Primjena integro-diferencijalne varijacijske razlomne zadaće i razlomnog pristupa integralima po putevima stohastičkom modeliranju

The fractional path integral approach is applied to stochastic models, in particular the financial derivatives and options pricing formulated within the framework of the fractional action-like variational approach recently introduced by the author. Many interesting features and consequences are revealed in some details.Proučavaju se stohastički modeli primjenom integrala po putevima, a posebno se razlažu novčane izvodnice i mogućnosti u određivanju cijena u okviru razlomnog djelotvornog varijacijskog pristupa nedavno uvedenog autorom. Mnoge se zanimljive odlike i posljedice otkrivaju djelomično

Primjena integro-diferencijalne varijacijske razlomne zadaće i razlomnog pristupa integralima po putevima stohastičkom modeliranju

The fractional path integral approach is applied to stochastic models, in particular the financial derivatives and options pricing formulated within the framework of the fractional action-like variational approach recently introduced by the author. Many interesting features and consequences are revealed in some details.Proučavaju se stohastički modeli primjenom integrala po putevima, a posebno se razlažu novčane izvodnice i mogućnosti u određivanju cijena u okviru razlomnog djelotvornog varijacijskog pristupa nedavno uvedenog autorom. Mnoge se zanimljive odlike i posljedice otkrivaju djelomično

Fractal universe and quantum gravity

We propose a field theory which lives in fractal spacetime and is argued to be Lorentz invariant, power-counting renormalizable, ultraviolet finite, and causal. The system flows from an ultraviolet fixed point, where spacetime has Hausdorff dimension 2, to an infrared limit coinciding with a standard four-dimensional field theory. Classically, the fractal world where fields live exchanges energy momentum with the bulk with integer topological dimension. However, the total energy momentum is conserved. We consider the dynamics and the propagator of a scalar field. Implications for quantum gravity, cosmology, and the cosmological constant are discussed.Comment: 4 pages. v2: typos corrected; v3: discussion improved, intuitive introduction added, matches the published versio

Multi-band D-TRILEX approach to materials with strong electronic correlations

We present the multi-band dual triply irreducible local expansion (D-TRILEX) approach to interacting electronic systems and discuss its numerical implementation. This method is designed for a self-consistent description of multi-orbital systems that can also have several atoms in the unit cell. The current implementation of the D-TRILEX approach is able to account for the frequency- and channel-dependent long-ranged electronic interactions. We show that our method is accurate when applied to small multi-band systems such as the Hubbard-Kanamori dimer. Calculations for the extended Hubbard, the two-orbital Hubbard-Kanamori, and the bilayer Hubbard models are also discussed

Amended criteria of oscillation for nonlinear functional dynamic equations of second-order

In this paper, the sharp Hille-type oscillation criteria are proposed for a class of secondorder nonlinear functional dynamic equations on an arbitrary time scale, by using the technique of Riccati transformation and integral averaging method. The obtained results demonstrate an improvement in Hille-type compared with the results reported in the literature. Some examples are provided to illustrate the significance of the obtained results. © 2021 by the authors. Licensee MDPI, Basel, Switzerland.The authors would like to thank anonymous referees for their careful reading of the entire manuscript, which helped significantly improve this paper’s quality. This work was supported by Research Deanship of Hail University under grant No. 0150396

Effect of vitamin D replacement on maternal and neonatal outcomes: a randomised controlled trial in pregnant women with hypovitaminosis D. A protocol

Introduction: The vitamin D recommended doses during pregnancy differ between societies. The WHO guidelines do not recommend routine prenatal supplementation, but they underscore the fact that women with the lowest levels may benefit most. The effects of routine supplementation during pregnancy on maternal and neonatal clinical outcomes have not been investigated in the Middle East, where hypovitaminosis D is prevalent. Our hypothesis is that in Middle Eastern pregnant women, a vitamin D dose of 3000?IU/day is required to reach a desirable maternal 25-hydroxyvitamin D [25(OH)D] level, and to positively impact infant bone mineral content (BMC).Methods and analysis: This is a multicentre blinded randomised controlled trial. Pregnant women presenting to the Obstetrics and Gynaecology clinics will be approached. Eligible women will be randomised to daily equivalent doses of cholecalciferol, 600?IU or 3000?IU, from 15 to 18?weeks gestation until delivery. Maternal 25(OH)D and chemistries will be assessed at study entry, during the third trimester and at delivery. Neonatal anthropometric variables and 25(OH)D level will be measured at birth, and bone and fat mass assessment by dual-energy X-ray absorptiometry scan at 1?month. A sample size of 280 pregnant women is needed to demonstrate a statistically significant difference in the proportion of women reaching a 25(OH)D level ?50?nmol/L at delivery, and a difference in infant BMC of 6 (10)g, for a 90% power and a 2.5% level of significance. The proportions of women achieving a target 25(OH)D level will be compared between the two arms, using ?2. An independent t test will be used to compare mean infant BMC between the two arms. The primary analysis is an intention-to-treat analysis of unadjusted results.Ethics and dissemination: The protocol has been approved by the Institutional Review Board at the American University of Beirut-Lebanon (IM.GEHF.22). The trial results will be published in peer-reviewed medical journals and presented at scientific conferences.Trial registration number: NCT02434380.<br/

Fractional Action Cosmology with Power Law Weight Function

Motivated by an earlier work on fractional-action cosmology with a periodic weight function [1], we extend it by choosing a power-law weight function in the action. In this approach, we obtain a varying gravitational coupling constant. We then model dark energy in this paradigm and obtain relevant cosmological parameters.Comment: 12 pages, 9 figures, Contributed talk published in the proceedings of "3rd Italian-Pakistani Workshop on Relativistic Astrophysics

Fractional Dynamics from Einstein Gravity, General Solutions, and Black Holes

We study the fractional gravity for spacetimes with non-integer dimensions. Our constructions are based on a geometric formalism with the fractional Caputo derivative and integral calculus adapted to nonolonomic distributions. This allows us to define a fractional spacetime geometry with fundamental geometric/physical objects and a generalized tensor calculus all being similar to respective integer dimension constructions. Such models of fractional gravity mimic the Einstein gravity theory and various Lagrange-Finsler and Hamilton-Cartan generalizations in nonholonomic variables. The approach suggests a number of new implications for gravity and matter field theories with singular, stochastic, kinetic, fractal, memory etc processes. We prove that the fractional gravitational field equations can be integrated in very general forms following the anholonomic deformation method for constructing exact solutions. Finally, we study some examples of fractional black hole solutions, fractional ellipsoid gravitational configurations and imbedding of such objects in fractional solitonic backgrounds.Comment: latex2e, 11pt, 40 pages with table of conten

Consanguinity and reproductive health among Arabs

Consanguineous marriages have been practiced since the early existence of modern humans. Until now consanguinity is widely practiced in several global communities with variable rates depending on religion, culture, and geography. Arab populations have a long tradition of consanguinity due to socio-cultural factors. Many Arab countries display some of the highest rates of consanguineous marriages in the world, and specifically first cousin marriages which may reach 25-30% of all marriages. In some countries like Qatar, Yemen, and UAE, consanguinity rates are increasing in the current generation. Research among Arabs and worldwide has indicated that consanguinity could have an effect on some reproductive health parameters such as postnatal mortality and rates of congenital malformations. The association of consanguinity with other reproductive health parameters, such as fertility and fetal wastage, is controversial. The main impact of consanguinity, however, is an increase in the rate of homozygotes for autosomal recessive genetic disorders. Worldwide, known dominant disorders are more numerous than known recessive disorders. However, data on genetic disorders in Arab populations as extracted from the Catalogue of Transmission Genetics in Arabs (CTGA) database indicate a relative abundance of recessive disorders in the region that is clearly associated with the practice of consanguinity

Geometry and field theory in multi-fractional spacetime

We construct a theory of fields living on continuous geometries with fractional Hausdorff and spectral dimensions, focussing on a flat background analogous to Minkowski spacetime. After reviewing the properties of fractional spaces with fixed dimension, presented in a companion paper, we generalize to a multi-fractional scenario inspired by multi-fractal geometry, where the dimension changes with the scale. This is related to the renormalization group properties of fractional field theories, illustrated by the example of a scalar field. Depending on the symmetries of the Lagrangian, one can define two models. In one of them, the effective dimension flows from 2 in the ultraviolet (UV) and geometry constrains the infrared limit to be four-dimensional. At the UV critical value, the model is rendered power-counting renormalizable. However, this is not the most fundamental regime. Compelling arguments of fractal geometry require an extension of the fractional action measure to complex order. In doing so, we obtain a hierarchy of scales characterizing different geometric regimes. At very small scales, discrete symmetries emerge and the notion of a continuous spacetime begins to blur, until one reaches a fundamental scale and an ultra-microscopic fractal structure. This fine hierarchy of geometries has implications for non-commutative theories and discrete quantum gravity. In the latter case, the present model can be viewed as a top-down realization of a quantum-discrete to classical-continuum transition.Comment: 1+82 pages, 1 figure, 2 tables. v2-3: discussions clarified and improved (especially section 4.5), typos corrected, references added; v4: further typos correcte