Let G be a connected semisimple Lie group. There are two natural duality constructions that assign to G: its Langlands dual group $$G^\vee $$ , and Poisson–Lie $$G^*$$ respectively. The main result of this paper is the following relation between these objects: integral cone defined by cluster structure Berenstein–Kazhdan potential on double Bruhat cell $$G^{\vee ; w_0, e} \subset G^\vee isomorp...

Given an arbitrary graph G, we study the basic covers algebra Ā(G), which is the symbolic fiber cone of the Alexander dual of the edge ideal of G. Extending results of Villarreal and Benedetti–Constantinescu–Varbaro, valid only in the case when G is bipartite, we characterize in a combinatorial fashion the situations when: 1) Ā(G) is a domain, and 2) Ā(G) is a domain and in addition (the edge i...

in this paper, we study spacelike dual biharmonic curves. we characterize spacelike dual biharmonic curves in terms of their curvature and torsion in the lorentzian dual heisenberg group . we give necessary and sufficient conditions for spacelike dual biharmonic curves in the lorentzian dual heisenberg group . therefore, we prove that all spacelike dual biharmonic curves are spacelike dual heli...

gerbera jamesoniiis of commercial significance and fifth most used cut flower in the world today. a pot experiment was performed to see the effect of co-inoculation of arbuscular mycorrhizal fungi (amf) i.e. (glomus mosseae andacaulospora laevis) with phosphate solubilizing bacteria pseudomonas fluorescensin the presence of different doses of superphosphate (low, medium, high) on growth establi...

The paper deals with group dualities. A duality is simply a pair (G,H) where G an abstract abelian and H subgroup of characters defined on G. topology τ compatible the (also called dual pair) if equipped has H. topological (G,τ) gives rise to natural (G,G∧), G∧ stands for continuous We prove that existence g-barrelled (G,G∧) equivalent semireflexivity in Pontryagin's sense endowed pointwise con...

let  $r$ be a commutative noetherian ring and $i$ be an ideal of $r$. we say that $i$ satisfies the persistence property if  $mathrm{ass}_r(r/i^k)subseteq mathrm{ass}_r(r/i^{k+1})$ for all positive integers $kgeq 1$, which $mathrm{ass}_r(r/i)$ denotes the set of associated prime ideals of $i$. in this paper, we introduce a class of square-free monomial ideals in the polynomial ring  $r=k[x_1,ld...

We show how to recursively construct all self–dual maps on the sphere together with their self–dualities, and classify them according to their edge–permutations. Although several well known classes of self–dual graphs, e.g., the wheels, have been known since the last century, [7], the general characteristics of self–dual graphs have only recently begun to be explored. In [10] two constructions ...

The purpose of this paper is to prove the existence of a renormalized solution of perturbed elliptic problems$ -operatorname{div}Big(a(x,u,nabla u)+Phi(u) Big)+ g(x,u,nabla u) = mumbox{ in }Omega,  $ in the framework of Orlicz-Sobolev spaces without any restriction on the $M$ N-function of the Orlicz spaces, where $-operatorname{div}Big(a(x,u,nabla u)Big)$ is a Leray-Lions operator defined f...

In this experiment eight 1,600 mL dual-flow continuous culture fermenters were used to measure the fermentation pattern of cultivable and pasture forages in camel. Two adult camels were used as rumen inocula donors. Fermenters were fed with 120 g of DM/d in 3 equal portions at 08:00, 16:00, and 24:00 h. The trial contained two treatments of four replicate each in a completely randomized design....

Given a 2-connected graph G on n vertices, let G∗ be its partially square graph, obtained by adding edges uv whenever the vertices u, v have a common neighbor x satisfying the condition NG(x) ⊆ NG[u] ∪ NG[v], where NG[x] = NG(x) ∪ {x}. In particular, this condition is satisfied if x does not center a claw (an induced K1,3). Clearly G ⊆ G∗ ⊆ G, where G is the square of G. For any independent tri...