Note on the computational complexity ofj-radii of polytopes in ℝ n

We show that, for fixed dimensionn, the approximation of inner and outerj-radii of polytopes in ℝ ⁿ , endowed with the Euclidean norm, is in ℙ. Our method is based on the standard polynomial time algorithms for solving a system of polynomial inequalities over the reals in fixed dimension.     

Parallel information-based complexity

We develop the theory of information-based complexity from a parallel point of view. For a model of computation with p processors, each being capable of arithmetic operations and decisions, we analyze the complexity of function approximation, numerical integration, and solution of Fredholm integral equations. We obtain tight bounds on the complexity, considered as a function of three variables simultaneously: the number of processors, the required precision, and (in the case of approximation and integral equations) the number of points, in which the approximate solution is to be determined.     

The structure of 32S I. Spectroscopy of highly-excited states

Assignments of I, π, T are made to 30 levels in ³²S between 7.35 and 11.76 MeV excitation energy, making the spectroscopy of the T= 0 states rather complete up to 10 MeV and that of the T = 1 states up to 12 MeV. A reassessment of existing data in the light of the new results clarifies the spectrum of I ^π = 1⁺, T = 1 states up to 15 MeV excitation energy. High-spin states (I = 52 - 7) below 10 MeV excitation energy have been investigated by n t γ angular-correlation measurements with the ²⁹Si(α, nγ) reaction at E _α 14.4 MeV. Five g-wave resonances of the ³¹P(p, γ) reaction, leading to the formation of I _π + 4⁺, 5⁺ states in ³²S, have been identified between 10 and 12 MeV excitation energy. The spectrum of T = 1 states between 10.7 and 12 MeV, has been investigated by measurements of γ-ray angular distributions on resonances of the ³¹P(p, γ) reaction and by measurements of resonance strengths. Several ³²S levels between 7.35 and 8.75 MeV excitation energy were studied as final states in resonance decays. Finally a search was performed for I ^π = 0⁺ resonances of the ²⁸Si(α, γ) reaction.     

Examination of a portable99Mo/99mTc isotope generator /SUBLITECHR/

Three SUBLITECH^R technetium generators were milked and generator products were tested for 5 d. Radionuclidic and radiochemical purity, pH of sodium pertechnetate solutions were -emitting impurities and pirogenity were not carried out. We can summarize that generators were running efficiently during our test period and in all cases the pertechnetate produced met the requirements of the European Pharmacopoeia.     

Theoretical study of the spin-orbit coupling in the X2Π state of OH

The spin-orbit coupling constant, A(r), as a function of internuclear distance (r) was computed for the X²Π state of OH, using the microscopic spin-orbit Hamiltonian, extended basis sets, and extensive configuration-interaction wavefunctions. Our best theoretical results are in excellent agreement with the “experimental” A(r) functions deduced from an inversion of the observed A_v. Our calculated first-order contributions to A_v, v ≤ 10, obtained by vibrationally averaging our theoretical A(r) function using the X²Π RKR potential, differ from experiment by less than 0.12%. A minimum occurs in the A_v at v = 7 in agreement with experiment, reflecting the local minimum in A(r) near 2.8 bohr. The second-order contributions to A_v are only about 0.1% for v ≤ 10. They arise mainly from the A²Σ⁺ state for the lower vibrational levels, but each of the A²Σ⁺, B²Σ⁺, (1)²Σ^?, (1)⁴Σ^?, and (1)²Δ states contributes significantly for higher vibrational levels. Spin-orbit centrifugal distortion parameters, A_Dv and a_Dv, are reported for v ≤ 6. The theoretical A_Dv are also in excellent agreement with experiment when the “experimental” A(r) function has the same slope at the equilibrium separation as that obtained from the effective spin-rotation constants of OH, OD, and OT.     

Submodular linear programs on forests

A general linear programming model for an order-theoretic analysis of both Edmonds' greedy algorithm for matroids and the NW-corner rule for transportation problems with Monge costs is introduced. This approach includes the model of Queyranne, Spieksma and Tardella (1993) as a special case. We solve the problem by optimal greedy algorithms for rooted forests as underlying structures. Other solvable cases are also discussed.     

On the feasibility of heat-exchange processes in uninsulated equipment

Strictly speaking, the common two-fluid heat exchanger is a special version of a three-fluid exchanger because the environment also participates in the energy exchange. In a number of situations this effect is significant and leads to either reduced or increased area requirements, depending on the purpose of the exchange operation. With certain combinations of the system parameters it is even impossible to achieve an envisaged temperature change. For some typical flow arrangements these combinations are established in an analytic form so that one can rapidly assess the feasibility of a desired process without actually performing the rather tedious design calculations.     

Multiply periodic real functions and their period sets

Multiply periodic real functions are rather pathological; continuous ones have to be constant and, as will be shown, measurable ones must be constant a.e. Beyond this, some other properties of these functions are discussed, and examples are given. Since the set of periods of a real function is a subgroup of (R,+), it is possible to apply algebraic methods to get a better survey. It will be shown that the homogeneous sets defined by Borel are just cosets of these subgroups; this leads to a transfer of theorems about homogeneous sets to results about period sets (and, at the same time, subgroups of (R,+)).