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We prove the existence of multi-soliton and kink-multi-soliton solutions of the Euler–Korteweg system in dimension one. Such solutions behave asymptotically in time like several travelling waves far away from each other. A kink is a travelling wave with different limits at ±∞. The main assumption is the linear stability of the solitons, and we prove that this assumption is satisfied at least in the transonic limit. The proof relies on a classical approach based on energy estimates and a compactness argument.
An in-house self-held respiration monitoring device (SHRMD) was developed for providing deep inspiration breath hold (DIBH) radiotherapy. The use of SHRMD is evaluated in terms of reproducibility, stability and heart dose reduction.
Methods and materials:
Sixteen patients receiving radiotherapy of left breast cancer were planned for treatment with both a free breathing (FB) scan and a DIBH scan. Both FB and DIBH plans were generated for comparison of the heart, left anterior descending (LAD) artery and lung dose. All patients received their treatments with DIBH using SHRMD. Megavoltage cine images were acquired during treatments for evaluating the reproducibility and stability of treatment position using SHRMD.
Compared with FB plans, the maximum dose to the heart by DIBH technique with SHRMD was reduced by 29·9 ± 15·6%; and the maximum dose of the LAD artery was reduced by 41·6 ± 18·3%. The inter-fractional overall mean error was 0·01 cm and the intra-fractional overall mean error was 0·04 cm.
This study demonstrated the potential benefits of using the SHRMD for DIBH to reduce the heart and LAD dose. The patients were able to perform stable and reproducible DIBHs.
This article examines the consociational democracy installed in Kosovo after the war. Starting from the premise that the electoral system is considered one of the key instruments for the engineering of post-conflict societies with deep ethnic divisions, the article analyzes the preferences of local and international actors for the type of electoral system. In particular, the United Nations Interim Administration Mission’s reluctance to organize elections without a prior creation of an institutional base, as well as grand governing coalitions. The mechanisms of consociational democracy aim at addressing elite cooperation between different ethnic communities for building peace and stability in post-conflict societies. But focusing on the intra- and inter-community dynamics of cooperation and confrontation between elites, I conclude that the main obstacle to building a democratic multi-ethnic society in Kosovo and implementing the power-sharing arrangements was the uncertainty over the status of Kosovo.
This paper presents a vision-based path planning strategy that aims to reduce the computational time required by a robot to find a feasible path from a starting point to the goal point. The proposed algorithm presents a novel strategy that can be implemented on any well-known path planning algorithm such as A*, D* and probabilistic roadmap (PRM), to improve the swiftness of these algorithms. This path planning algorithm is suitable for real-time scenarios since it reduces the computational time compared to the basis and traditional algorithms. To test the proposed path planning strategy, a tracking control strategy is implemented on a mobile platform. This control strategy consists of three major stages. The first stage deals with gathering information about the surrounding environment using vision techniques. In the second stage, a free-obstacle path is generated using the proposed reduced scheme. In the final stage, a Lyapunov kinematic tracking controller and two Artificial Neural Network (ANN) based-controllers are implemented to track the proposed path by adjusting the rotational and linear velocity of the robot. The proposed path planning strategy is tested on a Pioneer P3-DX differential wheeled mobile robot and an Xtion PRO depth camera. Experimental results prove the efficiency of the proposed path planning scheme, which was able to reduce the computational time by a large percentage which reached up to 88% of the time needed by the basis and traditional scheme, without significant adverse effect on the workability of the basis algorithm. Moreover, the proposed path planning algorithm has improved the path efficiency, in terms of the path length and trackability, challenging the traditional trade-off between swiftness and path efficiency.
Though significant efforts are made to develop mathematical models of the limit cycle walking (LCW), there is still a lack of a general and efficient framework to study the periodic solution and robustness of a complex model like human with knees, ankles and flat feet. In this study, a numerical framework of the LCW based on general multibody system dynamics is proposed, especially the impacts between the feet and the ground are modeled by Hunt–Crossley normal contact force and Coulomb friction force, and the modeling of the knee locking is presented as well. Moreover, event-based operating strategies are presented to deal with controls for the ground clearance and the knee locking. Importantly, a fast and efficient two-step algorithm is proposed to search for stable periodic gaits. Finally, maximum allowable disturbance is adopted as the index for stability analysis. All these features could be readily implemented in the framework. The presented solution is verified on a compass-like passive dynamic walking (PDW) walker with results in the literature. Based on this framework, a fairly complicated level-walking walkers with ankles and knees under control are analyzed and their periodic gaits are obtained, and surprisingly, double stable periodic gaits with, respectively, low speed and high speed are found.
The switching between a damped and an undamped Inertial Navigation System (INS) is an important technical method to ensure its long-term accuracy. The stability of switching is of great importance. This paper studies the switching stability problem between a damped and an undamped INS. A model of an inertial navigation switching system is established by introducing switched control. The average dwell time method is used to analyse stability and a sufficient condition of exponential stability is given. The condition is also extended to the switched system containing constant disturbance and the sufficient condition of exponential stability. The effect of introducing switched control for the smooth operation of the system is verified and the accuracy of a long-term INS is improved effectively.
Trajectory tracking of a mobile manipulator in the Cartesian space based on decentralized control is considered in this paper. The dynamic model is first rearranged to take the form of two interconnected subsystems with constraint flow, namely, a nonholonomic mobile platform subsystem and a holonomic manipulator subsystem. Secondly, using the inverse kinematics, the workspace desired trajectory of the mobile manipulator is transformed to the manipulator joint space as well as the platform desired trajectory. The kinematic control is developed from the desired trajectory of the platform. Then, the desired velocity is derived using the kinematic controller of the mobile platform, after which the velocity is used to obtain the control law of the mobile platform subsystem. Thirdly, the control law of the manipulator subsystem is developed based on the desired and real values of the manipulator, as well as the desired velocity. According to the Lyapunov stability theory, the proposed decentralized control strategy guarantees the global stability of the closed-loop system, and the tracking errors are bounded. Experimental results obtained on a 3-DOF manipulator mounted on a mobile platform are given to demonstrate the feasibility and effectiveness of the proposed approach. This is confirmed by a comparison with the computed torque approach.
This paper reexamines the Serendipity Theorem of Samuelson (1975) from the stability viewpoint, and shows that, for the Cobb–Douglas preference and CES technology, the most-golden golden-rule lifetime state being stable depends on parameter values. In some situations, the Serendipity Theorem fails to hold despite the fact that steady-state welfare is maximized at the population growth rate, since the steady state is unstable. Through numerical simulations, a more general case of CES preference and CES technology is also examined, and we discuss the realistic relevance of our results. We present the policy implication of our result, that is, in some cases, the steady state with the highest utility is unstable, and thus a policy that aims to achieve the social optima by manipulating the population growth rate may lead to worse outcomes.
The stability of organoclays prepared from smectites and organic cations depends on the type of used cation, among other factors. This study provides a prediction of the structure, stability and dynamic properties of organoclays based on montmorillonite (Mt) intercalated with two types of organic cations – tetrabutylammonium (TBA) and tetrabutylphosphonium (TBP) – using first-principle density functional theory. The results obtained from simulations were also used in the interpretation of the experimental infrared spectrum of the TBP-Mt organoclay. Analysis of interatomic distances showed that weak C–O···H hydrogen bonds were important in the stabilization of both TBA- and TBP-Mt models, with slightly stronger hydrogen bonds for the TBP cation. Calculated intercalation and adsorption reaction energies (ΔEint//ΔEads*/ΔEads**) confirmed that TBP-Mt structures (–72.4//–32.8/–53.8 kJ/mol) were considerably more stable than TBA-Mt structures (–56.7//–22.6/–37.4 kJ/mol). The stronger interactions of the alkyl chains of the TBP cation with Mt basal surfaces in comparison to those of the TBA cation were also correlated with the positions of the calculated bands of the C–H stretching vibrations.
A system of functional equations satisfied by the components of a quadratic function is derived via their corresponding circulant matrix. Given such a system of functional equations, general solutions are determined and a stability result for such a system is established.
In this study, we investigated the elastic constants, moduli, hardness, and electronic structures of Ti–Al intermetallic compounds (TiAl, Ti3Al, and TiAl3) using first-principles calculations. The cohesive energy and formation enthalpy of these compounds are negative, which indicates that they are thermodynamically stable. We calculated the elastic constants and moduli using the stress–strain method and Voigt–Reuss–Hill approximation, respectively. We evaluated the mechanical anisotropy of these compounds using the anisotropic index and found that the results are in good agreement with other experimental and theoretical data. We evaluated the chemical bonding of these compounds by calculating their density of states, the results of which revealed that the bonding behavior of all Ti–Al intermetallic compounds involved a mixture of metallic and covalent bonds. We also estimated the Debye temperature and sound velocities of these Ti–Al intermetallic compounds.
where Δp denotes the p-Laplacian on ( − 1, 1), with p > 1, and the function f:[ − 1, 1] × ℝ → ℝ is continuous, and the partial derivative fv exists and is continuous and bounded on [ − 1, 1] × ℝ. It will be shown that (under certain additional hypotheses) the ‘principle of linearized stability’ holds for equilibrium solutions u0 of (1). That is, the asymptotic stability, or instability, of u0 is determined by the sign of the principal eigenvalue of a suitable linearization of the problem (1) at u0. It is well-known that this principle holds for the semilinear case p = 2 (Δ2 is the linear Laplacian), but has not been shown to hold when p ≠ 2.
We also consider a bifurcation type problem similar to (1), having a line of trivial solutions. We characterize the stability or instability of the trivial solutions, and the bifurcating, non-trivial solutions, and show that there is an ‘exchange of stability’ at the bifurcation point, analogous to the well-known result when p = 2.
In this paper, I argue that a new principle of background justice should be added to Rawls’s Law of Peoples because climate change is an international and intergenerational problem that can destabilize the Society of Peoples and the well-ordered peoples therein. I start with explaining the nature of my project and Rawls’s conception of stability. I argue that climate change poses a realistic threat to the stability of climate-vulnerable liberal peoples and as a result undermines international peace and security. Despite the uncertainties due to the complexity of the climate system and about the resilience of liberal societies, liberal peoples’ fundamental interests in just basic institutions and national security call for the adoption of a precautionary principle. Rawls’s own principles are, I argue, inadequate to solve the stability problem from climate change. Still, his framework provides the theoretical resources to develop a new extension. I propose a new Rawlsian principle of international, intergenerational justice that guarantees the environmental background conditions under which well-ordered peoples can sustain their basic structure over generations and sketch the principle’s institutional implementation. I conclude with the theoretical and practical significance of this extension of Rawls’s theory.
The stability of a system is discussed in terms of the curvature of entropy as a function of internal energy and volume, then in terms of internal energy as a function of entropy and volume. Global and local conditions are given. The most difficult mathematical developments are differed to worked solutions and exercices. This analysis introduces the notion that phase diagrams may contain regions where distinct phases coexist. The slope of phase coexistence lines are deduced from thermodynamic principles and give the Clausius-Clapeyron formula. Equilibrium between coexisting phases is shown to imply the Gibbs phase rule which gives the number of degrees of freedom of a system in terms of the number of substances and phases present in the system. The van der Waals equation of state is discussed. In the worked solutions, a model is presented for a concrete case of phase coexistence, and observations from every day life are analysed, such as the melting temperature of salt water or the gas pressure of a bottle containing liquid in which gas is dissolved.
A class of graphs is bridge-addable if given a graph
in the class, any graph obtained by adding an edge between two connected components of
is also in the class. The authors recently proved a conjecture of McDiarmid, Steger, and Welsh stating that if
is bridge-addable and
is a uniform
-vertex graph from
is connected with probability at least
. The constant
is best possible, since it is reached for the class of all forests.
In this paper, we prove a form of uniqueness in this statement: if
is a bridge-addable class and the random graph
is connected with probability close to
is asymptotically close to a uniform
-vertex random forest in a local sense. For example, if the probability converges to
converges in the sense of Benjamini–Schramm to the uniformly infinite random forest
. This result is reminiscent of so-called “stability results” in extremal graph theory, the difference being that here the stable extremum is not a graph but a graph class.
The investigation of personality using the Rorschach Method has been historically established, however, its proper use requires continuous study, especially in regard to reliability, validity and normative references. This study’s objective was to verify stability indicators of Rorschach (French Approach) through a reassessment (after 15 years) of non-patient adults previously addressed in the normative study by Pasian (1998). A total of 88 adults, aged between 34 and 69 years old, of both sexes, with different socio-economic and educational levels, were reassessed in 2013 in the state of São Paulo, Brazil. The responses were independently rated by different judges, with adequate precision. The average results obtained collected in 1998 and 2013 were analyzed to determine if these two sets of data were significantly different from each other (Student’s t test, p ≤ .05) and the following variables were compared: Productivity indices, Apprehension Modes/Location, Formal Quality, Determinants, Contents and Banality. The overall stability level in these variables is considerable (mean r = .28, ± SD = 0.21). We discuss the theoretical approach of the Rorschach method regarding structural aspects of personality and developmental issues in personality assessment.
We study a class of parabolic equations which can be viewed as a generalized mean curvature flow acting on cylindrically symmetric surfaces with a Dirichlet condition on the boundary. We prove the existence of a unique solution by means of an approximation scheme. We also develop the theory of asymptotic stability for solutions of general parabolic problems.
In this paper, we study a two-component Lotka–Volterra competition systemon a one-dimensional spatial lattice. By the comparison principle, together with the weighted energy, we prove that the traveling wavefronts with large speed are exponentially asymptotically stable, when the initial perturbation around the traveling wavefronts decays exponentially as
$j\,+\,ct\,\to \,-\,\infty $
, but the initial perturbation can be arbitrarily large on other locations. This partially answers an open problem by J.-S. Guo and C.-H.Wu.
is an arbitrary function and
satisfies a certain condition.