Forcing strong convergence of Korpelevich’s method in Banach spaces with its applications in game theory

We develop a variant of Korpelevich’s method for solving variational inequality problems with pseudomonotone operators in Banach spaces. We establish the strong convergence of the sequence generated by the method under reasonable assumptions on the problem data. Finally, we justify the motivation of our theory by including compelling examples of infinite dimensional variational inequality problems for which our method is applicable.     

A Gleason–Kahane–Żelazko theorem for the Dirichlet space

We show that every linear functional on the Dirichlet space that is non-zero on nowhere-vanishing functions is necessarily a multiple of a point evaluation. Continuity of the functional is not assumed. As an application, we obtain a characterization of weighted composition operators on the Dirichlet space as being exactly those linear maps that send nowhere-vanishing functions to nowhere-vanishing functions.We also investigate possible extensions to weighted Dirichlet spaces with superharmonic weights. As part of our investigation, we are led to determine which of these spaces contain functions that map the unit disk onto the whole complex plane.     

Relative T -Injective Modules and Relative T -Flat Modules

Let T be a Wakamatsu tilting module. A module M is called (n, T)-copure injective (resp. (n, T)-copure flat) if ɛ _T ¹ (N, M) = 0 (resp. Γ₁ ^T (N, M) = 0) for any module N with T-injective dimension at most n (see Definition 2.2). In this paper, it is shown that M is (n, T)-copure injective if and only if M is the kernel of an I _n (T)-precover f: A → B with A ∈ Prod T. Also, some results on Prod T-syzygies are presented. For instance, it is shown that every nth Prod T-syzygy of every module, generated by T, is (n, T)-copure injective.     

A pointwise convergence for Sobolev space functions

Let 1<p<∞, and k,m be positive integers such that 0(k−2m)pn. Suppose ΩRⁿ is an open set, and Δ is the Laplacian operator. We will show that there is a sequence of positive constants c_j such that for every f in the Sobolev space W^k,p(Ω), for all xΩ except on a set whose Bessel capacity B_k−2m,p is zero.     

Copper chromite decorated on nitrogen-doped graphene aerogel as an efficient catalyst for thermal decomposition of ammonium perchlorate particles

Journal of Thermal Analysis and Calorimetry - The present study reports numerical simulations of water-based Al2O3 nanofluid flowing in a 2D channel with a heated wall-mounted obstacle. The...     

Synthesis of Some Novel γ-Spirolactones

Summary. We report on the addition of dialkyl acetylenedicarboxylate to 1-alkylisatins or tryptanthrine in the presence of triphenylphosphine which leads to highly functionalised novel unsaturated -spirolactones.     

Fibrous nanosilica spheres KCC-1@NH2 as highly effective and easily retrievable catalyst for the synthesis of chromenes

Research on Chemical Intermediates - A three-component reaction of naphthalene-1,5-diol, malononitrile and aromatic aldehydes has been achieved in the presence of fibrous nanosilica spheres...     

Effects of substrate on surface morphology, crystallinity, and photoluminescence properties of sputtered ZnO nano films

Effects of substrate on crystallinity, surface morphology, and luminescence properties of radio frequency sputtered zinc oxide (ZnO) thin films were investigated. A variety of materials such as Si (100), Si (111), Al₂O₃, quartz, and silicon carbide (SiC) wafers were examined as substrates for deposition of ZnO thin films. The results showed smooth and uniform growth of c-axis orientation films. The thickness of the layers was about 50 nm. The average grain sizes of films were about 10, 13, and 12 nm for Si (111), quartz, and SiC samples, respectively. The deposited film on Al₂O₃ showed the largest grain size, about 500 nm. Grazing incidence x-ray diffraction patterns of the samples revealed that sputtered layers on Al₂O₃ and quartz had better crystallinity with higher peak at (002) orientation compared to Si and SiC substrates. Moreover, the Al₂O₃ sample exhibited a weak peak at position of (100) planes of ZnO too. The photoluminescence spectra of the samples showed a typical luminescence behavior with a broad UV band, including a main peak at around 388 nm and a weak shoulder peak at around 381 nm, corresponding with bound excitonic recombination and free excitonic recombination, respectively. The luminescence peak revealed that the intensity of UV emission is not necessarily dependent on the grain sizes and the micro-structural quality of ZnO films.     

An output-feedback adaptive actuator failure compensation controller for systems with unknown state delays

This paper presents an output-feedback adaptive controller for a class of linear systems with unknown time-varying state delay and in the presence of actuator failures. We consider a common type of actuator failure in which some unknown system inputs may be stuck at some unknown fixed values and at unknown time instants. The adaptive controller is designed based on SPR–Lyapunov approach for relative degree one and two cases. Closed-loop system stability and asymptotic output tracking are proved using suitable Lyapunov–Krasovskii functional for each case. Simulation results are provided to demonstrate the effectiveness of the proposed results.