A forced derivation tree (FDT) of a sentence pair {f, e} denotes a derivation tree that can translate f into its accurate target translation e. In this paper, we present an approach that leverages structured knowledge contained in FDTs to train component models for statistical machine translation (SMT) systems. We first describe how to generate different FDTs for each sentence pair in training ...

Definition 1.2. The module of relative differential forms of B over A is a Bmodule ΩB/A, together with an A-derivation d : B → ΩB/A satisfying the following universal property: for any B-module M and for any A-derivation d : B → M , there exists a unique B-module homomorphism f : ΩB/A → M such that d ′ = f ◦d. If DerA(B,M) denotes the set of all A-derivations from B into M , then we have a natu...

Derivation of tight bounds for probability metrics and f -divergences is of interest in information theory and statistics. This paper provides elementary proofs that lead, in some cases, to significant improvements over existing bounds; they also lead to the derivation of some existing bounds in a simplified way. The inequalities derived in this paper relate between the Bhattacharyya parameter,...

The homological niteness property F P 3 and the combinatorial property of having nite derivation type both are necessary conditions for nitely presented monoids to admit a nite convergent presentation. For monoids in general, the property of having nite derivation type is strictly stronger than the property F P 3. Here we show that for groups these two properties are equivalent. The proof explo...

A system WF of subintuitionistic logic is introduced, weaker than Corsi’s basic subintuitionistic system F. A derivation system with and without hypotheses is given in line with the authors’ derivation system for F. A neighborhood semantics is introduced with a somewhat more complex definition than the neighborhood semantics for non-normal modal logics. Completeness is proved for WF with respec...

Let R be an associative prime ring, U a Lie ideal such that u2 ∈ U for all u ∈ U . An additive function F : R→ R is called a generalized derivation if there exists a derivation d : R→ R such that F(xy)= F(x)y + xd(y) holds for all x, y ∈ R. In this paper, we prove that d = 0 or U ⊆ Z(R) if any one of the following conditions holds: (1) d(x) ◦F(y)= 0, (2) [d(x),F(y) = 0], (3) either d(x) ◦ F(y) ...

After introducing double derivations of $n$-Lie algebra $L$ we‎ ‎describe the relationship between the algebra $mathcal D(L)$ of double derivations and the usual‎ ‎derivation Lie algebra $mathcal Der(L)$‎. ‎In particular‎, ‎we prove that the inner derivation algebra $ad(L)$‎ ‎is an ideal of the double derivation algebra $mathcal D(L)$; we also show that if $L$ is a perfect $n$-Lie algebra‎ ‎wit...

let $mathcal m$ be a factor von neumann algebra. it is shown that every nonlinear $*$-lie higher derivation$d={phi_{n}}_{ninmathbb{n}}$ on $mathcal m$ is additive. in particular, if $mathcal m$ is infinite type $i$factor, a concrete characterization of $d$ is given.

Let $mathfrak{A}$ be a Banach algebra. We say that a sequence ${D_n}_{n=0}^infty$ of continuous operators form $mathfrak{A}$ into $mathfrak{A}$ is a textit{local higher derivation} if to each $ainmathfrak{A}$ there corresponds a continuous higher derivation ${d_{a,n}}_{n=0}^infty$ such that $D_n(a)=d_{a,n}(a)$ for each non-negative integer $n$. We show that if $mathfrak{A}$ is a $C^*$-algebra t...

The Lie derivation of multivector fields along multivector fields has been introduced by Schouten (see cite{Sc, S}), and studdied for example in cite{M} and cite{I}. In the present paper we define the Lie derivation of differential forms along multivector fields, and we extend this concept to covariant derivation on tangent bundles and vector bundles, and find natural relations between them and...