Heating mechanism in relation to the laser machining process

Laser workpiece interaction mechanism is an important phenomenon which will assist in the development of laser machining systems. The interaction mechanism is generally complicated and depends on the laser and workpiece properties. In the present study a mathematical analysis for the laser material removal by evaporation and radial ejection of liquid is carried out. In the analysis the time unsteady problem is solved and nucleation explosions are predicted.     

Isolation and biological activity of new and known isolation and biological activity of new and known diterpenoids from Sideritis stricta Boiss. & Heldr

Nine known and one new ent-kaurene diterpenoid were isolated from the acetone extract of Sideritis stricta Boiss & Heldr. The new compound, identified as ent-1 beta-hydroxy-7 alpha-acetyl-15 beta,16 beta-epoxykaurane (1) by IR, 1D and 2D NMR techniques and mass spectra, was isolated along with sideroxol (2), 7-acetyl sideroxol (3), 7-epicandicandiol (4), linearol (5), ent-7 alpha,15 beta,18-trihydroxy-kaur-16-ene (6), ent-7 alpha-acetyl,15,18-dihydroxy-kaur-16-ene (7), foliol (8), sideridiol (9) and siderol (10). The antibacterial and antifungal activities of these compounds and the whole crude acetone extract were evaluated against E. coli, S. aureus, K. pneumeonia and C. albicans.     

Analytical Approach to Fractional Zakharov-Kuznetsov Equations by He＇s Homotopy Perturbation Method

The aim of this paper is to obtain the approximate analytical solution of a fractional Zakharov-Kuznetsov equation by using homotopy perturbation method （HPM）. The fractional derivatives are described in the Caputo sense. Several examples are given and the results are compared to exact solutions. The results reveal that the method is very effective and simple.     

Analytical Approach to Space- and Time-Fractional Burgers Equations

A scheme is developed to study numerical solution of the space- and time-fractional Burgers equations under initial conditions by the homotopy analysis method. The fractional derivatives are considered in the Caputo sense. The solutions are given in the form of series with easily computable terms. Numerical solutions are calculated for the fractional Burgers equation to show the nature of solution as the fractional derivative parameter is changed.     

Quivers of finite mutation type and skew-symmetric matrices

Quivers of finite mutation type are certain directed graphs that first arised in Fomin-Zelevinsky’s theory of cluster algebras. It has been observed that these quivers are also closely related with different areas of mathematics. In fact, main examples of finite mutation type quivers are the quivers associated with triangulations of surfaces. In this paper, we study structural properties of finite mutation type quivers in relation with the corresponding skew-symmetric matrices. We obtain a characterization of finite mutation type quivers that are associated with triangulations of surfaces and give a new numerical invariant for their mutation classes.     

Expected gain–loss pricing and hedging of contingent claims in incomplete markets by linear programming

We analyze the problem of pricing and hedging contingent claims in the multi-period, discrete time, discrete state case using the concept of a “λ gain–loss ratio opportunity”. Pricing results somewhat different from, but reminiscent of, the arbitrage pricing theorems of mathematical finance are obtained. Our analysis provides tighter price bounds on the contingent claim in an incomplete market, which may converge to a unique price for a specific value of a gain–loss preference parameter imposed by the market while the hedging policies may be different for different sides of the same trade. The results are obtained in the simpler framework of stochastic linear programming in a multi-period setting, and have the appealing feature of being very simple to derive and to articulate even for the non-specialist. They also extend to markets with transaction costs.     

Application of the Exp-function method for nonlinear differential-difference equations

In this paper, we established abundant travelling wave solutions for some nonlinear differential-difference equations. It is shown that the Exp-function method, with the help of symbolic computation, provides a very effective and powerful new method for discrete nonlinear evolution equations in mathematical physics.     

Unified scaling law in the coherent noise model

The waiting time distribution between successive events and the unified scaling law is studied using the coherent noise model. It is shown that, although this model generates uncorrelated event sizes and does not exhibit criticality, it still provides the unified scaling law. We argue the role of characteristic kink observed in the unified scaling law and the meaning of the parameter C$C$ used to fix the peak of the kink to unity. Our results indicate that the parameter C$C$ is indeed a physical quantity localizing the end of the linear tendency in the scaling law, which corresponds to the completion of the dominance of correlated events in time.     

Spectral,electron microscopic and chemical investigations of gamma-induced purple color zonings in amethyst crystals from the Dursunbey-Balıkesir region of Turkey

Amethyst crystals on matrix specimens from the Dursunbey-Bal?kesir region in Turkey have five representative purple color zonings: dark purple, light purple, lilac, orchid, and violet. The purple color zonings have been analyzed with optical absorption spectra in the visible wavelength region, chemical full trace element analyses (inductively coupled plasma-atomic emission spectroscopy and inductively coupled plasma-mass spectroscopy), and scanning electron microscopic images with high magnification. It can be proposed that the production of the purple color in amethyst crystals is due to three dominant absorption bands centered at 375, 530, and 675 nm, respectively. In addition, the purple color zonings are also due to four minor absorption bands centered at 435, 480, 620, and 760 nm. X-ray diffraction graphics of the investigated amethyst crystals indicate that these crystals are composed of a nearly pure alpha-quartz phase and do not include any moganite silica phase and/or other mineral implications. Trace element analyses of the amethyst crystals show five representative purple color zonings, suggesting that the absorption bands can be mainly attributed to extrinsic defects (chemical impurities). However, another important factor that influences all structural defects in amethyst is likely to be the gamma irradiation that exists during amethyst crystallization and its inclusion in host materials. This gamma irradiation originates from the large underlying intrusive granitoid body in the region of amethyst formation. Irradiation modifies the valence values of the impurity elements in the amethyst crystals. It is observed that the violet-colored amethyst crystals have the most stable and the least reversible coloration when exposed to strong light sources. This situation can be related to the higher impurity content of Fe (2.50 ppm), Co (3.1 ppm), Ni (38 ppm), Cu (17.9 ppm), Zn (10 ppm), Zr (3.9 ppm), and Mo (21.8 ppm).     

He's homotopy perturbation method for solving the shock wave equation

In this article, we discuss the analytic solution of the fully developed shock waves. The homotopy perturbation method is used to solve the shock wave equation, which describes the flow of gases. Unlike the various numerical techniques, which are usually valid for short period of time, the solution of the presented equation is analytic for 0 < t < ∞. The results presented converge very rapidly, indicating that the method is reliable and accurate.