Related papers: A code space for a generalized IFS
Within the new concept of a local iterated function system (local IFS), we consider a class of attractors of such IFSs, namely those that are graphs of functions. These new functions are called local fractal functions and they extend and…
We introduce local iterated function systems and present some of their basic properties. A new class of local attractors of local iterated function systems, namely local fractal functions, is constructed. We derive formulas so that these…
Quantum Iterated Function System on a complex projective space is defined by a family of linear operators on a complex Hilbert space. The operators define both the maps and their probabilities by one algebraic formula. Examples with…
The space complexity of functional programs is not well understood. In particular, traditional implementation techniques are tailored to time efficiency, and space efficiency induces time inefficiencies, as it prefers re-computing to…
We are concerned with sets of generic points for shift-invariant measures in the countable symbolic space. We measure the sizes of the sets by the Billingsley-Hausdorff dimensions defined by Gibbs measures. It is shown that the dimension of…
Not all approximations arise from information systems. The problem of fitting approximations, subjected to some rules (and related data), to information systems in a rough scheme of things is known as the \emph{inverse problem}. The inverse…
Gel'fand triples of test and generalized functionals in Gaussian spaces are constructed and characterized.
This paper presents generalized channel coding theorems for a time-slotted distributed communication system where a transmitter-receiver pair is communicating in parallel with other transmitters. Assume that the channel code of each…
A generic construction of linear codes over finite fields has recently received a lot of attention, and many one-weight, two-weight and three-weight codes with good error correcting capability have been produced with this generic approach.…
We investigate the set of invariant idempotent probabilities for countable idempotent iterated function systems (IFS) defined in compact metric spaces. We demonstrate that, with constant weights, there exists a unique invariant idempotent…
In this paper we studied generalization of Hermitian function field proposed by A.Garcia and H.Stichtenoth. We calculated a Weierstrass semigroup of the point at infinity for the case q=2, r>=3. It turned out that unlike Hermitian case, we…
Generalized Concatenated (GC), also known as Integrated Interleaved (II) Codes, are studied from an erasure correction point of view making them useful for Redundant Arrays of Independent Disks (RAID) types of architectures combining global…
We consider finitely generated shift-invariant spaces (SIS) with additional invariance in $L^2(\R^d)$. We prove that if the generators and their translates form a frame, then they must satisfy some stringent restrictions on their behavior…
We study smooth function spaces of Gelfand-Shilov type, with global behavior governed through a translation-invariant Banach function space and localized via a weight function system. We clarify the roles of the translation-invariant Banach…
In 1996, Strichartz introduced reverse iterated function systems (RIFS) $\mathcal{F}=\{f_i(x)=r_i x+b_i\}_{i=1}^m$ of expanding mappings on $\mathbb{Z}$ and left the determination of the general dimension formulas of invariant sets as an…
We give a full description of complete interpolating sequences for the shift-invariant space generated by the Gaussian. As a consequence, we rederive the known density conditions for sampling and interpolation.
We construct a converging geometric iterated function system on the moduli space of ordered triangles, for which the involved functions have geometric meanings and contain a non-contraction map under the natural metric.
Basic algebraic and combinatorial properties of finite vector spaces in which individual vectors are allowed to have multiplicities larger than $ 1 $ are derived. An application in coding theory is illustrated by showing that multispace…
We present an overview of some recent developments in the theory of generalized formal series, grounded in diffeological geometric framework. These constructions aim to offer new tools for understanding infinite-dimensional phenomena in…
Generalized symmetries (also known as categorical symmetries) is a newly developing technique for studying quantum field theories. It has given us new insights into the structure of QFT and many new powerful tools that can be applied to the…