformer based on pth root signal compression for enhanced ultrasound B-mode imaging

2017 ◽  
Author(s):  
Maxime Polichetti ◽  
Fancois Varray ◽  
Giulia Matrone ◽  
Alessandro Stuart Savoia ◽  
Jean-Christophe Bera ◽  
...  
Keyword(s):  
Signal Compression ◽  
Computationally Efficient ◽  
Non Linear ◽  
Root Signal

scholarly journals Quotient polynomials with positive coefficients

2014 ◽  
Vol 98 (542) ◽  
pp. 250-255
Author(s):  
Mark B. Villarino
Keyword(s):  
Efficient Method ◽  
Theoretical Basis ◽  
Present Author ◽  
Positive Root ◽  
Real Numbers ◽  
Image Position ◽  
Positive Coefficients

In a recent paper [1] Michael Hirschhorn and the present author had to prove that the polynomialis positive for all integers n ≥ 4. We did so by writing down the identitySince all the coefficients of the quotient polynomial are positive as well as the remainder, this shows by inspection that f(n) > 0 for n ≥ 5 and computing f(4) = 12025 completes the proof. This example illustrates a useful and efficient method for proving that polynomials have strictly positive values for all real numbers exceeding a given one. We leamed this method from a paper by Chen [2], (see [3] and the references cited there), and we have subsequently used it in our own researches [1,4].We also conjectured in [1] that the theoretical basis of the method is a true theorem and the present paper is dedicated to proving this conjecture.Theorem 1: Let f(x) be a polynomial with real coefficients whose leading coefficient is positive and with at least one positive root x = a. Then there exists an x = b ≥ a such thatwhere f(b), and all the coefficients of the quotient polynomial g(x), are non-negative.

Online-List Scheduling on a Single Bounded Parallel-Batch Machine to Minimize Makespan

2015 ◽  
Vol 32 (04) ◽  
pp. 1550028
Author(s):  
Wenhua Li ◽  
Jie Gao ◽  
Jinjiang Yuan
Keyword(s):  
Lower Bound ◽  
Competitive Ratio ◽  
Online Algorithm ◽  
Positive Root ◽  
List Scheduling ◽  
Batch Machine

In this paper, we consider the online-list scheduling on a single bounded parallel-batch machine to minimize makespan. In the problem, the jobs arrive online over list. The first unassigned job in the list should be assigned to a batch before the next job is released. Each batch can accommodate up to b jobs. For b = 2, we establish a lower bound 1 + γ of competitive ratio and provide an online algorithm with a competitive ratio of [Formula: see text], where γ is the positive root of γ(γ + 1)2 = 1. For b = 3, we establish a lower bound 1 + α of competitive ratio and provide an online algorithm with a competitive ratio of 2, where α is the positive root of the equation (1 + α)(1 + α2) = 2.

Root signal sets of morphological filters

1992 ◽  
Vol 28 (10) ◽  
pp. 952-953 ◽  
Author(s):  
Q. Wang ◽  
M. Gabbouj ◽  
Y. Neuvo
Keyword(s):  
Morphological Filters ◽  
Signal Sets ◽  
Root Signal

scholarly journals LAZY3 plays a pivotal role in positive root gravitropism in Lotus japonicus

2019 ◽  
Vol 71 (1) ◽  
pp. 168-177 ◽  
Author(s):  
Yaping Chen ◽  
Shaoming Xu ◽  
Lu Tian ◽  
Leru Liu ◽  
Mingchao Huang ◽  
...  
Keyword(s):  
Plasma Membrane ◽  
Auxin Transport ◽  
Positive Root ◽  
Lotus Japonicus ◽  
Polar Auxin Transport ◽  
Pivotal Role ◽  
Root Gravitropism ◽  
Root Stele

LAZY3, polarly localized to the plasma membrane in root stele cells, is involved in rootward polar auxin transport in roots and required for positive root gravitropism in Lotus japonicus.

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