•Journal•ISSN: 2391-5455

# Open Mathematics

About: Open Mathematics is an academic journal. The journal publishes majorly in the area(s): Geometry and topology & Number theory. It has an ISSN identifier of 2391-5455. It is also open access. Over the lifetime, 1853 publication(s) have been published receiving 12756 citation(s). The journal is also known as: Central European Journal of Mathematics.

Topics: Geometry and topology, Number theory, Boundary value problem, Nonlinear system, Banach space

##### Papers published on a yearly basis

##### Papers

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TL;DR: This work has investigated in more detail some new properties of this derivative and some useful related theorems and some new definitions have been introduced.

Abstract: Abstract Recently, the conformable derivative and its properties have been introduced. In this work we have investigated in more detail some new properties of this derivative and we have proved some useful related theorems. Also, some new definitions have been introduced.

282 citations

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TL;DR: In this paper, the authors discuss the origin, theory and applications of left-symmetric algebras (LSAs) in geometry in physics and give a survey of the fields where LSAs play an important role.

Abstract: In this survey article we discuss the origin, theory and applications of left-symmetric algebras (LSAs in short) in geometry in physics. Recently Connes, Kreimer and Kontsevich have introduced LSAs in mathematical physics (QFT and renormalization theory), where the name pre-Lie algebras is used quite often. Already Cayley wrote about such algebras more than hundred years ago. Indeed, LSAs arise in many different areas of mathematics and physics. We attempt to give a survey of the fields where LSAs play an important role. Furthermore we study the algebraic theory of LSAs such as structure theory, radical theory, cohomology theory and the classification of simple LSAs. We also discuss applications to faithful Lie algebra representations.

244 citations

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TL;DR: In this article, the authors extend the study of fractal operator theory for multivalued operators on complete b-metric spaces to the case of complete or compact metric spaces.

Abstract: Fractals and multivalued fractals play an important role in biology, quantum mechanics, computer graphics, dynamical systems, astronomy and astrophysics, geophysics, etc. Especially, there are important consequences of the iterated function (or multifunction) systems theory in several topics of applied sciences. It is known that examples of fractals and multivalued fractals are coming from fixed point theory for single-valued and multivalued operators, via the so-called fractal and multi-fractal operators. On the other hand, the most common setting for the study of fractals and multi-fractals is the case of operators on complete or compact metric spaces. The purpose of this paper is to extend the study of fractal operator theory for multivalued operators on complete b-metric spaces.

168 citations

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TL;DR: In this article, Miyachi et al. showed that a compact corigid object of a triangulated category induces a structure similar to a t-structure which they shall call a co-tstructure, and also showed that the coheart of this non-degenerate co-Tstructure is equivalent to Mod(End(End(\( \mathcal{S} \))op), and hence an abelian subcategory of the category.

Abstract: In the work of Hoshino, Kato and Miyachi, [11], the authors look at t-structures induced by a compact object, \( C \), of a triangulated category, \( \mathcal{T} \), which is rigid in the sense of Iyama and Yoshino, [12]. Hoshino, Kato and Miyachi show that such an object yields a non-degenerate t-structure on \( \mathcal{T} \) whose heart is equivalent to Mod(End(\( C \))op). Rigid objects in a triangulated category can the thought of as behaving like chain differential graded algebras (DGAs). Analogously, looking at objects which behave like cochain DGAs naturally gives the dual notion of a corigid object. Here, we see that a compact corigid object, \( \mathcal{S} \), of a triangulated category, \( \mathcal{T} \), induces a structure similar to a t-structure which we shall call a co-t-structure. We also show that the coheart of this non-degenerate co-t-structure is equivalent to Mod(End(\( \mathcal{S} \))op), and hence an abelian subcategory of \( \mathcal{T} \).

135 citations

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İnönü University

^{1}TL;DR: In this paper, the authors introduce anti-invariant Riemannian submersions from almost Hermitian manifolds onto Riemanian manifold and give necessary and sufficient conditions for a Langrangian submersion to be totally geodesic.

Abstract: We introduce anti-invariant Riemannian submersions from almost Hermitian manifolds onto Riemannian manifolds. We give an example, investigate the geometry of foliations which are arisen from the definition of a Riemannian submersion and check the harmonicity of such submersions. We also find necessary and sufficient conditions for a Langrangian Riemannian submersion, a special anti-invariant Riemannian submersion, to be totally geodesic. Moreover, we obtain decomposition theorems for the total manifold of such submersions.

108 citations