Clique-cutsets beyond chordal graphs

Truemper configurations (thetas, pyramids, prisms, and wheels) have played an important role in the study of complex hereditary graph classes (eg, the class of perfect graphs and the class of even-hole-free graphs), appearing both as excluded configurations, and as configurations around which graphs can be decomposed. In this paper, we study the structure of graphs that contain (as induced subgraphs) no Truemper configurations other than (possibly) universal wheels and twin wheels. We also study several subclasses of this class. We use our structural results to analyze the complexity of the recognition, maximum weight clique, maximum weight stable set, and optimal vertex coloring problems for these classes. Furthermore, we obtain polynomial -bounding functions for these classes.     

Self-adaptive gradient projection algorithms for variational inequalities involving non-Lipschitz continuous operators

Numerical Algorithms - In this paper, we introduce a self-adaptive inertial gradient projection algorithm for solving monotone or strongly pseudomonotone variational inequalities in real Hilbert...     

Law of the iterated logarithm for random graphs

A milestone in probability theory is the law of the iterated logarithm (LIL), proved by Khinchin and independently by Kolmogorov in the 1920s, which asserts that for iid random variables with mean 0 and variance 1 In this paper we prove that LIL holds for various functionals of random graphs and hypergraphs models. We first prove LIL for the number of copies of a fixed subgraph H. Two harder results concern the number of global objects: perfect matchings and Hamiltonian cycles. The main new ingredient in these results is a large deviation bound, which may be of independent interest. For random k‐uniform hypergraphs, we obtain the Central Limit Theorem and LIL for the number of Hamilton cycles.     

LIOUVILLE RESULTS FOR STABLE SOLUTIONS OF QUASILINEAR EQUATIONS WITH WEIGHTS

This paper is devoted to the quasilinear equation ■where p 2,Ω is a(bounded or unbounded) domain of R~N,w_1,w_2 are nonnegative continuous functions and f is an increasing function. We establish a Liouville type theorem for nontrivial stable solutions of the equation under some mild assumptions on Ω,w_1, w_2 and f, which extends and unifies several results on this topic.     

Medium modified fragmentation function: equivalence of the ACSX and QW formalisms in the high-Q2 region

We study the medium modified fragmentation function in high-energy heavy-ion collisions. We show that the ACSX and QW formalisms are equivalent to each other in the high-Q² limit in both theoretical and numerical aspects.     

Determination of Sulfide by Hematoxylin Multiwalled Carbon Nanotubes Modified Carbon Paste Electrode

This study investigates a new approach for the amperometric determination of sulfide using a hematoxylin multiwalled carbon nanotubes modified carbon paste electrode (HM‐MWCNTs/CPE). The experimental results show that HM‐MWCNTs/CPE significantly enhances the electrocatalytic activity towards sulfide oxidation. Cyclic voltammetric studies show that the peak potential of sulfide shifted from +400 mV at unmodified CPE to +175 mV at HM‐MWCNTs/CPE. The currents obtained from amperometric measurements at optimum conditions were linearly correlated with the concentration of sulfide. The calibration curve was obtained for sulfide concentrations in the range of 0.5–150×10^?6 mol L^?1. The detection limit was found to be 0.2×10^?6 mol L^?1 for the amperometric method. The proposed method was successfully applied to a river water sample in Pardubice, Czech Republic.     

Sun Exposure over a Lifetime in Australian Adults from Latitudinally Diverse Regions

Spatio‐temporal patterns in sun exposure underlie variations in skin cancer incidence and vitamin D deficiency, indicate effectiveness of sun protection programs and provide insights into future health risks. From 558 adults across four regions of Australia (Brisbane (27°S), Newcastle (33°S), Geelong and the Western Districts of Victoria (37°S) and Tasmania (43°S)), we collected: self‐report data on time‐in‐the‐sun from age 6 years; natural skin color and ethnicity; silicone skin casts (for cumulative skin damage); and serum for vitamin D status. Ambient ultraviolet radiation (UVR) at the location of residence, with time‐in‐the‐sun, was used to calculate a “UVR dose” for each year of life. Individuals maintained their ranking compared to their peers for time‐in‐the‐sun in summer compared to winter and across ages (Spearman rho 0.24–0.84, all P < 0.001). Time‐in‐the‐sun decreased with age in all birth cohorts, and over calendar time. Summer time‐in‐the‐sun increased with increasing latitude (P < 0.001). Seasonal variation in vitamin D status had greater amplitude and vitamin D deficiency increased with increasing latitude. Temporal patterns are consistent with effectiveness of sun protection programs. Higher relative time‐in‐the‐sun persists from childhood through adulthood. Lower summer time‐in‐the‐sun in the warmest location may have implications for predictions of UVR‐related health risks of climate change.