... insert an article, and of which article to insert Structure ofthe Translation Scheme Three dictionaries are envisaged: a stem dictionary, a prefix dictionary, and a suffix dictionary If one were ... passing that a disadvantage of Swahili is the absence of articles Some work must be done on this problem (paralleling [1]) to determine whether there are word patterns which are indicative ofthe need ... "he was awoken." TRANSLATION OF SWAHILI INTO ENGLISH (A means "he" or "she"; li denotes the past tense; amkwa is the verb stem meaning "be awoken.") The program translated this as He/She Past...
... Omitting the trailing term leads to the approximation in Antoniak (1974) However, we can obtain an exact formula for the expectation by utilising the relationship between the Digamma function and the ... representation for the state ofthe restaurant that doesn’t require explicit table tracking.6 Instead we maintain a histogram for each dish wi ofthe frequency ofa table having a particular number of ... 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...
... gcd (A) , d (A) = d (A − A) , Λ (A) = maxA − minA, Λ (A) = Λ (A) /d (A) Furthermore, let κ (A) = Λ (A) − , |A| − θ (A) = max (A) , Λ (A) T (A) = ( |A| − 2)( κ (A) + − κ (A) ) + and hA = {a1 + · · · + ah : a1 ... , ah ∈ A} For a specified set A, we simply write d, d , Λ, etc Our approach is based ona remarkable result of Lev [7] Using an a ne transformation of variables his theorem can be stated as follows ... or Then κ≥ k + − (k − )θ Proof We may assume that By Lemma we have (3) > 2κ − 1, otherwise the assertion is obvious {0, d , , td } ⊆ A − A, where t ≥ ( + − 2κ)Λ Put m = A Then any ofthe assumptions...
... recursion does 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 ... Unfortunately, the condition (k − 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 ... divide q Acknowledgement Support has been provided by a grant from NSERC References [1] A Frumkin and A Yakir, “Rank of inclusion matrices and modular representation theory”, Israel J Math 71 (1990),...
... C4 contains v ∗ as a vertex, we must have that every w ∈ A appears in at least one ofA or A+ (it may appear in both; in particular, v ∗ appears in both A and A+ as there are no antiparallel ... Hence, A ∪ A+ = A Thus, at least one of them has cardinality at least m/2 Assume, without loss of generality, that |A+ | ≥ m/2 (otherwise we can reverse the directions of all edges and the result ... be an Eulerian bipartite digraph We may assume that G does not contain antiparallel edges, since otherwise G has a directed cycle of length and we are done the electronic journal of combinatorics...
... there is a unique hamiltonian path of T that avoids this arc Hence, there are 2n−2 + distinct hamiltonian paths in a nearly transitive tournament of order n Lemma Let T be a strong tournament of order ... the arc → v1 gives the transitive tournament of order n As noted by Moon [1], there is a bijection between partitions of V \ {v1 , } and hamiltonian paths that include the arc → v1 , and there ... ∩ B| = Let {v} = A ∩ B, and let HA = P1 vP2 be a hamiltonian path of T [A] , and HB = Q1 vQ2 a hamiltonian path of T [B] We apply Lemma twice, and obtain paths R1 and R2 such that V (Ri ) = V (Pi...
... Corollary The class of circular interval graphs and the class of linear interval graphs are factorial Proof Corollary follows from the fact that both classes are subclasses ofthe class of circular ... representation of G Any graph that admits a circular interval representation is called a circular interval graph A special case of circular interval graphs are linear interval graphs which are defined ... C4 ) and it contains one ofthe minimal factorial classes (the class of complements of chain graphs) Conversely, suppose that Y is a factorial class and let G be an arbitrary n-vertex graph in...
... 11 The WACC calculations are made estimating the debt and equity participation in the total value ofthe firm for each period and calculating the contribution of each to the WACC after taxes As ... stock exchange This non-traded stock has a debt Dnt of 70 and equity of Ent of 145 and a tax rate of 35%, and then beta for the non-traded stock can be adjusted as Based on Robert S Hamada, “Portfolio ... the firm value it is necessary to know the WACC, but to calculate WACC, the firm value and the financing profile are needed That we obtain full advantage ofthe tax savings in the same year as...
... domain of attraction ofthe normal law, if there exist constants an > 0, bn ∈ R such that S n − bn d −→ N, an where N is the standard normal random variable We say that {Xn }n∈N satisfies the ... ASCLT for self-normalized partial 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 ... Anoteonthe 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...
... (3:12) Huang et al Journal of Inequalities and Applications 2011, 2011:92 http://www.journalofinequalitiesandapplications.com/content/2011/1/92 Page ofThe proof of Theorem 2.1 is complete Remark ... variable sequences and NA random variable sequences are the most important and special cases of pairwise NQD random variable sequences, then we have the following results as two corollaries of ... Huang et al Journal of Inequalities and Applications 2011, 2011:92 http://www.journalofinequalitiesandapplications.com/content/2011/1/92 Page of Kolmogorov-Chung-type strong law of large numbers,...
... independent random variables have been extended to dependent random variables by many authors The concept of negatively associated random variables was introduced by Alam and Saxena [6] and carefully ... associated random variables Theorem 1.4 Let {Xni, ≤ i ≤ kn, n ≥ 1} be an array of rowwise negatively associated random variables and {an, n ≥ 1} a sequence of nonnegative constants Suppose that the ... general than Theorem 1.4 Sung Journal of Inequalities and Applications 2011, 2011:76 http://www.journalofinequalitiesandapplications.com/content/2011/1/76 Page of Proof of Theorem 1.4 Note that...
... in a non-tangential angle of opening a at ζ, then a short calculation shows that lim sup z→ζ δϕ(D)(z) απ ≤ tan δD (z) and the assertion follows □ Jones Journal of Inequalities and Applications ... of Ω plays a complicated role in the behaviour of We conclude this section by constructing a domain that displays very bad boundary properties This answers a question of Madigan and Matheson ... References Anderson, JM: Bloch Functions: The Basic Theory Operators and Function Theory D Reidel 1–17 (1985) Madigan, K, Matheson, A: Compact Composition Operators onthe Bloch Space Trans Am Math...
... q-integral on Zp at q −1,” Journal of Mathematical Analysis and Applications, vol 331, no 2, pp 779–792, 2007 14 T Kim, Anoteon p-adic q-integral on Zp associated with q-Euler numbers,” Advanced ... numbers and its derivatives,” Journal of Mathematical Analysis and Applications, vol 339, no 1, pp 598–608, 2008 13 T Kim, Onthe analogs of Euler numbers and polynomials associated with p-adic ... “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, Ona q-analogue ofthe p-adic generalized...
... equations,” Transactions ofthe American Mathematical Society, vol 359, no 2, pp 637–648, 2007 [2] S Junca and M Rascle, “Strong relaxation ofthe isothermal Euler system to the heat equation,” ... towards those of (1.6) for arbitrary large initial data in BV (R) space Marcati and Milani [3] showed the derivation ofthe porous media equation as the limit ofthe isentropic Euler equations ... Boltzmann equation,” Hokkaido Mathematical Journal, vol 14, no 2, pp 249–275, 1985 Jiang Xu: Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China Email...
... row-span of this table Since the dimension ofthe row-span ofa matrix is equal to the dimension of its column-span, we can equally well study the dimension ofthe space spanned by the columns ofthe ... essentially what we are looking at (The defining representation of Sn consists ofthe direct sum ofthe reflection representation and the trivial representation This trivial summand has no significant ... generating functions fλ (q) as rational functions over a common denominator; then the dimension of their span is bounded above by plus the degree of their numerators For example, one can see without...
... 3-SAT formulas From the set of legal colorings ofa graph, Dunne and Zito singled out the special colorings that satisfy a maximality condition that, however, is a weaker form of maximality than ... help on numerical function maximization References [1] D Achlioptas and M Molloy, The analysis ofa list-coloring algorithms ona random graph,” in Proc 38th Annual Symposium on Foundations of ... denote the fact that the first two variables are fixed, while x, y are chosen arbitrarily from D the electronic journal of combinatorics (2000), #R29 Theorem The probability ofthe conditional...
... aB + k b ∼ exp √ in (A. 1) and note that in the matching region n/(2k b) ∼ We recall that a = b(1 − n2−k /b) The integrand in (A. 1) has a saddle point at B = a and a standard application ofthe ... large b and n, the conditions under which (c)–(e) apply may not be satisfied for any k However, for a fixed large b and k, we can always find a range of n such that each ofthe parts of Theorem apply ... [17]) are very useful In these applications, the parameter b is quite large, and may depend on n There are other applications of b-tries in computer science, communications and biology Among these...
... Theorem Rigid ∈ AM Proof The proof is an easy adaptation ofthe result of [7, 8] that the language NGI = {(G1 , G2 ) : G1 G2} is in AM In the formulation of AM given above, Merlin observes Arthur’s ... definition of AM Based on constructions like those of [12, 10, 11], one has AM ⊂ ΣP ∩ ΠP , com2 pleting the claim in the introduction One naturally wonders at the relationship of Dist to more familiar ... consist of all languages L for which L ∈ ΣP Above, k k the notation ·, · refers to some canonical pairing function With these definitions, NP = ΣP , coNP = ΠP , and the classes ΣP and ΠP form a neat...
... theory A survey paper by P K Wong [8] in 1982 refers to 70 publications The study of cages has led to interesting applications of algebra to graph theory Recently, it also attracted some attention ... using Hall’s Theorem that B has a 1-factor, M By the definition ofthe bipartite graph B, the distance between two end vertices of each edge in M is at least g − Now consider the k-regular graph ... completes the proof References [1] J .A Bondy and U.S.R Murty,Graph Theory with Applications, North Holland, Amsterdam, (1976) [2] G Brinkmann, B.D McKay, and C Saager, The smallest cubic graphs of girth...