It is shown that every almost linear Pexider mappings $f$, $g$, $h$ from a unital $C^*$-algebra $\mathcal A$ into a unital $C^*$-algebra $\mathcal B$ are homomorphisms when $f(2^n uy)=f(2^n u)f(y)$, $g(2^n uy)=g(2^nu)g(y)$ and $h(2^n uy)=h(2^n u)h(y)$ hold for all unitaries $u \in \mathcal A$, all $y \in \mathcal A$, and all $n\in \mathbb{Z}$, and that every almost linear continuous Pexider mappings $f$, $g$, $h$ from a unital $C^*$-algebra $\mathcal A$ of real rank zero into a unital $C^*$-algebra $\mathcal B$ are homomorphisms when $f(2^n uy)=f(2^n u)f(y)$, $g(2^n uy)=g(2^n u)g(y)$ and $h(2^n uy)=h(2^n u)h(y)$ hold for all $u \in \lbrace v\in \mathcal A\mid v=v^*\hspace{5.0pt}\text{and}\hspace{5.0pt}v\hspace{5.0pt}\text{is} \text{invertible}\rbrace $, all $y\in \mathcal A$ and all $n\in \mathbb{Z}$. Furthermore, we prove the Cauchy-Rassias stability of $*$-homomorphisms between unital $C^*$-algebras, and $\mathbb{C}$-linear $*$-derivations on unital $C^*$-algebras.
In this paper we investigate the global convergence result, boundedness and periodicity of solutions of the recursive sequence xn+1 = a0xn + a1xn−1 + . . . + akxn−k ⁄ b0xn + b1xn−1 + . . . + bkxn−k , n = 0, 1, . . . where the parameters ai and bi for i = 0, 1, . . . , k are positive real numbers and the initial conditions x−k, x−k+1, . . . , x0 are arbitrary positive numbers.
This paper deals with a multiobjective control problem for nonlinear discrete time systems. The problem consists of finding a control strategy which minimizes a number of performance indexes subject to state and control constraints. A solution to this problem through the Receding Horizon approach is proposed. Under standard assumptions, it is shown that the resulting control law guarantees closed-loop stability. The proposed method is also used to provide a robustly stabilizing solution to the problem of simultaneously minimizing a set of H∞ cost functions for a class of systems subject to bounded disturbances and/or parameter uncertainties. Numeric examples are reported to highlight the stabilizing action of the proposed control laws.
We obtain some sufficient conditions for the existence of the solutions and the asymptotic behavior of both linear and nonlinear system of differential equations with continuous coefficients and piecewise constant argument.
Performance of any machine tool is, under certain technological conditions, limited by chatter, which occurs during machining. The limit between machining without and with chatter is called limit of stability. It is expressed by so called stable depth of cut, which is defíned under certain conditions. The article deals with the investigation of optimal modal parameters for machine tool models. The criterion for this optimum is the highest limit of stability.
Safety monitoring and stability analysis of high slopes are important for high dam construction in mountainous regions or precipitous gorges. Slope stability estimation is an engineering problem that involves several parameters. To address these problems, a hybrid model based on the combination of Genetic algorithm (GA) and Back-propagation Artificial Neural Network (BP-ANN) is proposed in this study to improve the forecasting performance. GA was employed in selecting the best BP-ANN parameters to enhance the forecasting accuracy. Several important parameters, including the slope geological conditions, location of instruments, space and time conditions before and after measuring, were used as the input parameters, while the slope displacement was the output parameter. The results shown that the GA-BP model is a powerful computational tool that can be used to predict the slope stability.
This study deals with uncertainty, stability and robustness in reservoirs operation. These properties of control currently represent a new aspect in the utilization of water resources and their systems in changing conditions. The study is based on the modern control theory of dynamic systems. It also explains the aims and exacting nature of methodical approaches. Instead of analytical methods, simulation models were used for the solution of runoff stability during different flood situations. The flood protection effect of the reservoir was solved on the basis of a set of generated synthetic flood waves. Then, the stability of the runoff was investigated in different hydrological situations. The study concludes that the stability of the runoff from the reservoir is possible to reach only within certain limits, while in a catastrophic flood situation, it is unrealistic. It also concludes that the combination of different flood protection measures is purposeful, e.g. a larger flood-control storage, predischarge, intensification of the hydrometeorological forecast, stream-channel regulation, etc. Finally, the study suggests themes for further investigation in this field. and Studie se zabývá neurčitostí, stabilitou a robustností při operativním řízení nádrží. Tyto vlastnosti řízení se dnes stávají novými hledisky při využívání vodních zdrojů a jejich soustav v měnících se podmínkách. Studie vychází z moderní teorie řízení dynamických systémů, objasňuje její cíle a matematickou náročnost metodických postupů. Místo analytických metod byly ve studii využity pro řešení stability odtoku z nádrží za povodňových situací simulační modely. Ochranný účinek nádrže se řešil variantně na podkladě souborů generovaných syntetických povodňových vln. Stabilita odtoku se tak mohla zkoumat v různých hydrologických situacích. Studie dospěla k závěru, že stabilitu odtoku u vybudovaných nádrží lze zabezpečit zpravidla jen v jistých mezích, v katastrofálních situacích je tento požadavek nereálný. Účelná je tu kombinace různých protipovodňových opatření, např. většího ochranného prostoru nádrže, předvypouštění z nádrže, prohloubení hydrometeorologické předpovědi, úpravy koryta pod nádrží a j. Studie uvádí v závěru náměty na další výzkum v této oblasti.
The second part of the study presents the results of the control stability judgement of the Lipno reservoir in the flood situations. For this solution were used the generated synthetic flood waves. This part is the continuation of the first part with methodology, published in 1/2008 of the JHH. and Tato část studie uvádí výsledky posouzení stability řízení nádrže Lipno za povodňových situací. K tomu byly využity soubory generovaných syntetických povodňových vln. Navazuje na první část s metodickými postupy, publikovanou v č. 1/2008 Journal of Hydrology and Hydromechanics.
The control problem consists of stabilizing a control system while minimizing the norm of its transfer function. Several solutions to this problem are available. For systems in form, an optimal regulator can be obtained by solving two algebraic Riccati equations. For systems described by , either Wiener-Hopf optimization or projection results can be applied. The optimal regulator is then obtained using operations with proper stable rational matrices: inner-outer factorizations and stable projections. The aim of this paper is to compare the two approaches. It is well understood that the inner-outer factorization is equivalent to solving an algebraic Riccati equation. However, why are the stable projections not needed in the state-space approach? The difference between the two approaches derives from a different construction of doubly coprime, proper stable matrix fractions used to represent the plant. The transfer-function approach takes any doubly coprime fractions, while the state-space approach parameterizes such representations and those selected then obviate the need for stable projections.
Background. Previous research on the stability of personal values in the context of life transitions has usually focused on the presence of a single transition. However, life transitions in everyday life occur simultaneously with other life transitions. The aim of this longitudinal study was therefore to identify different trajectories of life transitions in young adults and to compare the stability of their personal values. Method. In the first wave of research, participants were 18-33 years old; in the second wave, they were 29-43 years old (N = 632; 392 women). In both waves, they completed Schwartzʼs Portrait Value Questionnaires (PVQ); in the second wave, they completed the Life History Calendar focusing on the presence of entry into life transitions. Results. Latent class analysis revealed two trajectories: Experienced transitions (people who experienced all observed transitions) and Partially experienced transitions (people who experienced only entry into regular employment and part of them entered cohabitation). Differential stability of personal values occurred in both trajectories. The differences in the stability of values found between the individual trajectories were insignificant, except for personal values universalism and tradition. Although before entry into life transitions, personal values were not significant predictors of belonging to a particular trajectory, after their experiencing people with the Experienced transitions trajectory more often reached lower levels of values associated with openness to change. and Dosavadní výzkum zabývající se stabilitou osobních hodnot v kontextu prožitých životních tranzic se obvykle soustředil na přítomnost jedi-né tranzice. Životní tranzice se však v běžném životě vyskytují zároveň s dalšími životními tranzicemi. Cílem této longitudinální studie byla proto identifikace různých trajektorií životních tranzic u mladých dospělých a srovnání stability jejich osobních hodnot. V první vlně výzkumu měli participanti 18–33 let; v druhé vlně měli 29–43 let (N = 632; 392 žen). V obou vlnách vyplnili Schwartzovy Dotazníky hodnotových portrétů (PVQ); v druhé vlně vyplnili Kalendář historie života zjišťující přítomnost životních tranzic. Analýza latentních tříd odhalila dvě trajektorie: Prožité tranzice (lidé, kteří prožili všechny sledované tranzice) a Částečně prožité tranzice (lidé, kteří prožili vstup do pravidelné-ho zaměstnání a část z nich kohabitaci). Dife-renciální stabilita osobních hodnot se objevila u obou trajektorií. Zjištěné rozdíly v stabilitě hodnot mezi jednotlivými trajektoriemi byly nevýznamné, vyjma osobních hodnot univerza-lismus a tradice. Ačkoli před prožitím životních tranzic nebyly osobní hodnoty významnými prediktory příslušnosti ke konkrétní trajektorii, po jejich prožití lidé s trajektorií Prožité tranzice dosahovali častěji nižší úrovně v hodnotách spo-jených s otevřeností změně.