On the Content of Polynomials Over Semirings and Its Applications

In this paper, we prove that Dedekind-Mertens lemma holds only for those semimodules whose subsemimodules are subtractive. We introduce Gaussian semirings and prove that bounded distributive lattices are Gaussian semirings. Then we introduce weak Gaussian semirings and prove that a semiring is weak Gaussian if and only if each prime ideal of this semiring is subtractive. We also define content semialgebras as a generalization of polynomial semirings and content algebras and show that in content extensions for semirings, minimal primes extend to minimal primes and discuss zero-divisors of a content semialgebra over a semiring who has Property (A) or whose set of zero-divisors is a finite union of prime ideals. We also discuss formal power series semirings and show that under suitable conditions, they are good examples of weak content semialgebras.Comment: Final version published at J. Algebra Appl., one reference added, three minor editorial change

SOME ABSTRACT PROPERTIES OF SEMIGROUPS APPEARING IN SUPERCONFORMAL THEORIES

A new type of semigroups which appears while dealing with $N=1$ superconformal symmetry in superstring theories is considered. The ideal series having unusual abstract properties is constructed. Various idealisers are introduced and studied. The ideal quasicharacter is defined. Green's relations are found and their connection with the ideal quasicharacter is established.Comment: 11 page

New distinguished classes of spectral spaces: a survey

In the present survey paper, we present several new classes of Hochster's spectral spaces "occurring in nature", actually in multiplicative ideal theory, and not linked to or realized in an explicit way by prime spectra of rings. The general setting is the space of the semistar operations (of finite type), endowed with a Zariski-like topology, which turns out to be a natural topological extension of the space of the overrings of an integral domain, endowed with a topology introduced by Zariski. One of the key tool is a recent characterization of spectral spaces, based on the ultrafilter topology, given in a paper by C. Finocchiaro in Comm. Algebra 2014. Several applications are also discussed

Phosphine Oxide Derivative as a Passivating Agent to Enhance the Performance of Perovskite Solar Cells

Defects of metal-halide perovskites detrimentally influence the optoelectronic properties of the thin film and, ultimately, the photovoltaic performance of perovskite solar cells (PSCs). Especially, defect-mediated nonradiative recombination that occurs at the perovskite interface significantly limits the power conversion efficiency (PCE) of PSCs. In this regard, interfacial engineering or surface treatment of perovskites has become a viable strategy for reducing the density of surface defects, thereby improving the PCE of PSCs. Here, an organic molecule, tris(5-((tetrahydro-2H-pyran-2-yl)oxy)pentyl)phosphine oxide (THPPO), is synthesized and introduced as a defect passivation agent in PSCs. The P=O terminal group of THPPO, a Lewis base, can passivate perovskite surface defects such as undercoordinated Pb2+. Consequently, improvement of PCEs from 19.87 to 20.70% and from 5.84 to 13.31% are achieved in n−i−p PSCs and hole-transporting layer (HTL)-free PSCs, respectively

Polarized Growth in the Absence of F-Actin in Saccharomyces cerevisiae Exiting Quiescence

Polarity establishment and maintenance are crucial for morphogenesis and development. In budding yeast, these two intricate processes involve the superposition of regulatory loops between polarity landmarks, RHO GTPases, actin-mediated vesicles transport and endocytosis. Deciphering the chronology and the significance of each molecular step of polarized growth is therefore very challenging.We have taken advantage of the fact that yeast quiescent cells display actin bodies, a non polarized actin structure, to evaluate the role of F-actin in bud emergence. Here we show that upon exit from quiescence, actin cables are not required for the first steps of polarized growth. We further show that polarized growth can occur in the absence of actin patch-mediated endocytosis. We finally establish, using latrunculin-A, that the first steps of polarized growth do not require any F-actin containing structures. Yet, these structures are required for the formation of a bona fide daughter cell and cell cycle completion. We propose that upon exit from quiescence in the absence of F-actin, secretory vesicles randomly reach the plasma membrane but preferentially dock and fuse where polarity cues are localized, this being sufficient to trigger polarized growth

Formin homology 2 domains occur in multiple contexts in angiosperms

BACKGROUND: Involvement of conservative molecular modules and cellular mechanisms in the widely diversified processes of eukaryotic cell morphogenesis leads to the intriguing question: how do similar proteins contribute to dissimilar morphogenetic outputs. Formins (FH2 proteins) play a central part in the control of actin organization and dynamics, providing a good example of evolutionarily versatile use of a conserved protein domain in the context of a variety of lineage-specific structural and signalling interactions. RESULTS: In order to identify possible plant-specific sequence features within the FH2 protein family, we performed a detailed analysis of angiosperm formin-related sequences available in public databases, with particular focus on the complete Arabidopsis genome and the nearly finished rice genome sequence. This has led to revision of the current annotation of half of the 22 Arabidopsis formin-related genes. Comparative analysis of the two plant genomes revealed a good conservation of the previously described two subfamilies of plant formins (Class I and Class II), as well as several subfamilies within them that appear to predate the separation of monocot and dicot plants. Moreover, a number of plant Class II formins share an additional conserved domain, related to the protein phosphatase/tensin/auxilin fold. However, considerable inter-species variability sets limits to generalization of any functional conclusions reached on a single species such as Arabidopsis. CONCLUSIONS: The plant-specific domain context of the conserved FH2 domain, as well as plant-specific features of the domain itself, may reflect distinct functional requirements in plant cells. The variability of formin structures found in plants far exceeds that known from both fungi and metazoans, suggesting a possible contribution of FH2 proteins in the evolution of the plant type of multicellularity