Dr. Cai Wen defined in his 1983 paper: the distance formula between a point x0 and an one-dimensional (1D) interval ; and the dependence function which gives the degree of dependence of a point with respect to a pair of included 1D-intervals. His paper inspired us to generalize the Extension Set to two-dimensions, i.e. in plane of real numbers R where one has a rectangle (instead of a seg...

q,f Mich:t\'g,afi and thro,ugh ,funds granted to the Institute for Research on fFqverty,"'at· the-University of Wisconsin-Madison pursuant to the provisions " of the' Economic <ppportunity Act of 1964. The opinions expressed and any erro;rs' are the responsibility of the author. ' " This study is an investigation of the extended properties of income-leisure preference structures. The methodolog...

Higher-order topological phases as the generalization of Berry attract an enormous amount research. The current theoretical models supporting higher-order phases, however, cannot give connection between lower-order and when extending lattice from lower to higher dimensions. Here, we theoretically propose experimentally demonstrate a corner state constructed edge states in one-dimensional lattic...

We attempt to study three significant tests of general relativity in higher dimensions, both commutative and non-commutative spaces. In the context geometry, we will consider a solution Einstein’s equation with source given by static, spherically symmetric Gaussian distribution mass. The resulting metric would describe regular or curvature singularity free black hole dimensions. should smoothly...