Let n ≥ 3. From the description of subdirectly irreducible complemented Arguesian lattices with four generators given by Herrmann, Ringel and Wille it follows that the subspace lattice of an n-dimensional vector space over a finite field is generated by four elements if and only if the field is a prime field. By exhibiting a 5-element generating set we prove that the subspace lattice of an n-di...

This paper proposed an even grid based lattice vector quantization method for audio coding. The method uses energy priority, with basic code book and the ball-type expansion, which is applicable to the low rate of the variable-rate vector quantization coding. The method uses the lattice characteristics to resolve rapid index distribution problem, as well as the compression of the basic code boo...

We elucidate the properties of mixed-gap vector surface solitons supported by the interface between a uniform medium and an optical lattice imprinted in a Kerr-type nonlinear medium. The components of such mixed-gap solitons emerge from different gaps of lattice spectrum and their mutual trapping results in the formation of stable vector states. The unstable soliton component is stabilized by t...

The unique Shortest vector problem (uSVP) in lattice theory plays a crucial role in many public-key cryptosystems. The security of those cryptosystems bases on the hardness of uSVP. However, so far there is no proof for the proper hardness of uSVP even in its exact version. In this paper, we show that the exact version of uSVP for `∞ norm is NP-hard. Furthermore, many other lattice problems inc...

We develop quenched chiral perturbation theory for vector mesons made of light quarks, in the limit where the vector meson masses are much larger than the pion mass. We use this theory to extract the leading nonanalytic dependence of the vector meson masses on the masses of the light quarks. By comparing with analogous quantities computed in ordinary chiral perturbation theory, we estimate the ...

In this paper, we introduce the concept of linear v{C}ech closure spaces and establish the properties of open sets in linear v{C}ech closure spaces (Lv{C}CS). Here, we observe that the concept of linearity is preserved by semi-open sets, g-semi open sets, $gamma$-open sets, sgc-dense sets and compact sets in Lv{C}CS. We also discuss the concept of relative v{C}ech closure operator, meet and pro...