Exact eigenvalue assignment of linear scalar systems with single delay using Lambert W function

Eigenvalue assignment problem of a linear scalar system with a single discrete delay is analytically and exactly solved. The existence condition of the desired eigenvalue is established when the current and delay states are present in the feedback loop. Design of the feedback controller is then followed. Furthermore, eigenvalue assignment for the input-delay system is also obtained as well. Numerical examples illustrate the procedure of assigning the desired eigenvalue

Beauty for the Present: Mill, Arnold, Ruskin and Aesthetic Education

The present thesis examines the idea of aesthetic education of three eminent Victorians: John Stuart Mill, Matthew Arnold and John Ruskin. By focusing on the essence of what they meant with ‘the cultivation of the beautiful’ and, more importantly, the way their ideas of beauty informed their criticism of society, my study aims to contribute to our understanding of the idea of aesthetic education in the Victorian context and, further, to participate in a recent debate about the nature of beauty and aesthetic education. Chapter One focuses on John Stuart Mill’s concept of ‘feeling’ in a series of essays. I will demonstrate how Mill’s idea of ‘aesthetic education’ was an ‘education of feelings,’ and moreover, how this idea was integrated into his literary criticism, his later critique of democratisation, his description of an ideal liberal society and even his own style of writing. Chapter Two contains a comparative study of Matthew Arnold and Friedrich Schiller. Through a rereading of Arnold, I will argue that his idea of aesthetic education is essentially Schillerian and that their resemblance consists primarily in their stress on the importance of aesthetic unity for modern life, which was becoming increasingly fragmentary and multitudinous. Chapter Three examines John Ruskin’s idea of aesthetic education and concentrates particularly on the cultivation of perception. Perception, as I shall show, was pivotal in Ruskin’s idea of aesthetic education. Just as what happened in Mill and Arnold, the emphasis on the education of seeing continued from his early writings well into his art and social criticisms. It not only differentiated him from his fellow art critics; the conviction that people should perceive with a pure heart also enabled him to link observation of artistic details with moral criticism of contemporary society and, thereby, to turn the cultivation of the beautiful into a moral-aesthetic experience

Beyond Minimal Lepton Flavored Dark Matter

We consider a class of flavored dark matter (DM) theories where dark matter interacts with the Standard Model lepton fields at the renormalizable level. We allow for a general coupling matrix between the dark matter and leptons whose structure is beyond the one permitted by the minimal flavor violation (MFV) assumption. It is assumed that this is the only new source of flavor violation in addition to the Standard Model (SM) Yukawa interactions. The setup can be described by augmenting the SM flavor symmetry by an additional $\mathrm{SU}(3)_{\chi}$, under which the dark matter $\chi$ transforms. This framework is especially phenomenologically rich, due to possible novel flavor-changing interactions which are not present within the more restrictive MFV framework. As a representative case study of this setting, which we call "beyond MFV" (BMFV), we consider Dirac fermion dark matter which transforms as a singlet under the SM gauge group and a triplet under $\mathrm{SU}(3)_{\chi}$. The DM fermion couples to the SM lepton sector through a scalar mediator $\phi$. Unlike the case of quark-flavored DM, we show that there is no $\mathbb{Z}_3$ symmetry within either the MFV or BMFV settings which automatically stabilizes the lepton-flavored DM. We discuss constraints on this setup from flavor-changing processes, DM relic abundance as well as direct and indirect detections. We find that relatively large flavor-changing couplings are possible, while the dark matter mass is still within the phenomenologically interesting region below the TeV scale. Collider signatures which can be potentially searched for at the lepton and hadron colliders are discussed. Finally, we discuss the implications for decaying dark matter, which can appear if an additional stabilizing symmetry is not imposed.Comment: 30 pages, 12 figures; minor corrections, added references and discussion on decaying dark matter, matches published versio