... 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 2
In this section we indicate how the arguments ... second
term on the right-hand side ofthe analogue of (2.93).
4. Proof of Theorem 3
In Sections 4–6 we prove Theorems 3–5. The proof follows the same line
of reasoning as in [3, §5], but there are ... and
generalization 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 correlations
into the probability of default kD over the interval Y D. To describe
the dependence ofthe probability of default on the state ofthe economy, we
use ... if the default
free 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.
9
Third, if the default free interest rate increases, the
spread...
... chamber.
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❅
❅
✘
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✘
✘
✘
✘
✘
✘
✘
✄
✄
✄
✄
✄
✄
✄
✄
✄
✄
The Coxeter complex of type BC
3
is
formed by all the mirrors of symmetry of
the cube; here they are shown by their
lines ofintersection with the faces of the
cube.
Figure 3.2: The Coxeter ... that the maps
r : z → z · e
2πi/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
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✡
✡
✡
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❏
❏
❏
❏
❏
❏
❏
✡
✡
✡
✡
✡
✟
✟
✟
✟
✟
✟
✟
✟
✟
✟
✟
✟
✟
✟
✡
✡
✡
✡
✡
✡
✡
✡
✡
❍
❍
❍
❍
❍
❍
❍
❍
❍
❏
❏
❏
❏
❏
❏
❏
❏
❏
❏
❏
❏❪
❏
❏
❏❫
s
✻
❄
t
A
BC
The group of symmetries of the
regular n-gon ∆ is generated
by 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 mentioned
papers, especially those of Song and Xu 11.
2. Preliminaries
Let S : {x ∈ X : x 1} be the unit sphere ofthe Banach space X. The space ... see 15.
References
1 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 aforementioned
phenomena: 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 can
be 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 regimes
is only one ofthe gestures ... character ofthe texture of these incorporeals’) and the
actual (the ‘discursive finitude of energetico-spatio-temporal Fluxes and
their propositional correlates’) is unclear, but the manner of this...
... The cost
of a path in a WFST is the product (⊗) ofthe initial
weight ofthe initial state, the weight of all the tran-
sitions, and the final weight ofthe final state. When
several 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: weights
are ... paths match
the same relation, the total cost is the cost of the
path with minimal cost. The following discussion
will 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 time
In this section, we consider the smoothness oftheintersection local
time. 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 S
H
and
S
H
, for an H =
1
2
and d ≥ 2. We have obtained
the following ... facts
for 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 time
In this section, we consider the smoothness ofthe intersectio n local time. Our main
object 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 is
complete.
The following theorem deals with the continuous dependence ofthe solution of (26)
and (27) on the functions F
1
, F
2
and 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 three
theorems.
Theorem 2.2.Supposeu, a, ... is decreasing in the second variable” in Theorem 2.5, then
Theorem 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...