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 Numerical Method for Abstract Cauchy Problem with Fractional Derivative of Caputo Type

We present an exponentially convergent numerical method to approximate the solution of the Cauchy problem for the inhomogeneous fractional differential equation with an unbounded operator coefficient and Caputo fractional derivative in time. The numerical method is based on the newly obtained solution formula that consolidates the mild solution representations of sub-parabolic, parabolic and sub-hyperbolic equations with sectorial operator coefficient $A$ and non-zero initial data. The involved integral operators are approximated using the sinc-quadrature formulas that are tailored to the spectral parameters of $A$, fractional order $\alpha$ and the smoothness of the first initial condition, as well as to the properties of the equation's right-hand side $f(t)$. The resulting method possesses exponential convergence for positive sectorial $A$, any finite $t$, including $t = 0$, and the whole range $\alpha \in (0,2)$. It is suitable for a practically important case, when no knowledge of $f(t)$ is available outside the considered interval $t \in [0, T]$. The algorithm of the method is capable of multi-level parallelism. We provide numerical examples that confirm the theoretical error estimates

The Neural Cell Adhesion Molecule Promotes Maturation of the Presynaptic Endocytotic Machinery by Switching Synaptic Vesicle Recycling from Adaptor Protein 3 (AP-3)- to AP-2-Dependent Mechanisms

Newly formed synapses undergo maturation during ontogenetic development via mechanisms that remain poorly understood. We show that maturation of the presynaptic endocytotic machinery in CNS neurons requires substitution of the adaptor protein 3 (AP-3) with AP-2 at the presynaptic plasma membrane. In mature synapses, AP-2 associates with the intracellular domain of the neural cell adhesion molecule (NCAM). NCAM promotes binding of AP-2 over binding of AP-3 to presynaptic membranes, thus favoring the substitution of AP-3 for AP-2 during formation of mature synapses. The presynaptic endocytotic machinery remains immature in adult NCAM-deficient (NCAM−/−) mice accumulating AP-3 instead of AP-2 and its partner protein AP180 in synaptic membranes and vesicles. NCAM deficiency or disruption of the NCAM/AP-2 complex in wild-type (NCAM+/+) neurons by overexpression of AP-2 binding-defective mutant NCAM interferes with efficient retrieval of the synaptic vesicle v-SNARE synaptobrevin 2. Abnormalities in synaptic vesicle endocytosis and recycling may thus contribute to neurological disorders associated with mutations in NCAM

The New Public Management paradigm as a further interaction of the public and private sectors

The purpose of this study is to determine the impact of the development of the paradigm of the new public management on improving the efficiency of the public administration system; the need to use the basic principles of theory in the practice of public administration; the state's opportunities to benefit from strengthening cooperation between the public and private sectors

Photophysical and electronic properties of bismuth-perovskite shelled lead sulfide quantum dots

Metal halide perovskite shelled quantum dot solids have recently emerged as an interesting class of solution-processable materials that possess the desirable electronic properties of both quantum dots and perovskites. Recent reports have shown that lead sulfide quantum dots (PbS QDs) with perovskite ligand-shells can be successfully utilized in (opto)electronic devices such as solar cells, photoconductors, and field-effect transistors (FETs), a development attributed to the compatibility of lattice parameters between PbS and certain metal halide perovskites that results in the growth of the perovskite shell on the PbS QDs. Of several possible perovskite combinations used with PbS QDs, bismuth-based variants have been shown to have the lowest lattice mismatch and to display excellent performance in photoconductors. However, they also display photoluminescence (PL), which is highly sensitive to surface defects. In this work, we present an investigation of the transport and optical properties of two types of bismuth-based perovskite (MA(3)BiI(6) and MA(3)Bi(2)I(9)) shelled PbS QDs. Our photophysical study using temperature-dependent PL spectroscopy between 5 and 290 K indicates that the PL efficiency of the reference oleic acid (OA) capped samples is much higher than that of the Bi-shelled ones, which suffer from traps, most likely formed at their surfaces during the phase-transfer ligand exchange process. Nevertheless, the results from electrical measurements on FETs show the successful removal of the native-OA ligands, displaying electron dominated transport with modest mobilities of around 10(-3) cm(2) [V s](-1) - comparable to the reported values for epitaxial Pb-based shelled samples. These findings advance our understanding of perovskite shelled QD-solids and point to the utility of these Bi-based variants as contenders for photovoltaic and other optoelectronic applications. Published under license by AIP Publishing