Given a prime p, a , nite group G and a non-identity element g, what is the largest number of p th roots g can have? We write ϱ, p(G), or just ϱ, p. . .

Hash functions have a very important role in network and telecommunication security. These functions play an important role in hashing a message which are widely used in cryptographic applications such as digital signatures, random number generator algorithms, authentication protocols, and so on. Rotational cryptanalysis is a relatively new attack that is part of a generic attack on hash functions and is effective on algorithms that have an ARX structure. In this paper, for the first time, we apply a rotational cryptanalysis and with the given assumption of the markov chain for the modular additions sequence employed in two algorithms Shabal and CubeHash, which are second-round candidates for the SHA-3 competition that use the ARX property in their structure. With the implementation of rotational cryptanalysis we arrived at the complexity of 2-3393. 58 for the entire 16+3-rounds Shabal algorithm and the complexity of 2-57. 6 for the en-tire 16-round CubeHash algorithm. According to the obtained results, it can be seen that due to the large number of modular additions with the given assumption of markov chain, the Shabal algorithm exhibits greater resistance to rotational cryptanalysis, compared to the CubeHash algorithm and is less likely to succeed.

A nontrivial graph is called nicely distance-balanced (nicely edge distance-balanced), whenever there exist positive integers γ _V (γ _E), such that for any adjacent vertices u and v in V(Γ ), there are exactly γ _V vertices in V(Γ ) (γ _E edges in E(Γ ) that are closer to u than v, and exactly γ _V vertices in V(Γ ) (γ _E edges in E(Γ )) that are closer to v than u. In this paper, we will prove that hyper cube Q_n and the folded cube F_n are nicely distance-balanced and Q_n is also nicely edge distance-balanced. A nontrivial graph is called nicely distance-balanced (nicely edge distance-balanced), whenever there exist positive integers γ _V (γ _E), such that for any adjacent vertices u and v in V(Γ ), there are exactly γ _V vertices in V(Γ ) (γ _E edges in E(Γ ) that are closer to u than v, and exactly γ _V vertices in V(Γ ) (γ _E edges in E(Γ )) that are closer to v than u. In this paper, we will prove that hyper cube Q_n and the folded cube F_n are nicely distance-balanced and Q_n is also nicely edge distance-balanced.

Some contemporary logicians have introduced a new simple method of logical consequences and reduced all immediate arguments to Conversion and Obversion. By dint of positive and infinite terms, one of the logicians, Reza Akbari, increased the four traditional quantified propositions to 32 ones: the 4 well-known positives, 4 subject-infinites, 4 predicate-infinites, 4 two-sided-infinites, and the same 16 with ‘A’ and ‘B’ in which converted. Akbari, also, stated among some of the 32 propositions the interrelations: the opposition square, conversion, conversion by contradiction, obversion, inversion, and two new relations: “contraposition of the subject” and the “unknown”. This theory extending the classical 4-quntified-theory can be named “32-quntified-theory”. In this paper, I show that the 32 propositions are equivalent four-by-four, hence, we can reduce the 32 propositions to 8 ones and their relations to the six: equivalence, implication, inconsistency, inclusive ‘or’, exclusive ‘or’ and none (which is the same as Akbari’s “unknown”. By this, I decrease the perplexities of the theory and express so easily and elegantly the relations between the eight in a cube similar to the “Square of Opposition,” which I call the “Cube of Opposition.”

Large eddy simulation of flow over a wall-mounted cube in a channel was performed at a Reynolds number of 40000. The structure function modeling of the subgrid-scale stress terms was used with three slightly varying versions of its selective type. The convective terms were discretized using a QUICK scheme, along with a relatively coarse grid. A series of time-averaged velocities and turbulent stresses were computed and compared with experimental data to examine the performance of these models. The structure function model yielded deficient mean flow structure and turbulence statistics compared with the selective structure function. While none of these models could reproduce experimental results exactly, the results of time-averaged streamline plots and turbulent kinetic energy for one of the selective structure function models showed less discrepancy with experimental data compared with other models. It was shown that implementation of a wall function does not improve the results considerably and, in general, with a coarse grid resolution, it is possible to obtain some reasonable results as compared to the experiment.        

Data warehouse and OLAP are essential elements of decision support systems (DSS) and have been studied in database issues extensively. The requirements of decision support systems are different from on-line transactional processing systems. Query optimization and efficient data cube computation have primary roles in improving functionality of DSS.This paper presents a new method for query processing in data warehouses and computing data cubes using bottom-up cube computation techniques. Results of implementation show that the proposed algorithm outperforms two best known algorithms (based on time criterion), and is much faster than them in answering to monotonic query with large volume of data. Furthermore, 2-dimensional view of ex-cube and transforming the data cube to a hyper graph structure, reduce the required space of the algorithm when we aggregate subsets of cube's dimension.

The data stored in data warehouse is used for making strategic decisions by integrating heterogeneous data from multiple sources at a single storage place, where data is used for querying and analysis purposes. With the advancement in the technology, Business Analytics and Business intelligence are being increasingly used in the financial sector for forecasting business decisions. Many On-Line Analytical Processing (OLAP) tools are being largely explored that can contribute to business decision making. Banking operation handles a lot of data as they operate daily. Subsequently, preparing of this tremendous volume of information requires instant and quick tools that can process the information at high processing speeds. Through this research paper, we represent the OLAP cube as one of the tools which can be used for business analysis. A case study of a bank and loan approval process is considered as one of the areas for implementation and analysis of business decisions using business intelligence which can serve as a key factor for increasing intelligence in the banking sector to make reliable business decisions. Higher management can forecast and predict various outcomes from the bank data warehouse using On-Line Analytical Processing technology which provided a multidimensional view of the data. Analysts can make business decisions by analyzing the reports and pattern trends in the graphs. Management can modify existing policies and procedures to increase the growth of the bank and can have a healthy competition with their competitors.