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1
Content available remote Ostrowski type inequalities for functions whose derivatives satisfy certain convexity assumptions
100%
Cerone P. , Dragomir S.
Demonstratio Mathematica
|
2004
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tom Vol. 37, nr 2
299--308
EN
Ostrowski type inequalities for absolutely continuous functions whose derivatives satisfy certain convexity assumptions are pointed out.
2
Content available remote On quasi convex functions and Hadamard's inequality
100%
Tseng K. , Tseng K. , Yang G. , Dragomir S.
Demonstratio Mathematica
|
2008
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tom Vol. 41, nr 2
323-336
EN
In this paper we establish some inequalities of Hadamard's type involving Godunova-Levin functions, P-functions, quasi-convex functions, J-quasi-convex functions, Wright-convex functions and Wright-quasi-convex functions.
3
Content available remote The Jensen inequality for s-Breckner convex functions in linear spaces
100%
Dragomir S. S. , Fitzpatrick S.
Demonstratio Mathematica
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2000
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tom Vol. 33, nr 1
43-49
EN
We derive some inequalities of Jensen's type for 5-convex functions in the sense of Breckner on subsets of linear spaces and give some applications connected with special means.
4
O zastosowaniu funkcji wypukłych w teorii wytężenia materiałów izotropowych. Propozycja warunków plastyczności metali
100%
Jemioło S. , Szwed A.
Prace Naukowe Politechniki Warszawskiej. Budownictwo
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1999
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tom z. 133
5-51
PL
Rozpatrujemy wypukłe izotropowe funkcje zależne od symetrycznego tensora drugiego rzędu, które stosuje się w teorii wytężenia i teorii plastyczności materiałów izotropowych. W jednolity sposób dyskutujemy nad zagadnieniami związanymi z wypukłością izotropowych funkcji względem tensora i wypukłością tych funkcji w nieczułym na permutacje zbiorze wartości własnych tensora. Podajemy interpretacje wektorowe i geometryczne tensorów, wynikające z twierdzenia o rozkładzie spektralnym symetrycznego tensora drugiego rzędu oraz interpretacje geometryczne powierzchni granicznych, skonstruowanych z wypukłych funkcji izotropowych. Omawiane problemy ilustrujemy licznymi, znanymi z literatury przykładami warunków plastyczności i hipotez wytężeniowych. Podajemy propozycje warunków plastyczności nieściśliwych metali, które są zależne od drugiego i trzeciego niezmiennika dewiatora naprężenia. Dyskutujemy warunki plastyczności metali o sześciokrotnych i trzykrotnych osiach symetrii w przekroju dewiatorowym. Z wymagań wypukłości wyprowadzamy ograniczenia na parametry materiałowe. Proponujemy typy testów doświadczalnych, z których można wyznaczyć stałe materiałowe. Wykazujemy, że niektóre znane z literatury kryteria plastyczności są szczególnymi przypadkami zaproponowanych warunków plastyczności.
EN
The convex scalar-valued isotropic functions dependent on the symmetric second-order tensor applied in the failure and plasticity theories of isotropic materials are considered. Issues connected with the convexity of the isotropic functions with respect to the tensor and the convexity of these functions in the set of the eigenvalues of the tensor are discussed in unified way. The vectorial and geometric interpretations resultant from the spectral decomposition theorem of the symmetric second-order tensor and also geometric interpretations of the failure surfaces constructed from the convex isotropic functions are given. The issues discussed are illustrated by a number of the yieid conditions and failure surfaces known from the literature. Yieid conditions dependent on the second and third invariants of the deviator of the stress tensor for incompressible metals are proposed. The failure conditions for metals with six or three axes of symmetry in the deviatoric crossection are discussed. The limitations on the material parameters are derived from the convexity requirements and experimental tests for the determination of the parameters are recommended. Some failure criteria, known from literature, are shown to be specific cases in the proposed failure criteria.
5
Content available remote Determination of convex bodies by infinity-chord functions
100%
Sójka G.
Demonstratio Mathematica
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2010
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tom Vol. 43, nr 1
187-202
EN
In 1998 A. Soranzo introduced the notions of +infinity - and - infinity-chord functions (see [16]). In this paper we give an answer to the question when a convex body is determined by the values of -infinity-chord functions at chosen internal points. We also give some partial results regarding + infinity chord functions.
6
Rougly e-convex functions
100%
Marian D.
Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka
|
2001
|
tom z. 25 [190]
121-129
EN
In this paper, we define first eight kinds of roughly E-convex functions, namely -convex, E-convex, midpoint E-convex, E-convex, lightly -E-convex, midpoint E-convex, strictly E-convex, strictly E-convexlike functions, which are a generalization of roughly convex functions respectively of E-convex functions. Concretely, the relations between these concepts are presented. Some properties concerning the minimum of midpoint E-convex functions and lightly E-convex functions are study, too. We also study the set of E-mimimizer of strictly E-convexlike functions.
7
Content available remote Hadamard inequalities for Wright-convex functions
88%
Tseng K.-L. , Yang G.-S. , Dragomir S. S.
Demonstratio Mathematica
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2004
|
tom Vol. 37, nr 3
525--532
EN
In this paper we establish several inequalities of Hadamard's type for Wright-convex functions.
8
Content available remote On the generalization of Wright-convexity
88%
Sobek B.
Journal of Mathematics and Applications
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2006
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tom Vol. 28
121-126
9
Content available remote Linear invariance and integral operators of univalence functions
75%
Dorff M. , Szynal J.
Demonstratio Mathematica
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2005
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tom Vol. 38, nr 1
47--57
EN
In this paper, we study a larger set than (1), namely the set of the minimal invariant family which contains (1), where / belongs to the linear invariant family, and thereby we obtain information about the univalence of (1). In particular, we determine the order of this minimal invariant family in the cases of univalent and convex univalent functions in D. As a result, we find the radius of close-to-convexity and the lower bound for the radius of univalence for the minimal invariant family in the case of convex univalent functions. This allows us to determine the exact region for (a, (3) where the corresponding minimal invariant family is univalent and close-to-convex. These results are sharp and generalize those which were obtained in [11].
10
Content available remote Characterization of subclasses of univalent functions
75%
Trojnar-Spelina L.
Demonstratio Mathematica
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2005
|
tom Vol. 38, nr 1
35--41
EN
We investigate the family of functions f(z) = z +(suma od n=2 do nieskończoności) anzn that are analytic in the unit disk with the property that the domain of values f(z) + 1+ei(alpha):2zf", (alpha is an element of (-pi,pi) is the parabolic region (Imw)2 < 2Rew - 1. Integral representation and convolution characterization are found and some coefficients bounds are given.
11
Content available remote Some results about +nieskończoność-, -nieskończoność- and i-chord functions
75%
Soranzo A. , Sójka G.
Demonstratio Mathematica
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2006
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tom Vol. 39, nr 1
183-194
EN
This paper concerns determination of a convex bodies by values of +oo- -oo-and i-chord functions. We prove that any at least two-dimensional convex body is not determined by values of -oo-chord functions at any two internal points. We also present some positive results on determination of convex bodies using -oo- or +oo-chord function at one point and i-chord function at other one.
12
Starlikeness of a class of functions
75%
Singh V.
Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka
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2002
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tom z. 26 [199]
135-139
EN
We improve a result in Mocanu and Oros [1].
13
Second order differential subordinations and certain subordination relations
75%
Kowalczyk J.
Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka
|
2002
|
tom z. 26 [199]
97-106
EN
In the present paper the second order differential subordination (1 - alpha)f(z/z + alphaf'{z) + betazf(z) [...] 1 + Mz \z is an element of U) is investigated. The best dominant of subordination (1) is founded. Connections between subordination (1) and subordination of f(z)/z, f'{z) are given. Further the convexity of the function / satisfying the subordination (1) for special choice of parameters a, alpha, beta and M are derived.
14
Content available remote On classes of meromorphic or complex harmonic functions with a pole at the infinity
75%
Jakubowski Z. , Sibelska A.
Demonstratio Mathematica
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2009
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tom Vol. 42, nr 3
479-489
EN
In this article we investigate some classes of meromorphic or complex harmonie functions with a pole, which are generated either by analytic conditions or by "coefficient inequalities". There are given theorems, which combine the geometrical properties of functions of the introduced classes. Some results broaden knowledge about the classes of functions, which were investigated in [15]. The main inspiration for the reaserch were the papers [4] and [11]. The part of results were presented in the XII-th International Mathematically-Informatical Conference in Chełm (2nd-5th July, 2006) [12].
15
Content available Forecasting stock index movement direction with CPL linear classifier
75%
Krawczuk J.
Zeszyty Naukowe Politechniki Białostockiej. Informatyka
|
2011
|
tom Z. 7
47-58
EN
Stocks, indexes, commodities, and precious metals price prediction is a difficult task where many approaches are used: traditional technical analysis, econometric time series or modern data mining techniques. One particular data mining technique - linear classifier is described in this article. Prediction based on linear classifier is done using current market state, which can be described by various data sets (attributes, features). The simplest form of this model could use data from yesterday’s price movement. Advanced models are using more historical price movements. Very advanced models include various historical price movements for indexes from other countries and other instruments like currencies, commodities, etc. Using more features requires extended time to estimate model parameters.We build the linear classifier models by the minimisation of a convex and piecewise-linear function which is very efficient comparing to other functions. Computational costs for building the model are similar to linear programming. We also use feature selection method called RLS. Those techniques allow us to explore data with many features. Four scenarios are considered, in each scenario a different amount of market data is used to create a model. In the simplest scenario only one day’s change in price is taken, in the most complicated one 421 historical prices of 43 different instruments are taken. Best results were achieved by using middle range of 52 attributes. In this scenario, the model was right 53.19% times. Meaning the directions of daily change in S&P500 index (up or down) were predicted correctly. This doesn’t seem a lot, but if those predictions would have been used for investing, they could produce a total profit of 77% in the tested time period from November 2008 to March 2011 (2 years 4 months), or an average of 28% per year.
PL
Prognozowanie cen akcji i wartośsci indeksów giełdowych jest zadaniem trudnym, dla którego użzywanych jest wiele różnych podejść. Artykuł ten przedstawia wprowadzenie do pewnych standardowych technik. Przedstawiona została tradycyjna analiza techniczna, ekonometryczne modele szeregów czasowych oraz współczesne metody eksploracji danych. Jedna z metod eksploracji danych, klasyfikator liniowy został przedstawiony bardziej szczegółowo. Został on użyty w przeprowadzonym eksperymencie do prognozowania wartości indeksu giełdy amerykańskiej. Prognozowanie takie oparte jest o dane opisujące obecny stan giełdy. Stan giełdy można opisać różną ilością danych (atrybutów, cech). W najprostszym przypadku może to być tylko jednodniowa zmiana ceny prognozowanego indeksu. W bardziej rozbudowanym modelu można użyć wielu cen historycznych. W modelu jeszcze bardziej rozbudowanym można użyć danych z innych giełd, kursów walut, cen towarów jak np. ropa. Użycie dużej ilości danych wymaga dłuższego czasu obliczeń parametrów modelu. W prezentowanym podejściu klasyfikator liniowy budowany jest w oparciu o minimalizację wypukłej i odcinkowo-liniowej funkcji kryterialnej. Metoda ta jest bardzo wydajna o koszcie zbliżonym do programowania liniowego. Dodatkowo użyta została metoda selekcji cech RLS. Techniki te pozwoliły na efektywną eksplorację danych o wielu wymiarach. W artykule przedstawiono cztery scenariusze o różnej ilości danych opisujących giełdę. W najprostszym użyto tylko jednej danej, w najbardziej rozbudowanym 421 danych o 43 instrumentach finansowych. Najlepsze wyniki uzyskano dla pośredniego modelu o 52 cechach, w którym model przewidział prawidłowo 53.19% kierunków dziennych zmian indeksu S&P500. Otrzymany wynik nie wydaje się być wysoki, jednak gdyby inwestowano w indeks zgodnie z modelem zysk z takich inwestycji wyniósłby 77% w okresie od października 2008 do marca 2011, dając średnio 28% zysku rocznie.
16
On convex mappings of the unit disc onto disjoining domains
75%
Stankiewicz Z. , Stankiewicz J.
Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka
|
1999
|
tom z. 23 [175]
21-27
EN
Let U = {z is an element of C : \z\ < 1} and let a1, a2, a3 is not equal to a2 be the given complex numbers. By M(01,02) we denote a family of all pairs of regular functions in U such that [...] denote the subclasses of M. of function which are univalent starlike or convex, respectively. In the paper the investigate the extrema of some functional defined on these families. In particular it is proved that [..].
17
Stability of convolution and dual sets for the class of k-uniformly convex and k-starlike functions
75%
Kanas S.
Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka
|
1998
|
tom z. 22 [170]
51-64
EN
Let k-UCV denote the class of k-uniformly convex functions and let k-ST be related class of k- starlike functions. Also, let f*g denote the Hadamard product (or convolution) of the analytic functions f and g, and V* denote the dual set of the set V. In this paper the classes k-UCV and k-ST in terms of dual sets are descibed. Duality of mentioned classes is also used to obtain other results in the class k-UCV and k-ST. Problem of neighbourhoods of functions as well as stability of convolution in the class k-UCV and k-ST are investigated.
18
Content available remote Properties of certain classes of analytic functions defined by Srivastava-Attiya operator
75%
Khairnar S. , More M.
Demonstratio Mathematica
|
2010
|
tom Vol. 43, nr 1
55-79
EN
In this paper we introduce the class K(s,b,beta,apha) of analytic functions defined by the Srivastava-Attiya convolution operator Js,b(f) involving the Hurwitz-Lerch Zeta function. We derive few subordination results for the functions in the class K(s,b,beta,alpha) and discuss the interesting applications of subordination results with the help of convex functions. Several other properties like coefficient inequalities growth and distortion theorems, extreme points, integral mean inequalities, partial sums and quasi-Hadamard product are investigated for the class K(s,b,beta,alpha). The authors also obtain Fekete-Szego inequality for normalized analytic functions f(z) defined on the open unit disc for which [....] lies in a region starlike with respect to 1 and is symmetric with respect to the real axis. Applications of our main result involving the Owa-Srivastava operator of fractional calculus are discussed. Finally as one of the applications of our result, we derive the Fekete-Szego inequality for a class of normalized analytic functions, defined using the Hadamard product and the Owa-Srivastava operator.
19
Content available remote On generalization of close-to-convexity for complex holomorphic functions in Cn
75%
Marchlewska A.
Demonstratio Mathematica
|
2005
|
tom Vol. 38, nr 4
847--856
EN
Sveral authors (I. I. Bawrin [1], K. Dobrowolska, I. Dziubinski, P. Liczberski, R. Sitarski [3], [4], [5], [13], S. Gong, S. S. Miller [6], Z. J. Jakubowski and J. Kaminski [8], J. Janiec [10] and others) studied various families of complex holomorphic functions in Cn and in Banach space, corresponding with famous subclasses of univalent functions. In this paper we study a class of holomorphic functions of n complex variables analogous to the class of close-to-convex functions of one variable considered by M. Biernacki, W. Kaplan and Z. Lewandowski (see [2], [11], [12]).
20
Content available remote Stability of the Hadamard product of k-uniformly convex and k-starlike functions in certain neighbourhood
75%
Bednarz U.
Demonstratio Mathematica
|
2005
|
tom Vol. 38, nr 4
837--845
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