Analytical evaluation of three wild growing Omani medicinal plants

Three wild Omani plants, Moringa peregrina, Acacia nilotica and Rhazya stricta, were selected for the present study. Na, K and Ca contents were determined using flame photometric analysis. M. peregrina seeds (22.5 mg/g) and pods (27.7 mg/g) had higher Na contents than A. nilotica (0.33 mg/g) and R. stricta (0.30 mg/g), whereas the K and Ca contents of R. stricta were significantly higher than those of the other two plants. The protein content was lowest in R. stricta (9.8%) and highest in M peregrina seeds (21.0%). The highest total phenolic contents (TPC) were found in M. peregrina seeds (350.3 mg/g) and the lowest in A. nilotica (66.1 mg/g). The major component of M. peregrina seed oil was oleic acid (74.7%). Gas chromatographic-mass spectrometric analysis (GC-MS) revealed that octadecanal (30.9%) was the major compound in A. nilotica. The presence of various phenolics and flavonoids in M. peregrina, A. nilotica and R. stricta were confirmed by high performance liquid chromatography (HPLC).     

Investigation of the effect of SSP in stabilizing the structure of condensation polymer blends via rheological measurements

We investigated the influence of solid-state polymerization (SSP) process on the reactions that could be taken place at the interphase of polycondensation polymer blends to stabilize the structure obtained after melt mixing. Polyethylene terephthalate (PET) and polyamide 66 (PA66) were melt blended in a mixer, and subsequent SSP process was performed for each sample. FTIR spectra indicated reactions between two polymers. Viscosity behavior and interfacial slip were investigated by measuring shear viscosity of components and blends before and after SSP and then compared with the viscosity calculated from the log-additivity model. The results showed that after SSP, there was no sign of interfacial slip, the slope of viscosity reduction with increasing shear rate became smaller, and the viscosity of blends showed positive deviation at all examined shear rate from the log-additivity model while this deviation was negative at higher shear rate before SSP. SEM micrographs, which were taken after shear stress was imposed on the samples, also indicated the morphological stability after SSP. Furthermore, we studied the effect of functional groups concentration on the reactions at the interphase by using hydrolyzed PET as a precursor for blends. The results showed that slip at the interface would decrease with increasing functional groups of the precursors. These results are particularly valuable for using recycled polymers.     

Nonlinear study of the dynamic behavior of a string-beam coupled system under combined excitations

In this paper,the nonlinear dynamic behavior of a string-beam coupled system subjected to external,parametric and tuned excitations is presented.The governing equations of motion are obtained for the nonlinear transverse vibrations of the string-beam coupled system which are described by a set of ordinary differential equations with two degrees of freedom.The case of 1:1 internal resonance between the modes of the beam and string,and the primary and combined resonance for the beam is considered.The method of multiple scales is utilized to analyze the nonlinear responses of the string-beam coupled system and obtain approximate solutions up to and including the second-order approximations.All resonance cases are extracted and investigated.Stability of the system is studied using frequency response equations and the phase-plane method.Numerical solutions are carried out and the results are presented graphically and discussed.The effects of the different parameters on both response and stability of the system are investigated.The reported results are compared to the available published work.     

Higher-Order Fourier Analysis Of {\mathbb{F}_{p}^n} And The Complexity Of Systems Of Linear Forms

In this article we are interested in the density of small linear structures (e.g. arithmetic progressions) in subsets A of the group \mathbbF_pⁿ{\mathbb{F}_{p}^n} . It is possible to express these densities as certain analytic averages involving 1 _A , the indicator function of A. In the higher-order Fourier analytic approach, the function 1 _A is decomposed as a sum f ₁ + f ₂ where f ₁ is structured in the sense that it has a simple higher-order Fourier expansion, and f ₂ is pseudo-random in the sense that the k-th Gowers uniformity norm of f ₂, denoted by ||f₂||_U^k{\|{f_2}\|_{U^k}}, is small for a proper value of k.     

The use of partition polynomial series in Laplace inversion of composite functions with applications in fractional calculus

This paper presents an analytical method towards Laplace transform inversion of composite functions with the aid of Bell polynomial series. The presented results are used to derive the exact solution of fractional distributed order relaxation processes as well as time‐domain impulse response of fractional distributed order operators in new series forms. Evaluation of the obtained series expansions through computer simulations is also given. The results are then used to present novel series expansions for some special functions, including the one‐parameter Mittag‐Leffler function. It is shown that truncating these series expansions when combined with using potential partition polynomials provides efficient approximations for these functions. At the end, the results are shown to be also useful in studying asymptotical behavior of partial Bell polynomials. Numerical simulations as well as analytical examples are provided to verify the results of this paper.     

Coupled nonlinear size-dependent behaviour of microbeams

The nonlinear resonant behaviour of a microbeam, subject to a distributed harmonic excitation force, is investigated numerically taking into account the longitudinal as well as the transverse displacement. Hamilton’s principle is employed to derive the coupled longitudinal-transverse nonlinear partial differential equations of motion based on the modified couple stress theory. The discretized form of the equations of motion is obtained by applying the Galerkin technique. The pseudo-arclength continuation technique is then employed to solve the discretized equations of motion numerically. Different types of bifurcations as well as the stability of solution branches are determined. The numerical results are presented in the form of frequency-response and force-response curves for different sets of parameters. The effect of taking into account the longitudinal displacement is highlighted.     

Nonlinear resonant behavior of microbeams over the buckled state

The present study investigates the nonlinear resonant behavior of a microbeam over its buckled (non-trivial) configuration. The system is assumed to be subjected to an axial load along with a distributed transverse harmonic load. The axial load is increased leading the system to lose the stability via a pitchfork bifurcation; the postbuckling configuration is obtained and the nonlinear resonant response of the system over the buckled state is examined. More specifically, the nonlinear equation of motion is obtained employing Hamilton’s principle along with the modified couple stress theory. The continuous system is truncated into a system with finite degrees of freedom; the Galerkin scheme is employed to discretize the nonlinear partial differential equation of motion into a set of ordinary differential equations. This set of equations is solved numerically employing the pseudo-arclength continuation technique; first a nonlinear static analysis is performed upon this set of equations so as to obtain the onset of buckling (supercritical pitchfork bifurcation) and the buckled configuration of the microbeam. The frequency-response and force-response curves of the system are then constructed over the buckled configurations. A comparison is made between the frequency-response curves obtained by means of the modified couple stress and the classical theories. The effect of different system parameters on the frequency-response and force-response curves is also examined.     

A study on spatially extended phase objects using speckle photography

We present an application of an improved speckle photography technique for spatially extended phase objects. A contour mapping of a thin lens displaying its phase variation is presented. A theoretical analysis is investigated followed by the experimental presentation. Reasonable interference fringes are obtained and compared with the fringes obtained for hot air. The phase information of the object is extracted using the point-by-point technique.     

IBMA–metal containing polymers

A new convenient route to metal containing polymers is described. This method involves emulsion co(ter) polymerization of a polar hydrocarbon soluble monomer, N-isobutoxymethylacrylamide (IBMA), with styrene or styrene/butadiene, followed by addition of metals. Metal incorporation is effected by latex or solution techniques. Preparative, atomic adsorption, spectroscopic, film observation, and dilute solution data are presented in support of metal complexation. Structures for the complexes are proposed.     

Circular chromatic index of graphs of maximum degree 3

This paper proves that if G is a graph (parallel edges allowed) of maximum degree 3, then χ′_c(G) ≤ 11/3 provided that G does not contain H₁ or H₂ as a subgraph, where H₁ and H₂ are obtained by subdividing one edge of K (the graph with three parallel edges between two vertices) and K₄, respectively. As χ′_c(H₁) = χ′_c(H₂) = 4, our result implies that there is no graph G with 11/3 < χ′_c(G) < 4. It also implies that if G is a 2‐edge connected cubic graph, then χ′_c(G) ≤ 11/3. © 2005 Wiley Periodicals, Inc. J Graph Theory 49: 325–335, 2005