Sharif Digital Repository

Nerve repositioning surgery is one of the treatments chosen for the patients with edentulous posterior atrophic mandible. Like any other treatments, this therapy has its advantages and disadvantages, indications and contraindications. The most important complication of this procedure is neurosensory disturbance. This problem may occur at different stages of the treatment. One common time when nerve damage happens is when the nerve is located outside the canal and drilling and insertion of the implant are performed. Accordingly, this report describes a simple and feasible method to retract and protect nerves outside the canal during the treatment of nerve transposition. This will reduce the... 

Nerve repositioning surgery is one of the treatments chosen for the patients with edentulous posterior atrophic mandible. Like any other treatments, this therapy has its advantages and disadvantages, indications and contraindications. The most important complication of this procedure is neurosensory disturbance. This problem may occur at different stages of the treatment. One common time when nerve damage happens is when the nerve is located outside the canal and drilling and insertion of the implant are performed. Accordingly, this report describes a simple and feasible method to retract and protect nerves outside the canal during the treatment of nerve transposition. This will reduce the... 

The main purpose of this article is to generalize a recent result about isometries of Lipschitz spaces. Botelho, Fleming and Jamison [2] described surjective linear isometries between vector-valued Lipschitz spaces under certain conditions. In this article, we extend the main result of [2] by removing the quasi-sub-reflexivity condition from Banach spaces  

The main purpose of this article is to generalize a characterization of constant functions to the context of metric-measure spaces. In fact, we approximate a measurable function, in terms of a certain integrability condition, by Lipschitz functions. Then, similar to Brezis (2002) [2], we establish a necessary and sufficient condition in order that any measurable function which satisfies an integrability condition to be constant a.e. Also, we provide a different proof for the main result of Pietruska-Pałuba (2004) [7] in the setting of Dirichlet forms  

The main purpose of this article is to generalize a theorem of Stepanov which provides a necessary and sufficient condition for almost everywhere differentiability of functions over Euclidean spaces. We state and prove an Lp-type generalization of the Stepanov theorem and then we extend it to the context of Orlicz spaces. Then, this generalized Rademacher-Stepanov type theorem is applied to the Sobolev and bounded variation maps with values into a metric space. It is shown that several generalized differentiability type theorems are valid for the Sobolev maps from a Lipschitz manifold into a metric space. As a byproduct, it is shown that the Sobolev spaces of Korevaar-Schoen and Reshetnyak... 

Let f : M {long rightwards arrow} over(M, -) be an isometric immersion between Riemannian manifolds. For certain conditions on M and over(M, -) in terms of curvatures and external diameter, we extend the non-embedding theorem of Chern and Kuiper to the isometric immersions of non-compact manifolds. Also, our results generalize and improve the main results of Jorge and Koutroufiotis [L. Jorge, D. Koutroufiotis, An estimate for the curvature of bounded submanifolds, Amer. J. Math. 103 (4) (1981) 711-725] and Veeravalli [A. R. Veeravalli, A sharp lower bound for the Ricci curvature of bounded hypersurfaces in space forms, Bull. Austral. Math. Soc. 62 (1) (2000) 165-170]. © 2008 Elsevier B.V.... 

The main purpose of this article is to generalize a characterization of Lipschitz functions in the context of metric-measure spaces. The results are established in the class of metric-measure spaces which satisfy a strong version of the doubling (Bishop-Gromov regularity) condition. Indeed, we establish a necessary and sufficient condition in order that any measurable function which satisfies an integrability condition to be essentially Lipschitzian. © 2019 Elsevier Inc  

In this article, we describe isometries over the Lipschitz spaces under certain conditions. Indeed, we provide a unified proof for the main results of and in a more general setting. Finally, we extend our results for some other functions spaces like the space of vector-valued little Lipschitz maps and pointwise Lipschitz maps. © 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim  

The purpose of this paper is to describe a simple proof for a result originally presented by H. Brezis in [B], with roots in J. Bourgain, H. Brezis and P. Mironescu [BBM]. © 2020 University of Houston  

The purpose of this article is to study the isometries between vector-valued absolutely continuous function spaces, over compact subsets of the real line. Indeed, under certain conditions, it is shown that such isometries can be represented as a weighted composition operator. © 2020 Alireza Ranjbar-Motlagh  

The purpose of this paper is to generalize the Liouville theorem for functions which are defined on the complete Riemannian manifolds. Then, we apply it to the isometric immersions between complete Riemannian manifolds in order to obtain an estimate for the size of the image of immersions in terms of the supremum of the length of their mean curvature vector in a quite general setting. The proofs are based on the Calabi's generalization of maximum principle for functions which are not necessarily differentiable. © 2007 Elsevier B.V. All rights reserved  

This article characterizes the isometries between spaces of all differentiable functions from a compact interval of the real line into a strictly convex Banach space. © 2021 Alireza Ranjbar-Motlagh  

The Poincaré inequality is extended to uniformly doubling metric-measure spaces which satisfy a version of the triangle comparison property. The proof is based on a generalization of the change of variables formula  

The purpose of this article is to study the Besov type function spaces for maps which are defined on abstract metric-measure spaces. We extend some of the embedding theorems of the classical Besov spaces to the setting of abstract spaces. © 2021 Elsevier Inc  

The Poincaré inequality is generalised to metric-measure spaces which support a strong version of the doubling condition. This generalises the Poincaré inequality for manifolds whose Ricci curvature is bounded from below and metric-measure spaces which satisfy the measure contraction property. Copyright Clearance Centre, Inc  

Knowing the rate of evaporation from surface water resources such as channels and reservoirs is essential for precise management of the water balance. Few detailed evaporation studies exist for small lakes or reservoirs in arid regions of the world. In this study, monthly evaporation was determined by Bowen Ratio Energy Budget technique (BREB) for Alghadir reservoir (Saveh, Iran) from 1995-2007 and compared with class-A pan. Daily data were obtained from IMO (Iran Meteorological Organization) weather station, located near the reservoir, for all of these years. Some variations have been observed on the estimated evaporation of the energy budget at different years, ranging from 151 cm for 1997... 

We report the rheological properties of ferro-fluid (FF) containing iron oxide nano-particles. At first, a FF was synthesized by using chemical co-precipitaton[1]. The microstructure study using SEM revealed that the FF contained nano-particles with the mean particle size of 35nm. The XRD study revealed that we have well crystallized structures of magnetite; they appeared to be approximately single crystalline structures. The rheological results proved that the FF has non Newtonian behavior, it is a shear thinning fluid in all magnetic fields, Moreover, the magnetic field increases the viscosity in a definite shear rate due to the nano-particles agglomerations and formation of chain-like... 

The main purpose of this article is to generalize a theorem about the size of minimal submanifolds in Euclidean spaces. In fact, we state and prove a non-existence theorem about harmonic maps from a stochastically complete manifold into a cone type domain. The proof is based on a generalized version of the maximum principle applied to the Lapalace-Beltrami operator on Riemannian manifolds. © 2009 Birkhäuser Verlag Basel/Switzerland