... yet; all the work has still to be done. 161 it reduces to checking whether the DCG derives one of a finite number of strings. Limit the DCG Another approach is to limit the size ofthe categories ... verify that the question whether theintersectionof a word-graph and an off- line parsable DCG is empty or not is decidable since 163 The intersectionofFinite State Automata and Definite Clause ... replace the usual string positions with the names ofthe states in the FSA. It is also straight- forward to show that the complexity of this process is cubic in the number of states ofthe FSA...
... yields the claim in (2.80). This completes the proof of Lemma 6.This completes the proof of Proposition 4 and hence of Theorem 1.3. Proof of Theorem 2In this section we indicate how the arguments ... secondterm on the right-hand side ofthe analogue of (2.93).4. Proof of Theorem 3In Sections 4–6 we prove Theorems 3–5. The proof follows the same line of reasoning as in [3, §5], but there are ... andgeneralization ofthe proof of Proposition 3 in [3]. We outline the main steps,while skipping the details.Step 1. One ofthe basic ingredients in the proof in [3] is to approximate the volume ofthe Wiener...
... can incorporate these correlationsinto the probability of default kD over the interval Y D. To describe the dependence ofthe probability of default on the state ofthe economy, weuse ... if the defaultfree spot interest rate increases, keeping the value ofthe ®rm constant, the mean ofthe assetÕs probability distribution increases and the probability of default declines. As the ... if the put option trades in- the- money, the volatility ofthe corporate debt is sensitive to the volatility of the underlying asset.9Third, if the default free interest rate increases, the spread...
... chamber.❍❍❍❍❍❆❆❆❆❆❅❅❅❅❅❅❅✘✘✘✘✘✘✘✘✘✘✄✄✄✄✄✄✄✄✄✄ The Coxeter complex of type BC3isformed by all the mirrors of symmetry of the cube; here they are shown by theirlines ofintersection with the faces of the cube.Figure 3.2: The Coxeter ... that the mapsr : z → z · e2πi/n,t : z → ¯z,where ¯ denotes the complex conjugation, generate the group of symmetries of ∆.2.3.8 Use the idea ofthe proof of Theorem ?? to find the orders of ... vector.42✡✡✡✡✡❏❏❏❏❏❏❏❏❏❏✡✡✡✡✡✟✟✟✟✟✟✟✟✟✟✟✟✟✟✡✡✡✡✡✡✡✡✡❍❍❍❍❍❍❍❍❍❏❏❏❏❏❏❏❏❏❏❏❏❪❏❏❏❫s✻❄tABC The group of symmetries of the regular n-gon ∆ is generatedby two reflections s and t in the mirrors passing through the midpoint and a vertex of a side of ∆.Figure 2.7: For the proof of Theorem...
... contraction, and the proof is complete.In the following theorem, which is the main result in this section, we establish the strong convergence ofthe sequence defined by 1.8.Theorem 3.2. Let ... improve some ofthe conditions and results in the mentionedpapers, especially those of Song and Xu 11.2. PreliminariesLet S : {x ∈ X : x 1} be the unit sphere ofthe Banach space X. The space ... see 15.References1 I. Yamada, The hybrid steepest-descent method for the variational inequality problem of the intersectionof fixed point sets of nonexpansive mappings,” in Inherently...
... on the two aforementionedphenomena: the effects of finite word length for the weights of the NN used for the classification, and the effects of the simplification ofthe activation functions ofthe ... Centroid. The spectral centroid ofthe ith frame canbe associated with the measure of brightness ofthe sound,and is obtained by evaluating the center of gravity of the spectrum. The centroid ... used to represent the 2’s complement ofthe integer portion ofthe number,(iii) y designates the number of bits used to represent the 2’s complement ofthe fractional part of such number.For...
... sufficient evidence for the identification of that constituent; e.g., if the leftmost daughter is either the specifier or the head of that constituent in the sense of Jacken- doff (1977). Third, ... CFPSG. The first set is explicitly designed to preserve the property of noncenter-embedding. The second is designed to maximize the use of prefixes on the basis of being able to predict the identity ... > of S. P2 ~ ~in, on, ] Among the expressions generated by the extended grammar G2 are those in E3. (E3) a. the boss knew that the teacher saw the child yesterday b. the friend of the...
... ‘working toward the assemblage ofthe verbal self – in symbiosis with the other assemblages of the emergent self – and thereby inaugurating a new mastery of the object, of touch, of a spatiality. ... from the impasses ofthe present, or,simply, belies the very presence ofthe infinite within the finite.However, as we have seen, the rupturing of given signifying regimesis only one ofthe gestures ... character ofthe texture of these incorporeals’) and the actual (the ‘discursive finitude of energetico-spatio-temporal Fluxes andtheir propositional correlates’) is unclear, but the manner of this...
... The cost of a path in a WFST is the product (⊗) ofthe initialweight ofthe initial state, the weight of all the tran-sitions, and the final weight ofthe final state. Whenseveral paths in the ... paths in the WFST match the same relation, the total cost is the sum (⊕) ofthe costs of all the paths.In NLP, the tropical semi-ring (R+∪{∞}, min, +, ∞, 0) is very often used: weightsare ... paths match the same relation, the total cost is the cost of the path with minimal cost. The following discussionwill apply to any semi-ring, with examples using the tropical semi-ring.2 The Equivalence...
... completes the proof of Theorem 2. 4. Smoothness oftheintersection local timeIn this section, we consider the smoothness oftheintersection localtime. Our main object is to explain and prove the ... Existence oftheintersection local time The aim of this section is to prove the existence ofthe intersection local time of SHandSH, for an H =12and d ≥ 2. We have obtained the following ... factsfor the chaos expansion. In Section 3, we study the existence of the intersection local time. In Section 4, we show that the intersection local time is smooth in the sense ofthe Meyer-Watanabe...
... 0. This completes the proof. □5. Regularity oftheintersection local time The main object of this section is to prove the next theorem.Theorem 9. Let Hd <2. Then, t he intersection local ... completes the proof of Theorem 2. □4. Smoothness oftheintersection local timeIn this section, we consider the smoothness ofthe intersectio n local time. Our mainobject is to explain and prove the ... facts for the chaos expansion. In Section 3, we study the existence oftheintersection lo cal time. In Section 4, we show that the intersection local time is smooth in the sense ofthe Meyer-Watanabe...
... n), and the proof iscomplete. The following theorem deals with the continuous dependence ofthe solution of (26)and (27) on the functions F1, F2and the initial value f (m), g(n).Theorem ... g(m, n) ≡ 0,q =1,p ≥ 1, then Theorem 2.1 reduces to [[13], Theorem 1].Following a similar process as the proof of Theorem 2.1, we have the following threetheorems.Theorem 2.2.Supposeu, a, ... is decreasing in the second variable” in Theorem 2.5, thenTheorem 2.5 reduces to [[14], Theorem 7]. Furthermore, if g(m, n ) ≡ 0, q =1,p ≥ 1,then Theorem 2.5 reduces to [[13], Theorem 3].Following...