7 Davis, J.A., Construction of relative difference sets in p-groups, Discrete Mathematics 103 (1992) 7-15. Jungnickel (1982) and Elliot and Butson (1966) have shown that (pi+ , p, pi+•, pi) relative difference sets exist in the elementary abelian p-group case (p an odd prime) and many 2-groups for the case p = 2. This paper provides two new constructions of relative difference sets with these p...

Let $mathcal {A} $ and $mathcal {B} $ be C$^*$-algebras. Assume that $mathcal {A}$ is of real rank zero and unital with unit $I$ and $k>0$ is a real number. It is shown that if $Phi:mathcal{A} tomathcal{B}$ is an additive map preserving $|cdot|^k$ for all normal elements; that is, $Phi(|A|^k)=|Phi(A)|^k $ for all normal elements $Ainmathcal A$, $Phi(I)$ is a projection, and there exists a posit...

Direct-phi perception elicited by a reverse-phi (i.e. reversed-polarity) stimulus may well be accounted for, if the front-end filters of a classical Reichardt unit are full-wave rectifiers. It is shown that reverse-phi perception is progressively replaced by direct-phi perception when either the spatial or the temporal modulation of the reversed-polarity stimuli are decreased. Reverse-phi perce...

Let $$N=2n^2-1$$ or $$N=n^2+n-1$$ , for any $$n\ge 2$$ . $$M=\frac{N-1}{2}$$ We construct families of prime knots with Jones polynomials $$(-1)^M\sum _{k=-M}^{M} (-1)^kt^k$$ Such have Mahler measure equal to 1. If N is prime, these are cyclotomic $$\Phi _{2N}(t)$$ up some shift in the powers t. Otherwise, they products such polynomials, including In particular, all roots unity $$\zeta _{2N}$$ o...

The notion of the square submodule of a module M over an arbitrary commutative ring R, which is denoted by RM, was introduced by Aghdam and Najafizadeh in [3]. In fact, RM is the R−submodule of M generated by the images of all bilinear maps on M. Furthermore, given a submodule N of an R−module M, we say that M is nil modulo N if μ(M×M) ≤ N for all bilinear maps μ on M. The main question about t...

Suppose that is an innnite set and k is a natural number. Let ] k denote the set of all k-subsets of and let F be a eld. In this paper we study the FSym(()-submodule structure of the permutation module F] k. Using the representation theory of nite symmetric groups, we show that every submodule of F] k can be written as an intersection of kernels of certain FSym(()-homomorphisms F] k ?! F] l for...

We theoretically show that in the presence of conventional or higher order van Hove singularities(VHS), bare finite momentum pairing, also known as pair density wave (PDW), susceptibility can be promoted to same most divergent BCS through a valley-contrasting flux 3$\phi$ each triangular plaquette at $\phi=\frac{\pi}{3}$ and $\phi=\frac{\pi}{6}$ moir\'e systems. This makes PDW possible leading ...

Searches for new low-mass matter and mediator particles have actively been pursued at fixed target experiments $e^+e^-$ colliders. It is challenging the CERN LHC, but they searched in Higgs boson decays $B$ meson by ATLAS CMS Collaborations, as well a low transverse momentum phenomena from forward scattering processes (e.g., FASER). We propose search scalar particle association with heavy vecto...

Submodule construction is the problem of finding a new submodule which, together with a given submodule, provides a behavior that conforms to a given desired global behavior. A new formulation of this problem and its solution in first-order logic is presented, and it is shown how the known solutions to this problem in the context of various communication paradigms and specification formalisms c...

An R-module A is called GF-regular if, for each a ∈ A and r ∈ R, there exist t ∈ R and a positive integer n such that r(n)tr(n)a = r(n)a. We proved that each unitary R-module A contains a unique maximal GF-regular submodule, which we denoted by M GF(A). Furthermore, the radical properties of A are investigated; we proved that if A is an R-module and K is a submodule of A, then MGF(K) = K∩M GF(A...