streaming flow past axisymmetric bodies a generalization of the blasius series

... Plate – The Blasius Solution D Streaming Flow past a Semi-Infinite Wedge – The Falkner–Skan Solutions E Streaming Flow past Cylindrical Bodies – Boundary-Layer Separation F Streaming Flow past Axisymmetric ... is that the total accumulation of a quantity B in a material control volume is the sum of the volume integral of the local accumulation of B at each fixed point in space, plus the total rate of ... recognized by a number of awards, including the Dreyfus Foundation Teacher-Scholar Award, a Guggenheim Fellowship, the Allan Colburn and Warren Walker Awards of the AIChE, the Bingham Medal of the Society...

Ngày tải lên: 02/04/2014, 16:45

... language and the derivation trees generated by a unification grammar are the ones generated by its ground grammar Thus one can consider a unification grammar as an abbreviation for a ground grammar The ... the set of lists s((Ao, An,B)) such that (Ao, An) ~ D n, (A' ,B) ~ D t, and s is the most general unifier of An and A' (after suitable renaming of variables) Then the set of ground instances of ... proving that the grammar is depth-bounded, or C a contains a pair of the form [A, A] , proving that the grammar is not depth-bounded The algorithm always halts, because the grammar is either depthbounded...

Ngày tải lên: 21/02/2014, 20:20

... coordinates and leaving Acol,s invariant n By a calculation of the character of Sn on the homology of the order complex of LAcol,s n and using a formula of Orlik & Solomon [10] we are able to describe the ... Let A be an arrangement of a ne hyperplanes in Cn Assume G ≤ Gln (C) is a finite subgroup that leaves A invariant Let ˆ be an additional element that is larger than any element of LA Then, UA ... Generalization of the Braid Arrangement The classical braid arrangement An in complex n-space is given by the “thick” diagonals Hij : zi = zj for ≤ i < j ≤ n The braid arrangement, also known as the...

Ngày tải lên: 07/08/2014, 06:20

... research process it was the other way round This proof was found first and provided (some of) the inspiration for the later proofs of Theorems and Step An equivalent statement of the Theorem We take ... provide a combinatorial interpretation of the constant term in terms of shifted plane partitions Recall that a shifted plane partition of shape (λ1 , λ2 , , λr ) is an array π of integers of the ... the last inequality being an assumption in the statement of the Theorem The product in the numerator of the right-hand side of (3.25) consists of factors of the form (x + y + a) = (2x + m + a) ...

Ngày tải lên: 07/08/2014, 06:20

... mapping, Theorem improves Theorem To deal with the generalization of the most important and most difficult case of Theorem — that of small m + n — we make a simplifying assumption that R satisfies the ... be an injective mapping from A to B Suppose that m + n ≥ q + Then τ √ |A + B| > q − q − In a certain (rather narrow) range of m, n and in the particular case of R induced by an injective mapping, ... and m = r, in which case the two last estimates of Theorem coincide Theorem is extremely sharp and in fact, establishes the minimum possible value of R the cardinality of the restricted sum A...

Ngày tải lên: 07/08/2014, 06:20

Ngày tải lên: 27/11/2015, 11:19

... Fellowship Author details Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia 2Center for Advanced Mathematics and Physics, National ... University of Science and Technology H-12, Islamabad, Pakistan Authors’ contributions All authors contributed equally to the manuscript and read and approved the final draft Competing interests The authors ... of the discrete variable can be thought of as the parts of the sheet lying over the grid lines of the integer values of n The sequence where the curve intersects the grid lines gives a path The...

Ngày tải lên: 21/06/2014, 02:20

Ngày tải lên: 05/08/2014, 15:20

Ngày tải lên: 05/08/2014, 15:20

... derivation of a family of q-Lagrange inversion formulas Al-Salam and Verma [2] employed the fact that the n-th q-difference of a polynomial of degree less than n is equal to zero, to show that 1− a ... Greatest factorial factorization and symbolic summation, J Symbolic Computation, 20 (1995), 235–268 [9] P Paule and A Riese, A Mathematica q-analogue of Zeilberger’s algorithm based on an algebraically ... solutions of q-difference s equations, preprint, 1995 [2] W Al-Salam and A Verma, On quadratic transformations of basic series, SIAM J Math Anal., 15 (1984), 414–421 [3] G Gasper, Summation, transformation,...

Ngày tải lên: 07/08/2014, 06:20

... from B the diagram squares having rank at most m − and the pairs (i, j) ∈ Om (π) Proof For any m ≥ 2, let D be the set of all diagram squares of rank at most m − The proof is based on the following ... Hence a4 (π) = and b4 (π) = The number am (π) can be read off immediately from the ranked diagram of π Proposition Let π ∈ Sn be a permutation Then am (π) equals the number of diagram squares of rank ... D1 the set of its diagram squares of rank at most m − 3, and by D2 the set of the remaining diagram squares Now define σ = Φm (π) to be the permutation in Sn whose set of diagram squares of rank...

Ngày tải lên: 07/08/2014, 07:21

... in a family resulting from a more general graph operation Instead of placing copies of the same graph Gi on all the lines parallel to the i-th axis, we may place different graphs from a fixed class ... class B of all bipartite graphs or the class S of graphs containing at most one edge? If each graph in G is k-colorable, then every graph in G d has chromatic number at most k d , since it is the ... that the chromatic number of the Cartesian product of G1 , , Gd is the maximum of the chromatic numbers of G1 , , Gd [12] In this paper, we consider bounds on the chromatic number of graphs...

Ngày tải lên: 07/08/2014, 21:21

... a special element of order s of the automorphism cyclic graph Gn (Ai ) For an arbitrary a ∈ Ai , let r = |a( k)| If r > 1, then the equivalence class a = {a, a, ka, −ka, , k s− 1a, −k s−1 a} ... a} contains 2r elements If r = then a = {a, a} In particular, 2, if a = a | a |= 1, if a = a By the symmetry of the graph Gn (Ai ) the clique number of Gn (Ai ) is the maximal order of cliques ... Proof First assume that [Ai ] = Then for arbitrary a ∈ M and y ∈ Ai , the element y − a is not in Ai By Definition ℓi (a) = Hence max{ℓi (a) |a ∈ M} = and the equality holds Then assume that [Ai...

Ngày tải lên: 08/08/2014, 11:20

... − a) −1 = a A b A\ {a} Proof Consider the polynomial f (x) = a A b A\ {a} (x − b) (a − b) Its degree is at most |A| − 1, and for all a ∈ A it takes value of Hence f ≡ and the coefficient of x |A| −1 ... )−1 · a i · i = a2 A2 , ,an ∈An i=2 b∈Ai \{ai }  ·  (b − a1 )−1 a1 A1 b A1 \ {a1 } b∈B1 (a1 − b) The last factor in this product can be simplified to the form (b − a1 )−1 , a1 A1 \B1 b∈ (A1 ... deg(fu ) to variable xu , M is then of maximal degree The assertion follows from Theorem Notice that in the above theorem the labels can be taken from arbitrary lists of size at least kl + Let...

Ngày tải lên: 08/08/2014, 11:20

... T is the set of diagonal matrices and µ is an arbitrary partition of n In 1982, Tanisaki [14] simplified their ideal; his simplification has since become known as the Tanisaki ideal Iµ For a representation ... the new diagram at Level i − will be a composition µ(i−1) of i − with a partial filling of the values i, , n in the remaining n − (i − 1) boxes of µ In the diagram at the end of the edge labelled ... on A( µ) Since A( µ) equals B(µ), Theorem 2.3.9 implies the cardinality of A( µ) equals the cardinality of the generating set of row-strict tableaux in M µ Also, Φ is a degree-preserving map so A( µ)...

Ngày tải lên: 08/08/2014, 12:23

... that x is the head of at least qds /2 free escaping pairs, completing the proof Recall that every x ∈ X is the head of at least qds escaping pairs Hence if there were no x ∈ X such that x is the ... X and y ∈ Ns (x) We call x the head and y the tail of the pair By the remark, the set A ∩ N(x) has at most A N (x) A m elements, and property (2) ensures that |Ns (x)| = |Ns (x)| ≥ qds That ... (1), the number of neighbors of u in X is at most m Remark It can be shown using a similar argument that every x ∈ X has at most m neighbors in A A By an escaping pair we mean a pair (x, y) of...

Ngày tải lên: 08/08/2014, 12:23

... with Multiplication (15) and the family of their translation duals References [1] A. A Albert: On the collineation groups of certain non–Desarguesian planes, Portugaliae Mathematica, 18 (1959), ... respectively, and since L(S) has rank 6, we have that P is a point of the plane π The last part of the statement simply follows from the facts that any plane of P, different from π, has weight or in L(S) and ... Such a prime is also called the characteristic of the semifield The additive group of a semifield of characteristic p is an elementary abelian p–group and it is always possible to choose the support...

Ngày tải lên: 08/08/2014, 12:23

... Proof A 2-balanced orientation of a graph is precisely a realization of that graph as a Hasse diagram So, we consider the posets which have Hasse diagram isomorphic to Km,n No such poset can have ... a 2-balanced orientation Recall that the girth of a graph is the length of its smallest cycle Then, for an orientation O of G to be k-balanced, it is necessary that the girth of G be at least ... = As a special k case, if G has a triangle, then g = and so XG = for k > Alternately, if g = ∞ (that is, G is a forest), then the condition that weak cycles are k-balanced is vacuous, so that...

Ngày tải lên: 08/08/2014, 12:23

... have the ranges of the variation for all variables of (2.8) It should be noticed that parameters of interest (l, b and μ) have the dimension as [sec-1] = [Hz] Let estimate l, the intensity of ... short period of time is negligible Main result (2. 8a) is the observation that about fold variation of the demand of oxygen can be satisfied without variation of blood flow by only the changes in ... changes of flow in any given capillary with time As the consequence of these heterogeneities of flow, the time T to pass microcirculation if no interruptions happen becomes the variable If T has...

Ngày tải lên: 13/08/2014, 16:20

... that arctan(k/n) ϕ(k) = k(n + k) π arctan x dx 1+x arctan x 1+x dx The 1−t 1+t to obtain Thus we only need to evaluate the integral I = to this is to make the change of variables x ← I= arctan ... U131, Mathematical Reflections (4) (2009) [2] G H Hardy and E M.Wright, An Introduction to the Theory of Numbers (5th ed.), Oxford University Press (1980) Omran Kouba Department of Mathematics ... σ(k) π2 = log(1 + a) n2 + ak 1 2a • Starting from lim n→∞ n n k=1 ϕ(k) = 2, k π which can be proved in the same way as (3), we conclude that, for every α ≥ 0, lim n→∞ Mathematical Reflections (2010)...

Ngày tải lên: 15/08/2014, 16:55