Theory of gravitation on the basis of the Poincaré-Weyl gauge group

The gauge theory for the Poincaré -Weyl group is constructed. It is shown that tetrads are not true gauge fields, but are functions of the true gauge fields: rotational, translational and dilatational ones. The equations of gauge fields, whose sources are an energy-momentum tensor, orbital and spin momemta as well as a dilatational current of an external field, are obtained. A new direct interaction of the rotational gauge field with the orbital momentum of an external field appears, which describes some new effects connected with the space gyroscope Probe B experiment. Plenary talk given at the International Conference RUSGRAV-13, June 23–28, 2008, PFUR, Moscow.     

Hyperbolic trigonometry and its application in the Poincaré ball model of hyperbolic geometry

Hyperbolic trigonometry is developed and illustrated in this article along lines parallel to Euclidean trigonometry by exposing the hyperbolic trigonometric law of cosines and of sines in the Poincaré ball model of n-dimensional hyperbolic geometry, as well as their application. The Poincaré ball model of three-dimensional hyperbolic geometry is becoming increasingly important in the construction of hyperbolic browsers in computer graphics. These allow in computer graphics the exploitation of hyperbolic geometry in the development of visualization techniques. It is, therefore, clear that hyperbolic trigonometry in the Poincaré ball model of hyperbolic geometry, as presented here, will prove useful in the development of efficient hyperbolic browsers in computer graphics. Hyperbolic trigonometry is governed by gyrovector spaces in the same way that Euclidean trigonometry is governed by vector spaces. The capability of gyrovector space theory to capture analogies and its powerful elegance is thus demonstrated once more.     

A new algorithm for the extraction of the surface waves for the Green''''s function in layered dielectrics

There exist the complicated waveguide modes as well as the surface waves in the electromagnetic field induced by a horizontal electric dipole in layered lossless dielectrics between two ground planes. In spectral domain, all these modes can be characterized by the rational parts with the real poles of the vector and scalar potentials. The accurate extraction of these modes plays an important role in the evaluation of the Green's function in spatial domain. In this paper, a new algorithm based on rational approximation is presented, which can accurately extract all the real poles and the residues of each pole simultaneously. Thus, we can get all the surface wave modes and waveguide modes, which is of great help to the calculation of the spatial domain Green's function. The numerical results demonstrated the accuracy and efficiency of the proposed method.     

Tests of resonances in the Painlevé analysis

Title of program: TPR Catalogue number: AATA Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland (see application form in this issue) Computer: SIEMENS 7536 Operating system: BS 2000 Programming language used: REDUCE 2 High speed storage required: depends on the problem, minimally 100 Kwords No. of bits in a word: 32 Number of lines in combined program and test deck: 131     

Poincaré inequalities with the Radon measure for differential forms

We establish the local and global Poincaré inequalities with the Radon measure for the solutions to the nonlinear elliptic partial differential equation for differential forms.     

A new algorithm for the extraction of the surface waves for the Green’s function in layered dielectrics

There exist the complicated waveguide modes as well as the surface waves in the electromagnetic field induced by a horizontal electric dipole in layered lossless dielectrics between two ground planes. In spectral domain, all these modes can be characterized by the rational parts with the real poles of the vector and scalar potentials. The accurate extraction of these modes plays an important role in the evaluation of the Green’s function in spatial domain. In this paper, a new algorithm based on rational approximation is presented, which can accurately extract all the real poles and the residues of each pole simultaneously. Thus, we can get all the surface wave modes and waveguide modes, which is of great help to the calculation of the spatial domain Green’s function. The numerical results demonstrated the accuracy and efficiency of the proposed method.     

Some local Poincaré inequalities for the composition of the sharp maximal operator and the Green’s operator

In this paper, we establish the local Poincaré-type inequalities for the composition of the sharp maximal operator and the Green’s operator with an Orlicz norm.     

Why do you return the favor in online knowledge communities? A study of the motivations of reciprocity

Online knowledge community administrators are attempting to encourage their users to contribute knowledge in order to provide value to members and maintain sustainability. A large number of online knowledge communities fail mainly due to the reluctance of users to return the favor and share knowledge. Many studies on this topic have highlighted the importance of reciprocity for knowledge contribution which forms a virtuous feedback loop for the community sustainability. However, it is unclear how reciprocity is developed and what influences its development. Motivated by this, this study focuses on investigating the antecedents of knowledge receivers’ reciprocity in online knowledge communities. It formulates and tests a theoretical model to explain reciprocity behavior of community members based on equity theory and Social Identity explanation of De-individuation Effects (SIDE) model. Our proposed model is validated through a large-scale survey in an online forum for English learning. Results reveal that indebtedness and community norm not only are key antecedents of intention to reciprocate but are also positively related to each other. The perceived anonymity of the online knowledge community not only has a positive effect on intention to reciprocate, but also has an interactive effect with community norm on intention to reciprocate. Theoretical and practical implications of this study are discussed.     

Smartphones or laptops in the collaborative classroom? A study of video-based learning in higher education

This paper explores how the use of smartphones vs. laptops influences students’ engagement, behaviour and experience watching academic videos in a collaborative classroom. Experiments were run in authentic teaching sessions with a total of 483 first-year higher education students. The methodology applied is a quasi-experimental design with post-test-only, being the independent variable, the device used to visualise the academic videos. Results indicate that the use of laptops has provided better results in terms of student’s engagement with the videos, their collaborative behaviour and satisfaction with the device. Hence, the findings of this research suggest that the type of mobile device used in activities that consider the use of videos in a collaborative class need to be carefully chosen to maximise the student’s comfortability – and in consequence, their engagement with the video-based learning activity and their positive behaviour and experience within the collaborative context.     

Fluid flow-based description of the geometrical features in fluidic channels using the Shannon’s information theory: an exploratory study

Microfluidic analytical devices manufactured on paper and similar inexpensive substrates (µ-PADs) have shown considerable promise for disease diagnostics in resource-limited regions. However, current commercialization approaches can be improved substantially by addressing existing technical challenges associated with µ-PADs. Among these, off-device plasma separation from whole blood is a critical challenge in µ-PAD technology that limits commercialization. Existing µ-PADs made by combining multiple components require extra fabrication steps and manufacturing material. Our approach utilizes a two-step plasma process to fabricate single-layer semi-enclosed µ-PADs directly on a commercially available blood plasma separation membrane to incorporate blood plasma separation functionality into the device. The semi-enclosed µ-PADs are bonded with low-cost adhesive plastic tape to provide mechanical support to the device and make it more mechanically robust for field applications. Detection zones of the µ-PADs have also been modified with a cellulose nanocrystal (CNC) to increase colorimetric signal homogeneity, thus enhancing signal quality. The CNC-modified µ-PADs have been used for colorimetric detection of two model analytes (glucose and albumin) in whole blood. Colorimetric signals for both glucose and albumin from whole blood samples were consistent with the calibration curves generated using stock solutions.

     

A formal proof of the ε-optimality of absorbing continuous pursuit algorithms using the theory of regular functions

The most difficult part in the design and analysis of Learning Automata (LA) consists of the formal proofs of their convergence accuracies. The mathematical techniques used for the different families (Fixed Structure, Variable Structure, Discretized etc.) are quite distinct. Among the families of LA, Estimator Algorithms (EAs) are certainly the fastest, and within this family, the set of Pursuit algorithms have been considered to be the pioneering schemes. Informally, if the environment is stationary, their ε-optimality is defined as their ability to converge to the optimal action with an arbitrarily large probability, if the learning parameter is sufficiently small/large. The existing proofs of all the reported EAs follow the same fundamental principles, and to clarify this, in the interest of simplicity, we shall concentrate on the family of Pursuit algorithms. Recently, it has been reported Ryan and Omkar (J Appl Probab 49(3):795–805, 2012) that the previous proofs for ε-optimality of all the reported EAs have a common flaw. The flaw lies in the condition which apparently supports the so-called “monotonicity” property of the probability of selecting the optimal action, which states that after some time instant t ₀, the reward probability estimates will be ordered correctly forever. The authors of the various proofs have rather offered a proof for the fact that the reward probability estimates are ordered correctly at a single point of time after t ₀, which, in turn, does not guarantee the ordering forever, rendering the previous proofs incorrect. While in Ryan and Omkar (J Appl Probab 49(3):795–805, 2012), a rectified proof was presented to prove the ε-optimality of the Continuous Pursuit Algorithm (CPA), which was the pioneering EA, in this paper, a new proof is provided for the Absorbing CPA (ACPA), i.e., an algorithm which follows the CPA paradigm but which artificially has absorbing states whenever any action probability is arbitrarily close to unity. Unlike the previous flawed proofs, instead of examining the monotonicity property of the action probabilities, it rather examines their submartingale property, and then, unlike the traditional approach, invokes the theory of Regular functions to prove that the probability of converging to the optimal action can be made arbitrarily close to unity. We believe that the proof is both unique and pioneering, and adds insights into the convergence of different EAs. It can also form the basis for formally demonstrating the ε-optimality of other Estimator algorithms which are artificially rendered absorbing.     

Precipitation of γ′ in the γ binder phase of WC-Al-Co-Ni cemented carbide: A phase-field study

High-temperature properties of WC-Co cemented carbides can be greatly improved by introducing ordered γ′ precipitates (L1₂ structure) into disordered γ Co-binder matrix (fcc structure). The microstructure evolution of γ′ precipitates in γ matrix was investigated by using multi-phase-field (MPF) method. In order to avoid indistinguishable miscibility during MPF simulations, a phenomenon caused by mistaking the chemical free energies of γ and γ′ phase for each other, the thermodynamic driving force and diffusivities were taken from CALPHAD databases with the Gibbs energies of ordered and disordered phases separated according to a single Gibbs energy expression in a thermodynamic database. The interfacial energy between γ and γ′ phases was estimated based on a thermodynamic model applied to coherent interfaces. The elastic strain energy was introduced to reproduce the cuboidal shape of the ordered γ′ precipitates. Specially, the MPF approach was applied to study the morphological evolution of γ + γ′ microstructure as a function of concentration, temperature and aging time. It was shown that with increasing of Al concentration the cuboidal shape of precipitates appears at early stages of growth. After long term aging at 1373K the γ′/γ interface becomes semi-coherent and some γ-channels are formed. The simulation results are in good agreement with experimental data and have demonstrated the ability of the model to capture the major structural characteristics of microstructural evolution in Al–Co–Ni binder system during long-term heat treatment. Based on the knowledge of microstructure evolution, it is possible to design the optimal process parameters efficiently instead of expensive and time-consuming experiments.     

Nonparametric representation of an approximated Poincaré map for learning biped locomotion

We propose approximating a Poincaré map of biped walking dynamics using Gaussian processes. We locally optimize parameters of a given biped walking controller based on the approximated Poincaré map. By using Gaussian processes, we can estimate a probability distribution of a target nonlinear function with a given covariance. Thus, an optimization method can take the uncertainty of approximated maps into account throughout the learning process. We use a reinforcement learning (RL) method as the optimization method. Although RL is a useful non-linear optimizer, it is usually difficult to apply RL to real robotic systems due to the large number of iterations required to acquire suitable policies. In this study, we first approximated the Poincaré map by using data from a real robot, and then applied RL using the estimated map in order to optimize stepping and walking policies. We show that we can improve stepping and walking policies both in simulated and real environments. Experimental validation on a humanoid robot of the approach is presented.     

Application of Dempster–Shafer theory in condition monitoring applications: a case study

This paper is concerned with the use of Dempster–Shafer theory in `fusion' classifiers. We argue that the use of predictive accuracy for basic probability assignments can improve the overall system performance when compared to `traditional' mass assignment techniques. We demonstrate the effectiveness of this approach in a case study involving the detection of static thermostatic valve faults in a diesel engine cooling system.     

A numerical study of the Navier–Stokes-αβ model

We present a numerical study of the NS-αβ model, which is a recently proposed multiscale variation of the NS-α model that attempts to recapture scales lost through over-regularization by separately modeling dissipation-range scales. We develop a similarity theory for the new model which shows that it is better equipped than the NS-α model to capture smaller-scale behavior. Next, we propose and study an unconditionally stable, optimally accurate, and efficient finite-element implementation for the NS-αβ model; rigorous proofs for stability and convergence are provided. Finally, we present results from two numerical experiments that demonstrate the advantages of the NS-αβ model over the NS-α model.     

How does a box work? A study in the qualitative dynamics of solid objects

This paper is an in-depth study of qualitative physical reasoning about one particular scenario: using a box to carry a collection of objects from one place to another. Specifically we consider the plan, plan1 “Load objects uCargo into box oBox one by one; carry oBox from location l1 to location l2”. We present qualitative constraints on the shape, starting position, and material properties of uCargo and oBox and on the characteristics of the motion that suffice to make it virtually certain that plan1 can be successfully executed. We develop a theory, consisting mostly of first-order statements together with two default rules, that supports an inference of the form “If conditions XYZ hold, and the agent attempts to carry out plan1 then presumably he will succeed”. Our theory is elaboration tolerant in the sense that carrying out the analogous inference for carrying objects in boxes with lids, in boxes with small holes, or on trays can reuse much of the same knowledge. The theory integrates reasoning about continuous time, Euclidean space, commonsense dynamics of solid objects, and semantics of partially specified plans.     

A theoretical study of π-stacking interactions in C-substituted tetrazoles

The π-stacking effects of benzene ring (Ben) with 1H- and 2H-tetrazole derivatives (1H-TZ-X and 2H-TZ-X) substituted at C5 (where X is Cl, COH, NO, NO₂, CN, NH₂, OH, OCH₃, SH and H) has been investigated by the quantum mechanical calculations at the M06-2X/6-311++G** level. The results indicate the 1H-TZ-X||Ben complexes (|| donates π-stacking interaction) are more stable than 2H-TZ-X||Ben while in unstacked forms, 1H-TZ-X is less stable than 2H-TZ-X. All substituents enhance the π-stacking interaction relative to the unsubstituted ones and enhancement is higher for the electron-withdrawing substituents (EWSs). Also, investigation of the local and direct effect of substituents in stacking interaction showed that all substituents regardless of whether are electron donating or electron withdrawing have an additive effect in π-stacking interaction. Excellent correlations were found between the binding energies of the complexes and combination of substituent constant terms. The results showed that the electrostatic interaction alone is not responsible for stacking stabilization but charge penetration is important. Furthermore, analysis of aromaticity, AIM, ESP and NPA were investigated to obtain aromaticity index, non-bonding interactions, chemical reactivity and polarity (dipole moment), respectively.     

Limit cycle analysis of the verge and foliot clock escapement using impulsive differential equations and Poincaré maps

The verge and foliot escapement mechanism of a mechanical clock is a classical example of a feedback regulator. In this paper we analyse the dynamics of this mechanism to understand its operation from a feedback perspective. Using impulsive differential equations and Poincaré maps to model the dynamics of this closed-loop system, we determine conditions under which the system possesses a limit cycle, and we analyse the period and amplitude of the oscillations in terms of the inertias of the colliding masses and their coefficient of restitution.