Commentary on An Enquiry into the Nature and Origin of Literary Property (1762)

One of a number of published commentaries contributing to the mid-eighteenth century debate concerning the nature of literary property. The author of An Enquiry sought to repudiate the concept of a natural authorial property right existing at common law. In so doing, he specifically engaged with various aspects of William Warburton's earlier commentary (see: uk_1747), as well as presenting arguments that drew upon the nature of property in general, the differences between the right claimed by proponents of the common law right and other acknowledged incorporeal properties, the similarities between patents and copyright, the history of literary property, the experience of other jurisdictions (drawing upon Venice in particular), and the consequences that would follow from conceding the existence of a perpetual right both for authors in particular and society in general. This commentary, in turn, drew its own response in the guise of A Vindication of the Exclusive Rights of Authors, to their own work (1762).

Symmetries and exact solutions of KP equation with an arbitrary nonlinear term

The generalized KP (GKP) equations with an arbitrary nonlinear term model and characterize many nonlinear physical phenomena. The symmetries of GKP equation with an arbitrary nonlinear term are obtained. The condition that must satisfy for existence the symmetries group of GKP is derived and also the obtained symmetries are classified according to different forms of the nonlinear term. The resulting similarity reductions are studied by performing the bifurcation and the phase portrait of GKP and also the corresponding solitary wave solutions of GKP
equation are constructed.

A framework for experimental determination of localised vertical pedestrian forces on full-scale structures using wireless attitude and heading reference systems

A major weakness among loading models for pedestrians walking on flexible structures proposed in recent years is the various uncorroborated assumptions made in their development. This applies to spatio-temporal characteristics of pedestrian loading and the nature of multi-object interactions. To alleviate this problem, a framework for the determination of localised pedestrian forces on full-scale structures is presented using a wireless attitude and heading reference systems (AHRS). An AHRS comprises a triad of tri-axial accelerometers, gyroscopes and magnetometers managed by a dedicated data processing unit, allowing motion in three-dimensional space to be reconstructed. A pedestrian loading model based on a single point inertial measurement from an AHRS is derived and shown to perform well against benchmark data collected on an instrumented treadmill. Unlike other models, the current model does not take any predefined form nor does it require any extrapolations as to the timing and amplitude of pedestrian loading. In order to assess correctly the influence of the moving pedestrian on behaviour of a structure, an algorithm for tracking the point of application of pedestrian force is developed based on data from a single AHRS attached to a foot. A set of controlled walking tests with a single pedestrian is conducted on a real footbridge for validation purposes. A remarkably good match between the measured and simulated bridge response is found, indeed confirming applicability of the proposed framework.

New Method Based on the UNIFAC–VISCO Model for the Estimation of Ionic Liquids Viscosity Using the Experimental Data Recommended by Mathematical Gnostics

The viscosity of ionic liquids (ILs) has been modeled as a function of temperature and at atmospheric pressure using a new method based on the UNIFAC–VISCO method. This model extends the calculations previously reported by our group (see Zhao et al. J. Chem. Eng. Data 2016, 61, 2160–2169) which used 154 experimental viscosity data points of 25 ionic liquids for regression of a set of binary interaction parameters and ion Vogel–Fulcher–Tammann (VFT) parameters. Discrepancies in the experimental data of the same IL affect the quality of the correlation and thus the development of the predictive method. In this work, mathematical gnostics was used to analyze the experimental data from different sources and recommend one set of reliable data for each IL. These recommended data (totally 819 data points) for 70 ILs were correlated using this model to obtain an extended set of binary interaction parameters and ion VFT parameters, with a regression accuracy of 1.4%. In addition, 966 experimental viscosity data points for 11 binary mixtures of ILs were collected from literature to establish this model. All the binary data consist of 128 training data points used for the optimization of binary interaction parameters and 838 test data points used for the comparison of the pure evaluated values. The relative average absolute deviation (RAAD) for training and test is 2.9% and 3.9%, respectively.

The proof of Kontsevich's periodicity conjecture on noncommutative birational transformations

For an arbitrary associative unital ring RR, let J1J1 and J2J2 be the following noncommutative, birational, partly defined involutions on the set M3(R)M3(R) of 3×33×3 matrices over RR: J1(M)=M−1J1(M)=M−1 (the usual matrix inverse) and J2(M)jk=(Mkj)−1J2(M)jk=(Mkj)−1 (the transpose of the Hadamard inverse).

We prove the surprising conjecture by Kontsevich that (J2∘J1)3(J2∘J1)3 is the identity map modulo the DiagL×DiagRDiagL×DiagR action (D1,D2)(M)=D−11MD2(D1,D2)(M)=D1−1MD2 of pairs of invertible diagonal matrices. That is, we show that, for each MM in the domain where (J2∘J1)3(J2∘J1)3 is defined, there are invertible diagonal 3×33×3 matrices D1=D1(M)D1=D1(M) and D2=D2(M)D2=D2(M) such that (J2∘J1)3(M)=D−11MD2(J2∘J1)3(M)=D1−1MD2.