On the Hochschild homology of open Frobenius algebras

We prove that the shifted Hochschild chain complex $C\_*(A,A)[m]$ of a symmetric open Frobenius algebra $A$ of degree $m$ has a natural homotopy coBV-algebra structure. As a consequence $HH\_*(A,A)[m]$ and $HH^*(A,A^\vee)[-m]$ are respectively coBV and BV algebras. The underlying coalgebra and algebra structure may not be resp. counital and unital. We also introduce a natural homotopy BV-algebra structure on $C\_*(A,A)[m]$ hence a BV-structure on $HH\_*(A,A)[m]$. Moreover we prove that the product and coproduct on $HH\_*(A,A)[m]$ satisfy the Frobenius compatibility condition i.e. $HH\_*(A,A)[m]$ is an open Frobenius algebras. If $A$ is commutative, we also introduce a natural BV structure on the shifted relative Hochschild homology $\widetilde{HH}\_*(A)[m-1]$. We conjecture that the product of this BV structure is identical to the Goresky-Hingston\cite{GH} product on the cohomology of free loop spaces when $A$ is a commutative cochain algebra model for $M$.Comment: Many corrections have been made and the signs are now given explicil

On algebraic structures of the Hochschild complex

We first review various known algebraic structures on the Hochschild (co)homology of a differential graded algebras under weak Poincar{\'e} duality hypothesis, such as Calabi-Yau algebras, derived Poincar{\'e} duality algebras and closed Frobenius algebras. This includes a BV-algebra structure on $HH^*(A,A^\vee)$ or $HH^*(A,A)$, which in the latter case is an extension of the natural Gerstenhaber structure on $HH^*(A,A)$. As an example, after proving that the chain complex of the Moore loop space of a manifold $M$ is a CY-algebra and using Burghelea-Fiedorowicz-Goodwillie theorem we obtain a BV-structure on the homology of the free space. In Sections 6 we prove that these BV/coBVstructures can be indeed defined for the Hochschild homology of a symmetric open Frobenius DG-algebras. In particular we prove that the Hochschild homology and cohomology of a symmetric open Frobenius algebra is a BV and coBV-algebra. In Section 7 we exhibit a BV structure on the shifted relative Hochschild homology of a symmetric commutative Frobenius algebra. The existence of a BV-structure on the relative Hochschild homology was expected in the light of Chas-Sullivan and Goresky-Hingston results for free loop spaces. In Section 8 we present an action of Sullivan diagrams on the Hochschild (co)chain complex of a closed Frobenius DG-algebra. This recovers Tradler-Zeinalian \cite{TZ} result for closed Froebenius algebras using the isomorphism $C^*(A ,A) \simeq C^*(A,A^\vee)$.Comment: This is the final version. Many improvements and corrections have been made.To appear in Free Loop Spaces in Geometry and Topology, IRMA Lectures in Mathematicsand Theoretical Physics, to be published by EMS-P

String topology of Poincare duality groups

Let G be a Poincare duality group of dimension n. For a given element g in G, let C_g denote its centralizer subgroup. Let L_G be the graded abelian group defined by (L_G)_p = oplus_{[g]}H_{p+n}(C_g) where the sum is taken over conjugacy classes of elements in G. In this paper we construct a multiplication on L_G directly in terms of intersection products on the centralizers. This multiplication makes L_G a graded, associative, commutative algebra. When G is the fundamental group of an aspherical, closed oriented n manifold M, then (L_G)_* = H_{*+n}(LM), where LM is the free loop space of M. We show that the product on L_G corresponds to the string topology loop product on H_*(LM) defined by Chas and Sullivan.Comment: This is the version published by Geometry & Topology Monographs on 22 February 200

Transportation system selection in open-pit mines (Truck-Shovel and IPCC systems) based on the technical, economic, environmental, safety, and social (TEcESaS) indexes

The production of raw materials through mining projects is nowadays very challenging, mainly due to the rapid progress in the industrial and technological fields. On the one hand, they have to fulfill industries' requirements in their demand for materials while making a profit based on the current technologies. On the other hand, they should consider all other limitations, primarily environmental and social challenges that are confronting. The transportation system in any mining project is one of the most significant parts, especially in the technical and economic issues. It must transfer the planned volume of ore/waste that the whole stream of the mining process would not be interrupted and, it can cover the technical challenges and the costs imposed on the project. Additionally, it should be designed and selected to have the lowest environmental impact and the highest safety during the operation. Accordingly, a transportation system selection process that considers all these factors is one of the challenging issues in any mining project. Although the Truck-Shovel system is known as the conventional transportation in open-pit mines, which is preferable because of the low capital cost and high flexibility, it still imposes a high rate of operating costs, safety issues as well as environmental footprints. In-Pit Crushing and Conveying (IPCC) systems are the alternative transportation systems for the Truck-Shovel systems, in which the material is crushed inside the mine’s pit limit and transferred into the outside through conveyor belts. Although these systems are not new, they are mostly neglected as a transportation option basically due to the high capital cost and low flexibility. On the contrary, they can offer more environmentally friendly and safer working areas and a lower operating cost. According to these facts, each transportation system is preferable in a couple of technical, economic, environmental, safety, and social issues. Accordingly, in each circumstance, one or more of these systems can be used in the mining project. However, there is not yet a way or tool that investigates the transportation system selection along with the mine life that takes into account all of these factors. To fill this gap, this project aims to define a model to introduce all these elements while it is interactively connected throughout the mine life. For this and as the first step, the system dynamics modeling is defined and used to build the model for all the technical, economic, environmental, safety, and social factors. As an output of this step, software entitled “TEcESaS Indexes” is designed and produced through Venapp that makes working with the model comfortable. As the second step, a selection method based on the Analytical Hierarchy Process (AHP) is performed that the transportation system selection regarding all the mentioned factors can be made. As the output in this step, the “Sustainability Index” software programmed in the Java language is developed. Considering a hypothetical copper open-pit mine as the case study and implementing the designed software, the results show although the Truck-Shovel system should be used in the first two years of the project (2016 and 2017) in the single expert and deterministic mode, the Fully Mobile In-Pit Crushing and Conveying (FMIPCC) system shows the highest sustainability index among other transportation systems from 2018 until the end of the mine life. While in the group decision making and deterministic simulation, the Truck-Shovel system should be utilized from 2016 to 2020. Additionally, in the group decision making and stochastic mode, the FMIPCC is the selected transportation system with the highest sustainability index probability

EFFECT OF SELENIUM ON GROWTH AND PHYSIOLOGICAL TRAITS OF BASIL PLANT (Ocimum basilicum L.) UNDER ARSENIC STRESS CONDITIONS

Arsenic is one of the common toxins in the environment that enters the environment through natural and artificial sources and causes stress in plants through various ways, including the effect on growth and metabolism of the plant. Further, the absorbance of this element in plants and the entry into the food chain create toxicity for humans. On the other hand, Selenium is a non-biological stress reliever and has a considerable impact on improved plant growth and photosynthesis and reduced stress. Due to the interaction of Arsenic and Selenium in soil and different plants and the importance of Basil plant, an experiment was performed to investigate the effect of Selenium on growth and some physiological traits of Basil plant (Ocimum basilicum L.) under Arsenic stress conditions. To implement this plan, a factorial pot experiment was carried out based on a randomized complete block design with three replications in Damghan Islamic Azad University. Arsenic concentrations of 0, 100, 200 and 300 micromoles with irrigation water were applied three times at regular intervals and Selenium concentrations of 0, 2.5, 5 and 10 mg L-1 were applied three times by solution spraying at regular intervals. In this experiment, it was found that growth traits decreased by increasing Arsenic. The lowest performance was related to Arsenic concentration of 300 μm, resulting in a 45% decrease in growth and by applying Selenium treatment, Arsenic toxicity effect was reduced. The best performance was associated with Selenium concentration of 5 mg L-1.

Discrete element modelling of the dynamic behaviour of non-spherical particulate materials

PhD ThesisA numerical model based on the discrete element (DE) method, for modelling the flow of irregularly shaped, smooth-surfaced particles in a 3-D system is presented. An existing DE program for modelling the contact between spherical particles in periodic space (without real walls or boundaries) was modified to model non-spherical particles in a system with containing walls. The new model was validated against analytical calculations of single particle movements and also experimentally against data from physical experiments using synthetic non-spherical particles at both a particle and bulk scale. It was then used to study the effect of particle shape on the flow behaviour of assemblies of particles with various aspect ratios discharging from a flat-bottomed hopper. The particles were modelled using the Multi-Sphere Method (MSM) which is based on the CSG (Constructive Solid Geometry) technique for construction of complex solids by combining primitive shapes. In this method particle geometry is approximated using overlapping spheres of arbitrary diameter which are fixed in position relative to each other. The contact mechanics and contact detection method are the same as those used for spheres, except that translation and rotation of element spheres are calculated with respect to the motion of the whole particle....Numerical simulations of packing and flow of particles from a flat-bottomed hopper with a range of aspect ratios were performed to investigate the effect of particle shape on packing and flow behaviour of a particulate assembly. It was found that the particle shape influenced both bed structure and flow characteristics such as flow pattern, shear band strength and the occurrence of bridging. The flow of the bed of spherical particles was smoother than the flow of beds of elongated particles in which flow was fluctuating and there was more resistance to shear.Ministry of Culture and Higher Education of IRAN: University of Mashhad