We prove that the endomorphism semiring of a nontrivial semilattice is always subdirectly irreducible and describe its monolith. The endomorphism semiring is congruence simple if and only if the semilattice has both a least and a largest element.

We survey the use of club guessing and other pcf constructs in the context of showing that a given partially ordered class of objects does not have a largest, or a universal element. 1

The doublesex (dsx) gene functions as a molecular switch at the base of the insect sex determination cascade, and triggers male or female somatic sexual differentiation in Drosophila. Having been reported from only seven current insect orders, the exact phylogenetic distribution of dsx within the largest Arthropod sub-phylum, the Hexapoda, is unknown. To understand the evolution of this integra...

A subsemigroup S of a semigroup Q is a local left order in Q if, for every group H-class H of Q, S ∩ H is a left order in H in the sense of group theory. That is, every q ∈ H can be written as ab for some a, b ∈ S ∩ H , where a denotes the group inverse of a in H . On the other hand, S is a left order in Q and Q is a semigroup of left quotients of S if every element of Q can be written as cd wh...

A subsemigroup S of a semigroup Q is a left order in Q and Q is a semigroup of left quotients of S if every element of Q can be expressed as ab where a, b ∈ S and if, in addition, every element of S that is square cancellable lies in a subgroup of Q. Here a denotes the inverse of a in a subgroup of Q. We say that a left order S is straight in Q if in the above definition we can insist that aR b...

and where the first inequality follows from the definition (2) of the weak-learning condition. Let λ∗ be a minimizer of the min-max expression. Unless the first entry of each-row of (Hλ∗ −B) is the largest, the right hand side of the min-max expression can be made arbitrarily large by choosing C ∈ Ceor appropriately. For example, if in some row i, the j0th element is strictly larger than the fi...

We consider a linear single-input single-output system on a Hilbert space X , with infinitesimal generator A, bounded control element b, and bounded observation element c. We address the problem of finding the largest feedback invariant subspace of X that is in the space c⊥ perpendicular to c. If b is not in c⊥, we show this subspace is c⊥. If b is in c⊥, a number of situations may occur, depen...

Germanane, a hydrogen-terminated graphane analogue of germanium has generated interest as a potential 2D electronic material. However, the incorporation and retention of extrinsic dopant atoms in the lattice, to tune the electronic properties, remains a significant challenge. Here, we show that the group-13 element Ga and the group-15 element As, can be successfully doped into a precursor CaGe2...

The paper submitted deals with the investigation of failures of railway structures by means of the Method of higher orders spectra. The reason why Method of higher orders spectra is prospective in future is that unlike other non-destructive methods this one offers a high-quality information on the existence of non-linear processes in material and geometrically complex investigated samples (stru...