2 An Interesting Tiling Problem We will work with a simply connected subset R ⊆ Z (thought of as a union of unit cubes). Usually we will think of R as being a hyper-rectangle, but it doesn’t have to be. Let ui denote the unit vector in the ith coordinate and let u∗ = (1, 1, . . . , 1). Let RL = {x ∈ R | ∃i ∈ [k], x− ui 6∈ R} denote the lower boundary of R. A subset S ⊆ R is a downset if RL ⊆ S ...

Disparate properties of gold(I) converge to produce the first known cube assembly of eight Au(I) atoms connected by four N-bridging amidinate ligands on the sides of the cube, capped above and below by hyper-coordinate carbon atoms from a phosphorous ylide. There are no phosphines coordinated to the Au(I) atoms. The cluster is formulated as [Au8{CH(NC8H9)2}4{(ηC)P(C6H5)2(CH3)}2]. It displays a ...

We discover unusual chemical bonding in a novel planar hyper-coordinate Ni2Ge free-standing 2D monolayer, and also in a nearly planar slightly buckled Ni2Si monolayer. This unusual bonding is revealed by Solid State Adaptive Natural Density Partitioning analysis. This analysis shows that a new type of 2c-2e Ni-Si σ and 3c-2e Ni-Ge-Ni σ bonds stabilize these 2D crystals. This is completely diffe...

Cycle time minimization is one of the major goals to achieve in manufacturing. Maximizing feedrate direct solution; however, physical motions need be under specified motion limits avoid high-frequency vibration, causing machining error. In this paper, a time-optimal scheduling approach with corner smoothing for 5-axis G1 toolpaths presented machining. One key feature proposed method describe or...

we present some connections between the max-min general fuzzy automaton theory and the hyper structure theory. first, we introduce a hyper bck-algebra induced by a max-min general fuzzy automaton. then, we study the properties of this hyper bck-algebra. particularly, some theorems and results for hyper bck-algebra are proved. for example, it is shown that this structure consists of different ty...

The role of dynamical pairing in induced fission dynamics is investigated using the time-dependent generator coordinate method Gaussian overlap approximation, based on microscopic framework nuclear energy density functionals. A calculation fragment charge yields for $^{228}$Th performed a three-dimensional space collective coordinates that, addition to axial quadrupole and octupole intrinsic de...

This  paper extends the notion of fuzzy $BCK$-subalgebras to fuzzy hyper $BCK$-subalgebras and defines an extended fuzzy $BCK$-subalgebras. This study  considers  a type of fuzzy hyper  $BCK$-ideals  in this  hyperstructure  and  describes   the  relationship  between hyper  $BCK$-ideals and  fuzzy hyper  $BCK$-ideals.  In fact, it tries to introduce   a  strongly  regular  relation  on hyper $...

A simple method is described, to prove some theorems for simple hyper K-algebras and to study positive implicative hyper K-ideals, weak (implicative ) hyper K-ideals in simple hyper K-algebras . Beside, some results on positive implicative and (weak) implicative simple hyper K-algebras are presented. Finally classification of simple hyper Kalgebras of order 4, which are satisfied in conditions ...