Topological methods for some boundary value problems

We establish existence of solutions for a finite difference approximation to y = f(x, y, y ') on [0, 1], subject to nonlinear two-point Sturm-Liouville boundary conditions of the form g(i)(y(i),y ' (i)) = 0, i = 0, 1, assuming S satisfies one-sided growth bounds with respect to y '. (C) 2001 Elsevier Science Ltd. All rights reserved.

Boundary value problems for systems of difference equations associated with systems of second-order ordinary differential equations

We study difference equations which arise as discrete approximations to two-point boundary value problems for systems of second-order ordinary differential equations. We formulate conditions which guarantee a priori bounds on first differences of solutions to the discretized problem. We establish existence results for solutions to the discretized boundary value problems subject to nonlinear boundary conditions. We apply our results to show that solutions to the discrete problem converge to solutions of the continuous problem in an aggregate sense. (C) 2002 Elsevier Science Ltd. All rights reserved.

Existence of multiple solutions for second-order discrete boundary value problems

We give conditions on f involving pairs of discrete lower and discrete upper solutions which lead to the existence of at least three solutions of the discrete two-point boundary value problem yk+1 - 2yk + yk-1 + f (k, yk, vk) = 0, for k = 1,..., n - 1, y0 = 0 = yn,, where f is continuous and vk = yk - yk-1, for k = 1,..., n. In the special case f (k, t, p) = f (t) greater than or equal to 0, we give growth conditions on f and apply our general result to show the existence of three positive solutions. We give an example showing this latter result is sharp. Our results extend those of Avery and Peterson and are in the spirit of our results for the continuous analogue. (C) 2002 Elsevier Science Ltd. All rights reserved.

Difference equations associated with fully nonlinear boundary value problems for second order ordinary differential equations

We study the continuous problem y"=f(x,y,y'), xc[0,1], 0=G((y(0),y(1)),(y'(0), y'(1))), and its discrete approximation (y(k+1)-2y(k)+y(k-1))/h(2) =f(t(k), y(k), v(k)), k = 1,..., n-1, 0 = G((y(0), y(n)), (v(1), v(n))), where f and G = (g(0), g(1)) are continuous and fully nonlinear, h = 1/n, v(k) = (y(k) - y(k-1))/h, for k =1,..., n, and t(k) = kh, for k = 0,...,n. We assume there exist strict lower and strict upper solutions and impose additional conditions on f and G which are known to yield a priori bounds on, and to guarantee the existence of solutions of the continuous problem. We show that the discrete approximation also has solutions which approximate solutions of the continuous problem and converge to the solution of the continuous problem when it is unique, as the grid size goes to 0. Homotopy methods can be used to compute the solution of the discrete approximation. Our results were motivated by those of Gaines.

Existence of multiple solutions for finite difference approximations to second-order boundary value problems

Error condition detected We consider discrete two-point boundary value problems of the form D-2 y(k+1) = f (kh, y(k), D y(k)), for k = 1,...,n - 1, (0,0) = G((y(0),y(n));(Dy-1,Dy-n)), where Dy-k = (y(k) - Yk-I)/h and h = 1/n. This arises as a finite difference approximation to y" = f(x,y,y'), x is an element of [0,1], (0,0) = G((y(0),y(1));(y'(0),y'(1))). We assume that f and G = (g(0), g(1)) are continuous and fully nonlinear, that there exist pairs of strict lower and strict upper solutions for the continuous problem, and that f and G satisfy additional assumptions that are known to yield a priori bounds on, and to guarantee the existence of solutions of the continuous problem. Under these assumptions we show that there are at least three distinct solutions of the discrete approximation which approximate solutions to the continuous problem as the grid size, h, goes to 0. (C) 2003 Elsevier Science Ltd. All rights reserved.

O método averagin e aplicações

Pós-graduação em Matemática - IBILCE

O método do Avering via teoria do grau de Brouwer e aplicações

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Training proposal in the degree of Master of Early Childhood Education for working the method of historical research in the classroom

Future teachers must be competent in creating educational settings, which provide tools to their students future they can develop a conscious mind, able to interpret their experiences, to make decisions and imagine innovative solutions to help you participate autonomously and responsible in society. This requires an educational system that allows them to integrate the subjective into a broader spatial and temporal context. La patrimonializatión of “Cultural artefacts” and oral history, the basis of which, are found in the active mind and links both the personal and the group experience, don’t only serve as a catalyst to achieving this goal, but rather, they facilitate the implementation of established practice in infant education. To gain this experience we offer the opportunity for students of their degree in Infant Education in the Public University of Navarre, training within the framework of social didactics, allowing students to learn about established practice from iconic, materials and oral sources in the Archive of Intangible Cultural Heritage of Navarra. The vidences points to their effectiveness and presented in a work in progress.

The Crosslinking Degree Controls The Mechanical, Rheological, And Swelling Properties Of Hyaluronic Acid Microparticles.

Viscosupplements, used for treating joint and cartilage diseases, restore the rheological properties of synovial fluid, regulate joint homeostasis and act as scaffolds for cell growth and tissue regeneration. Most viscosupplements are hydrogels composed of hyaluronic acid (HA) microparticles suspended in fluid HA. These microparticles are crosslinked with chemicals to assure their stability against enzyme degradation and to prolong the action of the viscosupplement. However, the crosslinking also modifies the mechanical, swelling and rheological properties of the HA microparticle hydrogels, with consequences on the effectiveness of the application. The aim of this study is to correlate the crosslinking degree (CD) with these properties to achieve modulation of HA/DVS microparticles through CD control. Because divinyl sulfone (DVS) is the usual crosslinker of HA in viscosupplements, we examined the effects of CD by preparing HA microparticles at 1:1, 2:1, 3:1, and 5:1 HA/DVS mass ratios. The CD was calculated from inductively coupled plasma spectrometry data. HA microparticles were previously sized to a mean diameter of 87.5 µm. Higher CD increased the viscoelasticity and the extrusion force and reduced the swelling of the HA microparticle hydrogels, which also showed Newtonian pseudoplastic behavior and were classified as covalent weak. The hydrogels were not cytotoxic to fibroblasts according to an MTT (3-[4,5-dimethylthiazol-2-yl]-2,5-diphenyltetrazolium bromide) assay. © 2014 Wiley Periodicals, Inc. J Biomed Mater Res Part A, 2014.

Histologic Correlation Of Expression Of Ki-67 In Squamous Cell Carcinoma Of The Glottis According To The Degree Of Cell Differentiation.

Squamous cell carcinoma is the most common neoplasm of the larynx and glottis, and its prognosis depends on the size of the lesion, level of local invasion, cervical lymphatic spread, and presence of distant metastases. Ki-67 (MKI67) is a protein present in the core, whose function is related to cell proliferation. To evaluate the expression of marker Ki-67 in squamous cell carcinoma of the larynx and glottis and its correlation to pathological findings. Experimental study with immunohistochemistry analysis of Ki-67, calculating the percentage of the cell proliferation index in glottic squamous cell carcinomas. Sixteen cases were analyzed, with six well-differentiated and 10 poorly/moderately differentiated tumors. There was a correlation between cell proliferation index and degree of cell differentiation, with higher proliferation in poorly/moderately differentiated tumors. The cell proliferation index, as measured by Ki-67, may be useful in the characterization of histological degree in glottic squamous cell tumors.

Risk Of Leukemia In First Degree Relatives Of Patients With Nonsyndromic Cleft Lip And Palate.

The aim of this study was to determine the frequency of leukemia in parents of patients with nonsyndromic cleft lip and/or cleft palate (NSCL/P). This case-control study evaluated first-degree family members of 358 patients with NSCL/P and 1,432 subjects without craniofacial alterations or syndromes. Statistical analysis was carried out using Fisher's test. From the 358 subjects with NSCL/P, 3 first-degree parents had history of leukemia, while 2 out of 1,432 subjects from the unaffected group had a family history of leukemia. The frequency of positive family history of leukemia was not significantly increased in first-degree relatives of patients with NSCL/P.

Effect Of 4-(n,n-dimethylamino)phenethyl Alcohol On Degree Of Conversion And Cytotoxicity Of Photo-polymerized Cq-based Resin Composites.

The aim of this study was to evaluate the degree of conversion (DC) and the cytotoxicity of photo-cured experimental resin composites containing 4-(N,N-dimethylamino)phenethyl alcohol (DMPOH) combined to the camphorquinone (CQ) compared with ethylamine benzoate (EDAB). The resin composites were mechanically blended using 35 wt% of an organic matrix and 65 wt% of filler loading. To this matrix was added 0.2 wt% of CQ and 0.2 wt% of one of the reducing agents tested. 5x1 mm samples (n=5) were previously submitted to DC measurement and then pre-immersed in complete culture medium without 10% (v/v) bovine serum for 1 h or 24 h at 37 °C in a humidifier incubator with 5% CO2 and 95% humidity to evaluate the cytotoxic effects of experimental resin composites using the MTT assay on immortalized human keratinocytes cells. As a result of absence of normal distribution, the statistical analysis was performed using the nonparametric Kruskal-Wallis to evaluate the cytotoxicity and one-way analysis of variance to evaluate the DC. For multiple comparisons, cytotoxicity statistical analyses were submitted to Student-Newman-Keuls and DC analysis to Tukey's HSD post-hoc test (=0.05). No significant differences were found between the DC of DMPOH (49.9%) and EDAB (50.7%). 1 h outcomes showed no significant difference of the cell viability between EDAB (99.26%), DMPOH (94.85%) and the control group (100%). After 24 h no significant difference were found between EDAB (48.44%) and DMPOH (38.06%), but significant difference was found compared with the control group (p>0.05). DMPOH presented similar DC and cytotoxicity compared with EDAB when associated with CQ.

Explosive Synchronization With Partial Degree-frequency Correlation.

Networks of Kuramoto oscillators with a positive correlation between the oscillators frequencies and the degree of their corresponding vertices exhibit so-called explosive synchronization behavior, which is now under intensive investigation. Here we study and discuss explosive synchronization in a situation that has not yet been considered, namely when only a part, typically a small part, of the vertices is subjected to a degree-frequency correlation. Our results show that in order to have explosive synchronization, it suffices to have degree-frequency correlations only for the hubs, the vertices with the highest degrees. Moreover, we show that a partial degree-frequency correlation does not only promotes but also allows explosive synchronization to happen in networks for which a full degree-frequency correlation would not allow it. We perform a mean-field analysis and our conclusions were corroborated by exhaustive numerical experiments for synthetic networks and also for the undirected and unweighed version of a typical benchmark biological network, namely the neural network of the worm Caenorhabditis elegans. The latter is an explicit example where partial degree-frequency correlation leads to explosive synchronization with hysteresis, in contrast with the fully correlated case, for which no explosive synchronization is observed.

Influence Of Successive Light-activation On Degree Of Conversion And Knoop Hardness Of The First Layered Composite Increment.

To evaluate the influence of light-activation of second, third and fourth increments on degree of conversion (DC) and microhardness (KHN) of the top (T) and bottom (B) surface of the first increment. Forty samples (n = 5) were prepared. In groups 1-4, after each increment light-activation (multiple irradiation), T and B of the first increment were measured in DC and KHN. In groups 5-8, only the first increment was made (single irradiation) and measurements of DC and KHN were taken at 15 min intervals. The light-activation modes were (XL) 500 mW/cm(2) × 38 s (G1/G5); (S) 1000 mW/cm(2) × 19 s (G2/G6), (HP) 1400 mW/cm(2) × 14 s (G3/G7); (PE) 3200 mW/cm(2) × 6 s (G4/G8). Data for DC and KHN were analyzed separately by using PROC MIXED for repeated measures and Tukey-Kramer test (α = 0.05). For KHN, B showed lower values than T. PE resulted in lower values of KHN in B surface. For single and multiple irradiations, T and B of first measurement showed the lowest KHN and the fourth measurement showed the highest, with significant difference between them. For single irradiation, first and second increments presented similar KHN, different from the third and fourth increment, which did not differ between them. For multiple irradiations, the second light-activation resulted in KHN similar to first, third and fourth increments. For DC, except QTH, T presented higher DC than B. The light-activation of successive increments was not able to influence the KHN and DC of the first increment.

Influence of the technological innovation degree on knowledge creation: Evidence from a Brazilian firm

The aim of this paper is to analyze the process of knowledge creation when developing high technology products in projects having various innovation degrees. The main contribution to the literature is the systematization of an approach to analyze knowledge creation during the product innovation process. Three innovation projects developed by a company specialized in industrial automation systems were investigated using case studies. The knowledge creation processes, which took place in these three projects, were analyzed comparatively. As a distinctive result of this paper, the main features of the knowledge creation processes influenced by a degree of technological innovation are identified.