An inexact hybrid projection-proximal point algorithm for solving generalized mixed variational inequalities

In this paper, we investigate an inexact hybrid projection-proximal method for solving a class of generalized mixed variational inequalities in Hilbert spaces. We construct a general inexact hybrid projection-proximal point algorithm, in which an inexact relaxed proximal point step is followed by a suitable orthogonal projection onto a hyperplane. Under some suitable conditions concerned with the pseudomonotone set-valued mapping T, the nonsmooth convex function f and the step size λ_k, we prove the convergence of the inexact hybrid projection-proximal point algorithm for solving generalized mixed variational inequalities in Hilbert spaces.     

Group path covering and distance two labeling of graphs

For a positive integer d, an L(d,1)-labeling f of a graph G is an assignment of integers to the vertices of G such that |f(u)−f(v)|?d if uv∈E(G), and |f(u)−f(v)|?1 if u and u are at distance two. The span of an L(d,1)-labeling f of a graph is the absolute difference between the maximum and minimum integers used by f. The L(d,1)-labeling number of G, denoted by λd,1(G), is the minimum span over all L(d,1)-labelings of G. An L^′(d,1)-labeling of a graph G is an L(d,1)-labeling of G which assigns different labels to different vertices. Denote by the L^′(d,1)-labeling number of G. Georges et al. [Discrete Math. 135 (1994) 103-111] established relationship between the L(2,1)-labeling number of a graph G and the path covering number of Gc, the complement of G. In this paper we first generalize the concept of the path covering of a graph to the t-group path covering. Then we establish the relationship between the L^′(d,1)-labeling number of a graph G and the (d−1)-group path covering number of Gc. Using this result, we prove that and for bipartite graphs G can be computed in polynomial time.     

Necessary optimality conditions for fuzzy variational problems

The main aims of this study are to derive the fuzzy Euler-Lagrange conditions for both fuzzy unconstrained and constrained variational problems based on the concepts of differentiability and integrability of a fuzzy mapping that may be parameterized by the left and right-hand functions of its α-level sets.     

Strong stability of the mono-tubular heat exchanger equation with output feedback

We investigate asymptotic behavior of the C₀-semigroup T(t) associated with the mono-tubular heat exchanger equation with output feedback by a perturbation method. It is shown that T(t) is bounded if a constraint is satisfied by the parameters and the spatial distribution function. Further, applying the Arendt-Batty-Lyubich-Vu theorem, a criterion is established to judge strong stability of T(t).     

Geoadditive expectile regression

Quantile regression has emerged as one of the standard tools for regression analysis that enables a proper assessment of the complete conditional distribution of responses even in the presence of heteroscedastic errors. Quantile regression estimates are obtained by minimising an asymmetrically weighted sum of absolute deviations from the regression line, a decision theoretic formulation of the estimation problem that avoids a full specification of the error term distribution. Recent advances in mean regression have concentrated on making the regression structure more flexible by including nonlinear effects of continuous covariates, random effects or spatial effects. These extensions often rely on penalised least squares or penalised likelihood estimation with quadratic penalties and may therefore be difficult to combine with the linear programming approaches often considered in quantile regression. As a consequence, geoadditive expectile regression based on minimising an asymmetrically weighted sum of squared residuals is introduced. Different estimation procedures are presented including least asymmetrically weighted squares, boosting and restricted expectile regression. The properties of these procedures are investigated in a simulation study and an analysis on rental fees in Munich is provided where the geoadditive specification allows for an analysis of nonlinear effects of the size of flats or the year of construction and the spatial distribution of rents simultaneously.     

Magnetic and Temperature‐Sensitive Release Gels from Supramolecular Polymers

Supramolecular gels consisting of trivalent polyisobutylene and bivalent poly(ethylene oxide) are generated. Strong hydrogen bonding interactions, affixed to the end‐group moieties of the respective polymers (binding constant K_assn = 10⁵ M ^–1), serve as molecular glue, leading to the formation of weak gels. Two different gels were prepared: one, with a short telechelic poly(ethylene glycol) (PEG) segment (gel A), and one with a longer PEG segment (number‐average molecular weight M_n = 2000 g mol^–1) (gel B). Both gels show a significant increase in viscosity upon mixing of the two polymeric components, with a lag time of several minutes, indicative of nucleation mechanisms as the formation principle. However, only gel A displays classical gel‐like behavior, with a loss modulus G′ larger than the storage modulus G″ after formation. Both gels display microphase‐separated behavior with a spacing between 4–5 nm as probed via small‐angle X‐ray scattering (SAXS) and transmission electron microscopy (TEM) measurements. The incorporation of magnetic nanoparticles (Fe₂O₃; radius r = 3.5 nm) is successfully achieved, generating new magnetic gels with strongly thermoresponsive properties, displaying a strong temperature‐dependent release profile of included dye molecules. Magnetic measurements indicate a superparamagnetic behavior of the incorporated nanoparticles, prospecting the application as magneto‐sensitive delivery gels for pharmaceutical purposes.     

H optimal approximation for causal spline interpolation

In this paper, we give a causal solution to the problem of spline interpolation using H^∞ optimal approximation. Generally speaking, spline interpolation requires filtering the whole sampled data, the past and the future, to reconstruct the inter-sample values. This leads to non-causality of the filter, and this becomes a critical issue for real-time applications.Our objective here is to derive a causal system which approximates spline interpolation by H^∞ optimization for the filter. The advantage of H^∞ optimization is that it can address uncertainty in the input signals to be interpolated in design, and hence the optimized system has robustness property against signal uncertainty.We give a closed-form solution to the H^∞ optimization in the case of the cubic splines. For higher-order splines, the optimal filter can be effectively solved by a numerical computation. We also show that the optimal FIR (finite impulse response) filter can be designed by an LMI (linear matrix inequality), which can also be effectively solved numerically. A design example is presented to illustrate the result.     

Photonic theory of noise

The paper proposes that 1/f noise in materials and devices under non-equilibrium conditions is of electromagnetic origin rather than being related to charge carriers. For samples represented by simple resistors the analysis shows that the noise is due to the discrete nature of photons constituting the impinging electromagnetic flux from the source feeding the resistor. The paper presents detailed analysis of the external and internal electromagnetic fields of the resistor environment, with appropriate interpretation in terms of discrete photons. From quantum theory photons are known to retain their energy under interactions in linear environments. This property implies a departure from macroscopic electromagnetics in that photons cannot be partially transmitted and partially reflected, a phenomenon requiring appropriate modifications of boundary conditions at the resistor surface. These special demands call for inclusion of a supplementary internal resistor mode, serving as a lossless idler which is active only for matching purposes. At the resistor terminals the impinging photons give rise to excitation of RF current and voltage noise with an exact 1/f frequency distribution, which is in agreement with all available experimental measurements. The paper presents detailed formulae for noise spectral densities under general drive conditions from DC and RF sources of arbitrary internal resistance. The presented theoretical noise formulae have the same form as earlier empirical formulae for 1/f noise. With an RF source at frequency f₀ the analysis predicts noise with 1/|f-f₀| frequency distribution, which is compatible with available experimental observations.     

Delay-dependent H∞ filtering for discrete-time singular Markovian jump systems with time-varying delay and partially unknown transition probabilities

This paper is concerned with the H_∞ filtering design for a class of discrete-time singular Markovian jump systems with time-varying delay and partially unknown transition probabilities. The class of systems under consideration is more general and covers the singular Markovian delay systems with completely known and completely unknown transition probabilities as two special cases. A mode-dependent filter is constructed and by defining an appropriate stochastic Lyapunov functional combined with using the discrete Jensen inequality, a delay-dependent bounded real lemma (BRL) for the considered systems is established in terms of linear matrix inequalities (LMIs). Based on this, a sufficient condition on the existence of the desired filter which guarantees the admissibility and the H_∞ performance of the corresponding filtering error system is presented by employing the LMIs technique. Some numerical examples are provided to illustrate the effectiveness of the developed theoretical results.