Non-deterministic exponential time has two-prover interactive protocols

We determine the exact power of two-prover interactive proof systems introduced by Ben-Or, Goldwasser, Kilian, and Wigderson (1988). In this system, two all-powerful noncommunicating provers convince a randomizing polynomial time verifier in polynomial time that the inputx belongs to the languageL. We show that the class of languages having tow-prover interactive proof systems is nondeterministic exponential time.We also show that to prove membership in languages inEXP, the honest provers need the power ofEXP only.The first part of the proof of the main result extends recent techniques of polynomial extrapolation used in the single prover case by Lund, Fortnow, Karloff, Nisan, and Shamir.The second part is averification scheme for multilinearity of a function in several variables held by an oracle and can be viewed as an independent result onprogram verification. Its proof rests on combinatorial techniques employing a simple isoperimetric inequality for certain graphs:     

Complementarity and Additivity for Covariant Channels

This paper contains several new results concerning covariant quantum channels in d ≥ 2 dimensions. The first part, Sec. 3, based on [4], is devoted to unitarily covariant channels, namely depolarizing and transpose-depolarizing channels. The second part, Sec. 4, based on [10], studies Weyl-covariant channels. These results are preceded by Sec. 2 in which we discuss various representations of general completely positive maps and channels. In the first part of the paper we compute complementary channels for depolarizing and transpose-depolarizing channels. This method easily yields minimal Kraus representations from non-minimal ones. We also study properties of the output purity of the tensor product of a channel and its complementary. In the second part, the formalism of discrete noncommutative Fourier transform is developed and applied to the study of Weyl-covariant maps and channels. We then extend a result in [16] concerning a bound for the maximal output 2-norm of a Weyl-covariant channel. A class of maps which attain the bound is introduced, for which the multiplicativity of the maximal output 2-norm is proven. The complementary channels are described which have the same multiplicativity properties as the Weyl-covariant channels.     

The lost-wax casting of icons, utensils, bells, and other items in South India

Indian artisans and craftsmen have long been masters at extracting and shaping metals and alloys, as proven by archaeological finds from the 2nd—3rd millennia B.C. For example, two well-known artifacts, castings of the dancing girl of Mohenjo Daro and the Mother Goddess of Adichanallur, Tamilnadu, depict a high degree of metallurgical knowledge. Those castings were formed by the lost wax process, which later was modified and became known as investment casting. In various parts of India, this age-old casting process is still being practiced, without any major modifications. This paper discusses details of the process used by the Indian artisans of Swamimalai, Tamilnadu, and Mannar, Kerala, South India in shaping copper-base alloys into icons and utensils, bells, and lamps.     

Analytical, numerical and experimental investigations of transverse fracture propagation from horizontal wells

This paper presents results of a comprehensive study involving analytical, numerical and experimental investigations into transverse fracture propagation from horizontal wells. The propagation of transverse hydraulic fractures from horizontal wells is simulated and investigated in the laboratory using carefully designed experimental setups. Closed-form analytical theories for Mode I (opening) stress intensity factors for idealized fracture geometries are reviewed, and a boundary element-based model is used herein to investigate non-planar propagation of fractures. Using the mixed mode fracture propagation criterion of the model, a reasonable agreement is found with respect to fracture geometry, net fracture pressures and fracture propagation paths between the modeled fractures and the laboratory tested fractures. These results suggest that the propagation of multiple fractures requires higher net pressures than a single fracture, the underlying reason of which is theoretically justified on the basis of local stress distribution.     

Inhibition of acid rock drainage from uranium ore waste using a conventional neutralization and precipitation treatment

Glass columns (length 50 cm, i.d. 4 cm) containing 900 g of uranium ore waste were subjected to a three-step process: (1) acid drainage generation, (2) neutralization and precipitation treatment and, again, (3) acid drainage generation. In the first acid generation step, lasting about one year, different variables (pyrite addition, inoculation and irrigation solution) were tested by measuring effluent pH, redox potential, total iron and sulphate. Conditions of acid generation were satisfactorily reproduced, reaching stable pH values around 2.0 that were determined mainly by pyrite addition and the type of irrigation solution used (distilled water or ferrous sulphate). The neutralization and precipitation treatment consisted of alternating irrigations of a neutralizing solution (CaO saturated plus NaOH) and a precipitating solution (ferric sulphate saturated). This treatment caused accumulation of basic iron sulphate and iron oxide precipitates according to SEM studies. After this treatment, the barrier effect created by the reaction products was checked, using irrigation solutions similar to the first step. The effluents collected showed higher pH and lower redox potential, total iron and sulphate values than those observed before the treatment, evidencing inhibition of acid drainage generation.