Black holes and the stability of gravitation

The existence of black holes in general relativity provides an effective cutoff to the negative gravitational potential. This results in a fundamental upper limit on the amount of energy that can be radiated away by any isolated system.     

Finding a statement of cosmic censorship

We consider possible mathematical formulations of the idea that gravitational collapse cannot result in the formation of naked singularities.National Science Foundation predoctoral fellow.     

Energy-momentum of isolated systems cannot be null

It is shown that neither the ADM nor the Bondi four-momentum of an isolated system in general relativity can be null. This strengthens recent results on positivity of energy by showing that the total four-moemtum must be strictly timelike (and future directed).     

Emission studies of the mechanism of gaseous biacetyl photolysis at 3450, 3650, 3880, and 4358 a and 28°C

The quantum yields of phosphorescence (Φ_p) of biacetyl have been determined in pure biacetyl, biacetyl-SO₂, and biacetyl-c-C₆H₁₂ mixtures in experiments using bands of radiation centered at 3450, 3650, 3880, and 4348 Å. It has been shown that the unexpected effect of gas concentration on the quantum yields of the sulfur dioxide triplet-sensitized phosphorescence of biacetyl resulted largely from the significant destruction of biacetyl triplets at the wall of the cell. The kinetics of the variation of Φ_p with [Ac₂], wavelength of the absorbed light, and added gases provide new estimates of the energy relations and the rate constants for the decomposition reaction of vibrationally rich biacetyl molecules in the first excited singlet state (¹Ac₂?): ¹Ac₂? → products (1), ¹Ac₂? + Ac₂ → ¹Ac₂ + Ac₂ (2); the minimum energy necessary in ¹Ac₂? for reaction (1) to occur is estimated to be about 72.8 kcal/mole above the ground state of biacetyl: k₁/k₂ = (4.3 ± 0.1) × 10^?3M at 3450 Å, (4.07 ± 0.04) × 10^?4M at 3650 Å, and (5.6 ± 0.4) × 10^?5M at about 3800 Å. The variation of the rate constant ratio is shown to be consistent with the expectations of the simple theory of excited molecule decomposition. Biacetyl triplet (³Ac₂) rate constants were determined by measurements of Φ_p in O₂ and NO-containing mixtures: ³Ac₂ + S → (Ac₂–S, products) (8); for O₂ = S, k₈ = (5.76 ± 0.40) × 10⁸ (3650 Å experiments), (5.76 ± 0.27) × 10⁸ (4358 Å); for NO = S, k₈ = (3.34 ± 0.20) × 10⁹ (3650 Å), (3.33 ± 0.18) × 10⁹ 1./mole-sec (4358 Å). A comparison between these and previous findings of the SO₂ triplet (³SO₂)-sensitized excitation of biacetyl [5,6] show that the decomposition of the initial ³Ac₂ product of the exothermic energy transfer reaction ³SO₂ + Ac₂ → SO₂ + ³Ac₂ is unimportant.     

The SO2-sensitized phosphorescence of biacetyl vapor in photolyses at 2650 and 2875 Å. The intersystem crossing ratio in sulfur dioxide

Quantum yields of the triplet sulfur dioxide (³SO₂)-sensitized phosphoresence (Φ_sens) in biacetyl (Ac₂) have been determined in experiments over a wide range of pressures of SO₂ and Ac₂. Excited singlet sulfur dioxide (¹SO₂) was generated using 2650-Å and 28757hyphen;Å light. The values of Φ_sens were dependent on the [SO₂]/[Ac₂] ratio, as anticpated theoretically. However, in runs at a fixed [SO₂]/[Ac₂] ratio, the measured Φ_sens values were dependent on the total pressure. This theoretically unexpected effect is probably largely the result of biacetyl triplet diffusion with deactivation at the cell wall. Treatment of the quantum yield data in terms of the complete mechanism gave new estimates of the following rate functions: ¹SO₂ + SO₂ → (2SO₂) (1), ¹SO₂ + SO₂ → ³SO₂ + SO₂ (2), k₂/(k₁ + k₂) = 0.082 ± 0.003 (2650 Å), 0.095 ± 0.005 (2875 Å) ³SO₂ + Ac₂ → SO₂ + ³Ac₂ (9a), ³SO₂ + Ac₂ → SO₂ + Ac₂ (9b), k_9a + k_9b = (8.4 ± 2.1) × 10¹⁰ (2650 Å), (8.1 ± 3.0) × 10¹⁰ l./mole-sec (2875 Å) ³SO₂ → SO₂ + hv_p (6), k₆ = (7.3 ± 1.3) × 10¹ sec^?1.     

A linear time approximation algorithm for multiprocessor scheduling

Givenn jobs andm identical processors anO(n) approximation algorithm is presented which tries to determine a nonpreemptive schedule with minimum finish time. Ifr is the number of jobs placed onto the processor with maximum finish time, then the worst case ratio of the new algorithm's finish time to the optimal solution is shown to be less thanrm/(rm–m+1). Extensive empirical results show that the new algorithm is competitive with the LPT algorithm in terms of quality of solution and faster in terms of computing time.