Existence of Solutions for a Non-Autonomous Evolution Equations with Nonlocal Conditions

The existence of mild solutions for non-autonomous evolution equations with nonlocal conditions in Banach space is studied in this article. We obtained the existence of at least one mild solution to the evolution equations by using Krasnoselskii’s fixed point theorem as well as the theory of the evolution family. The interest of this paper is that any assumptions are not imposed on the nonlocal terms and Green’s functions and a new alternative method is applied to prove the existence of mild solutions. The results obtained in this paper may improve some related conclusions on this topic. An example is given as an application of the results.

Square-mean Almost Periodic Solutions to Some Stochastic Evolution Equations

This paper concerns the square-mean almost periodic mild solutions to a class of abstract nonautonomous functional integro-differential stochastic evolution equations in a real separable Hilbert space. By using the so-called ＂Acquistapace–Terreni＂ conditions and the Banach fixed point theorem, we establish the existence, uniqueness and the asymptotical stability of square-mean almost periodic solutions to such nonautonomous stochastic differential equations. As an application, almost periodic solution to a concrete nonautonomous stochastic integro-differential equation is considered to illustrate the applicability of our abstract results.

Review and Study of Some Doubly-Weighted Pseudo-almost Periodic Solutions of Some Partial Evolution Equations

In this work, a characterization of the doubly-weighted Bohr spectrum of an almost periodic function is given. We showed precisely that such a spectrum is either empty or coincides with the Bohr spectrum of that function. Next, we investigate the existence of doubly-weighted pseudo-almost periodic solutions to some classes of non-autonomous partial evolution equations.

Existence of μ-Pseudo Almost Periodic Solutions to Some Classes of Nonautonomous Partial Evolution Equations

In this paper, we use a recent works [5], where the authors provide a new ap-proach for pseudo almost periodic solution under the measure theory, under Acquistpace-Terreni conditions, we make extensive use of interpolation spaces and exponential di-chotomy techniques to obtain the existence of μ-pseudo almost periodic solutions tosome classes of nonautonomous partial evolution equations.

Existence of local stable manifolds for some nondensely defined nonautonomous partial functional differential equations

In this paper,we establish the existence of local stable manifolds for a semi-linear differential equation,where the linear part is a Hille-Yosida operator on a Banach space and the nonlinear forcing term f satisfies the ψ-Lipschitz conditions,where ψ belongs to certain classes of admissible function spaces.The approach being used is the fixed point arguments and the characterization of the exponential dichotomy of evolution equations in admissible spaces of functions defined on the positive half-line.

Phylogenetic Analysis of the Plant-specific Zinc Finger-Homeobox and Mini Zinc Finger Gene Families

Zinc finger-homeodomain proteins （ZHD） are present in many plants; however, the evolutionary history of the ZHD gene family remains largely unknown. We show here that ZHD genes are plant-specific, nearly all intronless, and related to MINI ZINC FINGER （MIF） genes that possess only the zinc finger. Phylogenetic analyses of ZHD genes from representative land plants suggest that non.seed plant ZHD genes occupy basal positions and angiosperm homologs form seven distinct clades. Several clades contain genes from two or more major angiosperm groups, including eudicots, monocots, magnoliids, and other basal angiosperms, indicating that several duplications occurred before the diversification of flowering plants. In addition, specific lineages have experienced more recent duplications. Unlike the ZHD genes, MIFs are found only from seed plants, possibly derived from ZHDs by loss of the homeodomain before the divergence of seed plants. Moreover, the MIF genes have also undergone relatively recent gene duplications. Finally, genome duplication might have contributed substantially to the expansion of family size in angiosperms and caused a high level of functional redundancy/overlap in these genes.

Recent genome duplications facilitate the phenotypic diversity of Hb repertoire in the Cyprinidae

Whole-genome duplications(WGDs)are an important contributor to phenotypic innovations in evolutionary history.The diversity of blood oxygen transport traits is the perfect reflection of physiological versatility for evolutionary success among vertebrates.In this study,the evolutionary changes of hemoglobin(Hb)repertoire driven by the recent genome duplications were detected in representative Cyprinidae fish,including eight diploid and four tetraploid species.Comparative genomic analysis revealed a substantial variation in both membership composition and intragenomic organization of Hb genes in these species.Phylogenetic reconstruction analyses were conducted to characterize the evolutionary history of these genes.Data were integrated with the expression profiles of the genes during ontogeny.Our results indicated that genome duplications facilitated the phenotypic diversity of the Hb gene family;each was associated with species-specific changes in gene content via gene loss and fusion after genome duplications.This led to repeated evolutionary transitions in the ontogenic regulation of Hb gene expression.Our results revealed that genome duplications helped to generate phenotypic changes in Cyprinidae Hb systems.

An angiosperm NLR Atlas reveals that NLR gene reduction is associated with ecological specialization and signal transduction component deletion

Nucleotide-binding leucine-rich-repeat(NLR)genes comprise the largest family of plant disease-resis-tance genes.Angiosperm NLR genes are phylogenetically divided into the TNL,CNL,and RNL subclasses.NLR copy numbers and subclass composition vary tremendously across angiosperm genomes.However,the evolutionary associations between genomic NLR content and ecological adaptation,or between NLR content and signal transduction components,are poorly characterized because of limited genome avail-ability.In this study,we established an angiosperm NLR atlas(ANNA,https://biobigdata.nju.edu.cn/ANNA/)that includes NLR genes from over 300 angiosperm genomes.Using ANNA,we revealed that NLR copy numbers differ up to 66-fold among closely related species owing to rapid gene loss and gain.Interestingly,NLR contraction was associated with adaptations to aquatic,parasitic,and carnivorous life-styles.The convergent NLR reduction in aquatic plants resembles the lack of NLR expansion during the long-term evolution of green algae before the colonization of land.A co-evolutionary pattern between NLR subclasses and plant immune pathway components was also identified,suggesting that immune pathway deficiencies may drive TNL loss.Finally,we identified a conserved TNL lineage that may function independently of the EDS1-SAG101-NRG1 module.Collectively,these findings provide new insights into the evolution of NLR genes in the context of ecological adaptation and genome content variation.