... be considered as giving rise to another single suffix, namely, the concatenation (eni) ofthe two individual suffixes We may then write the translation program as if, without exception, only one ... in the stem dictionary for a source-language word, the last letter is elided, and a match sought for the truncated word This elision and comparison is continued until the first few letters ofthe ... two-letter ones are recognized first, in an attempt to prevent spurious recognitions If the first two letters are the same as an entry in the prefix dictionary, a note is made ofthe 76 prefix, these...
... integrating out the distribution G Note that as long as the base distribution P0 is fixed, predictions not depend onthe seating arrangement z−i , only onthe count of word w w in the previously ... tables Of particular note for our discussion is that in order to calculate these conditional distributions we must know the table assignments z−i for each ofthe words in w−i Moreover, in the Gibbs ... derivation Due to a misinterpretation of Antoniak (1974), GGJ06 use an approximation that leaves out all the P1 (w) terms from (4).1 Figure compares the approximation to the exact expectation when the...
... progressions with the difference ρ Precisely ϕr of them have length n/ρ and ϕ − ϕr are of length n/ρ Since these progressions are pairwise disjoint, there are at least (ϕ + ϕr )2 n/ρ the electronic ... comments Due to their suggestions we were able to prove the main result ofthenote in its present sharp form the electronic journal of combinatorics (2000), #R30 References [1] N Alon, Independent ... completes the proof of Theorem 2 Corollary The estimate (5) holds, provided k > ≥ and max 1+ln (k − ), 2(1 + ln +1 +1 ) < ln ρ (9) the electronic journal of combinatorics (2000), #R30 Proof We need...
... apply, with the same conclusion and proof as the above corollary In conclusion, we raise the question as to whether there is a q-analogue of formula (1), (q) i.e., for the (0,1)-inclusion matrix ... t) = in the hypothesis of our theorem precludes a new proof of Wilson’s theorem via our recursive formula In the special case when the characteristic p of F is larger than k, our recursion does ... completes the proof of (1) Corollary Over the rational field Q, rQ (Wt,k (v)) = ( v ), provided k + t ≤ v t Proof This is very easy using (1): note that the condition ”k + t ≤ v” is inherited by the...
... 1, , ρn Denote by M4 the block consisting ofthe rows i = |A+ | + 1, , m and the columns j = 2ρn+ 1, , n Denote by M5 the block consisting ofthe rows i = 1, , |A+ | and the columns ... mn/4 They conjectured (the case k = of Conjecture in [3]) that b(m, n) ≤ 2mn/3 In this paper we prove this conjecture, and together with a well-known construction obtain that it is sharp Furthermore, ... visualizes these terms Let c(s, k) denote the number of entries of M equal to k in the block Ms for s = 1, 2, 3, 4, and k = −1, 0, For normalization purposes, define f (s, k) = c(s, k)/mn Consider the...
... other arcs are ofthe form vi → vj with i < j In other words, reversing the arc → v1 gives the transitive tournament of order n As noted by Moon [1], there is a bijection between partitions of ... is not strong and that no sets A and B satisfy the lemma Let t be the number of strong components of T − v and let Wi be the set of vertices in the ith strong component If |W1 | ≥ 3, then choose ... apply the induction hypothesis using the paths P and Q to obtain a path R satisfying the lemma Next, we repeat the above argument with the portion of R beginning at um−1 and the vertex um Theorem...
... vertices, which is the main result ofthe paper The organization ofthe paper is as follows In the rest of this section we introduce basic notations In Section 2, we verify the conjecture for all ... partitioned into at most c subsets so that each ofthe subsets is either a clique or an independent set, and between any two of them there are either all possible edges or none of them The factorial ... 0, and the index ofthe class of all graphs equals infinity With this extension, the family of all hereditary classes is partitioned into countable number of subsets each of which consists of classes...
... is the cost of debt, T is the tax rate, D%t-1 is the proportion of debt onthe total market value for the firm, at t-1 and E%t-1 is the proportion of equity onthe total market value for the ... structure ofthe firm is the combination of debt and equity in it That is, VL the value ofthe levered firm is equal to VUL the value ofthe unlevered firm VL = VUL (3) And in turn, the value ofthe ... participation in the total value ofthe firm for each period and calculating the contribution of each to the WACC after taxes As a first step, we will not add up these components to find the value of...
... compensation for the erosion ofthe purchasing power of this investment by inflation The Bank uses this decomposition (commonly known as the Fisher relationship) and the real and nominal yield curves ... contrast the yield to maturity on a coupon bond is the single rate of interest which, when used to discount all future coupon payments and the redemption payment, gives the current price ofthe ... futures contract that settles onthe three-month BBA LIBOR rate prevailing onthe contract’s delivery date Contracts are standardised and traded between members ofthe London International Financial...
... removed the condition nP(|X1 | > ηn ) ≤ c(log n)ε0 , < ε0 < in theorem 1.1 of [12] Remark 1.4 If EX < ∞, then X is in the domain of attraction ofthe normal law Therefore, the class of random ... A noteonthe almost sure limit theorem for self-normalized partial sums of random variables in the domain of attraction ofthe normal law Qunying Wu1,2 College of Science, Guilin University of ... sums of random variables in the domain of attraction ofthe normal law, we will show that the ASCLT holds under a fairly general growth condition on dk = k−1 exp(ln k)α ), ≤ α < 1/2 Our theorem...
... for the strong stability of Jamison’s weighted sums But most of their results were achieved under the identically distributed condition and some results were obtained even under the condition of ... When these are compared with the corresponding results of independent random variable sequences, there still remains much to be desired The concept of complete convergence of a sequence of random ... variables converges completely to the expected value if the variance ofthe summands is finite Erdös [9] proved the converse The result of Hsu-Robbins-Erdös is a fundamental theorem in probability theory...
... P(|Xni | > δ) an n∈A i=1 The last inequality follows by J ≥ and the definition of A’ Hence, condition (ii) of Theorem 2.4 holds Finally, it remains to show that condition (i) of Theorem 2.4 holds That ... i=1 The rest ofthe proof is same as that of Theorem 1.6 except using Theorem 2.6 instead of Theorem 2.4 and is omitted ■ Acknowledgments The author would like to thank the referees for the helpful ... i=1 Hence, the result follows by conditions (i) and (ii) ■ Remark 2.7 As noted in the Introduction, Chen et al [9] have proved Theorem 2.6 under an additional condition (see also Theorem 1.5)...
... satisfies the hypotheses ofthe Theorem and that any ofthe equivalent conditions holds, then for r = |z| log |σ (z)| = o log log 1−r We also provide the following restatement ofthe hypotheses of Theorem ... we call the Kœnigs function and denote by s from here on In the study ofthe geometric properties of in relation to the operator theoretic properties of C, it has become evident that the Kœnigs ... and so in the above theorem, the first condition could read: C is compact on B, B0, BMOA and VMOA Before proceeding, we prove the following lemma Lemma Under the hypotheses ofthe theorem, w...
... Ahmad, Onthe nonautonomous Volterra-Lotka competition equations,” Proceedings ofthe American Mathematical Society, vol 117, no 1, pp 199–204, 1993 S Ahmad and A C Lazer, Onthe nonautonomous ... system They obtained the necessary or sufficient conditions for the permanence and the extinction For more works relevant to system 1.1 , one could refer to 1–9 and the references cited therein ... permanence conditions of for system 1.4 Theorem 1.2 will be proved in Section In Section 3, an example will be given to illustrate that 1.10 does not imply 1.9 ; that is, the condition 1.10 is...
... Equations Acknowledgments The authors express Their sincere gratitude to referees for their valuable suggestions and comments This work has been conducted by the Research Grant of Kwangwoon University ... Kurt, “Further remarks on multiple p-adic q-L-function of two variables,” Advanced Studies in Contemporary Mathematics, vol 14, no 1, pp 49–68, 2007 L.-C Jang, On a q-analogue ofthe p-adic ... pages, 2006 L.-C Jang and T Kim, Onthe distribution ofthe q-Euler polynomials and the q-Genocchi polynomials of higher order,” Journal of Inequalities and Applications, vol 2008, Article ID 723615,...
... equation as the limit ofthe isentropic Euler equations in one space dimension Recently, Coulombel and Goudon [1] constructed the uniform smooth solutions to (1.1) in the multidimensional case ... of fractional order (H σ+ε (Rd ), σ = + d/2, ε > 0) with the aid of Littlewood-Paley decomposition theory If fixed τ > 0, there are some efforts onthe global existence of smooth solutions to the ... Fang Together with the inequalities (4.8) and (4.21), (4.2) follows immediately, which completes the proof of Proposition 4.1 Proof of Theorem 1.1 In fact, Proposition 3.1 also holds onthe framework...
... of these fλ (q)’s We have: Proposition 1.2 dim Fn = D(n) Proof Consider the table ofthe characters χN ; we are interested in the dimension ofthe row-span of this table Since the dimension of ... function for the entries ofthe column corresponding to the λ-cycles The dimension ofthe column-span of our table is therefore equal to dim Fn , and the proposition is proved the electronic journal ... precisely the P n−j n partitions of n which contain n copies of j Let Sj be the collection j j of fλ ’s corresponding to these P n − j n j partitions One sees immediately that the dimension of the...
... When conditioning onthe event CP0 , the random graphs ofthe resulting probability space may contain edges only from within the edges that connect vertices of different partitions of P0 The number ... information on Maple) implementation ofthe downhill simplex function optimization method (see [13] for a good description ofthe method and a C implementation) to the maximize the expression This ... obtained in [2] is the exact computation ofthe probability involving the conjunction ofthe events using the occupancy problem for random placements of balls into bins We make use ofthe sharp estimates...