A formulation of the fractional Noether-type theorem for multidimensional Lagrangians

This paper presents the Euler-Lagrange equations for fractional variational problems with multiple integrals. The fractional Noether-type theorem for conservative and nonconservative generalized physical systems is proved. Our approach uses well-known notion of the Riemann-Liouville fractional derivative.Comment: Submitted 26-SEP-2011; accepted 3-MAR-2012; for publication in Applied Mathematics Letter

The use of nasal midazolam in reducing preoperative anxiety in children

Background: Surgery and anesthesia can cause a considerable distress with psychological consequences for children. This preoperative anxiety can lead to post operative emergence delirium, maladaptive behavioral changes such as night time crying, enuresis, feeding difficulties, apathy, and withdrawal.Objectives: The aim of this study is to investigate the effect of nasal midazolam as a routine intervention to reduce pre-operative anxiety and inducing anxiolysis in children undergoing day case procedure.Method: One hundred children were randomly allocated into two groups. The study group (N=50) were premedicated with nasal midazolam 0.2mg/kg and the control group (N=50) who received 0.04ml of normal saline. The children response to nasal administration was noticed and after 15 minutes children were taken to operating room. Anxiety at parental separation and at induction of anesthesia was measured using modified-Yale Preoperative Anxiety Scale.Results: Children who received nasal midazolam had a significantly better parental separation and induction of anesthesia. 88% of children who received nasal midazolam scored below 30-indicating absence of anxiety- on modified-Yale Preoperative Anxiety Scale compared to 32% in the control group. More than half of patients in both groups found nasal route to be unpleasant and stressful.Conclusion: For children undergoing elective brief surgical procedure, nasal midazolam is effective in reducing preoperative anxiety. Nasal midazolam was associated in more than half of patients with nasal irritation and crying, a route can not be recommended in children

Laparoscopy for the management of impalpable testis

Background: Cryptorchidism is encountered in 21% of preterm infants, 2-4% of all full term boys and 1% of one year old boys.Objectives:To present our experience in the utilization of diagnostic laparoscopy for the management of children with impalpable testes.Method:This is a retrospective study conducted between March 2010 and December 2011. The medical records of boys with impalpable testis were reviewed. Diagnostic laparoscopic findings regarding presence, morphological state, and location of testis were analyzed. Special attention to how initial laparoscopy influenced subsequent surgical procedures and management.Results:Fifty four boys underwent laparoscopy with 76 impalpable testes. Forty testes were unilateral impalpable testes, two third of them were left sided. Thirty seven testes were intraabdominal, eight of them were atrophied and excised laparoscopically. Twenty nine of them were viable, 90% of them underwent first stage Fowler-Stephens procedure, while the rest underwent primary laparoscopic orchidopexy. Vas and spermatic vessels were seen entering inguinal canal in 25 testes. This group had immediate inguinal exploration, 22 of testes underwent orchidopexy and three orchidectomy. Fourteen boys found to blind end vas and vessels with no further treatment needed.Conclusions: Laparoscopic exploration should be performed because it accurately identifies and localizes the missing testis. In addition, it facilitates the planning of definitive surgical management of orchidopexy, staged orchidopexy or orchidectomy. So we recommend that initial laparoscopic exploration should be performed for patient with impalpable testis.Keywords:Impalpable testis, Laparoscopy, Orchidopexy, Jordan

Fractional Euler-Lagrange differential equations via Caputo derivatives

We review some recent results of the fractional variational calculus. Necessary optimality conditions of Euler-Lagrange type for functionals with a Lagrangian containing left and right Caputo derivatives are given. Several problems are considered: with fixed or free boundary conditions, and in presence of integral constraints that also depend on Caputo derivatives.Comment: This is a preprint of a paper whose final and definite form will appear as Chapter 9 of the book Fractional Dynamics and Control, D. Baleanu et al. (eds.), Springer New York, 2012, DOI:10.1007/978-1-4614-0457-6_9, in pres

Generalized transversality conditions in fractional calculus of variations

Problems of calculus of variations with variable endpoints cannot be solved without transversality conditions. Here, we establish such type of conditions for fractional variational problems with the Caputo derivative. We consider: the Bolza-type fractional variational problem, the fractional variational problem with a Lagrangian that may also depend on the unspecified end-point phi(b), where x = phi(t) is a given curve, and the infinite horizon fractional variational problem. (C) 2012 Elsevier B.V. All rights reserved

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

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

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