Some remarks on computing the square parts of integers

Let n be a positive integer, and suppose is its prime factorization. Let , so that n/θ(n) is the largest squarefree factor of n. We show that π is deterministic polynomial time Turing reducible to , the Euler function. We also show that θ is reducible to λ, the Carmichael function. We survey other recent work on computing the square part of an integer and give upper and lower bounds on the complexity of solving the problem.     

Advances in the management of bronchial asthma

The ultrastructure of rat precorneal tear film was visualized by the quick freezing-freeze substitution (QF-FS) method and the conventional fixative method under the scanning electron microscope (SEM). In the QF-FS method, the eyeballs of rats were quickly frozen with an isopentane-propane mixture cooled by liquid nitrogen applied directly to the eyes. After enucleating the eyes and fracturing the frozen corneas, the corneas were prepared for SEM observation. In contrast to the conventional fixative method, by which the microvilli of the surface epithelial cells could be visualized clearly, a very thin membrane-like structure was observed to cover the corneal surface in the eyes prepared by the QF-Fs method. Between the membrane-like structure and corneal surface, a homogeneous and fine network-like structure was observed. The results suggest that the structure of the tear film might be different from the one we have believed to consist of three layers until now. The QF-FS method is considered to be useful for the morphological study of the precorneal tear film.     

Effect of HZSM zeolite in a catalyst on the indexes of hydroconversion of vacuum distillate

Translated from Khimiya i Tekhnologiya Topliv i Masel, No. 3, pp. 25–26, March, 1991.     

Numerical integration using Wang-Landau sampling

We report a new application of Wang-Landau sampling to numerical integration that is straightforward to implement. It is applicable to a wide variety of integrals without restrictions and is readily generalized to higher-dimensional problems. The feasibility of the method results from a reinterpretation of the density of states in statistical physics to an appropriate measure for numerical integration. The properties of this algorithm as a new kind of Monte Carlo integration scheme are investigated with some simple integrals, and a potential application of the method is illustrated by the evaluation of integrals arising in perturbation theory of quantum many-body systems.     

Differential diagnosis of attention deficit and conduct disorders using conditional probabilities.

Attention deficit and conduct disorders require an important yet often difficult differential diagnosis. Prior efforts to determine which symptoms are optimal for making this differential diagnosis have been limited by a reliance on statistics that do not supply the probability of the disorders given a symptom's presence (positive predictive power) or the probability that the disorder is not present given the absence of the symptom (negative predictive power). This investigation examined the utility of these latter statistics in the differential diagnosis of childhood attention deficit and conduct disorders. The data consisted of symptoms from a standardized maternal psychiatric interview collected for a sample of 76 clinic-referred boys. Results indicated that some symptoms are optimal as inclusion criteria, some as exclusion criteria, some as neither, and some as both. Furthermore, some symptoms that have been traditionally associated with the diagnosis of one disorder were actually found to be more useful in the diagnosis of the other disorder. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Structure–Function Relations in Supported Ni–W Sulfide Hydrogenation Catalysts

Ni–W catalysts were prepared by impregnation of commercial -alumina and silica supports. The sulfidation, performed directly after drying at 100°C, yielded fully sulfided Ni–W species on both supports (SEM-EDAX, XPS, XRD). At optimal metals loading (50 wt% NiO + WO₃, Ni/W = 2), the sulfided catalysts had similar texture (N₂ adsorption) and displayed similar activity in dibenzothiophene hydrodesulfurization (DBT HDS), while the activity of the Ni–W/SiO₂ catalyst in toluene hydrogenation (HYD) was six times higher than that of Ni–W/Al₂O₃. This is due to the more than two times higher WS₂ slabs stacking number in Ni–W/SiO₂ compared with Ni–W/Al₂O₃ (XRD, HR-TEM), yielding stronger adsorption of toluene (TPD).     

Cesium salt of a heteropolyacid in nanotubular channels and on the external surface of SBA-15 crystals: preparation and performance as acidic catalysts

The Cs-salt of heteropolyacid with stoichiometry Cs_2.5H_0.5PW₁₂O₄₀ (CsHPW) was deposited selectively at the external surface of the SBA-15 silica microcrystals, inside its mesoporous channels and simultaneously at both location modes. The structure, texture and performance of these CsHPW/SBA-15 composites were compared with that of a reference bulk salt of the same composition. Location of CsHPW salt on the external surface of SBA-15 microcrystals leads to disintegration of its agglomerates increasing acidity of the catalytic phase. A novel preparation strategy consisting of grafting the basic Cs-species at the internal pores surface of SBA-15 stabilized the CsHPW phase inside the channels in form of 5–8 nm nanocrystals at 30–70 wt.% loadings. The catalytic tests demonstrated that insertion of the CsHPW catalytic phase inside the nanotubular channels of SBA-15 in combination with location of an additional amount of this phase at the external surface of SBA-15 microcrystals allows to increase the specific activity of this phase in MTBE synthesis, propionylation of anisole and alkylation of catechol with t-butanol by a factor of 1.5–3. This level of specific activity in combination with high total loading of catalytic phase >60 wt.% permit to get composite catalytic materials with catalytic activity higher by a factor of 1.2–1.5 with respect to the bulk CsHPW catalyst and stabilizing the catalytic phase against colloidization in polar media.