Quasi-separation of the biharmonic partial differential equation

In this paper, we consider analytical and numerical solutions to the Dirichlet boundary-value problem for the biharmonic partial differential equation on a disc of finite radius in the plane. The physical interpretation of these solutions is that of the harmonic oscillations of a thin, clamped plate. For the linear, fourth-order, biharmonic partial differential equation in the plane, it is well known that the solution method of separation in polar coordinates is not possible, in general. However, in this paper, for circular domains in the plane, it is shown that a method, here called quasi-separation of variables, does lead to solutions of the partial differential equation. These solutions are products of solutions of two ordinary linear differential equations: a fourth-order radial equation and a second-order angular differential equation. To be expected, without complete separation of the polar variables, there is some restriction on the range of these solutions in comparison with the corresponding separated solutions of the second-order harmonic differential equation in the plane. Notwithstanding these restrictions, the quasi-separation method leads to solutions of the Dirichlet boundary-value problem on a disc with centre at the origin, with boundary conditions determined by the solution and its inward drawn normal taking the value 0 on the edge of the disc. One significant feature for these biharmonic boundary-value problems, in general, follows from the form of the biharmonic differential expression when represented in polar coordinates. In this form, the differential expression has a singularity at the origin, in the radial variable. This singularity translates to a singularity at the origin of the fourth-order radial separated equation; this singularity necessitates the application of a third boundary condition in order to determine a self-adjoint solution to the Dirichlet boundary-value problem. The penultimate section of the paper reports on numerical solutions to the Dirichlet boundary-value problem; these results are also presented graphically. Two specific cases are studied in detail and numerical values of the eigenvalues are compared with the results obtained in earlier studies.

Existence and Uniqueness of Solutions for Partial Differential-Functional Equations of the First Order with Deviating Argument of the Derivative of Unknown Function

We consider the existence and uniqueness problem for partial differential-functional equations of the first order with the initial condition for which the right-hand side depends on the derivative of unknown function with deviating argument.

Operational Rules for a Mixed Operator of the Erdélyi-Kober Type

2000 Mathematics Subject Classification: 26A33 (main), 44A40, 44A35, 33E30, 45J05, 45D05

On the Riemann-Liouville Fractional q-Integral Operator Involving a Basic Analogue of Fox H-Function

2000 Mathematics Subject Classification: 33D60, 26A33, 33C60

Cauchy-Type Problem for Diffusion-Wave Equation with the Riemann-Liouville Partial Derivative

2000 Mathematics Subject Classification: 35A15, 44A15, 26A33

Classification of the Maximal Subsemigroups of the Semigroup of all Partial Order-Preserving Transformations

Илинка А. Димитрова, Цветелина Н. Младенова - Моноида P Tn от всички частични преобразования върху едно n-елементно множество относно операцията композиция на преобразования е изучаван в различни аспекти от редица автори. Едно частично преобразование α се нарича запазващо наредбата, ако от x ≤ y следва, че xα ≤ yα за всяко x, y от дефиниционното множество на α. Обект на разглеждане в настоящата работа е моноида P On състоящ се от всички частични запазващи наредбата преобразования. Очевидно P On е под-моноид на P Tn. Направена е пълна класификация на максималните подполугрупи на моноида P On. Доказано е, че съществуват пет различни вида максимални подполугрупи на разглеждания моноид. Броят на всички максимални подполугрупи на POn е точно 2^n + 2n − 2.

Continuous measurement of carbon dioxid partial pressure in seawater in the region of the Iceland-Faroe Ridge (Table 1)

During the 14th expedition of the research vessel "Meteor" from the 2nd of July to the 7th of August 1968 continously recording instruments for measuring the CO2 partial pressure of seawater and atmospheric CO2 were developped by the Meteorological Institute, University of Frankfurt/M. During the Faroer expedition instrumental constants, such as relative and absolute accuracy, inertia and solvent power were tested. The performance of discontinous analyses of water samples was adopted to shipboard conditiones and correction factors depending on water volume, depth of sampling and water temperature were measured. After having computed average values of the continous records (atmosp. CO2 content, CO2 partial pressure, water temperature) geographical distribution, diurnal variation and dependence of diurnal averages were tested. At four different locations CO2 partial pressure was measured in various depths. During the voyage from the Faroer islands to Helgoland the measured concentrations of atmospheric CO2 content and CO2 partial pressure were tested with respect to a correlation of the geographical latitude.

Immune proteins in neurons : towards an understanding of the neuronal role of the immune protein CD3[Zeta] in NMDA receptor signaling and cytoskeleton remodeling

Otto-von-Guericke-Universität Magdeburg, Fakultät für Naturwissenschaften, Dissertation, 2016

2-(4-Amino-3-methylphenyl)-5-fluorobenzothiazole is a ligand and shows species-specific partial agonism of the Aryl Hydrocarbon Receptor

2-(4-Amino-3-methylphenyl)-5-fluorobenzothiazole (5F 203) and related compounds are a series of anti-cancer candidate pharmaceuticals (Table 1.), that have been shown to activate the AhR. We show that these compounds are high affinity ligands for the rat AhR, but a quantitative assay for their ability to induce CYP1A1 RNA in H4IIEC3 cells, a measure of activation of the AhR, showed a poor relationship between affinity for the AhR and ability to induce CYP1A1 RNA. 5F 203, an agonist with low potency, was able to antagonise the induction of CYP1A1 RNA by TCDD, while IH 445, a potent agonist, did not antagonise the induction of CYP1A1 RNA by TCDD, and Schild analysis confirmed 5F 203 to be a potent antagonist of the induction of CYP1A1 RNA by TCDD in H4IIEC3 cells. In contrast, several benzothiazoles show potent induction of CYP1A1 RNA in human MCF-7 cells, and 5F 203 is unable to detectably antagonise the induction of CYP1A1 RNA in MCF-7 cells, showing a species difference in antagonism. Evaluation of the antiproliferative activity of benzothiazoles showed that the ability to agonise the AhR correlated with growth inhibition both in H4IIEC3 cells for a variety of benzothiazoles, and between H4IIEC3 and MCF-7 cells for 5F 203, suggesting an important role of agonism of the AhR in the anti-proliferative activity of benzothiazoles.

Study Of The Homogeneity Of Drug Loaded In Polymeric Films Using Near-infrared Chemical Imaging And Split-plot Design.

Split-plot design (SPD) and near-infrared chemical imaging were used to study the homogeneity of the drug paracetamol loaded in films and prepared from mixtures of the biocompatible polymers hydroxypropyl methylcellulose, polyvinylpyrrolidone, and polyethyleneglycol. The study was split into two parts: a partial least-squares (PLS) model was developed for a pixel-to-pixel quantification of the drug loaded into films. Afterwards, a SPD was developed to study the influence of the polymeric composition of films and the two process conditions related to their preparation (percentage of the drug in the formulations and curing temperature) on the homogeneity of the drug dispersed in the polymeric matrix. Chemical images of each formulation of the SPD were obtained by pixel-to-pixel predictions of the drug using the PLS model of the first part, and macropixel analyses were performed for each image to obtain the y-responses (homogeneity parameter). The design was modeled using PLS regression, allowing only the most relevant factors to remain in the final model. The interpretation of the SPD was enhanced by utilizing the orthogonal PLS algorithm, where the y-orthogonal variations in the design were separated from the y-correlated variation.

Intraductal Carcinoma Of The Prostate: Interobserver Reproducibility Survey Of 39 Urologic Pathologists.

The diagnosis of intraductal carcinoma (IDC) of the prostate remains subjective because 3 sets of diagnostic criteria are in use. An internet survey was compiled from 38 photomicrographs showing duct proliferations: 14 signed out as high-grade prostatic intraepithelial neoplasia (HGPIN), 17 IDC, and 7 invasive cribriform/ductal carcinoma. Each image was assessed for the presence of 9 histologic criteria ascribed to IDC. Thirty-nine respondents were asked to rate images as (1) benign/reactive, (2) HGPIN, (3) borderline between HGPIN and IDC, (4) IDC, or (5) invasive cribriform/ductal carcinoma. Intraclass correlation coefficient was 0.68. There was 70% overall agreement with HGPIN, 43% with IDC, and 73% with invasive carcinoma (P < .001, χ(2)). Respondents considered 19 (50%) of 38 cases as IDC candidates, of which 5 (26%) had a two-thirds consensus for IDC; two-thirds consensus for either borderline or IDC was reached in 9 (47%). Two-thirds consensus other than IDC was reached in the remaining 19 of 38 cases, with 15 supporting HGPIN and 4 supporting invasive carcinoma. Findings that differed across diagnostic categories were lumen-spanning neoplastic cells (P < .001), 2× benign duct diameters (P < .001), duct space contours (round, irregular, and branched) (P < .001), papillary growth (P = .048), dense cribriform or solid growth (both P = .023), and comedonecrosis (P = .015). When the 19 of 38 images that attained consensus for HGPIN or invasive carcinoma were removed from consideration, lack of IDC consensus was most often attributable to only loose cribriform growth (5/19), central nuclear maturation (5/19), or comedonecrosis (3/19). Of the 9 histologic criteria, only 1 retained significant correlation with a consensus diagnosis of IDC: the presence of solid areas (P = .038). One case that attained IDC consensus had less than 2× duct enlargement yet still had severe nuclear atypia and nucleomegaly. Six fold nuclear enlargement was not significant (P = .083), although no image had both 6× nuclei and papillary or loose cribriform growth: a combination postulated as sufficient criteria for IDC. Finally, 20.5% of respondents agreed that an isolated diagnosis of IDC on needle biopsy warrants definitive therapy, 20.5% disagreed, and 59.0% considered the decision to depend upon clinicopathologic variables. Although IDC diagnosis remains challenging, we propose these criteria: a lumen-spanning proliferation of neoplastic cells in preexisting ducts with a dense cribriform or partial solid growth pattern. Solid growth, in any part of the duct space, emerges as the most reproducible finding to rule in a diagnosis of IDC. Comedonecrosis is a rarer finding, but in most cases, it should rule in IDC. Duct space enlargement to greater than 2× the diameter of the largest, adjacent benign spaces is usually present in IDC, although there may be rare exceptions.

Trichomes Related To An Unusual Method Of Water Retention And Protection Of The Stem Apex In An Arid Zone Perennial Species.

It is well known that trichomes protect plant organs, and several studies have investigated their role in the adaptation of plants to harsh environments. Recent studies have shown that the production of hydrophilic substances by glandular trichomes and the deposition of this secretion on young organs may facilitate water retention, thus preventing desiccation and favouring organ growth until the plant develops other protective mechanisms. Lychnophora diamantinana is a species endemic to the Brazilian 'campos rupestres' (rocky fields), a region characterized by intense solar radiation and water deficits. This study sought to investigate trichomes and the origin of the substances observed on the stem apices of L. diamantinana. Samples of stem apices, young and expanded leaves were studied using standard techniques, including light microscopy and scanning and transmission electron microscopy. Histochemical tests were used to identify the major groups of metabolites present in the trichomes and the hyaline material deposited on the apices. Non-glandular trichomes and glandular trichomes were observed. The material deposited on the stem apices was hyaline, highly hydrophilic and viscous. This hyaline material primarily consists of carbohydrates that result from the partial degradation of the cell wall of uniseriate trichomes. This degradation occurs at the same time that glandular trichomes secrete terpenoids, phenolic compounds and proteins. These results suggest that the non-glandular trichomes on the leaves of L. diamantinana help protect the young organ, particularly against desiccation, by deposition of highly hydrated substances on the apices. Furthermore, the secretion of glandular trichomes probably repels herbivore and pathogen attacks.

[consensus Of The Brazilian Society Of Rheumatology For The Diagnosis, Management And Treatment Of Lupus Nephritis].

To develop recommendations for the diagnosis, management and treatment of lupus nephritis in Brazil. Extensive literature review with a selection of papers based on the strength of scientific evidence and opinion of the Commission on Systemic Lupus Erythematosus members, Brazilian Society of Rheumatology. 1) Renal biopsy should be performed whenever possible and if this procedure is indicated; and, when the procedure is not possible, the treatment should be guided with the inference of histologic class. 2) Ideally, measures and precautions should be implemented before starting treatment, with emphasis on attention to the risk of infection. 3) Risks and benefits of treatment should be shared with the patient and his/her family. 4) The use of hydroxychloroquine (preferably) or chloroquine diphosphate is recommended for all patients (unless contraindicated) during induction and maintenance phases. 5) The evaluation of the effectiveness of treatment should be made with objective criteria of response (complete remission/partial remission/refractoriness). 6) ACE inhibitors and/or ARBs are recommended as antiproteinuric agents for all patients (unless contraindicated). 7) The identification of clinical and/or laboratory signs suggestive of proliferative or membranous glomerulonephritis should indicate an immediate implementation of specific therapy, including steroids and an immunosuppressive agent, even though histological confirmation is not possible. 8) Immunosuppressives must be used during at least 36 months, but these medications can be kept for longer periods. Its discontinuation should only be done when the patient achieve and maintain a sustained and complete remission. 9) Lupus nephritis should be considered as refractory when a full or partial remission is not achieved after 12 months of an appropriate treatment, when a new renal biopsy should be considered to assist in identifying the cause of refractoriness and in the therapeutic decision.

Chitosan Nanoparticles Loaded The Herbicide Paraquat: The Influence Of The Aquatic Humic Substances On The Colloidal Stability And Toxicity.

Polymeric nanoparticles have been developed for several applications, among them as carrier system of pesticides. However, few studies have investigated the fate of these materials in the environment in relation to colloidal stability and toxicity. In nature, humic substances are the main agents responsible for complexation with metals and organic compounds, as well as responsible for the dynamics of these nanoparticles in aquatic and terrestrial environments. In this context, the evaluation of the influence of aquatic humic substances (AHS) on the colloidal stability and toxicity of polymeric nanoparticles of chitosan/tripolyphosphate with or without paraquat was performed. In this study, the nanoparticles were prepared by the ionic gelation method and characterized by size distribution measurements (DLS and NTA), zeta potential, infrared and fluorescence spectroscopy. Allium cepa genotoxicity studies and ecotoxicity assays with the alga Pseudokirchneriella subcapitata were used to investigate the effect of aquatic humic substances (AHS) on the toxicity of this delivery system. No changes were observed in the physical-chemical stability of the nanoparticles due to the presence of AHS using DLS and NTA techniques. However some evidence of interaction between the nanoparticles and AHS was observed by infrared and fluorescence spectroscopies. The ecotoxicity and genotoxicity assays showed that humic substances can decrease the toxic effects of nanoparticles containing paraquat. These results are interesting because they are important for understanding the interaction of these nanostructured carrier systems with species present in aquatic ecosystems such as humic substances, and in this way, opening new perspectives for studies on the dynamics of these carrier systems in the ecosystem.