Positive Root Isolation for Poly-Powers

2016 ◽  
Author(s):  
Jing-Cao Li ◽  
Cheng-Chao Huang ◽  
Ming Xu ◽  
Zhi-Bin Li
Keyword(s):  
Positive Root ◽  
Root Isolation

scholarly journals Positive root isolation for poly-powers by exclusion and differentiation

2018 ◽  
Vol 85 ◽  
pp. 148-169 ◽  
Author(s):  
Cheng-Chao Huang ◽  
Jing-Cao Li ◽  
Ming Xu ◽  
Zhi-Bin Li
Keyword(s):  
Positive Root ◽  
Root Isolation

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.

scholarly journals Dynamics of a Prey–Predator System with Foraging Facilitation in Predators

2020 ◽  
Vol 30 (01) ◽  
pp. 2050009
Author(s):  
Yong Yao
Keyword(s):  
Numerical Simulations ◽  
Real Root ◽  
Qualitative Properties ◽  
Isolation Technique ◽  
Root Isolation ◽  
Number Of Equilibria ◽  
Complete Investigation ◽  
Theoretical Results ◽  
Predator System ◽  
Real Root Isolation

The dynamics of a prey–predator system with foraging facilitation among predators are investigated. The analysis involves the computation of many semi-algebraic systems of large degrees. We apply the pseudo-division reduction, real-root isolation technique and complete discrimination system of polynomial to obtain the parameter conditions for the exact number of equilibria and their qualitative properties as well as do a complete investigation of bifurcations including saddle-node, transcritical, pitchfork, Hopf and Bogdanov–Takens bifurcations. Moreover, numerical simulations are presented to support our theoretical results.

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