Fix an odd prime p, an algebraic closure Qp, and an isomorphism C ∼ → Qp. Fix an integer N ≥ 1 prime to p, and let T be the polynomial algebra over Z generated by the operators T!, ! ! Np, Up and 〈d〉 , d ∈ (Z/NZ). Set W = Spf(Zp[[Zp ]]), and let W = W rig be the rigid analytic space of characters of Zp together with its universal character χW : Z × p → O(W ) ; we embed Z in W (Qp) by mapping k ...

Exercise 1 (Maximal compact subgroups of G). A lattice in Qp is a finitelygenerated Zp-submodule of Qp that generates Qp as vector space. In particular, it’s free of rank n. Note that G acts transitively on the set of lattices in Qp . (i) Show that K = StabG(Zp ). (ii) Suppose that K ′ is a compact subgroup of G. Show that K ′ stabilises a lattice. (Hint: show that the K ′-orbit of Zp is finite...

Let p be a fixed prime number. Throughout this paper, the symbols Z, Zp, Qp, and Cp denote the ring of rational integers, the ring of p-adic integers, the field of p-adic rational numbers, and the completion of algebraic closure of Qp, respectively. Let N be the set of natural numbers, and Z N ∪ {0}. Let νp be the normalized exponential valuation of Cp with |p|p p−νp p p−1 see 1–24 . Let UD Zp ...

The birefringence of an optical fiber resulting from an asymmetry of the index profile is numerically evaluated using a finite element method with a full-vectorial formulation. Such asymmetric index profiles, assumed to vary exponentially across the fiber core, could be induced during the writing of fiber Bragg gratings with UV sideexposure techniques. The results reveal that the birefringence ...

The birefringence of a red blood cell (RBC) is quantitatively monitored as it becomes infected by a malarial parasite. Large changes occur in the cell's refractive index at different stages of malarial infection. The observed rotation of an optically trapped, malaria-infected RBC is not a simple function of shape distortion: the malarial parasite is found to itself exercise a profound influence...

We investigated the origin of birefringence in colloidal films of spherical silica particles. Although each particle is optically isotropic in shape, colloidal films formed by drop drying demonstrated birefringence. While periodic particle structures were observed in silica colloidal films, no regular pattern was found in blended films of silica and latex particles. However, since both films sh...

Using the elasto-optic effect we increase the frequency difference between the two orthogonally polarized modes, the so-called birefringence splitting, in standard single-mode oxideconfined GaAs-based vertical-cavity surface-emitting lasers (VCSELs). The birefringence may play an important role in the realization of ultrafast polarization modulation for highspeed data transmission. For practica...

BACKGROUND Although the Epstein-Barr virus (EBV) is associated with malignant and nonmalignant diseases, its lytic replication is predominantly associated with nonmalignant diseases such as acute infectious mononucleosis (IM) or chronic active EBV infection. Lytic replication is also associated with type B EBV more than with type A EBV. Sustained lytic replication, however, is not compatible wi...

Let p be a fixed odd prime number. Throughout this paper, Zp, Qp, and Cp will denote the ring of p-adic rational integers, the field of p-adic rational numbers, and the completion of algebraic closure of Qp, respectively. Let N be the set of natural numbers and Z N ∪ {0}. The p-adic absolute value on Cp is normalized so that |p|p 1/p. Assume that q ∈ Cp with |1 − q|p < 1. Let f be a continuous ...

Verifiable secret sharing (VSS) schemes [1–3] rely on the assumption that parties can not reliably fabricate false secret shares which pass the verification process. Here, we show that, for certain VSS implementations that use verification commitments bounded to a finite field, this assumption is incorrect. Let there be n shares of a secret and a threshold of t secret shares required to get the...