We study several joint facility location and inventory management problems with stochastic retailer demand. In particular, we consider cases with uncapacitated facilities, capacitated facilities, correlated retailer demand, stochastic lead times, and multicommodities. We show how to formulate these problems as conic quadratic mixed-integer problems. Valid inequalities, including extended polyma...

The massless 4-point one-loop amplitude computation in the pure spinor formalism is shown to agree with the computation in the RNS formalism.

Next, we claim that x ∈ Qp is a square if and only if x = py for n ∈ Z, and y ∈ Zp a padic unit. One direction is obvious. The second direction is also fairly obvious–just refer to the previous case, and also note that p is itself NOT a square in Qp (since if it had a square root, then that square root would have valuation 12 ). We can conclude then that [ Qp : Q×2 p ] = 4, and is given by {1, ...

Let π(x; d, a) denote the number of primes p ≤ x with p ≡ a(mod d). Chebyshev’s bias is the phenomenon for which “more often” π(x; d, n) > π(x; d, r), than the other way around, where n is a quadratic nonresidue mod d and r is a quadratic residue mod d. If π(x; d, n) ≥ π(x; d, r) for every x up to some large number, then one expects that N(x; d, n) ≥ N(x; d, r) for every x. Here N(x; d, a) deno...

With the help of a computer, we obtain the minimum distance of some codes belonging to two families of Z2k -linear codes: the first is the generalized Kerdock codes which aren’t as good as the best linear codes and the second is the Hensel lift of quadratic residue codes. In the latter, we found new codes with same minimum distances as the best linear codes of same length and same cardinality. ...

In this paper, we investigate the relationship between Milnor's K-group and Galois cohomology for the quotient eld of a 2-dimensional complete regular local ring with a nite residue eld. The results given in this paper are considered as a partial answer to the Bloch-Kato conjecture for such a eld.

A Riemannian metric on a manifold M induces a family of Riemannian metrics on the loop space LM depending on a Sobolev space parameter. In Part I, we compute the Levi-Civita connection for these metrics. The connection and curvature forms take values in pseudodifferential operators (ΨDOs), and we compute the top symbols of these forms. In Part II, we develop a theory of Chern-Simons classes CS ...

The quick growth of easy communication technologies concluded the last several decades has led in establishment strict standards for functioning productive systems. system execution is improved by reducing computation time with “Residue Number System (RNS)”. It extensively castoff “signal processing” “numeral analysis”, and “cryptoanalysis”, an exact graph-based technique designing perfect conv...

stormwater represents one of the least researched forms of wastewater in environmental science. contaminated industrial stormwater, that is stormwater generated by runoff from industrial sites such as refineries, smelters and mine sites, is even less well understood. however, contaminated industrial stormwater can have damaging environmental impacts because it generally occurs in sudden bursts ...