The combination of an amide containing a linear ligand (L1) and an organometallic molecular "clip" (clip-1) leads to the self-assembly of a Pt4 nanoscopic framework representing the first example of a Pt-based molecular rectangle (rectangle-1) incorporating amide functionality. A complementary approach was also followed to prepare a Pd(II)-based molecular rectangle (rectangle-2) by reaction of ...

We show that for any (partial) query function f : {0, 1} → {0, 1}, the randomized communication complexity of f composed with Indexm (with m = poly(n)) is at least the randomized query complexity of f times log n. Here Indexm : [m] × {0, 1} → {0, 1} is defined as Indexm(x, y) = yx (the xth bit of y). Our proof follows on the lines of Raz and Mckenzie [RM99] (and its generalization due to [GPW15...

We solve an open question posed by Akers and Krishnamurthy in 1986 [1, 3] concerning VLSI layout of star graphs. We show that the area of the optimal layout of an N-node star graph, hierarchical cubic network (HCN), or hierarchical folded-hypercube network (HFN) is N2=16 o(N2) under the Thompson model, or under the extended grid model where a node occupies a rectangle of sides that may range fr...

The authors develop finite difference methods for elliptic equations of the form V. ((x)Vu(x)) + (x)u(x) f(x) in a region in one or two space dimensions. It is assumed that gt is a simple region (e.g., a rectangle) and that a uniform rectangular grid is used. The situation is studied in which there is an irregular surface F of codimension contained in fl across which , a, and f may be discontin...

A series of 18 flume runs were conducted in a 6-m long, 0.5-m wide recirculating flume with a bed gradient of 0.8% to determine the influence of obstruction shape on the formation and characteristics of forced pools. Six differentshaped obstructions were added to the flume with the maximum width of the obstruction held constant at 20 cm, which equaled a 40% constriction of flow. The obstruction...

We prove a general Russo–Seymour–Welsh (RSW) result valid for any invariant bond percolation measure on Z2 satisfying positive association. This means that the crossing probability of long rectangle is related by universal homeomorphism to short rectangle.

Service Level Agreements (SLAs) serve as a foundation for a reliable and predictable job execution at remote grid sites. In this paper, we describe an error recovery mechanism for workflow within the SLA context, coping with catastrophic failure when one or several High Performance Computing Centers (HPCCs) are detached from the grid system. We propose an algorithm to detect all affected sub-jo...

My long-term goal is improving our understanding of interactions between sub-grid scale models and numerical errors, which affect simulation skill for physical and biological processes in estuaries and coastal ocean environments. For prognostic simulations, slow accumulation of truncation-level errors will progressively distort model results. Present sub-grid scale models selectively address ce...

Polyomino Venn (or polyVenn) diagrams are Venn diagrams whose curves are the perimeters of polyominoes drawn on the integer lattice. Minimum area polyVenn diagrams are those in which each of the 2n intersection regions, in a diagram of n polyominoes, consists of exactly one unit square. We construct minimum area polyVenn diagrams in bounding rectangles of size 2r×2c whenever r, c ≥ 2. Our const...

We consider a long-range growth dynamics on the two-dimensional integer lattice, initialized by a finite set of occupied points. Subsequently, a site x becomes occupied if the pair consisting of the counts of occupied sites along the entire horizontal and vertical lines through x lies outside a fixed Young diagram Z. We study the extremal quantity μ(Z), the maximal finite time at which the latt...