Y. Euh, J. Park and K. Sekigawa were the first authors who defined the concept of a weakly Einstein Riemannian manifold as a modification of that of an Einstein Riemannian manifold. The defining formula is expressed in terms of the Riemannian scalar invariants of degree two. This concept was inspired by that of a super-Einstein manifold introduced earlier by A. Gray and T. J. Willmore in the context of mean-value theorems in Riemannian geometry. The dimension $4$ is the most interesting case, where each Einstein space is weakly Einstein. The original authors gave two examples of homogeneous weakly Einstein manifolds (depending on one, or two parameters, respectively) which are not Einstein. The goal of this paper is to prove that these examples are the only existing examples. We use, for this purpose, the classification of $4$-dimensional homogeneous Riemannian manifolds given by L. Bérard Bergery and, also, the basic method and many explicit formulas from our previous article with different topic published in Czechoslovak Math. J. in 2008. We also use Mathematica 7.0 to organize better the tedious routine calculations. The problem of existence of non-homogeneous weakly Einstein spaces in dimension $4$ which are not Einstein remains still unsolved.
A Lie algebra $L$ is called 2-step nilpotent if $L$ is not abelian and $[L, L]$ lies in the center of $L$. 2-step nilpotent Lie algebras are useful in the study of some geometric problems, and their classification has been an important problem in Lie theory. In this paper, we give a classification of 2-step nilpotent Lie algebras of dimension 9 with 2-dimensional center., Ren Bin, Zhu Lin Sheng., and Obsahuje bibliografii
The property of being a D’Atri space (i.e., a space with volume-preserving symmetries) is equivalent to the infinite number of curvature identities called the odd Ledger conditions. In particular, a Riemannian manifold $(M,g)$ satisfying the first odd Ledger condition is said to be of type $\mathcal {A}$. The classification of all 3-dimensional D’Atri spaces is well-known. All of them are locally naturally reductive. The first attempts to classify all 4-dimensional homogeneous D’Atri spaces were done in the papers by Podesta-Spiro and Bueken-Vanhecke (which are mutually complementary). The authors started with the corresponding classification of all spaces of type $\mathcal {A}$, but this classification was incomplete. Here we present the complete classification of all homogeneous spaces of type $\mathcal {A}$ in a simple and explicit form and, as a consequence, we prove correctly that all homogeneous 4-dimensional D’Atri spaces are locally naturally reductive.
When dealing with the curse of dimensionality (small sample size with many dimensions), feature selection is an important preprocessing strategy for the analysis of biomedical data. This issue is particularly germane to the classification of high-dimensional class-labeled biomedical spectra as is often acquired from magnetic resonance and infrared spectrometers. A technique is presented that stochastically selects feature subsets with varying cardinality for automated discrimination using two types of neural network classifiers. The results are benchmarked against classifiers using the entire feature set with and without averaging. Stochastic feature subset selection had significantly fewer misclassifications than either of the benchmarks.
An interesting topic in the ring theory is the classification of finite rings. Although rings of certain orders have already been classified, a full description of all rings of a given order remains unknown. The purpose of this paper is to classify all finite rings (up to isomorphism) of a given order. In doing so, we introduce a new concept of quasi basis for certain type of modules, which is a useful computational tool for dealing with finite rings. Then, using this concept, we give structure and isomorphism theorems for finite rings and state our main result to classify (up to isomorphism) the finite rings of a given order. Finally, based on these results, we describe an algorithm to calculate the structure of all such rings. We have implemented our new algorithm in Maple, and we apply it to an example.
An electronic nose system for herbs clcissification is designed and tested. The system uses the Figaro TGS800 series sensors with an integrated heating element. The testing of the system was carried out using diíferent types of herbs where it was proved to be successful in classifying them into diíferent classes [10, 11]. Database-based software was designed to interface the built hardware and to process the electronic nose signals before being classified.
Let R be a commutative ring with nonzero identity and J(R) the Jacobson radical of R. The Jacobson graph of R, denoted by JR, is defined as the graph with vertex set RJ(R) such that two distinct vertices x and y are adjacent if and only if 1 − xy is not a unit of R. The genus of a simple graph G is the smallest nonnegative integer n such that G can be embedded into an orientable surface Sn. In this paper, we investigate the genus number of the compact Riemann surface in which JR can be embedded and explicitly determine all finite commutative rings R (up to isomorphism) such that JR is toroidal., Krishnan Selvakumar, Manoharan Subajini., and Obsahuje seznam literatury
Semi-dry grasslands are of high nature conservation interest both at national and European scales due to their high biodiversity and species richness. For effective conservation, however, the variation in floristic composition and distribution of these grasslands need first to be described. In Hungary, there is currently no comprehensive survey and classification of semi-dry grasslands. Therefore, the aim of this study was to (i) describe the variation in species composition of Hungarian semi-dry grasslands by a country-scale cluster analysis based on a large database; (ii) describe the types (clusters) and compare these descriptions with those in the phytosociological literature, and finally (iii) formulate a new syntaxonomical system for Hungarian semi-dry grasslands. For this analysis 699 relevés were selected in which the percentage cover of at least one of the grasses Brachypodium pinnatum, Bromus erectus, Danthonia alpina, Avenula adsurgens, A. pubescens or A. compressa reached >10%. A geographical stratification of the dataset was performed and then it was split randomly into two equal parts (training and test datasets). Following outlier exclusion and noise elimination, clustering was performed separately for both datasets. The optimal number of clusters was determined by validation. The number of valid clusters was the highest at the level of ten clusters, where seven clusters appeared to be valid. The valid clusters are separated geographically; however, there are considerable overlaps in the species compositions. According to our results, all the grasslands belong to the Cirsio-Brachypodion alliance. The seven valid clusters are assigned to five main groups of semi-dry grasslands in Hungary: 1. Brachypodium pinnatum (and partly Bromus erectus) dominated, species rich meadow-steppe-like grasslands occurring on deep loess in central Pannonia, identified as Euphorbio pannonicae-Brachypodietum Horváth 2009; 2. Brachypodium pinnatum dominated mountain grasslands restricted to the Bükk Mountains; identified as Polygalo majoris-Brachypodietum Wagner 1941; 3. mostly Bromus erectus dominated grasslands on shallow, calcium/rich soils of the Dunántúl region, proposed as a new association Sanguisorbo minoris-Brometum erecti Illyés, Bauer & Botta-Dukát 2009; 4. Brachypodium pinnatum and Danthonia alpina dominated stands occurring mainly in the Északi-középhegység Mts, characterized by species of nutrient poor soils, proposed as a new association Trifolio medii-Brachypodietum pinnati Illyés, Bauer & Botta-Dukát 2009; 5. transition towards meadows and successional stands dominated mainly by Brachypodium pinnatum.
Multi-Layer Perceptron Neural Networks (MLP NNs) are the commonly used NNs for target classification. They purposes not only in simulated environments, but also in actual situations. Training such NNs has significant importance in a way that many researchers have been attracted to this field recently. Conventional gradient descent and recursive method has long been used to train NNs. Improper classification accuracy, slow convergence speed and trapping in local minimums are disadvantages of the traditional methods. In order to overcome these issues, in recent years heuristic and meta-heuristic algorithms are widely used. This paper uses Gray Wolf Optimization (GWO) algorithm for training the NN. This algorithm is inspired by lifestyle and hunting method of GWs. GWO has a superior ability to solve the high-dimension problems, so we try to classify the Sonar dataset using this algorithm. To test the proposed method, this algorithm is compared to Particle Swarm Optimization (PSO) algorithm, Gravitational Search Algorithm (GSA) and the hybrid algorithm (i.e. PSOGSA) using three sets of data. Measured metrics are convergence speed, the possibility of trapping in local minimum and classification accuracy. The results show that the proposed algorithm in most cases provides better or comparable performance compared to the other mentioned algorithms.
In 1985, Amin presented a new system for the classification of the Acanthocephala in Crompton and Nickol's (1985) book ''Biology of the Acanthocephala'' and recognized the concepts of Meyer (1931, 1932, 1933) and Van Cleave (1936, 1941, 1947, 1948, 1949, 1951, 1952). This system became the standard for the taxonomy of this group and remains so to date. Many changes have taken place and many new genera and species, as well as higher taxa, have been described since. An updated version of the 1985 scheme incorporating new concepts in molecular taxonomy, gene sequencing and phylogenetic studies is presented. The hierarchy has undergone a total face lift with Amin's (1987) addition of a new class, Polyacanthocephala (and a new order and family) to remove inconsistencies in the class Palaeacanthocephala. Amin and Ha (2008) added a third order (and a new family) to the Palaeacanthocephala, Heteramorphida, which combines features from the palaeacanthocephalan families Polymorphidae and Heteracanthocephalidae. Other families and subfamilies have been added but some have been eliminated, e.g. the three subfamilies of Arythmacanthidae: Arhythmacanthinae Yamaguti, 1935; Neoacanthocephaloidinae Golvan, 1960; and Paracanthocephaloidinae Golvan, 1969. Amin (1985) listed 22 families, 122 genera and 903 species (4, 4 and 14 families; 13, 28 and 81 genera; 167, 167 and 569 species in Archiacanthocephala, Eoacanthocephala and Palaeacanthocephala, respectively). The number of taxa listed in the present treatment is 26 families (18% increase), 157 genera (29%), and 1298 species (44%) (4, 4 and 16; 18, 29 and 106; 189, 255 and 845, in the same order), which also includes 1 family, 1 genus and 4 species in the class Polyacanthocephala Amin, 1987, and 3 genera and 5 species in the fossil family Zhijinitidae.