In this paper, we study the categorical and algebraic properties, such as limits and colimits of the category Pos-S with respect to order dense embeddings. Injectivity with respect to this class of monomorphisms has been studied by the author and used to obtain information about injectivity relative to regular monomorphisms. Then, we study three di erent kinds of essentiality, usually used in literature, with respect to the class of all order dense embed-dings of S-posets, and investigate their relations to order dense injectivity. We will see, among other things, that although all of these essential extensions are not necessarily equivalent, they behave equivalently with respect to order dense injectivity. More precisely, it is proved that order dense injectivity well behaves regarding these essentialities. Finally, a characterization of these essentialities over pogroups is given.

Let M and P be right R-modules. A submodule K of an R-module M is called P-dense if for each m Î M; (K: m) is a P-faithful right ideal of R: PR is nonsingular if and only if, for each R-module M; every essential submodule of M is a P-dense submodule. For any R-module M, we obtain P-rational extention of M and equivalent condition in order that M is equal with its P-rational extention is found. An R-module P is called right Kasch if every simple R-module can be embedded in P: Finally, we given some equivalent conditions for an R-module P to be right Kasch.

One of the obvious reasons for most disorders in network service provisioning is network path congestion. Congestion avoidance in today's networks is too costly and sometimes impossible. With the introduction of SDN, centralizing the equipment's control plane has become possible. This paper presents an enhanced method named ESV-DBRA to avoid congestion in multi-tenant SDN networks. At first, ESV-DBRA monitors the traffic load and delay of all network paths for each tenant individually. Then, by merging the parameters obtained from the monitoring, the Service Level Agreements (SLA), and a novel proposed cost function, it calculates the cost of the network paths per tenant. As a result, traffic for each tenant is routed through the path/paths at the lowest possible cost from the tenant's perspective. Next, the bandwidth quotas will be calculated and assigned to the tenants over their optimal routes. Afterward, whenever congestion is likely to occur in a path, ESV-DBRA automatically changes the route or bandwidth of the tenants' traffic related to this path to avoid congestion. Related algorithms are also proposed.Eventually, simulations show that the proposed method effectively increases bandwidth utilization by 10.76%.

Let M be a class of (mono) morphisms in a category A. To study mathematical notions, such as injectivity, tensor products and flatness, one needs to have some categorical and algebraic in-formation about the pair (A, M). In this paper we take A to be the category Act-S of S-acts, for a semigroup S, and Msd to be the class of stronglys-dense monomorphisms and study the categorical properties, such as limits and colimits, of this class.

‎In this paper we take A to be the category Pos-S‎ ‎of S-posets‎, ‎for a posemigroup S‎, Mpd to‎ ‎be the class of partially ordered sequantially-dense‎ ‎monomorphisms and study the categorical properties‎, ‎such as‎ ‎limits and colimits‎, ‎of this class‎. ‎These properties are usually‎ ‎needed to study the homological notions‎, ‎such as injectivity‎, ‎of‎ S-posets‎. Also we show that it is actually equivalent to Cpd-density resulting from a closure operator.

The submodules with the property of the title (a submodule N of an R -module M is called strongly dense in M, denoted by N£sd M, if for any index set I, ΠIN£d ΠIM) are introduced and fully investigated. It is shown that for each submoduleN of M there exists the smallest subsetD′ ÍM such that N+D′ is a strongly dense submodule of M and D′ ∩ N=0. We also introduce a class of modules in which the two concepts of strong essentiality and strong density coincide. It is also shown that for any module M, dense submodules in M are strongly dense if and only if M £sd ~E (M), where ~E (M) is the rational hull of M. It is proved that R has no strongly dense left ideal if and only if no nonzeroelement of every cyclic R -module M has a strongly dense annihilator in R. Finally, some properties and new concepts related to strong density are studied.

Different types of contact, including contact between node pairs, any-contact of nodes, and contacts of the entire network, are used to characterize social relations in mobile social networks. Different modes of routing, from the point of view of message delivery semantics, encompass unicasting, multicasting, any-casting, and broadcasting. Studies have shown that using probability distribution functions of contact data, which is mainly assumed to be homogeneous for nodes, improves the performance of these networks. However, there exists an important challenge in studies on distributions. A lot of works apply the distribution of one type of contact to other types. Hence in routing applications, it causes to use of the distribution of one type of contact for any mode of routing. This study provides a complete solution to model each type of homogeneous contact data distribution and to use them in different modes of routing. We propose a routing algorithm that uses this new model. Results show that our solution improves the average latency of comparing methods Epidemic, TCCB, and DR about 3.5-times, 30%, and 45%, respectively. It achieves a delivery rate of about 5% and 6%, and average latency about 6% and 8% better than that of DR and TCCB, respectively.

Considering the great significant role that routing protocols play in transfer rate and choosing the optimum path for exchange of data packages, and further in the amount of consumed energy in the routing protocol, the present study has focused on developing an efficient compound energy algorithm based on cluster structure which is called active node with cluster structure. The purpose of this algorithm is to distribute the heavy traffic of data and equal load of highly-consumed energy throughout the networks by introducing unequal and unbalanced clusters into the network. In the second stage, the light sensor mechanism which is called active node sensor algorithm has been proposed. The major purpose of this mechanism is to prevent excessive interfering data of sensors through incorporating a set of active nodes in each cluster with a defensive shield near to the incident node. The third stage has aimed at proposing an active node algorithm for complexity of internal and external addressing due to clusters routing in high density distribution based on the values within node range. The obtained results indicate relative success of the design in terms of energy optimization on the basis of routing protocol.

Monitoring and evaluation of transformers are essential to prevent their insulation failure. In this paper, the use of 2-furan-carboxaldehyde (2-FAL) and methanol (MeOH) concentrations as the main products of paper insulation degradation, and insulation condition markers, has been studied. In order to study the degradation process and production of degradation products, the thermal aging process of the transformer insulation system was implemented in laboratory conditions. The results of laboratory studies show that in the early stages of degradation the amount of MeOH is significant compared to 2-FAL. Also, the estimation of the degree of polymerization (DP) in the early stages of degradation (DP>800) through MeOH concentration and with decreasing DP (DP <800) through 2-FAL concentration is closer to the real value. The results of studies performed on 35 distribution transformers confirm the production of significant amounts of MeOH in the early stages of degradation. Also, the estimated DP values for the studied transformers were obtained through 2-FAL and MeOH concentration. The results show that estimating the amount of DP through MeOH concentration is associated with a probability of error of about 9% compared to estimating DP through 2-FAL concentration.