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The problem of finding necessary and sufficient conditions to decompose a complete tripartite graph K(r, s, t) into 5-cycles was first considered by Mahmoodian and Mirzakhani (1995). They stated some necessary conditions and conjectured that these conditions are also sufficient. Since then, many cases of the problem have been solved by various authors; however the case when the partite sets r ≤ s ≤ t have odd and distinct sizes remains open. A necessary condition is t ≤ 3r. Billington and Cavenagh (2011) have shown that when r, s, and t are all odd and r ≤ s ≤ t ≤ κr, where κ ≈ 1.0806, then the conjectured necessary conditions for decomposing are also sufficient. We extend this result... 

Let G be a graph. The energy of G, (Formula presented.), is defined as the sum of absolute values of its eigenvalues. Here, it is shown that if G is a graph and (Formula presented.) is an edge partition of G, such that (Formula presented.) are spanning; then (Formula presented.) if and only if (Formula presented.), for every (Formula presented.) and (Formula presented.), where (Formula presented.) is the adjacency matrix of (Formula presented.). It was proved that if G is a graph and (Formula presented.) are subgraphs of G which partition edges of G, then (Formula presented.). In this paper we show that if G is connected, then the equality is strict, that is (Formula presented.). © 2022... 

A gauge invariant partition function is defined for gauge theories which leads to the standard quantization. It is shown that the descent equations and consequently the consistent anomalies and Schwinger terms can be extracted from this modified partition function naturally  

Let R be a ring with non-zero identity. The unit graph G(R) of R is a graph with elements of R as its vertices and two distinct vertices a and b are adjacent if and only if a + b is a unit element of R. It was proved that if R is a commutative ring and is a maximal ideal of R such that |R/| = 2, then G(R) is a complete bipartite graph if and only if (R, ) is a local ring. In this paper we generalize this result by showing that if R is a ring (not necessarily commutative), then G(R) is a complete r-partite graph if and only if (R, ) is a local ring and r = |R/| = 2n for some n ∞ N or R is a finite field. Among other results we show that if R is a left Artinian ring, 2 U(R) and the clique... 

A new local composition model was used to study the phase behavior of polymer-polymer and polymer-salt aqueous two-phase systems. The proposed model has three terms which account for the combinatorial, the long-range and the short-range effects in solution. The Flory-Huggins and the Debye-Hückel models were used for the combinatorial and long-range contributions. The interaction parameters of the model studied in this work can be regressed using a non-liner regression between the experimental data and those obtained from the proposed model. Also, this model was applied for modeling the partitioning of biomolecules in polymer-polymer and polymer-salt aqueous two-phase systems. The results... 

This chapter at first proposes a framework to solve set covering problems (SCPs) with block-angular structures through solving their sub-problems and then develop the method for solving general SCPs without this structure. The proposed framework generates a guaranteed solution for the SCPs with block-angular structure based on a theorem which relates the optimal solution of the original problem to the optimal solutions of its sub-problems. Therefore, since sub-problems involve much fewer constraints and variables than the original problem, the complexity to solve the original SCP is much reduced. In addition, a method to exploit the block-angular structure of SCPs is proposed, using... 

This chapter at first proposes a framework to solve set covering problems (SCPs) with block-angular structures through solving their sub-problems and then develop the method for solving general SCPs without this structure. The proposed framework generates a guaranteed solution for the SCPs with block-angular structure based on a theorem which relates the optimal solution of the original problem to the optimal solutions of its sub-problems. Therefore, since sub-problems involve much fewer constraints and variables than the original problem, the complexity to solve the original SCP is much reduced. In addition, a method to exploit the block-angular structure of SCPs is proposed, using... 

In this paper, we propose a low power register file architecture for embedded processors. The proposed architecture, "Value-Aware Partitioned Register File (VAP-RF)", employs a partitioning technique that divides the register file into two partitions such that the most frequently accessed registers are stored in the smaller register partition. In our partitioning algorithm, we introduce an aggressive clock-gating scheme based on narrow-value registers to furthermore reduce power. Experimental results on an ARM processor for selected MiBench workloads show that the proposed architecture has an average power saving of 70% over generic register file structure  

Two main sources for power dissipation in parallel buses are data transitions on each wire and coupling between adjacent wires. So far, many techniques have been proposed for reducing the self and coupling powers. Most of these methods utilize one (or more) control bit(s) to manage the behavior of data transitions on the parallel bus. In this paper, we propose a new coding scheme, referred to as GPH, to reduce power dissipation of these control bits. GPH coding scheme employs partitioned Bus Invert and Odd Even Bus-Invert coding techniques. This method benefits from Particle Swarm Optimization (PSO) algorithm to efficiently partition the bus. In order to reduce self and coupling powers of... 

Today, public awareness about the benefits of using ontologies in information processing and the semantic web has increased. Since ontologies are useful in various applications, many large ontologies have been developed so far. But various areas like publication, maintenance, validation, processing, and security policies need further research. One way to better tackle these areas is to partition large ontologies into sub partitions. In this paper, we present a new method to partition large ontologies. For the proposed method, three steps are required: (1) transforming an ontology to a weighted graph, (2) partitioning the graph with an algorithm which recognizes the most important concepts,... 

Let R be a ring with unity. The graph (R) is a graph with vertices as elements of R, where two distinct vertices a and b are adjacent if and only if Ra + Rb = R. Let 2(R) be the subgraph of (R) induced by the non-unit elements of R. Let R be a commutative ring with unity and let J(R) denote the Jacobson radical of R. If R is not a local ring, then it was proved that: (a) If 2(R)J(R) is a complete n-partite graph, then n = 2. (b) If there exists a vertex of 2(R)J(R) which is adjacent to every vertex, then R ≅ ℤ2 × F, where F is a field. In this note we generalize the above results to non-commutative rings and characterize all non-local ring R (not necessarily commutative) whose 2(R)J(R) is a... 

An aqueous two-phase system (ATPS) containing polyethylene glycol (PEG) and potassium phosphate (K2HPO4) was used for partitioning and partial purification of alkaline protease produced by Bacillus licheniformis ATCC 21424. The effect of PEG molar mass, pH and concentration of NaCl salt addition on partition coefficient, yield and purification factor (PF) for ATPS were studied. The highest partition coefficient (5.3) was achieved in an ATPS of 25% (w/w) PEG 10,000 (g/mol) and 10% (w/w) NaCl at pH 9. Cation and anion exchange chromatography was employed for purification of alkaline protease from protein mixture and the yield and PF for enzyme fractions were obtained to make a comparison... 

Hardware/Software partitioning is one of the most important issues of codesign of embedded systems, since the costs and delays of the final results of a design will strongly depend on partitioning. We present an algorithm based on Particle Swarm Optimization to perform the hardware/software partitioning of a given task graph for minimum cost subject to timing constraint. By novel evolving strategy, we enhance the efficiency and result's quality of our partitioning algorithm in an acceptable run-time. Also, we compare our results with those of Genetic Algorithm on different task graphs. Experimental results show the algorithm's effectiveness in achieving the optimal solution of the HW/SW... 

This paper is aimed at investigating some computational aspects of different isoperimetric problems on weighted trees. In this regard, we consider different connectivity parameters called minimum normalized cuts/isoperimetric numbers defined through taking the minimum of the maximum or the mean of the normalized outgoing flows from a set of subdomains of vertices, where these subdomains constitute a partition/subpartition. We show that the decision problem for the case of taking k-partitions and the maximum (called the max normalized cut problem NCP^M), and the other two decision problems for the mean version (referred to as IPP^m and NCP^m) are NP-complete problems for weighted trees. On... 

The regular number of a graph (Formula presented.) denoted by (Formula presented.) is the minimum number of subsets into which the edge set of (Formula presented.) can be partitioned so that the subgraph induced by each subset is regular. In this work we answer to the problem posed as an open problem in Ganesan et al. (J Discrete Math Sci Cryptogr 15(2-3):49-157, 2012) about the complexity of determining the regular number of graphs. We show that computation of the regular number for connected bipartite graphs is NP-hard. Furthermore, we show that, determining whether (Formula presented.) for a given connected (Formula presented.)-colorable graph (Formula presented.) is NP-complete. Also, we... 

In many popular applications like peer-to-peer systems, large amounts of data are distributed among multiple sources. Analysis of this data and identifying clusters is challenging due to processing, storage, and transmission costs. In this paper, we propose GDCluster, a general fully decentralized clustering method, which is capable of clustering dynamic and distributed data sets. Nodes continuously cooperate through decentralized gossip-based communication to maintain summarized views of the data set. We customize GDCluster for execution of the partition-based and density-based clustering methods on the summarized views, and also offer enhancements to the basic algorithm. Coping with... 

An unconditionally energy stable time stepping scheme is introduced to solve Cahn-Morral-like equations in the present study. It is constructed based on the combination of David Eyre's time stepping scheme and Schur complement approach. Although the presented method is general and independent of the choice of homogeneous free energy density function term, logarithmic and polynomial energy functions are specifically considered in this paper. The method is applied to study the spinodal decomposition in multi-component systems and optimal space tiling problems. A penalization strategy is developed, in the case of later problem, to avoid trivial solutions. Extensive numerical experiments... 

It seems that the index theory for non-compact spaces has found its ultimate formulation in the realm of coarse spaces and K-theory of related operator algebras. Relative and partitioned index theorems may be mentioned as two important and interesting examples of this program. In this paper we formulate a combination of these two theorems and establish a partitioned-relative index theorem. © 2019 Elsevier Masson SAS