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This work is devoted to the hyperbolic sine function (HSF) control-based finite-time bipartite synchronization of fractional-order spatiotemporal networks and its application in image encryption. Initially, the addressed networks adequately take into account the nature of anisotropic diffusion, i.e., the diffusion matrix can be not only non-diagonal but also non-square, without the conservative requirements in plenty of the existing literature. Next, an equation transformation and an inequality estimate for the anisotropic diffusion term are established, which are fundamental for analyzing the diffusion phenomenon in network dynamics. Subsequently, three control laws are devised to offer a detailed discussion for HSF control law's outstanding performances, including the swifter convergence rate, the tighter bound of the settling time and the suppression of chattering. Following this, by a designed chaotic system with multi-scroll chaotic attractors tested with bifurcation diagrams, Poincaré map, and Turing pattern, several simulations are pvorided to attest the correctness of our developed findings. Finally, a formulated image encryption algorithm, which is evaluated through imperative security tests, reveals the effectiveness and superiority of the obtained results. [ABSTRACT FROM AUTHOR]

The Mostar index M o (G) is the sum of absolute values of the differences between n u (e) and n v (e) over all edges e = u v of G, where n u (e) and n v (e) are the number of vertices of G lying closer to vertex u than to vertex v and the number of vertices of G lying closer to vertex v than to vertex u, respectively. In this article, for given cata-condensed hexagonal systems with p hexagons, which have exactly two full-hexagons, we determine the extremal hexagonal system with the greatest Mostar index, and the corresponding formula of Mostar index is given. [ABSTRACT FROM AUTHOR]

Let C k + 1 be a cycle of length k + 1 and C t + 1 be a cycle of length t + 1. A polygon flower with two centers, denoted by F = F (C k + 1 ; P 1 , ... , P k ; C t + 1 ; P k + 1 , ... , P k + t) is obtained by identifying the i th edge of C k + 1 with an edge ei that belongs to an end-polygon of Pi for i = 1 , ... , k , and identifying the j th edge of C t + 1 with an edge ej that belongs to an end-polygon of Pj for j = k + 1 , ... , k + t , where C k + 1 and C t + 1 have a common edge h. In this paper, we determine the order of sandpile group S(F) of F, which can be viewed as generalized of results in paper (Haiyan Chen, Bojan Mohar. The sandpile group of a polygon flower. Discrete Applied Mathematics, 2019). Moreover, the formula and structure for sandpile group of polygon flower can be obtained. Finally, as application of our result, we also present the sandpile group of cata-condensed system with two branched hexagons. [ABSTRACT FROM AUTHOR]

Let G be a simple connected graph with vertex set V(G) and edge set E(G) that admits a perfect matching M. A forcing set of M is a subset of M contained in no other perfect matchings of G. The minimum cardinality of forcing sets is the forcing number of M. A complete forcing set of G, recently introduced by Xu et al. [Complete forcing numbers of catacondensed hexagonal systems, J. Combin. Optim. 29(4) (2015) 803-814], is a subset S of E(G) on which the restriction of any perfect matching M of G is a forcing set of M. A complete forcing set of the smallest cardinality is called a minimum complete forcing set, and its cardinality is the complete forcing number of G, denoted by cf(G). In this paper, we present the complete forcing sets and complete forcing number of random multiple hexagonal chains. [ABSTRACT FROM AUTHOR]

Phenolic acids are the major secondary metabolites and significant bioactive constituents of the medicinal plant Salvia miltiorrhiza. Many enzyme-encoding genes and transcription factors involved in the biosynthesis of phenolic acids have been identified, but the underlying post-translational regulatory mechanisms are poorly understood. Here, we demonstrate that the S. miltiorrhiza Kelch repeat F-box protein SmKFB5 physically interacts with three phenylalanine ammonia-lyase (PAL) isozymes and mediates their proteolytic turnover via the ubiquitin-26S proteasome pathway. Disturbing the expression of SmKFB5 reciprocally affected the abundance of SmPAL protein and the accumulation of phenolic acids, suggesting that SmKFB5 is a post-translational regulator responsible for the turnover of PAL and negatively controlling phenolic acids. Furthermore, we discovered that treatment of the hairy root of S. miltiorrhiza with methyl jasmonate suppressed the expression of SmKFB5 while inducing the transcription of SmPAL1 and SmPAL3. These data suggested that methyl jasmonate consolidated both transcriptional and post-translational regulation mechanisms to enhance phenolic acid biosynthesis. Taken together, our results provide insights into the molecular mechanisms by which SmKFB5 mediates the regulation of phenolic acid biosynthesis by jasmonic acid, and suggest valuable targets for plant breeders in tailoring new cultivars. [ABSTRACT FROM AUTHOR]

A forcing set of a perfect matching M of a graph G is a subset of M contained in no other perfect matchings of G. A global forcing set of G, introduced by Vukičević et al., is a subset of E(G) on which there are distinct restrictions of any two different perfect matchings of G. Combining the above"forcing" and "global" ideas, Xu et al. [Journal of Combinatorial Optimization 29, no. 4 (2015): 803–14] introduced a complete forcing set of G defined as a subset of E(G) on which the restriction of any perfect matching M of G is a forcing set of M. The minimum cardinality of complete forcing set is the complete forcing number of G. In this paper, we give the explicit expressions for the complete forcing numbers of several classes of spiro hexagonal systems. Moreover, we also discuss some propositions of spiro cata-condensed hexagonal system with perfect matching related to the concept of forcing numbers. [ABSTRACT FROM AUTHOR]