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MITTAG-LEFFLER STABILITY OF SYSTEMS OF FRACTIONAL NABLA DIFFERENCE EQUATIONS
Eloe, Paul,Jonnalagadda, Jaganmohan Korean Mathematical Society 2019 대한수학회보 Vol.56 No.4
Mittag-Leffler stability of nonlinear fractional nabla difference systems is defined and the Lyapunov direct method is employed to provide sufficient conditions for Mittag-Leffler stability of, and in some cases the stability of, the zero solution of a system nonlinear fractional nabla difference equations. For this purpose, we obtain several properties of the exponential and one parameter Mittag-Leffler functions of fractional nabla calculus. Two examples are provided to illustrate the applicability of established results.
THE METHOD OF QUASILINEARIZATION AND A THREE-POINT BOUNDARY VALUE PROBLEM
Eloe, Paul W.,Gao, Yang Korean Mathematical Society 2002 대한수학회지 Vol.39 No.2
The method of quasilinearization generates a monotone iteration scheme whose iterates converge quadratically to a unique solution of the problem at hand. In this paper, we apply the method to two families of three-point boundary value problems for second order ordinary differential equations: Linear boundary conditions and nonlinear boundary conditions are addressed independently. For linear boundary conditions, an appropriate Green\`s function is constructed. Fer nonlinear boundary conditions, we show that these nonlinearities can be addressed similarly to the nonlinearities in the differential equation.
Mittag-Leffler stability of systems of fractional nabla difference equations
Paul Eloe,Jaganmohan Jonnalagadda 대한수학회 2019 대한수학회보 Vol.56 No.4
Mittag-Leffler stability of nonlinear fractional nabla difference systems is defined and the Lyapunov direct method is employed to provide sufficient conditions for Mittag-Leffler stability of, and in some cases the stability of, the zero solution of a system nonlinear fractional nabla difference equations. For this purpose, we obtain several properties of the exponential and one parameter Mittag-Leffler functions of fractional nabla calculus. Two examples are provided to illustrate the applicability of established results.
The method of quasilinearization and a three-point boundary value problem
Paul~W.~Eloe,Yang Gao 대한수학회 2002 대한수학회지 Vol.39 No.2
The method of quasilinearization generates a monotone iterationscheme whose iterates converge quadratically to a unique solutionof the problem at hand. In this paper, we apply the method to twofamilies of three-point boundary value problems for second orderordinary differential equations: Linear boundary conditions andnonlinear boundary conditions are addressed independently. Forlinear boundary conditions, an appropriate Green's function isconstructed. For nonlinear boundary conditions, we show thatthese nonlinearities can be addressed similarly to thenonlinearities in the differential equation.
POSITIVE SOLUTIONS FOR A SYSTEM OF SINGULAR SECOND ORDER NONLOCAL BOUNDARY VALUE PROBLEMS
Asif, Naseer Ahmad,Eloe, Paul W.,Khan, Rahmat Ali Korean Mathematical Society 2010 대한수학회지 Vol.47 No.5
Sufficient conditions for the existence of positive solutions for a coupled system of nonlinear nonlocal boundary value problems of the type -x"(t) = f(t, y(t)), t $\in$ (0, 1), -y"(t) = g(t, x(t)), t $\in$ (0, 1), x(0) = y(0) = 0, x(1) = ${\alpha}x(\eta)$, y(1) = ${\alpha}y(\eta)$, are obtained. The nonlinearities f, g : (0,1) $\times$ (0, $\infty$ ) $\rightarrow$ (0, $\infty$) are continuous and may be singular at t = 0, t = 1, x = 0, or y = 0. The parameters $\eta$, $\alpha$, satisfy ${\eta}\;{\in}\;$ (0,1), 0 < $\alpha$ < $1/{\eta}$. An example is provided to illustrate the results.
POSITIVE SOLUTIONS FOR A SYSTEM OF SINGULAR SECOND ORDER NONLOCAL BOUNDARY VALUE PROBLEMS
Naseer Ahmad Asif,Paul W. Eloe,Rahmat Ali Khan 대한수학회 2010 대한수학회지 Vol.47 No.5
Sufficient conditions for the existence of positive solutions for a coupled system of nonlinear nonlocal boundary value problems of the type [수식],[수식],[수식]are obtained. The nonlinearities f, g : (0, 1) × (0,1)→ (0,∞) are continuous and may be singular at t = 0, t = 1, x = 0, or y = 0. The parameters η,α satisfy η ∈ (0, 1), 0 < α < 1/η. An example is provided to illustrate the results.
Immobilization of commercial acid phosphatases from wheat germ and potato onto ion exchangers
Lima Frederico Alves,Martins Pedro Alves,Wilson Galvão de Morais Júnior,Ribeiro Eloízio Júlio,Guisán José Manuel,de Resende Miriam Maria 한국화학공학회 2023 Korean Journal of Chemical Engineering Vol.40 No.9
A very simple and fast immobilization technique based on ion exchange was investigated to improve the thermal stability of acid phosphatase from wheat germ and potato. Immobilization was not efficient for the DEAE-sepharose, and MANAE-agarose supports. On the other hand, Toyopearl DEAE-650s proved to be a promising support, with immobilization yield above 95% and recovery of activity above 85% for both enzymes. A second step was introduced in the immobilization protocol to improve the thermal stability of these biocatalysts. For this, oxidation and reduction of glycosidic chains of acid phosphatase were carried out, allowing the formation of aldehyde groups and subsequent interaction with the amine groups to further stabilize the different forms (free and immobilized). Both biocatalysts showed residual activity after 1 hour of inactivation at the temperature of 60 °C, a fact not observed for the free enzyme. The wheat germ acid phosphatase derivative was the most stable, with residual activity of 66.7% for the only immobilized derivative and 76.2% for the oxidized/reduced derivative. Also, the derivatives prepared by ion exchange adsorption on Toyopearl (TOYO), followed by oxidation/reduction and intramolecular crosslinking, were approximately 15 and 41 times more stable than the free enzyme from wheat germ.
Ana Carolina Tolentino Brandão,Miriam Maria de Resende,Eloízio Júlio Ribeiro 한국화학공학회 2020 Korean Journal of Chemical Engineering Vol.37 No.10
This paper studied bioethanol production at very high gravity (VHG) conditions using flocculent Saccharomyces cerevisiae, evaluating the response yield, ethanol concentration, productivity, and residual sugar through a central composite design (CCD). This CCD was evaluated at 12 and 24 h fermentation times. In the CCD evaluated for 12 h of fermentation, the best condition for alcoholic fermentation was 27 oC, 260 g/L substrate concentration and a 30% v/v cell concentration; a maximum overall desirability of 0.937 was achieved. For CCD at 24 h of fermentation, the best condition was 27 oC, 300 g/L substrate concentration, and a 26% v/v cell concentration. The desirability achieved was 0.811. These conditions allowed us to verify, experimentally, that the CCD models described the fermentation behavior well. VHG alcoholic fermentation in fed-batch with the reuse of cells without chemical treatment was performed using the optimum conditions obtained from the desirability function (27 oC, 300 g/L, 26% v/v). This resulted in favorable alcohol content 132.90 g/L in comparison to the conventional fermentation process.
Pâmela Letícia dos Santos,Rafael Scaf de Molon,Thallita Pereira Queiroz,Roberta Okamoto,Ana Paula de Souza Faloni,Jéssica Lemos Gulinelli,Eloá Rodrigues Luvizuto,Idelmo Rangel Garcia Junior 대한치주과학회 2016 Journal of Periodontal & Implant Science Vol.46 No.3
Purpose: We sought to evaluate the effectiveness of bone substitutes in circumferential periimplant defects created in the rabbit tibia. Methods: Thirty rabbits received 45 implants in their left and right tibia. A circumferential bone defect (6.1 mm in diameter/4 mm depth) was created in each rabbit tibia using a trephine bur. A dental implant (4.1 mm × 8.5 mm) was installed after the creation of the defect, providing a 2-mm gap. The bone defect gaps between the implant and the bone were randomly filled according to the following groups: blood clot (CO), particulate Bio-Oss® (BI), and Bio-Oss® Collagen (BC). Ten animals were euthanized after periods of 15, 30, and 60 days. Biomechanical analysis by means of the removal torque of the implants, as well as histologic and immunohistochemical analyses for protein expression of osteocalcin (OC), Runx2, OPG, RANKL, and TRAP were evaluated. Results: For biomechanics, BC showed a better biological response (61.00±15.28 Ncm) than CO (31.60±14.38 Ncm) at 30 days. Immunohistochemical analysis showed significantly different OC expression in CO and BC at 15 days, and also between the CO and BI groups, and between the CO and BC groups at 60 days. After 15 days, Runx2 expression was significantly different in the BI group compared to the CO and BC groups. RANKL expression was significantly different in the BI and CO groups and between the BI and BC groups at 15 days, and also between the BI and CO groups at 60 days. OPG expression was significantly higher at 60 days postoperatively in the BI group than the CO group. Conclusions: Collectively, our data indicate that, compared to CO and BI, BC offered better bone healing, which was characterized by greater RUNX2, OC, and OPG immunolabeling, and required greater reversal torque for implant removal. Indeed, along with BI, BC presents promising biomechanical and biological properties supporting its possible use in osteoconductive grafts for filling peri-implant gaps.
Elo a Moreira-Marconi,Carla F. Dionello,Danielle S. Morel,Danubia C. S a-Caputo,Cintia R. Souza-Gonçalves,Laisa L. Paineiras-Domingos,Eliane O. Guedes-Aguiar,Pedro J. Marin,Borja del Pozo Cruz,Mario B 대한골다공증학회 2016 Osteoporosis and Sarcopenia Vol.2 No.4
Objective: The aim of this study was to review the literature about the relevance of the whole body vibration (WBV) in decreasing the number of fractures in osteoporotic women. Methods: Searches were performed by three independent researchers through the PubMed and PEDro databases. Results: Only 0.1% of the publications with “Fracture and osteoporosis” have a relation with WBVexercise. The achievements have revealed a positive effect of this exercise in patients with risk factors for fractures like osteoporosis. Protocols were performed two to three times a week, from 6 up to 18 months, and with 12.6 up to 40 Hz as frequencies. Different tools were used to evaluate the effects of the WBV exercise in conditions that could cause fractures in postmenopausal women. Conclusions: Although the paucity of research regarding direct effects of WBV in decreasing fractures, WBV could be a feasible and effective way to modify well-recognized risk factors for falls and fractures, improvements in some aspects of neuromuscular function and balance. More studies have to be performed establish protocols with well controlled parameters.