In a recent work [FR], Frenkel and Reshetikhin developed the theory of q-vertex operators. They showed that n-point correlation functions associated to q-vertex operators satisfy a qdifference equation called q-deformed Kniznik-Zamolodchikov equation. In the derivation of this equation, a crucial point is that the quantum affine algebra is a quasi-triangular Hopf algebra. By using several prope...

Grid cells in the entorhinal cortex fire when animals that are exploring a certain region of space occupy the vertices of a triangular grid that spans the environment. Different neurons feature triangular grids that differ in their properties of periodicity, orientation, and ellipticity. Taken together, these grids allow the animal to maintain an internal, mental representation of physical spac...

The dual band microstrip antenna is realized by placing the open circuit stub or by cutting the slot inside the patch. The compact microstrip antenna is realized by placing the shorting post or plate along the zero field line at the fundamental mode of the patch. In this paper, a compact variation of equilateral triangular microstrip antenna, a shorted 600 sectoral microstrip antenna is discuss...

The existence and construction of self-dual codes in a permutation module of a finite group for the semisimple case are described from two aspects, one is from the point of view of the composition factors which are self-dual modules, the other one is from the point of view of the Galois group of the coefficient field.

let $m$ be an $r$-module and $0 neq fin m^*={rm hom}(m,r)$. we associate an undirected graph $gf$ to $m$ in which non-zero elements $x$ and $y$ of $m$ are adjacent provided that $xf(y)=0$ or $yf(x)=0$. weobserve that over a commutative ring $r$, $gf$ is connected anddiam$(gf)leq 3$. moreover, if $gamma (m)$ contains a cycle,then $mbox{gr}(gf)leq 4$. furthermore if $|gf|geq 1$, then$gf$ is finit...

Аliieva L. І., Levchenko V. M., Aliiev I. S., Kartamyshev D. O. The development of triangular kinematic module to calculate the deformation pressure in extrusion processes
 article presents universal developed on basis energy upper bound method, designed for use mathematical simulations combined processes cold forging. In particular, this can be used force regime simulating and tool loads ...

Visual Question Answering (VQA) aims to appropriately answer a text question by understanding the image content. Attention-based VQA models mine implicit relationships between objects according feature similarity, which neglects explicit objects, for example, relative position. Most Scene Graph-based exploit positions or visual construct scene graph, while they suffer from semantic insufficienc...

One of the purposes in the computation of cohomology groups is to establish invariants which may be helpful in the classification of the objects under consideration. In the theory of continuous Hochschild cohomology for operator algebras R. V. Kadison and J. R. Ringrose proved [10] that for any hyperfinite von Neumann algebra M and any dual normal M-bimodule S, all the continuous cohomology gro...