VARIATION ON A THEME BY KISELEV AND NAZAROV: HÖLDER ESTIMATES FOR NONLOCAL TRANSPORT-DIFFUSION, ALONG A NON-DIVERGENCE-FREE BMO FIELD

We prove uniform Hölder regularity estimates for a transport-diffusion equation with a fractional diffusion operator and a general advection field in of bounded mean oscillation, as long as the order of the diffusion dominates the transport term at small scales; our only requirement is the smallness of the negative part of the divergence in some critical Lebesgue space. In comparison to a celebrated result by Silvestre, our advection field does not need to be bounded. A similar result can be obtained in the supercritical case if the advection field is Hölder continuous. Our proof is inspired by Kiselev and Nazarov and is based on the dual evolution technique. The idea is to propagate an atom property (i.e., localisation and integrability in Lebesgue spaces) under the dual conservation law, when it is coupled with the fractional diffusion operator.

Pottery complex of the Bronze Age burial ground of Kulevchi VI: typology and technical-technological analysis

This paper presents the results of the typological study and technical-technological analysis of the pottery complex from the Late Bronze Age burial ground of Kulevchi VI (Southern Ural, Russia). The typological analysis of 107 objects yielded 10 types of the vessels correlated with four cultural and chronological groups: Petrovka; Early Alakul; Alakul and Alakul-Fedorov. The presence of all designated groups and types of vessels in the burial ground indicates functioning of the necropolis during the whole period of existence of the Alakul Culture: types IА, IБ and IВ — the formation stage of the actual Alakul Culture associated with the pottery of the Petrovka type of the sites; types IIБ, IIВ, III — the golden age of the Alakul Culture; and type IIГ — the late stage of the Alakul Cul-ture, reflecting the engagement with sub-cultural groups of the Fedorovskaya population. The technical-technological analysis using the method developed by A.A. Bobrinsky revealed the pottery skills of the population making different types of vessels. Amongst the studied population, only natural clays were used for pottery. The molding composition included organic additives and talcum gruss, and sometimes also chamotte. One program of constructing of the clay blank, the vaulted bottom type, has been identified, and the use of the patchwork spiral applique has been recorded. The surface of the vessels was smoothened and subjected to glazing. The firing of pottery items was carried out in fire-pits and hearths. Close similarity of the potters’ skills at different stages of pottery making has been observed for the items of the Petrovka, Early and Classical Alakul and Alakul-Fedorov Cultures. Correlation of the collected information with the known data on the ceramics of the Petrovka and Alakul types demonstrates commonality of the skills possessed by these groups of the population of Southern Ural and Northern Kazakhstan. On the basis of similarity of the pottery-making technologies of different chronological groups of the burial grounds of Kulevchi VI, it has been established that the development of the pottery-making traditions of the population was taking place within affinal groups. The similarity of the pottery traditions and gra-dual evolution of the Petrovka, Early Alakul; Alakul and Alakul-Fedorov groups allow considering them within the framework of the same phenomenon — the Alakul Culture.

Research on Multi-UAV Collaborative Search in Dynamic Environment

Combine the uncertainty of dynamic targets, a multi-UAV reconnaissance scheduling problem model was constructed under dynamic environment, take advantage of the characteristics of dual evolution, the insertion point operator and reverse sequence operator are improved, and the problem is solved by the artificial bee colony algorithm based on the semi-random search strategy. Finally, the simulation experiment was done in the background of South China Sea, and the experimental result shows the effectiveness and feasibility of the proposed algorithm for solving the multi-UAV reconnaissance scheduling problem.

Optimal Control of Evolution Macro-Hybrid Mixed Variational Inclusions

Optimal control problems governed by primal and dual evolution macro-hybrid mixed variational state inclusions, in reflexive Banach spaces, are studied. This is a spatially localized macro-hybrid variational version of our mixed optimal control theory published in Appl. Math. Optim. 68, 2013, 445-473, where the solvability analysis of the state systems is given in terms of duality principles, and the mixed optimality analysis is performed via a perturbation conjugate duality method. Applications to nonlinear constrained problems from mechanics exemplify the theory.