We prove that the property of being closed (resp., rich, privileged trapezoidal, balanced) is expressible in first-order logic for automatic (and some related) sequences. It therefore follows that the characteristic function of those n for which an automatic sequence x has a closed (resp., privileged, rich, trapezoidal, balanced) factor of length n is automatic. For privileged words this requir...

The Soil-Water Characteristic Curve (SWCC) is an important soil function relating the water content of a soil to soil suction. Many unsaturated soil properties (or soil property functions) can be related to the water content versus suction relationship of a soil. Hydraulic conductivity, shear strength, chemical diffusivity, water storage, unfrozen volumetric water content, specific heat, and th...

We prove that every 2-transitive group has a property called the EKR-module property. This gives characterization of maximum intersecting sets permutations in group. Specifically, characteristic vector any set is linear combination vectors stabilizers points and their cosets. also consider when derangement graph connected subgroup or coset subgroup.

We propose a finite difference scheme for the Heisenberg equation and the LandauLifshitz equation. These equations have a length-preserving property and energy conservation or dissipation property. Our proposed scheme inherits both characteristic properties. We also show that the boundedness of finite difference solutions and an unique solvability of our scheme. Finally, we show some numerical ...

I demonstrate the existence in protein domain sequences of sets of statistically significant periodic signals, characteristic of the architectures of those domains. It is shown that, although the frequencies of the signals characteristic of a particular architecture have definite wave numbers, they can occur in any physical property. The characteristic signals define sequence units, which may c...