Polynomial Definiteness and Semidefiniteness

1970 ◽  
Vol 92 (2) ◽  
pp. 394-397 ◽  
Author(s):  
Chiou-Shiun Chen ◽  
Edwin Kinnen
Keyword(s):  
Quadratic Form ◽  
Sufficient Conditions ◽  
Higher Order ◽  
Real Polynomial ◽  
Reduction Procedure ◽  
Sign Definiteness ◽  
Order Polynomial ◽  
The Individual ◽  
New Variables ◽  
Engineering Stability

A reduction procedure is described for determining the sign definiteness and semidefiniteness of an mth order, n dimensional real polynomial. The higher order polynomial is reduced to a quadratic form in new variables such that conditions can be obtained on the coefficients of the individual terms of the original polynomial. The procedure presents sufficient conditions only. It has been found, however, to be a relatively systematic technique for engineering stability problems where alternate effective methods for determining sign definiteness are unknown.

scholarly journals Center Conditions for a Class of Rigid Quintic Systems

2019 ◽  
pp. 1-8
Author(s):  
Fei Fei Lu
Keyword(s):  
Differential Equation ◽  
Polynomial System ◽  
Sufficient Conditions ◽  
Higher Order ◽  
Necessary And Sufficient Conditions ◽  
Central Focus ◽  
Periodic Differential Equation ◽  
Order Polynomial ◽  
Center Conditions ◽  
Necessary And Sufficient

The problem of determining necessary and sufficient conditions on P and Q for system. x = - y+P(x+y),y = x+Q(x+y) to have a center at the origin is known as the Poincaré center-focus problem. So far, people has tried many ways to solve the problem of central focus. However, it is difficult to solve the center focus problem of higher order polynomial system. In this paper, we use the Poincaré and Alwash-Lloyd methods to study the center focus problem and derive the center conditions of the five periodic differential equation.

scholarly journals On the equivalence and qualitative behavior of the rational differential equations

Filomat ◽  
2017 ◽  
Vol 31 (14) ◽  
pp. 4379-4391
Author(s):  
Zhengxin Zhou
Keyword(s):  
Differential Equations ◽  
Polynomial System ◽  
Sufficient Conditions ◽  
Polynomial Systems ◽  
Higher Order ◽  
Qualitative Behavior ◽  
Differential Systems ◽  
Wide Range ◽  
Order Polynomial ◽  
Made In

Recent study has shown great interest in the existence of center for planar differential systems. Sufficient conditions have been given for a critical point of some polynomial systems to be a center. However, it is challenging to generalize these results to higher-order or non-polynomial systems by traditional methods. In this paper, we tackle the problem by studying the equivalence of differential systems using the Mironenko?s method. Our method includes the construction of RF- integrals for the rational differential equations, we give some new criterions for two differential equations to be equivalent. Applying these results to the study of center of planar differential systems, we generalize the conclusions made in existing literature for a specific polynomial system to a wide range of higher-order polynomial or non-polynomial systems.

Associations Between Higher-Order Values Vary with Age, Education, and Income

2020 ◽  
Author(s):  
Maksim Rudnev
Keyword(s):  
Cognitive Abilities ◽  
Developed Countries ◽  
European Social Survey ◽  
Higher Order ◽  
Group Differences ◽  
Social Survey ◽  
Value Structures ◽  
Younger Age ◽  
The Individual ◽  
Representative Samples

A theory of basic human values relies on the similarity of value structures across countries. It has been well established that the quasi-circumplex value structure as a whole is indeed universal. However, less attention has been paid to the associations between specific values. This study investigated associations between four higher-order values across age, education, and income groups. We analyzed the data from national representative samples collected in 29 countries as part of the fourth round of the European Social Survey with a series of multilevel regressions. Younger age, higher levels of education and income coincided with higher independence of the four adjacent higher-order values, whereas among older, less educated, and less wealthy groups, values tended to merge into a single dimension of Social versus Person Focus. These differences were slightly weaker in more economically developed countries. The group differences in value associations may follow from corresponding differences in the degree of societal and individual empowerment, cognitive abilities, and socialization experiences. Accounting for the individual differences in relations between values may bring deeper understanding and higher predictive power to the studies of links between values and various behaviors or attitudes. , value structure, value interactions, European Social Survey

scholarly journals Oscillatory behavior of nonlinear Hilfer fractional difference equations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Tuğba Yalçın Uzun
Keyword(s):  
Difference Equations ◽  
Sufficient Conditions ◽  
Higher Order ◽  
Oscillatory Behavior ◽  
Fractional Difference ◽  
Fractional Difference Equations ◽  
All Solutions ◽  
Alpha Beta

AbstractIn this paper, we study the oscillation behavior for higher order nonlinear Hilfer fractional difference equations of the type $$\begin{aligned}& \Delta _{a}^{\alpha ,\beta }y(x)+f_{1} \bigl(x,y(x+\alpha ) \bigr) =\omega (x)+f_{2} \bigl(x,y(x+ \alpha ) \bigr),\quad x\in \mathbb{N}_{a+n-\alpha }, \\& \Delta _{a}^{k-(n-\gamma )}y(x) \big|_{x=a+n-\gamma } = y_{k}, \quad k= 0,1,\ldots,n, \end{aligned}$$ Δ a α , β y ( x ) + f 1 ( x , y ( x + α ) ) = ω ( x ) + f 2 ( x , y ( x + α ) ) , x ∈ N a + n − α , Δ a k − ( n − γ ) y ( x ) | x = a + n − γ = y k , k = 0 , 1 , … , n , where $\lceil \alpha \rceil =n$ ⌈ α ⌉ = n , $n\in \mathbb{N}_{0}$ n ∈ N 0 and $0\leq \beta \leq 1$ 0 ≤ β ≤ 1 . We introduce some sufficient conditions for all solutions and give an illustrative example for our results.

scholarly journals Nonexistence Results for Higher Order Fractional Differential Inequalities with Nonlinearities Involving Caputo Fractional Derivative

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1866
Author(s):  
Mohamed Jleli ◽  
Bessem Samet ◽  
Calogero Vetro
Keyword(s):  
Fractional Derivative ◽  
Caputo Fractional Derivative ◽  
A Priori Estimates ◽  
Sufficient Conditions ◽  
Global Solutions ◽  
Higher Order ◽  
Differential Inequalities ◽  
Structure Of Solutions ◽  
Nonlinear Capacity ◽  
Fractional Differential

Higher order fractional differential equations are important tools to deal with precise models of materials with hereditary and memory effects. Moreover, fractional differential inequalities are useful to establish the properties of solutions of different problems in biomathematics and flow phenomena. In the present work, we are concerned with the nonexistence of global solutions to a higher order fractional differential inequality with a nonlinearity involving Caputo fractional derivative. Namely, using nonlinear capacity estimates, we obtain sufficient conditions for which we have no global solutions. The a priori estimates of the structure of solutions are obtained by a precise analysis of the integral form of the inequality with appropriate choice of test function.

Partial Higher-Order Specifications1

1992 ◽  
Vol 16 (2) ◽  
pp. 101-126
Author(s):  
Egidio Astesiano ◽  
Maura Cerioli
Keyword(s):  
Sufficient Conditions ◽  
Higher Order ◽  
Necessary And Sufficient Conditions ◽  
Important Case ◽  
Deduction System ◽  
Closure Properties ◽  
Inference System ◽  
Conditional Specification ◽  
Necessary And Sufficient

In this paper the classes of extensional models of higher-order partial conditional specifications are studied, with the emphasis on the closure properties of these classes. Further it is shown that any equationally complete inference system for partial conditional specifications may be extended to an inference system for partial higher-order conditional specifications, which is equationally complete w.r.t. the class of all extensional models. Then, applying some previous results, a deduction system is proposed, equationally complete for the class of extensional models of a partial conditional specification. Finally, turning the attention to the special important case of termextensional models, it is first shown a sound and equationally complete inference system and then necessary and sufficient conditions are given for the existence of free models, which are also free in the class of term-generated extensional models.

The weighted Cauchy problem for linear functional differential equations with strong singularities

2011 ◽  
Vol 18 (3) ◽  
pp. 577-586
Author(s):  
Zaza Sokhadze
Keyword(s):  
Cauchy Problem ◽  
Differential Equations ◽  
Linear Functional ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Initial Point ◽  
Higher Order ◽  
Well Posedness ◽  
Deviating Arguments ◽  
Functional Differential

Abstract The sufficient conditions of well-posedness of the weighted Cauchy problem for higher order linear functional differential equations with deviating arguments, whose coefficients have nonintegrable singularities at the initial point, are found.

scholarly journals Comparisons between SCIAMACHY and ground-based FTIR data for total columns of CO, CH<sub>4</sub>, CO<sub>2</sub> and N<sub>2</sub>O

2006 ◽  
Vol 6 (7) ◽  
pp. 1953-1976 ◽  
Author(s):  
B. Dils ◽  
M. De Mazière ◽  
J. F. Müller ◽  
T. Blumenstock ◽  
M. Buchwitz ◽  
...  
Keyword(s):  
Near Infrared ◽  
Polynomial Interpolation ◽  
Global Network ◽  
Target Species ◽  
Time Period ◽  
Order Polynomial ◽  
Temporal And Spatial ◽  
The Individual ◽  
Near Future ◽  
Total Column

Abstract. Total column amounts of CO, CH4, CO2 and N2O retrieved from SCIAMACHY nadir observations in its near-infrared channels have been compared to data from a ground-based quasi-global network of Fourier-transform infrared (FTIR) spectrometers. The SCIAMACHY data considered here have been produced by three different retrieval algorithms, WFM-DOAS (version 0.5 for CO and CH4 and version 0.4 for CO2 and N2O), IMAP-DOAS (version 1.1 and 0.9 (for CO)) and IMLM (version 6.3) and cover the January to December 2003 time period. Comparisons have been made for individual data, as well as for monthly averages. To maximize the number of reliable coincidences that satisfy the temporal and spatial collocation criteria, the SCIAMACHY data have been compared with a temporal 3rd order polynomial interpolation of the ground-based data. Particular attention has been given to the question whether SCIAMACHY observes correctly the seasonal and latitudinal variability of the target species. The present results indicate that the individual SCIAMACHY data obtained with the actual versions of the algorithms have been significantly improved, but that the quality requirements, for estimating emissions on regional scales, are not yet met. Nevertheless, possible directions for further algorithm upgrades have been identified which should result in more reliable data products in a near future.

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