Search results for " Elliptic"

The periods of the generalized Jacobian of a complex elliptic curve

2015

Abstract We show that the toroidal Lie group G = ℂ2/Λ, where Λ is the lattice generated by (1, 0), (0, 1) and (τ̂, τ͂), with τ̂ ∉ ℝ, is isomorphic to the generalized Jacobian JL of the complex elliptic curve C with modulus τ̂, defined by any divisor class L ≡ (M) + (N) of C fulfilling M − N = [℘ (τ͂) : ℘´(τ͂) : 1] ∈ C. This follows from an apparently new relation between the Weierstrass sigma and elliptic functions.

Dimensional analysis and stage-discharge relationship for weirs: a review

2017

Deducing the weir flow stage-discharge relationship is a classical hydraulic problem. In this regard Buckingham’s theorem of dimensional analysis can be used to find simple and accurate formulas to obtain the rating curves of different weir types. At first, in this review paper the rectangular weir that is a very common hydraulic structure is studied. It is indicated that the crest shape, approach channel width, obliquity (angle between the weir crest and the direction normal to the flow motion) and vertical inclination (pivot weir) are the key-parameters affecting the flow over the rectangular weirs. The flow over the triangular, labyrinth, parabolic, circular, elliptical, and W-weirs are …

A user-friendly control system to easy reconfigure a manufacturing cell

2006

Generic manufacturing enterprises need to interact with an environment characterized by a strong competition. In order to react to the mutable requests of market, control systems should confer to the manufacturing system capabilities for easy modifiability, and this can be achieved by reducing the necessary time to reconfigure the existing system. Following this main requirement, this paper presents a user-friendly control system that pursues three operational goals: - Ability to easy re-program the sequence of operations of the manufacturing equipments of a manufacturing cell; - Reconfigurability of the system, by allowing to add/remove a new/existing component in/from the manufacturing ce…

Elliptic problems involving the 1–Laplacian and a singular lower order term

2018

Bounded solutions to the 1-Laplacian equation with a critical gradient term

2012

Uniqueness of positive radial solutions to singular critical growth quasilinear elliptic equations

2015

In this paper, we prove that there exists at most one positive radial weak solution to the following quasilinear elliptic equation with singular critical growth \[ \begin{cases} -\Delta_{p}u-{\displaystyle \frac{\mu}{|x|^{p}}|u|^{p-2}u}{\displaystyle =\frac{|u|^{\frac{(N-s)p}{N-p}-2}u}{|x|^{s}}}+\lambda|u|^{p-2}u & \text{in }B,\\ u=0 & \text{on }\partial B, \end{cases} \] where $B$ is an open finite ball in $\mathbb{R}^{N}$ centered at the origin, $1<p<N$, $-\infty<\mu<((N-p)/p)^{p}$, $0\le s<p$ and $\lambda\in\mathbb{R}$. A related limiting problem is also considered.

A sub-supersolution approach for Neumann boundary value problems with gradient dependence

2020

Abstract Existence and location of solutions to a Neumann problem driven by an nonhomogeneous differential operator and with gradient dependence are established developing a non-variational approach based on an adequate method of sub-supersolution. The abstract theorem is applied to prove the existence of finitely many positive solutions or even infinitely many positive solutions for a class of Neumann problems.

On critical behaviour in systems of Hamiltonian partial differential equations

2013

Abstract We study the critical behaviour of solutions to weakly dispersive Hamiltonian systems considered as perturbations of elliptic and hyperbolic systems of hydrodynamic type with two components. We argue that near the critical point of gradient catastrophe of the dispersionless system, the solutions to a suitable initial value problem for the perturbed equations are approximately described by particular solutions to the Painlevé-I (P $$_I$$ I ) equation or its fourth-order analogue P $$_I^2$$ I 2 . As concrete examples, we discuss nonlinear Schrödinger equations in the semiclassical limit. A numerical study of these cases provides strong evidence in support of the conjecture.

Anisotropic elliptic equations with gradient-dependent lower order terms and L^1 data

2023

&lt;abstract&gt;&lt;p&gt;We prove the existence of a weak solution for a general class of Dirichlet anisotropic elliptic problems such as $ \mathcal Au+\Phi(x, u, \nabla u) = \mathfrak{B}u+f $ in $ \Omega $, where $ \Omega $ is a bounded open subset of $ \mathbb R^N $ and $ f\in L^1(\Omega) $ is arbitrary. The principal part is a divergence-form nonlinear anisotropic operator $ \mathcal A $, the prototype of which is $ \mathcal A u = -\sum_{j = 1}^N \partial_j(|\partial_j u|^{p_j-2}\partial_j u) $ with $ p_j &amp;gt; 1 $ for all $ 1\leq j\leq N $ and $ \sum_{j = 1}^N (1/p_j) &amp;gt; 1 $. As a novelty in this paper, our lower order terms involve a new class of operators $ \mathfrak B $ such…

Random effects elliptically distributed in unbalanced linear models

2008

In linear mixed effects models, random effects are used for modelling the variance-covariance structure of the response variable. These models are based on the assumption that the random effects are normally distributed, but in literature alternative random effect distributions have been proposed and the consequences of misspecification are investigated. These studies consider only balanced designs. Aim of this paper is to study an unbalanced linear mixed model with random effects elliptically distributed.