Convergence Rate of the Pham Dinh–Le Thi Algorithm for the Trust-Region Subproblem

We obtain sufficient conditions for the linear convergence of the iterative sequences produced by the Pham Dinh–Le Thi algorithm for the trust-region subproblem. In addition, we give two examples to show that, if the sufficient conditions are not satisfied, then the sequences may not be linearly convergent.     

On division subrings normalized by almost subnormal subgroups in division rings

Periodica Mathematica Hungarica - Let D be a division ring with infinite center, K a proper division subring of D and N an almost subnormal subgroup of the multiplicative group $$D^*$$ of D. The...     

Calculus rules of the generalized contingent derivative and applications to set-valued optimization

Positivity - In the paper, we develop sum and chain rules of the generalized contingent derivative for set-valued mappings. Then, their applications to sensitivity analysis and optimality...     

Recurrent points and non-wandering points of graph maps

Let G be a graph and f:G→G be a continuous map. Denote by P(f), R(f) and Ω(f) the sets of periodic points, recurrent points and non-wandering points of f, respectively. In this paper we show that: (1) If L=(x,y) is an open arc contained in an edge of G such that {fm(x),fk(y)}⊂(x,y) for some m,k∈N, then R(f)∩(x,y)≠∅; (2) Any isolated point of P(f) is also an isolated point of Ω(f); (3) If x∈Ω(f)−Ω(fn) for some n∈N, then x is an eventually periodic point. These generalize the corresponding results in W. Huang and X. Ye (2001) [9] and J. Xiong (1983, 1986) [17] and [19] on interval maps or tree maps.     

Diffusion of additives and plasticizers in poly(vinyl chloride)—II: The self-diffusion of the stabilizers dibutyltin dilaurate and dibutyltin bismonobutylmaleate in plasticized poly(vinyl chloride)

The self-diffusion coefficient, D, of dibutyltin dilaurate and dibutyltin bismonobutylmaleate have been obtained at 35, 45 and 55° in samples of poly(vinyl chloride) plasticized with 34, 60 and 100 phr of di(2-ethylhexyl)phthalate. D at 2 phr of the laurate is 3–5 times larger than for the smaller maleate molecule. In all cases, D increases with increasing plasticizer concentration, an effect interpreted in terms of the free volume theory of diffusion. D for the laurate increases by a factor of about 2.7 when the laurate diffusant concentration is increased from 0 to 4 phr. The activation energies for diffusion, E_D, lie between 50 and 90 kJ mol^?1. They increase with increasing plasticizer concentration but become constant at higher plasticizer concentrations (60–100 phr). It is impossible to correlate all the known data on diffusion in plasticized PVC with an equation of the form log D₀ = C₁ + C₂ E_D/RT     

A bifurcation-based decohesion model for simulating the transition from localization to decohesion with the MPM

Based on recent experimental observations on the formation of localization before delamination, a bifurcation-based decohesion approach is proposed in this paper to simulate the transition from localization to decohesion involved in the delamination process of compressed films. The onset and orientation of discontinuous failure are identified from the discontinuous bifurcation analysis. A discrete constitutive model is then formulated based on the bifurcation analysis to predict the evolution of material failure as decohesion or separation of continuum. The Material Point Method, that does not employ fixed mesh-connectivity, is developed as a robust spatial discretization method to accommodate the multi-scale discontinuities involved in the film delamination. To demonstrate the potential of the proposed approach, a parametric study is conducted to explore the effects of aspect ratio and failure mode on the evolution of failure patterns under different boundary conditions, which provides a better understanding on the physics behind the film delamination process.Received: January 16, 2003; revised: August 11, 2003     

An Arc as the Inverse Limit of a Single Bonding Map of Type N on [0,1]

Let I = [0, 1], c ₁, c ₂ ∈ (0, 1) with c ₁ < c ₂ and f : I⊸I be a continuous map satisfying: are both strictly increasing and is strictly decreasing. Let A = {x ∈ [0, c ₁]∣f(x) = x}, a=max A, a ₁ =max(A\{a}), and B = {x ∈ [c ₂, 1]∣f(x) = x}, b=minB, b ₁ =min(B\{b}). Then the inverse limit (I, f) is an arc if and only if one of the following three conditions holds: (1) If c ₁ < f (c ₁) ≤ c ₂ (resp. c ₁ ≤ f (c ₂) < c ₂), then f has a single fixed point, a period two orbit, but no points of period greater than two or f has more than one fixed point but no points of other periods, furthermore, if A≠φ and B≠φ, then f (c ₂) > a (resp. f (c ₁) < b). (2) If f (c ₁) ≤ c ₁ (resp. f (c ₂) ≥ c ₂), then f has more than one fixed point, furthermore, if B≠φ and A\ {a} ≠φ, f (c ₂) ≥ a or if a ₁ < f (c ₂) < a, f ² (c ₂) > f (c ₂), (resp. f has more than one fixed point, furthermore, if A≠φ and B\{b}≠φ, f (c ₁) ≤ b or if b < f (c ₂) < b ₁, f ² (c ₁) < f (c ₁)). (3) If f (c ₁) > c ₂ and f (c ₂) < c ₁, then f has a single fixed point, a single period two orbit lying in I\(u, v) but no points of period greater than two, where u, v ∈ [c ₁, c ₂] such that f (u) = c ₂ and f (v) = c ₁. Supported by the National Natural Science Foundation of China (No. 19961001, No. 60334020) and Outstanding Young Scientist Research Fund. (No. 60125310)     

Monotonic optimization for sensor cover energy problem

We study the sensor cover energy problem (SCEP) in wireless communication—a difficult nonconvex problem with nonconvex constraints. A local approach based on DC programming called DCA was proposed by Astorino and Miglionico (Optim Lett 10(2):355–368, 2016) for solving this problem. In the present paper, we propose a global approach to (SCEP) based on the theory of monotonic optimization. By using an appropriate reformulation of (SCEP) we propose an algorithm for finding quickly a local optimal solution along with an efficient algorithm for computing a global optimal solution. Computational experiments are reported which demonstrate the practicability of the approach.     

Simulation of container filling process with two inlets by improved smoothed particle hydrodynamics (SPH) method

In this article, an improved smoothed particle hydrodynamics (SPH) method is proposed to simulate the filling process with two inlets. Improvements are achieved by deriving a corrected kernel gradient of SPH and a density re-initialisation. In addition, a new treatment of solid wall boundaries is presented. Thus, the improved SPH method has higher accuracy and better stability, and conserves both linear and angular momentums. The validity of the new boundary treatment is shown by simulating the spin-down problem. The bench tests are also presented to demonstrate the performance of the improved SPH method. Then the filling process with a single inlet is simulated to show the ability to capture complex-free surface of the proposed method. Finally, the filling process with two inlets is numerically investigated. The numerical results show that the filling patterns are affected significantly by Reynolds number, aspect ratio of the container and the location of the inlets.     

Existence, uniqueness and stability of C m solutions of iterative functional equations

In this paper we discuss a relatively general kind of iterative functional equation G(x,f(x), ...,f ⁿ (x)) = 0 (for allx ∈J), whereJ is a connected closed subset of the real number axis ℝ,G∈C ^m (J ⁿ⁺¹, ℝ) andn ≥ 2. Using the method of approximating fixed points by small shift of maps, choosing suitable metrics on functional spaces and finding a relation between uniqueness and stability of fixed points of maps of general spaces, we prove the existence, uniqueness and stability ofCm solutions of the above equation for any integer m ≥ 0 under relatively weak conditions, and generalize related results in reference in different aspects.