We introduce a new family of polyominos that are inscribed in a rectangle of given size for which we establish a number of exact formulas and generating functions. In particular, we study polyominos inscribed in a rectangle with minimum area and minimum area plus one. These results are then used for the enumeration of lattice trees inscribed in a rectangle with minimum area plus one. Résumé. No...

Abstract. This paper deals with the rectangle packing problem, of filling a big rectangle with smaller rectangles, while the rectangle dimensions are real numbers. A new nonlinear programming formulation is presented and the validity of the formulation is proved. In addition, two cases of the problem are presented, with and without rotation of smaller rectangles by 90. The mixed integer piecewi...

Corner reflectors are widely applied to the precise monitoring of crustal deformation. As shown in recently, however, the machining tolerance of rectangle trihedral corner reflectors in the production and deploy process often results in the changes of RCS. The Radar Cross Section (RCS) of rectangle trihedral corner reflectors are calculated based on Physical Optics Method (PO), the objective of...

The article constructs a complete uniform asymptotic expansion in small parameter of the solution first boundary value problem. problem is posed for singularly perturbed linear inhomogeneous second-order partial differential equation with two independent variables parabolic type. investigated on rectangle. peculiarities are presence front heat conduction operator, existence corner layers at low...

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.

Pulsatile tinnitus (PT) is often an initial presenting symptom of dural arteriovenous fistula (dAVF), but it may be overlooked or diagnosed late if not suspected on initial diagnostic work-up. Here, we assess anatomical features, treatment outcomes, and clinical implications of patients with PT due to dAVF. Of 220 patients who were diagnosed with dAVF between 2003 and 2014, 30 (13.6%) presented...

While the popular DNA sequence alignment tools incorporate powerful heuristics to allow for fast and accurate alignment of DNA, most of them still optimize the classical Needleman Wunsch scoring scheme. The development of novel scoring schemes is often hampered by the difficulty of finding an optimizing algorithm for each non-trivial scheme. In this paper we define the broad class of rectangle ...

The concept of rectangle-of-influence (RI) drawings is old and well-studied in the area of graph drawing. A graph has such a drawing if we can assign points to its vertices such that for every edge (v, w) the supporting rectangle (i.e., the minimal closed axis-aligned rectangle R(v, w) containing v and w) contains no other points. In the original setup, the graph had to have an edge for every p...

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...