Linear programming under uncertainty: A basic property of the optimal solution

Summary We show that if the two-stage linear programming problem under uncertainty has an optimal solution, then it has an optimal solution in which the column vectors corresponding to the positive first stage decision variables are linearly independent. This leads to the result that if an optimal solution exists, then there exists an optimal solution in which not more than m + ¯m of the first stage decision variables are positive. These results extend to the multi-stage case.This research was partially supported by the Office of Naval Research under Contract Nonr-222(83), the National Science Foundation under Contract GP-4593, the Army Research Office under Contract DA-31-124-ARO-D-331 and the University of California. Reproduction in whole or part is permitted for any purpose of the United States Government.     

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.     

Iodine mediated synthesis of some new imidazo[1,2-a]pyridine derivatives and evaluation of their antimicrobial activity

Herein, we reported a series of new 2-(5-methyl-1-aryl-1H-1,2,3-triazol-4-yl)imidazo[1,2-a]pyridines by using iodine and NH₄OAc in good yields. The structures of the titled compounds were characterized by the elemental analysis, ¹H NMR, ¹³C NMR, IR, and mass spectral analysis. All the titled compounds were screened for their in vitro antibacterial and antifungal activities by using streptomycin and Nystatin as standard drugs. The compounds 3k , 3l , 3g , and 3c exhibited potent activity against the tested bacterial strains and 3k , 3l , and 3c exhibited potent activity against the tested fungal strains than the reference drugs.     

Further studies of the reaction kernel structure and stabilization of jet diffusion flames

The structure of axisymmetric laminar jet diffusion flames of ethane, ethylene, acetylene, and propane in quasi-quiescent air has been studied numerically in normal earth gravity (1g) and zero gravity (0g). The time-dependent full Navier–Stokes equations with buoyancy were solved using an implicit, third-order accurate numerical scheme, including a C₃-chemistry model and an optically thin-media radiation model for heat losses. Observations of the flames were also made at the NASA Glenn 2.2-Second Drop Tower. For all cases of the fuels and gravity levels investigated, a peak reactivity spot, i.e., reaction kernel, was formed in the flame base, thereby holding a trailing diffusion flame. The location of the reaction kernel with respect to the burner rim depended inversely on the reaction-kernel reactivity or velocity. In the C₂ and C₃ hydrocarbon flames, the H₂–O₂ chain reactions were important at the reaction kernel, yet the CH₃ + O → CH₂O + H reaction, a dominant contributor to the heat-release rate in methane flames studied previously, did not outweigh other exothermic reactions. Instead of the C₁-route oxidation pathway in methane flames, the C₂ and C₃ hydrocarbon fuels dehydrogenated on the fuel side and acetylene was a major hydrocarbon fragment burning at the reaction kernel. The reaction-kernel correlations between the reactivity (the heat-release or oxygen-consumption rate) and the velocity, obtained previously for methane, were developed further for various fuels in more universal forms using variables related to local Damköhler numbers and Peclet numbers.     

Computational complexity of parametric linear programming

We establish that in the worst case, the computational effort required for solving a parametric linear program is not bounded above by a polynomial in the size of the problem.This research is partially supported by Air Force Office of Scientific Research, Air Force Number AFOSR-78-3646.     

Cup-burner flame structure and extinguishment by CF3Br and C2HF5 in microgravity

The effects of fire-extinguishing agents CF₃Br and C₂HF₅ on the structure and extinguishing processes of microgravity cup-burner flames have been studied numerically. Propane and a propane–ethanol–water fuel mixture, prescribed for a Federal Aviation Administration (FAA) aerosol can explosion simulator test, were used as the fuel. The time-dependent, two-dimensional numerical code, which includes a detailed kinetic model (177 species and 2986 reactions), diffusive transport, and a gray-gas radiation model, revealed unique flame structure and predicted the minimum extinguishing concentration of agent when added to the air stream. The peak reactivity spot (i.e., reaction kernel) at the flame base stabilized a trailing flame. The calculated flame temperature along the trailing flame decreased downstream due to radiative cooling, causing local extinction at <1250 K and flame tip opening. As the mole fraction of agent in the coflow (X_a) was increased gradually: (1) the premixed-like reaction kernel weakened (i.e., lower heat release rate) (but nonetheless formed at higher temperature); (2) the flame base stabilized increasingly higher above the burner rim, parallel to the axis, until finally blowoff-type extinguishment occurred; (3) the calculated maximum flame temperature remained at nearly constant (≈1700 K) or mildly increased; and (4) the total heat release of the entire flame decreased (inhibited) for CF₃Br but increased (enhanced) for C₂HF₅. In the lifted flame base with added C₂HF₅, H₂O (formed from hydrocarbon-O₂ combustion) was converted further to HF and CF₂O through exothermic reactions, thus enhancing the heat-release rate peak. In the trailing flame, “two-zone” flame structure developed: CO₂ and CF₂O were formed primarily in the inner and outer zones, respectively, while HF was formed in both zones. As a result, the unusual (non-chain branching) reactions and the combustion enhancement (increased total heat release) due to the C₂HF₅ addition occurred primarily in the trailing diffusion flame.     

Deciphering aromatic oligoamide foldamer-DNA interactions

Finest selection: Side-chain selective, end-group selective, diastereoselective, and RNA- vs. DNA-selective interactions have been revealed between multiturn helical aromatic amide foldamers having cationic side chains and G-quadruplex aptamers.     

Photolytic-interference-free, femtosecond two-photon fluorescence imaging of atomic hydrogen

We discuss photolytic-interference-free, high-repetition-rate imaging of reaction intermediates in flames and plasmas using femtosecond (fs) multiphoton excitation. The high peak power of fs pulses enables efficient nonlinear excitation, while the low energy nearly eliminates interfering single-photon photodissociation processes. We demonstrate proof-of-principle, interference-free, two-photon laser-induced fluorescence line imaging of atomic hydrogen in hydrocarbon flames and discuss the method's implications for certain other atomic and molecular species.