The Application of Fractal Transform and Entropy for Improving Fault Tolerance and Load Balancing in Grid Computing Environments

This paper applies the entropy-based fractal indexing scheme that enables the grid environment for fast indexing and querying. It addresses the issue of fault tolerance and load balancing-based fractal management to make computational grids more effective and reliable. A fractal dimension of a cloud of points gives an estimate of the intrinsic dimensionality of the data in that space. The main drawback of this technique is the long computing time. The main contribution of the suggested work is to investigate the effect of fractal transform by adding R-tree index structure-based entropy to existing grid computing models to obtain a balanced infrastructure with minimal fault. In this regard, the presented work is going to extend the commonly scheduling algorithms that are built based on the physical grid structure to a reduced logical network. The objective of this logical network is to reduce the searching in the grid paths according to arrival time rate and path’s bandwidth with respect to load balance and fault tolerance, respectively. Furthermore, an optimization searching technique is utilized to enhance the grid performance by investigating the optimum number of nodes extracted from the logical grid. The experimental results indicated that the proposed model has better execution time, throughput, makespan, latency, load balancing, and success rate.     

Cross-polarization with magic-angle spinning kinetics and impedance spectroscopy study of proton mobility,local disorder,and thermal equilibration in hydrogen-bonded poly(methacrylic acid)

The ¹H–¹³C cross-polarization with magic-angle spinning (CP MAS) kinetics was studied in poly(methacrylic acid) (PMAA) having the purpose to track the links between the local order in the main chain and the proton dynamics in peripheral hydrogen bond networks. The experimental CP MAS kinetic curves were analyzed applying the models of isotropic and anisotropic spin-diffusion with thermal equilibration. The fractal dimension D_p ≈ 3 was deduced that indicates that PMAA behaves as an isotropic 3D-system. No proton conductivity in the neat PMAA was deduced from the impedance spectroscopy data analyzing the frequency dependences of the complex dielectric permittivity. The value of local order parameter S = 0.70 for CH₂ in PMAA occupies an intermediate position between 0.63 and 0.85 deduced for CH₂ sites in the main chains of poly(vinyl phosphonic acid) and poly(2-hydroxyethyl methacrylate), that is, the true proton conductor and the polymer that contains the H-bond network, however, no proton conductivity, respectively.     

Construction Theory of Function on Local Fields

We establish the construction theory of function based upon a local field K p as underlying space. By virture of the concept of pseudo-differential operator, we introduce "fractal calculus"(or, p-type calculus, or, Gibbs-Butzer calculus). Then, show the Jackson direct approximation theorems, Bermstein inverse approximation theorems and the equivalent approximation theorems for compact group D( Kp) and locally compact group K+p(= Kp), so that the foundation of construction theory of function on local fields is established. Moreover, the Jackson type, Bernstein type,and equivalent approximation theorems on the H ?lder-type space Cσ(Kp), σ 0, are proved; then the equivalent approximation theorem on Sobolev-type space Wrσ(Kp),σ≥ 0, 1 ≤ r +∞, is shown.     

Nonlinear Measures to Evaluate Upright Postural Stability: A Systematic Review

Conventional biomechanical analyses of human movement have been generally derived from linear mathematics. While these methods can be useful in many situations, they fail to describe the behavior of the human body systems that are predominately nonlinear. For this reason, nonlinear analyses have become more prevalent in recent literature. These analytical techniques are typically investigated using concepts related to variability, stability, complexity, and adaptability. This review aims to investigate the application of nonlinear metrics to assess postural stability. A systematic review was conducted of papers published from 2009 to 2019. Databases searched were PubMed, Google Scholar, Science-Direct and EBSCO. The main inclusion consisted of: Sample entropy, fractal dimension, Lyapunov exponent used as nonlinear measures, and assessment of the variability of the center of pressure during standing using force plate. Following screening, 43 articles out of the initial 1100 were reviewed including 33 articles on sample entropy, 10 articles on fractal dimension, and 4 papers on the Lyapunov exponent. This systematic study shows the reductions in postural regularity related to aging and the disease or injures in the adaptive capabilities of the movement system and how the predictability changes with different task constraints.     

A note on the finite fractal dimension of the global attractors for dissipative nonlinear Schrödinger‐type equations

In this article, we present, throughout two basic models of damped nonlinear Schrödinger (NLS)–type equations, a new idea to bound from above the fractal dimension of the global attractors for NLS‐type equations. This could answer the following open issue: consider, for instance, the classical one‐dimensional cubic nonlinear Schrödinger equation $$u_t+i{u}_{xx}+i|u{|}^{2}u+\gamma u=f,f\in {\mathrm{??}}^2(?).$$ “How can we bound the fractal dimension of the associate global attractor without the need to assume that the external forcing term f has some decay at infinity (that is belonging to some weighted Lebesgue space)?”     

Long-time dynamics for a nonlinear Timoshenko system with delay

This paper is concerned with a nonlinear Timoshenko system with a time delay term in the internal feedback together with initial data and Dirichet boundary conditions. Under some suitable assumptions on the weights of feedback, we obtain the existence of a global attractor with finite fractal dimension for the case of equal speed wave propagation. Furthermore, the existence of exponential attractors is also derived.     

Gelation Kinetics-Structure Analysis of pH-triggered Low Molecular Weight Hydrogelators

Properties such as shear modulus, gelation time, structure of supramolecular hydrogels are strongly dependent on self-assembly, gelation triggering mechanism and processes used to form the gel. In our work we extend reported rheology analysis methodologies to pH-triggered supramolecular gels to understand structural insight using a model system based on N−N’ Dibenzoyl-L-Cystine pH-triggered hydrogelator and Glucono-δ-Lactone as the trigger. We observed that Avrami growth model when applied to time-sweep rheological data of gels formed at lower trigger concentrations provide estimates of fractal dimension which agree well compared with visualization of the microstructure as seen via Confocal Laser Scanning Microscopy, for a range of gelator concentrations.     

GLOBAL ATTRACTOR FOR HASEGAWA-MIMA EQUATION

The long time behavior of solution of the Hasegawa-Mima equation with dissipation term was considered. The global attractor problem of the Hasegawa-Mima equation with initial periodic boundary condition was studied. Applying the uniform a priori estimates method, the existence of global attractor of this problem was proved, and also the dimensions of the global attractor was estimated.