On amalgamated Banach algebras

If F(z) is a polynomial of degree n having all zeros in \(|z|\le k,~k>0\) and f(z) is a polynomial of degree \(m\le n\) such that \(|f(z)|\le |F(z)|\) for \(|z|=k\), then it was formulated by Rather and Gulzar (Adv Inequal Appl 2:16–30, 2013) that for every \(|\delta |\le 1, |\beta |\le 1,~R>r\ge k\) and \(|z|\ge 1,\)

$$\begin{aligned} |B[fo\sigma ](z)+\psi B[fo\rho ](z)|\le |B[Fo\sigma ](z)+\psi B[Fo\rho ](z)|, \end{aligned}$$

where B is a \(B_{n}\) operator, \(\sigma (z){=}Rz, \rho (z){=}rz\) and \(\psi {:=}\psi (R,r,\delta ,\beta ,k) {=}\beta \bigg \{\bigg (\frac{R+k}{r+k}\bigg )^{n}{-}|\delta |\bigg \}{-}\delta \). The authors have assumed that \(B\in B_{n}\) is a linear operator which is not true in general. In this paper, besides discussing assumption of authors and their followers (see e.g, Rather et al. in Int J Math Arch 3(4):1533–1544, 2012), we present the correct proof of the above inequality. Moreover our result improves many prior results involving \(B_{n}\) operators and a number of polynomial inequalities can also be deduced by a uniform procedure.

     

Composition of the essential oil of Stachys benthamiana Boiss. from the south of Iran

The chemical composition of the essential oil (EO) obtained from the aerial parts of Stachys benthamiana Boiss. was analysed by using GC and GC/MS. Thirty-three components were identified in the oil. β-Bisabolene (19.2%), humulene epoxide II (10.7%), epi-α-bisabolol (7.2%), (E)-γ-bisabolene (6.9%), n-decanal (6.8%) and caryophyllene oxide (6.6%), were the main compounds in the EOs. This is the first report on the different chemical compositions of S. benthamiana EOs from the south of Iran.     

On uniqueness and selectivity in three-component parallel factor analysis

Unambiguous recovery of profiles is a distinguishable advantage of Parallel Factor Analysis (PARAFAC) as a trilinear model and has made it a promising exploratory tool for data analysis. Linear dependency in profiles destroys trilinearity and will increase ambiguity in the curve resolution of three-way data sets. PARAFAC uniqueness deteriorates totally or partially in data sets with linearly dependent loadings. Exploiting a reliable method for determination and direct visualization of feasible bands in the PARAFAC model can be helpful not only in full characterization of uniqueness conditions but also in the investigation of the effects of constraints on the PARAFAC feasible solutions. The purpose of this paper is twofold. First, the calculation of rotational ambiguity in the PARAFAC model extends to three components system. The principle behind the algorithm is described in detail and tested for simulated and real data sets. Completely general and thoroughly investigated results are presented for the three component cases. Secondly, the effects of selective regions in the profiles on the resolution of systems that suffered from the rank deficiency problem, due to rank overlap, are emphasized. In the case of two-way data sets the effect of selectivity constraint on the unique recovery of profiles was investigated and applied. However, to our knowledge, in this report, for the first time, the effect of the presence of selective windows in the profiles, on the unique resolution of three-way data sets has been systematically investigated.     

Multivariate investigation of interaction between porphyrin ligands and human telomeric DNA

G-quadruplexes are formed by association of DNA strands containing multiple contiguous guanines. The capability of drugs to induce formation or stabilize G-quadruplexes is an active area of cancer therapy investigation. We evaluated interaction between two cationic tetrapyridinoporphyrazines with Na⁺ and K⁺ forms of human telomeric G-quadruplex DNA by chemometrics method. An antiparallel quadruplex structure was found to be stabilized more greatly by these two isomers in the presence of K⁺ and Na⁺ ions. Equilibrium model of a ligand binding with DNA oligomer has been considered as a process of small molecule adsorption on to a lattice of multiple binding sites. In multivariate analysis methods, it is accounted this assertion that during saturation of the macromolecule by a ligand should expect effect of cooperativity due to changes in DNA conformation or the mutual influence between bound ligands. Such phenomenon cannot be entirely described by the classical stepwise complex formation model. From the results of absorption and circular dichroism measurements, the unique site for the ligand binding is suggested to be the intercalating in guanine tetrad plane quadruplex. We found a 2:1 binding stoichiometry for both ligands and Tel22.     

On the determination of the impulsive Sturm–Liouville operator with the eigenparameter-dependent boundary conditions

In the present work, we consider the inverse problem for the impulsive Sturm–Liouville equations with eigenparameter-dependent boundary conditions on the whole interval (0,π) from interior spectral data. We prove two uniqueness theorems on the potential q(x) and boundary conditions for the interior inverse problem, and using the Weyl function technique, we show that if coefficients of the first boundary condition, that is, h₁,h₂, are known, then the potential function q(x) and coefficients of the second boundary condition, that is, H₁,H₂, are uniquely determined by information about the eigenfunctions at the midpoint of the interval and one spectrum or partial information on the eigenfunctions at some internal points and some of two spectra.     

Mechanisms of Non-Newtonian Polymer Flow Through Porous Media Using Navier–Stokes Approach

This study includes solving non-Newtonian Navier–Stokes equation in three-dimensions (real rock images) and two-dimensions (simplified pore geometries) using the finite-difference method. The purpose of this study is to improve understanding of local phenomena leading to the mobilization of residual oil. This involves local pressure variations for non-Newtonian polymers and compares it with Newtonian fluid behavior. When a higher degree of shear thickening is induced, more flow diversion to side channels perpendicular to the main flow path and larger drag on fluids inside side channels will occur. This is consistent with oil mobilization and lowering of residual oil saturation.