the bft approach is used to formulate the electronic states in graphene through a non-commutative space in the presence of a constant magnetic field b for the first time. in this regard, we introduce a second class of constrained system, which is not gauge symmetric but by applying bft method and extending phase space, the second class constraints  converts  to the first class constraints so th...

We study the problem of embedding degree an abelian variety over a finite field. In particular, we show that for prescribed CM field L ≥4, integers m, n and prime ℓ≡1(modm⋅n) splits completely in L, there exists ordinary with endomorphism algebra respect to ℓ full m⋅n ℓ. also class absolutely simple higher dimensional varieties whose algebras are central imaginary quadratic fields.

‎By considering a degenerate $p(x)-$Laplacian equation‎, ‎a generalized compact embedding in weighted variable‎ ‎exponent Sobolev space is presented‎. ‎Multiplicity of positive solutions are discussed by applying fibering map approach for the‎ ‎corresponding Nehari manifold‎. 

‎It is well known that every (real or complex) normed linear space $L$ is isometrically embeddable into $C(X)$ for some compact Hausdorff space $X$‎. ‎Here $X$ is the closed unit ball of $L^*$ (the set of all continuous scalar-valued linear mappings on $L$) endowed with the weak$^*$ topology‎, ‎which is compact by the Banach--Alaoglu theorem‎. ‎We prove that the compact Hausdorff space $X$ can ...