With every Lie semi-group, Π, possessing certain regularity properties, there is associated a Lie algebra, A; and with every strongly continuous representation of Π in a Banach space there is associated a representation A(a) of A. Certain theorems regarding this representation are established. The above theorems are valid for a representation of a Lie group also. In this case, it is shown that ...

It is easy to think of possible tensions between one’s faith and academic reality, but I wish to address here a positive relation, namely, the fact that the academy is itself indebted to religious faith. In particular, I want to point to the impact of Jewish and Christian traditions on a phase of thought that began at the end of the nineteenth century. A significant theme of this thinking was t...

Considering a commutative unital quantale L as the truth value table and using the tool of L-generalized convergence structures of stratified L-filters, this paper introduces a kind of fuzzy upper topology, called fuzzy S-upper topology, on L-preordered sets. It is shown that every fuzzy join-preserving L-subset is open in this topology. When L is a complete Heyting algebra, for every completel...

In this paper, we investigate more relations between the symmetric residuated lattices $L$ with their corresponding intuitionistic fuzzy residuated lattice $tilde{L}$. It is shown that some algebraic structures of $L$ such as Heyting algebra, Glivenko residuated lattice and strict residuated lattice are preserved for $tilde{L}$. Examples are given for those structures that do not remain the sam...

Relational Lattice is a succinct mathematical model for Relational Algebra. It reduces the set of six classic relational algebra operators to two: natural join and inner union. In this paper we push relational lattice theory in two directions. First, we uncover a pair of complementary lattice operators, and organize the model into a bilattice of four operations and four distinguished constants....

A problem of frictional contact between an elastic beam and a moving foundation and the resulting wear of the beam is considered. The process is assumed to be quasistatic, the contact is modeled with normal compliance, and the wear is described by the Archard law. Existence and uniqueness of the weak solution for the problem is proved using the theory of strongly monotone operators and the Cauc...

We construct a new operation among representations of the symmetric group that interpolates between the classical internal and external products, which are defined in terms of tensor product and induction of representations. Following Malvenuto and Reutenauer, we pass from symmetric functions to non-commutative symmetric functions and from there to the algebra of permutations in order to relate...

The main contribution of this article is to provide a combinatorial Hopf algebra on set partitions, which can be seen as a Hopf subalgebra of the free quasi-symmetric functions, and which is free, cofree and self-dual. This algebraic construction comes naturally from a combinatorial algorithm, an analogous of the Robinson-Schensted correspondence on set partitions. This correspondence also give...

Recently Benno van den Berg [1] introduced a new class of realizability toposes which he christened Herbrand toposes. These toposes have strikingly different properties from ordinary realizability toposes, notably the (related) properties that the ‘constant object’ functor from the topos of sets preserves finite coproducts, and that De Morgan’s law is satisfied. In this paper we show that these...

This  paper extends the notion of fuzzy $BCK$-subalgebras to fuzzy hyper $BCK$-subalgebras and defines an extended fuzzy $BCK$-subalgebras. This study  considers  a type of fuzzy hyper  $BCK$-ideals  in this  hyperstructure  and  describes   the  relationship  between hyper  $BCK$-ideals and  fuzzy hyper  $BCK$-ideals.  In fact, it tries to introduce   a  strongly  regular  relation  on hyper $...