Let Φ be a trace-preserving, positivity-preserving linear map on the algebra of complex 2 × 2 matrices, and let Ω be any finite-dimensional completely positive map. For p = 2 and p ≥ 4, we prove that the maximal p-norm of the product map Φ⊗Ω is the product of the maximal p-norms of Φ and Ω. Restricting Φ to the class of completely positive maps, this settles the multiplicativity question for al...

We investigate the interrelationships between the dynamical properties of commuting continuous maps of a compact metric space. Let X be a compact metric space. First we show the following. If τ : X → X is an expansive onto continuous map with the pseudo-orbit tracing property (POTP) and if there is a topologically mixing continuous map φ : X → X with τφ = φτ , then τ is topologically mixing. If...

A new generalization of the Gray map is introduced. The new generalization Φ : Z 2 → Z k−1 n 2 is connected with the known generalized Gray map φ in the following way: if we take two dual linear Z2k -codes and construct binary codes from them using the generalizations φ and Φ of the Gray map, then the weight enumerators of the binary codes obtained will satisfy the MacWilliams identity. The cla...

Kluwer Academic Publishers 2000 Homological Perturbation Theory – A theory that concerns itself with of a collection of techniques for deriving chain complexes which are both smaller and chain homotopy equivalent to a given chain complex (cf. also Complex (in homological algebra)). It is motivated by the desire to find effective algorithms in homological algebra. The cornerstone of the theory i...

where dA is the normalized area measure in D. The case where α = 0 is known as the (unweighted) Bergman space, often simply denoted by A2. Let φ be an analytic map from the open unit disk D into itself. The operator that takes the analytic map f to f ◦ φ is a composition operator and is denoted by Cφ . A natural generalization of a composition operator is an operator that takes f to ψ · f ◦ φ, ...

in this paper, the notion of $psi -$weak contraction cite{rhoades} isextended to fuzzy metric spaces. the existence of common fixed points fortwo mappings is established where one mapping is $psi -$weak contractionwith respect to another mapping on a fuzzy metric space. our resultgeneralizes a result of gregori and sapena cite{gregori}.

Ü Ü • Seeking scoring function as: H(x) = ∑T t=1 αtht(x) • Optimizing pair-wise loss, equivalent to AUC: L = ∑ yi H(xj)]] • Weak rankers h(x): decision stumps and grids (trees of depth 2) • Use weak outputs as new features Φ(x) = (α1h1(x), . . . , αThT (x)) • H can be viewed as linear discrim. rule H(x) = 〈w,Φ(x)〉 for w = 1̄ • T may be too big to store training Φ(xi) + want to explo...

In this paper, we prove the existence and uniqueness of fixed points for cyclic (α,β)-admissible type F-contraction and F−weak contraction under the setting of modular spaces, where the modular is convex and satisfying the ∆2-condition. Later, we prove some periodic point results for self-mappings on a modular space. We also give some examples to s...

A (projective) manifoldX of dimension 2n+1 together with a subbundle F ⊂ TX of rank 2n is a contact manifold if the pairing F × F → TX/F =: L defined by the Lie bracket is everywhere non-degenerate. An alternative description is as follows: there is a (sub-)line bundle L ⊂ ΩX such that the induced contact form θ ∈ H(X,ΩX⊗L) is non-degenerate in the sense that in local coordinates the form θ ∧ (...

Jachymski [ Proc. Amer. Math. Soc., 136 (2008), 1359-1373] gave modified version of a Banach fixed point theorem on a metric space endowed with a graph. In the present paper, (G, Φ)-graphic contractions have been de ned by using a comparison function and studied the existence of fixed points. Also, Hardy-Rogers G-contraction have been introduced and some fixed point theorems have been proved. S...