Product property of global $P$-extremal functions

2021 ◽  
Vol 127 (3) ◽  
Author(s):  
Nguyen Quang Dieu ◽  
Tang Van Long
Keyword(s):  
Product Formula ◽  
Extremal Functions ◽  
Product Property ◽  
Sublevel Sets ◽  
Original Product

In this note, we establish a product property for $P$-extremal functions in the same spirit as the original product formula due to J. Siciak in Ann. Polon. Math., 39 (1981), 175–211. As a consequence, we obtain convexity for the sublevel sets of such extremal functions. Moreover, we also generalize the product property of $P$-extremal functions established by L. Bos and N. Levenberg in Comput. Methods Funct. Theory 18 (2018), 361–388, and later by N. Levenberg and M. Perera, in Contemporary Mathematics 743 (2020), 11–19, in which no restriction on $P$ is needed.

Product Property of Certain Extremal Functions

2003 ◽  
Vol 48 (8) ◽  
pp. 681-694 ◽  
Author(s):  
Nguyen Quang Dieu ◽  
Nguyen Van Trao†
Keyword(s):  
Extremal Functions ◽  
Product Property

scholarly journals Convexity of sublevel sets of plurisubharmonic extremal functions

1998 ◽  
Vol 68 (3) ◽  
pp. 267-273 ◽  
Author(s):  
Finnur Lárusson ◽  
Patrice Lassere ◽  
Ragnar Sigurdsson
Keyword(s):  
Extremal Functions ◽  
Sublevel Sets

scholarly journals Sublevel sets of certain extremal functions

2007 ◽  
Vol 101 (2) ◽  
pp. 184
Author(s):  
Nguyen Quang Dieu ◽  
Tang van Long
Keyword(s):  
Extremal Functions ◽  
Sublevel Sets

Conception And Fabrication Of Straight Axes Using Knowledge Management Principles

2014 ◽  
Vol 1 (1) ◽  
pp. 365-368
Author(s):  
Ionela Magdalena Rotaru ◽  
Sorin Borza
Keyword(s):  
Knowledge Management ◽  
Work Environment ◽  
Automotive Industry ◽  
Central Element ◽  
Theoretical Concepts ◽  
Application Field ◽  
Design And Manufacturing ◽  
Original Product ◽  
Practical Level

Abstractthe paper continues the research started in the paper “Conception and fabrication using knowledge management principles”. The theoretical guidelines found in the mentioned paper crystallises at a practical level in an original product – a software solution. The proposed solution has as a central element notion concerning the design and manufacturing of straight axes in the automotive industry. The application field for the proposed example regards the educational area; the software guides the user by theoretical concepts, examples, problems through practical aspects concerning the design and manufacturing of a part belonging to the axes family specific to the automotive industry. The software was developed using the Access work environment.

scholarly journals BIOSIMILARS IN INFLAMMATORY BOWEL DISEASES: an important moment for Brazilian gastroenterologists

2015 ◽  
Vol 52 (1) ◽  
pp. 76-80 ◽  
Author(s):  
Fábio Vieira TEIXEIRA ◽  
Paulo Gustavo KOTZE ◽  
Aderson Omar Mourão Cintra DAMIÃO ◽  
Sender Jankiel MISZPUTEN
Keyword(s):  
Small Molecules ◽  
Inflammatory Bowel Diseases ◽  
Generic Drugs ◽  
Specific Data ◽  
Chemical Structures ◽  
Bowel Diseases ◽  
Original Product ◽  
Inflammatory Bowel ◽  
The One ◽  
Extrapolation Of Indications

ABSTRACT Biosimilars are not generic drugs. These are more complex medications than small molecules, with identical chemical structures of monoclonal antibodies that lost their patency over time. Besides identical to the original product at the end, the process of achieving its final forms differs from the one used in the reference products. These differences in the formulation process can alter final outcomes such as safety and efficacy of the drugs. Recently, a biosimilar of Infliximab was approved in some countries, even to the management of inflammatory bowel diseases. However, this decision was based on studies performed in rheumatologic conditions such as rheumatoid arthritis and ankylosing spondylitis. Extrapolation of the indications from rheumatologic conditions was done for Crohn’s disease and ulcerative colitis based on these studies. In this article, the authors explain possible different mechanisms in the pathogenesis between rheumatologic conditions and inflammatory bowel diseases, that can lead to different actions of the medications in different diseases. The authors also alert the gastroenterological community for the problem of extrapolation of indications, and explain in full details the reasons for being care with the use of biosimilars in inflammatory bowel diseases without specific data from trials performed in this scenario.

scholarly journals On the Boundary Dieudonné–Pick Lemma

Mathematics ◽  
2021 ◽  
Vol 9 (10) ◽  
pp. 1108
Author(s):  
Olga Kudryavtseva ◽  
Aleksei Solodov
Keyword(s):  
Fixed Point ◽  
Interior Point ◽  
Sharp Estimate ◽  
General Boundary ◽  
Extremal Functions ◽  
Angular Derivative ◽  
Additional Information ◽  
Carathéodory Theorem ◽  
Class Of Functions ◽  
Boundary Fixed Point

The class of holomorphic self-maps of a disk with a boundary fixed point is studied. For this class of functions, the famous Julia–Carathéodory theorem gives a sharp estimate of the angular derivative at the boundary fixed point in terms of the image of the interior point. In the case when additional information about the value of the derivative at the interior point is known, a sharp estimate of the angular derivative at the boundary fixed point is obtained. As a consequence, the sharpness of the boundary Dieudonné–Pick lemma is established and the class of the extremal functions is identified. An unimprovable strengthening of the Osserman general boundary lemma is also obtained.

Complex group algebras of the direct product of non-isomorphic Suzuki groups

2019 ◽  
Vol 19 (02) ◽  
pp. 2050036
Author(s):  
Morteza Baniasad Azad ◽  
Behrooz Khosravi
Keyword(s):  
Direct Product ◽  
Group Algebra ◽  
Irreducible Character ◽  
Prime Numbers ◽  
Product Formula ◽  
Character Degrees ◽  
Group Algebras ◽  
Complex Group ◽  
Complex Group Algebra ◽  
Suzuki Groups

In this paper, we prove that the direct product [Formula: see text], where [Formula: see text] are distinct numbers, is uniquely determined by its complex group algebra. Particularly, we show that the direct product [Formula: see text], where [Formula: see text]’s are distinct odd prime numbers, is uniquely determined by its order and three irreducible character degrees.

scholarly journals Initial logarithmic coefficients for functions starlike with respect to symmetric points

2021 ◽  
Vol 27 (3) ◽  
Author(s):  
Paweł Zaprawa
Keyword(s):  
Exact Result ◽  
Positive Real Part ◽  
Additional Benefit ◽  
Extremal Functions ◽  
Positive Real ◽  
Logarithmic Coefficients ◽  
Symmetric Points

AbstractIn this paper, we obtain the bounds of the initial logarithmic coefficients for functions in the classes $${\mathcal {S}}_S^*$$ S S ∗ and $${\mathcal {K}}_S$$ K S of functions which are starlike with respect to symmetric points and convex with respect to symmetric points, respectively. In our research, we use a different approach than the usual one in which the coeffcients of f are expressed by the corresponding coeffcients of functions with positive real part. In what follows, we express the coeffcients of f in $${\mathcal {S}}_S^*$$ S S ∗ and $${\mathcal {K}}_S$$ K S by the corresponding coeffcients of Schwarz functions. In the proofs, we apply some inequalities for these functions obtained by Prokhorov and Szynal, by Carlson and by Efraimidis. This approach offers a additional benefit. In many cases, it is easily possible to predict the exact result and to select extremal functions. It is the case for $${\mathcal {S}}_S^*$$ S S ∗ and $${\mathcal {K}}_S$$ K S .

scholarly journals A new product formula involving Bessel functions

2021 ◽  
pp. 1-17
Author(s):  
Mohamed Amine Boubatra ◽  
Selma Negzaoui ◽  
Mohamed Sifi
Keyword(s):  
Bessel Functions ◽  
New Product ◽  
Product Formula
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