We consider the problem to control a vibrating string to rest in a given finite time. The string is fixed at one end and controlled by Neumann boundary control at the other end. We give an explicit representation of the L 2-norm minimal control in terms of the given initial state. We show that if the initial state is sufficiently regular, the same control is also L p -norm...

The aim of this work is the resolution of a non-autonomous abstract differential equation of elliptic type set on unbounded domain. The study is performed in the framework of Hölder spaces. An example for a concrete elliptic problem in nonsmooth cylindrical domains will illustrate the theory.Open image in new window

In this paper, we investigate some properties of semi-Fredholm operators on Banach spaces. These results are applied to the determination of the stability of various essential spectra of closed densely defined linear operators. Also, we generalize some results in the literature and we extend and unify those obtained in Jeribi (J Math Anal Appl 271:343–358, 2002), Jeribi (J Math...

The p-adic semistable laws are characterized as weak limits of scaled summands of p-adic-valued, rotation-symmetric, independent, and identically distributed random variables whose tail probability satisfies some condition. In this article it is verified such scaled sums do not converge in probability, and some more precise estimates, corresponding to the law of iterated...

We prove in this paper that the intersection numbers between periodic orbits have an intrinsic meaning for the variational problem (J,C β ) {Bahri (Pseudo-Orbits of Contact Forms Pitman Research Notes in Mathematics Series No. 173, 1984), Bahri (C R Acad Sci Paris 299, Serie I 15:757–760, 1984), Bahri (Classical and Quantic periodic motions of multiply polarized spin-manifolds...

We establish in what follows the fact that the linking number between two periodic orbits does not decrease along the decreasing flow-lines of a suitable pseudo-gradient for the action functional of the variational problem (J, C β ) and its extension ( J ∞ , ∪ Γ 2 k ) , [2–4]. This is used to compute almost explicitly the value of the intersection operator for periodic orbits for...

We address in this paper the Fredholm and compactness issues for the variational problem (J,C β ), Bahri (Pitman Research Notes in Mathematics Series No. 173. Scientific and Technical, London, 1988), Bahri (C. R. Acad. Sci. Paris 299, Serie I, 15, 757–760, 1984). We prove that the intersection operator restricted to periodic orbits of the Reeb vector-field ∂per does not mix with...

This paper contains a detailed study of the behavior of the first exotic contact structure of J. Gonzalo and F. Varela on S3 along a remarkable vector field v in its kernel found by Martino (Adv Nonlinear Stud, 2011). All contact forms are assumed to verify the condition that reads as follows: d(θ α)(v,.) is a contact form with the same orientation than α. α is the first exotic...

In this paper, we implement automatic procedures to enumerate all Nash maximal subsets of a bimatrix game and compute their dimensions. We propose a linear programming approach to identify extreme perfect Nash equilibria, enumerate all Selten maximal subsets and compute their dimensions. We present the Eχ-MIPerfect and the EEE-Perfect algorithms which enumerate all extreme...

We introduce large vector spaces M of multivariate homogeneous polynomials with a prescribed lower bound for the rank of each non-zero element of M.Open image in new window

Let R be a Noetherian ring. We denote by G(R) the simple graph whose vertices are elements of R and in which two distinct vertices x and y are joined by an edge if x − y is a zero-divisor of R. Let \({\overline{G}(R)}\) be the complementary graph to G(R) and \({\overline{\chi}(R)}\) be the chromatic number of the graph \({\overline{G}(R)}\). In this paper, we determine the...

We introduce two generalizations, the first of which generalizes the concept of multiresolution analysis. We define the irregular generalized multiresolution analysis (IGMRA). This structure is defined taking translations on sets that are not necessarily regular lattices, for which certain density requirements are required, and without using dilations, also allows each subspace...

Sufficient conditions which guarantee the convergence of the nonoscillatory solutions or oscillation of all solutions of a difference equation with several deviating arguments and oscillating coefficients are presented. Corresponding difference equations of both retarded and advanced type are studied. Examples illustrating the results are also given.

In this paper, we investigate a boundary value problem for fractional differential equations with fractional derivative condition. Some new existence results are obtained using Banach contraction principle and Leray–Schauder nonlinear alternative.

Let n ≥ 1 be a fixed integer. Let R be a semiprime ring and S an additive subgroup of R, σ, τ two endomorphisms of R and F : R → R an additive mapping of R. In the present paper, we prove that (1) if R is (n + 1)!-torsion free, S is (n + 1)-power closed and [ F ( x ) , σ ( x ) n ] ∈ Z ( R ) for all x ∈ S , then [ F ( x ) , σ ( x ) n ] = 0 for all x ∈ S ; (2) if R is 3!-torsion...

In this paper, we present a new adapted algorithm for defining the solution set of a multiobjective linear programming problem, where the decision variables are upper and lower bounded. The method is an extension of the direct support method developed by Gabasov and Kirillova in single programming. Its particularity is that it avoids the preliminary transformation of the decision...

In this paper, we consider the problem y IV + q x y = λ y , 0 < x < 1 , y ″ ′ 1 - - 1 σ y ″ ′ 0 + α y ′ 0 + γ y 0 = 0 , y ″ 1 - - 1 σ y ″ 0 + β y 0 = 0 , y ′ 1 - - 1 σ y ′ 0 = 0 , y 1 - - 1 σ y 0 = 0 where λ is a spectral parameter; q x ∈ L 1 0 , 1 is a complex-valued function; α , β , γ are arbitrary complex constants and σ = 0 , 1 . The boundary conditions of this problem are...

The aim of this paper is to obtain Bayesian estimations of scale parameter of the exponential distribution based on upper record range (R n ). We accomplish this purpose in two steps: point and interval. As the first step, the quadratic, squared error and absolute error, loss functions are considered for obtaining Bayesian-point estimations. Also in the next step, we find the...

In this paper, we propose a new iterative scheme for finding a minimizer of a constrained convex minimization problem and prove that the sequence generated by our new scheme converges strongly to a solution of the constrained convex minimization problem in a real Hilbert space.

The flow inside two concentric cylinders is one dimensional and an exact solution for quantities is easily found. However, when the cylinders axes are displaced by a small distance, two dimensional effects become obvious. In this research, the equations governing an incompressible viscous flow between two rotating cylinders are considered in polar coordinates that can be...

In this paper, we introduce some new kinds of generalized convexity, which include (semistrict) G-semipreinvexity and (semistrict) G-semipreincavity. Moreover, we establish the relations with common generalized convexity, present properties of (semistrictly) G-semipreinvex and (semistrictly) G-semipreincave functions, and also give characterizations of the classes of G...

Exact values are obtained of the n-widths of 2π-periodic functions of the form f ( x ) = 1 2 π ∫ 0 2 π K ( x − t ) φ ( t ) d t = ( K ∗ φ ) ( x ) in space L2[0, 2π] and satisfy condition ( ∫ 0 h ω m p ( φ ; t ) sin γ nt d t ) 1 / p ≤ 1 , 0 < h ≤ π / n , γ > 0 , 0 < p ≤ 2 , where ω m (φ; t)−mth order modulus of continuity of function φ(x) ∈ L2[0, 2π]. Some further generalizations...

In this paper, we study the class of rings in which every flat ideal is finitely projective. We investigate the stability of this property under localizations and homomorphic images, and its transfer to various contexts of constructions such as direct products, amalgamation of rings \({A \bowtie^{f} J}\), and trivial ring extensions. Our results generate examples which enrich the...

Let k be an algebraically closed field of characteristic p ≠ 0 and \({X_{g} \subset A_{k}^{3}}\) be a normal surface defined by an equation of the form z p = g(x, y). The two original algorithms for calculating the group of Weil divisors of X g contain key errors. This paper presents an algorithm that corrects and improves upon the earlier attempts.