... divisors of n, Ω(n) is the number of prime power divisors of n, π(x) is the number of primes ≤ x, τ (n) is the number of divisors of n P(s, t) is the set of positive integers composed of prime ... denote the sequence of Farey frac1 Q tions of order Q, and let N (Q) denote the number of distinct gaps between successive terms ofthe sequence Then Q2 (log Q)δ (log log Q)3/2 N (Q) Proof The ... author enjoyed the hospitality ofthe Institute of Mathematics and Informatics, Bulgarian Academy of Sciences Finally, the author acknowledges the referee for a thorough reading ofthe paper and...
... investigate the effect ofthe exact distributionofthe language inventory size on the nature ofthe degree distributionofthe consonants through a synthetic approach based on the principle of preferential ... consideration the β -distribution rather than just the mean value ofthe inventory size that can explain the negative slope ofthe first regime We look forward to the same as a part of our future work Rather, ... Figure 2: Degree distributionof PlaNet for the set VL The figure in the inner box is a magnified version of a portion ofthe original figure Degree Distributionof PlaNet The degree of a node u, denoted...
... order ofthe sum of two functions is not greater than the larger ofthe orders ofthe two summands, and if the orders ofthe summands and ofthe sum are all equal, then 21 the type ofthe sum ... greater than the larger ofthe types ofthe two summands In addition, if one ofthe two functions is of larger growth than the other, then the sum has the same order and type as the function of larger ... analogue of Rolle’s theorem Theorem (Gauss-Lucas Theorem [50, p 8],[57, Theorem 1.2.1]) If p(z) is a non-constant polynomial, then the zeros of p (z) belong in the convex hull ofthe zeros of p(z) The...
... SES ofthe younger female population ofthe practice Most of these measures are taken early during pregnancy and refer to the health, housing and SES ofthe mother prior to the birth ofthe ALSPAC ... income ofthe child and the quality to which they have access In terms ofthe second part ofthe explanation for the lack of gradient, we not find strong evidence that the quality ofthe GP to ... cohort of children born in one region ofthe UK in the early 1990s The cohort is the Avon Longitudinal Study of Parents and Children (ALSPAC) The advantages ofthe ALSPAC data are twofold First, the...
... in Rn Proof of Theorem 4.1 The ubiquity version of Theorem 4.2 An auxiluary lemma 4.3 Proof of Theorem Proof of Theorem Proof of Theorem Proof of Theorem Various generalizations 8.1 Theorem for ... completes the proof of Theorem 10 in the case that G is finite C.3 Proof of Theorem 10: G = ∞ The proof of Theorem 10 in the case that G is infinite follows the same strategy as the proof when G ... < ψ(Q)/Q Proof of Theorem modulo Theorem This is trivial Given the hypotheses of Theorem 7, the hypotheses of Theorem are clearly satisfied Fix an interval I ⊆ I0 By Theorem 7, there exist constants...
... trajectory data There is a one way flow of data from the tracker consisting of frame by frame updates to the position in the image plane ofthe centroid of uniquely labelled objects The detection of atypical ... number of training feature vectors and the point density ofthe prototypes within the feature space will approximate the pdf ofthe feature vectors [6] The model is thus more accurate in areas of ... should be close in the vector space ofthe representation and vice versa We model sequences of flow vectors by modelling the sequence of activations they cause on the outputs ofthe first network’s...
... THEDISTRIBUTIONOF WORD LENGTH IN TECHNICAL RUSSIAN k (LENGTH in LETTERS) Figure 39 40 ANTHONY G OETTINGER ... 55 (part), 59, 64, 65, 71, 122 REFERENCE Oettinger, A G., "A Study for the Design of an Automatic Dictionary," Doctoral Thesis, Harvard University (1954) 537 351 438 325 577 579 795 591 557 517...
... ofthe dollar against a basket of currencies ofthe other Group of Ten countries plus Switzerland which is also published in the Federal Reserve Bulletin The weights used in the calculation of ... actual rate of return on the market portfolio, e is the actual rate of appreciation in the foreign-currency value ofthe domestic currency, and r is the actual percentage rate of change in the domestic ... net borrowers of funds, the sign of this coefficient should be negative empirically Finally, in the third term in (12), the sign ofthe coefficient on the unexpected change in the domestic loan...
... Journal of Science, Earth Sciences 23 (2007) 110-115 gradually decreased time by time However the management ofthe exploitation of peanutworms is hindered by the lack of scientific knowledge on their ... [1] The content of DO in water depends on the condition of tide, wave and sea currents, so the content of DO in peanut - worm flats is quite high, ranging from 6.2 to 7.9 mgO2/l The result of ... important for thedistributionof peanutworms Sediment grain size in environmental geochemistry study is one ofthe main factors to determine the behavior of elements, and in study of peanut-worm...
... fluctuations ofthe matrix elements for the desymmetrized quantum cat map We present a conjecture for thedistributionofthe normalized matrix elements, namely that their distribution is that of a certain ... d Then I is an O-ideal, and the matrix of α acting on I by multiplication in the basis v1 , v2 is precisely A The choice of basis of I gives an identification I ∼ Z2 = and the action of O on the ... t(ω(kB1 , −lB2 ) + ω(mB3 , −nB4 )) N The proof of Lemma 11 is an extension ofthe arguments proving the analogous (4.1) in the proof of Proposition and is left to the reader 5.3 Exponential sums over...
... only 8% ofthe health workers, while the quintile with the most health workers has 46% ofthe workers The value ofthe Gini index is 0.229 Part ofthe inequality in thedistributionof health ... Following the economics literature on the measurement of inequality in thedistributionof income, we use the Lorenz curve and the Gini index in order to characterize inequality in thedistributionof ... the high end ofthedistribution compared to the district at the lower end Of course, some of these differences are planned for The referral system implies that some districts are sup- Page of...
... 2004 at the Cancer Center of Sun Yat-Sen University All the patients underwent radical surgery, and none of them had undergone either chemotherapy or radiotherapy before the collection ofthe samples ... Committee of our institution Patients were informed ofthe investigational nature ofthe study and provided their written informed consent The count of tryptase-positive mast cells in the cancer ... MCCstroma, the count of tryptase-positive mast cells in the cancer stroma ofthe primary colon tumor; MCCadjacent, the count of tryptase-positive mast cells in the normal mucosa adjacent to the colon...
... 2004 at the Cancer Center of Sun Yat-Sen University All the patients underwent radical surgery, and none of them had undergone either chemotherapy or radiotherapy before the collection ofthe samples ... Committee of our institution Patients were informed ofthe investigational nature ofthe study and provided their written informed consent The count of tryptase-positive mast cells in the cancer ... MCCstroma, the count of tryptase-positive mast cells in the cancer stroma ofthe primary colon tumor; MCCadjacent, the count of tryptase-positive mast cells in the normal mucosa adjacent to the colon...
... respectively, the ring of p-adic rational integers, the field of p-adic rational numbers and the p-adic completion ofthe algebraic closure of Qp The p-adic absolute value in Cp is 1/p When one talks of ... 1.16 The purpose of this paper is to give thedistributionof extended higher order q-Euler and q-Genocchi polynomials In 24 , Choi-Anderson-Srivastava have studied the q-extension ofthe Apostol-Euler ... Apostol-Bernoulli numbers in their paper are exactly the same as the definition ofthe q-extension of Genocchi numbers Finally, they conjecture that the following q -distribution relation holds: m k−1 m−1 q...
... q) = w∈W the q-Eulerian distributionofthe Coxeter system (W, S), or the q-Eulerian distributionof W by abuse of notation (We caution the reader that this is not the same notion as the q-Eulerian ... t, since there are w∈W t only finitely many values {0, 1, 2, , |S| − 1} of des(w) and hence infinitely many group elements w with the same value of des(w) On the other hand, the length distribution ... encompassing the qEulerian distributions ofthe entire family of groups as in equation (1) We derive a general result (Theorem 4) along these lines, and use it to recover known generating functions for the...
... fn−1 By way of illustration, let us mention that this point of view leads immediately to the interpretation ofthe nth Fibonacci number as the cardinality ofthe set of compositions of n by {1, ... pictures of weight k A card of weight k is a pair consisting of a picture of weight k and a k-element subset of N that we will call the label set ofthe card A hand of weight n and size l is a set of ... a partition of {1, 2, , n} into l disjoint groups The goal of labelled counting is to establish a relation between the cardinality ofthe sets of hands and the cardinality ofthe decks For...
... occur is deferred to the last section because it involves a series of fairly lengthy constructions and is not needed for the proof ofthe other theorems The case R = of Theorem was done by Bell ... behaviors the electronic journal of combinatorics 2000, R33 Let ≤ R ≤ ∞ be the radius of convergence of C(x) If R = 0, the mass ofthedistribution is concentrated at because Cn /An → by Theorem ... distributionofthe size ofthe largest component when objects of size n are selected uniformly at random? We not discuss this See Gourdon [14] for some results The limiting distributionofthe number of...
... because the parity ofthe number of cycles in the structure D chosen there must be opposite the parity of |S| so that the final structure will have an odd number of cycles See Example below for further ... Example Partitions of Sets Let Gn be the partitions of [n] and let the fixed points be the blocks of size Then Gn,K = Dn−|K| Let [xn y k ] F (x, y) denote the coefficient of xn y k in the generating ... Thus, the lack of further discontinuities in the graph of f (15, r) may, at first, seem counterintuitive We discuss it in the next section To explore the presence of this gap behavior in other...
... shape is determined by the sequence of opening and closing vertices of G The row sums ofthe filling L(G) give the left degrees of G and the column sums give the right degrees Then G has a k-crossing ... sketch ofthe counting by hand Proof of Fact Let F be the diagram with shape (5, 5, 4, 3) First we show that N 01 (F ; 8; ne = 1, se = 2) = 10 Label the cells of F as on the left hand-side of Figure ... is fixed Let N (F ; m; ne = k, se = l) be the number of arbitrary fillings of F where the sum ofthe entries is m, the longest ne chain has length k and the longest se chain has length l We add...