Since Li and Yorke first gave the definition of chaos by using strict mathematical language in 1975 [1], the research on chaos has greatly influenced modern science, not just natural sciences but also several social sciences, such as economics, sociology, and philosophy. The theory of chaos convinced scientists that a simple definite system can produce complicated features and a complex system ...

The notion of central path plays a fundamental role in the development of interior point methods which, in turn, have become important tools for solving various optimization problems. The central path equation is algebraic in nature and is derived from the KKT optimality conditions of a certain logarithmic barrier problem; meanwhile, the primal variable portion of the very same central path can...

In this paper, we extend previous works on the relation between mass and inner slope in dark matter density profiles. We calculate that range going from dwarf galaxies to cluster of galaxies. This was done thanks a modeling energy transfer via SN AGN feedback, as well dynamical friction baryon clumps. show that, above galaxy masses (Groups clusters), slope-mass changes its trend. It flattens (t...

Most interest in Fechner’s work went to the law of outer psychophysics, which relates external stimulus intensity and sensory experience. Yet, according to Fechner’s own conviction the validity of this law depends entirely on inner psychophysics’ prescription that brain activity and experience are different aspects of the same entity. This means there must be lawful connections between the two ...

A di erential-geometric structure of the manifold PD(n) of all the n n positive-de nite matrices is studied by means of informatin geometry. It is given by a pair of dual at a ne connections with an invariant Riemannian metric and a divergence function. Special attention is paid to the geometry induced in the isospectral submanifolds and the natural gradient ow induced in it. Its relation to th...

We have studied the mass distribution in the lensing galaxy 2237+0305 using constraints from both gravitational lensing and photometric and spectroscopic observations. We find that with sufficient dynamical information we can constrain the mass-to-light ratio of the luminous components and determine the dynamical contribution of the disk. In addition, future observations should allow us to plac...

the study of the dynamic behavior of a rigid body with one fixed point (gyroscope) has a long history. a number of famous mathematicians and mechanical engineers have devoted enormous time and effort to clarify the role of dynamic effects on its movement (behavior) – stable, periodic, quasi-periodic or chaotic. the main objectives of this review are: 1) to outline the characteristic features of...

In this paper, we study both the static and dynamic stabilities of submerged and inclined concentric pipes conveying uid. The governing equation for the inner tubular beam is derived under small deformation assumptions. We obtain the dis-cretized dynamical equations using spatial nite diierence schemes. In the case of steady ow, both buckling and utter instabilities are investigated. In the cas...

A systematic exploration of the chaotic structure of the asteroid belt is presented, first taking into account only the perturbations provided by the four giant planets and then including also the effects of the inner planets. We find that both the inner belt (a< 2.5 AU) and the outer part of the main belt (a> 2.8 AU) are mostly chaotic. In the outer part of the belt, chaos is due to the presen...

We report the detection of dust emission at sub-millimeter wavelengths from HD 107146, a G2V star with an age estimated to lie between 80 and 200 Myr. The emission is resolved at 450 μm with a size 300 AU × 210 AU. A fit to the spectral energy distribution gives a dust temperature of 51 K and dust mass of 0.10 M⊕. No excess emission above the photosphere was detected at 18 μm showing that there...