<abstract xmlns="http://www.w3.org/1999/xhtml">We consider the paracomplex version of the notion of mixed linear spaces introduced by M. Jurchescu in [<xref ref-type="bibr" rid="j_ausm-2017-0020_ref_001_w2aab3b7ab1b6b1ab1ab1Aa">4</xref>] by replacing the complex unit i with the paracomplex unit j, j2 = 1. The linear algebra of these spaces is studied with a special view towards their morphisms.</abstract>

Para-mixed linear spaces

<abstract xmlns="http://www.w3.org/1999/xhtml">In this paper we give the best form of a strongly starlikeness condition. Some consequences of this result are deduced. The basic tool of the research is the method of differential subordinations.</abstract>

The sharp version of a strongly starlikeness condition

<abstract xmlns="http://www.w3.org/1999/xhtml">In this paper we analyze the monotony of the function 
<inline-formula><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_ausm-2017-0022_eq_001.png"></inline-graphic><math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mrow><mfrac><mrow><mtext>ln</mtext><mi> </mi><mi>Γ</mi><mo>(</mo><mtext>x</mtext><mo>)</mo></mrow><mrow><mtext>ln</mtext><mi> </mi><mo>(</mo><msup><mtext>x</mtext><mn>2</mn></msup><mo>+</mo><mi>τ</mi><mo>)</mo><mo>-</mo><mtext>ln</mtext><mi> </mi><mo>(</mo><mtext>x</mtext><mo>+</mo><mi>τ</mi><mo>)</mo></mrow></mfrac></mrow></math><tex-math>${{{\rm{ln}}\,\Gamma ({\rm{x}})} \over {{\rm{ln}}\,({\rm{x}}^2 + \tau) - {\rm{ln}}\,({\rm{x}} + \tau)}}$</tex-math></alternatives></inline-formula>
, for τ > 0. Such functions have been used from different authors to obtain inequalities concerning the gamma function.</abstract>

Department of Mathematics-Informatics, Faculty of Technical and Human, Sciences

Sapientia Hungarian University of Transylvania

Department of Mathematics-Informatics, Faculty of Technical and Human Sciences

A result regarding monotonicity of the Gamma function

<abstract xmlns="http://www.w3.org/1999/xhtml">Given an endofunctor F of an arbitrary category, any maximal element of the lattice of congruence relations on an F-coalgebra (A, a) is called a coatomic congruence relation on (A, a). Besides, a coatomic congruence relation K is said to be factor split if the canonical homomor-phism ν : AK → A<italic>∇</italic>A splits, where <italic>∇</italic>A is the largest congruence relation on (A, a). Assuming that F is a covarietor which preserves regular monos, we prove under suitable assumptions on the underlying category that, every quotient coalgebra can be made extensional by taking the regular quotient of an F-coalgebra with respect to a coatomic and not factor split congruence relation or its largest congruence relation.</abstract>

Extensional quotient coalgebras

<abstract xmlns="http://www.w3.org/1999/xhtml">In this paper by using the notion of sesquilinear form we introduce a new class of numerical range and numerical radius in normed space 𝒱, also its various characterizations are given. We apply our results to get some inequalities.</abstract>

Young Researchers and Elite Club, Mashhad Branch

Department of Mathematics, Mashhad Branch

Mathematics, College of Engineering and Science

Sesquilinear version of numerical range and numerical radius

<abstract xmlns="http://www.w3.org/1999/xhtml">The hyperbolic Pascal triangle <italic>HPT</italic>4,q (q <italic>≥</italic> 5) is a new mathematical construction, which is a geometrical generalization of Pascal’s arithmetical triangle. In the present study we show that a natural pattern of rows of <italic>HPT</italic>4,5 is almost the same as the sequence consisting of every second term of the well-known Fibonacci words. Further, we give a generalization of the Fibonacci words using the hyperbolic Pascal triangles. The geometrical properties of a <italic>HPT</italic>4,q imply a graph structure between the finite Fibonacci words.</abstract>

Fibonacci words in hyperbolic Pascal triangles

<abstract xmlns="http://www.w3.org/1999/xhtml">In the paper, the authors derive an explicit formula for derivative polynomials of the tangent function, deduce an explicit formula for tangent numbers, pose an open problem about obtaining an alternative and explicit formula for derivative polynomials of the tangent function, and recommend some papers closely related to derivative polynomials of other elementary and applicable functions.</abstract>

Inner Mongolia University for Nationalities

Department of Mathematics, College of Science

An explicit formula for derivative polynomials of the tangent function

<abstract xmlns="http://www.w3.org/1999/xhtml">Having in mind a well-known connection between norms and metrics on vector spaces, for an additively written group X, we establish a natural Galois connection between functions of X to ℝ and X2 to ℝ.</abstract>

A natural Galois connection between generalized norms and metrics

<abstract xmlns="http://www.w3.org/1999/xhtml">It is shown that for the question of the title the answer is yes. We construct a plane in the hyperbolic space which is Euclidean.</abstract>

Does another Euclidean plane exist other than the parasphere?

<abstract xmlns="http://www.w3.org/1999/xhtml">In this paper, we discuss the problem of meromorphic functions sharing small function and present one theorem which extend a result of K. S. Charak and Banarasi Lal [<xref ref-type="bibr" rid="j_ausm-2017-0029_ref_016_w2aab3b7b9b1b6b1ab1ac16Aa">16</xref>].</abstract>

Department of Mathematics, Jnanabharathi Campus

Uniqueness of polynomial and differential monomial

AHEAD OF PRINT

Volume 15 (2023): Issue 2 (December 2023)

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Volume 14 (2022): Issue 2 (December 2022)

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Acta Universitatis Sapientiae, Mathematica

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