Synthesis,structural characterization,and cytotoxic activity of new spirocyclic octachlorocyclotetraphosphazenes

Octachlorocyclotetraphosphazene, N₄P₄Cl₈, (1) was reacted with N, N′-dibenzylethylenediamine to synthesize partially substituted monospiro- (2), dispiro- (5) and tetraspirocyclotetraphosphazene (8) derivatives. The reactions of 2 and 5 with excess pyrrolidine and morpholine produced fully substituted pyrrolidino (3 and 6) and morpholino (4 and 7) spirocyclotetraphosphazenes. The structures of the compounds were determined with 1D (¹H, ¹³C, ³¹P, and DEPT) NMR, 2D (HSQC) NMR, ESI-MS, FTIR, and elemental analysis. The solid-state structures of 6 and 7 were examined by X-ray crystallography. In 7, intramolecular C-H…O hydrogen bonds link the molecules into centrosymmetric dimmers. The cytotoxic activity of all the compounds against human cervix carcinoma cell lines (HeLa) was investigated. The study showed that these compounds exert limited cytotoxic, apoptotic and necrotic effects on HeLa cancer cell lines.     

Oscillation Criteria for Certain Fourth-Order Nonlinear Delay Differential Equations

In this article, we establish some new criteria for the oscillation of fourth-order nonlinear delay differential equations of the form

$$(r_2(t)(r_1(t)(y''(t))^\alpha)')' + p(t)(y''(t))^\alpha + q(t)f(y(g(t))) = 0$$

provided that the second-order equation

$$(r_2(t)z'(t))') + \frac{p(t)}{r_1(t)}z(t) = 0$$

is nonoscillatory or oscillatory.

     

The Cauchy–Kowalewski Theorem in the Space of Pseudo Q-holomorphic Functions

In this work, we prove the Cauchy–Kowalewski theorem for the initial-value problem

$$\begin{aligned} \frac{\partial w}{\partial t}= & {} Lw \\ w(0,z)= & {} w_{0}(z) \end{aligned}$$

where

$$\begin{aligned} Lw:= & {} E_{0}(t,z)\frac{\partial }{\partial \overline{\phi }}\left( \frac{ d_{E}w}{dz}\right) +F_{0}(t,z)\overline{\left( \frac{\partial }{\partial \overline{\phi }}\left( \frac{d_{E}w}{dz}\right) \right) }+C_{0}(t,z)\frac{ d_{E}w}{dz} \\&+G_{0}(t,z)\overline{\left( \frac{d_{E}w}{dz}\right) } +A_{0}(t,z)w+B_{0}(t,z)\overline{w}+D_{0}(t,z) \end{aligned}$$

in the space \(P_{D}\left( E\right) \) of Pseudo Q-holomorphic functions.

     

A new approach to the Assad–Kirk fixed point theorem

In the present paper, considering the Wardowski’s technique, we give a new approach to the Assad–Kirk fixed point theorem on metrically convex metric spaces.We also provide a nontrivial example showing that our result is a proper extension of the Assad–Kirk fixed point theorem.     

A nonlinear stochastic growth model on discrete time domains

In this paper, we introduce nonlinear stochastic dynamic problems on discrete time domains where events may occur at unevenly spaced time points. We define Euler equation and transversality condition for the problem. We prove that the Euler equation and the transversality condition are sufficient for the existence of the optimal solution. Next we generalize discrete time Cagan type rational expectation model to multivariate case. As an application of the main results, we obtain an explicit solution to a log-linearized nonlinear stochastic growth model.     

On the geometry of complex ‐spaces

It is known that applying an ‐homothetic deformation to a complex contact manifold whose vertical space is annihilated by the curvature yields a condition which is invariant under ‐homothetic deformations. A complex contact manifold satisfying this condition is said to be a complex ‐space. In this paper, we deal with the questions of Bochner, conformal and conharmonic flatness of complex ‐spaces when , and prove that such kind of spaces cannot be Bochner flat, conformally flat or conharmonically flat.     

Thermal deformation thermodynamics of a smectite mineral

A method has been purposed to calculate some of the thermodynamic quantities for the thermal deformation of a smectite without using any basic thermodynamic data. The Hanç?l? (Keskin, Ankara, Turkey) bentonite containing a smectite of 88% by volume was taken as material. Thermogravimetric (TG) and differential thermal analysis (DTA) curves of the sample were obtained. Bentonite samples were heated at various temperatures between 25–900°C for the sufficient time (2 h) until to establish the thermal deformation equilibrium.Cation-exchange capacity (CEC) of heated samples was determined by using the methylene blue standard method. The CEC was used as a variable of the equilibrium. An arbitrary equilibrium constant (K _a) was defined similar to chemical equilibrium constant and calculated for each temperature by using the corresponding CEC-value. The arbitrary changes in Gibbs energy (ΔG _a ⁰ ) were calculated from K _a-values. The real change in enthalpy (ΔH ⁰) and entropy (ΔS ⁰) was calculated from the slopes of the lnK vs. 1/T and ΔG vs. T plots, respectively. The real changes in Gibbs energy (ΔG ⁰) and real equilibrium constant (K) were calculated by using the ΔH ⁰ and ΔS ⁰ values. The results at the two different temperature intervals are summarized as below: ΔG ₁ ⁰ =ΔH ₁ ⁰ ?ΔS ₁ ⁰ T=?RTlnK ₁=47000?53t, (200–450°C), and ΔG ₂ ⁰ =ΔH ₂ ⁰ -ΔS ₂ ⁰ T=?RTlnK ₂=132000?164T, (500–800°C).     

Water vapour barrier performance of corn-zein coated polypropylene (PP) packaging films

The novel film structure of corn-zein coated on polypropylene (PP) synthetic film for packaging industry was developed to examine the feasibility of resulting coated films as an alternative water barrier performance for food packaging. The effects of coating formulation (solvent, corn-zein, plasticizer concentration and plasticizer type) on final properties of films were observed. Corn-zein is the most important protein of corn and has good film forming property. Composites structures of PP films coated with corn-zein were obtained through a simple solvent casting method. Polyethylene glycol (PEG) and glycerol (GLY) were used as plasticizer to increase film flexibility. Statistical analysis based on full factorial design was performed to observe coating formulation effects. The high water vapour barriers were obtained for films coated with coating formulation consisting of higher amounts of corn-zein plasticized by GLY. The lower glass transition temperatures (T _g) of films were obtained by plasticization of films and T _g decreased by increasing plasticizer content. The statistical analysis defined the key parameters of coating formulation that had major effects on the final properties of coated PP films as corn-zein, plasticizer concentration and plasticizer type. In conclusion, corn-zein coatings could have potential as an alternative to conventional synthetic polymers used in composite multilayer structures for food packaging applications.     

On the Riesz difference sequence space

In the present paper, we define the difference sequence space r ^q (p, Δ), which is defined as follows: