On the Approximate Controllability for Hilfer Fractional Evolution Hemivariational Inequalities

The paper is concerned with the approximate controllability of some Hilfer fractional evolution hemivariational inequalities. Using two classes of operators and their fundamental properties, we derive sufficient conditions for approximate controllability of linear and semilinear controlled systems via a fixed point theorem for multivalued maps. Finally, an example is given to illustrate our theory.     

Tractable approximate knowledge fusion using the Horn fragment of serial propositional dynamic logic

In this paper we investigate a technique for fusing approximate knowledge obtained from distributed, heterogeneous information sources. This issue is substantial, e.g., in modeling multiagent systems, where a group of loosely coupled heterogeneous agents cooperate in achieving a common goal. Information exchange, leading ultimately to knowledge fusion, is a natural and vital ingredient of this process. We use a generalization of rough sets and relations [30], which depends on allowing arbitrary similarity relations.The starting point of this research is [6], where a framework for knowledge fusion in multiagent systems is introduced. Agents’ individual perceptual capabilities are represented by similarity relations, further aggregated to express joint capabilities of teams. This aggregation, expressing a shift from individual to social level of agents’ activity, has been formalized by means of dynamic logic. The approach of Doherty et al. (2007) [6] uses the full propositional dynamic logic, which does not guarantee tractability of reasoning. Our idea is to adapt the techniques of Nguyen [26], [27] and [28] to provide an engine for tractable approximate database querying restricted to a Horn fragment of serial dynamic logic. We also show that the obtained formalism is quite powerful in applications.     

Learning mathematics through algorithmic and creative reasoning

There are extensive concerns pertaining to the idea that students do not develop sufficient mathematical competence. This problem is at least partially related to the teaching of procedure-based learning. Although better teaching methods are proposed, there are very limited research insights as to why some methods work better than others, and the conditions under which these methods are applied. The present paper evaluates a model based on students’ own creation of knowledge, denoted creative mathematically founded reasoning (CMR), and compare this to a procedure-based model of teaching that is similar to what is commonly found in schools, denoted algorithmic reasoning (AR). In the present study, CMR was found to outperform AR. It was also found cognitive proficiency was significantly associated to test task performance. However the analysis also showed that the effect was more pronounced for the AR group.     

Approximating solutions of nonlinear hybrid differential equations

We prove the existence as well as approximations of the solutions of initial value problems of first order ordinary nonlinear hybrid differential equations. We rely our results on a recent hybrid fixed point theorem of Dhage (2014) in partially ordered normed linear spaces. A realization is also indicated to illustrate the abstract theory developed in the paper.     

Approximate counting:a martingale approach

Approximate counting is a probabilistic algorithm for keeping track of large numbers of events by means of a counter of limited range. In this paper we present an analysis of this algorithm using the elementary theory of martingales. The methods are also applicable to the analysis of the counter which occurs in the exponential back off protocol     

Moving in and out of contexts in collaborative reasoning about equations

This case study investigates how a group of 12-year-old pupils contextualizes a task formulated as an equation expressed in a word problem. Of special interest is to explore in detail the phenomenon of pupils working with manipulative-based equation-solving methods in a task involving another real world context. The pupils’ small group discussions were videotaped and analyzed in terms of how the pupils contextualized the task in their attempts to arrive at an answer. The results highlight the importance of giving pupils opportunities to realize the particular position of symbolic mathematical representations when dealing with mathematical concepts. While an abstract concept describes something general, concrete representations and specific real-world examples always describe something specific. No one particular example incorporates the rich meaning of an abstract concept. This central distinction needs to be included in teaching practices.     

A new method to find series solutions of a nonlinear wave equation

We show that first-order approximate symmetries of a class of nonlinear wave equations contain Lie symmetries as particular cases. Then we present a new approach to find series solutions of the nonlinear wave equation which cannot be obtained by the standard Lie symmetry and approximate symmetry methods.     

用平移网络逼近函数及其导数

若Х（ｘ）∈Ｗ１Ｍ（Ｒ＾ｄ）,利用Х构造出具体的平移网络逼近Ｓｏｂｏｌｅｖ空间中的函数并给出逼近阶的估计。     

Parallel implementation of a multiblock method with approximate subdomain solution

Solution of large linear systems encountered in computational fluid dynamics often naturally leads to some form of domain decomposition, especially when it is desired to use parallel machines. It has been proposed to use approximate solvers to obtain fast but rough solutions on the separate subdomains. In this paper approximate solutions via (1) an inner preconditioned GMRES iteration to fixed tolerance, and (2) incomplete factorization (RILU, restricted to the diagonal) are considered. Numerical experiments for a fundamental test problem are included which show speedups obtained on a cluster of workstations as well as on a distributed memory parallel computer. Additionally, the parallel implementation of GCR is addressed, with particular focus on communication costs associated with orthogonalization processes. This consideration brings up questions concerning the use of Householder reflections with GCR.     

Radio Frequency Fingerprint extraction based on Multiscale Approximate Entropy

Radio Frequency (RF) fingerprinting is the technology of recognizing the transmitter using the non-linear characteristics of an intercepted RF signal. The underlying inevitable impairments of the hardware chain in transmitters are used as unique RF signatures for the distinct identification of various radios. The technique can be applied to distinguish not only between the radio of different make but also between the radios of the same make and type. In this paper, we propose a novel RF fingerprinting method, based on Multi-Scale Approximate Entropy (MSAE) which utilizes the steady-state section of the RF signal, extracted through the Higuchi Fractal Dimension (HFD) method. The MSAE feature extraction method is validated using real-world data-set for Very High Frequency (VHF) radios. The proposed method uses MSAE features which are subsequently fed to Machine Learning (ML) algorithms for classification accuracy comparison. In terms of classification accuracy, the proposed MSAE features outperforms some of the existing steady-state methods, especially at low SNR.