We study the connection between STFT multipliers A1⊗mg1,g2 having windows g1,g2, symbols a(x,ω)=(1⊗m)(x,ω)=m(ω), (x,ω)∈R2d, and Fourier Tm2 with symbol m2 on Rd. find sufficient necessary conditions m,m2 g1,g2 for equality Tm2=A1⊗mg1,g2. For m=m2 former holds only particular choices of window functions in modulation spaces, whereas it never occurs realm Lebesgue spaces. In general, multiplier A...

We derive an inductive, combinatorial definition of a polynomial-valued regular isotopy invariant of links and tangled graphs. We show that the invariant equals the Reshetikhin-Turaev invariant corresponding to the exceptional simple Lie algebra G2. It is therefore related to G2 in the same way that the HOMFLY polynomial is related to An and the Kauffman polynomial is related to Bn, Cn, and Dn....

The concept of the D-brane probe provides the link between gauge theory and geometry. It has proven to be one of the most important ideas among recent developments in string theory, shedding new light on strong coupling gauge theory dualities, providing a physical interpretation of previously obscure algebraic-geometric constructions, and resulting in examples of the AdS/CFT correspondence with...

The equations of motion of the massless sector of the two dimensional string theory, obtained by compactifying the heterotic string theory on an eight dimensional torus, is known to have an affine o(8, 24) symmetry algebra generating an O(8, 24) loop group. In this paper we study how various known discrete Sand T duality symmetries of the theory are embedded in this loop group. This allows us t...

for two given graphs g1 and g2, the ramseynumber r(g1,g2) is the smallest integer n such that for anygraph g of order n, either $g$ contains g1 or the complementof g contains g2. let tn denote a tree of order n andwm a wheel of order m+1. to the best of our knowledge, only r(tn,wm) with small wheels are known.in this paper, we show that r(tn,wm)=3n-2 for odd m with n>756m^{10}.

We classify biharmonic and harmonic homomorphisms f:(G,g1)⟶(G,g2) where G is a connected simply three-dimensional unimodular Lie group g1 g2 are left invariant Riemannian metrics.