Let V be a vector space of dimension n+1 over a field k, and consider the scheme X = PV ∼= Pk ∼= Proj(k[x0, . . . , xn]). Consider F a quasi-coherent sheaf over X. We can examine its Cech cohomology which coincides with its sheaf (nonetale) cohomology because X is Noetherian and separated (cf. Hartshorne, ch. III theorem 4.5.). Particularly, H(X,F) ∼= Γ(F , X). However Γ(F , X) ∼= HomX(OX ,F). ...

This paper is a sequel to [6], in which we introduced quadratic forms on a module over a supertropical semiring R and analyzed the set of bilinear companions of a single quadratic form V → R in case the module V is free. Any (semi)module over a semiring gives rise to what we call its minimal ordering, which is a partial order iff the semiring is “upper bound.” Any polynomial map q (or quadratic...

In this work we present our entry for the Voice Conversion Challenge 2016, denoting new features to previous work on GMM-based voice conversion. We incorporate frequency warping and pitch transposition strategies to perform a normalisation of the spectral conditions, with benefits confirmed by objective and perceptual means. Moreover, the results of the challenge showed our entry among the high...

We extend the known result that bilinear pseudo-differential operators with symbols in Hörmander class $$BS^{-n/2}_{0,0}(\mathbb {R}^n)$$ are bounded from $$L^2 \times L^2$$ to $$h^1$$ . show those also $$L^r $$ for every $$1< r\le 2$$ Moreover we give similar results symbol classes wider than of limited smoothness.

It is shown that the bilinear Hilbert transforms Hα,β(f, g)(x) = p.v. Z R f(x− αt)g(x− βt) dt t map L1(R)×L2(R)→ L(R) uniformly in the real parameters α, β when 2 < p1, p2 <∞ and 1 < p = p1p2 p1+p2 < 2. Combining this result with the main result in [9], it follows that the operators H1,α map L (R) × L∞(R) → L(R) uniformly in the real parameter α ∈ [0, 1], as conjectured by A. Calderón.

Both vector 1-forms (tensor elds of type (1,1)) and Lie brackets map (tangent) vectors to the same. The former do so in a manner that is linear over the ring of functions; the latter are bilinear, but only over the constants. By composing one Lie bracket and m vector 1-forms (we consider 2 m 4) in all possible ways many maps of vector elds are obtained, bilinear over the constants. We study lin...

The notion of the square submodule of a module M over an arbitrary commutative ring R, which is denoted by RM, was introduced by Aghdam and Najafizadeh in [3]. In fact, RM is the R−submodule of M generated by the images of all bilinear maps on M. Furthermore, given a submodule N of an R−module M, we say that M is nil modulo N if μ(M×M) ≤ N for all bilinear maps μ on M. The main question about t...

Let F : M → N be a harmonic map between complete Riemannian manifolds. Assume that N is simply connected with sectional curvature bounded between two negative constants. If F is a quasiconformal harmonic diffeomorphism, then M supports an infinite dimensional space of bounded harmonic functions. On the other hand, if M supports no non-constant bounded harmonic functions, then any harmonic map o...

We construct an interactive identification scheme based on the bilinear Diffie-Hellman problem and analyze its security. This scheme is practical in terms of key size, communication complexity, and availability of identity-variance provided that an algorithm of computing the Weil-pairing is feasible. We prove that this scheme is secure against active attacks as well as passive attacks if the bi...

We construct two efficient Identity Based Encryption (IBE) systems that are selective identity secure without the random oracle model in groups equipped with a bilinear map. Selective identity secure IBE is a slightly weaker security model than the standard security model for IBE. In this model the adversary must commit ahead of time to the identity that it intends to attack, whereas in the sta...