We construct a two-sided discontinuous piecewise linear minimal valid function for the 1-row Gomory–Johnson model which is not extreme, but which is not a convex combination of other piecewise linear minimal valid functions. This anomalous behavior results from combining features of Hildebrand’s two-sided discontinuous extreme functions and Basu–Hildebrand–Köppe’s piecewise linear extreme funct...

Background: Ensuring adequate depth of anesthesia during surgery is essential for anesthesiologists to prevent the occurrence of unwanted alertness during surgery or failure to return to consciousness. Since the purpose of using anesthetics is to affect the central nervous system, brain signal processing such as electroencephalography (EEG) can be used to predict different levels of anesthesia....

We construct the exact solution for a family of one-half spin chains explicitly. The Hamiltonian corresponds to an isotropic Heisenberg Hamiltonian, with staggered exchange couplings that take only two different values. work out solutions in one-excitation subspace. Regarding problem quantum state transfer, we use and some theorems concerning approximation irrational numbers, show appearance co...

In this paper, we determine the isomorphic classes of Morita equivalent subalgebras of irrational rotation algebras. It is based on the solution of the quadratic Diophantine equations. We determine the irrational rotation algebras that have locally trivial inclusions. We compute the index of the locally trivial inclusions of irrational rotation algebras.

Let b ≥ 2 be an integer. We prove that the b-ary expansion of every irrational algebraic number cannot have low complexity. Furthermore, we establish that irrational morphic numbers are transcendental, for a wide class of morphisms. In particular, irrational automatic numbers are transcendental. Our main tool is a new, combinatorial transcendence criterion.

Bridging the gap between an abstract definition of pseudo-differential operators, such as (−1) for − 1 2 < γ < 1 2 , and a concrete way to represent them has proved difficult; deriving stable numerical schemes for such operators is not an easy task either. Thus, the framework of diffusive representations, as already developed for causal fractional integrals and derivatives, is being applied to ...

In this paper we appraise current agricultural subsidy policy in the EU. Several sources of its inefficiency are identified: it is inefficient for supporting farmers' incomes or guaranteeing food security, and irrational transfer payments decoupled from actual performance that may be negative for environmental protection, social cohesion, etc. Based on a simplified economic model, we prove that...