Synthesis and spectroscopic characterization of novel 2-amino-4,5,6,7-tetrahydro-3H-cyclopenta[d]pyrimidine and pyrimido[1,2-a]pyrimidine derivatives

2-Aminocyclopenta[d]pyrimidines 3a-c were achieved via a one-pot, three-component reactions of cyclopentanone 1, aromatic aldehyde and guanidine hydrochloride (1:2:1 molar ratio). Also, cyclization of 2,5-bis-(arylmethylidene)cyclopentanones 2 with guanidine hydrochloride (1:1 molar ratio) in methanol in the presence of sodiummethoxide afforded cyclopenta-[d]pyrimidines 3. Compound 3a has been shown to be a useful building block for the synthesis of some novel pyrimido[1,2-a]pyrimidines 5, 7 and 12. The structures of the newly synthesized compounds were confirmed on the basis of analytical and spectral data.     

A numerical method based on hybrid orthonormal Bernstein and improved block-pulse functions for solving Volterra–Fredholm integral equations

This paper deals with the numerical solution of the integral equations of linear second kind Volterra–Fredholm. These integral equations are commonly used in engineering and mathematical physics to solve many of the problems. A hybrid of Bernstein and improved block-pulse functions method is introduced and used where the key point is to transform linear second-type Volterra–Fredholm integral equations into an algebraic equation structure that can be solved using classical methods. Numeric examples are given which demonstrate the related features of the process.     

Dynamical instability of shear-free collapsing star in extended teleparallel gravity

We study the spherically symmetric collapsing star in terms of dynamical instability. We take the framework of extended teleparallel gravity with a non-diagonal tetrad, a power-law form of the model presenting torsion and a matter distribution as a non-dissipative anisotropic fluid. The vanishing shear scalar condition is adopted to gain insight in a collapsing star. We apply a first order linear perturbation scheme to the metric, the matter, and f(T) functions. The dynamical equations are formulated under this perturbation scheme to develop collapsing equation for finding dynamical instability limits in two regimes, such as the Newtonian and the post-Newtonian regime. We obtain a constraint-free solution of a perturbed time dependent part with the help of a vanishing shear scalar. The adiabatic index exhibits the instability ranges through the second dynamical equation which depend on physical quantities such as the density, the pressure components, the perturbed parts of the symmetry of the star, etc. We also develop some constraints on the positivity of these quantities and obtain instability ranges to satisfy the dynamical instability condition.     

Soliton solutions of Burgers equations and perturbed Burgers equation

This paper carries out the integration of Burgers equation by the aid of tanh method. This leads to the complex solutions for the Burgers equation, KdV-Burgers equation, coupled Burgers equation and the generalized time-delayed Burgers equation. Finally, the perturbed Burgers equation in (1+1) dimensions is integrated by the ansatz method.     

Warm modified Chaplygin gas shaft inflation

In this paper, we examine the possible realization of a new inflation family called “shaft inflation” by assuming the modified Chaplygin gas model and a tachyon scalar field. We also consider the special form of the dissipative coefficient \(\Gamma ={a_0}\frac{T^{3}}{\phi ^{2 }}\) and calculate the various inflationary parameters in the scenario of strong and weak dissipative regimes. In order to examine the behavior of inflationary parameters, the \(n_s \)–\( \phi ,\, n_s \)–r, and \(n_s \)–\( \alpha _s\) planes (where \(n_s,\, \alpha _s,\, r\), and \(\phi \) represent the spectral index, its running, tensor-to-scalar ratio, and scalar field, respectively) are being developed, which lead to the constraints \(r< 0.11\), \(n_s=0.96 \pm 0.025\), and \(\alpha _s =-0.019 \pm 0.025\). It is quite interesting that these results of the inflationary parameters are compatible with BICEP2, WMAP \((7+9)\) and recent Planck data.     

Rational design of biocompatible IPNs hydrogels containing carboxymethyl starch and trimethyl chitosan chloride with high antibacterial activity

Cellulose - Antimicrobial hydrogels have enticed a major concern for repairing soft tissues, particularly prohibiting bacterial infections that are frequently accompanied by impaired wound healing....     

Modified simple equation method for nonlinear evolution equations

This paper reflects the implementation of a reliable technique which is called modified simple equation method (MSEM) for solving evolution equations. The proposed algorithm has been successfully tested on two very important evolution equations namely Fitzhugh-Nagumo equation and Sharma-Tasso-Olver equation. Numerical results are very encouraging.     

Transient thin film flow of nonlinear radiative Maxwell nanofluid over a rotating disk

In this letter, a mathematical model for transient nature thin film flow of Maxwell nanofluid over a rotating disk is studied in the presence of a uniform magnetic field and non-linear thermal radiation. The Brownian motion and thermophoresis features due to nanofluid are captured by adopting the Buongiorno model. The prime emphasize is to explore the temperature field and nanoparticles volume fraction in nanofluid thin film flow. The reduced system of differential equations is solved numerically by finite difference based method namely bvp4c. The numerical outcomes regarding film thickness, Nusselt number, Sherwood number, velocity, temperature, and concentration are revealed for varying estimation of involved physical parameters. It is shown that the film thickness decreases with increasing values of the magnetic number. Further, the impact of thermophoresis and thermal radiation parameters is worthwhile in enhancing the fluid temperature. The Solute concentration is found to decrease with Brownian motion and Schmidt number.     

Electric impedance study of elastic alternating propylene-carbon monoxide copolymer (PCO-200)

The electrical properties of elastic alternating propylene-carbon monoxide copolymer (PCO-200) were investigated using the impedance spectroscopy technique. The results revealed a phase transition at about 70 °C where the material transforms from its insulating phase of conductivity in the order of 6×10⁻⁹ to about 9×10⁻⁵ (Ω m)⁻¹, The second phase is characterized by temperature dependent electrical relaxation phenomena. The plot of the complex electric modulus and the complex impedance yields semicircles in the temperature range 70 up to 110 °C and a decreasing radius with increasing temperature. The activation energy was found to be in the order of 0.8 eV.     

Study on the normalized Laplacian of a penta-graphene with applications

Let L _n denote a linear pentagonal chain with 2n pentagons. The penta-graphene (penta-C), denoted by R _n is the graph obtained from L _n by identifying the opposite lateral edges in an ordered way, whereas the pentagonal Möbius ring is the graph obtained from the L _n by identifying the opposite lateral edges in a reversed way. In this paper, through the decomposition theorem of the normalized Laplacian characteristic polynomial and the relationship between its roots and the coefficients, an explicit closed-form formula of the multiplicative degree-Kirchhoff index (resp. Kemeny's constant, the number of spanning trees) of R _n is obtained. Furthermore, it is interesting to see that the multiplicative degree-Kirchhoff index of R _n is approximately of its Gutman index. Based on our obtained results, all the corresponding results are obtained for .