Fuzzy Modeling of Surficial Uranium Prospectivity in British Columbia(Canada)with a Weighted Fuzzy Algebraic Sum Operator

This paper demonstrates knowledge-guided fuzzy logic modeling of regional-scale surficial uranium(U)prospectivity in British Columbia(Canada).The deposits/occurrences of surficial U in this region vary from those in Western Australia and Namibia;thus,requiring innovative and carefully-thought techniques of spatial evidence generation and integration.As novelty,this papers introduces a new weighted fuzzy algebraic sum operator to combine certain spatial evidence layers.The analysis trialed several layers of spatial evidence based on conceptual mineral system model of surficial U in British Columbia(Canada)as well as tested various models of evidence integration.Non-linear weighted functions of(a)spatial closeness to U-enriched felsic igneous rocks was employed as U-source spatial evidence,(b)spatial closeness to paleochannels as fluid pathways spatial evidence,and(c)surface water U content as chemical trap spatial evidence.The best models of prospectivity created by integrating the layers of spatial evidence for U-source,pathways and traps predicted at least 85%of the known surficial U deposits/occurrences in>10%of the study region with the highest prospectivity fuzzy scores.The results of analyses demonstrate that,employing the known deposits/occurrences of surficial U for scrutinizing the spatial evidence layers and the final models of prospectivity can pinpoint the most suitable critical processes and models of data integration to reduce bias in the analysis of mineral prospectivity.

Some Properties of the Sum and Geometric Differences of Minkowski

The sets of Minkowski algebraic sum and geometric difference are considered. The purpose of the research in this paper is to apply the properties of Minkowski sum and geometric difference to fractional differential games. This paper investigates the geometric properties of the Minkowski algebraic sum and the geometric difference of sets. Various examples are considered that calculate the geometric differences of sets. The results of the research are presented and proved as a theorem. At the end of the article, the results were applied to fractional differential games.

Discrete integrable couplings associated with modified Korteweg-de Vries lattice and two hierarchies of discrete soliton equations

A direct way to construct integrable couplings for discrete systems is presented by use of two semi-direct sum Lie algebras. As their applications, the discrete integrable couplings associated with modified Korteweg-de Vries （m-KdV） lattice and two hierarchies of discrete soliton equations are developed. It is also indicated that the study of integrable couplings using semi-direct sums of Lie algebras is an important step towards the complete classification of integrable couplings.

Hamiltonian Forms for a Hierarchy of Discrete Integrable Coupling Systems

A semi-direct sum of two Lie algebras of four-by-four matrices is presented,and a discrete four-by-fourmatrix spectral problem is introduced.A hierarchy of discrete integrable coupling systems is derived.The obtainedintegrable coupling systems are all written in their Hamiltonian forms by the discrete variational identity.Finally,we prove that the lattice equations in the obtained integrable coupling systems are all Liouville integrable discreteHamiltonian systems.

INTEGRABLE COUPLINGS OF THE TB HIERARCHY AND ITS HAMILTONIAN STRUCTURE

In this paper,we obtain integrable couplings of the TB hierarchy using the new subalgebra of the loop algebra A.Then the Hamiltonian structure of the above system is given by the quadratic-form identity.