相关论文: Substitutes for the non-existent square lattice de…
Bacterial colonies can form a wide variety of shapes and structures based on ambient and internal conditions. To help understand the mechanisms that determine the structure of and the diversity within these colonies, various numerical…
Adding grains at a single site on a flat substrate in the Abelian sandpile models produce beautiful complex patterns. We study in detail the pattern produced by adding grains on a two-dimensional square lattice with directed edges (each…
This paper investigates the competition between both simple (e.g. stripes, hexagons) and ``superlattice'' (super squares, super hexagons) Turing patterns in two-component reaction-diffusion systems. ``Superlattice'' patterns are formed from…
The design spectrum has been determined for ten of the 15 graphs with six vertices and ten edges. In this paper we solve the design spectrum problem for the remaining five graphs with three possible exceptions.
Response surface designs are usually described as being run under complete randomization of the treatment combinations to the experimental units. In practice, however, it is often necessary or beneficial to run them under some kind of…
The finite lattice method of series expansion has been used to extend low-temperature series for the partition function, order parameter and susceptibility of the $q$-state Potts model to order $z^{56}$ (i.e. $u^{28}$), $z^{47}$, $z^{43}$,…
A new multifermion formulation of lattice QCD is proposed. The model is free of spectrum doubling and preserves all nonanomalous chiral symmetries up to exponentially small corrections. It is argued that a small number of fermion fields may…
We construct solvable models on the honeycomb lattice by combining three faces of the square lattice solvable models into a hexagon face. These models contain two independent, anisotropy controlling, spectral parameters and their transfer…
Orthogonal array, a classical and effective tool for collecting data, has been flourished with its applications in modern computer experiments and engineering statistics. Driven by the wide use of computer experiments with both qualitative…
This paper surveys the theory of multiple packings and coverings. The study of multiple arrangements started in the 60s of the last century, and it was restricted mostly to lattice arrangements on the plane or of general arrangements of…
We provide a method to construct $t$-designs from weighing matrices and association schemes. One instance of our method can produce a $3$-design from any (symmetric or skew-symmetric) conference matrix, thereby providing a partial answer to…
We study a construction, which produces surfaces $Y \subset P_3$ with cusps. For example we obtain surfaces of degree six with 18, 24 or 27 three-divisible cusps. For sextic surfaces in a particular family of up to 30 cusps the codes of…
Large sets of combinatorial designs has always been a fascinating topic in design theory. These designs form a partition of the whole space into combinatorial designs with the same parameters. In particular, a large set of block designs,…
For paired comparison experiments involving competing options described by two-level attributes several different methods of constructing designs having block paired observations under the main effects model are presented. These designs are…
A \textbf{single change covering design} is a $v$-set $X$ and an ordered list $\cL$ of $b$ blocks of size $k$ where every $t$-set must occur in at least one block. Each pair of consecutive blocks differs by exactly one element. A single…
A detailed investigation of all possible textures of Fritzsch-like and non-Fritzsch like, 144 for texture 6 zero and 432 for texture 5 zero mass matrices, have been carried out to ascertain their compatibility with the existing quark mixing…
The possibility of creating different geometries with the help of an extra synthetic dimension in optical lattices is studied. Additional linear potential and Raman assisted tunnelings are used to engineer well controlled tunnelings between…
There are three quarks with masses at or below the characteristic scale of QCD dynamics: up, down and strange. However, twisted mass lattice QCD relies on quark doublets. Various options for including three quark flavors within the twisted…
This paper studies a problem of Erd\"{o}s concerning lattice cubes. Given an $N \times N \times N$ lattice cube, we want to find the maximum number of vertices one can select so that no eight corners of a rectangular box are chosen…
We classify lattice $3$-polytopes of width larger than one and with exactly $6$ lattice points. We show that there are $74$ polytopes of width $2$, two polytopes of width $3$, and none of larger width. We give explicit coordinates for…