Abstract. We propose a new notion of weak solutions (dissipative solutions) for nonisotropic, degenerate, second order, quasi-linear parabolic equations. This class of solutions is an extension of the notion of dissipative solutions for scalar conservation laws introduced by L. C. Evans. We analyze the relationship between the notions of dissipative and entropy weak solutions for non-isotropic,...

We report here the first demonstration of a mode-locked fiber laser delivering parabolic pulses (similaritons) at 1534 nm. The use of a Raman-based gain medium potentially allows its implementation at any wavelength. The 22nJ output similariton pulses have a true parabolic shape both in the time and spectral domains and a linear chirp. Linear recompression close to Fourier limit is demonstrated...

Abstract Despite having very high solar irradiance, Pakistan still does not have any installed concentrated power (CSP) plant. Several studies shown that multiple locations within the country are suitable for CSP plants, but there is limited availability of comprehensive comparative studies. Therefore, this article presents a analysis different technologies in Pakistan, focusing on their potent...

Heliothermic technologies are affected by their low density, intermittence and economic competitiveness. Hybrid solar–waste heat power systems can increase plant conversion efficiency generation while reducing intermittence. This study focused on the development of software (AERES) to economically optimize hybrid in terms technology selection, sizing, operating conditions block characteristics....

We characterize the essentially normal composition operators induced on the Hardy space H2 by linear fractional maps; they are either compact, normal, or (the nontrivial case) induced by parabolic non-automorphisms. These parabolic maps induce the first known examples of nontrivially essentially normal composition operators. In addition we characterize those linearfractionally induced compositi...

There are several compression methods for phase to amplitude converter for sine function. In this paper, the linear and parabolic approximation of equi-section division utilizing the symmetry property and amplitude approximation of a sinusoidal waveform for direct digital frequency synthesizer (DDS) and also for other waveform applications, e.g. function generators and telecommunication devices...

We consider linear inhomogeneous non-autonomous parabolic problems associated to sesquilinear forms, with discontinuous dependence of time. We show that for these problems, the property of maximal parabolic regularity can be extrapolated to time integrability exponents r 6= 2. This allows us to prove maximal parabolic L r-regularity for discontinuous non-autonomous second-order divergence form ...

The direct steam generation (DSG) in parabolic trough collectors is an attractive option regarding the economic improvement of parabolic trough technology for solar thermal electricity generation in the multi Megawatt range. The European DISS project has proven the feasibility of the direct steam generation under real solar conditions in more than 4000 operation hours. Within the European R&D p...

Conditional Lie symmetries of semi-linear 1D Schrödinger and diffusion equations are studied if the mass (or the diffusion constant) is considered as an additional variable. In this way, dynamical symmetries of semi-linear Schrödinger equations become related to the parabolic and almostparabolic subalgebras of a three-dimensional conformal Lie algebra (conf3)C. We consider nonhermitian represen...

In this paper we first give a unified method by introducing the concept of admissible triplets to study local and global Cauchy problems for semi-linear parabolic equations with a general nonlinear term in different Sobolev spaces. In particular, we establish the local well-posedness and small global well-posedness of the Cauchy problem for semi-linear parabolic equations without the homogeneou...