<abstract xmlns="http://www.w3.org/1999/xhtml">

In this paper, we use a characterization of the mutual multifractal Hausdorff dimension in terms of auxiliary measures to investigate the projections of measures with small supports.
</abstract>

Projections of measures with small supports

<abstract xmlns="http://www.w3.org/1999/xhtml">

We study the existence of solutions for random system of fractional differential equations with boundary nonlocal initial conditions. Our approach is based on random fixed point principles of Schaefer and Perov, combined with a vector approach that uses matrices that converge to zero. We prove existence and uniqueness results for these systems. Some examples are presented to illustrate the theory.
</abstract>

System of boundary random fractional differential equations via Hadamard derivative

<abstract xmlns="http://www.w3.org/1999/xhtml">

This paper investigates the problem of the existence and uniqueness of solutions under the generalized self-similar forms to the space-fractional diffusion equation. Therefore, through applying the properties of Schauder’s and Banach’s fixed point theorems; we establish several results on the global existence and blow-up of generalized self-similar solutions to this equation.
</abstract>

Laboratoire de Mathématique et Physique Appliquées

Laboratory of Pure and Applied Mathematics

Global existence and blow-up of generalized self-similar solutions for a space-fractional diffusion equation with mixed conditions

Examples of non connective <italic>C</italic>*-algebras

<abstract xmlns="http://www.w3.org/1999/xhtml">

We introduce the definition of the three-element equivalential algebra <bold>R</bold> with conjunction on the regular elements. We study the variety generated by <bold>R</bold> and prove the Representation Theorem. Then, we construct the finitely generated free algebras and compute the free spectra in this variety.
</abstract>

Equivalential algebras with conjunction on the regular elements

<abstract xmlns="http://www.w3.org/1999/xhtml">

In this article we define a metrizable space of multivalued maps. We show that the metric defined in this space is closely related to the homotopy of multivalued maps. Moreover, we study properties of this space and give a few practical applications of the new metric.
</abstract>

Metrizable space of multivalued maps

<abstract xmlns="http://www.w3.org/1999/xhtml">

We study the property of <italic>continuous Castelnuovo-Mumford regularity</italic>, for semihomogeneous vector bundles over a given Abelian variety, which was formulated in A. Küronya and Y. Mustopa [Adv. Geom. 20 (2020), no. 3, 401-412]. Our main result gives a novel description thereof. It is expressed in terms of certain normalized polynomial functions that are obtained via the Wedderburn decomposition of the Abelian variety’s endo-morphism algebra. This result builds on earlier work of Mumford and Kempf and applies the form of the Riemann-Roch Theorem that was established in N. Grieve [New York J. Math. 23 (2017), 1087-1110]. In a complementary direction, we explain how these topics pertain to the <italic>Index</italic> and <italic>Generic Vanishing Theory</italic> conditions for simple semihomogeneous vector bundles. In doing so, we refine results from M. Gulbrandsen [Matematiche (Catania) 63 (2008), no. 1, 123–137], N. Grieve [Internat. J. Math. 25 (2014), no. 4, 1450036, 31] and D. Mumford [Questions on Algebraic Varieties (C.I.M.E., III Ciclo, Varenna, 1969), Edizioni Cremonese, Rome, 1970, pp. 29-100].
</abstract>

Wedderburn components, the index theorem and continuous Castelnuovo-Mumford regularity for semihomogeneous vector bundles

<abstract xmlns="http://www.w3.org/1999/xhtml">

Let <italic>L</italic> be a not necessarily saturated lattice in ℤ<italic>n </italic>with a defining matrix <italic>B</italic>. We explicitly compute the set of circuits of <italic>L</italic> in terms of maximal minors of <italic>B</italic>. This has a variety of applications from toric to tropical geometry, from Gröbner to Graver bases, and from linear to binomial ideals.
</abstract>

A determinantal formula for circuits of integer lattices

Report of Meeting: 19th International Conference on Functional Equations and Inequalities, B¦dlewo, Poland, September 11–18, 2021

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