Finite-Dimensionality of Tempered Random Uniform Attractors

Finite-dimensional attractors play an important role in finite-dimensional reduction of PDEs in mathematical modelization and numerical simulations. For non-autonomous random dynamical systems, Cui and Langa (J Differ Equ, 263:1225–1268, 2017) developed a random uniform attractor as a minimal compact random set which provides a certain description of the forward dynamics of the underlying system by forward attraction in probability. In this paper, we study the conditions that ensure a random uniform attractor to have finite fractal dimension. Two main criteria are given, one by a smoothing property and the other by a squeezing property of the system, and neither of the two implies the other. The upper bound of the fractal dimension consists of two parts: the fractal dimension of the symbol space plus a number arising from the smoothing/squeezing property. As an illustrative application, the random uniform attractor of a stochastic reaction–diffusion equation with scalar additive noise is studied, for which the finite-dimensionality in $$L^2$$ L 2 is established by the squeezing approach and that in $$H_0^1$$ H 0 1 by the smoothing framework. In addition, a random absorbing set that absorbs itself after a deterministic period of time is also constructed.

Uniform attractors for nonautonomous reaction-diffusion equations with the nonlinearity in a larger symbol space

<p style='text-indent:20px;'>Existence and structure of the uniform attractors for reaction-diffusion equations with the nonlinearity in a weaker topology space are considered. Firstly, a weaker symbol space is defined and an example is given as well, showing that the compactness can be easier obtained in this space. Then the existence of solutions with new symbols is presented. Finally, the existence and structure of the uniform attractor are obtained by proving the <inline-formula><tex-math id="M1">\begin{document}$ (L^{2}\times \Sigma, L^{2}) $\end{document}</tex-math></inline-formula>-continuity of the processes generated by solutions.</p>

Space as Symbol in Sacred Architecture. The Problem of Christian Sacred Architecture

In contemporary research (theoretical and architectural projects) of Christian sacred architecture it has been observed that there is a lack of understanding of the phenomenon of space as one of the symbols of sacred architecture.The goal of this paper is to point out the importance of observing the space (architecture) as a sacred symbol, because a problem has been recognised, dealing with the lack of fundemantel definition in the interpretation of the sacred space.In this paper, the research will be carried out by a comparative analysis of the religious concepts of the great religions of Hinduism, Buddhism, Judaism, Christianity, and Islam, as well as their materialisation through space.The expected result of the research is to confirm the hypothesis that space, as well as rituals, images, artistic works, etc. in sacred architecture has the role of a symbol. Space has the task of keeping the basic concepts of religions and of being a mediator of the experience of faith.

A Novel Efficient Sphere Decoding with Reed-Solomon Code in MIMO Detection

An optimal receiver recovering transmitted signals across a noisy communication channel employs an efficient impact as Sphere Decoding (SD) benchmark to reduce the probability of error. This system can employ a coding strategy for information security where the data symbol space forms a scant lattice. The sparsity structure is resolved through channel code. In this article, motivated by this idea, we present novel efficient detection-decoding combinational techniques using Reed-Solomon (RS) decoding followed by the single tree search (STS) algorithm in SD detection. The simulation results determine that the proposed method of improving the performance of 1.6 dB at the bit error rate (BER) of has a significant impact.

Structural condition assessment using entropy-based time series analysis

We present a time-series-based algorithm to identify structural damage in the structure. The method is in the context of non-model-based approaches; hence, it eliminates the need of any representative numerical model of the structure to be built. The method starts by partitioning the state space into a finite number of subsets which are mutually exclusive and exhaustive and each subset is identified by a distinct symbol. Partitioning is performed based on a maximum entropy approach which takes into account the sparsity and distribution of information in the time series. After constructing the symbol space, the time series data are uniquely transformed from the state space into the constructed symbol space to create the symbol sequences. Symbol sequences are the simplified abstractions of the complex system and describe the evolution of the system. Each symbol sequence is statistically characterized by its entropy which is obtained based on the probability of occurrence of the symbols in the sequence. As a consequence of damage occurrence, the entropy of the symbol sequences changes; this change is implemented to define a damage indicative feature. The method shows promising results using data from two experimental case studies subject to varying excitation. The first specimen is a reinforced concrete jack arch which replicates one of the major structural components of the Sydney Harbor Bridge and the second specimen is a three-story frame structure model which has been tested at Los Alamos National Laboratory. The method not only could successfully identify the presence of damage but also has potential to localize it.

First-principles prediction of a new high pressure polymorph of the BaSi2 compound

In this paper, we present a study of the structural stability of BaSi 2 under high pressure based on first-principles calculations using the projector augmented wave method and generalized gradient approximation as implemented in the ABINIT code. The equations of state of three known polymorphs of BaSi 2 and four candidate structures are calculated along with their structural parameters and their enthalpies of formation. A new polymorph of BaSi 2, not yet reported experimentally, is found to be more stable than all the other structures at high pressure and 0 K. It corresponds to the MgZn 2-type (h) hexagonal structure with hP12 Pearson symbol (space group: P63/mmc. The stiffness coefficients Bij and elastic properties including bulk modulus B0 with its first and second pressure derivative (B′, B′′), Young's modulus (E) and Poisson's ratio (ν) are computed using the stress–strain method.

Recognizing Gestures for Humanoid Robot Using Proto-Symbol Space

This paper describes the non Verbal communication method for developing a gesture-based system using Mimesis model. The proposed method is applicable to any hand gesture represented by a multi-dimensional signal. The entire work concentrates mainly on hand gestures recognition. It develops a way to communicate between Humans and the Humanoid Robots through gestural medium. The Mimesis is the technique of performing human gestures through imitation, recognition and generation. Different Gestures are being converted into code words through the use of code book. These code words are then converted into Proto-Symbols, these proto symbol then forms basis for training of the Humanoid robot. The recognition part is performed through a “distance vector”, a novel algorithm developed by us which is a combination of Euclidean distance and K-nearest neighbor. The generation part is done through the use of WEBOTS which include use of Humanoid robot HOAP 2 having 25 degrees of freedom. All the process of training, recognition and generation are simulated through MATLAB.