Macrocycles and p-benzoquinones (p-BQ) have been generally connected as potential co-synergist redox models in aerobic oxidation. To get insight for the synergist oxidation of hydroquinones (H2Q), thus, we synthesized and characterized dibenzotetraaza [14]annulene type macrocycles of FeIII and CoII metal ions and described by utilizing different examinations inc...

and Applied Analysis 3 With respect to the pointwise order u ≤ v ⇐⇒ ( ∀x ∈ Ω : u (x) ≤ v (x) ) (11) the setNL(Ω) is a Dedekind complete lattice. In particular, the supremum and infimum of a setA ⊂ NL(Ω) is given by inf A = (I ∘ S) (φ) , (12) supA = (I ∘ S) (ψ) , (13) respectively, where φ : Ω ∋ x 󳨃→ inf{u(x) : u ∈ A} and ψ : Ω ∋ x 󳨃→ sup{u(x) : u ∈ A}. Furthermore, the lattice NL(Ω) is fully di...

H+ insertion/Zn4(OH)6SO4 precipitation is the dominant charge-storage mechanism of crystalline ZnMn2O4@CNF in ZnSO4 (aq), despite specific Zn2+ lattice sites.

The complexity of a lattice polynomial is defined inductively, with variables having complexity 0. If p=plv'"vOk or p=plA'''/XOk is the canonical expression of the polynomial O, then the complexity c(p) = l+max{c(p~):l<-i-k}. An n-k lattice inclusion is an inclusion of the form p <-o-with c(p)<-n and c(o-)-k. In this note we use the main result of Day [1] to show that if all the congruence latt...

We construct a complete lattice Z such that the binary supremum function sup : Z × Z → Z is discontinuous with respect to the product topology on Z × Z of the Scott topologies on each copy of Z. In addition, we show that bounded completeness of a complete lattice Z is in general not inherited by the dcpo C(X,Z) of continuous functions from X to Z where X may be any topological space and where o...

and Applied Analysis 3 f : [0, τ] ×N ×N → N is smooth enough and there are constants a, c ∈ N, with c ̸ = − 1, such that sup (t,z,u)∈q τ 󵄨󵄨󵄨󵄨f (t, z, u) − az − cu 󵄨󵄨󵄨󵄨 < ∞, (12) where q τ = [0, τ] ×N ×N. (2) The interior controllability of the semilinear Laguerre equation

We present a silicon optomechanical nanobeam design with a dynamically tunable acoustic mode at 10.2 GHz. The resonance frequency can be shifted by 90 kHz/V2 with an on-chip capacitor that was optimized to exert forces up to 1 µN at 10 V operation voltage. Optical resonance frequencies around 190 THz with Q-factors up to 2.2 × 106 place the structure in the well-resolved s...

This lecture—based on the author's book, General Lattice Theory , Birkhäuser Verlag, 1978—briefly introduces the basic concepts of lattice theory, as needed for the lecture " Some combinatorial aspects of congruence lattice representations ". 1.1. Posets. A partially ordered set A; ≤≤ consists of a nonvoid set A and a binary relation ≤ on A such that the relation ≤ satisfies properties (P1)–(P3...

In 1975 Philipp showed that for any increasing sequence (nk) of positive integers satisfying the Hadamard gap condition nk+1/nk > q > 1, k ≥ 1, the discrepancy DN of (nkx) mod 1 satisfies the law of the iterated logarithm 1/4 ≤ lim sup N→∞ NDN(nkx)(N log logN) −1/2 ≤ Cq a.e. Recently, Fukuyama computed the value of the lim sup for sequences of the form nk = θ , θ > 1, and in a preceding paper t...