On Nonlocal Modified Gravity and its Cosmological Solutions

During hundred years of General Relativity (GR), many significant gravitational phenomena have been predicted and discovered. General Relativity is still the best theory of gravity. Nevertheless, some (quantum) theoretical and (astrophysical and cosmological) phenomenological difficulties of modern gravity have been motivation to search more general theory of gravity than GR. As a result, many modifications of GR have been considered. One of promising recent investigations is Nonlocal Modified Gravity. In this article we present a brief review of some nonlocal gravity models with their cosmological solutions, in which nonlocality is expressed by an analytic function of the d'Alembert-Beltrami operator $\Box$. Some new results are also presented.Comment: 16 page

Nonlocal de Sitter gravity and its exact cosmological solutions

This paper is devoted to a simple nonlocal de Sitter gravity model and its exact vacuum cosmological solutions. In the Einstein-Hilbert action with $\Lambda$ term, we introduce nonlocality by the following way: $R - 2 \Lambda = \sqrt{R-2\Lambda}\ \sqrt{R-2\Lambda} \to \sqrt{R-2\Lambda}\ F(\Box)\ \sqrt{R-2\Lambda} ,$where${F} (\Box) = 1 + \sum_{n= 1}^{+\infty} \big( f_n \Box^n + f_{-n} \Box^{-n} \big) $is an analytic function of the d'Alembert-Beltrami operator$\Box$and its inverse$\Box^{-1}$. By this way,$R$and$\Lambda$enter with the same form into nonlocal version as they are in the local one, and nonlocal operator$F(\Box)$is dimensionless. The corresponding equations of motion for gravitational field$g_{\mu\nu}$are presented. The first step in finding some exact cosmological solutions is solving the equation$\Box \sqrt{R-2\Lambda} = q \sqrt{R-2\Lambda} , $where$ q =\zeta \Lambda \quad (\zeta \in \mathbb{R})$is an eigenvalue and$\sqrt{R-2\Lambda}$is an eigenfunction of the operator$\Box .$ We presented and discussed several exact cosmological solutions for homogeneous and isotropic universe. One of these solutions mimics effects that are usually assigned to dark matter and dark energy. Some other solutions are examples of the nonsingular bounce ones in flat, closed and open universe. There are also singular and cyclic solutions. All these cosmological solutions are a result of nonlocality and do not exist in the local de Sitter case.Comment: 27 pages, 5 figures. Comments welcom

Genetic and phenotypic variability of yield components in wheat (Triticum aestivum L.)

Variability, heritability and components of variance for number of grains per spike and grain weight per spike have been studied in 10 winter wheat varieties from different selection centers (Arsenal, KG-56, Gruza, Mironovskaya 808, Norin 10, Rana Niska, Spartanka, Sterna, Osjecanka, and Szegedi 765). The experiment was performed in randomized block design in three replications on the experimental field of Small Grains Research Centre, Kragujevac in three years. Average estimated values for number of grains per spike and grain weight per spike differed significantly among years and among varieties. The highest average value for number of grains per spike had Szegedi 765 variety ( x = 75.1) and the lowest value was found in Spartanka ( x = 56.0). During investigated period the highest average value for grain weight per spike was determined in Gruza ( Norin 10 ( x = 2.9 g), and the lowest value in x = 2.0 g). The average variation coefficient for number of grains per spike was 17.4%, and for grain weight per spike was 21.4%. The lowest variability for number of grains per spike and grain weight per spike was established in Sterna variety (V = 13.0%; 16.2%, respectively) and the highest in Norin 10 variety (V = 21.6%; 25.1%, respectively). Obtained heritability value in broad sense for number of grains per spike was about 60%, and for grain weight per spike about 40%. Statistical analysis of variance established highly significant differences in mean values for number of grains per spike and grain weight per spike. Phenotypic analysis of variance indicated that ecological factors had higher impact on the expression of number of grains per spike and grain weight per spike than genetic factors

Putting the cart before the horse: co-evolution of the universe and observers as an explanatory hypothesis

The answer to the fine-tuning problem of the universe has been traditionally sought in terms of either design or multiverse. In philosophy circles, this is sometimes expanded by adding the option of explanatory nihilism – the claim that there is no explanation for statements of that high level of generality: fine-tunings are brute facts. In this paper, we consider the fourth option which, at least in principle, is available to us: co-evolution of the universe and obsevers. Although conceptual roots of this approach could be found already in ancient stoicism, it is still the least investigated explanatory option for resolving the problem of empirical fine tunings. We offer two preliminary models along which the co-evolution hypothesis could be developed further. They are still on the level of speculative metaphysics, but there are opportunities along the way to generate predictions which are in principle testable, especially in the domain of large-scale numerical simulations

Kinetic Study of Oxidation Degradation of Polyphenols in Sour Cherry and Blackberry Extracts During Storage

In this study was to investigate the influence of storage time, light and temperature on stability of polyphenols in sour cherry (Prunus cerasus) and blackberry (Rubus fruticosus), were harvested in western Serbia (Rasinski region). Total phenol content was monitored in the fruit extracts during 23 days stored at 7°C under darkness and 90 days storage at 23°C in oxygen. For analyzed extracts, first-order reaction kinetics was established for the degradation process of polyphenols. The temperature dependence of the polyphenols degradation rate constants was expressed by the temperature coefficients Q10 of the process. It is found that the Q10 values of polyphenols degradation in sour cherry and blackberry extracts were 1.247 and 3.239, respectively

Uticaj prirodnog ekstrakta ruzmarina na oksidativnu stabilnost prženog kukuruznog čipsa

In this paper, the effects of the natural extract of rosemary on oxidative stability and the sensory properties of corn chips without antioxidant, with antioxidant and antioxidant and linseed (4%) was observed. The natural extract of rosemary Synerox HT (antioxidant) was added in an amount of 1250 ppm (0.125%) on the amount of palm oil for frying the corn chips. Corn chips without antioxidant after 3 months of storage in laboratory conditions (30 °C), is already slightly rancid (1.53 mg of malonaldehyde kg-1 of the final product). Corn chips with antioxidant do not show signs of rancidity after 4 months of storage in laboratory conditions (1.05 mg of malonaldehyde kg-1 of the final product).U ovom radu posmatran je uticaj prirodnog ekstrakta ruzmarina na promenu oksidativne stabilnosti i senzornih osobina kukuruznog čipsa bez antioksidansa, sa antioksidansom i antioksidansom i semenkama lana (4%). Prirodni ekstrakt ruzmarina Synerox HT (antioksidans) dodat je u količini od 1250 ppm (0,125%) na količinu palminog ulja za prženje kukuruznog čipsa. Kukuruzni čips bez antioksidansa nakon 3. meseca čuvanja u laboratorijskim uslovima (30 °C), već je blago užegao (1,53 mg malonaldehida kg-1 gotovog proizvoda). Kukuruzni čips sa antioksidansom ne pokazuje znake užeglosti nakon 4. meseca čuvanja u laboratorijskim uslovima (1,05 mg malonaldehida kg-1 gotovog proizvoda)

О нелокальной модифицированной гравитации

In the last hundred years many significant gravitational phenomena have been predicted anddiscovered by General Relativity (GR), which is still the best theory of gravity. Nevertheless,due to the great observational discoveries of 20th century some (quantum) theoretical and(astrophysical and cosmological) phenomenological difficulties of modern gravity have beenmotivation to search more general theory of gravity than GR. As a result, many modificationsof GR have been considered. One of promising recent investigations is Nonlocal ModifiedGravity. In this article we present a review of some nonlocal gravity models with theirexact cosmological solutions, in which nonlocality is expressed by an analytic function of thed’Alembert–Beltrami operator. Some of obtained solutions contain effects which are usuallyassigned to the dark matter and dark energy.За последние сто лет многие существенные гравитационные явления были предсказаны и обнаружены Общей теорией относительности (GR), которая до сих пор остается лучшей теорией гравитации. Тем не менее, из-за великих наблюдательных открытий 20-го века некоторые (квантовые) теоретические и (астрофизические и космологические) феноменологические трудности современной гравитации были мотивацией для поиска болееобщей теории гравитации, чем ОТО. В результате были рассмотрены многие модификации ТО. Одним из многообещающих недавних исследований является нелокальная модифицированная гравитация. В этой статье мы представляем обзор некоторых нелокальных гравитационных моделей с их точными космологическими решениями, в которых нелокальность выражается аналитической функцией от оператора Даламбера — Бельтрами. Некоторые из полученных решений содержат эффекты, которые обычно присваиваютсятемной материи и темной энергии