On the rescaled Riemannian metric of Cheeger Gromoll type on the cotangent bundle

Let $(M,g)$ be an n-dimensional Riemannian manifold and $T^{*}M$ be its cotangent bundle equipped with a Riemannian metric of Cheeger Gromoll type which rescale the horizontal part by a nonzero differentiable function. The main purpose of the present paper is to discuss curvature properties of $T^{*}M$ and construct almost paracomplex Norden structures on $T^{*}M$. We investigate conditions for these structures to be para-K\"ahler (paraholomorphic) and quasi-K\"ahler. Also, some properties of almost paracomplex Norden structures in context of almost product Riemannian manifolds are presented

Spaces of uτu\tau-Dunford-Pettis and uτu\tau-Compact Operators on Locally Solid Vector Lattices

Suppose $X$ is a locally solid vector lattice. It is known that there are several non-equivalent spaces of bounded operators on $X$. In this paper, we consider some situations under which these classes of bounded operators form locally solid vector lattices. In addition, we generalize some notions of $uaw$-Dunford-Pettis operators and $uaw$-compact operators defined on a Banach lattice to general theme of locally solid vector lattices. With the aid of appropriate topologies, we investigate some relations between topological and lattice structures of these operators. In particular, we characterize those spaces for which these concepts of operators and the corresponding classes of bounded ones coincide.Comment: 7 pages. To appear in MATEMATI\v{C}KI VESNIK journa

Stress Response of Dietary Phytochemicals in a Hormetic Manner for Health and Longevity

The stress responses observed in mammalian cells can be classified as heat shock response, unfolded protein response, autophagic response, deoxyribonucleic acid damage response, antioxidant response, and sirtuin response at the intracellular and molecular levels. Factors that strengthen the hemodynamic structure causing low-level molecular damage and activating one or several stress response pathways are called hormetins. Hormetins can be categorized as physical, physiological, biological, and nutritional hormetins. Nutritional hormetins provide an interesting, comprehensive research topic because of their effects on health and lifespan. Dietary phytochemicals, with their low-level stress-inducing effects, are potential nutritional hormetins. Resveratrol, curcumin, epicatechin, isothiocyanates, ferulic acid, and certain vitamin-minerals can induce a heat shock response, unfolded protein response, autophagic response, deoxyribonucleic acid damage response, antioxidant response, and sirtuin response causing the stimulation of kinases and transcription factors. Studies have shown that these phytochemicals are related to nuclear factor-erythroid 2, sirtuins, nuclear factor-kappa B, and heat shock response pathways. In this chapter, the stress response of dietary phytochemicals will be systematically examined in a hormetic manner for delay of age-related diseases, healthy aging, and longevity based on current data