Approximate solution for Fokker-Planck equation

In this paper, an approximate solution to a specific class of the Fokker-Planck equation is proposed. The solution is based on the relationship between the Schr\"{o}dinger type equation with a partially confining and symmetrical potential. To estimate the accuracy of the solution, a function error obtained from the original Fokker-Planck equation is suggested. Two examples, a truncated harmonic potential and non-harmonic polynomial, are analyzed using the proposed method. For the truncated harmonic potential, the system behavior as a function of temperature is also discussed.Comment: 12 pages, 8 figure

Laparoscopy Pneumoperitoneum Fuzzy Modeling

Abstract: Gas volume to intra-peritoneal pressure fuzzy modeling for evaluating pneumoperitoneum in videolaparoscopic surgery is proposed in this paper. The proposed approach innovates in using fuzzy logic and fuzzy set theory for evaluating the accuracy of the prognosis value in order to minimize or avoid iatrogenic injuries due to the blind needle puncture. In so doing, it demonstrates the feasibility of fuzzy analysis to contribute to medicine and health care. Fuzzy systems is employed here in synergy with artificial neural network based on backpropaga tion, multilayer perceptron architecture for building up numerical functions. Experimental data employed for analysis were collected in the accomplishment of the pneumoperitoneum in a random population of patients submitted to videolaparoscopic surgeries. Numerical results indicate that the proposed fuzzy mapping for describing the relation from the intra peritoneal pressure measures as function injected gas volumes succeeded in determinining a fuzzy model for this nonlinear system when compared to the statistical model

II in generalized supergravity

We showed in previous work that for homogeneous Yang-Baxter (YB) deformations of AdS$_5\times$S$^5$, the open string metric and coupling, and as a result the closed string density $e^{-2 \Phi} \sqrt{g}$, remain undeformed. In this work, in addition to extending these results to the deformation associated with the modified CYBE, or $\eta$-deformation, we identify the Page forms as the open string counterpart for RR fields and demonstrate case by case that the non-zero Page forms remain invariant under YB deformations. We give a physical meaning to the Killing vector $I$ of generalized supergravity and show for all YB deformations: 1) $I$ appears as a current for center of mass motion on the worldvolume of a D-branes probing the background, 2) $I$ is equal to the divergence of the noncommutativity parameter, 3) $I$ exhibits "holographic" behavior, where the radial component of $I$ vanishes at the AdS boundary, and 4) in pure spinor formalism $I$ is related to a certain state in the BRST cohomology.Comment: 11 pages, 2 column; v2 references updated; v3 to appear in EPJ