An improved algorithm for decomposing arc flows into multipath flows

We consider a multipath maximum flow problem introduced by Kishimoto (Networks 27(4)(1996)279-291). The focus is on efficient transformation from arc flows into multipath flows, where a multipath flow is a nonnegative combination of multipaths. A new algorithm that is more efficient than existing ones is proposed for the transformation.     

On the solubility of copper and nickel complexes of rapox in organic solvents

The solubilities of copper and nickel complexes of RAPOX were determined in thirteen different organic solvents colorimetrically employing Lumetron 402-E. Both these chelates possessed maximum solubility in cyclohexanone, namely, 1·04 gm. for Cu-RAPOXimate and 1·710 gm. for Ni-RAPOXimate respectively in 100 ml. of the solution.     

Lithiation of N‐protected‐dihydro‐1,4‐benzoxaziness

Lithiation of N‐protected‐2,3‐dihydro‐1,4‐benzoxazines is described. Lithiation of N‐(tert‐butoxycarbonyl)‐2,3‐dihydro‐1,4‐benzoxazine ( 1 ) with BuLi/TMEDA occurred in the α‐position to nitrogen on the heterocyclic ring, leading to the unexpected ring‐opened product 3 . On the other hand, lithiation of N‐methyl‐2,3‐dihydro‐1,4‐benzoxazine ( 4 ) took place at the oxygen‐adjacent ortho‐position of the aromatic ring.     

Some NP-complete problems in linear programming

Degeneracy checking in linear programming is NP-complete. So is the problem of checking whether there exists a basic feasible solution with a specified objective value.     

Colorimetric estimation of rapox by ferric chloride solution

A method has been developed for estimating even one part per million RAPOX in aqueous medium using Lumetron photoelectric colorimeter 402-E and 620-M filter. The colour of RAPOX ferric complex has been found to obey Beer’s law in the range 10^?5?2·2×10^?4 mole per litre of the aqueous solution. The method depends on the development of colour on mixing aqueous RAPOX with ferric chloride solution in water.     

Mass Spectrometry Based Mechanistic Insights into Formation of Tris Conjugates: Implications on Protein Biopharmaceutics

We present here extensive mass spectrometric studies on the formation of a Tris conjugate with a therapeutic monoclonal antibody. The results not only demonstrate the reactive nature of the Tris molecule but also the sequence and reaction conditions that trigger this reactivity. The results corroborate the fact that proteins are, in general, prone to conjugation and/or adduct formation reactions and any modification due to this essentially leads to formation of impurities in a protein sample. Further, the results demonstrate that the conjugation reaction happens via a succinimide intermediate and has sequence specificity. Additionally, the data presented in this study also shows that the Tris formation is produced in-solution and is not an in-source phenomenon. We believe that the facts given here will open further avenues on exploration of Tris as a conjugating agent as well as ensure that the use of Tris or any ionic buffer in the process of producing a biopharmaceutical drug is monitored closely for the presence of such conjugate formation.

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Some NP-complete problems in quadratic and nonlinear programming

In continuous variable, smooth, nonconvex nonlinear programming, we analyze the complexity of checking whether

1. a given feasible solution is not a local minimum, and
2. the objective function is not bounded below on the set of feasible solutions.

We construct a special class of indefinite quadratic programs, with simple constraints and integer data, and show that checking (a) or (b) on this class is NP-complete. As a corollary, we show that checking whether a given integer square matrix is not copositive, is NP-complete.     

Spanning cactus of a graph: Existence,extension, optimization,and approximation

We show that testing if an undirected graph contains a bridgeless spanning cactus is NP-hard. As a consequence, the minimum spanning cactus problem (MSCP) on an undirected graph with 0–1 edge weights is NP-hard. For any subgraph $S$ of $K_n$, we give polynomially testable necessary and sufficient conditions for $S$ to be extendable to a cactus in $K_n$ and the weighted version of this problem is shown to be NP-hard. A spanning tree is shown to be extendable to a cactus in $K_n$ if and only if it has at least one node of even degree. When $S$ is a spanning tree, we show that the weighted version can also be solved in polynomial time. Further, we give an $O\left(n^3\right)$ algorithm for computing a minimum cost spanning tree with at least one vertex of even degree on a graph on $n$ nodes. Finally, we show that for a complete graph with edge-costs satisfying the triangle inequality, the MSCP is equivalent to a general class of optimization problems that properly includes the traveling salesman problem and they all have the same approximation hardness.     

A linear time algorithm for the Koopmans–Beckmann QAP linearization and related problems

An instance of the quadratic assignment problem (QAP) with cost matrix $Q$ is said to be linearizable if there exists an instance of the linear assignment problem (LAP) with cost matrix $C$ such that for each assignment, the QAP and LAP objective function values are identical. The QAP linearization problem can be solved in $O\left(n^4\right)$ time. However, for the special cases of Koopmans–Beckmann QAP and the multiplicative assignment problem the input size is of $\Omega \left(n^2\right)$. We show that the QAP linearization problem for these special cases can be solved in $O\left(n^2\right)$ time. For symmetric Koopmans–Beckmann QAP, Bookhold [I. Bookhold, A contribution to quadratic assignment problems, Optimization 21 (1990) 933–943.] gave a sufficient condition for linearizability and raised the question if the condition is necessary. We show that Bookhold’s condition is also necessary for linearizability of symmetric Koopmans–Beckmann QAP.