We prove that an involution on certain examples of surfaces of general type with , acts as identity on the Chow group of zero cycles of the relevant surface. In particular we consider examples of such surfaces when the quotient is an Enriques surface and show that the Bloch conjecture holds for such surfaces

We define the notion of Tate–Shafarevich group and Selmer group of the Chow group of zero cycles of degree zero of an abelian variety defined over a global function field and prove that the Selmer group is finite

Let S be a certain affine algebraic surface over Q such that it admits a regular map to A2/Q. We show that any non-trivial torsion element in the Chow group CH1(S) can be pulled back to ideal classes of quadratic fields whose order can be made as large as possible. This gives an affirmative answer to a question analogous to one raised by Agboola and Pappas, in the case of certain affine algebraic surfaces. Spreading out S over Z and for a closed point P?A2/Z, we show that the cardinality of a subgroup of the Picard group of the fiber SP remains unchanged when P varies over a Zariski open subset in A2/Z. We also show by constructing an element of odd order n?3 in the class group of certain imaginary quadratic fields that the Picard group of SP has a subgroup isomorphic to Z/nZ. © The Author(s), under exclusive licence to Springer-Verlag GmbH Austria, part of Springer Nature 2024.

A secret image transmission technique has been put forward in this paper using (3,3) visual cryptographic shares generated from secret image that are fabricated into frames in Graphics Interchange Format (GIFs) to prevent any intruder from knowing the secret contained in the GIFs. The (3, 3) Visual Cryptography technique creates shares from a binary secret image. Using GIFs as communication hosts, each share has been embedded into the Least Significant Bit (LSB) of the pixels of any single meaningful frame of GIFs. The shares obtained from the corresponding meaningful frames of the GIFs, during decoding, are combined to create the authenticated image. The combination of visual cryptography (VC) technique and steganographic principles ensures not only the secure distribution of shares but also adds an extra layer of protection through the integration of the GIF format.

This paper examines unbiased Non-Data-Aided (NDA) Signal-to-Noise Ratio (SNR) estimation for hyper-cubic modulated signals in Additive White Rayleigh Noise (AWRN) channels. We investigate the Crame’r-Rao Lower Bound (CRLB) derivation, noting sensitivity to hyper-cubic constellation dimensions at low SNR. At higher SNR, we identify a unified behavior between multi-order square-QAM and hyper-cubic constellations, yielding a closed-form CRLB expression. Higher dimensions in hyper-cubic constellations increase the CRLB, mitigated by augmenting observations for improved precision. This study offers insights into optimizing SNR estimation precision across signal environments.