Most learning systems applied to problem solving have the goal of learning knowledge for solving problems more eeciently. However, very few systems have focused on the acquisition of planning operator descriptions. In this paper, we present a system that learns operator deenitions from the interaction with a completely unknown environment. In order to achieve better learning convergence, severa...

Let Γ be a cofinite Fuchsian group acting on hyperbolic two-space H. Let M = Γ\H be the corresponding quotient space. For γ, a closed geodesic of M , let l(γ) denote its length. The prime geodesic counting function πM (u) is defined as the number of Γ-inconjugate, primitive, closed geodesics γ such that el(γ) ≤ u. The prime geodesic theorem states that: πM (u) = ∑ 0≤λM,j≤1/4 li(uM,j ) +OM ( u3/...

In this paper, it is shown that the diagonal coset vertex operator algebra C(Lg(k+2,0),Lg(k,0)⊗Lg(2,0)) rational and C2-cofinite in case g=so(2n), n≥3 k an admissible number for gˆ. It also C(Lsl2(k+4,0),Lsl2(k,0)⊗Lsl2(4,0)) sl2ˆ. Furthermore, irreducible modules of are classified a positive odd integer.

It is proved that any vertex operator algebra for which the image of the Virasoro element in Zhu’s algebra is algebraic over complex numbers is finitely generated. In particular, any vertex operator algebra with a finite dimensional Zhu’s algebra is finitely generated. As a result, any rational vertex operator algebra is finitely generated. Although many well known vertex operator algebras are ...

In this paper, the (infinite) direct product of fields is investigated. particular, finiteness a given set characterized in terms some ring-theoretic observations. Next, certain localization (whose multiplicative formed by cofinite sets) studied. Finally, it shown that every X can be made into separated scheme, and scheme an affine if only finite set.

Let A be a random set constructed by picking independently each element of {1,…,n} with probability α∈(0,1). We give formula for the that rational number q belongs to ratio A/A≔{a/b:a,b∈A}. This generalizes previous result Cilleruelo and Guijarro-Ordóñez. Moreover, we make some considerations about formulas event ⋁i=1k(qi∈A/A), where q1,…,qk are numbers, showing they related study connected com...

in this paper, we nd the relationships between module contractibility of abanach algebra and its ideals. we also prove that module contractibility ofa banach algebra is equivalent to module contractibility of its module uniti-zation. finally, we show that when a maximal group homomorphic image ofan inverse semigroup s with the set of idempotents e is nite, the moduleprojective tensor product ...