Método de perturbación con transformada de Laplace para resolver problemas no lineales de múltiples soluciones, con condiciones a la frontera mixtas y Neumann / Laplace transform-perturbation method to solve nonlinear perturbative multiple solutions problems with mixed and Neumann boundary conditions

RESUMEN El campo de las ecuaciones diferenciales ha cobrado auge en la actualidad por el desarrollo científico y tecnológico. Por esta situación, el estudio de nuevas metodologías para solucionarlas se ha vuelto importante. A partir de la combinación del método de Laplace Transform (LT) y el método de perturbación (PM) este trabajo presenta el método LT-PM, y su motivación se encuentra en la aplicación conocida de la LT a ecuaciones diferenciales ordinarias lineales. El objetivo de este trabajo fue presentar una modificación del método de perturbación (PM), el método de perturbación con transformada de Laplace (LT-PM), con el fin de resolver problemas perturbativos no lineales, con condiciones a la frontera definidas en intervalos finitos. La metodología consistió en aplicar LT a la ecuación diferencial por resolver y después de asumir que la solución de la misma se puede expresar como una serie de potencias de un parámetro perturbativo, se obtiene la solución del problema aplicando sistemáticamente la transformada inversa de Laplace. Los principales resultados de este trabajo se muestran a partir de dos casos de estudio presentados, donde se observa que LT-PM es potencialmente útil para encontrar soluciones múltiples de problemas no lineales. Además, LT-PM mejora la aplicabilidad del método de perturbación en algunos casos de condiciones a la frontera mixtas y de Neumann, donde PM simplemente no funciona. Con el fin de verificar la exactitud de los resultados obtenidos, se calculó su error residual cuadrático (SRE), el cual resultó muy bajo, de donde se dedujo su precisión y la potencialidad de LT-PM. Se concluye que si bien el método propuesto resulta eficiente en los casos particulares presentados, se espera que sea una herramienta potencialmente eficiente y útil para otros casos de estudio, particularmente, en aquellos relacionados con aplicaciones prácticas en ciencias e ingeniería.

ABSTRACT The field of differential equations has recently gained attention due to recent developments in science and technology. For this reason, the analysis for the use of new methodologies to solve them has become important. Based on the combination of Laplace Transform method (LT) and Perturbation Method (PM) this article pro- poses the Laplace transform-Perturbation Method (LT-PM) which finds its motivation on the application of LT to linear ordinary differential equations. The goal of this work is to propose a modification of PM - the LT-PM), in order to solve nonlinear perturbative problems with boundary conditions defined on finite intervals. The proposed methodology consisted on the application of LT to the differential equation to solve and then, assuming that its solutions can be expressed as a series of perturbative parameter powers. Thus, the solution of the problem is obtained by systematically applying the transformed inverse LT. The main results of this paper were shown through two case studies, where LT-PM is identified as potentially useful for finding multiple solutions to nonlinear problems. Additionally, the LT-PM enhances the applicability of PM, in some cases of mixed and Neumann boundary conditions, where PM is unsuitable to provide the results. With the purpose of verifying the accuracy of the obtained results, the Square Residual Error (SRE) was calculated. The resulting value was extremely low, which showed the precision and potential of LT-PM. We conclude that, although the proposed method resulted efficient for the case studies presented in this article, it is expected that LT-PM can be a potentially useful tool for other case studies. Particularly those related to the practical applications of science and engineering.

Application of one kind of method in judging the fissurefracture by using image enhancement / 中国医学装备

Objective:A more effective approach to judge the fissure fracture by using image enhancement is presented.Methods:The Gradient image after 5×5 median filtering smoothing was used to mask the laplace image, and to add the original image in order to informing the sharpening image, and then the adaptive contrast histogram equalization is put in shaping image and to compare the effect of the image enhancement.Results: The algorithm to enhance the X-Ray fracture image can highlight the shape of the fissure fracture clearly. The enhanced image is more effective than the image by using one way alone.Conclusion: This method is valuable in judging the fissure fracture in clinical diagnosis.

Noninvasive measurement of human blood glucose under flow control of time gate / 国际生物医学工程杂志

Objective In order to further improve the noninvasive measurement precision of human blood glucose and achieve clinical requirements,experiments were conducted to measure human blood glucose by a novel measurement method our group proposed.Methods The blood flow of the tested parts was stopped by pressure,and dynamic distribution of transmission spectra was measured by time-correlated single-photon counting (TCSPC) technology under the dual wavelength light incident.Oral glucose tolerance test (OGTT) was conducted on three human subjects,and the early arriving photons were selected by Laplace transform.Meanwhile,the human blood glucose concentration was measured using the Roche glucose meter.Results The best curve fitting was got when the Laplace parameter was 1Gs-1 (determining parameter R2=0.0922).Conclusions The experimental results showed that better measurement accuracy can be obtained by selecting appropriate Laplace parameter,and noninvasive measurement of human blood glucose under flow control of time gate was feasible.

Theoretical assessment of the impact of seeding on the exploitation of some economically viable marine populations / Evaluación teórica del impacto de siembra en la explotación de algunas poblaciones marinas económicamente importantes / Avaliação teórica do impacto do plantio na exploração de algumas populações marinhas economicamente importantes

Many rural communities in the developing world practice small-scale harvesting of marine species of various kinds (fish, crustaceans, mollusks) as their main economic activity. Lack of regulation or enforcement or both has led in many cases to overexploitation of resources and consequent decline of the populations of organisms on which the communities depend. This situation, common along the north-central Chilean coast, served as the starting point of the present work. Recent advances in biotechnology and aquaculture, however, have made plausible halting or even reversing the trend towards resource depletion, favorably affecting the economic wellbeing of the communities. In this paper the theoretical implications of seeding the habitual harvesting grounds of a hypothetical community with individuals produced in the laboratory is explored. In particular, we examine the effect of periodic seeding of hatchlings or juveniles on the population of an economically important species harvested under either one of two modes of extraction, constant harvest or harvest proportional to the stock level. The population dynamics is modeled by a first order ordinary differential equation containing a series of delta functions, and which in words reads as follows: the population growth rate is equal to the natural growth rate minus the harvest rate plus the seeding rate. It was found that, at least from a theoretical standpoint, seeding could potentially lead to a notable increase in the productivity and well-being of these sea-based economies.

Muchas comunidades rurales en el mundo en desarrollo practican la recolección de especies marinas de varios tipos (peces, crustáceos, moluscos) como actividad económica principal. La falta de regulación o de aplicación de leyes ha conllevado en muchos casos a la sobreexplotación de los recursos y disminución de poblaciones de organismos de los que dependen estas comunidades. Esta situación, común en las zonas norte y centro del litoral chileno, sirvió como punto de partida para este trabajo. Avances recientes en biotecnología y acuicultura han hecho creíble la posibilidad de detener e incluso revertir la tendencia hacia el agotamiento del recurso y así afectar favorablemente el bienestar de la comunidad. En este trabajo se explora las implicaciones teóricas de la siembra con individuos producidos en el laboratorio en sectores usuales de captura de una comunidad hipotética; en particular, el efecto de la siembra periódica de crías o juveniles sobre la población de una especie económicamente importante cuya recolección se hace bajo uno de dos modos de extracción, constante o proporcional a la población. La dinámica poblacional se modela por una ecuación diferencial ordinaria de primer orden que contiene una serie de funciones delta y que, en palabras, dice que la tasa de crecimiento de la población es igual a la tasa natural de crecimiento menos la tasa de extracción más la tasa de siembra. Se encontró que, al menos desde el punto de vista teórico, la siembra podría potencialmente llevar a un incremento notable en la productividad y bienestar de estas comunidades marino-dependientes.

Muitas comunidades rurais no mundo em desenvolvimento praticam a colheita de espécies marinhas de vários tipos (peixes, crustáceos, moluscos) como atividade econômica principal. A falta de regulamentação ou de aplicação de leis tem conduzido em muitos casos à superexploração dos recursos e diminuição de populações de organismos dos quais dependem estas comunidades. Esta situação, comum nas zonas norte e centro do litoral chileno, serviu como ponto de partida para este trabalho. Avanços recentes em biotecnologia e aqüicultura têm tornado aceitável a possibilidade de deter e inclusive reverter a tendência para o esgotamento do recurso e assim afetar favoravelmente o bem-estar da comunidade. Neste trabalho se explora as implicações teóricas do plantio com indivíduos produzidos no laboratório em setores usuais de captura de uma comunidade hipotética; em particular, o efeito do plantio periódico de filhotes ou juvenis sobre a população de uma espécie economicamente importante cuja colheita se faz sob um de dois modos de extração, constante ou proporcional à população. A dinâmica populacional se modela por uma equação diferencial ordinária de primeira ordem que se representa por uma série de funções delta e que, em palavras, diz que a taxa de crescimento da população é igual à taxa natural de crescimento menos taxa de extração mais taxa de semeadura. Encontrou-se que, pelo menos desde o ponto de vista teórico, o plantio poderia potencialmente levar a um incremento notável na produtividade e bem-estar destas comunidades marinho-dependentes.

Establishment of a network pharmacokinetic model for multiple component drugs and parameter analyses / 中国临床药理学与治疗学

AIM:To establish a network pharmacoki- netic model for studying multiple drug components and analyzing their parameters.METHODS:A model has been set up based on the compartment and linear kinetic theories,and the solutions have been obtained by Laplace transform method.The relations between the whole comp- artment model and network model for multiple component have been comparatively studied and their kinetic parame- ters have also been estimated and analyzed.RESULTS: The multiple component network pharmacokinetics follow a first order linear mammillary model.C_i is a polynomial of power index number e,which is similar to the whole compartment model.Various parameters(transit constant) were calculated by the expression of matrix consisting of?_i and the compartment parameters.Its kinetic parameters can be obtained on the basis of the whole compartment model.CONCLUSION:The multiple component net- work pharmacokinetic parameters can be obtained and an- alyzed similarly as the whole compartment model.