Heaviside generalized functions and shock waves for a Burger kind equation

The purpose of the work is to study the existence and nonexistence of shock wave solutions for the Burger equations. The study is developed in the context of Colombeau's theory of generalized functions (GFs). This study uses the equality in the strict sense and the weak equality of GFs. The shock wave solutions are given in terms of GFs that have the Heaviside function, in x and ( x, t) variables, as macroscopic aspect. This means that solutions are sought in the form of sequences of regularizations to the Heaviside function, in R-n and R-n x R, in the distributional limit sense.

Which kind of miniplate to use in mandibular sagittal split osteotomy? An in vitro study

This study verified the resistance to displacement of six miniplate fixation methods after sagittal split osteotomy (SSO). SSO was performed in 30 polyurethane synthetic mandible replicas. The distal segments were advanced (4 mm) and specimens were grouped according to the fixation method: four-hole standard miniplate; four-hole locking miniplate; six-hole standard miniplate; six-hole locking miniplate; six-hole standard sagittal miniplate; six-hole locking sagittal miniplate. Biomechanical evaluation was performed by applying compression loads to three points on the second molar region, using an Instron universal testing machine until a 3 mm displacement of the segments occurred. Compression loads able to produce 3 mm displacement were recorded in kN and subjected to analysis of variance (P < 0.01) and Tukey's tests for comparison between groups (P < 0.05). The locking sagittal miniplate showed higher resistance to displacement than the regular four- and six-hole locking and standard miniplates. No significant differences were observed between the locking sagittal miniplate and the regular sagittal or the four-hole locking miniplates. Two of the three groups with the best results had locking plate fixation methods. Fixation of SSO with a single miniplate is better accomplished using six-hole locking sagittal miniplates, six-hole standard sagittal miniplates, or four-hole locking miniplates; these methods are more resistant to displacement.

Zeros of Jacobi functions of second kind

The number of zeros in (- 1, 1) of the Jacobi function of second kind Q(n)((alpha, beta)) (x), alpha, beta > - 1, i.e. The second solution of the differential equation(1 - x(2))y (x) + (beta - alpha - (alpha + beta + 2)x)y' (x) + n(n + alpha + beta + 1)y(x) = 0,is determined for every n is an element of N and for all values of the parameters alpha > - 1 and beta > - 1. It turns out that this number depends essentially on alpha and beta as well as on the specific normalization of the function Q(n)((alpha, beta)) (x). Interlacing properties of the zeros are also obtained. As a consequence of the main result, we determine the number of zeros of Laguerre's and Hermite's functions of second kind. (c) 2005 Elsevier B.V. All rights reserved.

An electrode of the second kind for aspirin determination in tablet formulations

This paper describes the construction of an electrode of the second kind, Pt\Hg\Hg-2(Salic)(2)\Graphite, sensitive to salicylate. This electrode responds to the salicylate ion with a sensivity of 58.66 mV/decade over the range 6.0x10(-4) - 1.0x10(-1) mol/l at pH 6.0 and an ionic strength of 0.500 - 3.00 mol/l, adjusted with NaClO4. The electrode is easily constructed, shows a fast response time, is low in cost, has excellent response stability, and has a lifetime greater than 18 months, which is much longer than those reported earlier for other systems. The influence of 10 different carboxylate and inorganic anions on the electrode response showed that there was negligible interference by most of these ions. It was used to determine aspirin in tablets (after hydrolysis of acetylsalicylic acid to salicylate) by means of the standard additions method. The results obtained using this electrode for aspirin determination, in three different samples of antithermic drugs, compared favorably with the results given by the British Pharmacopoeia method.

An electrode of the second kind for benzoate determination in medicinal syrups

This paper describes the construction of an electrode of the second kind, Pt\Hg\Hg-2(Bzt)(2)\graphite, sensitive to benzoate ion (Bzt). The electrode provides a near-Nernstian response (-58.19 mV/decade at 25 degrees C) to benzoate ion in the concentration range 1.11 x 10(-1) to 5.00 x 10(-4) M at pH 7.0 and ionic strength 0.500-3.00M, adjusted with NaClO4. The electrode is easily constructed, shows a fast response time, is low in cost, has excellent response stability, and has a lifetime greater than 24 months. which is much longer than those earlier reported for other systems. A further salient feature of the electrode is that perchlorate does not interfere in its response, which may be advantageous in the analysis of perchloric acid-treated samples. It was applied to the determination of sodium benzoate in some commercial expectorating medicinal syrups using the standard additions method. The results obtained by the proposed procedure compare very favorably with those obtained through the reference method recommended by the United States Pharmacopeia. (C) 1998 Academic Press.