A structure model for the Ge(111)-(4×4)-Ag surface is proposed. The model was derived by applying direct methods to surface X-ray diffraction data. It is a missing top layer reconstruction with six Ag atoms placed on Ge substitutional sites in one triangular subunit of the surface unit cell. A ring-like assembly containing nine Ge atoms is found in the other triangular subunit. The stability of...

A radiation pattern synthesis technique for large planar arrays with active element pattern (AEP) method and fine-grained parallel micro-genetic algorithm (FGPMGA) is presented. Based on the AEP method, the mutual coupling between array elements can be taken into account. Analysis problems of large rectangular and triangular grid planar arrays are divided into small linear array problems. And f...

Recent experiments on triangular lattice organic Mott insulators have found evidence for a two-dimensional 2D spin liquid in close proximity to the metal-insulator transition. A Gutzwiller wave function study of the triangular lattice Heisenberg model with a four-spin ring exchange term appropriate in this regime has found that the projected spinon Fermi sea state has a low variational energy. ...

Let R be a left and right Noetherian ring and n, k any non-negative integers. R is said to satisfy the Auslander-type condition Gn(k) if the right flat dimension of the (i+1)-st term in a minimal injective resolution of RR is at most i+ k for any 0 ≤ i ≤ n− 1. In this paper, we prove that R is Gn(k) if and only if so is a lower triangular matrix ring of any degree t over R.

We describe a new method of describing the pucker of an N-member monocyclic ring using N - 3 parameters. To accomplish this, three ring atoms define a reference plane, and the remainder of the ring is decomposed into triangular flaps. The angle of incidence for each flap upon the reference plane is then measured. The combination of these angles is characteristic of the ring's pucker. This pucke...

Both ring oscillators and relaxation oscillators are subsets of RC oscillators featuring large tuning ranges and small areas. Figure 19.5.1 shows a typical relaxation oscillator with a capacitor and two switched current sources. Such relaxation oscillators have two advantages with respect to ring oscillators: 1) they have a constant frequency tuning gain; and 2) their phase can be read out cont...

Let A be a local commutative principal ideal ring. We study the double coset space of GLn(A) with respect to the subgroup of upper triangular matrices. Geometrically, these cosets describe the relative position of two full flags of free primitive submodules of A. We introduce some invariants of the double cosets. If k is the length of the ring, we determine for which of the pairs (n, k) the dou...

Let $\Delta =\left(\begin{smallmatrix} A & {_AN_B}\\ {_BM_A} B \\\end{smallmatrix}\right)$ be a Morita ring with $M\otimes_{A}N=0=N\otimes_{B}M$.We first study how to construct (complete) duality pairs of $\Delta$-modules using $A$-modules and $B$-modules, generalizing the result Mao (Comm. Algebra, 2020, 12: 5296--5310) about over triangular matrix ring. Moreover, we Gorenstein projective modu...