Abstract: Aim of this chapter is analytical representation of one wide class of geometric figures (lines, surfaces and bodies) and their complicated displacements. The accurate estimation of physical characteristics (such as volume, surface area, length, or other specific parameters) relevant to human organs is of fundamental importance in medicine. One central idea of this article is, in this respect, to provide a general methodology for the evaluation, as a function of time, of the volume and center of gravity featured by moving of one class of bodies used of describe different human organs.

Abstract: The low-pressure hollow cathode discharge made of a hollow circular tube and an anode is a type of simple structure discharge system. In particular, under the arc discharge mode, hollow cathodes have high plasma density and energy density with a wide range of adaptability of pressure and current. Low-pressure hollow cathode arc (HCA) discharges have been widely used as plasma sources in various fields such as manufacturing, vacuum welding, and aerospace since the 1960s. Despite the early experimental and applied researches on low-pressure HCA discharges, the basic theoretical study was relatively lagged much behind, resulting in many unanswered questions, such as the optimal discharge operating parameters, the power deposition inside the cathode, the causes of plasma instability, and how to effectively reduce cathode erosion and so on. Due to the special discharge structure of the hollow cathode, it is difficult to make an accurate experimental diagnosis, so a reasonable numerical simulation is an effective study method. However, up to now, there is still a lack of complete and effective numerical models which can evaluate various physical fields in the low-pressure hollow cathode discharges. To address the above problems and difficulties, a comprehensive and self-consistent 2D multi-physical coupling numerical model based on a commercial program of finite element method, the COMSOL Multiphysics, was provided in this paper. The model involves plasma transport, arc flow and heat transfer, and cathode thermal equilibrium, and can consider the effect of an applied magnetic field. The processes of secondary electron emission, thermal-field electron emission, ions and backflow high-energy electrons bombardment, and thermal radiation from the cathode surface are considered in the cathode thermal equilibrium process. Based on the above background, this paper works from the following aspects： In Chapter 1, the basic concepts of low-pressure HCA discharge including the hollow cathode effect, the basic characteristics, and operation modes were introduced firstly; Secondly, the application fields, development history, and overseas and domestic research status of hollow cathode discharge were reviewed; finally, the problems were presented and the research background was explained, and the research purpose of this paper was clarified. In Chapter 2, a complete and self-consistent numerical model of low-pressure hollow cathode discharge was proposed based on the fundamental theory and assumptions, and the set of control equations and boundary conditions in the model were elaborated. In addition, the electron energy distribution function, the collision processes, the solving tools of this model, and calculation schemes were introduced in detail. Finally, a validation example was given to test the rationality and applicability of the numerical model. In Chapter 3, the fundamental plasma properties of low-pressure hollow cathode arcs were investigated. Firstly, the ion Joule heating effect was studied. The results showed that the temperature distributions of the arc and cathode are only able to approach the experimental measurements after considering the ion Joule heating, which shows that the Joule heating of ions is crucial for the heating of the arc plasma. Secondly, by comparing the radial distribution of electron and ion density inside the cathode, the structure of the cathode sheath could be simulated well using this model. Finally, it was shown that the thermal radiation from the cathode surface is an important cooling mechanism of the cathode and only under higher surface emissivity can balance the larger heat flow given by the plasma to the cathode, and the temperature distribution of the cathode shows a non-monotonic increasing trend and is consistent with the profile of experimental measurement so that the so-called active zone is formed. In Chapter 4, the power deposition in the low-pressure HCA was studied in simulation. Two main aspects were considered: the power deposition into particles (both electrons and heavy particles) and the power deposition onto the cathode. It was found that the deposited power into particles increases with the rise of discharge current, but there is no effect on the total power deposition onto the cathode. In high-density plasmas, Coulomb collisions between electrons and ions also become very important, especially since a portion of the deposition energy on heavy particles comes mainly from the energy transfer from electrons to ions. It was also found that regardless of external parameters, half of the power deposition onto the cathode always comes from the particle contribution, while the other half is the net contribution of heat transfer and cathode radiation. The HCA model also allows the simulation of multiple discharge modes for low-pressure HCA discharges over a wide range of gas flow rates. It was also shown that the discharge operating conditions and the external magnetic field can change the distribution of the particle flow on the cathode wall. In Chapter 5, the ion sputtering erosion process on the cathode was simulated by coupling the HCA numerical model with the moving grid technique. The results showed that the ion sputtering erosion on the cathode depends on the ion flux and the plasma potential near the cathode wall and that their distribution and magnitude jointly determine the erosion morphology of the cathode. It was also found that the location of the most severe erosion on the cathode is located in the region of the densest ion flux on the cathode wall, rather than in the longitudinal correspondence with the central region of the internal positive column (IPC). The external magnetic fields can mitigate the cathode erosion and reduce the erosion depth, but stronger magnetic fields lead to a concentration of current density at the cathode tip, which can enhance erosion slightly at the cathode outlet end. Finally, the conclusions and innovation highlights were summarized, and prospects for future work were discussed.

Abstract: Gielis transformations, with their origin in botany, are used to define square waves and trigonometric functions of higher order. They are rewritten in terms of Chebyshev polynomials. The origin of both, a uniform descriptor and the origin of orthogonal polynomials, can be traced back to a letter of Guido Grandi to Leibniz in 1713 on the mathematical description of the shape of flowers. In this way geometrical description and analytical tools are seamlessly combined.

Abstract: Socially responsible investments can be defined as an investment process that integrates ethical values and environmental protection, improving social conditions, and good governance into a traditional investment decision. This integration is mainly a consequence of the growing importance that investors give to environmental, social, and governance (ESG) criteria, resulting in more sustainable development. Also, in the real estate sector, increased attention is being paid to the contributions made to integrate economic, environmental, and social factors into decisions. The ESG framework looks closely at how companies are managed, and the impact related to their market value. The factors for investors’ focus are summarized as environmental, social, and governance. The term ESG was coined in a 2004 United Nations (UN) report titled “Who Cares Wins,” aimed at raising awareness regarding the importance of environmental, social, and corporate governance issues in financial markets. The ESG criteria’s specific purpose is to guide investors in recognizing sustainable investments without evaluating how sustainable the asset is or the investment value represented by sustainability. It is essential to underline that ESG does not take specific economic interests into account. The rationale behind this apparent gap is that investors investigate the economic aspects before investing. However, by not explicitly linking ESG and economic criteria, attractive investments are often misjudged and not implemented. For example, investments that only show their value in the longer term or indirectly influence value by achieving a higher retention rate among incumbent tenants, reducing or eliminating friction costs. A product–service system (PSS) refers to a market proposition (business model) that builds on a product’s traditional functionality by incorporating additional services. Although services are already offered, the PSS function is to link the service to a product. The service thereby supports the operation of the product and generates additional benefits. It encompasses the integrated solutions of products and services to satisfy customers' needs and generate maximum value. According to Sutanto et al., a PSS is designed to focus on sustainability characterized in three dimensions. 1. The economic dimension 2. The environmental dimension 3. The social dimension When discussing sustainability in this thesis, we use the criteria listed above related to socially responsible investments. The link between PSS and ESG is that a PSS focuses on creating a sustainable system, and ESG makes sustainability more visible to investors. Therefore, when PSS are recognized and implemented in buildings, they must be evaluated using ESG analysis methods. Product-Service Systems (PSS) try to find a way to offer services on top of a product. The product is essentially secondary to the result that is delivered from the services. For example, the modem (product) that a cable company provides will be of secondary importance to the connectivity (service). Alternatively, it will be less critical how heat is made (product) than the intended set point is achieved in the building. PSSs transform the supply of products into services. In doing so, the responsibility shifts from delivering a product (once only) to continuous service delivery. Therefore, it is in the best interest of the service provider to deliver the outcome of the service as efficiently (read: lowest cost) as possible. A direct consequence of this is that the service provider will want to use the product as efficiently as possible and as long as possible to reduce his costs. Therefore, the supplier will also want to recover and maximize the reuse of his product based on the same rationale. A positive impact on the environment and the used raw materials is thus to be expected. The whole process of servitization (transforming products into services) in real estate will positively impact the Economic, Environmental and Social factors. Therefore, demonstrating this proposition is the main objective of this thesis. Smart PSS is the same idea as Product-Service systems but in which the digitization of the services plays a key role. It will be shown that by digitizing services, a broader range can be offered. It will be demonstrated that products that provide services at the building level can, through their interconnectedness, also provide services to external systems (e.g. electricity grid, urban planning, mobility, ...). At the same time, digitizing the products and services will also underpin trust in the systems and allow for proper remuneration. In this PhD, different standard systems in a building, such as the reservation system, the water heater, or the fire detection system, are equipped with additional services. A PSS is often specifically designed to focus on economic, social, and environmental dimensions. These dimensions correspond to the investor’s examination as part of the ESG analysis before investing. As the PSS is often specifically designed to integrate sustainability, there is a close link between the sustainability performance of the PSS and the ESG criteria evaluated by the investor. Throughout the work, the owner is considered to be the user of the building. It is not the case that only an owner-user can generate cash flow. In essence, if they have sufficient rights to the underlying product, any building user can activate services that generate cash flow. In today's market, it is logical that this is viewed in the owner-user context as they will usually choose the products to be installed in larger technical installations. They may have previously used a PSS or choose to move to one. However, a building’s tenant could choose to lease out their meeting rooms if they are not contractually prohibited from doing so since, in practice, contracts have begun to prohibit certain services. For example, rental contracts that actively prohibit renting out a property through platforms such as Airbnb. Thus, the user’s function could potentially impact how the PSS is designed. This work does not explicitly explore the impact of this aspect. The owner-user is assumed throughout this manuscript. The second chapter describes the state of affairs concerning PSSs in a broad framework evolving towards focusing on the real estate sector. After which, in the second chapter, ESG and the link to real estate and how smart real estate (smart buildings) is missing from this evaluation are discussed in more detail. Chapter 3 shows from a fire alarm system, which was extended with an evacuation support system, the usefulness, and the risk of data. Further work was done to demonstrate the added value in terms of Economic, Environmental and Social factors of standard installations in buildings. In Chapter 4, a simple sanitary hot water boiler is extended with a service that allows controlling this boiler according to the status of the electricity grid (surplus or shortage of energy). The supply and demand of energy on the power grid must be equal at all times. By equipping a classic water heater (product) with additional intelligence (service), it becomes possible to adjust the energy use to the grid's needs. The grid operators are prepared to pay for this. This payment can be linked to different energy markets (long term market, spot market, ...). This study looked at the fee that would have to be paid when the adjustment of the energy use can be made instantaneously so that the fee must be settled according to the prices on the imbalance market. In chapter 5, we look at the impact of the service to rent out free spaces as co-working places on a broad market (external to the building), compared to a regular reservation system. By renting out unused workplaces on a broad market, the utilization of the existing patrimony will be higher. The demand for new square meters with the same function will decrease as the supply-demand curve changes, and so will the price. This makes it less interesting to build new buildings. Less construction of new buildings will result in fewer resources being used, which will positively affect the environment. In addition, fewer new buildings with an office function will leave more space for buildings with another function. Also, the city's infrastructure will be less burdened (roads, sewerage, electricity grid,...). In The Hague, the decreasing need for new square meters of office buildings can lead to more space for affordable housing, for which the city has a great need. Chapter 6 will frame the valuation of service as a real options method that gives an impetus to a general valuation methodology to value the flexibility that Smart PSS inherently has. Finally, this thesis demonstrates that (smart) PSSs impact real estate profitability, while positively influencing environmental and social factors. Further research and the limitations of the studies conducted are documented. This PhD concludes that Product-Service systems should break the silos between different stakeholders, resulting in a lower total cost of ownership of buildings in the longer term. This can only be achieved if the valuation of Product-Service systems is done correctly and is recognized by every stakeholder in the real estate process.