A Clarke–Ledyaev Type Inequality for Certain Non–Convex Sets

We consider the question whether the assumption of convexity of the set involved in Clarke-Ledyaev inequality can be relaxed. In the case when the point is outside the convex hull of the set we show that Clarke-Ledyaev type inequality holds if and only if there is certain geometrical relation between the point and the set.

Best Constant in the Weighted Hardy Inequality: The Spatial and Spherical Version

Mathematics Subject Classification: 26D10.

Sobolev-Morrey Type Inequality for Riesz Potentials, Associated with the Laplace-Bessel Differential Operator

2000 Mathematics Subject Classification: 42B20, 42B25, 42B35

Hardy Inequality in Variable Exponent Lebesgue Spaces

Mathematics Subject Classification: 26D10, 46E30, 47B38

The Stein-Weiss Type Inequality for Fractional Integrals, Associated with the Laplace-Bessel Differential Operator

2000 Math. Subject Classification: Primary 42B20, 42B25, 42B35

On Limiting Case of the Stein-Weiss Type Inequality for the B-Riesz Potentials

Mathematics Subject Classification: Primary 42B20, 42B25, 42B35

Fekete-Szegö Inequality for Universally Prestarlike Functions

MSC 2010: 30C45

Investigation of a Stolarsky type Inequality for Integrals in Pseudo-Analysis

MSC 2010: 03E72, 26E50, 28E10

An Inequality for Generalized Chromatic Graphs

Асен Божилов, Недялко Ненов - Нека G е n-върхов граф и редицата от степените на върховете му е d1, d2, . . . , dn, а V(G) е множеството от върховете на G. Степента на върха v бележим с d(v). Най-малкото естествено число r, за което V(G) има r-разлагане V(G) = V1 ∪ V2 ∪ · · · ∪ Vr, Vi ∩ Vj = ∅, , i 6 = j такова, че d(v) ≤ n − |Vi|, ∀v ∈ Vi, i = 1, 2, . . . , r е означено с ϕ(G). В тази работа доказваме неравенството ...

Discrete Generalization of Gronwall-Bellman Inequality with Maxima and Application

Снежана Христова, Кремена Стефанова, Лиляна Ванкова - В работата са решени няколко нови видове линейни дискретни неравенства, които съдържат максимума на неизвестната функция в отминал интервал от време. Някои от тези неравенства са приложени за изучаване непрекъснатата зависимост от смущения при дискретни уравнения с максимуми.

A solution of the trigonometric moment problem via Tagamlitzki's "Theorem of the Cones"

In 1952 Y. Tagamlitzki gave an elegant proof of the classical Bochner’s theorem on the positively definite functions. Unfortunately, he never published his proof. In this paper we consider a related but simpler problem, the trigonometric moment problem, by using Tagamlitzki’s approach.

First-Order Conditions for Optimization Problems with Quasiconvex Inequality Constraints

2000 Mathematics Subject Classification: 90C46, 90C26, 26B25, 49J52.

Is pregnancy a teachable moment for diet and physical activity behaviour change? An interpretative phenomenological analysis of the experiences of women during their first pregnancy

OBJECTIVES: Pregnancy may provide a 'teachable moment' for positive health behaviour change, as a time when women are both motivated towards health and in regular contact with health care professionals. This study aimed to investigate whether women's experiences of pregnancy indicate that they would be receptive to behaviour change during this period. DESIGN: Qualitative interview study. METHODS: Using interpretative phenomenological analysis, this study details how seven women made decisions about their physical activity and dietary behaviour during their first pregnancy. RESULTS: Two women had required fertility treatment to conceive. Their behaviour was driven by anxiety and a drive to minimize potential risks to the pregnancy. This included detailed information seeking and strict adherence to diet and physical activity recommendations. However, the majority of women described behaviour change as 'automatic', adopting a new lifestyle immediately upon discovering their pregnancy. Diet and physical activity were influenced by what these women perceived to be normal or acceptable during pregnancy (largely based on observations of others) and internal drivers, including bodily signals and a desire to retain some of their pre-pregnancy self-identity. More reasoned assessments regarding benefits for them and their baby were less prevalent and influential. CONCLUSIONS: Findings suggest that for women who conceived relatively easily, diet and physical activity behaviour during pregnancy is primarily based upon a combination of automatic judgements, physical sensations, and perceptions of what pregnant women are supposed to do. Health professionals and other credible sources appear to exert less influence. As such, pregnancy alone may not create a 'teachable moment'. Statement of contribution What is already known on this subject? Significant life events can be cues to action with relation to health behaviour change. However, much of the empirical research in this area has focused on negative health experiences such as receiving a false-positive screening result and hospitalization, and in relation to unequivocally negative behaviours such as smoking. It is often suggested that pregnancy, as a major life event, is a 'teachable moment' (TM) for lifestyle behaviour change due to an increase in motivation towards health and regular contact with health professionals. However, there is limited evidence for the utility of the TM model in predicting or promoting behaviour change. What does this study add? Two groups of women emerged from our study: the women who had experienced difficulties in conceiving and had received fertility treatment, and those who had conceived without intervention. The former group's experience of pregnancy was characterized by a sense of vulnerability and anxiety over sustaining the pregnancy which influenced every choice they made about their diet and physical activity. For the latter group, decisions about diet and physical activity were made immediately upon discovering their pregnancy, based upon a combination of automatic judgements, physical sensations, and perceptions of what is normal or 'good' for pregnancy. Among women with relatively trouble-free conception and pregnancy experiences, the necessary conditions may not be present to create a 'teachable moment'. This is due to a combination of a reliance on non-reflective decision-making, perception of low risk, and little change in affective response or self-concept.

Liquidity and asset pricing: A comparison between three-factor and three-moment capital asset pricing models

Liquidity is an important attribute of an asset that investors would like to take into consideration when making investment decisions. However, the previous empirical evidence whether liquidity is a determinant of stock return is not unanimous. This dissertation provides a very comprehensive study about the role of liquidity in asset pricing using the Fama-French (1993) three-factor and Kraus and Litzenberger (1976) three-moment CAPM as models for risk adjustment. The relationship between liquidity and well-known determinants of stock returns such as size and book-to-market are also investigated. This study examines the liquidity and asset pricing issues for both intertemporal as well as cross-sectional data. ^ The results indicate an existence of a liquidity premium, i.e., less liquid stocks would demand higher rate of return than more liquid stocks. More specifically, a drop of 1 percent in liquidity is associated with a higher rate of return of about 2 to 3 basis points per month. Further investigation reveals that neither the Fama-French three-factor model nor the three-moment CAPM captures the liquidity premium. Finally, the results show that well-known determinants of stock return such as size and book-to-market do not serve as proxy for liquidity. ^ Overall, this dissertation shows that a liquidity premium exists in the stock market and that liquidity is a distinct effect, and is not influenced by the presence of non-market factors, market factors and other stock characteristics.^