uniform flow past a solid sphere at small but nonzero reynolds number
advanced transport phenomena
... Small, but Nonzero, Reynolds Number E Heat Transfer from a Body of Arbitrary Shape in a Uniform Streaming Flow at Small, but Nonzero, Peclet Numbers F Heat Transfer from a Sphere in Simple Shear Flow ... Shear Flow G Solidification at a Planar Interface H Heat Transfer in Unidirectional Flows Steady-State Heat Transfer in Fully Developed Flow through a Heated (or Cooled) Section of a Circular ... mean of the appropriate quantity over the (inevitable) molecular fluctuations The motivation for this approach, apart from an anticipated simplification of the problem, is that, in many applications...
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Tài liệu Báo cáo khoa học: "A GENERALIZATION OF THE OFFLINE PARSABLE GRAMMARS" doc
... of derivation trees and the language that it generates just as we for a context-free grammar The language and the derivation trees generated by a unification grammar are the ones generated by ... The author conjectures that grammars whose acyclic backbone is depth-bounded in fact generate the same languages as the offline parsable grammars Conclusion The offline parsable grammars apparently ... under alphabetic variance Since the ground grammar for G ' allows arbitrarily long chain derivations, DN÷ t must contain at least one element, say (Ao, AN+I) This list contains two terms that belong...
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Báo cáo toán học: " Colored partitions and a generalization of the braid arrangemen" docx
... n-space To each arrangement A corresponds an n-dimensional complex manifold MA = Cn \ H The space MA is called the complement of the arrangement H A A The combinatorial object associated to an arrangement ... union UA = c H of H A ˇ an arrangement A The result by Ziegler & Zivaljevi´ is actually far more general and c is valid for general arrangements of linear subspaces Here, we state an equivariant ... with the space Cn Note, that in general LA is actually not H∈∅ a lattice but a meet-semilattice (i.e., infima exist but suprema in general not) The link between the combinatorics of LA and the topology...
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Báo cáo toán học: "DETERMINANT IDENTITIES AND A GENERALIZATION OF THE NUMBER OF TOTALLY SYMMETRIC SELF-COMPLEMENTARY PLANE PARTITIONS" pptx
... nonintersecting lattice paths [6, Cor 2; 15, Theorem 1.2] (see Proposition A1 ) this determinant has an interpretation in terms of nonintersecting lattice paths By a lattice path we mean a lattice path in ... that can be evaluated This two-parameter generalization is the subject of our next theorem We formulate it only for integral x and y But in fact, with a generalized definition of factorials and ... the alternative proofs by Andrews and Burge [2] However, it became clear rather quickly that this is not possible (at least not routinely) In fact, the aforementioned proofs take advantage of a...
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Báo cáo toán học: "RESTRICTED SET ADDITION IN GROUPS, II. ˝ A GENERALIZATION OF THE ERDOS-HEILBRONN CONJECTURE" pptx
... correspond at least m + n − q pairs (a, b) (with a ∈ A, b ∈ B) such that a + b = s, and for any such pair we have (a, b) ∈ R Totally, we have at least |S|(m + n − q) pairs (a, b) ∈ R On the other hand, ... journal of combinatorics (2000), #R4 (a) to any fixed a0 ∈ A there corresponds at most one b ∈ B such that (a0 , b) ∈ R; (b) to any fixed b0 ∈ B there corresponds at most one a ∈ A such that (a, ... [1] N Alon, M.B Nathanson and I.Z Ruzsa, Adding distinct congruence classes modulo a prime, American Math Monthly, 102 (1995), 250–255 [2] N Alon, M.B Nathanson and I.Z Ruzsa, The Polynomial Method...
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báo cáo hóa học: " A new generalization of the Riemann zeta function and its difference equation" docx
... 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 declare that they have no ... Chaudhry MA, Zubair SM: On a Class of Incomplete Gamma Functions with Applications Chapman and Hall (CRC Press), Boca Raton; 2001 Magnus W, Oberhettinger F, Tricomi FG: Tables of Integral Transforms,...
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Báo cáo toán học: "A Generalization of Gosper’s Algorithm to Bibasic" docx
... 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, and expansion ... quadratic, cubic, and quartic summation and transformation formulas, Canad J Math., 42 (1990), 1–27 [5] G Gasper and M Rahman, Basic Hypergeometric Series, Encyclopedia of Mathematics and its Applications, ... 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 motivated approach...
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Báo cáo toán học: "A generalization of Simion-Schmidt’s bijection for restricted permutations" doc
... Wilf-equivalence of the pattern sets Am and Bm , that is, there are as many permutations in Sn which avoid every pattern of Am as those which avoid every pattern of Bm An analytical proof of ... = 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 at least ... of a diagram form Young diagrams For a diagram square, its rank is defined to be the number of dots northwest of it Clearly, connected diagram squares have the same rank In this paper, permutation...
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Báo cáo toán học: "Chromatic number for a generalization of Cartesian product graphs" pot
... implies that each graph in S d is d-colorable (when d ≥ 3) Also graphs in S are bipartite, since cycles in such a graph alternate between horizontal and vertical edges In general, graphs in S d are ... log d and assume k ≥ We randomly generate a graph G with vertex set [2k]d As before an element z in [d] × [2k]d−1 designates a line in [2k]d parallel to some axis We place a random perfect matching ... Bound, an upper bound on the probability that a sum of independent random variables deviates greatly from its expected value (see [7] for more details) Proposition If X is a random variable equal...
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Báo cáo toán học: "A generalization of generalized Paley graphs and new lower bounds for R(3, q)" pot
... 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} contains 2r elements If r = then a = {a, a} In particular, 2, if a = a | a |= 1, ... = Lemma [Ai ] = + max{ℓi (a) |a ∈ M} 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 ... Clapham, A class of self-complementary graphs and lower bounds of some Ramsey numbers, J Graph Theory, (1979), 287-289 [4] R E Greenwood, A M Gleason, Combinatorial relations and chromatic graphs,...
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Báo cáo toán học: "A generalization of Combinatorial Nullstellensatz" pot
... − 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 ... that in the above theorem the labels can be taken from arbitrary lists of size at least kl + Let us conclude the paper with the following remark Suppose that we want to use classical Combinatorial...
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Báo cáo toán học: "A Hessenberg generalization of the Garsia-Procesi basis for the cohomology ring of Springer varieties" ppt
... h-tableau-tree, we define a barless tableau and give a lemma that instructs us how to fill this object to construct a tableau Definition 3.2.5 (Barless tableau) Fix n A barless tableau is a diagram ... recall what Garsia and Procesi did Then we give an example that makes this algorithm more transparent Lastly we define our modification and give our specific results Remark 2.3.1 Although Garsia and ... now place the bars into this tableau yielding a filling of µ Remark 3.2.10 Observe that travelling from a barless tableau at Level i − down to a barless tableau at Level i, Lemma 3.2.8 asserts...
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Báo cáo toán học: "On a Generalization of Meyniel’s Conjecture on the Cops and Robbers Game" potx
... control at most 3msds c escaping paths By controlling each escaping path, the cops can decrease the number of free escaping pairs by at most (as each path has two endpoints), hence the number ... neighbors in A A By an escaping pair we mean a pair (x, y) of vertices with x ∈ 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, ... y)-paths are uncontrolled We just need to prove that there is an x ∈ X such that x is the head of at least qds /2 free escaping pairs, because then x would be a safe vertex, and the robber, having...
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Báo cáo toán học: "A generalization of some Huang–Johnson semifields" pot
... describe an algebraic structure with at least two elements and two binary operations, satisfying all axioms for a skewfield except (possibly) associativity of the multiplication In this paper we are ... classes are not isotopic and the families Fi , for i = 0, 3, 4, are closed under the transpose and the translation dual operations The linear set L associated with a semifield in class F3 has ... distribution of a linear set associated with a presemifield is invariant up to isotopy and up to the transpose operation Proof Let S1 and S2 be two presemifields with associated spread sets of linear...
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Báo cáo toán học: "A quasisymmetric function generalization of the chromatic symmetric function" pptx
... orientations are necessarily acyclic, but they have the additional property that every weak cycle has at least edges oriented both forward and backward, due to the fact that Hasse diagrams include ... can see that an orientation is acyclic if and only if it is 1balanced Similarly, a graph is a Hasse graph if and only if it has a 2-balanced orientation Recall that the girth of a graph is the ... 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 chain of length...
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Báo cáo y học: "Stochasticity of flow through microcirculation as a regulator of oxygen delivery" doc
... 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 intensity of vasomotion Additionally, ... JL: Capillary lengths, anastomoses, and estimated capillary transit times in skeletal muscle [abstract] Am J Physiol 1977, 233(1):H122-H129 Bertuglia S, Colantuoni A, Arnold M, Witte H: Dynamic ... Regulation of oxygen consumption by vasomotion Math Biosci 2004, 191(1):101-108 15 Pradhan RK, Chakravarthy VS, Prabhakar A: Effect of chaotic vasomotion in skeletal muscle on tissue oxygenation...
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A Generalization of Riemann Sums Omran Kouba
... 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 ... This ends the proof of Theorem Applications • It is known that Euler’s totient function ϕ has very erratic behaviour, but on the mean we have the following beautiful result, see [2, 18.5], n→∞...
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