We introduce the concepts of unitary, almost unitary and strongly almost unitary subset of an ordered semigroup. For the notions of almost unitary and strongly almost unitary subset of an ordered semigroup, we use the...We introduce the concepts of unitary, almost unitary and strongly almost unitary subset of an ordered semigroup. For the notions of almost unitary and strongly almost unitary subset of an ordered semigroup, we use the notion of translational hull of an ordered semigroup. If (S,⋅,≤) is an ordered semigroup having an element e such that e ≤ e<sup>2</sup> and U is a nonempty subset of S such that u ≤ eu, u ≤ ue for all u ∈ U, we show that U is almost unitary in S if and only if U is unitary in . Also if (S,⋅,≤) is an ordered semigroup, e ∉ S, U is a nonempty subset of S, S<sup>e</sup>:= S ∪ {e} and U<sup>e</sup>:= U ∪ {e}, we give conditions that an (“extension” of S) ordered semigroup and the subset U<sup>e</sup> of S<sup>e</sup> must satisfy in order for U to be almost unitary or strongly almost unitary in S (in case U is strongly almost unitary in S, then the given conditions are equivalent).展开更多
Based on the second order hydroelasticity theory of ships, the numerical methods and the calculated results of the non-linear hydroelastic responses of a ship traveling in rough seas were investigated. The non-linear ...Based on the second order hydroelasticity theory of ships, the numerical methods and the calculated results of the non-linear hydroelastic responses of a ship traveling in rough seas were investigated. The non-linear hydrodynamic actions induced by the rigid body rotations and the variations of instantaneous wetted surface area were included in the second order analysis. The first order wave potentials and responses, which are sure to make the major contributions to the second order hydrodynamic actions, were obtained by employing the translating and pulsating source Green function and the Kelvin steady wave flow solution based on the linear three-dimensional hydroelasticity theory. The influences of the forward speed and the steady wave flow on the responses, and the differences of the predicted non-linear responses were illustrated by the numerical examples of a SWATH ship traveling with forward speed of 12 kn in irregular waves.展开更多
文摘We introduce the concepts of unitary, almost unitary and strongly almost unitary subset of an ordered semigroup. For the notions of almost unitary and strongly almost unitary subset of an ordered semigroup, we use the notion of translational hull of an ordered semigroup. If (S,⋅,≤) is an ordered semigroup having an element e such that e ≤ e<sup>2</sup> and U is a nonempty subset of S such that u ≤ eu, u ≤ ue for all u ∈ U, we show that U is almost unitary in S if and only if U is unitary in . Also if (S,⋅,≤) is an ordered semigroup, e ∉ S, U is a nonempty subset of S, S<sup>e</sup>:= S ∪ {e} and U<sup>e</sup>:= U ∪ {e}, we give conditions that an (“extension” of S) ordered semigroup and the subset U<sup>e</sup> of S<sup>e</sup> must satisfy in order for U to be almost unitary or strongly almost unitary in S (in case U is strongly almost unitary in S, then the given conditions are equivalent).
文摘Based on the second order hydroelasticity theory of ships, the numerical methods and the calculated results of the non-linear hydroelastic responses of a ship traveling in rough seas were investigated. The non-linear hydrodynamic actions induced by the rigid body rotations and the variations of instantaneous wetted surface area were included in the second order analysis. The first order wave potentials and responses, which are sure to make the major contributions to the second order hydrodynamic actions, were obtained by employing the translating and pulsating source Green function and the Kelvin steady wave flow solution based on the linear three-dimensional hydroelasticity theory. The influences of the forward speed and the steady wave flow on the responses, and the differences of the predicted non-linear responses were illustrated by the numerical examples of a SWATH ship traveling with forward speed of 12 kn in irregular waves.
