Elliptic curve cryptosystems are usually implemented over fields of characteristic two or over (large) prime fields. For large prime fields, projective coordinates are more suitable as they reduce the computational workload in a point multiplication. In this case, choosing for parameter a the value −3 further reduces the workload. Over Fp, not all elliptic curves can be rescaled through isomorp...

where σd is a parameter, and x is the projected point in frame t. Pt′→t(Dt′(x′)) denotes the transformed disparity value according to the camera parameters between frames t and t. The transformed disparity is denoted as Pt′→t(Dt′(x′)). We denote the projective matrix from frame t to frame t as [R|t], and the intrinsic matrix of frame t as K. The 2D position of x is denoted as (u, v). Then Pt′→t...

Associated to a variation of polarized Hodge structure there is a period mapping ty : S —• Y\P, where S is the parameter space and T\P denotes the corresponding modular variety of polarized Hodge structures (the primary example to keep in mind is that arising from a family of smooth projective varieties parametrized by S) [3], [4]. The local study of the singularities of \p ([5]) reduces to the...

ADHM invariants are equivariant virtual invariants of moduli spaces of twisted cyclic representations of the ADHM quiver in the abelian category of coherent sheaves of a smooth complex projective curve X. The goal of the present paper is to present a generalization of this construction employing a more general stability condition which depends on a real parameter. This yields a chamber structur...

A one-parameter symplectic group {e}t∈R derives proper canonical transformations on a Boson Fock space. It has been known that the unitary operator Ut implementing such a proper canonical transformation gives a projective unitary representation of {e}t∈R and that Ut can be expressed as a normal-ordered form. We rigorously derive the self-adjoint operator ∆(Â) and a phase factor e i ∫ t 0 τ Â (s...

A projective multiset is a collection of projective points, which are not necessarily distinct. A linear code can be represented as a projective multiset, by taking the columns of a generator matrix as projective points. Projective multisets have proved very powerful in the study of generalised Hamming weights. In this paper we study relations between a code and its dual.

We show that Souslin Absoluteness and Projective Regularity holds ii Souslin Uniformization does. As a result, Souslin Absoluteness plus 1 n Projective Regularity implies 1 n+1 Projective Regularity. Another result is that 1 5 Souslin Absoluteness implies 1 4 Projective Regularity, and 1 6 Souslin Absoluteness implies 1 5 Projective Regularity.

This paper studies the usefulness of the projective approach to structure from motion (SFM). We conduct an essentially algorithm{independent experimental comparison of projective versus Euclidean reconstruction. Our results show that Euclidean reconstruction is essentially as accurate as pro-jective reconstruction, even with signiicant calibration error and for the pure projective structure. Th...

We proved in Theorem 3. 15 b that free modules have the precise same property that. projective modules 2 attributes to projective modules. In fact, it is easy to use.BIG PROJECTIVE MODULES ARE FREE. Finitely generated proiective modules rise significantly in certain geometric nd.dorff space X and finitely generated projective modules over the ring of continuous real-valued functions on X. A num...

We show that the bounded proper forcing axiom BPFA implies that there is a well-ordering of P(ω1) which is Δ1 definable with parameter a subset of ω1. Our proof shows that if BPFA holds then any inner model of the universe of sets that correctly computes א2 and also satisfies BPFA must contain all subsets of ω1. We show as applications how to build minimal models of BPFA and that BPFA implies t...