A rocket/ space vehicle is constrained to fly vertically in atmosphere and gravitational space, in the first case with uniform acceleration with the help of a variable thrust program and in the second case with exponentially timevarying velocity. In either case endurance, ie, time of flight, burnout velocity, burnout altitude ,over-all altitude attained and the controlled thrust are determined. Also evaluated is the propellant mass consumption. Finally some more problems of variable thrust are posed and solved.

In this paper, we have investigated the role of bulk viscosity in present scenario of the evolution in FRW model universe in the framework of Lyra's geometry. We derived the field equations when the source for energy-momentum tensor is composed of a bulk viscous fluid with cosmic strings. The Einstein's field equations are solved by assuming a constant deceleration parameter. In this work, the displacement vector is considered to be a function of time. The kinematic and physical properties of the model are also discussed by using some acceptable physical assumptions of scale factor for flat, open, and closed universe.

We consider a ball moving in the xy-plane spinning about an axis perpendicular to the plane on the motion. The typical trajectory of the ball is shown in figure 1.

The geodynamo is crucial for the activity of Earth’s outer core, which is mainly made of fluid iron. The ab initio molecular dynamics were adopted on the calculations of ion-ion dynamic structure factors and the equations of states of pure iron under Earth’s core condition. The calculated static structure factors, ion-ion dynamic structure factors, and dispersion curve of pure iron were consistent with the reported in situ x-ray diffraction and inelastic x-ray scattering measurements. A multivariate polynomial method based on the ab initio calculated pressure-volume-temperature data was proposed in the formulation of the equations of states with high accuracy, by which the pressure and temperature dependent thermoelastic properties can be directly calculated by definitions. From the isentropic profiles in the Earth’s outer core, the iron exhibited about 10% higher density, 7% lower sound velocity, and an almost identical adiabatic bulk modulus when compared to the preliminary reference Earth model. The adiabatic sound velocities calculated by dynamic structure factors and the equations of states methods were physically equivalent. However, the sound velocity of iron calculated by the fitted equation of state is about 5% lower than that by the dynamic structure factors method.

In this paper, inspired by the work of [4,7] and [8-10], we are gonging to present a short proof of the well-known Minkowski’s inequality and give an interpolation and a renement of it.

It is increasingly being used in electrical and magnetic exploration unmanned aerial vehicles. In this case, the measuring devices are not located on the surface of the earth, but at a significant height above this surface. Below are the results of mathematical modeling for the case when the exciter of the normal magnetic field is a closed loop of electric current lying on the surface of the earth, and the sources of the anomalous field are local magnetized objects located under this surface. The results of the modeling showed what effect these objects have on different components of the magnetic field.

The Cauchy problem of the 2D fractional X-ray diffraction optics designed to describe the mathematical model of the X-ray propagation via the imperfect crystal has been described in terms of the matrix integral Fredholm–Volterra equation. Using the general Green function formalism, the matrix Resolvent solution of the Cauchy problem of the 2D fractional X-ray diffraction optics has been built and analyzed for the case of the coherent two-beam X-ray diffraction by imperfect crystals under the non-locality interaction of the X-ray with atoms of crystal medium along the crystal thickness. In the case, when the crystal-lattice elastic displacement field is the linear function f (R) = ax + b, coeffcients a, b = const, the analytical solution of the 2D fractional diffraction optics Cauchy problem has been obtained and analysed for arbitrary fractional order parameter α, α (0,1].

In this study, we investigated the effect of CO2 laser energy on the surface of a variety of polyester textiles with thicknesses ranging from 2 to 3mm. To evaluate the laser action on the surface texture of this type of textile, the laser power was changed from 80 W to 120 W. A series of SEM images were made of knitted samples treated with different laser powers. The rate of engraving operations increases as the incident laser power increases, and it is dependent on the thickness, chemical, and physical features of the irradiated fabric. According to the results of engraving samples, SEM photos demonstrate that laser treatment causes etching in all treated fabrics, even at a low incident laser power of 80W. When it comes to selecting the correct laser, the material's features are critical. The CO2 laser was used to effectively mark and engrave synthetic textile fabrics, as well as cut and weld them. So the CO2 laser system is a suitable laser system for the surface treatment of synthetic textile materials in the marking, engraving, cutting, and welding operation