On multipliers on compact Lie groups

In this note we announce Lp multiplier theorems for invariant and non-invariant operators on compact Lie groups in the spirit of the well-known Hormander-Mikhlin theorem on Rn and its variants on tori Tn. Applications are given to the mapping properties of pseudo-differential operators on Lp-spaces and to a-priori estimates for non-hypoelliptic operators.Comment: 8 page

Global functional calculus for operators on compact Lie groups

In this paper we develop the functional calculus for elliptic operators on compact Lie groups without the assumption that the operator is a classical pseudo-differential operator. Consequently, we provide a symbolic descriptions of complex powers of such operators. As an application, we give a constructive symbolic proof of the G\r{a}rding inequality for operators in $(\rho,\delta)$-classes in the setting of compact Lie groups.Comment: 23 pages; minor correction

Dispersive estimates for hyperbolic systems with time-dependent coefficients

This paper is devoted to the study of time-dependent hyperbolic systems and the derivation of dispersive estimates for their solutions. It is based on a diagonalisation of the full symbol within adapted symbol classes in order to extract the essential information about representations of solutions. This is combined with a multi-dimensional van der Corput lemma to derive dispersive estimates.Comment: 35 page

The Necessity for Sustainable Development in Indonesia: A Governmental Analysis and Carbon Neutral Coliving Recommendation

This thesis explores two distinct topics: first, Indonesia’s current emissions and implementation of sustainability practices; second, the current state of coliving spaces and a proposal of a sustainable space in Indonesia,. The two topics are connected by the fact that the implementation of sustainability practices within Indonesia are necessary from more than just an environmental standpoint, but also from the economic and governmental perspectives. We exemplify the necessity for sustainable transition within the country through three critical points: first, we show that Indonesia’s exceptional tourist growth is highly dependent on sustaining the natural wonders within the country; second, current coal emissions lead to severe health externalities that are incurred by the Indonesian government; third, we explore the complexity of indigenous rights throughout the many Islands, show how these rights are being compromised by the rise of national sustainability organizations, and suggest a solution that connects more closely with local populations in the fight for sustainability. The discussion, then, shifts towards focusing on the broader coliving trend globally and offers a specific vision for how that ought to be actualized in Indonesia. We begin by outlining the shift away from homeownership to renting and nomadism among Millennials. This trend legitimizes our argument that coliving spaces offer a sustainable alternative to broader living choices and contemporary industrialization within Indonesia. Finally, we conclude with a discussion of the critical components of a sustainable building to underpin the feasibility of implementing such within Indonesia

Physical and mathematical justification of the numerical Brillouin zone integration of the Boltzmann rate equation by Gaussian smearing

Scatterings of electrons at quasiparticles or photons are very important for many topics in solid state physics, e.g., spintronics, magnonics or photonics, and therefore a correct numerical treatment of these scatterings is very important. For a quantum-mechanical description of these scatterings Fermi's golden rule is used in order to calculate the transition rate from an initial state to a final state in a first-order time-dependent perturbation theory. One can calculate the total transition rate from all initial states to all final states with Boltzmann rate equations involving Brillouin zone integrations. The numerical treatment of these integrations on a finite grid is often done via a replacement of the Dirac delta distribution by a Gaussian. The Dirac delta distribution appears in Fermi's golden rule where it describes the energy conservation among the interacting particles. Since the Dirac delta distribution is a not a function it is not clear from a mathematical point of view that this procedure is justified. We show with physical and mathematical arguments that this numerical procedure is in general correct, and we comment on critical points

Signaling Pathways Regulating the Pathophysiological Responses of Astrocytes: A Focus on the IKK/NF-κB System

Astrocytes are highly responsive to changes in their microenvironment, and undergo prominent functional alterations in pathological conditions, a process called astrogliosis. In such conditions, astrocytes can gain immune cell-like functions, form glial scars and promote brain repair and regeneration. However, astrogliosis can also contribute to disease pathogenesis by exacerbating inflammation and perturbing the normal physiological functions of astrocytes. The IKK/NF-κB signaling system is a master regulator of inflammation, cell survival and differentiation, which also controls astrocyte functions, in particular their responses to pathological conditions. Activation of IKK/NF-κB signaling in astrocytes is a key driver of neuroinflammation and astrogliosis, which can interfere with normal brain development and homeostasis and can aggravate various central nervous system (CNS) pathologies. Besides IKK/NF-κB signaling, several other signaling pathways regulate pathophysiological responses of astrocytes, in particular hypertrophy, proliferation and the reactivation of neural stem cell-like properties of astrocytes. Further dissection of the role of these signaling pathways in the control of physiological functions and pathophysiological plasticity of astrocytes will reveal new insights into the pathogenesis of neurological diseases and might indicate new neuroprotective and regenerative therapeutic approaches