We prove the logarithmic concavity of the Duistermaat-Heckman measure of an Hamiltonian (n− 2)-dimensional torus action for which there exists an effective commuting symplectic action of a 2-torus with symplectic orbits. Using this, we show that any symplectic (n− 2)-torus action with non-empty fixed point set which satisfies this additional 2-torus condition must be Hamiltonian.

We introduce the notion of a local torus action modeled on the standard representation (for simplicity, we call it a local torus action). It is a generalization of a locally standard torus action and also an underlying structure of a locally toric Lagrangian fibration. For a local torus action, we define two invariants called a characteristic pair and an Euler class of the orbit map, and prove ...

In this note, we study the lattice structure on the class of all weak hyper K-ideals of a hyper K-algebra. We first introduce the notion of (left,right) scalar in a hyper K-algebra which help us to characterize the weak hyper K-ideals generated by a subset. In the sequel, using the notion of a closure operator, we study the lattice of all weak hyper K-ideals of ahyper K-algebra, and we prove a ...

The intuitionistic fuzzification of (strong, weak, s-weak) hyperBCK-ideals is introduced, and related properties are investigated. Characterizationsof an intuitionistic fuzzy hyper BCK-ideal are established. Using acollection of hyper BCK-ideals with some conditions, an intuitionistic fuzzyhyper BCK-ideal is built.

A charged particle in a uniform magnetic field in a two-dimensional torus has a discrete noncommutative translation symmetry instead of a continuous commutative translation symmetry. We study topology and symmetry of a particle in a magnetic field in a torus of arbitrary dimensions. The magnetic translation group (MTG) is defined as a group of translations that leave the gauge field invariant. ...

In this note we consider the notion of intuitionistic fuzzy (weak) dual hyper K-ideals and obtain related results. Then we classify this notion according to level sets. After that we determine the relationships between intuitionistic fuzzy (weak) dual hyper K-ideals and intuitionistic fuzzy (weak) hyper K-ideals. Finally, we define the notion of the product of two intuitionistic fuzzy (weak) du...

The paper devotes to the slow–fast behaviors of a higher-dimensional non-smooth system with coupling two scales. Some novel bursting attractors and interesting phenomena are presented, especially so-called mixed-torus oscillations, in which trajectory moves along different tori turn, though attractor still behaves quasi-periodic form. Based on 4-D hyper-chaotic model scrolls, modified version i...

In this note first we define the notions of fuzzy positive implicativehyper BCK-ideals of types 1,2,3 and 4. Then we prove some theorems whichcharacterize the above notions according to the level subsets. Also we obtainthe relationships among these notions, fuzzy (strong, weak, reflexive) hyperBCK-ideals and fuzzy positive implicative hyper BCK-ideals of types 5,6,7and 8. Then, we define the no...

background: generalized joint hyper mobility predisposes some individuals to a wide variety of musculoskeletal complaints. given the critical role of scapular position in function of shoulder, the aim of this study was to compare scapular position between persons with and without general joint hyper mobility. methods: by nonprobability sampling 30 hyper mobile persons at average of 22.86 ±2.77 ...