In this study, polypyrrole (PPy) prepared by chemical and electrochemical polymerization was investigated as the electrode of electrochemical supercapacitor (ES). New strategies were developed for the fabrication of nano-structured PPy and PPy based nano-composites, which included discovery of advanced anionic dopants and multi-functional nano-crystals, and development of co-dispersing agents. These methods improved the capacitive performance and cycle stability of PPy electrodes. The results indicated that high material loading and good capacitance retention of PPy was achieved using an electrochemical polymerization method and Ni plaque as the current collectors. Nano-crystalline (CTA)2S2O8 formed by a chemical precipitation method from solutions, containing anionic oxidant (S2O82-) and cationic surfactant (CTA+), could be used as the oxidant to synthesize PPy nano-fibers. We demonstrated that multi-wall carbon nanotubes (MWCNT) can be efficiently dispersed using such nano-crystals. Application of multi-functional nano-crystals is a conceptually new approach for the fabrication PPy coated MWCNT. Moreover, safranin and malachite green were found as universal dispersing and charging agents for cataphoretic deposition of graphene, MWCNT and PPy nano-fibers. It opens new strategies in colloidal and electrochemical processing of PPy nano-composites for ES electrodes. PPy coated MWCNT, prepared by the multi-functional nano-crystals (CTA)2S2O8, was employed for the fabrication of N-doped activated carbon-coated MWCNT (N-AC-MWCNT). The obtained N-AC-MWCNT was uniformly coated and possessed with high surface area. The use of N-AC-MWCNT enabled the fabrication of ES electrodes with high mass loading and high active material to current collector mass ratio. Symmetric and asymmetric ES cells, fabricated by N-AC-MWCNT and aqueous Na2SO4 electrolyte, showed high specific capacitance, good capacitance retention and large voltage window. The positive electrode of asymmetric ES, MnO2 coated MWCNT, was successfully prepared by the chemical reaction between KMnO4 and N-AC-MWCNT. The problem of degradation of MWCNT was avoided by the use of N-AC as the sacrificial carbon. Significant progress on ES technology has allowed for the development of capacitive dyes removal (CDR) methods using ES devices. In our study, porous carbon materials, N-doped activated carbon coated MWCNT (N-AC-MWCNT) and N-doped activated carbon nano-fibers (N-AC-NF), were developed as the electrodes for CDR applications. The experimental results indicated that capacitive performance of ES cells was influenced by the chemical structure, size, charge-to mass ratio, concentration and redox-active ligands of the dyes. CDR is a promising method for removal of various cationic and anionic dyes, which offers advantages of energy saving and simple electrode regeneration. / Thesis / Doctor of Philosophy (PhD)

We provide a combinatorial interpretation of the frequency of any irreducible representation of Sn in representations of Sn arising from group actions on words. Recognizing that representations arising from group actions naturally split across orbits yields combinatorial interpretations of the irreducible decompositions of representations from similar group actions. The generalization from group actions on words to group actions on matrices gives rise to representations that prove to be much less transparent. We share the progress made thus far on the open problem of determining the irreducible decomposition of certain representations of Sm × Sn arising from group actions on matrices.

In 2020, Huh, Matherne, Mészáros, and St. Dizier established the Lorentzian property of normalized Schur polynomials and conjectured the Lorentzian nature of other Schur-type symmetric polynomials. More recently in 2022, Matherne, Morales, and Selover proved that chromatic symmetric functions of indifference graphs of abelian Dyck paths are Lorentzian. In this thesis, we study the more general class of Lorentzian polynomials that is also invariant under the standard permutation action on variables. Throughout this work, we give exposition to the classical theory of symmetric polynomials and Lorentzian polynomials. Then we present several fundamental results on symmetric Lorentzian polynomials and highlight potential avenues for future research. / År 2020 bevisade Huh-Matherne-Mészáros-St.Dizier att normaliserade schur polynom är lorentziska och antog att andra symmetriska polynom av Schur-typ också är det. År 2022 bevisade Matherne-Morales-Selover att kromatiska symmetriska funktioner för indifferensgrafer av abeliska Dyck-paths är lorentziska. Motiverade av dessa resultat studerar vi den mer allmänna klassen av lorentziska polynom som också är invarianta under standardpermutationsverkan på variabler. I avhandlingen ger vi några grundläggande resultat om symmetriska lorentziska polynom och pekar på möjliga framtida riktningar.

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