Controllability properties for finite dimensional quantum Markovian master equations

Various notions from geometric control theory are used to characterize the behavior of the Markovian master equation for N-level quantum mechanical systems driven by unitary control and to describe the structure of the sets of reachable states. It is shown that the system can be accessible but neither small-time controllable nor controllable in finite time. In particular, if the generators of quantum dynamical semigroups are unital, then the reachable sets admit easy characterizations as they monotonically grow in time. The two level case is treated in detail.Comment: 15 page

Exact Boundary Controllability of a System of Mixed Order with Essential Spectrum

International audienceWe address in this work the exact boundary controllability of a linear hyperbolic system of the form $u^{\prime\prime}+Au=0$ with $u=\left(u_{1},u_{2}\right)^{T}$ posed in $(0,T)\times(0,1)^{2}$. A denotes a self-adjoint operator of mixed order that usually appears in the modelization of a linear elastic membrane shell. The operator A possesses an essential spectrum which prevents the exact controllability from holding uniformly with respect to the initial data $\left(u^{0},u^{1}\right)$. We show that the exact controllability holds by one Dirichlet control acting on the first variable $u_{1}$ for any initial data $\left(u^{0},u^{1}\right)$ generated by the eigenfunctions corresponding to the discrete part of the spectrum of A. The proof relies on a suitable observability inequality obtained by way of a full spectral analysis and the adaptation of an Ingham-type inequality for the Laplacian in two spatial dimensions. This work provides a nontrivial example of a system controlled by a number of controls strictly lower than the number of components. Some numerical experiments illustrate our study

Controllability and optimality in economic stabilisation theory

This thesis is a contribution to the theory of economic policy under certainty, viewed in abstract rather than specific terms. Concern is not for particular applications, such as the debate over monetarism and fiscalism but for theoretical principles. More precisely, the thesis is built around the two fundamental issues of existence and design. By existence is meant the primary ability to stabilise a given economic system; by design, the techniques employed to construct a stabilising policy once existence is assured. This thesis contends, firstly, that the question of existence has been ignored in the theory of dynamic stabilisation; and secondly, that several aspects of dynamic design theory yield profitably to further analysis

A variational approach to approximate controls for system with essential spectrum : Application to membranal arch

We address the numerical approximation of boundary controls for systems of the form $\boldsymbol{y^{\prime\prime}}+\boldsymbol{A_M}\boldsymbol{y}=\boldsymbol{0}$ which models dynamical elastic shell structure. The membranal operator $\boldsymbol{A_M}$ is self-adjoint and of mixed order, so that it possesses a non empty and bounded essential spectrum $\sigma_{ess}(\boldsymbol{A_M})$. Consequently, the controllability does not hold uniformly with respect to the initial data. Thus the numerical computation of controls by the way of dual approachs and gradient methods may fail, even if the initial data belongs to the orthogonal of the space spanned by the eigenfunctions associated with $\sigma_{ess}(\boldsymbol{A_M})$. In that work, we adapt a variational approach introduced in [Pablo Pedregal, \textit{Inverse Problems} (26) 015004 (2010)] for the wave equation and obtain a robust method of approximation. This approach does not require any information on the spectrum of the operator $\boldsymbol{A_M}$. We also show that it allows to extract, from any initial data $(\boldsymbol{y^0},\boldsymbol{y^1})$, a controllable component for the mixed order system. We illustrate these properties with some numerical experiments in the full controllability context as well as a partial controllability one

Contrôlabilité de systèmes gouvernés par des équations aux dérivées partielles

Contrôlabilité de systèmes gouvernés par des équations aux dérivées partiellesControllability of systems governed by partial differential equationsBESANCON-Bib. Electronique (250560099) / SudocSudocFranceF

Proceedings of FORM 2022. Construction The Formation of Living Environment

This study examines the integration of building information modelling (BIM) technologies in operation & maintenance stage in the system of managing real estate that helps to reduce transaction costs. The approach and method are based on Digital Twin technology and Model Based System Engineering (MBSE) approach. The results of the development of a service for digital facility management and digital expertise are presented. The connection between physical and digital objects is conceptualized

A causal model of external marketing research information utilization in British companies

The main objectives of this research are to enhance the academic understanding and managerial practice of the utilization of external marketing research information with special reference to British companies. To achieve these objectives, this thesis proposes a causal model of external marketing research information utilization and tests its hypotheses empirically in British industry. This model builds on and develops existing theoretical and empirical work. The research evolved through three major phases. The first phase of the research was conceptual concerned with demonstrating the practical and theoretical importance of researching the topic of utilization, determining the appropriate perspective to studying it and establishing a valid and reliable framework for its definition and measurement. This part has relied on review of the literature on utilization of information in marketing and other management areas along with available secondary data about the UK market research industry as the institutional context of this research. The second phase of the research was concerned with model building which concentrated on conceptually constructing the proposed causal model. Building the proposed model has drawn on exploratory work undertaken through a series of unstructured in-depth interviews at the outset of the research with key marketing personnel in various British industries, a review of previous similar models in the marketing area, and independent deductive reasoning. Variables thought to have a significant impact on the level and quality of external marketing research information utilization (causality dimension) were identified and classified according to the parties controlling them(controllability dimension).A set of empirically testable hypotheses were derived based on the causal model. The third phase of the research was concerned with empirical analysis, testing the proposed model's hypotheses empirically in a cross sectional context. This stage has involved the design of a structured questionnaire that was subsequently completed by senior marketing executives in 258 British companies. Measurement scales were developed by a combination of advice from further semi-structured interviews and the modification of relevant established scales and the questionnaire was piloted to determine its suitability. Additionally, some secondary data were collected about respondents companies in order to obtain a profile of such organizations. The measures used were generally found to be reliable and valid and multiple regression analysis was used to analyze the data and test the model empirically. The variables that were found to have the most significant impact on the level and quality of utilization were organizational culture, individual decision making style, nonprogrammability of the decision situation, technical quality of the research report, degree of competition, user experience in marketing decision making, exploratory research objectives and quantifiability of research information. The thesis concludes with some theoretical conclusions and policy implications with a view toward improving the academic understanding and managerial pursuit of the process of utilizing external marketing research information in British companies

A causal model of external marketing research information utilization in British companies

The main objectives of this research are to enhance the academic understanding and managerial practice of the utilization of external marketing research information with special reference to British companies. To achieve these objectives, this thesis proposes a causal model of external marketing research information utilization and tests its hypotheses empirically in British industry. This model builds on and develops existing theoretical and empirical work. The research evolved through three major phases. The first phase of the research was conceptual concerned with demonstrating the practical and theoretical importance of researching the topic of utilization, determining the appropriate perspective to studying it and establishing a valid and reliable framework for its definition and measurement. This part has relied on review of the literature on utilization of information in marketing and other management areas along with available secondary data about the UK market research industry as the institutional context of this research. The second phase of the research was concerned with model building which concentrated on conceptually constructing the proposed causal model. Building the proposed model has drawn on exploratory work undertaken through a series of unstructured in-depth interviews at the outset of the research with key marketing personnel in various British industries, a review of previous similar models in the marketing area, and independent deductive reasoning. Variables thought to have a significant impact on the level and quality of external marketing research information utilization (causality dimension) were identified and classified according to the parties controlling them(controllability dimension).A set of empirically testable hypotheses were derived based on the causal model. The third phase of the research was concerned with empirical analysis, testing the proposed model's hypotheses empirically in a cross sectional context. This stage has involved the design of a structured questionnaire that was subsequently completed by senior marketing executives in 258 British companies. Measurement scales were developed by a combination of advice from further semi-structured interviews and the modification of relevant established scales and the questionnaire was piloted to determine its suitability. Additionally, some secondary data were collected about respondents companies in order to obtain a profile of such organizations. The measures used were generally found to be reliable and valid and multiple regression analysis was used to analyze the data and test the model empirically. The variables that were found to have the most significant impact on the level and quality of utilization were organizational culture, individual decision making style, nonprogrammability of the decision situation, technical quality of the research report, degree of competition, user experience in marketing decision making, exploratory research objectives and quantifiability of research information. The thesis concludes with some theoretical conclusions and policy implications with a view toward improving the academic understanding and managerial pursuit of the process of utilizing external marketing research information in British companies