Preparation and Characterization of Hydrophobic Nano Silver Film on Butterfly Wings as Bio-template

Hydrophobic nano silver films were fabricated on butterfly wings as bio-template. The micrometric/nano structures and hydrophobicity of the surfaces were investigated with the help of scanning electron microscope（SEM） and video-based contact angle meter. The hydrophobic mechanism of silver film was analyzed with the aid of Cas- sie＇s formula. On the nano silver films of various thicknesses（5, 10, 20, 40, 60, 80, 100 nm）, all the contact an- gles（CAs） of water were bigger than 120°. When the silver film was 5 nm, the CAs of water on it on the wing surfa- ces of Mimathyma nycteis and Speyeria aglaja were 143.2° and 139.2°, respectively. Coated with the sliver film of the same thickness, butterfly wing surface exhibited the CA remarkably bigger than glass slide surface, exhibiting its high hydrophobicity. With the increase of silver film thickness on butterfly wing surface, the hydrophobicity kept de- creasing. The micrometric/nano hierarchical structures on butterfly wing surface result in the transition of metal silver from hydrophilicity to hydrophobicity.     

Several classes of linear codes with few weights from the closed butterfly structure

Linear codes with few weights have applications in data storage systems, secret sharing schemes and authentication codes. In this paper, inspired by the butterfly structure [6], [29] and the works of Li, Yue and Fu [21] and Jian, Lin and Feng [19], we introduce a new defining set with the form of the closed butterfly structure and consequently we obtain three classes of 3-weight binary linear codes and a class of 4-weight binary linear codes whose dual is optimal. The lengths and weight distributions of these four classes of linear codes are completely determined by some detailed calculations on certain exponential sums. Computer experiments show that many (almost) optimal codes can be obtained from our construction.     

Large butterfly Cayley graphs and digraphs

We present families of large undirected and directed Cayley graphs whose construction is related to butterfly networks. One approach yields, for every large $k$ and for values of $d$ taken from a large interval, the largest known Cayley graphs and digraphs of diameter $k$ and degree $d$. Another method yields, for sufficiently large $k$ and infinitely many values of $d$, Cayley graphs and digraphs of diameter $k$ and degree $d$ whose order is exponentially larger in $k$ than any previously constructed. In the directed case, these are within a linear factor in $k$ of the Moore bound.     

Weakly distance-regular digraphs

We introduce the concept of weakly distance-regular digraph and study some of its basic properties. In particular, the (standard) distance-regular digraphs, introduced by Damerell, turn out to be those weakly distance-regular digraphs which have a normal adjacency matrix. As happens in the case of distance-regular graphs, the study is greatly facilitated by a family of orthogonal polynomials called the distance polynomials. For instance, these polynomials are used to derive the spectrum of a weakly distance-regular digraph. Some examples of these digraphs, such as the butterfly and the cycle prefix digraph which are interesting for their applications, are analyzed in the light of the developed theory. Also, some new constructions involving the line digraph and other techniques are presented.     

Queue layouts of iterated line directed graphs

In this paper, we study queue layouts of iterated line directed graphs. A k-queue layout of a directed graph consists of a linear ordering of the vertices and an assignment of each arc to exactly one of the k queues so that any two arcs assigned to the same queue do not nest. The queuenumber of a directed graph is the minimum number of queues required for a queue layout of the directed graph.We present upper and lower bounds on the queuenumber of an iterated line directed graph L^k(G) of a directed graph G. Our upper bound depends only on G and is independent of the number of iterations k. Queue layouts can be applied to three-dimensional drawings. From the results on the queuenumber of L^k(G), it is shown that for any fixed directed graph G, L^k(G) has a three-dimensional drawing with O(n) volume, where n is the number of vertices in L^k(G). These results are also applied to specific families of iterated line directed graphs such as de Bruijn, Kautz, butterfly, and wrapped butterfly directed graphs. In particular, the queuenumber of k-ary butterfly directed graphs is determined if k is odd.     

A proof of the butterfly theorem by an argument from statics

The butterfly theorem is proved by assigning point masses to the four vertices of the wings and using the distributive property of the mass centre of a mechanical system.     

MRI, CT, and plain film appearance of anterior spina bifida

Anterior spina bifida or butterfly vertebral body has a well known and characteristic appearance on plain film and CT. Its appearance on magnetic resonance imaging also appears to be characteristic and should not be mistaken for more serious abnormalities.