On a computer-aided approach to the computation of Abelian integrals

An accurate method to compute enclosures of Abelian integrals is developed. This allows for an accurate description of the phase portraits of planar polynomial systems that are perturbations of Hamiltonian systems. As an example, it is applied to the study of bifurcations of limit cycles arising from a cubic perturbation of an elliptic Hamiltonian of degree four

Hull Consistency Under Monotonicity

International audienceWe prove that hull consistency for a system of equations or inequalities can be achieved in polynomial time providing that the underlying functions are monotone with respect to each variable. This result holds including when variables have multiple occurrences in the expressions of the functions, which is usually a pitfall for interval-based contractors. For a given constraint, an optimal contractor can thus be enforced quickly under monotonicity and the practical significance of this theoretical result is illustrated on a simple example

The High-Flux Backscattering Spectrometer at the NIST Center for Neutron Research

We describe the design and current performance of the high-flux backscattering spectrometer located at the NIST Center for Neutron Research. The design incorporates several state-of-the-art neutron optical devices to achieve the highest flux on sample possible while maintaining an energy resolution of less than 1mueV. Foremost among these is a novel phase-space transformation chopper that significantly reduces the mismatch between the beam divergences of the primary and secondary parts of the instrument. This resolves a long-standing problem of backscattering spectrometers, and produces a relative gain in neutron flux of 4.2. A high-speed Doppler-driven monochromator system has been built that is capable of achieving energy transfers of up to +-50mueV, thereby extending the dynamic range of this type of spectrometer by more than a factor of two over that of other reactor-based backscattering instruments

The Complexity of Flat Freeze LTL

We consider the model-checking problem for freeze LTL on one-counter automata (OCAs). Freeze LTL extends LTL with the freeze quantifier, which allows one to store different counter values of a run in registers so that they can be compared with one another. As the model-checking problem is undecidable in general, we focus on the flat fragment of freeze LTL, in which the usage of the freeze quantifier is restricted. Recently, Lechner et al. showed that model checking for flat freeze LTL on OCAs with binary encoding of counter updates is decidable and in 2NEXPTIME. In this paper, we prove that the problem is, in fact, NEXPTIME-complete no matter whether counter updates are encoded in unary or binary. Like Lechner et al., we rely on a reduction to the reachability problem in OCAs with parameterized tests (OCAPs). The new aspect is that we simulate OCAPs by alternating two-way automata over words. This implies an exponential upper bound on the parameter values that we exploit towards an NP algorithm for reachability in OCAPs with unary updates. We obtain our main result as a corollary

On the convex central configurations of the symmetric (ℓ + 2)-body problem

For the 4-body problem there is the following conjecture: Given arbitrary positive masses, the planar 4-body problem has a unique convex central configuration for each ordering of the masses on its convex hull. Until now this conjecture has remained open. Our aim is to prove that this conjecture cannot be extended to the (ℓ + 2)-body problem with ℓ ⩾ 3. In particular, we prove that the symmetric (2n + 1)-body problem with masses m1 = … = m2n−1 = 1 and m2n = m2n+1 = m sufficiently small has at least two classes of convex central configuration when n = 2, five when n = 3, and four when n = 4. We conjecture that the (2n + 1)-body problem has at least n classes of convex central configurations for n > 4 and we give some numerical evidence that the conjecture can be true. We also prove that the symmetric (2n + 2)-body problem with masses m1 = … = m2n = 1 and m2n+1 = m2n+2 = m sufficiently small has at least three classes of convex central configuration when n = 3, two when n = 4, and three when n = 5. We also conjecture that the (2n + 2)-body problem has at least [(n +1)/2] classes of convex central configurations for n > 5 and we give some numerical evidences that the conjecture can be true

Probability Theory Compatible with the New Conception of Modern Thermodynamics. Economics and Crisis of Debts

We show that G\"odel's negative results concerning arithmetic, which date back to the 1930s, and the ancient "sand pile" paradox (known also as "sorites paradox") pose the questions of the use of fuzzy sets and of the effect of a measuring device on the experiment. The consideration of these facts led, in thermodynamics, to a new one-parameter family of ideal gases. In turn, this leads to a new approach to probability theory (including the new notion of independent events). As applied to economics, this gives the correction, based on Friedman's rule, to Irving Fisher's "Main Law of Economics" and enables us to consider the theory of debt crisis.Comment: 48p., 14 figs., 82 refs.; more precise mathematical explanations are added. arXiv admin note: significant text overlap with arXiv:1111.610

Experimental Correlation of Combined Heat and Mass Transfer for NH 3 -H 2 0 falling film absorption

vection. The main conclusion from this study is that the negative concentration gradient of the surface tension is a trigger for inducement of Marangoni convection before the additive solubility, while the imbalance of the surface tension and the interfacial tension is a trigger after the solubility limit. Acknowledgment The authors thank Mr. K. Iizuka, Tokyo University of Agriculture and Technology, for his experimental assistance. The authors acknowledge that this work has been partially funded by the Japan Science and Technology Corporation (JST). References Beutler, A., Greiter, I., Wagner, A., Hohhmann, L., Schreier, S., and Alefeld, G., 1996, "Surfactants and Fluid Properties," Int. J. Refrigeration, Vol. 19, No. 5, pp. 342-346. Chavepeyer, G" Salajan, M., Platten, J. K., and Smet, P., 1995, "InterfacialTension and Surface Adsorption in j-Heptanol/Water Systems," Journal of Colloid and Interface Science, Vol. 174, Daiguji, H,, Hihara, E., and Saito, T., 1997, "Mechanism of Absorption Enhancement by Surfactant," Int. J. Heat and Mass Transfer, Vol. 40, No. 8, pp. 1743-1752. Fujita, T., 1993, "Falling Liquid Films in Absorption Machines," Int. J. Refrigeration, Vol. 16, No. 4, pp. 282-294. Hihara, E" and Saito, T., 1993 Journal of Heat Transfer TL = temperature of the fluid far away from the plate t' = time t R = reference time u = velocity of the fluid UD = reference velocity at' = frequency X,, = distance of the transition point from the leading edge |3 = coefficient of volume expansion p = density e = amplitude (constant) 9 = nondimensional temperature u = nondimensional velocity i = y-i Introduction Transient laminar-free convection flow past an infinite vertical plate under different plate conditions was studied by many researchers. The first closed-form solutions for Prandtl number Pr = 1.0 in case of a step change in wall temperature with time was derived by Illingworth (1950) and for Pr # 1.0, he derived the solution in integral form. Siegel (1958) studied the unsteady freeconvection flow past a semi-infinite vertical plate under stepchange in wall temperature or surface heat flux by employing the momentum integral method. Experimental evidence for such a situation was presented by Goldstein and Eckert (1960). For a semi-infinite vertical plate, unsteady free-convection flow was studied analytically b