河北大学

We study the distribution of mesh patterns of length 2 on layered permutations, extending recent work on the distribution of mesh patterns on arbitrary permutations. We classify all mesh patterns of length 2 into exactly 35 equidistribution classes and derive a formula for the distribution of each class. With one exception, the corresponding avoidance sequences appear in the Online Encyclopedia of Integer Sequences, revealing connections with the Fibonacci and Tribonacci numbers, certain integer compositions, and restricted words. We also refine several of our enumerative results by jointly tracking five classical permutation statistics: descents, left-to-right maxima and minima, and right-to-left maxima and minima.

In the context of the transition from clean energy to sustainable development, as an emerging low-carbon energy carrier, hydrogen is of crucial importance. The planning of a hydrogenation facility network (HFN) with a reliable hydrogen supply has thus become an important research topic in the field of hydrogen energy provision. This study investigates the planning of the HFN from the perspectives of economic cost and network reliability, under conditions of uncertain hydrogen supply capacity. To address the challenges posed by uncertainty, the renewable energy-powered hydrogen production process is categorized into multiple scenarios. We formulate an ambiguity set using the Kullback-Leibler (KL) divergence and establish ambiguous chance constraints, thereby proposing a novel bi-objective distributionally robust HFN optimization model (DR-HFN). Based on the decision-maker’s preferences in practice, an economic-oriented optimization model and a reliability-oriented optimization model are developed, respectively. Subsequently, a mixed-integer linear programming (MILP) representation is derived from the proposed model to ensure computational tractability. A customized branch-and-cut (BC) algorithm is further designed to enhance the model’s solvability and scalability. Finally, a practical case study conducted in Guangdong Province, China demonstrates that our proposed method can withstand uncertainties in hydrogen supply capacity with a probability of 90%. Moreover, the comparison with the sample average approximation (SAA) method shows that our method only generates a robustness cost of about 0.087% when addressing distributional uncertainty. This further demonstrates that our method is capable of generating high-quality decision solutions while also exhibiting strong robustness and applicability.

The main aim of this paper is to establish a polynomial analogue of (n+1)!Cn=2n(2n−1)!! (with Cn as the n-th Catalan number) in the setting of labeled plane trees and increasing plane trees. This analogue is formulated in terms of improper edges of labeled plane trees and yields explicit formulas for the generating polynomials defined on labeled plane trees refined by improper and proper edges, together with a root-degree refinement for trees rooted at 0. To prove this result, we construct a new involution on labeled plane trees, which implies that the number of improper edges and the number of proper edges are equidistributed over the set of labeled plane trees. We further apply this involution to establish pairwise symmetry properties of multivariable polynomials defined on labeled plane trees involving several classes of leaves and interior vertices. More precisely, certain specializations of these polynomials are invariant under the subgroup of S6 generated by the three disjoint transpositions (12), (34), and (56). As special cases, our results recover the symmetry properties for plane trees and tip-augmented plane trees due to Dong, Du, Ji and Zhang. Finally, via the Koganov–Janson correspondence, improper edges of labeled plane trees correspond bijectively to improper arcs of quasi-Stirling permutations, leading to an explicit formula for the generating function defined on quasi-Stirling permutations refined by improper arcs.

Abstract In this study, magnetic activated carbon (MAC, nano- Fe 3 O 4 loaded activated carbon) was used to assist alkali activated slag to capture CO 2 from the air. Fresh alkali activated slag slurry containing MAC was exposed to an external magnetic field, the MAC particles were attracted and moved to the surface of the specimen, forming a CO 2 capture layer. The characteristics of MAC and the influence of magnetic induced movement of MAC on alkali activated slag were studied. The results show that: (1) MAC has higher pore volume and higher CO 2 adsorption capacity than activated carbon. (2) Higher external magnetic field intensity and higher water/binder ratio result in the higher content of MAC at the outer layer of the specimen. (3) The magnetic induced movement of activated carbon increases the pore volume of alkali activated slag. (4) In an environment with CO 2 concentration of 660 ± 10 ppm , MAC distributed on specimen surfaces significantly increases the CO 2 absorption capacity and compressive strength of alkali activated slag.

Clarifying the grazing effects on the carbon sink function on the Tibetan Plateau is highly important under climate change. Based on parallel carbon flux and meteorological observations in nearby grazing and grazing-excluded alpine meadows, the effects of grazing were studied. The results indicated that gross primary productivity (GPP) was dominated by soil temperature (TS) and soil water content (SWC) in both the grazing and grazing-excluded meadows. During the whole growing season, in both meadows, TS exerted the strongest control effects on GPP, whereas the dominant factor shifted to SWC during the peak growing season. During the early and late stages of the growing season, the dominant factor for GPP shifted from SWC to TS in the grazing meadow, whereas the dominant factor remained SWC in the grazing-excluded meadow. The grazing-excluded meadow showed improved temperature conditions, resulting in a lower sensitivity of GPP to TS. In contrast, the grazing meadow showed better water conditions, leading to a lower sensitivity of GPP to SWC, which might result in stronger resistance to droughts. Proper grazing could improve GPP and shift the sensitivity of GPP to environmental factors, providing implications for the sustainable management of alpine meadows.