Dirac cone can be tilted in condensed matter setting. As a result of tilt, the Lorentz Symmetry is reduced to what we call tilted-Lorentz Symmetry. In this paper we derive the tilted-Lorentz transformations that leave a world with tilted Dirac cone invariant.

The Schwarzschild solution was obtained in 1916 as the first solution to Einstein’s field equations based on spherical Symmetry, which was considered a new idea in the use of Symmetry at the time. In this study, it is tried to reformulate the solutions of Einstein’s field equations with spherical Symmetry in both the presence and absence of the cosmological constant based on the invariants (or first integrals) of the Symmetry groups. The method used in this article is a combination of four well-known symmetries: Lie point Symmetry, λ-Symmetry, Darboux polynomials, and the extended Prelle-Singer method. In this method, to resolve the Schwarzschild problem, a combination of the mentioned symmetries is used in such a way that the independent invariants are obtained in a systematic and algorithmic way. Based on this, a Symmetry theory is provided for us. With the help of this theory, one can use symmetries in the best possible way, far from any confusion, and achieve the desired solutions with a specific solution, which is to find independent invariants.

On analyzing the Euclidean graph of fullerene C60, we have obtained the automorphism group of the Euclidean graphs of this molecule. It is proven that this group has order 120 and is isomorphic to Z2 x A5, where Z2 is a cyclic group of order 2 and A5 is the alternating group on five symbols.

Painting (screen reading, mourning ceremony), performance arts, miniature, Islamic calligraphy, architecture of mosque, art and Islamic mysticism using techniques and art values appropriately, and coffee house or Saqqa-khaneh are all examples of sacred arts, and constitute samples of the combination of form and contents and indicate interaction between art and human thoughts. Here, what remains a main question today is now that among the greatest immortal literary and art works that become globally significant due to their facilitation power in conveying meaning, massage, and medium displaying speed, then why religious teachings get a very low share in this respect? Although, in the past, using media and art was less possible, art was used more by Islamic scholars so that the oldest and most valuable religious and historical works within Islamic territories have survived for the sake of their mingling with art. Noticing that the use of artistic tools depends on the creator of artistic works who can use them in any way he or she desires, visual arts, literature, and all media are capable of being utilized to boost spiritual life, revival of nature, and spiritual wisdom and truth.

Within the semi-classical approximation of Thomas-Fermi, which is based on a statistical approach, the phase-space occupation equation number of nuclear matter is obtained by employing the Landau Fermi-Liquid theory. At the first, using the NN-interactions of Myers and Swiatecki, known as TF(96) and TF(90), the equation of state of nuclear matter (EOS) is derived. Then, a special attention is devoted to studying the behavior of Symmetry energy and Symmetry free energy quantities which have a substantial effect on the equation of state. Hence, the stiffer behavior of the EOS in the TF(90) interaction compared to the TF(96) interaction, refers to the important effects of these quantities. The extensibility feature of the present model is shown by determining the saturation density and the saturation incompressibility coefficient. In addition to the comparison of Symmetry energy, Symmetry free energy and incompressibility coefficient with the results of other models, the temperature effects on these quantities are also studied.