Search results for "Mathematical analysis"
showing 10 items of 2409 documents
A Nonlinear Primal-Dual Method for Total Variation-Based Image Restoration
1999
We present a new method for solving total variation (TV) minimization problems in image restoration. The main idea is to remove some of the singularity caused by the nondifferentiability of the quantity $|\nabla u|$ in the definition of the TV-norm before we apply a linearization technique such as Newton's method. This is accomplished by introducing an additional variable for the flux quantity appearing in the gradient of the objective function, which can be interpreted as the normal vector to the level sets of the image u. Our method can be viewed as a primal-dual method as proposed by Conn and Overton [ A Primal-Dual Interior Point Method for Minimizing a Sum of Euclidean Norms, preprint,…
Frictionless contact-detachment analysis: iterative linear complementarity and quadratic programming approaches.
2012
The object of the paper concerns a consistent formulation of the classical Signorini’s theory regarding the frictionless contact problem between two elastic bodies in the hypothesis of small displacements and strains. The employment of the symmetric Galerkin boundary element method, based on boundary discrete quantities, makes it possible to distinguish two different boundary types, one in contact as the zone of potential detachment, called the real boundary, the other detached as the zone of potential contact, called the virtual boundary. The contact-detachment problem is decomposed into two sub-problems: one is purely elastic, the other regards the contact condition. Following this method…
Corrigendum to “Multi-layer canard cycles and translated power functions” [J. Differential Equations 244 (2008) 1329–1358]
2008
On semi-fredholm properties of a boundary value problem inR + n
1988
The paper considers a boundary value problem with the help of the smallest closed extensionL ∼ :H k →H k 0×B h 1×...×B h N of a linear operatorL :C (0) ∞ (R + n ) →L(R + n )×L(R n−1)×...×L(R n−1). Here the spacesH k (the spaces ℬ h ) are appropriate subspaces ofD′(R + n ) (ofD′(R n−1), resp.),L(R + n ) andC (0) ∞ (R + n )) denotes the linear space of smooth functionsR n →C, which are restrictions onR + n of a function from the Schwartz classL (fromC 0 ∞ , resp.),L(R n−1) is the Schwartz class of functionsR n−1 →C andL is constructed by pseudo-differential operators. Criteria for the closedness of the rangeR(L ∼) and for the uniqueness of solutionsL ∼ U=F are expressed. In addition, ana prio…
A Linear Programming Method for Bounding Plastic Deformations
1988
A method for providing upper and lower bounds to plastic deformations is presented, which has the feature of being applicable both below and above the structure shakedown limit. The bounds provided are expressed in terms of some fictitious plastic strains obeying relaxed yielding laws, whose evaluation is made by means of a suitable LP-based algorithm.
Linear Perspective: or, A New Method Of Representing justly all manner of Objects As they appear to the Eye in all situations
1715
Extremal Problems for Elliptic Systems
1998
The specific properties of optimal control problems for elliptic systems, if compared with the case of a single equation, are described. Within them are: strong closures of sets of feasible states; the relaxability via convexification; the type of necessary optimality conditions.
UNIQUENESS OF PERIODIC SOLUTIONS OF THE LIENARD EQUATION
1981
This chapter analyzes the uniqueness of periodic solutions of the Lienard equation. It considers the Lienard equation = y − F ( x ) and y = − x where F (0) = 0 , F ( x ) ∈ Lip( R ). The chapter discusses the existence of periodic solutions. It highlights that the origin is the only stationary point of the system = y − F ( x ) and y = − x , and therefore all nontrivial periodic solutions must circle around the origin. The existence of at least one periodic solution is proved by constructing a Poincare–Bendixson domain. The chapter also emphasizes that to prove the uniqueness of periodic solutions, additional assumptions are also needed. In the literature there are numerous uniqueness results…
Multiple period annuli in Liénard type equations
2010
Abstract We consider the equation x ″ x 1 − x 2 x ′ 2 + g ( x ) = 0 , where g ( x ) is a polynomial. We provide the conditions for existence of multiple period annuli enclosing several critical points.