arXiv subjects

Mariia Soloviova

Publications and source records attributed to Mariia Soloviova.

6 recordsLinked to original sources

arXiv2024

A mathematical model for fibrous dysplasia: The role of the flow of mutant cells

Fibrous dysplasia (FD) is a mosaic non-inheritable genetic disorder of the skeleton in which normal bone is replaced by structurally unsound fibro-osseous tissue. There is no curative treatment for FD, partly because its pathophysiology is not yet fully known. We present a simple mathematical model of the disease incorporating its basic known biology, to gain insight on the dynamics of the involved bone-cell populations, and shed light on its pathophysiology. Our mathematical models account for the dynamic evolution over time of several interacting populations of bone cells averaged over a volume of bone of sufficient size in order to obtain consistent results. We develop an analytical study of the model and study its basic properties. The existence and stability of steady states are studied, an analysis of sensitivity on the model parameters is done, and different numerical simulations provide findings in agreement with the analytical results. We discuss the model dynamics match with known facts on the disease, and how some open questions could be addressed using the model.

q-bio.TO↗

arXiv2020

Efficient representation of supply and demand curves on day-ahead electricity markets

Our paper aims to model supply and demand curves of electricity day-ahead auction in a parsimonious way. Our main task is to build an appropriate algorithm to present the information about electricity prices and demands with far less parameters than the original one. We represent each curve using mesh-free interpolation techniques based on radial basis function approximation. We describe results of this method for the day-ahead IPEX spot price of Italy.

q-fin.PR↗

arXiv2017

Quantitative version of the Bishop-Phelps-Bollobás theorem for operators with values in a space with the property $β$

The Bishop-Phelps-Bollobás property for operators deals with simultaneous approximation of an operator $T$ and a vector $x$ at which $T: X\rightarrow Y$ nearly attains its norm by an operator $F$ and a vector $z$, respectively, such that $F$ attains its norm at $z$. We study the possible estimates from above and from below for parameters that measure the rate of approximation in the Bishop-Phelps-Bollobás property for operators for the case of $Y$ having the property $β$ of Lindenstrauss.

math.FA↗

arXiv2017

$Γ$-flatness and Bishop-Phelps-Bollobás type theorems for operators

The Bishop-Phelps-Bollobás property deals with simultaneous approximation of an operator $T$ and a vector $x$ at which $T$ nearly attains its norm by an operator $T_0$ and a vector $x_0$, respectively, such that $T_0$ attains its norm at $x_0$. In this note we extend the already known results about {the} Bishop-Phelps-Bollobás property for Asplund operators to a wider class of Banach spaces and to a wider class of operators. Instead of proving a BPB-type theorem for each space separately we isolate two main notions: $Γ$-flat operators and Banach spaces with ACK$_ρ$ structure. In particular, we prove a general BPB-type theorem for $Γ$-flat operators acting to a space with ACK$_ρ$ structure and show that uniform algebras and spaces with the property $β$ have ACK$_ρ$ structure. We also study the stability of the ACK$_ρ$ structure under some natural Banach space theory operations. As a consequence, we discover many new examples of spaces $Y$ such that the Bishop-Phelps-Bollobás property for Asplund operators is valid for all pairs of the form ($X,Y$).

math.FA↗

arXiv2016

Norm attaining Lipschitz functionals

We prove that for a given Banach space $X$, the subset of norm attaining Lipschitz functionals in $\mathrm{Lip}_0(X)$ is weakly dense but not strongly dense. Then we introduce a weaker concept of directional norm attainment and demonstrate that for a uniformly convex $X$ the set of directionally norm attaining Lipschitz functionals is strongly dense in $\mathrm{Lip}_0(X)$ and, moreover, that an analogue of the Bishop-Phelps-Bollobás theorem is valid.

math.FA↗

arXiv2014

Two refinements of the Bishop-Phelps-Bollobás modulus

Extending the celebrated result by Bishop and Phelps that the set of norm attaining functionals is always dense in the topological dual of a Banach space, Bollobás proved the nowadays known as the Bishop-Phelps-Bollobás theorem, which allows to approximate at the same time a functional and a vector in which it almost attains the norm. Very recently, two Bishop-Phelps-Bollobás moduli of a Banach space have been introduced [J. Math. Anal. Appl. 412 (2014), 697--719] to measure, for a given Banach space, what is the best possible Bishop-Phelps-Bollobás theorem in this space. In this paper we present two refinements of the results of that paper. On the one hand, we get a sharp general estimation of the Bishop-Phelps-Bollobás modulus as a function of the norms of the point and the functional, and we also calculate it in some examples, including Hilbert spaces. On the other hand, we relate the modulus of uniform non-squareness with the Bishop-Phelps-Bollobás modulus obtaining, in particular, a simpler and quantitative proof of the fact that a uniformly non-square Banach space cannot have the maximum value of the Bishop-Phelps-Bollobás modulus.

math.FA↗