###### The self-similarity properties and multifractal analysis of DNA sequences

as the human genome, are made up of 3000 million base pairs [ 1 ]. In the National Center for Biotechnology Information (NCBI) directories are the databases that contain complete genomes, complete sequences of chromosomes, sequences of mRNAs, and proteins. The importance to analyse the large DNA databases in the Nonlinear Dynamics context is based on the work conducted earlier by Jeffrey [ 2 ], who proposed a graphic representation of these databases via an extended chaos game. Other contributions similarly based on a statistical description of DNA sequences take

###### Shapley-Folkman-Lyapunov theorem and Asymmetric First price auctions

∫ 0 x e − t 2 d t , $$\begin{array}{} \displaystyle erf (z)=\frac{2}{\sqrt\pi}\int_0^x e^{-t^2 } dt, \end{array}$$ see ( Abramowitz and Stegun 1964 ). Matlab code for this simple two bidder case was written by ( Fibich and Gavish 2011 ). In the next two graphs are presented two bidder’s distribution valuations. Fig. 1 Fixed point iterations result of the ratios of the two bidders’ valuations CDF/PDF functions Fig. 2 Newtons iterations result of the two CDF/PDF bidders’ valuations functions 5 Conclusion As it is known

###### Optimal control problems for differential equations applied to tumor growth: state of the art

growth of a tumor. They use ordinary differential equations [ 2 , 6 , 13 , 54 ], partial differential equations [ 1 , 3 , 34 ], stochastic processes [ 38 ], game theory [ 52 ], etc. In this review, we focus on 4 applications of the control theory to the growth of tumors: The first is referred to the application of the theory of optimal control to compartmental models. The second deals with the theory of optimal control of brain tumors. The third deals with a topic that is becoming more and more important: the resistance in tumors to different treatments