Proving a conjecture on the upper bound of semistrong chromatic indices of graphs

Let $G=(V(G), E(G))$ be a graph with maximum degree $\Delta$. For a subset $M$ of $E(G)$, we denote by $G[V(M)]$ the subgraph of $G$ induced by the endvertices of edges in $M$. We call $M$ a semistrong matching if each edge of $M$ is incident with a vertex that is of degree 1 in $G[V(M)]$. Given a positive integer $k$, a semistrong $k$-edge-coloring of $G$ is an edge coloring using at most $k$ colors in which each color class is a semistrong matching of $G$. The semistrong chromatic index of $G$, denoted by $\chi'_{ss}(G)$, is the minimum integer $k$ such that $G$ has a semistrong $k$-edge-coloring. Recently, Lu\v{z}ar, Mockov\v{c}iakov\'a and Sot\'ak conjectured that $\chi'_{ss}(G)\le \Delta^{2}-1$ for any connected graph $G$ except the complete bipartite graph $K_{\Delta,\Delta}$. In this paper, we settle this conjecture by proving that each such graph $G$ other than a cycle on $7$ vertices has a semistrong edge coloring using at most $\Delta^{2}-1$ colors.Comment: 20 pages, 9 figure

Spin-dependent Rotating Wigner Molecules in Quantum dots

The spin-dependent trial wave functions with rotational symmetry are introduced to describe rotating Wigner molecular states with spin degree of freedom in four- and five-electron quantum dots under magnetic fields. The functions are constructed with unrestricted Hartree-Fock orbits and projection technique in long-range interaction limit. They highly overlap with the exact-diagonalized ones and give the accurate energies in strong fields. The zero points, i.e. vortices of the functions have straightforward relations to the angular momenta of the states. The functions with different total spins automatically satisfy the angular momentum transition rules with the increase of magnetic fields and explicitly show magnetic couplings and characteristic oscillations with respect to the angular momenta. Based on the functions, it is demonstrated that the entanglement entropies of electrons depend on the z-component of total spin and rise with the increase of angular momenta

Aharonov-Bohm phase operations on a double-barrier nanoring charge qubit

We present a scheme for charge qubit implementation in a double-barrier nanoring. The logical states of the qubit are encoded in the spatial wavefunctions of the two lowest energy states of the system. The Aharonov-Bohm phase introduced by magnetic flux, instead of tunable tunnelings, along with electric fields can be used for implementing the quantum gate operations. During the operations, the external fields should be switched smoothly enough to avoid the errors caused by the transition to higher-lying states. The structure and field effects on the validity of the qubit are also studied.Comment: 6 pages, 7 figure

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Master'sMASTER OF SCIENCE (MANAGEMENT

Extended imaginary gauge transformation in a general nonreciprocal lattice

Imaginary gauge transformation (IGT) provides a clear understanding of the non-Hermitian skin effect by transforming the non-Hermitian Hamiltonians with real spectra into Hermitian ones. In this work, we extend this approach to the complex spectrum regime in a general nonreciprocal lattice model. We unveil the validity of IGT hinges on a class of pseudo-Hermitian symmetry. The generalized Brillouin zone of Hamiltonian respect such pseudo-Hermiticity is demonstrated to be a circle, which enables easy access to the continuum bands, localization length of skin modes, and relevant topological numbers. Furthermore, we investigate the applicability of IGT and the underlying pseudo-Hermiticity beyond nearest-neighbour hopping, offering a graphical interpretation. Our theoretical framework is applied to establish bulk-boundary correspondence in the nonreciprocal trimer Su-Schrieffer-Heeger model and analyze the localization behaviors of skin modes in the two-dimensional Hatano-Nelson model.Comment: 16 pages, 6 figure

Analysis of compression/expansion stage on compressed air energy storage cogeneration system

Compressed Air Energy Storage (CAES) technology has risen as a promising approach to effectively store renewable energy. Optimizing the efficient cascading utilization of multi-grade heat can greatly improve the efficiency and overall system performance. Particularly, the number of compressor and expander stages is a critical factor in determining the system’s performance. In this study, we focused on the Advanced Adiabatic Compressed Air Energy Storage system with Combined Heat and Power (AA-CAES -CHP). Both economic and thermodynamic models were established for the AA-CAES-CHP system. To systematically study the effects of compression and expansion stages, the influence of 3 different compressor stages and expander stages was comprehensively analyzed under 4 operating conditions. Key findings reveal that the count of compressor and expander stages have a notable impact on the exergy losses of the AA-CAES-CHP system. As for the investment cost, the proportion of investment cost for expanders decreases when the stage numbers of compressors and expanders are the same. Furthermore, both thermodynamic and economic characteristics allow us to optimize the AA-CAES-CHP system’s performance. One of our cases demonstrates that doubling the air mass flow rate results in a doubled total energy output with a relatively modest increase (41.1%–65.1%) in the total investment cost

Oblique impact breakage unification of nonspherical particles using discrete element method

Particle breakage commonly occurs during processing of particulate materials, but a mechanistic model of particle impact breakage is not fully established. This article presents oblique impact breakage characteristics of nonspherical particles using discrete element method (DEM) simulations. Three different particle shapes, i.e. spherical, cuboidal and cylindrical, are investigated. Constituent spheres are agglomerated with bridging bonds to model the breakage characteristics under impact conditions. The effect of agglomerate shapes on the breakage pattern, damage ratio, and fragment size distribution is fully investigated. By using a newly proposed oblique impact model, unified breakage master surfaces are theoretically constructed for all the particle shapes under oblique impact conditions. The developed approach can be applied to modelling particulate processes where nonspherical particles and oblique impact breakage are prevailing.</p

Homologous haplotypes, expression, genetic effects and geographic distribution of the wheat yield gene TaGW2

BACKGROUND: TaGW2-6A, cloned in earlier research, strongly influences wheat grain width and TKW. Here, we mainly analyzed haplotypes of TaGW2-6B and their effects on TKW and interaction with haplotypes at TaGW2-6A. RESULTS: About 2.9 kb of the promoter sequences of TaGW2-6B and TaGW2-6D were cloned in 34 bread wheat cultivars. Eleven SNPs were detected in the promoter region of TaGW2-6B, forming 4 haplotypes, but no divergence was detected in the TaGW2-6D promoter or coding region. Three molecular markers including CAPS, dCAPS and ACAS, were developed to distinguish the TaGW2-6B haplotypes. Haplotype association analysis indicated that TaGW2-6B has a stronger influence than TaGW2-6A on TKW, and Hap-6B-1 was a favored haplotype increasing grain width and weight that had undergone strong positive selection in global wheat breeding. However, clear geographic distribution differences for TaGW2-6A haplotypes were found; Hap-6A-A was favored in Chinese, Australian and Russian cultivars, whereas Hap-6A-G was preferred in European, American and CIMMYT cultivars. This difference might be caused by a flowering and maturity time difference between the two haplotypes. Hap-6A-A is the earlier type. Haplotype interaction analysis between TaGW2-6A and TaGW2-6B showed additive effects between the favored haplotypes. Hap-6A-A/Hap-6B-1 was the best combination to increase TKW. Relative expression analysis of the three TaGW2 homoeologous genes in 22 cultivars revealed that TaGW2-6A underwent the highest expression. TaGW2-6D was the least expressed during grain development and TaGW2-6B was intermediate. Diversity of the three genes was negatively correlated with their effect on TKW. CONCLUSIONS: Genetic effects, expression patterns and historic changes of haplotypes at three homoeologous genes of TaGW2 influencing yield were dissected in wheat cultivars. Strong and constant selection to favored haplotypes has been found in global wheat breeding during the past century. This research also provides a valuable case for understanding interaction of genes that control complex traits in polyploid species

Epigenetic repression of PDZ-LIM domain-containing protein 2 promotes ovarian cancer via NOS2-derived nitric oxide signaling.

Ovarian cancer constitutes one of the most lethal gynaecological malignancies worldwide and currently no satisfactory therapeutic approaches have been established. Therefore, elucidation of molecular mechanisms to develop targeted therapy of ovarian cancer is crucial. PDLIM2 is critical to promote ubiquitination of nuclear p65 and thus its role in inflammation has been highlighted recently. We demonstrate that PDLIM2 is decreased in both ovarian high-grade serous carcinoma and in various human ovarian cancer cell lines compared with normal ovary tissues and human ovarian surface epithelial cells (HOSE). Further functional analysis revealed that PDLIM2 is epigenetically repressed in ovarian cancer development and inhibition of PDLIM2 promoted ovarian cancer growth both in vivo and in vitro via NOS2-derived nitric oxide signaling, leading to recruitment of M2 type macrophages. These results suggest that PDLIM2 might be involved in ovarian cancer pathogenesis, which could serve as a promising therapeutic target for ovarian cancer patients