We show that the number (Formula presented.) of partitions with m even parts and largest hook length n is strongly unimodal with mode (Formula presented.) for (Formula presented.). We establish this result by inductio...
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The present paper constructs a finite-dimensional observer subject to boundary measurement for a cascaded heat-heat system with different reaction coefficients. The observer design is proposed via the modal decomposit...
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The Euclidean distance matrix (EDM) completion problem has been widely used in molecular conformation, protein structure determination and localization. This problem can be troublesome for many off-the-shelf algorithm...
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We find a positive eI-expansion for the chromatic symmetric function of KPKP graphs, which are graphs obtained by connecting a vertex in a complete graph with a vertex in the maximal clique of a lollipop graph by a pa...
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We establish the e-positivity of cycle-chord graphs by using the composition method which is developed by Zhou and the author recently. Our method is simpler than the (e)-positivity approach which is used for handling...
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We extend the results of [Commun. Partial. Differ. Equ. 44(12), 1431–1465 (2019)] by the third and fourth author globally in time. More precisely, we prove uniform-in-N Strichartz estimates for the solutions $$\phi $...
We extend the results of [Commun. Partial. Differ. Equ. 44(12), 1431–1465 (2019)] by the third and fourth author globally in time. More precisely, we prove uniform-in-N Strichartz estimates for the solutions $$\phi $$ , $$\Lambda $$ and $$\Gamma $$ of a coupled system of Hartree–Fock–Bogoliubov type with interaction potential $$V_N(x-y)=N^{3 \beta }v(N^{\beta }(x-y))$$ for $$\beta <1$$ . The potential v satisfies some technical conditions, but is not small. The initial conditions have finite energy and the “pair correlation” part satisfies a smallness condition, but are otherwise general functions in suitable Sobolev spaces, and the expected correlations in $$\Lambda $$ develop dynamically in time. The estimates are expected to improve the Fock space bounds of [Ann. Henri Poincaré 23(2), 615–673 (2021)] by the first and fifth author. This will be addressed in a subsequent paper.
The present paper addresses a boundary stabilization problem for a cascaded heat-heat system with different reaction coefficients. A sufficient condition about two reaction coefficients of the cascaded model is found ...
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In this short paper, we prove Strichartz estimates for N-body Schrödinger equations in the waveguide manifold setting (i.e. on semiperiodic spaces Rm×Tn where m ≥ 3), provided that interaction potentials ar...
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We develop a composition method to unearth positive eI-expansions of chromatic symmetric functions XG, where the subscript I stands for compositions rather than integer partitions. Using this method, we derive positiv...
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We introduce path-conjoined graphs defined for two rooted graphs by joining their roots with a path, and investigate the chromatic symmetric functions of its two generalizations: spider-conjoined graphs and chain-conj...
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