Existing approaches (in particular graph theoretic) for generating floorplans focus on constructing floorplans for given adjacencies without considering boundary layout or room shapes. With recent developments in designs, ...
This paper proposes a linear time algorithm for the customization of a slicing floor plan design, which can be done by customizing its modules in the following two ways:
—-by modifying the aspect ratio or by modifying ...
A majority of previous research on the problem of floor planning has been limited to constructing floor plans with rectangular exterior boundaries. It includes rectangular floor plans (RFPs) (Kozminski and Kinnen in IEEE ...
In literature, the generation of floor plans has mainly been confined to dimensionless floor plans with rectangular boundaries having no open spaces within the floor plan. In this paper, the user is allowed to construct a ...
A non-rectangular floor plan (NRFP) is one with a rectilinear exterior boundary containing rectangular modules. An NRFP is identified as a T-shaped floor plan if the rectilinear exterior boundary forms a T-shape with two ...
The generation of floor plan layouts has been extensively studied in recent years, driven by the need for efficient and functional architectural designs. Despite significant advancements, existing methods often face ...
We present a novel workflow where non-rectangular floor plans (NRFPs), namely plans with at least one concave corner, are self-generated using a model that directly encodes key optimisation factors on spatial quality and ...
The enhanced power graph of a finite group G is the simple undirected graph whose vertex set is G and two distinct vertices x,y are adjacent if x,y∈⟨z⟩ for some z∈G. An L(2,1)-labeling of graph Γ is an integer labeling of ...
The power graph of a finite group G is the simple undirected graph with vertex set G whose two vertices are adjacent if one is a power of the other. The enhanced power graph of a finite group G is the simple undirected ...
The goal of this paper is to establish singular Adams type inequality for biharmonic operator on Heisenberg group. As an application, we establish the existence of a solution to
where
is a bounded domain, The special ...
In this article, we establish the existence of three weak solutions for a nonlinear Kirchho¤ type elliptic
equation involving polyharmonic operator by using variational methods. We assume that the nonlinearity
satis es ...
In this article, we derive a generalised nonlinear Picone's identity for p sub-Laplacian on the Heisenberg group. Our main result generalises the Picone's identity established by Niu et al.(Proceedings of the American ...
We prove the existence of a weak solution to the problem
−Δpu+V(x)|u|p−2uu(x)=f(u,|∇u|p−2∇u), >0 ∀x∈RN,
where Δpu=div(|∇u|p−2∇u) is the p-Laplace operator, 1<p<N and the nonlinearity f:R×RN→R is continuous and it ...
This article deals with the existence of a weak solution to the Kirchhoff problem:
where
is a bounded and smooth domain in . We assume that f, h and A are continuous functions and the growth of the non linearity is ...
In this article, we prove the existence of a solution to a nonlocal biharmonic equation with nonlinearity depending on the gradient and the Laplacian. We employ an iterative technique based on the mountain pass theorem to ...
This paper aims to establish the existence of a weak solution for the following problem:
(−Δ)sHu(x)+V(x)h(x,x,|u|)u(x)=(∫RNK(y)F(u(y))|x−y|λdy)K(x)f(u(x)) in RN,
where N≥1, s∈(0,1),λ∈(0,N),H(x,y,t)=∫|t|0h(x,y,r)r dr, ...
We establish the existence of a solution to the following problem:
where , is a smooth and bounded domain and , where is the ith eigenvalue of symmetric matrix . We assume that and are parameters. Moreover, we assume that ...
This article is focused on the existence of a ground state solution to the Kirchhoff problem:
where
is a bounded domain with smooth boundary and . We assume that f satisfies critical exponential growth at infinity but ...
This paper aims to establish the existence of a weak solution for the nonlocal problem:
where is a bounded and smooth domain containing two open and connected subsets and such that
and is the -Laplace operator. We assume ...
The goal of this paper is to prove the existence of two weak
solutions for the following problem:
− div(|∇u|p(x)−2∇u+μ(x)|∇u|q(x)−2∇u)
=λh(x)u
−η(x)+ξ(x)|u|s(x)−2u in Ω,
u = 0 on ∂Ω,
where Ω ⊂ RN, N ≥ 2 is a bounded ...