abstract         background and objective: microalgae are a group of algae that produce biochemical products consisting of a wide range of carbohydrates, lipids and proteins that are commercially valuable. interest in microalgal cultivation is currently blossoming globally. species of dunaliella are found in freshwater, euryhaline habitats of all continents, oceans including the dead sea and ev...

In this paper, we provide descriptions of the boundedness and compactness for Toeplitz operators Tμ,β between distinct weighted Bergman spaces $$L_a^p\left(\omega \right)$$ $$L_a^q\left(\omega 0 < p ⩽ 1, q = −1 α, β ∞ 1 ∞, α respectively. Part our results are new even in unweighted spaces.

Abstract Introduction β-catenin is a protein molecule of the E-cadherin/catenin adhesion complex that maintains epithelial cell-cell and intracellular signalling. The mutation overexpression leads to cancer, including pancreatic ductal adenocarcinoma (PDAC). FLYWCH1 newly identified with zinc-finger type DNA-binding domain interacts nuclear β-catenin, leading increased cell-matrix in cancer ste...

Fifteen compounds, which included six chiral lignans and nine phenolic glycosides, were separated from the butanol fraction of Averrhoa carambola L. root and identified. All of the compounds, namely 3,4,5-trimethoxyphenol-1-O-β-D-glucopyranoside, benzyl-1-O-β-D-glucopyranoside, (+)-5'-methoxyisolariciresinol 3α-O-β-D-gluco-pyranoside, (+)-isolariciresinol 3α-O-β-D-glucopyranoside, koaburaside, ...

and Applied Analysis 3 nonlinear third-order differential equations. Section 5 gives the corresponding results for those obtained in Sections 2, 3, and 4, but for the fifth-order differential equations. In Section 6, we present some numerical results exhibiting the accuracy and efficiency of our numerical algorithms. 2. SJG Method for Third-Order Differential Equations with Constant Coefficient...

These sets were introduced in the domain of quasicrystallography, see e.g. [2]. It is not difficult to see that Z−β =Z when β ∈Z, and that Z−β = {0} when β < 1+ √ 5 2 . For β ≥ 1+ √ 5 2 , Ambrož et al. [1] showed that Z−β can be described by the fixed point of an anti-morphism on a possibly infinite alphabet. They also calculated explicitely the set of distances between consecutive (−β )-intege...

These sets were introduced in the domain of quasicrystallography, see e.g. [2]. It is not difficult to see that Z−β =Z when β ∈Z, and that Z−β = {0} when β < 1+ √ 5 2 . For β ≥ 1+ √ 5 2 , Ambrož et al. [1] showed that Z−β can be described by the fixed point of an anti-morphism on a possibly infinite alphabet. They also calculated explicitely the set of distances between consecutive (−β )-intege...