and Applied Analysis 3 Definition 1.10 see 5 . Let X,G be a G-metric space and f, g : X → X be given mappings. We say that f is a generalized weakly G-contraction mapping of type B with respect to g if for all x, y, z ∈ X, the following inequality holds: ψ ( G ( fx, fy, fz )) ≤ ψ ( G ( gx, gx, fy ) G ( gy, gy, fz ) G ( gz, gz, fx ) 3 ) − φGgx, gx, fy, Ggy, gy, fz, Ggz, gz, fx, 1.2

Frizzled and Smoothened are homologous seven-transmembrane proteins functioning in the Wnt and Hedgehog signaling pathways, respectively. They harbor an extracellular cysteine-rich domain (FZ-CRD), a mobile evolutionary unit that has been found in a number of other metazoan proteins and Frizzled-like proteins in Dictyostelium. Domains distantly related to FZ-CRDs, in Hedgehog-interacting protei...

Ral is a small Ras-like GTPase that regulates membrane trafficking and signaling. Here, we show that in response to planar cell polarity (PCP) signals, Ral modulates asymmetric Notch signaling in the Drosophila eye. Specification of the initially equivalent R3/R4 photoreceptor precursor cells in each developing ommatidium occurs in response to a gradient of Frizzled (Fz) signaling. The cell wit...

We enlarge the problem of valuations of triads on so called lines. A line in an e-structure A = 〈A, F,E〉 (it means that 〈A, F 〉 is a semigroup and E is an automorphism or an antiautomorphism on 〈A,F 〉 such that E ◦ E = Id ↾ A) is, generally, a sequence A ↾ B, A ↾ Uc, c ∈ FZ (where FZ is the class of finite integers) of substructures of A such that B ⊆ Uc ⊆ Ud holds for each c ≤ d. We denote thi...

Canonical Wnt/beta-catenin signaling has central roles in development and diseases, and is initiated by the action of the frizzled (Fz) receptor, its coreceptor LDL receptor-related protein 6 (Lrp6), and the cytoplasmic dishevelled (Dvl) protein. The functional relationships among Fz, Lrp6 and Dvl have long been enigmatic. We demonstrated previously that Wnt-induced Lrp6 phosphorylation via gly...

The frizzled (fz) gene is required for the development of distally pointing hairs on the Drosophila wing. It has been suggested that fz is needed for the propagation of a signal along the proximal distal axis of the wing. The directional domineering non-autonomy of fz clones could be a consequence of a failure in the propagation of this signal. We have tested this hypothesis in two ways. In one...

Drosophila sensory organ precursor cells (SOPs) divide asymmetrically along the anterior-posterior (a-p) body axis to generate two different daughter cells. Planar Cell Polarity (PCP) regulates the a-p orientation of the SOP division. The localization of the PCP proteins Van Gogh (Vang) and Frizzled (Fz) define anterior and posterior apical membrane domains prior to SOP division. Here, we inves...

Wingless (Wg) protein is a founding member of the Wnt family of secreted proteins which have profound organizing roles in animal development. Two members of the Frizzled (Fz) family of seven-pass transmembrane proteins, Drosophila Fz and Fz2, can bind Wg and are candidate Wg receptors. However, null mutations of the fz gene have little effect on Wg signal transduction and the lack of mutations ...

Wnts are secreted proteins that are essential for a wide array of developmental and physiological processes. They signal across the plasma membrane by interacting with serpentine receptors of the Frizzled (Fz) family and members of the low-density-lipoprotein-related protein (LRP) family. Activation of Fz-LRP promotes the stability and nuclear localization of beta-catenin by compromising the ab...

Enzymatic disproportionation of cyclohex-2-enone was screened using Agilent J&W GC columns. Published by Elsevier B. V. Essential oils of six Juniperus taxa indigenous in Greece Parasitology Research, 110, 1829-1839 (2012) Tags F. Vourlioti-Arapi et al. HP-5ms, 7890A GC, 5957C MSD, clinical research, disease research Abstract Juniper essential oils were analyzed on an Agilent J&W HP-5ms column ...