INDUCTION—POLYMERIZATION OF PREPARING POLYMERS OF REGULAR STRUCTURE

Induction-Polymerization is a novel method for preparing polymers of regular structure. In the presence of a special macromolecular compound, monomer molecules are aggregeted regularly around one or more growth points and polymerized to polymer of regular structure. Regularity of structure of the polyacrylamide prepared by this means has been verified with electron diffractograms, DSC curve and IR spectrum of the polymer.

Ore-controlling Regularities of Thrust-fold structures and features of Tectono-geochemical Anomalies at the Xiaozhuqing Exploration Area in the Huize Zn-Pb District

1 Introduction The huize Zn-Pb ore district in Yunnan province is locatedinthecentralsouthernofthe Sichuan—Yunnan—GuizhouPb-ZnPoly-metallic Mineralization Area in the southwestern margin of the Yangtze Block,and is strictly controlled by fault structures.It has developed to one of the famous production bases of lead&zinc and germanium in China.

A systematic review of structured sparse learning

High-dimensional data arising from diverse scientific research fields and industrial development have led to increased interest in sparse learning due to model parsimony and computational advantage. With the assumption of sparsity, many computational problems can be handled efficiently in practice. Structured sparse learning encodes the structural information of the variables and has been quite successful in numerous research fields. With various types of structures discovered, sorts of structured regularizations have been proposed. These regularizations have greatly improved the efficacy of sparse learning algorithms through the use of specific structural information. In this article, we present a systematic review of structured sparse learning including ideas, formulations, algorithms, and applications. We present these algorithms in the unified framework of minimizing the sum of loss and penalty functions, summarize publicly accessible software implementations, and compare the computational complexity of typical optimization methods to solve structured sparse learning problems. In experiments, we present applications in unsupervised learning, for structured signal recovery and hierarchical image reconstruction, and in supervised learning in the context of a novel graph-guided logistic regression.

Piecewise linear approximation for the dynamical Φ34 model

We construct a piecewise linear approximation for the dynamicalΦ3~4 model on T^3.The approximation is based on the theory of regularity structures developed by Hairer(2014).They proved that renormalization in a dynamicalΦ3~4 model is necessary for defining the nonlinear term.In contrast to Hairer(2014),we apply piecewise linear approximations to space-time white noise,and prove that the solutions of the approximating equations converge to the solution of the dynamicalΦ_3~4 model.In this case,the renormalization corresponds to multiplying the solution by a t-dependent function,and adding it to the approximating equation.

Global Spiral Patterns in Galaxies : A Review of the Density Wave Theory from the Theoretical Perspective

The density wave theory of galactic spirals is a semi empirical theory consisting of the analysis of physically plausible mathematical models, the synthesis of extensive observational data, and an examination of the applicability of the theoretical predictions of particular models for the interpretation of observational data. In this paper, the theory is reviewed from the general perception of order and chaos in dynamical systems. Prominent among the observational data is the well established morphological classification of galaxies according to Edwin Hubble, the luminosity class of Sidney van den Bergh, and the coexistence of regular and irregular global structures in many galaxies, as was first discovered in the whirlpool galaxy M51 by Fritz Zwicky. The regular structure is prominently observed in red and in infrared, and the irregular in blue and at 21 cm radio frequency. These and other data led to the concept of the existence of an essentially standing wave pattern in the older evolved stars, which in turn acts as a backbone for the global structure of the galaxy as a whole. Dynamically, the existence of irregular structures in the interstellar medium reflects the natural state of turbulent motion in gaseous motion at high speeds. In contrast, the essentially collisionless stellar system has a substantial 'microscale' of epicyclic motion that prevents, or smoothes out, irregularities on scales. It is pointed out that the spiral structure in galaxies is but one class of interesting phenomena that crucially relates to universal gravitation. Astronomical phenomena on all scales, from planets and satellites to protostars, stars and galaxies and the whole universe present other challenges to both theorists and observers, representing a wide field of opportunities for fruitful research. At the present time, they are being successfully met in individual cases through the development of new observational techniques to cover all frequencies of electromagnetic radiation and through the development of new analytical and computational methods.

Markov branching processes with immigration-migration and resurrection

We consider a modified Markov branching process incorporating with both state-independent immigration-migration and resurrection. The effect of state-independent immigration-migration is firstly in- vestigated in detail. The explicit expressions for the extinction probabilities and mean extinction times are presented. The ergodicity and stability properties of the process incorporating with resurrection structure are then investigated. The conditions for recurrence, ergodicity and exponential ergodicity are obtained. An explicit expression for the equilibrium distribution is also presented. As a preparation, the criteria for regularity and uniqueness for such structure are firstly established.