In the paper, dealing with a question of Lahiri (1999), we study the uniqueness of meromorphic functions in the case when two certain types of nonlinear differential polynomials, which are the derivatives of some typical linear expression, namely h n (h − 1)m (h = f, g), share a non-zero polynomial with finite weight. The results obtained in the paper improve, extend, supplement and generalize some recent results due to Sahoo (2013), Li and Gao (2010). In particular, we have shown that under a suitable choice of the sharing non-zero polynomial or when the first derivative is taken under consideration, better conclusions can be obtained.
In this paper we study nonlinear elliptic boundary value problems with monotone and nonmonotone multivalued nonlinearities. First we consider the case of monotone nonlinearities. In the first result we assume that the multivalued nonlinearity is defined on all $\mathbb{R}$. Assuming the existence of an upper and of a lower solution, we prove the existence of a solution between them. Also for a special version of the problem, we prove the existence of extremal solutions in the order interval formed by the upper and lower solutions. Then we drop the requirement that the monotone nonlinearity is defined on all of $\mathbb{R}$. This case is important because it covers variational inequalities. Using the theory of operators of monotone type we show that the problem has a solution. Finally, in the last part we consider an eigenvalue problem with a nonmonotone multivalued nonlinearity. Using the critical point theory for nonsmooth locally Lipschitz functionals we prove the existence of at least two nontrivial solutions (multiplicity theorem).
The paper is devoted to the analysis of an abstract evolution inclusion with a non-invertible operator, motivated by problems arising in nonlocal phase separation modeling. Existence, uniqueness, and long-time behaviour of the solution to the related Cauchy problem are discussed in detail.
Doubly stochastic point processes driven by non-Gaussian Ornstein-Uhlenbeck type processes are studied. The problem of nonlinear filtering is investigated. For temporal point processes the characteristic form for the differential generator of the driving process is used to obtain a stochastic differential equation for the conditional distribution. The main result in the spatio-temporal case leads to the filtering equation for the conditional mean.
We consider a nonlinear fractional differential inclusion with nonlocal fractional integro-differential boundary conditions in a Banach space. The existence of at least one solution is proved by using the set-valued analog of Mönch fixed point theorem associated with the technique of measures of noncompactness.
In this paper we attempt to form a neural network to code nonlinear iterated function system. Our approach to this problem consists of finding an error function which will be minimized when the network coded attractor is equal to the desired attractor. First, we start with a given iterated function system attractor, with a random set of weights of the network. Second, we compare the consequent images using this neural network with the original image. On the basis of the result of this comparison, we can update the weight functions and the code of the nonlinear iterated function system (NLIFS). A common metric or error function used to compare between the two image fractal attractors is the Hausdorff distance. The error function gives us good means to measurement the difference between the two images.
This work is focused on determninig a nonlinear output error (OE) model, i.e., a dynamic system, by training a two layer neural network with a Levenberg-Marquardt method. Selected as a case study is application of a dynamic model to predict cutting force in machining processes. A model crated by using Artificial Neural Networks (ANN), able to predict the process output, is introduced in order to deal with the characteristics of such an ill-defined process. This model describes the dynamic response of the output before the changes in the process input command (feed rateú and the process parameters (depth of cut). The model provides a sufficiently accurate predition of cutting foce, since the process-dependent specific dynamic properties are adequately reflected.
This paper deals with neural-predictive algorithm for some nonlinear
processes in the industry. Neural model predictive control (NMPC) uses artificial neural networks (ANN) for modeling the process and for configuration of the optimizer. The optimizer sets up on-line controller parameters by predicting next control action signals. Depending on the number of prediction steps, the optimizer can predict the process behavior in the future. Therefore this type of predictive control is very useful for the control of the highly nonlinear processes, which are known for their various behaviors. One practical example is the isothermal polymerization reactor where the NMPC Controls the oiitput variable very robustly. Finally, this control method is compared with the linear PID controller designed to solve this problém using a genetic algorithm.
This paper presented 2D numerical linear and nonlinear site response analyses based on the scaled boundary finite-element method (SBFEM) and compared their results with those of the DEEPSOIL software. In linear time-domain analysis, the seismic boundary traction was applied to lines in the near-field with the same vertical coordinates using seismic time history load. The far-field was modeled utilizing an improved continued-fraction-based high-order transmitting boundary. The constitutive relationship of the boundary was determined utilizing the SBFEM equation in the dynamic stiffness model. It was shown that the results of the SBFEM had a good agreement with those obtained from the DEEPSOIL software. The results of spectral acceleration demonstrated period lengthening. The nonlinear site responses were analyzed using both the DEEPSOIL software and the coupling of SBFEM/FEM. The one-dimensional nonlinear site response was analyzed using the tools in the DEEPSOIL software including the strength correction, pressure-dependent modulus reduction, and the damping ratio curve of sand. In the nonlinear-coupled analysis, the bounded domain was also modeled in OpenSees using a pressure-dependent multi-yield plasticity soil model. The comparison of the results demonstrated the accuracy of the nonlinear analysis using the coupled SBFEM/FEM. The coupling method underestimated spectral acceleration in low periods compared with the DEEPSOIL software. The absolute residual was also obtained less than 0.2.
A study of energetic femtosecond laser pulses interaction with multicomponent glasses was performed. The nonlinear interaction was analysed by registration of spectral broadening, caused mainly by selfphase modulation effect. The source of the pulses was a femtosecond Cr:Forsterite laser system working at wavelength of 1240 nm and providing gigawatt peak power pulses. Using various multicomponent glasses linear dependency between the measured spectral broadening and nonlinear refractive index n2 values, determined previously by Z-scan method, was identified. Moreover, correction of broadening values for real interaction intensity was performed considering the reflection and absorption losses in the glass samples, resulting in significant increase of the linear approximation correlation. The results express reasonable correspondence with experimental Z-scan method values in the case of samples with lower nonlinear refractive index. Using an appropriate reference sample with known n2, the presented method has potential to estimate the nonlinear refractive index of arbitrary new sample. and Interakcia energetických femtosekundových laserových impulzov s viaczložkovými sklami bola študovaná. Nelineárna interakcia bola analyzovaná na základe registrácie rozšírenia spektra, ktorá bola zapríčinená hlavne javom samomodulácie fázy. Zdrojom impulzov bol femtosekundový Cr:Forsteritový laserový systém generujúci impulzy na vlnovej dĺžke 1240 nm s gigawattovými špičkovými výkonmi. Pomocou rozličných viaczložkových skiel bola identifikovaná lineárna závislosť medzi rozšírením spektra a nelineárnym indexom lomu n2, získaným z predošlých meraní metódou Z-scan. Okrem toho korekcia na reálnu interakčnú intenzitu bola prevedená, do ktorej boli zahrnuté odrazové a absorpčné straty vzoriek, vedúca k značnému zlepšeniu lineárity študovanej závislosti. Výsledky vykazujú rozumnú koreláciu s hodnotami získanými experimentálnou metódou Z-scan pri vzorkách s menším nelineárnym indexom lomu. Použitím vhodnej referenčnej vzorky so známym n2 predkladaná metóda može byť využitá na približné určenie nelineárneho indexu lomu ľubovoľnej novej vzorky.