The category of the title is called $mathcal{W}$. This has all free objects $F(I)$ ($I$ a set). For an object class $mathcal{A}$, $Hmathcal{A}$ consists of all homomorphic images of $mathcal{A}$-objects. This note continues the study of the $H$-closed monoreflections $(mathcal{R}, r)$ (meaning $Hmathcal{R} = mathcal{R}$), about which we show ({em inter alia}): $A in mathcal{A}$ if and  only if...

we find an explicit expression of the tutte polynomial of an $n$-fan. we also find a formula of the tutte polynomial of an $n$-wheel in terms of the tutte polynomial of $n$-fans. finally, we give an alternative expression of the tutte polynomial of an $n$-wheel and then prove the explicit formula for the tutte polynomial of an $n$-wheel.

Abstract We consider Walsh’s conformal map from the exterior of a compact set $$E \subseteq \mathbb {C}$$ E ⊆ C onto lemniscatic domain. If E is simply connected, domain circle, while if has several components, generalized lemniscate and determined by l...

     In this article we introduce the notion of textit{Fractal $omega$-operad} emerging from  a natural $omega$-operad associated to any coglobular object in the category of higher operads in Batanin's sense, which in fact is a coendomorphism $omega$-operads. We have in mind coglobular object of higher operads which algebras are kind of higher transformations. It follows that this natural $omeg...

A weakly nonlinear oscillator of natural frequency omega(0) and damping ratio delta is driven by an amplitude-modulated force of dimensionless amplitude epsilon, carrier frequency omega, and modulation frequency omega(1). Each of (omega - omega(0))/omega(0), omega(1)/omega(0), and delta is O(epsilon(2/3)) as epsilon --> 0. The response in this resonant neighborhood is a slowly modulated sine wa...

Haglund, Luoto, Mason, and van Willigenburg introduced a basis for quasisymmetric functions called the quasisymmetric Schur function basis, generated combinatorially through fillings of composition diagrams in much the same way as Schur functions are generated through reverse column-strict tableaux. We introduce a new basis for quasisymmetric functions called the row-strict quasisymmetric Schur...

In the following we investigate the computational complexity of various !-GRAPH ACCESSIBILITY PROBLEMs on the most general restricted type of !-branching programs for which, up to now, exponential lower bounds on the size can be proved. By means of exponential lower bounds on various ranks of certain communication matrices we prove that !GRAPH ACCESSIBILITY PROBLEMs can not be computed by bound...

We show how to determine the k-th bit of Chaitin’s algorithmically random real number Ω by solving k instances of the halting problem. From this we then reduce the problem of determining the k-th bit of Ω to determining whether a certain Diophantine equation with two parameters, k and N , has solutions for an odd or an even number of values of N . We also demonstrate two further examples of Ω i...