We consider the discrete Dirichlet boundary value problem for a discrete elliptic pseudodifferential equation in the quadrant and study its solvability in discrete counterparts of the ...Sobolev–Slobodetskii space. The study is based on a special factorization of the elliptic symbol. We compare the solutions to the discrete Dirichlet problem and its continuous counterpart.
A model elliptic pseudodifferential equation in a polyhedral cone is considered, and the situation when some of the parameters of the cone tend to their limiting values is investigated. In ...Sobolev–Slobodetskii spaces, a solution of the equation in the cone is constructed in the case of a special wave factorization of the elliptic symbol. It is shown that a limit solution of the boundary value problem with an additional integral condition can exist only under additional constraints on the boundary function.
We consider discrete pseudo-differential equations with elliptic symbols and the corresponding discrete boundary-value problems in special canonical domains of multidimensional spaces. The ...solvability of such equations and boundary-value problems in discrete analogs of Sobolev–Slobodetsky spaces is examined.
On Certain Operator Families Vasilyev, V. B.
Journal of mathematical sciences,
04/2022, Letnik:
262, Številka:
6
Journal Article
Recenzirano
Odprti dostop
In this paper, we propose an abstract scheme for the study of special operators and apply this scheme to examining elliptic pseudo-differential operators and related boundary-value problems on ...manifolds with nonsmooth boundaries. In particular, we consider cases where boundaries may contain conical points, edges of various dimensions, and even peak points. Using the constructions proposed, we present well-posed formulations of boundary-value problems for elliptic pseudo-differential equations on manifolds discussed in Sobolev–Slobodecky spaces.
Neutrophil myeloperoxidase (MPO) plays an important role in protecting the body against infections. MPO products–hypohalous acids and phenoxyl radicals–are strong oxidants that can damage not only ...foreign intruders but also host tissues, including blood plasma proteins. Here, we compared the MPO-induced oxidation of two plasma proteins with antioxidant properties–human serum albumin (HSA) and ceruloplasmin (CP). Incubation of both proteins with hypochlorite (NaOCl) or catalytically active MPO (MPO + H
2
O
2
), which synthesizes hypochlorous acid (HOCl) in the presence of chloride ions, resulted in the quenching of protein tryptophan fluorescence. Oxidation-induced changes in the structures of HSA and CP were different. HSA efficiently neutralized MPO-generated oxidants without protein aggregation, while CP oxidation resulted in the formation of large aggregates stabilized by strong covalent bonds between the aromatic amino acid residues. Tyrosine is present in the plasma as free amino acid and also as a component of the polypeptide chains of the proteins. The number of tyrosine residues in a protein does not determine its propensity for aggregate formation. In the case of C P, protein aggregation was primarily due to the high content of tryptophan residues in its polypeptide chain. MPO-dependent oxidation of free tyrosine results in the formation of tyrosyl radicals, that do not oxidize aromatic amino acid residues in proteins because of the high rate of recombination with dityrosine formation. At the same time, free tyrosine can influence MPO-induced protein oxidation due to its ability to modulate HOCl synthesis in the MPO active site.
On Discrete Neumann Problem in a Quadrant Mashinets, A. A.; Vasilyev, A. V.; Vasilyev, V. B.
Lobachevskii journal of mathematics,
03/2023, Letnik:
44, Številka:
3
Journal Article
Recenzirano
Odprti dostop
We study a discrete analogue on the Neumann boundary value problem for elliptic pseudo-differential equation in a quadrant. This approach is based on a special factorization of an elliptic symbol ...which permits to construct a general solution for a discrete pseudo-differential equation in discrete analogues of Sobolev–Slobodetskii spaces. The discrete Neumann boundary conditions are considered in the paper. Unique solvability of discrete Neumann boundary value problem is proved and a comparison between discrete and continuous solutions is given.
We study some discrete boundary value problems for discrete elliptic pseudo-differential equations in a half-space. These statements are related with a special periodic factorization of an elliptic ...symbol and a number of boundary conditions depends on an index of periodic factorization. This approach was earlier used by authors for studying special types of discrete convolution equations. Here we consider more general equations and functional spaces.
Discrete analogs of pseudo-differential operators and equations in discrete Sobolev–Slobodetsky spaces are considered. Using suitable discrete boundary conditions, we prove the unique solvability of ...the discrete boundary-value problem.
The pathogenesis of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection involves dysregulations of iron metabolism, and although the mechanism of this pathology is not yet fully ...understood, correction of iron metabolism pathways seems a promising pharmacological target. The previously observed effect of inhibiting SARS-CoV-2 infection by ferristatin II, an inducer of transferrin receptor 1 (TfR1) degradation, prompted the study of competition between Spike protein and TfR1 ligands, especially lactoferrin (Lf) and transferrin (Tf). We hypothesized molecular mimicry of Spike protein as cross-reactivity of Spike-specific antibodies with Tf and Lf. Thus, strong positive correlations (R
2
> 0.95) were found between the level of Spike-specific IgG antibodies present in serum samples of COVID-19-recovered and Sputnik V-vaccinated individuals and their Tf-binding activity assayed with peroxidase-labeled anti-Tf. In addition, we observed cross-reactivity of Lf-specific murine monoclonal antibody (mAb) towards the SARS-CoV-2 Spike protein. On the other hand, the interaction of mAbs produced to the receptor-binding domain (RBD) of the Spike protein with recombinant RBD protein was disrupted by Tf, Lf, soluble TfR1, anti-TfR1 aptamer, as well as by peptides RGD and GHAIYPRH. Furthermore, direct interaction of RBD protein with Lf, but not Tf, was observed, with affinity of binding estimated by K
D
to be 23 nM and 16 nM for apo-Lf and holo-Lf, respectively. Treatment of Vero E6 cells with apo-Lf and holo-Lf (1–4 mg/mL) significantly inhibited SARS-CoV-2 replication of both Wuhan and Delta lineages. Protective effects of Lf on different arms of SARS-CoV-2-induced pathogenesis and possible consequences of cross-reactivity of Spike-specific antibodies are discussed.
The paper is devoted to studying limit behavior for a solution of model elliptic pseudo-differential equation with some integral boundary condition in 4-wedge conical canonical 3D singular domain ...with two parameters. It is shown that the solution of such boundary value problem can have a limit with respect to endpoint values of the parameters in appropriate Sobolev–Slobodetskii space if the boundary function is a solution of a special functional singular integral equation.
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