西北大学(南非)

This paper investigates the regularity and fractal dimensions of the Katugampola fractional integral of the generalized Takagi function Ta,b(x) =infinity & sum;infinity(n=0)a-ndist(bnx,& Zopf;) with parameters satisfying b > a > 1. While fractional integral is known to smooth fractal functions, the precise effect of the Katugampola operator on the generalized Takagi function has remained unexplored. This operator unifies the Riemann-Liouville fractional integral and the Hadamard fractional integral. We aim to characterize how the fractional order alpha > 0 and the auxiliary parameter rho > 0 affect the H & ouml;lder regularity and the fractal dimensions of . Using analytical estimates, the -dimension technique, and H & ouml;lder mapping theory, we obtain sharp uniform H & ouml;lder exponents for all parameter regimes, including critical cases where logarithmic corrections appear. For the Riemann-Liouville case , it has been shown that dim(B)graph(F) = max{1,2 - log(b)a-alpha}, which confirms a linear decay with alpha. For general rho > 0, we provide rigorous upper and lower bounds alongside a conjecture. Numerical experiments also validate these theoretical results. Our findings quantify how the parameter rho interpolates continuously between strong smoothing in the Riemann-Liouville sense and weak smoothing in the Hadamard sense, thereby offering a tunable framework for signal processing and image analysis.

We present a systematic X-ray spectral analysis of 27 giant radio galaxies (GRGs) using archival XMM-Newton and Chandra data. Roughly 44% of the sample show intrinsic absorption (NH,int≳1021cm−2), while several exhibit narrow Fe Kα emission lines with equivalent widths up to  ∼ 570 eV. Soft X-ray features are also common, including thermal plasma emission (kT ∼ 0.2–0.8 keV) and ionized absorbers, in some cases consistent with high-velocity outflows. The photon indices are typically hard (median Γ ∼ 1.6), in line with radio-loud AGN. A comparison between nuclear X-ray luminosity and extended radio power shows that many sources host relatively strong X-ray cores compared to their lobes, pointing toward possible restarted nuclear activity. For 10 GRGs with published black hole masses, we explore preliminary relations with X-ray luminosity, Eddington ratio, and photon index. We find a positive trend between MBH and L2−10keV, while Eddington ratios show no clear dependence on mass. A tentative negative relation between λEdd and Γ hints at inefficient accretion, although confirmation will require larger samples. Overall, GRGs display diverse nuclear conditions and accretion states, supporting scenarios where obscuration, episodic or restarted activity, and low-efficiency accretion shape their long-term evolution.

Jet fuel with high thermal stability serves as both an energy source to power the aircraft and a coolant to reduce its thermal load. However, when jet fuel is used as a coolant and flows through various systems, it interacts with dissolved trace iron, reducing its thermal stability. Using decalin as a model fuel, we conduct thermal oxidation experiments on decalin with metallic iron using PetroOxy equipment. The oxidation products at different oxidation levels of the model fuel were separated and characterized, and the possible reaction pathway between metallic iron and decalin was studied by DFT. The results showed that the presence of iron accelerated fuel oxidation throughout the entire oxidation process. At low oxidation levels, higher concentrations of metallic iron resulted in greater oxidation rates, while at high oxidation levels, higher concentrations led to lower oxidation rates. DFT calculations revealed that the addition of iron made the normally stable carbon sites of decalin more reactive with O2, generating a lower-energy product complex (RO-Fe-OH). Compared to the initial hydroperoxide (ROOH) state, the O-O bond in this structure was more easily broken, facilitating the release of RO center dot and HO center dot radicals. The required energy for this process was lower than that needed for thermal decomposition of free hydroperoxide. However, as the oxidation degree increased, the oxidation rate initially increased and then decreased. This phenomenon was attributed to the formation of an iron complex (ROO-Fe-OOR) with a stable electronic structure and lower energy. In this complex, the iron atoms coordinate with oxygen atoms, stabilizing the peroxide radical (ROO center dot) and terminating the oxidation chain. These results demonstrate the influence of metallic iron on the thermal oxidation stability of decalin and elucidate its interaction mechanism with hydrocarbon molecules. This understanding contributes to a better comprehension of metallic iron's effects on jet fuel thermal oxidation.

We study a half-interval distribution problem for polynomial residues modulo an odd prime p: how often the fractional part of φ(x)/p lies in the upper half of the unit interval as x ranges over 1≤x 12}=p4+Oφ(plog2⁡p). We then show that the error term can be improved to Oφ(plog⁡p) for arbitrary quadratic polynomials and for polynomials satisfying suitable reflection symmetries. For even monomials φ(x)=xm, we further obtain the bound Om(plog⁡log⁡p) under the Generalized Riemann Hypothesis. Finally, in the case m=2, we prove an unconditional matching lower bound, showing that the factor log⁡log⁡p is best possible in this setting.