scholarly journals Cospectral Graphs and Regular Orthogonal Matrices of Level 2

10.37236/2383 ◽  
2012 ◽  
Vol 19 (3) ◽  
Author(s):  
Aida Abiad ◽  
Willem H Haemers
Keyword(s):  
Adjacency Matrix ◽  
Discrete Math ◽  
Orthogonal Matrix ◽  
Orthogonal Matrices ◽  
Switching Operation ◽  
Cospectral Graphs ◽  
New Methods ◽  
Almost All ◽  
Isomorphic Graphs ◽  
Level 2

For a graph $\Gamma$ with adjacency matrix $A$, we consider a switching operation that takes $\Gamma$ into a graph $\Gamma'$ with adjacency matrix $A'$, defined by $A'=Q^\top A Q$, where $Q$ is a regular orthogonal matrix of level $2$ (that is, $Q^\top Q=I$, $Q$1 $=$ 1, $2Q$ is integral, and $Q$ is not a permutation matrix). If such an operation exists, and $\Gamma$ is nonisomorphic with $\Gamma'$, then we say that $\Gamma'$ is semi-isomorphic with $\Gamma$. Semi-isomorphic graphs are $\mathbb {R}$-cospectral, which means that they are cospectral and so are their complements. Wang and Xu [On the asymptotic behavior of graphs determined by their generalized spectra, Discrete Math. 310 (2010)] expect that almost all pairs of nonisomorphic $\mathbb {R}$-cospectral graphs are semi-isomorphic.Regular orthogonal matrices of level $2$ have been classified. By use of this classification we work out the requirements for this switching operation to work in case $Q$ has one nontrivial indecomposable block of size $4$, $6$, $7$ or $8$. Size $4$ corresponds to Godsil-McKay switching. The other cases provide new methods for constructions of $\mathbb {R}$-cospectral graphs. For graphs with eight vertices all these constructions are carried out. As a result we find that, out of the 1166 graphs on eight vertices which are $\mathbb {R}$-cospectral to another graph, only 44 are not semi-isomorphic to another graph.

scholarly journals Generalized Spectral Characterization of Graphs Revisited

10.37236/3748 ◽  
2013 ◽  
Vol 20 (4) ◽  
Author(s):  
Wei Wang
Keyword(s):  
Adjacency Matrix ◽  
Numerical Experiments ◽  
Large Family ◽  
Orthogonal Matrix ◽  
Spectral Characterization ◽  
Positive Density ◽  
Integral Matrix ◽  
Generalized Spectrum ◽  
Almost All

A graph $G$ is said to be determined by its generalized spectrum (DGS for short) if for any graph $H$, $H$ and $G$ are cospectral with cospectral complements implies that $H$ is isomorphic to $G$. Wang and Xu (2006) gave some methods for determining whether a family of graphs are DGS. In this paper, we shall review some of the old results and present some new ones along this line of research.More precisely, let $A$ be the adjacency matrix of a graph $G$, and let $W=[e,Ae,\cdots,A^{n-1}e]$ ($e$ is the all-one vector) be its walk-matrix. Denote by $\mathcal{G}_n$ the set of all graphs on $n$ vertices with $\det(W)\neq 0$. We define a large family of graphs $$\mathcal{F}_n=\{G\in{\mathcal{G}_n}|\frac{\det(W)}{2^{\lfloorn/2\rfloor}}\mbox{is square-free and }2^{\lfloorn/2\rfloor+1}\not|\det(W)\}$$ (which may have positive density among all graphs, as suggested by some numerical experiments). The main result of the paper shows that for any graph $G\in {\mathcal{F}_n}$, if there is a rational orthogonal matrix $Q$ with $Qe=e$ such that $Q^TAQ$ is a (0,1)-matrix, then $2Q$ must be an integral matrix (and hence, $Q$ has well-known structures). As a consequence, we get the conclusion that almost all graphs in $\mathcal{F}_n$ are DGS.

scholarly journals ROTATION MATRIX SAMPLING SCHEME FOR MULTIDIMENSIONAL PROBABILITY DISTRIBUTION TRANSFER

2016 ◽  
Vol III-7 ◽  
pp. 103-110
Author(s):  
P. Srestasathiern ◽  
S. Lawawirojwong ◽  
R. Suwantong ◽  
P Phuthong
Keyword(s):  
Probability Distribution ◽  
Orthogonal Matrix ◽  
Rotation Matrix ◽  
Sampling Scheme ◽  
Uniform Rotation ◽  
Householder Transformation ◽  
Orthogonal Matrices ◽  
Matrix Sampling ◽  
Paper Address ◽  
Multidimensional Probability

This paper address the problem of rotation matrix sampling used for multidimensional probability distribution transfer. The distribution transfer has many applications in remote sensing and image processing such as color adjustment for image mosaicing, image classification, and change detection. The sampling begins with generating a set of random orthogonal matrix samples by Householder transformation technique. The advantage of using the Householder transformation for generating the set of orthogonal matrices is the uniform distribution of the orthogonal matrix samples. The obtained orthogonal matrices are then converted to proper rotation matrices. The performance of using the proposed rotation matrix sampling scheme was tested against the uniform rotation angle sampling. The applications of the proposed method were also demonstrated using two applications i.e., image to image probability distribution transfer and data Gaussianization.

scholarly journals Phyto-Nanocatalysts: Green Synthesis, Characterization, and Applications

Molecules ◽  
2019 ◽  
Vol 24 (19) ◽  
pp. 3418 ◽  
Author(s):  
Fierascu ◽  
Ortan ◽  
Avramescu ◽  
Fierascu
Keyword(s):  
Chemical Composition ◽  
Plant Extracts ◽  
Metallic Nanoparticles ◽  
Chemical Processes ◽  
Metallic Oxides ◽  
New Methods ◽  
Methods Of Synthesis ◽  
Promising Area ◽  
Shape Of Nanoparticles ◽  
Almost All

Catalysis represents the cornerstone of chemistry, since catalytic processes are ubiquitous in almost all chemical processes developed for obtaining consumer goods. Nanocatalysis represents nowadays an innovative approach to obtain better properties for the catalysts: stable activity, good selectivity, easy to recover, and the possibility to be reused. Over the last few years, for the obtaining of new catalysts, classical methods—based on potential hazardous reagents—have been replaced with new methods emerged by replacing those reagents with plant extracts obtained in different conditions. Due to being diversified in morphology and chemical composition, these materials have different properties and applications, representing a promising area of research. In this context, the present review focuses on the metallic nanocatalysts’ importance, different methods of synthesis with emphasis to the natural compounds used as support, characterization techniques, parameters involved in tailoring the composition, size and shape of nanoparticles and applications in catalysis. This review presents some examples of green nanocatalysts, grouped considering their nature (mono- and bi-metallic nanoparticles, metallic oxides, sulfides, chlorides, and other complex catalysts).

Orthogonal Matrices in Four-Space

1949 ◽  
Vol 1 (1) ◽  
pp. 69-72
Author(s):  
C. C. MacDuffee
Keyword(s):  
Orthogonal Transformation ◽  
Orthogonal Matrix ◽  
Orthogonal Matrices ◽  
Image Position ◽  
Proper Orthogonal ◽  
The Relationship

Every proper orthogonal matrix A can be writtenwhere Q is a skew matrix [6], and conversely every such matrix A is orthogonal. It is also known that every proper orthogonal transformation in real Euclidean four-space may be characterized in term of quaternions [1, 3] by the equationdetermines with the origin a vector having the coordinates (XQ, XI, x2, x3). The relationship between these two representations was clearly shown by Murnaghan [5].

Crop nutrients: control and efficiency of use

1985 ◽  
Vol 310 (1144) ◽  
pp. 175-191
Keyword(s):  
Computer Simulation ◽  
Elemental Composition ◽  
Soil Nutrients ◽  
Crop Yield ◽  
Uptake Rate ◽  
Chemical Fertilizers ◽  
Improve Efficiency ◽  
New Methods ◽  
Crop Nutrients ◽  
Almost All

Inputs of chemical fertilizers are essential in almost all intensive agricultures to reach maximum crop yield, but efficiency of use, expressed as the fraction recovered in the harvested crop, is often low. The more accurate control of quantity and better timing of application could improve efficiency, and new methods for achieving this are discussed, including computer simulation. Some species and cultivars are particularly efficient in their use of soil nutrients, partly by having a low content in their tissues, but more often by special root processes and symbionts that aid uptake. Greater use of these should be possible. More exact control of crop elemental composition can be important for quality. Plant processes which control composition via uptake rate are only now being investigated, but possible methods of modifying these are considered.

scholarly journals Collocation in beginner learner writing: A longitudinal study

2021 ◽  
Author(s):  
Anna Siyanova
Keyword(s):  
Second Language ◽  
Longitudinal Study ◽  
Middle Level ◽  
Advanced Learners ◽  
L2 Learners ◽  
Level 3 ◽  
Level 1 ◽  
Almost All ◽  
Intensive Course ◽  
Level 2

© 2015 Elsevier Ltd. The fact that second-language (L2) learners have problems with collocation is widely attested. However, few studies have investigated the development of L2 collocational knowledge longitudinally. Fewer still have employed more than a handful of participants. In addition, almost all studies to date have looked at advanced learners of English. Other L2 proficiencies and backgrounds have, by and large, been disregarded. The lacuna left by this paucity motivated the present study. Thirty-six Chinese beginner learners of Italian wrote a composition at the beginning (Level 1), in the middle (Level 2), and at the end (Level 3) of an intensive course. A small corpus of L2 Italian was compiled with the aim of investigating N + Adj combinations. Analyses revealed that the number of combinations at the beginning and at the end of the course was comparable, the number of higher frequency items, however, was greater in Level 3 compositions than Level 1 compositions. Importantly, analyses showed an increase in strongly associated collocations in Level 3 writings compared to Level 1 writings. Thus, Level 3 compositions contained not only more higher frequency combinations, but also more strongly associated collocations than did Level 1 compositions. Taken together, the study provides new insights into the development of L2 collocational competence.

scholarly journals Constructing Fifteen Infinite Classes of Nonregular Bipartite Integral Graphs

10.37236/732 ◽  
2008 ◽  
Vol 15 (1) ◽  
Author(s):  
Ligong Wang ◽  
Cornelis Hoede
Keyword(s):  
Number Theory ◽  
Adjacency Matrix ◽  
Diophantine Equations ◽  
Matrix Theory ◽  
Discrete Math ◽  
Computer Search ◽  
Characteristic Polynomials ◽  
Integral Property ◽  
Open Problems ◽  
Integral Graphs

A graph is called integral if all its eigenvalues (of the adjacency matrix) are integers. In this paper, the graphs $S_1(t)=K_{1,t}$, $S_2(n,t)$, $S_3(m,n,t)$, $S_4(m,n,p,q)$, $S_5(m,n)$, $S_6(m,n,t)$, $S_8(m,n)$, $S_9(m,n,p,q)$, $S_{10}(n)$, $S_{13}(m,n)$, $S_{17}(m, n, p, q)$, $S_{18}(n,p,q,t)$, $S_{19}(m,n,p,t)$, $S_{20}(n,p,q)$ and $S_{21}(m,t)$ are defined. We construct the fifteen classes of larger graphs from the known 15 smaller integral graphs $S_1-S_6$, $S_8-S_{10}$, $S_{13}$, $S_{17}-S_{21}$ (see also Figures 4 and 5, Balińska and Simić, Discrete Math. 236(2001) 13-24). These classes consist of nonregular and bipartite graphs. Their spectra and characteristic polynomials are obtained from matrix theory. We obtain their integral property by using number theory and computer search. All these classes are infinite. They are different from those in the literature. It is proved that the problem of finding such integral graphs is equivalent to solving Diophantine equations. We believe that it is useful for constructing other integral graphs. The discovery of these integral graphs is a new contribution to the search of integral graphs. Finally, we propose several open problems for further study.

scholarly journals DESAIN APLIKASI MOBILE PANDUAN SHOLAT DAN DOA UNTUK ANAK GANGGUAN PENDENGARAN

2018 ◽  
Vol 10 (3) ◽  
pp. 290-297
Author(s):  
Bambang Robi'in ◽  
Zahra Arwaning Tyas
Keyword(s):  
Hearing Loss ◽  
Mobile Application ◽  
Special Schools ◽  
Collection Data ◽  
Children With Hearing Loss ◽  
Interesting Learning ◽  
Almost All ◽  
Daily Prayer ◽  
Prototype Design ◽  
Level 2

Children with hearing loss are children who experience learning difficulties. They have limited vocabulary and language in communication that hampers the learning process. They need a special way of learning and are usually educated in special schools. Level 2 elementary students at SLB B Karnnamanohara have difficulty learning prayer and daily prayer. Almost all elementary level 2 students cannot pronounce daily prayers and prayers. They need interesting learning resources and according to their characteristics. This study aims to design multimedia mobile application of prayer and daily prayers guides for children with hearing loss. The research method consists of five stages: data collection, data analysis, storyboard making, prototype design, and prototype evaluation. This research has been designed to multimedia mobile applications of prayer and prayers guides for children hearing impairments according to the needs of users who have different characteristics with users in general. The results showed that the prototype design of the multimedia mobile application prayer and prayer daily guides for children with hearing loss had met the needs of users with evaluation values of 4.42 from a scale of 5.

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