京都大学 / 0048 / 新制・論文博士 / 博士(理学) / 乙第13201号 / 論理博第1560号 / 新制||理||1635(附属図書館) / 京都大学大学院理学研究科数学・数理解析専攻 / (主査)教授 宍倉 光広, 教授 泉 正己, 教授 國府 寛司 / 学位規則第4条第2項該当 / Doctor of Science / Kyoto University / DFAM

Masks have become an important part of everyday life, protecting both the wearer and individuals nearby from the spread of infectious diseases, most notably severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), the coronavirus that causes coronavirus disease 2019 (COVID-19). However, these masks are easily contaminated, whether through continued use or by the wearer touching the mask fabric with contaminated hands, therefore reducing the efficacy and exposing the user to these contagions. When the mask becomes contaminated, it can be discarded, which produces large amounts of waste that will end up in a landfill, or it can be washed, which is costly, wasteful, and time consuming. Our solution to this problem is a mask apparatus that can sanitize itself quickly on demand. The user wears the shell, which contains the fully retracted mask, on a string like they would a necklace. When the mask is required, it is easily pulled out of the shell and can be worn for as long as the user needs it. When it is safe to remove the mask, the user simply pushes a button and the mask retracts back into the shell, where it is then sanitized for the next use. The design of the apparatus features a retractable cloth mask that is sanitized using ultraviolet-C (UVC) radiation while confined safely within an outer shell, minimizing unwanted exposure to the wearer. UVC radiation at wavelength 222 nm has been shown to destroy the outer shell of coronaviruses similar to SARS-CoV-2, inactivating 99.9% of the virus when exposed at a dosage of 2 mJ/cm2. The 28 light-emitting diode (LED) lamps used in this prototype produce this specified wavelength UVC and are separated into 4 strips located in different locations within the shell. Glass rods were used within the shell to guide the mask fabric into a zig-zag shape when fully retracted to maximize exposure to the UVC. To further reduce waste, two lithium-ion rechargeable batteries were used as the power supply for the lamps. The efficacy of this design for inactivating the SARS-CoV-2 coronavirus on the mask was determined indirectly using nano membrane UV sensors placed on the mask fabric, showing that the specified wavelength of UVC radiation can be applied for the required time on all surfaces of the mask. This mask apparatus can directly benefit both front-line healthcare workers as well as individuals going about their daily lives by eliminating pathogens present on their masks, therefore reducing the spread of deadly infectious diseases.

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A minimal covering of a graph G with isomorphic copies of graph H is a set {H1, H2, H3, ... , Hn} where Hi is isomorphic to H, the vertex set of Hi is a subset of G, the edge set of G is a subset of the union of Hi's, and the cardinality of the union of Hi's minus G is minimum. Some studies have been made of covering the complete graph in which case an added condition of the edge set of Hi is the subset of the edge set of G for all i which implies no additional restrictions. However, if G is not the complete graph, then this condition may have implications. We will give necessary and sufficient conditions for minimal coverings of complete bipartite graph with 6-cycles, which we call minimal unrestricted coverings. We also give necessary and sufficient conditions for minimal coverings of the complete bipartite graph with 6-cycles with the added condition the edge set of Hi is a subset of G for all i, and call these minimal restricted coverings.

In this thesis, we consider packings and coverings of various complete graphs with the 4-cycle with a pendant edge. We consider both restricted and unrestricted coverings. Necessary and sufficient conditions are given for such structures for (1) complete graphs Kv, (2) complete bipartite graphs Km,n, and (3) complete graphs with a hole K(v,w).

Let H be the Hawaiian Earring, and let H denote its fundamental group. Assume (Bi) is an inverse system of bouquets of circles whose inverse limit is H. We give an explicit bijection between finite normal covering spaces of H and finite normal covering spaces of Bi. This bijection induces a correspondence between a certain family of inverse sequences of these covering spaces. The correspondence preserves the inverse limit of these sequences, thus offering two methods of constructing the same limit. Finally, we characterize all spaces that can be obtained in this fashion as a particular type of fibrations of H.

In the Swedish labor market the immigrant, compared to the native individual, is seen to experience both stigma and discrimination to a bigger degree. This in turn generates some immigrants to have a negative experience correlated to the Swedish worklife in consideration to the unfair treatment in the recruitment process. In this study we investigate the experiences of women from Syria in consideration to their experiences of stigma and discrimination in the Swedish labor market. We have conducted a qualitative study in the form of semi-qualitative interviews with a total of six Syrian migrated women as a measure to gather the women's experience in search for common or shared experiences of discrimination or injustice taking place in the Swedish labor market. Our data analysis is based on three occurring themes where we linked our empirical evidence to former research done in the field, also to relevant theories presented by sociologists investigating the subject of stigma. The study's results show that all women shared the common experience of discrimination and stigma in consideration to the hiring process in the Swedish labor market. Different factors such as their cultural background, language skills, their physical appearance and name were also of importance. / På den svenska arbetsmarknaden tycks invandraren, jämfört med den infödda, uppleva både stigmatisering och diskriminering i högre grad. Detta leder i sin tur till att vissa invandrare får en negativ upplevelse kopplat till det svenska arbetslivet med hänsyn till orättvis behandling i rekryteringsprocessen. I denna studie undersöker vi erfarenheterna av kvinnor från Syrien med hänsyn till deras erfarenheter av stigma och diskriminering på den svenska arbetsmarknaden. Vi har genomfört en kvalitativ studie i form av semi-kvalitativa intervjuer med totalt sex syriska migrerande kvinnor som en insats för att samla kvinnornas erfarenheter i sökandet efter gemensamma eller delade erfarenheter av diskriminering eller orättvisor som äger rum på den svenska arbetsmarknaden. Vår dataanalys är baserad på tre förekommande teman där vi kopplat våra empiriska bevis till tidigare forskning gjord på området, även till relevanta teorier som presenterats av sociologer som undersökt ämnet stigma. Studiens resultat visar att samtliga kvinnor delade en gemensam erfarenhet av diskrimineringoch stigma i hänsyn till anställningsprocessen på den svenska arbetsmarknaden. Olika faktorer såsom deras kulturella bakgrund, språkkunskaper, deras fysiska utseende och namn var också av betydelse.

A configuration space is a space whose points represent the possible states of a given physical system. As such they appear naturally both in theoretical physics and technical applications. For an example of the former, in analytical mechanics, the Lagrangian and Hamiltonian formulations of classical mechanics depend heavily on the use of a physical system’s configuration space for the description of its kinematical and dynamical behavior, and importantly, its evolution in time. As an example of a technical application, consider robotics, where the space of possible configurations of the mechanical linkages that make up a robot is an important tool in motion planning. In this case it is of particular interest to study the singularities of these mechanical linkages, to see if a given configuration is singular or not. This can be done with the help of configuration spaces and their topological properties. Arguably, the simplest configuration space possible arises when the system is just a collection of point-like particles in a plane. Despite its simplicity, the corresponding configuration space has substantial complexity and is of great interest in mathematics, physics and technology: For instance, it arises naturally in the mathematical modelling of robots performing tasks in a warehouse. In this thesis we go through the mathematics necessary to study the behaviour of paths in this space, which corresponds to motions of the particles. We use the theory of groups, algebraic topology, and manifolds to examine the properties of the configuration space of point-like particles in a plane. An important role in the discussion will be played by braids, which are certain collections of curves, interlaced in three-space. They are connected to many different topics in algebra, geometry, and mathematical physics, such as representation theory, the Yang-Baxter equation and knot theory. They are also important in their own right. Here we focus on their relation to configurations of points.

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