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1

Second-order characterization of convex functions and its applications

Nadi Mohammad Taghi, Yao Jen Chih, Zafarani Jafar

Journal of Applied Analysis

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2019

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Vol. 25, nr 1

49--58

EN

Some developments of the second-order characterizations of convex functions are investigated by using the coderivative of the subdifferential mapping. Furthermore, some applications of the second-order subdifferentials in optimization problems are studied.

2

Kinematic and dynamic analysis for a new MacPherson strut suspension system

Dehbari S., Marzbanrad J.

Mechanics and Mechanical Engineering

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2018

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Vol. 22, nr 4

1223--1238

EN

The present paper undertakes kinematic and dynamic analysis of front suspension system. The investigated model is a full-scale Macpherson which is a multibody system. Two degree of freedom model is considered here to illustrate the vertical displacement of sprung mass and unsprung mass with using displacement matrix. Ride and handling parameters including displacement of sprung and unsprung masses, camber/caster angle, and track changes are derived from the relationships. Moreover, geometrical model and equations are validated by Adams/Car software. The kinematic and dynamic results have been compared in both analytical and numerical outputs for verification. The proposed analytical model shows less than 5% differences with a complicated multibody model.

3

Approximations by multivariate sublinear and Max-product operators under convexity

Anastassiou G. A.

Demonstratio Mathematica

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2018

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Vol. 51, nr 1

85--105

EN

Here we search quantitatively under convexity the approximation of multivariate function by general multivariate positive sublinear operators with applications to multivariate Max-product operators. These are of Bernstein type, of Favard-Szász-Mirakjan type, of Baskakov type, of sampling type, of Lagrange interpolation type and of Hermite-Fejér interpolation type. Our results are both: under the presence of smoothness and without any smoothness assumption on the function to be approximated which fulfills a convexity assumption.

4

Multivariate and abstract approximation theory for Banach space valued functions

Anastassiou G. A.

Demonstratio Mathematica

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2017

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Vol. 50, nr 1

208--222

EN

Here we study quantitatively the high degree of approximation of sequences of linear operators acting on Banach space valued Fréchet differentiable functions to the unit operator, as well as other basic approximations including those under convexity. These operators are bounded by real positive linear companion operators. The Banach spaces considered here are general and no positivity assumption is made on the initial linear operators for which we study their approximation properties. We derive pointwise and uniform estimates, which imply the approximation of these operators to the unit assuming Fréchet differentiability of functions, and then we continue with basic approximations. At the end we study the special case where the approximated function fulfills a convexity condition resulting into sharp estimates. We give applications to Bernstein operators.

5

L*-operators of convexity

Kulpa W.

Mathematica Applicanda

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2015

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Vol. 43, No. 2

145--156

EN

A notion of L^*-spaces is investigated as a generalization of convex subspaces. This gives some topological extensions for celebrated theorems due to Maynard Smith, Brouwer and Nash.

PL

W pracy jest badane pojęcie uogólnionej wypukłości, które umożliwia otrzymanie bardzo prostych dowodów twierdzenia Maynarda Smitha o istnieniu strategii ewolucyjnych w modelach biologicznych oraz twierdzenia o sygnaturach dających znaczne rozszerzenia twierdzenia Nasha o równowadze.

6

On the geometrical properties of some classes of complex harmonic functions defined by analytic or coefficient conditions with complex parameter

Sibelska A.

Journal of Applied Analysis

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2014

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Vol. 20, nr 1

77--85

EN

In the paper there are determined, for some classes defined by coefficient or analytic conditions, the sets of complex parameter γ, for which all the functions of the appropriate family have some geometrical properties. There are also provided the examples of the mappings showing that some inclusions between classes are impossible or confirming that sets of the parameter γ cannot be extended in some cases without loss of these geometric properties.

7

Dziwne szyby

Płoński J.

Świat Szkła

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2013

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R. 18, nr 6

7--8, 10

8

Wpływ asymetrycznego walcowania na poprawę wskaźników techniczno-ekonomicznych procesu walcowania blach na gorąco

Kawałek A., Dyja H., Knapiński M.

Hutnik, Wiadomości Hutnicze

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2008

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Vol. 75, nr 6

316-320

PL

W pracy przedstawiono efekty ekonomiczne uzyskane w wyniku opracowania i wdrożenia komputerowego systemu kształtowania szczeliny walcowniczej z wykorzystaniem sztucznej sieci neuronowej oraz asymetrycznego walcowania w dwóch ostatnich klatkach układu ciągłego walcowni gorącej blach. Zastosowanie i wdrożenie nowej technologii wpłynęło na zmniejszenie falistości produkcji towarowej w wybraku użytecznym, niedowalcowań, wypukłości pasma, wskaźnika zużycia walców oraz pozwoliło rozszerzyć asortyment walcowanych blach cienkich.

EN

The paper presents economic effects achieved as a result of development and implementation of a computer system for roll gap control using an artificial neural network and asymmetrical rolling in the last two stands of the continuous hotplate rolling mill system. The application and implementation of the new technology has contributed to reduction ofwaviness of commodity production in the usable reject, misrolling, strip convexity and roll wear rate and has enabled to expand the rolled sheet range.

9

On multivalently analytic and multivalently meromorphic functions

Irmak H., Stankiewicz J., Wilczek K.

Journal of Mathematics and Applications

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2006

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Vol. 28

75-84

EN

In the present investigation, some theorems involving certain inequalities between multivalently analytic functions in the unit disk U and multivalently meromorphic functions in the punctured unit disk D are stated. AIso certain interesting consequences of main results are given.

10

Rotundity, smoothness and duality

Penot J.-P.

Control and Cybernetics

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2003

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Vol. 32, no 4

711-733

EN

The duality between smoothness and rotundity of functions is studied in a nonlinear abstract framework. Here smoothness is enlarged to subdifferentiability properties and rotundity is formulated by means of approximation properties.

11

Extension theorems in axiomatic theory of convexity

Kubiś W.

Bulletin of the Polish Academy of Sciences. Mathematics

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2000

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Vol. 48, no 1

89-96

EN

We present a criterion for extending convexity preserving maps of convexity spaces. In a special case of convexity generated by a lattice structure this gives Sikorski's Extension Criterion for extending of maps of lattices. We also consider the class of convexity absolute extensors. It appears that complete Boolean algebras with a natural convexity belong to this class. In particular, we present an analogue of Tietze-Urysohn's Extension Theorem for maps of convexity spaces with values in a complete Boolean algebra.

12

On influenece of the Taylor series remainder on unanticipated rates of return on fixed income bond portfolios

Olbryś J.

Control and Cybernetics

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1999

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Vol. 28, no 4

789-797

EN

Changes in spot rates, unknown aprriori to investors, induce unanticipated rates of return on all financial market instruments. In this paper we introduce and investigate a concept of the rest of a bond. The concept is related to the Taylor series remainder and gives a better approximation to an unanticipated rate of return of fixed income bonds and bond portfolios. It is shown that the rest of the portfolio composed of fixed income bounds is a convex combination of the rests of these bonds. A stronger version of the theorem on rates of return on fixed income bond portfolios is given.

13

Construction of a k-immunization strategy with the highest convexity

Zaremba L.

Control and Cybernetics

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1998

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Vol. 27, no 1

135-144

EN

Assuming that interest rate shocks are proportional to their values plus one, we prove in Theorem 1 the existence of and construct a portfolio Z[sup *] with the highest convexity in the class of portfolios that solve the immunization problem to meet the liability to pay C dollars K years from now. Z[sup *] appears to be a barbell strategy with two zero-coupon bonds with the shorest and the longest maturities. This intuitively clear result has been obtained here in a rigorous way by means of the K-T conditions. In addition, we show that our result is stricly related to the problem of maximization of the unanticipated rate of return on a portfolio solving the above immunization problem (Theorem 2). Two more results concerning the unanticipated return after K years are provided with proofs. An example illustrating the role of convexity in maximization of the unanticipated return is included. Despite the fact that there exists a pretty vast literature on bond portfolio strategies, the present paper offers a new methodological approach to this area (see Ingersoll, Skelton, Weil, 1978).