Dominant Root Research Articles

On the Domination Polynomial of Some Graph Operations

Let G be a simple graph of order n. The domination polynomial of G is the polynomial D(G,λ)=∑i=0n‍d(G,i)λi, where d(G,i) is the number of dominating sets of G of size i. Every root of D(G,λ) is called the domination root of G. In this paper, we study the domination polynomial of some graph operations.

Occurrence and distribution of fungi associated with grapevine decline in Kurdistan region-Iraq

A survey was carried out in five locations representing the main grapevine production areas of Duhok governorate-Iraq during 2008-2009 in four seasons, winter (Dec.Feb.), spring (Mar.May.), summer (Jun. – Aug.), and fall (Sept. – Nov.) Decline symptoms on grapevines included plants that failed to thrive normal, with reducing shoot growth and chlorotic interveinal areas that later became necrotic. In a cross section of grapevine arms, the internal wood tissues were frequently dark brown to black with a wedge-shaped necrotic sector. Severe symptoms were noted during spring to summer almost in all locations. Canes (bark and wood), buds, trunks or arms (bark and wood), and roots were sampled for fungal isolation. Fungal pathogens belonging to 18 genera were isolated from green growth and roots of the grapevine samples during the four seasons. Cylindrocarpon destructans, Neofusicoccum parvum, and Tognignia minima were the main trunk pathogens found in all grape-growing regions. These three species were reported for the first time in Iraq. N. parvum was isolated with a high frequency (98-100%) from wood of arms and canes in Bajelor and Badi locations during summer and fall. T. minima was found commonly in Zawita by 37-75% of isolation in the wood of arms and canes during fall. C. destructans was the most dominant root rot fungus and was frequently isolated from almost all locations particularly in Badi (41-75% of isolation).

Algorithms for quaternion polynomial root-finding

In 1941 Niven pioneered root-finding for a quaternion polynomial P(x), proving the fundamental theorem of algebra (FTA) and proposing an algorithm, practical if the norm and trace of a solution are known. We present novel results on theory, algorithms and applications of quaternion root-finding. Firstly, we give a new proof of the FTA resulting in explicit formulas for both exact and approximate quaternion roots of P(x) in terms of exact and approximate complex roots of the real polynomial F(x)=P(x)P¯(x), where P¯(x) is the conjugate polynomial. In particular, if |F(c)|≤ϵ, then for a computable quaternion conjugate q of c, |P(q)|≤ϵ. Consequences of these include relevance of root-finding methods for complex polynomials, computation of bounds on zeros, and algebraic solution of special quaternion equations. Secondly, working directly in the quaternion space, we develop Newton and Halley methods and analyze their local behavior. Surprisingly, even for a quadratic quaternion polynomial Newton’s method may not converge locally. Finally, we derive an analogue of the Bernoulli method in the quaternion space for computing the dominant root in certain cases. This requires the development of an independent theory for the solution of quaternion homogeneous linear recurrence relations. These results also lay a foundation for quaternion polynomiography.

On the Roots of Domination Polynomials

The domination polynomial of a graph G of order n is the polynomial $${D(G, x) = \sum_{i=\gamma(G)}^{n} d(G, i)x^i}$$ where d(G, i) is the number of dominating sets of G of size i, and ?(G) is the domination number of G. We investigate here domination roots, the roots of domination polynomials. We provide an explicit family of graphs for which the domination roots are in the right half-plane. We also determine the limiting curves for domination roots of complete bipartite graphs. Finally, we prove that the closure of the roots is the entire complex plane.

The Structure of Performance of a Sport Rock Climber

This study is a contribution to the discussion about the structure of performance of sport rock climbers. Because of the complex and multifaceted nature of this sport, multivariate statistics were applied in the study. The subjects included thirty experienced sport climbers. Forty three variables were scrutinised, namely somatic characteristics, specific physical fitness, coordination abilities, aerobic and anaerobic power, technical and tactical skills, mental characteristics, as well as 2 variables describing the climber’s performance in the OS (Max OS) and RP style (Max RP). The results show that for training effectiveness of advanced climbers to be thoroughly analysed and examined, tests assessing their physical, technical and mental characteristics are necessary. The three sets of variables used in this study explained the structure of performance similarly, but not identically (in 38, 33 and 25%, respectively). They were also complementary to around 30% of the variance. The overall performance capacity of a sport rock climber (Max OS and Max RP) was also evaluated in the study. The canonical weights of the dominant first canonical root were 0.554 and 0.512 for Max OS and Max RP, respectively. Despite the differences between the two styles of climbing, seven variables – the maximal relative strength of the fingers (canonical weight = 0.490), mental endurance (one of scales : The Formal Characteristics of Behaviour–Temperament Inventory (FCB–TI; Strelau and Zawadzki, 1995)) (−0.410), climbing technique (0.370), isometric endurance of the fingers (0.340), the number of errors in the complex reaction time test (−0.319), the ape index (−0.319) and oxygen uptake during arm work at the anaerobic threshold (0.254) were found to explain 77% of performance capacity common to the two styles.

Tin Ore Tailing Reservoir Dominant Plants Heavy Metal Accumulation Characteristics of Yunnan

According to the field investigation, collecting five kinds of dominant plant from tin ore tailing reservoir of Gejiu and tailing reservoir soil samples by flame atomic absorption spectrometry for the determination of five kinds of dominant plant roots, stems, leaves and its growth soil’s Pb, Zn, Cu and Cd contents, and analyzes five kinds of plant transfer and accumulation coefficient. The results showed that: soil heavy metal pollution is serious, especially Cd pollution; Lactuca indic L、Cattail、Alopecurus aequalis and Cyperus rotundus L. plants of heavy metal contents are the same, all is Zn﹥Cu﹥Pb﹥Cd, but four kinds of heavy metal contents are Pb﹥Zn﹥Cu﹥ Cd in Neyruadia plants; Lactuca indic L、Cyperus rotundus L、Alopecurus aequalis and Cattail to Pb, Zn, Cu and Cd four kinds of heavy metals accumulation ability is weaker. But from the root to the ground part organ transfer ability aspects: four kinds of heavy metal in Lactuca indic L is strong, Pb and Cd two elements in the Cyperus rotundus L is more stronger, Cd in Alopecurus aequalis is more stronger, Zn, Cu and Cd in Cattail is more stronger; the accumulation and transfer coefficient are larger than one, it was a better plant which removes Pb.

Root locus analysis and design of the adaptation process in active noise control

This paper applies root locus theory to develop a graphical tool for the analysis and design of adaptive active noise control systems. It is shown that the poles of the adaptation process performed in these systems move on typical trajectories in the z-plane as the adaptation step-size varies. Based on this finding, the dominant root of the adaptation process and its trajectory can be determined. The first contribution of this paper is formulating parameters of the adaptation process root locus. The next contribution is introducing a mechanism for modifying the trajectory of the dominant root in the root locus. This mechanism creates a single open loop zero in the original root locus. It is shown that appropriate localization of this zero can cause the dominant root of the locus to be pushed toward the origin, and thereby the adaptation process becomes faster. The validity of the theoretical findings is confirmed in an experimental setup which is implemented using real-time multi-threading and multi-core processing techniques.

Questioning the idea of the individual as an autonomous moral agent

This paper examines ways in which current moral values are influenced by earlier patterns of thinking carried forward in root metaphors whose meanings were often framed by the analogues settled upon in the past by thinkers who were influenced by the silences and prejudices of their culture. It is argued that such tacitly inherited metaphors reproduce the myth of the individual as a moral agent and that this both is ecologically unsustainable and undermines other important ways of understanding the individual. In various ways the form of critical thinking to which it gives rise stands in the way of individuals exercising what Gregory Bateson refers to as their ‘ecological intelligence’ in a manner that properly takes account of the interdependent nature of cultural and natural ecologies. It is argued that if in the West (at least) a shift could be made to relying on ‘ecology’ as the dominant root metaphor the whole system of Western moral values would undergo a radical change to one better suited to a current Western environmental situation.

Golden rule optimality in stochastic OLG economies

This study examines conditional golden rule optimality (CGRO) in stochastic overlapping generations models to complement the existing results on conditional Pareto optimality (CPO). Although an example in which CPO implies CGRO is presented, it is shown that such a situation is avoidable under strictly convex preferences. Under such preferences, both CPO and CGRO are characterized by the conditions on the dominant root for the agents’ common matrix of marginal rates of substitution. We demonstrate that CGRO requires the dominant root being exactly equal to one, whereas CPO allows it to be less than one. By adopting CGRO rather than CPO, we provide welfare theorems in the financial economy.

Time-Delay Estimation using the Characteristic Roots of Delay Differential Equations

Problem statement: For ordinary dynamic systems (i.e., non-delayed), various methods such as linear least-squares, gradient-weighted least-squares, Kalman filtering and other robust techniques have been widely used in signal processing, robotics, civil engineering. On the other hand, time-delay estimation of systems with unknown time-delay is still a challenging problem due to difficulty in formulation caused. Approach: The presented method makes use of the Lambert W function and analytical solutions of scalar first-order Delay Differential Equations (DDEs). The Lambert W function has been known to be useful in solving delay differential equations. From the solutions in terms of the Lambert W function, the dominant characteristic roots can be obtained and used to estimate time-delays. The function is already embedded in various software packages (e.g., MATLAB) and thus, the presented method can be readily used for time-delay systems. Results: The presented method and the provided examples show ease of formulation and accuracy of time-delay estimation. Conclusion: Estimation of time-delays can be conducted in an analytical way. The presented method will be extended to general systems of DDEs and application to physical systems.

Algebraic Integers as Chromatic and Domination Roots

Let G be a simple graph of order n and λ∈ℕ. A mapping f:V(G)→{1,2,…,λ} is called a λ-colouring of G if f(u)≠f(v) whenever the vertices u and v are adjacent in G. The number of distinct λ-colourings of G, denoted by P(G,λ), is called the chromatic polynomial of G. The domination polynomial of G is the polynomial D(G,λ)=∑i=1nd(G,i)λi, where d(G,i) is the number of dominating sets of G of size i. Every root of P(G,λ) and D(G,λ) is called the chromatic root and the domination root of G, respectively. Since chromatic polynomial and domination polynomial are monic polynomial with integer coefficients, its zeros are algebraic integers. This naturally raises the question: which algebraic integers can occur as zeros of chromatic and domination polynomials? In this paper, we state some properties of this kind of algebraic integers.

Why the CCM won't lose: the roots of single-party dominance in Tanzania

This paper provides an empirical investigation of the factors contributing to single-party dominance in Tanzania. Despite the fact that Tanzania has had a multi-party democracy since 1995, the party which governed during single-party rule, the Chama Cha Mapinduzi (CCM), has won the vast majority of seats in the National Assembly in the first four multi-party elections. In order to understand the CCM's grip on power, this article analyses the results of a survey conducted amongst subsistence farmers in Tanzania, which provides information on farmers’ livelihood conditions, access to media and political views, and hence provides insight into the preferences underlying voting behaviour. It discusses the dominant reasons for CCM support, as well as the characteristics of farmers who are more likely to support an opposition party. It concludes by discussing possible policy options for enhancing political competition in Tanzania.

Transient stability analysis of a power system with one generator connected to an infinite bus system

This paper presents a novel method to identify the fault that would affect the transient stability of one machine to an infinite bus. Here, the swing equation of each machine is expressed in the form of a closed-loop transfer function in Laplace ss-domain. In the transfer function, the duration of the fault and the changes in maximum electrical power output of the machine during and after the fault are considered. Then, the real value of the dominant root of each machine's characteristic equation is identified on the real axis of the s-plane. In this method, the generator has been considered unstable based on the position of the real value of the dominant root in the left half or very close to the imaginary axis or in the right half of the s-plane. The results obtained by the proposed method are compared with those of the conventional step-by-step method on the basis of different fault clearing times, and good agreements have been demonstrated.

Wind-induced leaning (toppling) in young Pinus radiata plantations in Chile

The toppling of young trees considerablyreduces the value of the first log in Pinus radiata plantations.Although wind is the main cause of toppling, the quality and type of plants,planting techniques, soil fertility and soil preparation may play an importantrole in the susceptibility of the species to toppling. This article analyzesthe influence of ripping and soil type on the probability of P. radiatatoppling after severe windstorms in central south Chile. To this aim, pairs ofsimilar trees with and without toppling were selected in 2001 in six soil typeswith and without soil ripping. Root system differences in toppled versusstraight trees were compared to gain better insight into the causes of thephenomenon. Among all root measurements, the quality of thetap root measured through the Menzies scale was significantly correlated with the probability oftoppling. Trees with a strong, dominant and well-developed tap root (Menziesvalue equal to zero) showed a toppling probability of 0.34 (1 of each 3 treesbeing damaged). At the other extreme, trees with a horizontal tap root or withno tap root (Menzies value equal to 10) showed a toppling probability of 0.72 (i.e.,three of each four trees were damaged). A toppling probability of 0.50 (ordamage observed in one of each two trees) was found for trees with a tap rootdistinctly hooked but functional (Menzies value equal to 4). Ripping reducedthe toppling probability from 0.56 to 0.44 by improving the quality of the taproot consistently across all soil types from Menzies 5.7 to Menzies 2.5. Theworst tap root qualities were found for sandy soils (Menzies equal to 7.0,toppling probability of 0.62), followed by metamorphic soils (Menzies equal to4.5, toppling probability of 0.52). Alluvial, granitic, red clay and volcanicash soils did not differ in tap root quality (Menzies equal to 3.3, topplingprobability of 0.47). In conclusion, the study suggests that all measures favoring a strong, dominant andwell-developed tap root, in the nursery and in the field, are likely to considerablyreduce toppling damage in young P. radiata plantations in Chile

Genotypic variation in phosphorus acquisition from sparingly soluble P sources is related to root morphology and root exudates in Brassica napus

Genotypic variations in the adaptive response to low-phosphorus (P) stress and P-uptake efficiency have been widely reported in many crops. We conducted a pot experiment to evaluate the P-acquisition ability of two rapeseed (Brassica napus) genotypes supplied with two sparingly soluble sources of P, Al-P and Fe-P. Then, the root morphology, proton concentrations, and carboxylate content were investigated in a solution experiment to examine the genotypic difference in P-acquisition efficiency. Both genotypes produced greater biomass and accumulated more P when supplied with Al-P than when supplied with Fe-P. The P-efficient genotype 102 showed a significantly greater ability to deplete sparingly soluble P from the rhizosphere soil because of its greater biomass and higher P uptake compared with those of the P-inefficient genotype 105. In the solution experiment, the P-efficient genotype under low-P conditions developed dominant root morphological traits, and it showed more intensive rhizosphere acidification because of greater H(+) efflux, higher H(+)-ATPase activity, and greater exudation of carboxylates than the P-inefficient genotype. Thus, a combination of morphological and physiological mechanisms contributed to the genotypic variation in the utilization of different sparingly soluble P sources in B. napus.

The Roots of Social Dominance: Aggression, Prosocial Behavior, and Social Interdependence

ABSTRACT The authors examined the nature of dominant students in Grades 3–5 in a midwestern school system in the United States. Previous research has indicated 2 ways a student may gain dominance—through bullying and prosocial behaviors. A cluster analysis for dominant children was conducted using social interdependence attitude scores, children's self-reports of bullying and prosocial behaviors, and teacher reports of bullying and prosocial behaviors. Dominant children were clustered into cooperative-prosocial, competitive-aggressive, and individualistic groups. Competitive-aggressive children received higher teacher ratings of dominance than did cooperative-prosocial children, there was no significant among the clusters on perceived leadership by peers, and cooperative-prosocial children tended to have teachers who used more cooperative learning in their classroom.

On the graphs with four distinct domination roots

The domination polynomial of a graph G of order n is the polynomial , where d(G, i) is the number of dominating vertex sets of G with cardinality i. A root of D(G, x) is called a domination root of G. In this paper, we characterize graphs with exactly four distinct domination roots .

CSR and leadership: can China lead a new paradigm shift?

Globally, corporate social responsibility (CSR) needs to find its sustainable development via the recognition of tangible benefits that CSR will bring to organizations and their stakeholders. The less tangible but likely most important benefit lies in the continual improved leadership and management quality emerging from organizations investing in CSR. Companies’ failure to act in a CSR way and the lack of wise leadership and quality management is a dominant root factor in the past scandals and financial crisis. Looking at current interactions between Chinese companies and their various influencing environmental, society and government (ESG) factors, many of the motivational drivers for Western companies to invest in CSR are today still being challenged here based on China’s market specifics. More rapid development of the regulatory framework with adequate enforcement resources, as well as incorporation of CSR “value” education at universities can accelerate this needed development. In the short term, foreign companies as “guests” of China should also be a catalyst as role models. Apart from a foreign investor’s actions, it is equally important to acknowledge and address local China challenges remaining to provide the right climate for a foreign company’s CSR programs to be successfully executed here. The world is at a cross roads of a new value-based leadership paradigm. With global interdependence accelerating and hence, management and leadership complexity expanding, there is a need for a new leadership model, bringing “common wisdom” more pronounced to the forefront, arising from a renewed focus and strengthening of an aligned set of values between family, society, and corporate life. China’s unique demographic challenges and economic progress provide a fertile environment to lead the world in this development.

Root exudation of sugars, amino acids, and organic acids by maize as affected by nitrogen, phosphorus, potassium, and iron deficiency

AbstractRoot exudates play a major role in the mobilization of sparingly soluble nutrients in the rhizosphere. Since the amount and composition of major metabolites in root exudates from one plant species have not yet been systematically compared under different nutrient deficiencies, relations between exudation patterns and the type of nutrient being deficient remain poorly understood. Comparing root exudates from axenically grown maize plants exposed to N, K, P, or Fe deficiency showed a higher release of glutamate, glucose, ribitol, and citrate from Fe‐deficient plants, while P deficiency stimulated the release of γ‐aminobutyric acid and carbohydrates. Potassium‐starved plants released less sugars, in particular glycerol, ribitol, fructose, and maltose, while under N deficiency lower amounts of amino acids were found in root exudates. Principal‐component analysis revealed a clear separation in the variation of the root‐exudate composition between Fe or P deficiency versus N or K deficiency in the first principal component, which explained 46% of the variation in the data. In addition, a negative correlation was found between the amounts of sugars, organic and amino acids released under deficiency of a certain nutrient and the diffusion coefficient of the respective nutrient in soils. We thus hypothesize that the release of dominant root exudates such as sugars, amino acids, and organic acids by roots may reflect an ancient strategy to cope with limiting nutrient supply.

A stability study on first-order neutral systems with three rationally independent time delays

First-order linear time invariant and time-delayed dynamics of neutral type is taken into account with three rationally independent delays. There are two main contributions of this study. (a) It is the first complete treatment in the literature on the stability analysis of systems with three delays. We use a recent procedure, the cluster treatment of characteristic roots (CTCR), for this purpose. This procedure results in an exact and exhaustive stability tableau in the domain of the three delays. (b) It provides a proof of a complex concept called the delay-stabilisability (also known as strong stability) as a by-product of CTCR. Furthermore, we deploy a numerical method (infinitesimal generator approach) to approximate the dominant characteristic roots of this class of systems, which concur with the stability outlook generated by CTCR.