In this paper, we present the concept of D􀀀, topological dual of a BC􀀀, module X with a D􀀀, norm k: kD, X and we , nd D􀀀, topological duals of D􀀀, normed bicomplex BC􀀀, modules l| p (BC) for 1 ,p < 1: We also investigate some fundamental topological properties of bicomplex BC􀀀, modules l| p (BC) by de, ning some topological concepts such as solid space, monotone space, BK􀀀, space, symmetric space in the bicomplex setting by using the D􀀀, norm j: j|:

Equality of hh -curvatures of the Berwald and Cartan connections leads to a new class of Finsler metrics, so-called BC-generalized Landsberg metrics. Here, we prove that every BC-generalized Landsberg metric of scalar flag curvature with dimension greater than two is of constant flag curvature.

In this paper, we introduce the notion of hyper pseudo BC K - algebras, which is a generalization of pseudo BC K -algebras and hyper BC K -algebras and we investigates some related properties. In follow, we define some kinds of hyper pseudo BC K -ideals of a hyper pseudo BC K - algebra and we find the relations among them. Finally, we characterize the hyper pseudo BC K -ideals of type 4 generated by a nonempty subset.  

During the late fourth millennium B. C some changes took place in many archaeological sites of south eastern Iran that affected the different aspects of life in the region. By expanding of local cultures in the late 4th millennium B. C, at the same time we are witnessing the presence of proto Elamite cultural materials near some key sites and consequently remarkable increasing in trade exchanges with distant areas. In fact, some evidence of foreign merchants with Banesh/proto Elamite elements that has specialization on storing goods, commodity management and trade in long distances. These evidence have been documented by archaeological excavations near Shahdad, Konar Sandal and Shahr i Sokhta. All these sites are the big cities in the first centuries of third millennium B. C. It seems that in spite of expansion of Aliabad culture in Kerman, Baluchestan, Makran and near Sistan since 3700 B. C to 3300 B. C that consequently followed by local cultures in each area from 3300 to 3000 B. C, the main factor for starting and developing of urbanization in south east of Iran is connected to presence of proto Elamite culture and building the exchange centers or Bazar in the areas with good potential for the natural resource. These areas became the urban centers in the beginning of third millennium B. C. In fact, the art of those merchants was learning to local people that how to control their valuable resource and crafts for exchange and interaction with the other people.