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Let X be a connected K-complete normal complex space. If for every closed discrete set A in X there exists a family F of holomorphic functions on X such that N(F)=A, then the K-envelope H(X) of hol...

Control system design packages like MATLAB, SICLAB, OCTAVE, etc. have become essential components of both undergraduate and graduate courses in the field of systems and controls. In particular, the most important subject related to control system design in the undergraduate course is the analysis of a nonlinear equation that is based on iterative methods. In this paper, applications of three basic theorems, –implicit function theorem, Newton-Kantorovich theorem, and fixed point theorem– are proposed to be taught in the numerical analysis in the control engineering course. In order to demonstrate the usefulness of these theorems, several important features are discussed. Furthermore, a practice exercise based on the practical control problem is discussed for proving the useful subject of the numerical analysis in the control engineering course in the graduate level.

An incentive Stackelberg game for a class of Markov jump linear stochastic systems with multiple leaders and followers is investigated in this letter. An incentive structure is developed that allows the leader’s Nash equilibrium to be achieved. In the game, the followers are assumed to behave in two ways under the leader’s incentive strategy set. One involves achieving a Pareto-optimal solution, and the other involves achieving Nash equilibrium. Consequently, it can be verified that irrespective of how the followers behave, they can be induced to achieve the leader’s Nash equilibrium by using a corresponding incentive strategy set. It is shown that the incentive strategy set can be obtained by solving the cross-coupled stochastic algebraic Riccati-type equations. As another important contribution, a novel concept of incentive possibility is proposed for a special case. In order to demonstrate the effectiveness of the proposed scheme, a numerical example is solved.

The authors discuss an incentive Stackelberg game with one leader and multiple non-cooperative followers, for a class of discrete-time stochastic systems with an external disturbance. In this game, the leader achieves a team-optimal solution by attenuating the external disturbance under their H ∞ constraint, whereas the followers adopt Nash equilibrium strategies according to the leader's incentive Stackelberg strategy set (declared in advance) while considering the worst-case disturbance. Using our proposed method, we demonstrate that the incentive Stackelberg strategy set can be found by solving a set of matrix-valued equations. Techniques are presented for both the finite- and infinite-horizon cases. In addition, through an academic and a practical numerical examples, we verify the efficacy of the proposed method in providing the incentive Stackelberg strategy set.

The incentive Stackelberg game for a class of Markov jump linear stochastic systems with one leader and multiple non-cooperative followers subjected to the H∞ constraint is investigated. An incentive structure is adopted that allows the leader’s team-optimal solution with the H∞ constraint to be achieved. It is shown that the incentive strategy set can be obtained by solving the cross-coupled stochastic algebraic Riccati-type equations (CCSAREs). In order to demonstrate the effectiveness of the proposed scheme, a numerical example is solved.

An incentive Stackelberg game for a class of Markov jump linear stochastic systems (MJLSS) with multiple leaders and followers under H_∞ constraint is investigated. The main objective is to develop an incentive structure of a two-level hierarchy in which the leaders achieve state feedback Nash equilibrium, attenuating the external disturbance under an H-infinity constraint. On the other hand, followers attain their state feedback Nash equilibrium/Pareto optimality, ensuring incentive Stackelberg strategies of the leaders while considering the worst-case disturbance. As a result, regardless of the behavior of the followers non-cooperative/cooperative, they are induced by the incentive strategy to achieve Nash equilibrium of the leaders. It is shown that the proposed strategy set can be obtained by solving cross-coupled stochastic algebraic Riccati equations (SAREs). Furthermore, as another important contribution, a design of a mode independent incentive strategy set is developed in case the current mode cannot be observed accurately. A simple numerical example demonstrates the existence of the proposed strategy set.

In this paper, an infinite-horizon incentive Stackelberg game with multiple leaders and multiple followers is investigated for a class of linear stochastic systems with H ∞ constraint. In this game, an incentive structure is developed in such a way that leaders achieve Nash equilibrium attenuating the disturbance under H ∞ constraint. Simultaneously, followers achieve their Nash equilibrium ensuring the incentive Stackelberg strategies of the leaders while the worst-case disturbance is considered. In our research, it is shown that by solving some cross-coupled stochastic algebraic Riccati equations (CCSAREs) and matrix algebraic equations (MAEs) the incentive Stackelberg strategy set can be obtained. Finally, to demonstrate the effectiveness of our proposed scheme, a numerical example is solved.

In this paper, H ∞ constraint incentive Stackelberg game for discrete-time stochastic systems is investigated. Unlike the existing ordinary Stackelberg strategy set, an incentive structure in which the team-optimal strategy under the H ∞ constraint is achieved is considered. A strategy set designed by solving a set of stochastic backward difference Riccati equations (SBDREs) is presented. As an important extension, the infinite-horizon case is also discussed. A numerical example demonstrating the effectiveness and usefulness of the proposed strategy set is presented.

[Formula: see text] constraint Pareto optimal strategy for stochastic linear parameter varying (LPV) systems with multiple decision makers is investigated. The modified stochastic bounded real lemma and linear quadratic control (LQC) for the stochastic LPV systems are reformulated by means of linear matrix inequalities (LMIs). In order to decide the strategy set of multiple decision makers, Pareto optimal strategy is considered for each player and the [Formula: see text] constraint is imposed. The solvability conditions of the problem are established from cross-coupled matrix inequalities (CCMIs). The efficiency of the proposed strategy set is demonstrated using a numerical example.

Photoneutron cross sections were measured for the seven stable samarium isotopes ${}^{144,147,148,149,150,152,154}\mathrm{Sm}$ near the neutron threshold with quasi-monochromatic laser-Compton scattering $\ensuremath{\gamma}\phantom{\rule{0.28em}{0ex}}\mathrm{rays}$. Our photoneutron cross sections are found to be low by 20%--37% relative to existing data. The photoneutron data are analyzed with the talys reaction code by considering the Skyrme Hartree-Fock-Bogoliubov (HFB) plus quasiparticle random phase approximation (QRPA) model and the axially symmetric deformed Gogny HFB plus QRPA model of the $E1$ $\ensuremath{\gamma}\text{\ensuremath{-}}\mathrm{ray}$ strength. Using the $\ensuremath{\gamma}\text{\ensuremath{-}}\mathrm{ray}$ strength function constrained by the present photoneutron data, we made a thorough analysis of the reverse $(n,\ensuremath{\gamma})$ cross sections including the radioactive nucleus $^{151}\mathrm{Sm}$ with a half-life of 90 yr. The radiative neutron capture cross section for $^{153}\mathrm{Sm}$ with the half-life of 1.928 d is deduced with the $\ensuremath{\gamma}\text{\ensuremath{-}}\mathrm{ray}$ strength function method.

We formulate and study a strong harmonic structure under which eigenvalues of the Laplacian on a p.c.f. self-similar set are completely determined according to the dynamical system generated by a rational function. We then show that, with some additional assumptions, the eigenvalue counting function ρ(λ) behaves so wildly that ρ(λ) does not vary regularly, and the ratio $$\rho (\lambda )/\lambda ^{d_s /2} $$ is bounded but non-convergent as λϖ∞, whered s is the spectral dimension of the p.c.f. self-similar set.

We consider a general finitely ramified fractal set called a nested fractal which is determined byN number of similitudes. Basic properties of the integrated density of statesN(x) for the discrete Laplacian on the associated nested prefractal are investigated. In particulardN is shown to be purely discontinuous ifM

We work with increasing finite setsV m called pre-gaskets approximating the finite Sierpinski gasket located inR N−1 (N ≥ 3). The eigenvalues of the discrete Laplacian onV m under the Dirichlet and Neumann boundary conditions are completely determined using the decimation method due to Rammal.

Discrete as well as continuum $\ensuremath{\gamma}$-ray energy spectra from the neutron capture by $^{186}\mathrm{Os}$, $^{187}\mathrm{Os}$, and $^{189}\mathrm{Os}$ have been taken for the first time at $5\ensuremath{\leqslant}{E}_{n}\ensuremath{\leqslant}90$ keV by an anti-Compton NaI(Tl) spectrometer. The detection of a weak discrete \ensuremath{\gamma}-ray, about 0.5% of total \ensuremath{\gamma}-ray strength, demonstrates the high sensitivity of the present measurement. The energy spectra enabled us to accurately determine the reaction cross sections with a small systematic uncertainty. Based on the new cross sections, we reestimate on the basis of a careful reaction cross section calculation the correction factor ${F}_{\ensuremath{\sigma}}$ for the neutron capture on the 9.75-keV first excited state in $^{187}\mathrm{Os}$ as a function of stellar temperature, as required to derive the age of the galaxy within the Re-Os chronology.