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+(S) for someS ⊂ N∗(Z). In this paper we give a constructive method to show that the odd cyclesare regular integral sum graphs, which extends the classes of integral sum graphs andcompletely solves an open problem posed by[r]

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16.2. LINEAR INTEGRAL EQUATIONS OF THE SECOND KIND WITH VARIABLE INTEGRATION LIMIT 815Let w = w(x) be a solution of the simpler auxiliary equation with f (x) ≡ 1 and a = 0,Aw(x)+Bx0K(x – t)w(t) dt = 1.(16.2.3.9)In this case, the solution of the origi[r]

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is a sentence. We referto a sentence (in another paper) in which there isan explicit citation of d as a citing sentence of d.When a paper is cited, it is often discussed consec-utively in more than one sentence near the citation,thus intuitively we would like to consider a windowof sen[r]

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Problem Statement A thief robbing a store and can carry a maximal weight of W into their knapsack. There are n items and i th item weigh wi and is worth vi dollars. What items should thief take?
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THE AMERICAN MATHEMATICAL MONTHLY 12-2008

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/(x − bi),usingthe given conditions to show that all the ciare positive, then appealing to theorem (∗)and to the translation invariance of Lebesgue measure. References provided for theo-rem (∗) were: (1) G. Boole, “On a general theorem of definite integration,” Camb[r]

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0 0,f0 β, f∞ 1, 1.2called the Blasius problem 1, has been used to describe the steady t wo-dimensional flow ofa slightly viscous incompressible fluid past a flat plate, where η is the similarity boundary-layer ordinate, fη is the similarity stre[r]

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lBnx and 0 ≤ l <1,then ljAxj+ ljBnxjÎ Q for j sufficiently large,(iv) B is uniformly asymptotically regular with respect to A.Then, A + B has a fixed point in Q.AcknowledgementsThe authors would like to thank the referee for the insightful comments and suggestions.[r]

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=∂F∂q.We assume that solution (13.2.1.6) and equation (13.2.1.1) can be solved for the deriva-tives p and q, i.e.,p = ϕ1(x, y, w, C1), q = ϕ2(x, y, w, C1). (13.2.1.8)574 FIRST-ORDER PARTIAL DIFFERENTIAL EQUATIONSThe first equation of this system can be treated as an ordinary diff[r]

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Economics, vol. 42, no. 1, pp. 459–465, 2008.3 E. Furman and R. Zitikis, “Weighted risk capital allocations,” Insurance: Mathematics and Economics,vol. 43, no. 2, pp. 263–269, 2008.4 E. Furman and R. Zitikis, “Weighted pricing functionals with applications to insurance: an overview[r]

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Sunday, two months before prom, I finally mustered up the courage to ask a girl, whom weshall call H.B., short for heartbreak. In asking her, I followed the philosophy, “If you are going togo, go all out!” The look of shock on H.B.’s face when I appeared at her door[r]

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enduntil end ;Note that, the loop to update the priorities and the loop to find the minimumare combined: each time we remove a vertex from the fringe, we pass throughall the vertices, updating their priority if necessary, and keeping track of t[r]

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i(t)],(1:3)for (m, n) Î [m0, m1) ∩ N+×[n0, n1) ∩ N+,wherea(m, n), b(m, n) are nonnegativeand nonde-creasing functions in each variable. Inequalities (1.1), (1.2), and (1.3) are thediscrete versions of Agarwal et al. [18] and Chen et al. [19]. They not only generalizedthe forms with one variable int[r]

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L2(Q,σ ),where C is a constant independent of u and f.AcknowledgementsThis work was supported by National Foundation for Science and Technology Development (NAFOSTED), Vietnam,under project no. 101.01.58.09.Author details1Department of Mathematics, Hanoi National University of Education, Hanoi, Viet[r]

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7cycles. On the other hand, when the damage tolerant curve isabove the Goodman line, this indicates that a crack could initiate but would not propagate.These two separate regions constitute two types of material behavior: damage intolerantwhen the damage tolerant c[r]

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