Resolving dominating partitions in graphs Hernando, Carmen; Mora, Mercè; Pelayo, Ignacio M.
Discrete Applied Mathematics,
08/2019, Letnik:
266
Journal Article, Publication
Recenzirano
Odprti dostop
A partition Π={S1,…,Sk} of the vertex set of a connected graph G is called a resolving partition of G if for every pair of vertices u and v, d(u,Sj)≠d(v,Sj), for some part Sj. The partition ...dimensionβp(G) is the minimum cardinality of a resolving partition of G. A resolving partition Π is called resolving dominating if for every vertex v of G, d(v,Sj)=1, for some part Sj of Π. The dominating partition dimensionηp(G) is the minimum cardinality of a resolving dominating partition of G.
In this paper we show, among other results, that βp(G)≤ηp(G)≤βp(G)+1. We also characterize all connected graphs of order n≥7 satisfying any of the following conditions: ηp(G)=n, ηp(G)=n−1, ηp(G)=n−2 and βp(G)=n−2. Finally, we present some tight Nordhaus–Gaddum bounds for both the partition dimension βp(G) and the dominating partition dimension ηp(G).
Groups with semi-partitions Foguel, T.; Mahmoudifar, A.; Moghaddamfar, A. R. ...
Journal of algebra and its applications,
08/2023, Letnik:
22, Številka:
8
Journal Article
Recenzirano
Odprti dostop
A group partition is a group cover in which the components have trivial pairwise intersection. Based on an idea of I. M. Isaacs in this paper we define the semi-partition of a group as a group cover ...in which the intersection of any three components is trivial. We examine some of the properties of groups with semi-partitions, including its relation to the covering number and partition number for groups.
Developing an alternative and benign method for DNA extraction is imperative due to the high cost and potential harms associated with conventional techniques. Investigation of Ionic liquid (IL) as a ...solvent for DNA storage and stability revealed the ability of IL to assist DNA processes. IL–based aqueous biphasic system emerges as a comprehensive extraction platform capitalizing on the task–specificity of ILs and the wide applicability of ABS for biomolecule extractions. Therefore, it is beneficial to optimize an IL–based ABS specifically for DNA extraction, taking into account the fundamental interactions between the IL and DNA.
The primary objective was to design ABS consisting of Ammonium based ILs, and Potassium phosphate buffer as the salting–out agent for the partitioning of salmon sperm DNA. The analysis focused on optimizing biocompatible anions for the extraction. Moreover, the stability of the DNA in the IL rich phases was analysed to validate the method. The proposed process was then employed for extracting plasmid DNA from bacteria, demonstrating results comparable to those obtained with a commercially available kit. Further validation using agarose gel electrophoresis and transformation of the extracted DNA into E.coli were conducted, producing promising outcomes. Although there is room for improvement in terms of recovery of DNA and reusability of ABS, the described approach is comparable with the conventional one while being cost–effective, and showcases a noticeable and convincing link to eco–friendly processes.
There is limited literature on IL–based ABS for DNA extraction, and the existing studies predominantly concentrate on systems derived from Cholinium ILs. However, their high hydrophilicity limits the choice of the second–phase forming component to polymers for the formation of ABS. Ammonium ILs efficiently form biphasic systems with various available salting–out agents, and biocompatible anions are introduced to mitigate the toxicity of the ILs.
Display omitted
•Aqueous biphasic system formation of ionic liquids based on biocompatible anions.•Partitioned DNA showed stability in ionic liquid rich phase.•Efficient DNA extraction from bacterial cells by propanoate-based system.•Extracted DNA was successfully transformed to competent cells.
Chalcophile element partitioning among base-metal sulfide, oxide and silicate phases during magmatic processes is poorly constrained in part because there are very few studies of reliable sulfide ...melt–silicate melt partition coefficients (Ds) and because the crystallization history of the sulfide liquid is ignored in most studies. Here we present laser ablation-inductively coupled plasma-mass spectrometry (LA-ICP-MS) analyses of sulfide droplets and their host fresh mid-ocean-ridge basalt (MORB) glasses. The compositions of the sulfide droplets suggest that they formed in magma chambers beneath the mid-ocean ridges and equilibrated with their host silicate melt, enabling us to calculate new Ds for chalcophile elements. These are Co (45±4.5), Ni (776±98), Cu (1334±210), Zn (3.5±0.9), Se (345±37), Ag (1138±245), Cd (107±47), Sn (11±1.6), Te (4478±1146), Pb (57±10) and Bi (316±38). The contents of the highly siderophile elements in the glasses were too low to be determined using LA-ICP-MS. The whole rock values were used as a proxy for the glass and these allow an estimate of minimum Ds in the 10000 to 40000 range for the platinum-group elements (PGE) and 870 for Re. Partition coefficient values are affected by oxygen fugacity; comparison of our values with those from experimental studies suggests that oxygen fugacities of the MORBs considered here were between FMQ and FMQ-1. From the determined D values we calculate the contribution of the sulfides to bulk partition coefficient during mantle melting. Considering these values in combination with what is known about the behavior of the chalcophile elements during mantle partial melting, we suggest that Co, Ni, Zn, Te, PGE and Au behave as compatible elements during mantle melting, with Ni, Co and Zn being controlled mainly by the silicate and oxide minerals and the PGE, Au and Te being controlled mainly by the sulfides (or other discrete metallic phases). Copper, Se, Ag, Cd, Sn, Re, Pb and Bi are slightly to strongly incompatible during mantle melting. MORB sulfide droplets consist mainly of monosulfide solid solution (MSS), which is the first mineral to crystallize from a sulfide liquid, and intermediate solid solution (ISS), which crystallizes from the remaining liquid. The distribution of the chalcophile elements within the sulfide droplets shows that Co and Re have a slight preference for MSS, whereas the Cu, Zn, Ag, Cd, Sn, Te, Au, Bi and Pb partition into ISS. Selenium is present in approximately equal amounts in both MSS and ISS, and Pt and Pd are also present in both phases. Previous experimental and empirical studies have shown that Os, Ir, Ru and Rh partition into MSS and a portion of these elements exsolve from the sulfides as platinum-group minerals (PGM) during cooling. The same studies show that most of the Pt and Pd partition into the liquid and eventually crystallize from the late fractionated liquid as PGM. We examined our MORB sulfide droplets closely for platinum group-minerals (PGM) but none were found. We suggest that because the rocks sustained rapid cooling PGM were unable to exsolve from the sulfide minerals and the liquid did not fractionate sufficiently to permit the crystallization of the Pt or Pd minerals. Thus the PGE are present in MSS and ISS.
•We calculate partition coefficients for Ni, Cu, Co, Zn, Se, Ag, Sn, Te, Pb and Bi.•We determine the distribution of chalcophile elements between MSS and ISS.•During mantle melting Ni, Cu, Co, Zn and Te are compatible elements.•During mantle melting Se, Ag, Sn, Pb and Bi are incompatible elements.•All the chalcophile elements are in solid solution in the sulfide droplets.
Versatile video coding (VVC) further improves video coding gain by introducing a new Quad-tree (QT) with nested multi-type tree (QTMT) partition structure, which includes QT partition, horizontal and ...vertical binary-tree (BT) partition, and horizontal and vertical ternary-tree (TT) partition. However, the coding gain is achieved at the cost of drastically increased coding complexity. We propose an early intra coding unit (CU) size partition method for VVC based on a tunable decision model. The distortion of the CU is firstly obtained by the difference between the original luminance pixel and the predicted one. By exploiting the distortion, two decision models are established for the early skipping of BT and TT partition for each CU, respectively. Then, a tunable decision model is presented to achieve different trade-off between encoding loss and complexity reduction. Extensive experimental results show that the proposed approach reduces the encoding time ranging from 22.6% to 67.6% with the BD-Rate increase ranging from 0.56% to 2.61%. It is also suitable for parallel implementation by exploiting the pipeline structure of the VVC encoder due to its independency with neighboring CU blocks.
Let $b_{\ell, k}(n)$ denote the number of $(\ell, k)$-regular partition of $n$. Recently, some congruences modulo $2$ for $ (3, 8), (4, 7)$-regular partition and modulo $8$, modulo $9$ and modulo ...$12$ for $(4, 9)$-regular partition has been studied. In this paper, we use theta function identities and Newman results to prove some infinite families of congruences modulo $2$ for $(2, 7)$, $(5, 8)$, $(4, 11)$-regular partition and modulo $4$ for $(4, 5)$-regular partition.
The partition dimension is the most complicated resolving parameter of all the resolvability parameters. In this parameter, the vertex set of a graph is completely subdivided into subsets so that ...each vertex of a graph has a unique identification in terms of the partitioning of its selected subsets. In this paper, we consider Carbon nanocone structure (CNC) more specifically one pentagonal carbon nanocone CNCζ,5. It is also regarded as a useful structure in terms of various applications. To delve deeper into this structure, we provide a graphical representation of it and identified sharp bounds for the partition dimension. We conclude that the pentagonal carbon nanocone CNCζ,5 has partition dimension ≤4.
The development and widespread use of computer systems has increased the need for secure storage of data. At the same time, the analysis of digital data storage devices is very important for forensic ...IT professionals who aim to access information to clarify the crime. File systems of disk drives use partition structures to securely store data and prevent problems such as corruption. In this study, deletion or corruption of partitions on commonly used DOS / Master Boot Record (MBR) configured hard disk drives are investigated by using forensic tools. In order to analyze hard disk drives, Forensic Tool Kit (FTK), Magnet AXIOM, Encase, Autopsy and The Sleuth Kit (TSK), which are widely used as commercial and open source, are analyzed by using a presented scenario. In the scenario, the primary partition and the extended partition are created using the DOS / MBR partitioning structure on the test disk. Test files are added to the sections and the sections are deleted. The digital forensics tools were tested on the presented scenario. According to the obtained results, TSK and Encase are successful tools for DOS / MBR structured HDD analysis. However, FTK, Magnet AXIOM and Autopsy could not achieve information detection on DOS/MBR structured disks. These results clearly demonstrated that crime data can be hidden in MBR structured HDD. To carve these data, the correct methodology should be selected.
George Andrews and Peter Paule have recently conjectured an infinite family of congruences modulo powers of 3 for the 2-elongated plane partition function d2(n). This congruence family appears ...difficult to prove by classical methods. We prove a refined form of this conjecture by expressing the associated generating functions as elements of a ring of modular functions isomorphic to a localization of ZX.
PDF
