In this paper we study complex representations of the factorpower FP(G,M) of a finite group G acting on a finite set M . This includes the finite monoid FP+(Sn), which can be seen as a kind of a “balanced” generalization of the symmetric group Sn inside the semigroup of all binary relations. We describe all irreducible representations of FP(G,M) and relate them to irreducible representations of...

Let G be a connected graph with vertex set V (G), order n = |V (G)|, minimum degree δ and edge-connectivity λ. Define the inverse degree of G as R(G) = ∑ v∈V (G) 1 d(v) , where d(v) denotes the degree of the vertex v. We show that if R(G) < 2 + 2 δ(δ + 1) + n− 2δ (n− δ − 2)(n− δ − 1) , then λ = δ. We also give an analogous result for triangle-free graphs.

Good, but does an inverse g of f have to exist? A necessary condition is that f(1) 6= 0. Indeed, if g is the inverse of f , then 1 = I(1) = (f ∗ g)(1) = f(1)g(1). We now show that this necessary condition is also sufficient. We assume that f(1) 6= 0 and we try and solve for g. What this means is that we are solving for infinitely many unknowns: g(1), g(2), . . . . From the above, we see that th...

We propose a gauged U(1)B?L extended two Higgs doublet model to explain both neutrino mass and lepton anomalous magnetic moments (g?2). Neutrino is generated via an inverse seesaw mechanism by introducing singlet fermions. Especially, we update the result of muon (g?2) in light very recent report E989 experiment at Fermilab, indicating a?FNAL=116592040(54)×10?11. Combining BNL result, have foll...

in this paper, we demonstrate the existence and uniqueness a semianalytical solution of an inverse heat conduction problem (ihcp) in the form: ut = uxx in the domain d = {(x, t)| 0 < x < 1, 0 < t t}, u(x, t) = f(x), u(0, t) = g(t), and ux(0, t) = p(t), for any 0 t t. some numerical experiments are given in the final section.

For any group G and any set A, a cellular automaton (CA) is a transformation of the configuration space A G defined via a finite memory set and a local function. Let CA(G; A) be the monoid of all CA over A G. In this paper, we investigate a generalisation of the inverse of a CA from the semigroup-theoretic perspective. An element τ ∈ CA(G; A) is von Neumann regular (or simply regular) if there ...

This paper presents a simple unknown input estimation technique using generalized matrix inverse. The full order observer constructed by g-inverse is extended and implemented for this purpose. The necessary and sufficient condition has been introduced for existence of such an estimator. The proposed method is illustrated by numerical example (Two loop autopilot in pitch plane) and the MATLAB si...

Citation: Moe S, Antonelli G, Teel AR, Pettersen KY and Schrimpf J (2016) Set-Based Tasks within the Singularity-Robust Multiple Task-Priority Inverse Kinematics Framework: General Formulation, Stability Analysis, and Experimental Results. Front. Robot. AI 3:16. doi: 10.3389/frobt.2016.00016 Set-Based Tasks within the Singularity-Robust Multiple Task-Priority Inverse Kinematics Framework: Gener...