in this paper, let $l$ be a completeresiduated lattice, and let {bf set} denote the category of setsand mappings, $lf$-{bf pos} denote the category of $lf$-posets and$lf$-monotone mappings, and $lf$-{bf cslat}$(sqcup)$, $lf$-{bfcslat}$(sqcap)$ denote the category of $lf$-completelattices and $lf$-join-preserving mappings and the category of$lf$-complete lattices and $lf$-meet-preserving mapping...

In this paper, let $L$ be a completeresiduated lattice, and let {bf Set} denote the category of setsand mappings, $LF$-{bf Pos} denote the category of $LF$-posets and$LF$-monotone mappings, and $LF$-{bf CSLat}$(sqcup)$, $LF$-{bfCSLat}$(sqcap)$ denote the category of $LF$-completelattices and $LF$-join-preserving mappings and the category of$LF$-complete lattices and $LF$-meet-preserving mapping...

For a compact Hausdorff space X, let J be the ordered set associated with of all finite open covers X such that there exists nJ, where nJ is dimension ∂. Therefore, we have Hˇp(X;Z), 0≤p≤n=nJ. continuous self-map f on α∈J an cover and Lf(α)={Lf(U)|U∈α}. Then, fiber L˙f(α) Xf induced by Lf(α). In this paper, define topological entropy entL(f) as supremum ent(f,L˙f(α)) through Xf={Lf(U);U⊂X}, Lf(...

and Applied Analysis 3 then lim k Uf Lf, ∀f ∈ C X . 3.2 Moreover, if X is a compact metric space, then the convergence is uniform. Proof. Let f ∈ C X . The case when Lf f is trivial. Indeed, in this case, since Lf ∈ V andU preserves the elements of V, we haveUf ULf Lf , and hence Uf Lf , k 1, 2, . . . . If Lf / f , for sufficiently small ε > 0, the inverse image of the open set −ε, ε under the ...

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Proof. Consider the function class F = {f(·,x) | x ∈ P} as defined in (SP1), that is f(i,x) = fi(x). Since fi(·) each is assumed to be Lipschitz continuous with Lipschitz constant Li, we must have |fi(x)− fi(y)| ≤ LF ‖x− y‖, where LF ≡ max{L1, . . . , Ln}. Moreover, the index set P ∈ R for the function class F is assume to be bounded. Therefore all conditions for Lemma 2 are satisfied and hence...

For a function f : {0, 1} → R and an invertible linear transformation L ∈ GLn(2), we consider the function Lf : {0, 1} → R defined by Lf(x) = f(Lx). We raise two conjectures: First, we conjecture that if f is Boolean and monotone then I(Lf) ≥ I(f), where I(f) is the total influence of f . Second, we conjecture that if both f and L(f) are monotone, then f = L(f) (up to a permutation of the coord...

Let f be a cusp form of the Hecke space M0(λ, k, ) and let Lf be the normalized L-function associated to f . Recently it has been proved that Lf belongs to an axiomatically defined class of functions S̄. We prove that when λ ≤ 2, Lf is always almost primitive, i.e., that if Lf is written as product of functions in S̄, then one factor, at least, has degree zeros and hence is a Dirichlet polynomial...