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We introduce a formalism for constructing cohomological field theories (CohFT) out of nonlinear PDEs based on the first author's previous work (arXiv:2202.12425). We apply the formalism to the generalized Seiberg-Witten equations and show that the obtained CohFT functionals agree with the existing ones proposed by physicists. This leads to a unified perspective from which to view the full supersymmetric functionals of the Donaldson-Witten, Seiberg-Witten, and Kapustin-Witten theories and understand the relations between them. We also outline a quantization program for our framework and discuss its potential to produce manifold invariants and quantum cohomologies., Comment: 31 pages, 2 figures

Formaldehyde (FA) is widely used in industry and also common in daily life. Finding an efficient method to determine FA is quite an industrial challenge. Herein, a novel method based on a resonance light scattering (RLS) technique was developed for the detection of FA with high sensitivity. Carbon dots (CDs) were used as RLS probes. CDs were obtained via one-pot solvothermal treatment from o-phenylenediamine. CDs showed yellow fluorescence with a quantum yield of 0.41. Due to the multiple amino groups on the surface of CDs, FA can be captured easily by formation of a covalent C = N bond based on the Schiff-base reaction. Owing to the covalent crosslinking, CD nanoparticles aggregated, and even formed precipitate. The aggregation of CDs induced RLS enhancement, where the RLS increment was linearly related to the concentration of FA ranging from 4 nM to 1.6 mM, with a limit of detection (LOD) of 1.6 nM. In comparison with many previous reports, the present RLS method showed a wider linear range and lower LOD. Furthermore, the RLS system was successfully used to detect FA in real food samples. The proposed system has prospective applicability in the detection of FA in food fields.

Formaldehyde (FA) is widely used in industry and also common in daily life. Finding an efficient method to determine FA is quite an industrial challenge. Herein, a novel method based on a resonance light scattering (RLS) technique was developed for the detection of FA with high sensitivity. Carbon dots (CDs) were used as RLS probes. CDs were obtained via one-pot solvothermal treatment from o-phenylenediamine. CDs showed yellow fluorescence with a quantum yield of 0.41. Due to the multiple amino groups on the surface of CDs, FA can be captured easily by formation of a covalent C = N bond based on the Schiff-base reaction. Owing to the covalent crosslinking, CD nanoparticles aggregated, and even formed precipitate. The aggregation of CDs induced RLS enhancement, where the RLS increment was linearly related to the concentration of FA ranging from 4 nM to 1.6 mM, with a limit of detection (LOD) of 1.6 nM. In comparison with many previous reports, the present RLS method showed a wider linear range and lower LOD. Furthermore, the RLS system was successfully used to detect FA in real food samples. The proposed system has prospective applicability in the detection of FA in food fields.

Formaldehyde (FA) is widely used in industry and also common in daily life. Finding an efficient method to determine FA is quite an industrial challenge. Herein, a novel method based on a resonance light scattering (RLS) technique was developed for the detection of FA with high sensitivity. Carbon dots (CDs) were used as RLS probes. CDs were obtained via one-pot solvothermal treatment from o-phenylenediamine. CDs showed yellow fluorescence with a quantum yield of 0.41. Due to the multiple amino groups on the surface of CDs, FA can be captured easily by formation of a covalent C = N bond based on the Schiff-base reaction. Owing to the covalent crosslinking, CD nanoparticles aggregated, and even formed precipitate. The aggregation of CDs induced RLS enhancement, where the RLS increment was linearly related to the concentration of FA ranging from 4 nM to 1.6 mM, with a limit of detection (LOD) of 1.6 nM. In comparison with many previous reports, the present RLS method showed a wider linear range and lower LOD. Furthermore, the RLS system was successfully used to detect FA in real food samples. The proposed system has prospective applicability in the detection of FA in food fields.

Formaldehyde (FA) is widely used in industry and also common in daily life. Finding an efficient method to determine FA is quite an industrial challenge. Herein, a novel method based on a resonance light scattering (RLS) technique was developed for the detection of FA with high sensitivity. Carbon dots (CDs) were used as RLS probes. CDs were obtained via one-pot solvothermal treatment from o-phenylenediamine. CDs showed yellow fluorescence with a quantum yield of 0.41. Due to the multiple amino groups on the surface of CDs, FA can be captured easily by formation of a covalent C = N bond based on the Schiff-base reaction. Owing to the covalent crosslinking, CD nanoparticles aggregated, and even formed precipitate. The aggregation of CDs induced RLS enhancement, where the RLS increment was linearly related to the concentration of FA ranging from 4 nM to 1.6 mM, with a limit of detection (LOD) of 1.6 nM. In comparison with many previous reports, the present RLS method showed a wider linear range and lower LOD. Furthermore, the RLS system was successfully used to detect FA in real food samples. The proposed system has prospective applicability in the detection of FA in food fields.

Formaldehyde (FA) is widely used in industry and also common in daily life. Finding an efficient method to determine FA is quite an industrial challenge. Herein, a novel method based on a resonance light scattering (RLS) technique was developed for the detection of FA with high sensitivity. Carbon dots (CDs) were used as RLS probes. CDs were obtained via one-pot solvothermal treatment from o-phenylenediamine. CDs showed yellow fluorescence with a quantum yield of 0.41. Due to the multiple amino groups on the surface of CDs, FA can be captured easily by formation of a covalent C = N bond based on the Schiff-base reaction. Owing to the covalent crosslinking, CD nanoparticles aggregated, and even formed precipitate. The aggregation of CDs induced RLS enhancement, where the RLS increment was linearly related to the concentration of FA ranging from 4 nM to 1.6 mM, with a limit of detection (LOD) of 1.6 nM. In comparison with many previous reports, the present RLS method showed a wider linear range and lower LOD. Furthermore, the RLS system was successfully used to detect FA in real food samples. The proposed system has prospective applicability in the detection of FA in food fields.

In this paper, we provide the notions of connection $1$-forms and curvature $2$-forms on graphs. We prove a Weitzenb\"ock formula for connection Laplacians in this setting. We also define a discrete Yang-Mills functional and study its Euler-Lagrange equations., Comment: 24 pages,4 figures

In this dissertation, we developed a mathematical framework for cohomological field theories (CohFTs) in the language of ``QK-manifolds', which unifies the previous ones in (Baulieu and Singer 1988; Baulieu and Singer 1989; Ouvry, Stora, and Van Baal 1989; Atiyah and Jeffrey 1990; Birmingham et al. 1991; Kalkman 1993; Blau 1993). Within this new framework, we classified the (gauge invariant) solutions to the descent equations in CohFTs (with gauge symmetries). We revisited Witten’s idea of topological twisting and showed that the twisted super-Poincaré algebra gives rise naturally to a ``QK-structure'. We also generalized the Mathai-Quillen construction of the universal Thom class via a variational bicomplex lift of the equivariant cohomology. Our framework enables a uniform treatment of examples like topological quantum mechanics, topological sigma model, and topological Yang-Mills theory.

In this paper, we provide the notions of connection $1$-forms and curvature $2$-forms on graphs. We prove a Weitzenb\"ock formula for connection Laplacians in this setting. We also define a discrete Yang-Mills functional and study its Euler-Lagrange equations., Comment: 24 pages,4 figures

In this dissertation, we developed a mathematical framework for cohomological field theories (CohFTs) in the language of ``QK-manifolds', which unifies the previous ones in (Baulieu and Singer 1988; Baulieu and Singer 1989; Ouvry, Stora, and Van Baal 1989; Atiyah and Jeffrey 1990; Birmingham et al. 1991; Kalkman 1993; Blau 1993). Within this new framework, we classified the (gauge invariant) solutions to the descent equations in CohFTs (with gauge symmetries). We revisited Witten’s idea of topological twisting and showed that the twisted super-Poincaré algebra gives rise naturally to a ``QK-structure'. We also generalized the Mathai-Quillen construction of the universal Thom class via a variational bicomplex lift of the equivariant cohomology. Our framework enables a uniform treatment of examples like topological quantum mechanics, topological sigma model, and topological Yang-Mills theory.