On monotone method for first and second order periodic boundary value problems and periodic solutions of functional differential equations

AbstractIn this paper, we show that the method of monotone iterative technique is valid to obtain two monotone sequences that converge uniformly to extremal solutions of first and second order periodic boundary value problems and periodic solutions of functional differential equations. We obtain some new results relative to the lower solution α and upper solution β with α⩽β

Erratum: Low-energy photon and pion scattering in holographic QCD

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Distributionally robust optimization for virtual power plant clusters considering carbon emission-based dynamic dispatch priority

A virtual power plant (VPP) is an effective way to manage distributed energy resources. Virtual power plant cluster (VPPC) is constructed due to the increasing number of VPPs. It has great potential in carbon emission reduction through coordination between VPPs. Therefore, a dynamic dispatch priority model is proposed. The model adjusts the dispatch sequence of VPPs based on carbon emissions. The higher the carbon emissions, the lower the dispatch priority. The VPPC participates in carbon trading and the carbon trading cost is included in the optimization objective. There are still many uncontrolled distributed energy resources, e.g., wind power, out of the VPPC. The distributionally robust optimal method is used to deal with the uncertainty of wind power. Finally, this paper proposes a two-stage distributionally robust optimal model of VPPC considering carbon emission-based dynamic dispatch priority. This model can be solved by the column-and-constraint generation (C&CG) algorithm. A VPPC with four VPPs is used in case studies, which verify the economic benefit and low carbon of the proposed model

Novel Constructions of Mutually Unbiased Tripartite Absolutely Maximally Entangled Bases

We develop a new technique to construct mutually unbiased tripartite absolutely maximally entangled bases. We first explore the tripartite absolutely maximally entangled bases and mutually unbiased bases in $\mathbb{C}^{d} \otimes \mathbb{C}^{d} \otimes \mathbb{C}^{d}$ based on mutually orthogonal Latin squares. Then we generalize the approach to the case of $\mathbb{C}^{d_{1}} \otimes \mathbb{C}^{d_{2}} \otimes \mathbb{C}^{d_{1}d_{2}}$ by mutually weak orthogonal Latin squares. The concise direct constructions of mutually unbiased tripartite absolutely maximally entangled bases are remarkably presented with generality. Detailed examples in $\mathbb{C}^{3} \otimes \mathbb{C}^{3} \otimes \mathbb{C}^{3},$ $\mathbb{C}^{2} \otimes \mathbb{C}^{2} \otimes \mathbb{C}^{4}$ and $\mathbb{C}^{2} \otimes \mathbb{C}^{5} \otimes \mathbb{C}^{10}$ are provided to illustrate the advantages of our approach

Multiple Events of Allopolyploidy in the Evolution of the Racemose Lineages in Prunus (Rosaceae) Based on Integrated Evidence from Nuclear and Plastid Data.

Prunus is an economically important genus well-known for cherries, plums, almonds, and peaches. The genus can be divided into three major groups based on inflorescence structure and ploidy levels: (1) the diploid solitary-flower group (subg. Prunus, Amygdalus and Emplectocladus); (2) the diploid corymbose group (subg. Cerasus); and (3) the polyploid racemose group (subg. Padus, subg. Laurocerasus, and the Maddenia group). The plastid phylogeny suggests three major clades within Prunus: Prunus-Amygdalus-Emplectocladus, Cerasus, and Laurocerasus-Padus-Maddenia, while nuclear ITS trees resolve Laurocerasus-Padus-Maddenia as a paraphyletic group. In this study, we employed sequences of the nuclear loci At103, ITS and s6pdh to explore the origins and evolution of the racemose group. Two copies of the At103 gene were identified in Prunus. One copy is found in Prunus species with solitary and corymbose inflorescences as well as those with racemose inflorescences, while the second copy (II) is present only in taxa with racemose inflorescences. The copy I sequences suggest that all racemose species form a paraphyletic group composed of four clades, each of which is definable by morphology and geography. The tree from the combined At103 and ITS sequences and the tree based on the single gene s6pdh had similar general topologies to the tree based on the copy I sequences of At103, with the combined At103-ITS tree showing stronger support in most clades. The nuclear At103, ITS and s6pdh data in conjunction with the plastid data are consistent with the hypothesis that multiple independent allopolyploidy events contributed to the origins of the racemose group. A widespread species or lineage may have served as the maternal parent for multiple hybridizations involving several paternal lineages. This hypothesis of the complex evolutionary history of the racemose group in Prunus reflects a major step forward in our understanding of diversification of the genus and has important implications for the interpretation of its phylogeny, evolution, and classification

Mutually unbiased maximally entangled bases from difference matrices

Based on maximally entangled states, we explore the constructions of mutually unbiased bases in bipartite quantum systems. We present a new way to construct mutually unbiased bases by difference matrices in the theory of combinatorial designs. In particular, we establish $q$ mutually unbiased bases with $q-1$ maximally entangled bases and one product basis in $\mathbb{C}^q\otimes \mathbb{C}^q$ for arbitrary prime power $q$. In addition, we construct maximally entangled bases for dimension of composite numbers of non-prime power, such as five maximally entangled bases in $\mathbb{C}^{12}\otimes \mathbb{C}^{12}$ and $\mathbb{C}^{21}\otimes\mathbb{C}^{21}$, which improve the known lower bounds for $d=3m$, with $(3,m)=1$ in $\mathbb{C}^{d}\otimes \mathbb{C}^{d}$. Furthermore, we construct $p+1$ mutually unbiased bases with $p$ maximally entangled bases and one product basis in $\mathbb{C}^p\otimes \mathbb{C}^{p^2}$ for arbitrary prime number $p$.Comment: 24 page

Quantum kk-uniform states from quantum orthogonal arrays

The quantum orthogonal arrays define remarkable classes of multipartite entangled states called $k$-uniform states whose every reductions to $k$ parties are maximally mixed. We present constructions of quantum orthogonal arrays of strength 2 with levels of prime power, as well as some constructions of strength 3. As a consequence, we give infinite classes of 2-uniform states of $N$ systems with dimension of prime power $d\geq 2$ for arbitrary $N\geq 5$; 3-uniform states of $N$-qubit systems for arbitrary $N\geq 6$ and $N\neq 7,8,9,11$; 3-uniform states of $N$ systems with dimension of prime power $d\geq 7$ for arbitrary $N\geq 7$.Comment: 26 pages, 1 figure

Antiguo Palacio Gubernamental y Residencia del dignatario Mu en la ciudad Lijiang-Centro de Experiencia de la vida histórico-tradicional.

Debido al desarrollo de la sociedad que conlleva la modernización de las costumbres, en China no se siente un especial aprecio por el conocimiento del patrimonio cultural. Si tomamos como ejemplo la ciudad de Lijiang nos encontramos que aún hay pocos avances en la promoción y gestión del Bien de Interés Cultural a pesar de que el gobierno continúa aumentando los esfuerzos para restaurar y proteger este conjunto histórico. La mayor parte del acervo cultural inmueble se utiliza solamente para que los turistas los vean. En el caso de este trabajo se toma como ejemplo el antiguo Palacio Gubernamental y Residencia del dignatario Mu en la ciudad Lijiang. Se plantea una nueva forma de gestión del desarrollo de este bien inmueble que permita al público conocer más sobre la historia y cultura de este complejo palaciego a través de una serie de actividades lúdicas. Se propone la grabación de vídeos de personas caracterizadas con trajes de la época histórica, espectáculos de teatro sobre la historia de este palacio, concursos con el fin de llegar a un grado mayor de conocimiento de este patrimonio. Sobre la base del análisis de este proyecto también se propone un método de gestión que pueda utilizarse en el desarrollo de otros bienes culturales de todo el país.<br /