Notes on set theory, mainly forcing. The first four sections closely follow the lecture notes Williams [8] and the book Kunen [4]. The last section covers topics from various sources, as indicated there. Hopefully, all errors are mine. 1. The Suslin problem 1.1. The Suslin hypothesis. Recall that R is the unique dense, complete and separable order without endpoints (up to isomorphism). It follo...

In this study, dual S-scheme ZnIn2S4–Al2O3–ZnO (ZIS–Al–Zn) heterojunctions were produced by a facile, low cost, and rapid combustion technique. These accelerated the photocatalytic hydrogen production due to multi-channel-promoted separation of photocarriers. By optimizing content components, synthesized ZIS–Al–Zn composite with 20 wt% ZnIn2S4 30 Al2O3 in demonstrated highest rate 54.2 mmol g–1...

We consider drawings of graphs that contain dense subgraphs. We introduce intersection-link representations for such graphs, in which each vertex u is represented by a geometric object R(u) and each edge (u, v) is represented by the intersection between R(u) and R(v), if it belongs to a dense subgraph, or by a curve connecting the boundaries ofR(u) andR(v), otherwise. We study a notion of plana...

, (p s c S p th cepstral coefficient of the s th sub-bands { c 1 (1,p) = c(p) is the p th full-band cepstral parameter} S number of sub-bands Y(k) k th log spectral magnitude K number of log spectral magnitudes) (k Y ′ ′ k th log-energy outputs of the mel-scale filterbank K ′ ′ number of log-energy outputs of the mel-scale filterbank h t weight associated with the t th segment U number of compe...

Natural gas is a promising elective source of methane (CH4) due to its accessibility and renewability. However, unfortunately, high rate carbon dioxide (CO2) very little hydrogen sulfide (H2S) found in this CH4 source. These compounds must be removed get natural satisfactory quality. One the most modern common strategies synchronous CO2 and...