If I and J are two ideals in a ring R, we call I a z_J-ideal if M_a ∩ J ⊆ I, ∀ a ∈ I, where M_a is the intersection of all maximal ideals containing a. Whenever J ⊈ I and I is a z_J-ideal, we say that I is a relative z-ideal or briefly a rez-ideal, and we call J a z-factor of I. If I is an ideal in a semisimple ring and Ann(I) ≠ (0), we have shown that I is a rez-ideal and the converse is also true for each finitely generated ideal in C(X). Small and large rez-ideals and z-factors are investigated and the largest z-factor of a given semiprime ideal and maximal z_J-ideals for a given ideal J are obtained. Minimal z-factors of a given ideal in a reduced ring are also characterized and it turns out that minimal z-factors of a given ideal I in C(X) are precisely the minimal ideals of C(X) which are not contained in I. Finally, we show that the space X is an F-space if and only if the sum of every rez-ideal and every convex ideal in C(X) is convex, and spaces X for which the intersection of every two semiprime rez-ideals in C(X) is a rez-ideal are characterized.

Let R be a commutative ring. An ideal I of R is called a d-ideal (f d-ideal) provided that for each a ∈ I (finite subset F of I) and b ∈ R, Ann(a) ⊆ Ann(b) (Ann(F) ⊆ Ann(b)) implies that b ∈ I. It is shown that, the class of z0-ideals (hence all sz0-ideals), maximal ideals in an Artinian or in a Kasch ring, annihilator ideals, and minimal prime ideals over a d-ideal are some distinguished classes of d-ideals. Furthermore, we introduce the class of f d-ideals as a subclass of d-ideals in a commutative ring R. In this regard, it is proved that the ring R is a classical ring with property (A) if and only if every maximal ideal of R is an f d-ideal. The necessary and sufficient condition for which every prime f d-ideal of a ring R being a maximal or a minimal prime ideal is given. Moreover, the rings for which their prime d-ideals are z0-ideals are characterized. Finally, we prove that every prime f d-ideal of a ring R is a minimal prime ideal if and only if for each a ∈ R there exists a finitely gene...

Exoskeletons are robotic devices which are used in power augmentation and rehabilitation robotics. The exoskeleton control system is one of the most challenging issues in human-robot interaction systems. Although the rehabilitation robotic control methods are well studied, little research has been conducted on power augmenting control methods. This paper presents a novel idea in control system of exoskeletons for load carrying and power augmentation. Here, the desired linear velocity of the exoskeleton in interaction points are taken to be proportional to interaction force at the corresponding location. The introduced control method is merely based on kinematic model and thus easy to implement practically. The result of simulation on a seven segmented dynamic model of Human-Exoskeleton shows that the interaction forces tend to zero and the position tracking error of exoskeleton is less than 2° degree.

In this note we present an investigation of J -spaces and other types of spaces related to J -spaces. We characterise these spaces using the notion of relatively connected subsets. For a completely...