Non‐self‐adjoint singular second‐order dynamic operators on time scale

In this study, maximal dissipative second‐order dynamic operators on semi‐infinite time scale are studied in the Hilbert space , that the extensions of a minimal symmetric operator in limit‐point case. We construct a self‐adjoint dilation of the dissipative operator together with its incoming and outgoing spectral representations so that we can determine the scattering function of the dilation as stated in the scheme of Lax‐Phillips. Moreover, we construct a functional model of the dissipative operator and identify its characteristic function in terms of the Weyl‐Titchmarsh function of a self‐adjoint second‐order dynamic operator. Finally, we prove the theorems on completeness of the system of root functions of the dissipative and accumulative dynamic operators.     

Nonexistence of nontrivial global solutions for nonlocal in time differential inequalities

In this paper, some nonlocal in time differential inequalities of Sobolev type are considered. Using the nonlinear capacity method, sufficient conditions for the nonexistence of nontrivial global classical solutions are provided.     

The spectral analysis and exponential stability of a bi‐directional coupled wave‐ODE system

In this paper, an unstable linear time invariant (LTI) ODE system is stabilized exponentially by the PDE compensato—a wave equation with Kelvin‐Voigt (K‐V) damping. Direct feedback connections between the ODE system and wave equation are established: The velocity of the wave equation enters the ODE through the variable v_t(1,t); meanwhile, the output of the ODE is fluxed into the wave equation. It is found that the spectrum of the system operator is composed of two parts: point spectrum and continuous spectrum. The continuous spectrum consists of an isolated point , and there are two branches of asymptotic eigenvalues: the first branch approaches to , and the other branch tends to ?∞. It is shown that there is a sequence of generalized eigenfunctions, which forms a Riesz basis for the Hilbert state space. As a consequence, the spectrum‐determined growth condition and exponential stability of the system are concluded.     

含分布时滞的时滞微分系统多步龙格-库塔方法的时滞相关稳定性

本文研究了一类含分布时滞的时滞微分系统的多步龙格-库塔方法的稳定性.基于辐角原理，本文给出了多步龙格-库塔方法弱时滞相关稳定性的充分条件，并通过数值算例验证了理论结果的有效性.     

Influence of imide functionalized organo‐modified Mg‐Al layered double hydroxide on the thermal and mechanical properties of new aliphatic‐aromatic poly (amide‐imide)

A new dicarboxylic acid modified Mg‐Al LDH (DLDH) containing imide groups was prepared and its effects on the thermal and mechanical properties of the new synthesized aliphatic‐aromatic poly (amide‐imide) (PAI) were investigated via preparation of PAI/nanocomposite films by solution casting method. The results of X‐ray diffraction (XRD), field emission‐scanning electron microscopy (FE‐SEM) and transmission electron microscopy (TEM) showed a uniform dispersion for LDH layers into the PAI matrix. For comparison, the effects of polyacrylic acid‐co‐poly‐2‐acrylamido‐ 2‐methylpropanesulfonic acid (PAMPS‐co‐PAA) modified Mg‐Al LDH (ALDH) on the PAI properties were also studied. The thermogravimetric analysis (TGA) results exhibited that the temperature at 5 mass% loss (T₅) increased from 277 °C to 310 °C for nanocomposite containing 2 mass% of DLDH, while T₅ for nanocomposite containing 2 mass% of ALDH increased to 320 °C, along with the more enhancement of char residue compared to the neat PAI. According to the tensile test results, with 5 mass% DLDH loading in the PAI matrix, the tensile strength increased from 51.6 to 70.8 MPa along with an increase in Young's modulus. Also the Young's modulus of PAI nanocomposite containing 5 mass% ALDH reduced from 1.95 to 0.81 GPa.     

A mixed hp FEM for the approximation of fourth‐order singularly perturbed problems on smooth domains

We consider fourth‐order singularly perturbed problems posed on smooth domains and the approximation of their solution by a mixed Finite Element Method on the so‐called Spectral Boundary Layer Mesh. We show that the method converges uniformly, with respect to the singular perturbation parameter, at an exponential rate when the error is measured in the energy norm. Numerical examples illustrate our theoretical findings.     

Two validated chromatographic determinations of an antifungal drug,its toxic impurities and degradation product: A comparative study

Tolnaftate, a thionoester anti‐fungal drug, was subjected to alkaline hydrolysis to produce methyl(m‐tolyl)carbamic acid and β ‐naphthol (tolnaftate impurity A). N‐Methyl‐m‐toluidine, tolnaftate impurity D, was synthesized and structurally elucidated along with tolnaftate alkaline degradation products using IR, H¹NMR and MS. Two stability‐indicating HPTLC and RP‐HPLC methods were developed and validated, for the first time, for determination of tolnaftate, its alkaline degradation products and toxic impurities in the presence of methyl paraben, as a preservative in Tinea Cure^® cream. The proposed HPTLC method depended on separation of the studied components on TLC silica gel F₂₅₄ plates using hexane–glacial acetic acid (8:2, v/v) as a developing system and scanning wavelength of 230 nm. The proposed RP‐HPLC method was based on separation of the five components on an Eclipse plus C₁₈ column. The mobile phase used was acetonitrile–water containing 1% ammonium formate (40:60, v/v), with a flow rate of 1 mL/min and detection wavelength of 230 nm. The proposed methods allowed the assay of tolnaftate toxic impurities, β ‐naphthol and N‐methyl‐m‐toluidine, down to 2%, allowing tracing of β ‐naphthol that could be absorbed by the skin causing systemic toxic effects, unlike tolnaftate, indicating the high significance of such determination. International Conference on Harmonization guidelines were followed for validation.     

Oxotitanium(IV) complexes of some bis‐unsymmetric Schiff bases: Synthesis,structural elucidation and biomedical applications

A number of oxotitanium(IV) complexes of the type TiOL with bis‐unsymmetric dibasic tetradentate Schiff base (LH₂) containing ONNO donor atoms have been synthesized. Mono‐Schiff base (OPD‐HNP) was prepared by the condensation of 1:3 molar ratio of 2‐hydroxy‐1‐naphthaldehyde (HNP) with o‐phenylenediamine (OPD). Dibasic unsymmetric tetradentate diamine Schiff bases were prepared by the reaction of OPD‐HNP with 2‐hydroxyacetophenone, 2‐hydroxypropeophenone, benzoylacetone, acetylacetone and ethylacetoacetate. Further, titanylacetylacetonate was reacted with these ligands to obtain their metal complexes. On the basis of analytical and physiochemical data, the formation of complexes as TiOL was suggested having square pyramidal geometry. Quantum mechanical approach also confirmed this geometry. The assessment of the synthesized ligands and their complexes showed that some behave as good inhibitors of mycelial growth against selected phytopathogic fungi but weak inhibitors against some selected bacteria. A few of them also showed antioxidant properties.