Dendriform Structure Research Articles

Silver‐anchored dendrimer efficiently Light‐drive conversion of p‐nitrophenol

AbstractEfficient use of solar energy for photocatalytic organic synthesis and degradation of organic matter is one of the most promising ways to solve energy shortage and environmental pollution. Silver/sulfur‐doped polyimide (Ag/SPI) was successfully prepared by anchoring silver nanoparticles on sulfur doped polyimide with dendriform structure by an open‐loop and closed‐loop method. Through the analysis of the structure, morphology and photoelectric properties by different characteristics, it is found that the anchoring of silver nanoparticles greatly reduces the electron‐hole recombination rate of SPI, and the cyclic stability is relatively good, and the electrons generated by photoexcitation can participate in the reduction of p‐nitrophenol more. Therefore, the activity of degradation of organic pollutants was greatly improved under the irradiation of visible light. At 5 minutes, the degradation rate of p‐nitrophenol reached 100 %, and the only product p‐nitrophenol was generated. The reaction time was 12 times that of SPI without anchored metal particles. The Ag/SPI dual‐function catalyst provides a new idea for the application of p‐nitrophenol wastewater treatment and the conversion of p‐aminophenol and provides a new reference direction for the field of organic wastewater treatment and organic synthesis.

Weak stuffle algebras

Motivated by $q$-shuffle products determined by Singer from $q$-analogues of multiple zeta values, we build in this article a generalisation of the shuffle and stuffle products in terms of weak shuffle and stuffle products. Then, we characterise weak shuffle products and give as examples the case of an alphabet of cardinality two or three. We focus on a comparison between algebraic structures respected in the classical case and in the weak case. As in the classical case, each weak shuffle product can be equipped with a dendriform structure. However, they have another behaviour towards the quadri-algebra and the Hopf algebra structure. We give some relations satisfied by weak stuffle products.

Five new species of Trichoderma from moist soils in China.

Trichoderma isolates were collected from moist soils near a water source in different areas of China. ITS sequences were submitted to MIST (Multiloci Identification System for Trichoderma) and meets the Trichoderma [ITS76] standard. Combined analyses of phylogenetic analyses of both phylograms (tef1-α and rpb2) and morphological characteristics, revealed five new species of Trichoderma, namely Trichodermahailarense, T.macrofasciculatum, T.nordicum, T.shangrilaense and T.vadicola. Phylogenetic analyses showed T.macrofasciculatum and T.shangrilaense belong to the Polysporum clade, T.hailarense, while T.nordicum and T.vadicola belong to the Viride clade. Each new taxon formed a distinct clade in phylogenetic analysis and have unique sequences of tef1-α and rpb2 that meet the Trichoderma new species standard. The conidiation of T.macrofasciculatum typically appeared in white pustules in concentric rings on PDA or MEA and its conidia had one or few distinctly verrucose. Conidiophores of T.shangrilaense are short and rarely branched, phialides usually curved and irregularly disposed. The aerial mycelium of T.hailarense and T.vadicola formed strands to floccose mat, conidiation tardy and scattered in tufts, conidiophores repeatedly rebranching in dendriform structure. The phialides of T.nordicum lageniform are curved on PDA and its conidia are globose to obovoidal and large.

A simplicial complex splitting associativity

We introduce a simplicial object ({Dyckm}m≥0,Fi,Sj) in the category of non-symmetric algebraic operads, satisfying that Dyck0 is the operad of associative algebras and Dyck1 is J.-L. Loday’s operad of dendriform algebras. The dimensions of the operad Dyckm are given by the Fuss-Catalan numbers.Given a family of partially ordered sets P={Pn}n≥1 we show that, under certain conditions, the vector space spanned by the set of m-simpleces of P is a Dyckm algebra. This construction, applied to certain combinatorial Hopf algebras, whose associative product comes from a dendriform structure, provides examples of Dyckm algebras.

Shuffle-Compatible Permutation Statistics II: The Exterior Peak Set

This paper is a continuation of the work "Shuffle-compatible permutation statistics" by Gessel and Zhuang (but can be read independently from the latter). We study the shuffle-compatibility of permutation statistics — a concept introduced by Gessel and Zhuang, although various instances of it have appeared throughout the literature before. We prove that (as Gessel and Zhuang have conjectured) the exterior peak set statistic (Epk) is shuffle-compatible. We furthermore introduce the concept of an "LR-shuffle-compatible" statistic, which is stronger than shuffle-compatibility. We prove that Epk and a few other statistics are LR-shuffle-compatible. Furthermore, we connect these concepts with the quasisymmetric functions, in particular the dendriform structure on them.

Dual Creation Operators and a Dendriform Algebra Structure on the Quasisymmetric Functions

AbstractThe dual immaculate functions are a basis of the ring QSym of quasisymmetric functions and form one of the most natural analogues of the Schur functions. The dual immaculate function corresponding to a composition is a weighted generating function for immaculate tableaux in the same way as a Schur function is for semistandard Young tableaux; an immaculate tableau is defined similarly to a semistandard Young tableau, but the shape is a composition rather than a partition, and only the first column is required to strictly increase (whereas the other columns can be arbitrary, but each row has to weakly increase). Dual immaculate functions were introduced by Berg, Bergeron, Saliola, Serrano, and Zabrocki in arXiv:1208.5191, and have since been found to possess numerous nontrivial properties.In this note, we prove a conjecture of M. Zabrocki that provides an alternative construction for the dual immaculate functions in terms of certain “vertex operators”. The proof uses a dendriform structure on the ring QSym; we discuss the relation of this structure to known dendriformstructures on the combinatorial Hopf algebras FQSym andWQSym.

Generalized Prioritized Multicriteria Aggregation

After investigating prioritized multicriteria decision-making or aggregation problems in depth, we reveal that priority relationships among criteria may be incomplete. In a complex and practical multicriteria decision-making problem, the relationships of a pair of criteria can be multiform including priority relationships, except for independence. For such cases, we present a generalized prioritized multicriteria aggregation (GPMA) model with incomplete priority relationships in this paper. First, we elaborate GPMA problems, and describe them by using a dendriform structure after designing a top-to-bottom method to form priority hierarchies according to the given priority relationships. Furthermore, a common process for handling GPMA problems is proposed based on the premeditation that the weights associated with the lower-priority criteria need to be revised according to the satisfaction of the higher-priority criteria. At length, we develop two GPMA operators with respect to the GPMA with strictly and weakly ordered prioritizations, respectively, based on triangular norms, and we verify that both of them are aggregation functions.

Reliability and Sensitivity Analysis of Dendriform Structure

Reliability, sensitivity and correlation of dendriform structure are deeply investigated, respectively. Firstly, reliability of dendriform structures is carried out. Members in the dendriform structures are classified into four types according to their layouts. Wall thickness, external radius, Young's Modulus of members and vertical load are defined as random variables, respectively. Four kinds of performance functions, e.g., maximal nodal deflection, maximal stress, natural frequency and buckling eigenvalue, are taken into consideration. Secondly, sensitivity of above-mentioned four performance functions was presented to identify the effect of different kinds of random variables and different positions of members. Finally, correlations among performance functions are investigated. Numerical results can provide a reference for the design of dendriform structure.

Multi-tree Coding Method (MCM) for drainage networks supporting high-efficient search

River coding method for drainage networks plays an very important role in the physical simulation of river basins. In this study we developed a new river coding method named Multi-tree Coding Method (MCM), which has the following features: (1) it is established on a topological pattern reflecting the dendriform structure of drainage networks; (2) the multi-tree code can be effectively managed by the database to perform convenient topological search toward drainage networks using Structured Query Language (SQL); (3) the multi-tree code does not exhibit digital overflow problems in the computer, thus any resolution and scale drainage networks can easily be coded; and (4) it supports high-efficient search process. A river reach can be directly positioned in a drainage network under MCM, without the complex search process from all river reaches. This feature has great potential to improve the computational performance of basin models. We demonstrate here the efficiency and practicality of MCM by testing it in the Yalu Tsangpo river basin, Tibet. A drainage network with 140,745 digital reaches was extracted from the digital elevation model (DEM), and the multi-tree codes of all river reaches were obtained.

Al 3+-directed self-assembly and their electrochemistry properties of three-dimensional dendriform horseradish peroxidase/polyacrylamide/platinum/single-walled carbon nanotube composite film

A novel general methodology for protein immobilization and third-generation biosensor construction is demonstrated, which involves Al 3+-directed polyacrylamide (PAM) self-assembly into an ordered dendriform structure, easily immobilizing enzymes and nanoparticles. Platinum/single-walled carbon nanotube (Pt/SWCNT) heterojunction nanomaterials were for the first time fabricated via an EDTA-directed synthesis strategy. The Pt/SWCNTs were employed as a supporting matrix to explore a novel immobilization and biosensing platform of redox proteins through cooperating Al 3+-directed PAM self-assembly. Compared with the almost single-layer horseradish peroxidase (HRP)/PAM film electrode, multilayer HRP/PAM/Pt/SWCNT film electrode exhibited a pair of much stronger redox peaks at −0.22 V (vs. Ag/AgCl). Moreover, with advantages of the ordered multilayer HRP/PAM/Pt/SWCNT film, facilitated direct electron transfer of the metalloenzymes with an apparent heterogeneous electron transfer rate constant ( k s) of 14.94 ± 1.36 s −1 and smaller peak-to-peak separation (Δ E p) of about 37 mV was acquired on the PAM/Pt/SWCNT-based enzyme electrode. The PAM/Pt/SWCNT-based biosensor demonstrated significant electrocatalytic activity for the reduction of hydrogen peroxide with a small apparent Michaelis–Menten constant (87 μM), wide linear range (1–270 μM), very low detection limit (0.08 μM, S/ N = 3), and high sensitivity (372 mA cm −2 M −1). Together, these indicated that the Al 3+-directed HRP/PAM/Pt/SWCNT film was one of ideal candidate materials for direct electrochemistry of redox proteins and the construction of the related enzyme biosensors, and may find potential applications in biomedical, food, and environmental analysis and detection.

A Magnus- and Fer-Type Formula in Dendriform Algebras

We provide a refined approach to the classical Magnus (Commun. Pure Appl. Math. 7:649–673, [1954]) and Fer expansion (Bull. Classe Sci. Acad. R. Belg. 44:818–829, [1958]), unveiling a new structure by using the language of dendriform and pre-Lie algebras. The recursive formula for the logarithm of the solutions of the equations X=1+λ a ≺ X and Y=1−λ Y ≻ a in A[[λ]] is provided, where (A,≺,≻) is a dendriform algebra. Then we present the solutions to these equations as an infinite product expansion of exponentials. Both formulae involve the pre-Lie product naturally associated with the dendriform structure. Several applications are presented.

The fractal structures in highly sulfonated polyaniline

Using transmission electron microscope (TEM), the fractal structures have been found both in the colloid aggregates and in the colloidal particles of highly sulfonated polyaniline. In the present paper, the concept and mathematics model of fractal have been introduced into conjugated polymer. The colloid aggregates appear as an open dendriform structure with fractal dimension 1.43 and its growing process can be simulated by the Diffusion Limited Cluster Aggregate (DLCA) model. The simulated pattern by computer and the theoretic fractal dimension are consistent with the experimental results. Since the colloidal particle is generated in the evenness field formed by the dispersion media, the screening effect has been weakened and the colloidal particle is a spherical structure with fractal dimension 1.86, which is denser than colloid aggregates. The Random Rain (RR) model can be applied here and the simulation pattern and fractal dimension are coincident with the experiment results. So the system can be accounted as multi-fractals structure.