Existence of the solution to a nonlocal-in-time evolutional problem

This work is devoted to the study of a nonlocal-in-time evolutional problem for the first order differential equation in Banach space. Our primary approach, although stems from the convenient technique based on the reduction of a nonlocal problem to its classical initial value analogue, uses more advanced analysis. That is a validation of the correctness in definition of the general solution representation via the Dunford-Cauchy formula. Such approach allows us to reduce the given existence problem to the problem of locating zeros of a certain entire function. It results in the necessary and sufficient conditions for the existence of a generalized (mild) solution to the given nonlocal problem. Aside of that we also present new sufficient conditions which in the majority of cases generalize existing results.Comment: This article is an extended translation of the part of Dmytro Sytnyk's PhD Thesi

Exponentially Convergent Algorithms for Abstract Differential Equations

This book presents new accurate and efficient exponentially convergent methods for abstract differential equations with unbounded operator coefficients in Banach space. These methods are highly relevant for the practical scientific computing since the equations under consideration can be seen as the meta-models of systems of ordinary differential equations (ODE) as well as the partial differential equations (PDEs) describing various applied problems. The framework of functional analysis allows one to obtain very general but at the same time transparent algorithms and mathematical results whic

SNPs Associated with Foliar Phylloxera Tolerance in Hybrid Grape Populations Carrying Introgression from <i>Muscadinia</i>

Leaf-feeding phylloxera decreases the photosynthetic activity of a grape plant, leading to decreasing number of fruit buds. In addition, phylloxera larvae emerging from the leaf galls may colonize the roots, negatively affecting the growth of the grape plant. In this study, we evaluated host tolerance of three grapevine hybrid populations obtained from crossing of the same maternal grapevine M. no. 31-77-10 with interspecific hybrids carrying introgressions from Muscadinia and other North American Vitis species against leaf-feeding grape phylloxera. Combining genotyping data of the populations obtained with 12,734 SNPs and their resistance phenotypes evaluated in the laboratory experiment, we performed an association study. As the result of GWAS, nine SNPs with the lowest significant p-values were discovered in the whole sample of 139 hybrids as associated with variation of the scores ‘the percentage of infested leaves’ and ‘intensity of gall formation’. Three of the SNPs on LG 7 were located in the same chromosome interval where a major QTL (RDV6) for root phylloxera resistance was reported from Muscadine background. Two SNPs on LG 8 were detected within the gene, encoding E3 ubiquitin-protein ligase UPL4 involved in apoptosis. SNPs detected on LG 13 and LG 18 may overlap with the previously reported QTLs for phylloxera resistance inherited from V. cinerea