the theory of c-frames and c-bessel mappings are the generalizationsof the theory of frames and bessel sequences. in this paper, weobtain several equivalent conditions for dual of c-bessel mappings.we show that for a c-bessel mapping $f$, a retrievalformula with respect to a c-bessel mapping $g$ is satisfied if andonly if $g$ is sum of the canonical dual of $f$ with a c-besselmapping which  wea...

Using the notion of “belongingness ($epsilon$)” and “quasi-coincidence (q)” of fuzzy points with fuzzy sets, we introduce the concept of an ($ alpha, beta$)- fuzzyHv-ideal of an Hv-ring, where , are any two of {$epsilon$, q,$epsilon$ $vee$ q, $epsilon$ $wedge$ q} with $ alpha$ $neq$ $epsilon$ $wedge$ q. Since the concept of ($epsilon$, $epsilon$ $vee$ q)-fuzzy Hv-ideals is an important and ...

This paper develops a two-gene, single fitness peak model for determining the equilibrium distribution of genotypes in a unicellular population which is capable of genetic damage repair. The first gene, denoted by sigma(via), yields a viable organism with first-order growth rate constant k>1 if it is equal to some target "master" sequence sigma(via,0). The second gene, denoted by sigma(rep), yi...

In this paper, by using the sequence of adjointable operators from pro-C*-algebra $ mathcal{A} $ into a Hilbert $ mathcal{A} $-module $ E $. We introduce frames with bounds in pro-C*-algebra $ mathcal{A} $. New frames in Hilbert modules over pro-C*-algebras are called standard $ ast $-frames of multipliers. Meanwhile, we study several useful properties of standard $ ast $-frames in Hilbert modu...

Timing synchronization of an early WIND-FLEX prototype is discussed in this paper. Simulation results for different low-complexity timing synchronization metrics are given in an AWGN (additive white Gaussian noise) channel. Simulations take into account frame detection via a threshold comparison followed by symbol timing estimation using a maximum search. Training symbols are fixed. A novel low...

We discuss two distinct realizations of the diffeomorphism group for metric gravity, which give rise to theories that are classically equivalent, but quantum mechanically distinct. renormalize them in $d=2+\epsilon$ dimensions, developing a new procedure dimensional continuation and highlighting connections with constructions previously appeared literature. Our hope is frame candidates ultravio...

In this paper, we study frames for bounded linear operators and defined the notion of Ad-operator frame for Banach spaces. A necessary and sufficient condition for a sequence of bounded linear operators to be an Ad-operator frame has been given. Some characterizations of Ad-operator frames have been discussed. Further, a method has been given to generate a -Banach frame using a Schauder frame. ...