We consider the energy representation for the gauge group. The gauge group is the set of C∞mappings from a compact Riemannian manifold to a semi-simple compact Lie group. In this paper, we obtain irreducibility of the energy representation of the gauge group for any dimension of M . To prove irreducibility for the energy representation, we use the fact that each operator from a space of test fu...

The concept of fuzzy set was introduced by Zadeh in his classical paper [1]. This concept provides a natural foundation for treating mathematically the fuzzy phenomena, which exist pervasively in our real world, and for building new branches of fuzzy mathematics. In the area of Fuzzy Topology, introduced by Chang [2], much attention has been paid to generalize the basic concepts of General Topo...

In recent years, learning methods are desirable because of their reliability and efficiency in real-world problems. We propose a novel method to find infinitely many kernel combinations for learning problems with the help of infinite and semi-infinite optimization regarding all elements in kernel space. This will provide to study variations of combinations of kernels when considering heterogene...

We show the existence result of viable solutions to the differential inclusion ẋ(t) ∈ G(x(t)) + F (t, x(t)) x(t) ∈ S on [0, T ], where F : [0, T ] × H → H (T > 0) is a continuous set-valued mapping, G : H → H is a Hausdorff upper semi-continuous set-valued mapping such that G(x) ⊂ ∂g(x), where g : H → R is a regular and locally Lipschitz function and S is a ball, compact subset in a separable H...

The aim of this paper is to introduce various functions associated with semi*α-open sets. Here semi*αcontinuous, semi*α-irresolute, contra-semi*α-continuous and contra-semi*α-irresolute functions are defined. Characterizations for these functions are given. Further their fundamental properties are investigated. Many other functions associated with semi*α-open sets and their contra versions are ...

The problem of optimal query processing in distributed database systems was shown to be NPhard. However, for a special type of queries called star queries, we have developed a polynomial optimal algorithm. In an earlier paper, we described an approach to obtain the optimal semi-join program for a star query by gradually reducing the search space to a minimal set S without making any assumptions...

threats are one of the most fundamental problems of our modern societies that daily will affect citizens in urban spaces. this becomes more problematic when the people in their everyday living spaces encounter with behaviors that cause lack of security and should have been feel comfort and their families used these spaces freely. this causes many problems for citizens. in today cities because o...