A generalized neutral-type inclusion problem in the frame of the generalized Caputo fractional derivatives

In this paper, we study the existence of solutions for a generalized sequential Caputo-type fractional neutral differential inclusion with generalized integral conditions. The used fractional operator has the generalized kernel in the format of $( \vartheta (t)-\vartheta (s)) $ ( ϑ ( t ) − ϑ ( s ) ) along with differential operator $\frac{1}{\vartheta '(t)}\,\frac{\mathrm{d}}{\mathrm{d}t}$ 1 ϑ ′ ( t ) d d t . We obtain existence results for two cases of convex-valued and nonconvex-valued multifunctions in two separated sections. We derive our findings by means of the fixed point principles in the context of the set-valued analysis. We give two suitable examples to validate the theoretical results.

Fixed Point Results for Multivalued Mappings with Applications

In this manuscript, using the concept of multivalued contractions, some new Banach- and Caristi-type fixed point results are established in the context of metric spaces. For the reliability of the presented results, some examples and applications to Volterra integral type inclusion are also studied. The established results unify and generalize some existing results from the literature.

Comparative Pathogenesis, Genomics and Phylogeography of Mousepox

Ectromelia virus (ECTV), the causative agent of mousepox, has threatened laboratory mouse colonies worldwide for almost a century. Mousepox has been valuable for the understanding of poxvirus pathogenesis and immune evasion. Here, we have monitored in parallel the pathogenesis of nine ECTVs in BALB/cJ mice and report the full-length genome sequence of eight novel ECTV isolates or strains, including the first ECTV isolated from a field mouse, ECTV-MouKre. This approach allowed us to identify several genes, absent in strains attenuated through serial passages in culture, that may play a role in virulence and a set of putative genes that may be involved in enhancing viral growth in vitro. We identified a putative strong inhibitor of the host inflammatory response in ECTV-MouKre, an isolate that did not cause local foot swelling and developed a moderate virulence. Most of the ECTVs, except ECTV-Hampstead, encode a truncated version of the P4c protein that impairs the recruitment of virions into the A-type inclusion bodies, and our data suggest that P4c may play a role in viral dissemination and transmission. This is the first comprehensive report that sheds light into the phylogenetic and geographic relationship of the worldwide outbreak dynamics for the ECTV species.

Transfer of rare earth to alloy and inclusion during slag-metal reaction

Rare earth metal transfer from slag to alloy and inclusion was investigated by slag-metal reaction method. Rare earth oxide (CeO2) employed in the refining slags was used a sample case. The results show that direct application of rare earth oxide in the slag is an alternative to traditional way which uses pure rare earth metal or rare-earth ferrous alloy to add rare earth in an alloy. Slag-metal reaction method proves to be an effective way to improve the rare earth transfer from slags to alloys with high content of Al. The content of Ce in the alloy increased with the increasing CeO2/Al2O3 mass ratio of the slag. As the Ce concentration of molten alloy increased from 0 to 105 ppm, the Al2O3 type inclusion was changed into cerium oxide, cerium sulfide and cerium oxy-sulfide inclusions. In addition, the morphology of inclusions was transformed from irregular to near spherical. Finally, the mechanism was discussed by thermodynamic analysis.