We prove the absence of a mass gap and confinement in the Polyakov model with massless complex fermions in any representation of the gauge group. A U(1)∗ topological shift symmetry protects the masslessness of one dual photon. This symmetry emerges in the IR as a consequence of the Callias index theorem and abelian duality. For matter in the fundamental representation, the infrared limits of th...

Single crystals of Schiff base compound 2-[(2-chloro-4-nitrophenyl) iminomethyl] phenol (1) were grown by the slow evaporation technique at room temperature. The crystal structure of the title compound was determined by single crystal X-ray diffraction. The title compound crystallizes in the monoclinic system, space group P21, with two symmetry independent molecules. Intramolecular O-H···N hydr...

A wide class of models, built of the three component unit vector field living in the (3+1) Minkowski space-time, which break explicitly global O(3) symmetry are discussed. The symmetry breaking occurs due to the so-called dielectric function multiplying a standard symmetric term. Integrability conditions are found. Moreover, for some particular forms of the Lagrangian exact toroidal solutions w...

The restricted partial-cycle-index (RPCI) method has been developed by starting from the partial-cycle-index (PCI) method of the unit-subduced-cycle-index (USCI) approach (S. Fujita, “Symmetry and Combinatorial Enumeration in Chemistry”, Springer-Verlag (1991)), where enumerated derivatives are generated by means of vertex substitution (monodentate ligands) and/or edge substitution (bidentate l...

a topological index of a molecular graph g is a numeric quantity related to g which isinvariant under symmetry properties of g. in this paper we obtain the randić, geometricarithmetic,first and second zagreb indices , first and second zagreb coindices of tensorproduct of two graphs and then the harary, schultz and modified schultz indices of tensorproduct of a graph g with complete graph of ord...