Journal articles: 'Decomposition'

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Crâşmăreanu, Mircea. "Particular trace decompositions and applications of trace decomposition to almost projective invariants." Mathematica Bohemica 126, no. 3 (2001): 631–37. http://dx.doi.org/10.21136/mb.2001.134205.

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BANKS, JOHN. "Regular periodic decompositions for topologically transitive maps." Ergodic Theory and Dynamical Systems 17, no. 3 (June 1997): 505–29. http://dx.doi.org/10.1017/s0143385797069885.

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One may often decompose the domain of a topologically transitive map into finitely many regular closed pieces with nowhere dense overlap in such a way that these pieces map into one another in a periodic fashion. We call decompositions of this kind regular periodic decompositions and refer to the number of pieces as the length of the decomposition. If $f$ is topologically transitive but $f^{n}$ is not, then $f$ has a regular periodic decomposition of some length dividing $n$. Although a decomposition of a given length is unique, a map may have many decompositions of different lengths. The set of lengths of decompositions of a given map is an ideal in the lattice of natural numbers ordered by divisibility, which we call the decomposition ideal of $f$. Every ideal in this lattice arises as a decomposition ideal of some map. Decomposition ideals of Cartesian products of transitive maps are discussed and used to develop various examples. Results are obtained concerning the implications of local connectedness for decompositions. We conclude with a comprehensive analysis of the possible decomposition ideals for maps on 1-manifolds.

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Fontanil, Lauro, and Eduardo Mendoza. "Common complexes of decompositions and complex balanced equilibria of chemical reaction networks." MATCH Communications in Mathematical and in Computer Chemistry 87, no. 2 (2021): 329–66. http://dx.doi.org/10.46793/match.87-2.329f.

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A decomposition of a chemical reaction network (CRN) is produced by partitioning its set of reactions. The partition induces networks, called subnetworks, that are "smaller" than the given CRN which, at this point, can be called parent network. A complex is called a common complex if it occurs in at least two subnetworks in a decomposition. A decomposition is said to be incidence independent if the image of the incidence map of the parent network is the direct sum of the images of the subnetworks' incidence maps. It has been recently discovered that the complex balanced equilibria of the parent network and its subnetworks are fundamentally connected in an incidence independent decomposition. In this paper, we utilized the set of common complexes and a developed criterion to investigate decomposition’s incidence independence properties. A framework was also developed to analyze decomposition classes with similar structure and incidence independence properties. We identified decomposition classes that can be characterized by their sets of common complexes and studied their incidence independence. Some of these decomposition classes occur in some biological and chemical models. Finally, a sufficient condition was obtained for the complex balancing of some power law kinetic (PLK) systems with incidence independent and complex balanced decompositions. This condition led to a generalization of the Deficiency Zero Theorem for some PLK systems.

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Kahle, Thomas, Ezra Miller, and Christopher O’Neill. "Irreducible decomposition of binomial ideals." Compositio Mathematica 152, no. 6 (April 1, 2016): 1319–32. http://dx.doi.org/10.1112/s0010437x16007272.

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Building on coprincipal mesoprimary decomposition [Kahle and Miller, Decompositions of commutative monoid congruences and binomial ideals, Algebra and Number Theory 8 (2014), 1297–1364], we combinatorially construct an irreducible decomposition of any given binomial ideal. In a parallel manner, for congruences in commutative monoids we construct decompositions that are direct combinatorial analogues of binomial irreducible decompositions, and for binomial ideals we construct decompositions into ideals that are as irreducible as possible while remaining binomial. We provide an example of a binomial ideal that is not an intersection of irreducible binomial ideals, thus answering a question of Eisenbud and Sturmfels [Binomial ideals, Duke Math. J. 84 (1996), 1–45].

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Borup, Lasse, and Morten Nielsen. "On anisotropic Triebel-Lizorkin type spaces, with applications to the study of pseudo-differential operators." Journal of Function Spaces and Applications 6, no. 2 (2008): 107–54. http://dx.doi.org/10.1155/2008/510584.

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A construction of Triebel-Lizorkin type spaces associated with flexible decompositions of the frequency spaceℝdis considered. The class of admissible frequency decompositions is generated by a one parameter group of (anisotropic) dilations onℝdand a suitable decomposition function. The decomposition function governs the structure of the decomposition of the frequency space, and for a very particular choice of decomposition function the spaces are reduced to classical (anisotropic) Triebel-Lizorkin spaces. An explicit atomic decomposition of the Triebel-Lizorkin type spaces is provided, and their interpolation properties are studied. As the main application, we consider Hörmander type classes of pseudo-differential operators adapted to the anisotropy and boundedness of such operators between corresponding Triebel-Lizorkin type spaces is proved.

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Wakamatsu, Masashi. "Is gauge-invariant complete decomposition of the nucleon spin possible?" International Journal of Modern Physics A 29, no. 09 (April 8, 2014): 1430012. http://dx.doi.org/10.1142/s0217751x14300129.

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Is gauge-invariant complete decomposition of the nucleon spin possible? Although it is a difficult theoretical question which has not reached a complete consensus yet, a general agreement now is that there are at least two physically inequivalent gauge-invariant decompositions (I) and (II) of the nucleon. In these two decompositions, the intrinsic spin parts of quarks and gluons are just common. What discriminate these two decompositions are the orbital angular momentum parts. The orbital angular momenta of quarks and gluons appearing in the decomposition (I) are the so-called "mechanical" orbital angular momenta, while those appearing in the decomposition (II) are the generalized (gauge-invariant) "canonical" ones. By this reason, these decompositions are also called the "mechanical" and "canonical" decompositions of the nucleon spin, respectively. A crucially important question is which decomposition is more favorable from the observational viewpoint. The main objective of this concise review is to try to answer this question with careful consideration of recent intensive researches on this problem.

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Li, Haitao, Jie Xiong, Jianhui Xie, Zhongbao Zhou, and Jinlong Zhang. "A Unified Approach to Efficiency Decomposition for a Two-Stage Network DEA Model with Application of Performance Evaluation in Banks and Sustainable Product Design." Sustainability 11, no. 16 (August 14, 2019): 4401. http://dx.doi.org/10.3390/su11164401.

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Data envelopment analysis (DEA) is a data-driven tool for performance evaluation, benchmarking and multiple-criteria decision-making. This article investigates efficiency decomposition in a two-stage network DEA model. Three major methods for efficiency decomposition have been proposed: uniform efficiency decomposition, Nash bargaining game decomposition, and priority decomposition. These models were developed on the basis of different assumptions that led to different efficiency decompositions and thus confusion among researchers. The current paper attempts to reconcile these differences by redefining the fairness of efficiency decomposition based on efficiency rank, and develops a rank-based model with two parameters. In our new rank-based model, these three efficiency decomposition methods can be treated as special cases where these parameters take special values. By showing the continuity of the Pareto front, we simplify the uniform efficiency decomposition, and indicate that the uniform efficiency decomposition and Nash bargaining game decomposition can converge to the same efficiency decomposition. To demonstrate the merits of our model, we use data from the literature to evaluate the performance of 10 Chinese banks, and compare the different efficiency decompositions created by different methods. Last, we apply the proposed model to the performance evaluation of sustainable product design in the automobile industry.

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von Brasch, Thomas, Håkon Grini, Magnus Berglund Johnsen, and Trond Christian Vigtel. "A Two-Stage Bennet Decomposition of the Change in the Weighted Arithmetic Mean." Journal of Official Statistics 39, no. 1 (March 1, 2023): 123–37. http://dx.doi.org/10.2478/jos-2023-0006.

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Abstract The weighted arithmetic mean is used in a wide variety of applications. An infinite number of possible decompositions of the change in the weighted mean are available, and it is therefore an open question which of the possible decompositions should be applied. In this article, we derive a decomposition of the change in the weighted mean based on a two-stage Bennet decomposition. Our proposed decomposition is easy to employ and interpret, and we show that it satisfies the difference counterpart to the index number time reversal test. We illustrate the framework by decomposing aggregate earnings growth from 2020Q4 to 2021Q4 in Norway and compare it with some of the main decompositions proposed in the literature. We find that the wedge between the identified compositional effects from the proposed two-stage Bennet decomposition and the one-stage Bennet decomposition is substantial, and for some industries, the compositional effects have opposite signs.

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ĐOKOVIĆ, DRAGOMIR Ž., and KAIMING ZHAO. "RATIONAL JORDAN DECOMPOSITION OF BILINEAR FORMS." Communications in Contemporary Mathematics 07, no. 06 (December 2005): 769–86. http://dx.doi.org/10.1142/s0219199705001945.

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This is a continuation of our previous work on Jordan decomposition of bilinear forms over algebraically closed fields of characteristic 0. In this note, we study Jordan decomposition of bilinear forms over any field K0 of characteristic 0. Let V0 be an n-dimensional vector space over K0. Denote by [Formula: see text] the space of bilinear forms f : V0 × V0 → K0. We say that f = g + h, where f, g, [Formula: see text], is a rational Jordan decomposition of f if, after extending the field K0 to an algebraic closure K, we obtain a Jordan decomposition over K. By using the Galois group of K/K0, we prove the existence of rational Jordan decompositions and describe a method for constructing all such decompositions. Several illustrative examples of rational Jordan decompositions of bilinear forms are included. We also show how to classify the unimodular congruence classes of bilinear forms over an algebraically closed field of characteristic different from 2 and over the real field.

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Kiana, E., S. Homayouni, M. A. Sharifi, and M. R. Farid-Rohani. "COMPARISON OF DECOMPOSITION METHODS OVER AGRICULTURAL FIELDS USING THE UAVSAR POLARIMETRIC SYNTHETIC APERTURE RADAR." ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XLII-4/W18 (October 18, 2019): 649–53. http://dx.doi.org/10.5194/isprs-archives-xlii-4-w18-649-2019.

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Abstract. This paper investigates and compares the potential of five model-based polarimetric decompositions, namely those developed by Eigenvector-based decomposition (Van Zyl), Model-based decomposition (Freeman-Durden three-component decomposition and Yamaguchi four-component decomposition), An & Yang3 and An & Yang4 for crop biomass detection over agricultural fields covered by various crops. The time series of Uninhabited Aerial Vehicle Synthetic Aperture Radar (UAVSAR) data and the ground truth of soil and vegetation characteristics collected during the Soil Moisture Active Passive (SMAP) Validation Experiment in 2012 (SMAPVEX12) were used to compare the five decomposition methods with related to the scattering mechanisms and the biomass retrieval performances. The results show that the performance of each decomposition method for biomass retrieval depends on the crop types and the crop phenological stages. Finally, an overall biomass underestimation was observed from the five decompositions, and the highest regression value of 99% was obtained from Freeman decomposition as a result of the enhanced volume scattering. Indeed, Freeman-Durden model provided the best results.

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Fekete, Dorottya, Sandra Palau, Juan Carlos Pardo, and Jose Luis Pérez. "Backbone Decomposition of Multitype Superprocesses." Journal of Theoretical Probability 34, no. 3 (February 27, 2021): 1149–78. http://dx.doi.org/10.1007/s10959-021-01076-7.

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AbstractIn this paper, we provide a construction of the so-called backbone decomposition for multitype supercritical superprocesses. While backbone decompositions are fairly well known for both continuous-state branching processes and superprocesses in the one-type case, so far no such decompositions or even description of prolific genealogies have been given for the multitype cases. Here we focus on superprocesses, but by turning the movement off, we get the prolific backbone decomposition for multitype continuous-state branching processes as an easy consequence of our results.

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Abseher, Michael, Nysret Musliu, and Stefan Woltran. "Improving the Efficiency of Dynamic Programming on Tree Decompositions via Machine Learning." Journal of Artificial Intelligence Research 58 (April 25, 2017): 829–58. http://dx.doi.org/10.1613/jair.5312.

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Dynamic Programming (DP) over tree decompositions is a well-established method to solve problems - that are in general NP-hard - efficiently for instances of small treewidth. Experience shows that (i) heuristically computing a tree decomposition has negligible runtime compared to the DP step; and (ii) DP algorithms exhibit a high variance in runtime when using different tree decompositions; in fact, given an instance of the problem at hand, even decompositions of the same width might yield extremely diverging runtimes. We thus propose here a novel and general method that is based on selection of the best decomposition from an available pool of heuristically generated ones. For this purpose, we require machine learning techniques that provide automated selection based on features of the decomposition rather than on the actual problem instance. Thus, one main contribution of this work is to propose novel features for tree decompositions. Moreover, we report on extensive experiments in different problem domains which show a significant speedup when choosing the tree decomposition according to this concept over simply using an arbitrary one of the same width.

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13

Adkins, William A. "Primary decomposition of torsionR[X]-modules." International Journal of Mathematics and Mathematical Sciences 17, no. 1 (1994): 41–46. http://dx.doi.org/10.1155/s0161171294000074.

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This paper is concerned with studying hereditary properties of primary decompositions of torsionR[X]-modulesMwhich are torsion free asR-modules. Specifically, if anR[X]-submodule ofMis pure as anR-submodule, then the primary decomposition ofMdetermines a primary decomposition of the submodule. This is a generalization of the classical fact from linear algebra that a diagonalizable linear transformation on a vector space restricts to a diagonalizable linear transformation of any invariant subspace. Additionally, primary decompositions are considered under direct sums and tensor product.

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Bagchi, Susmit. "Projective and Non-Projective Varieties of Topological Decomposition of Groups with Embeddings." Symmetry 12, no. 3 (March 12, 2020): 450. http://dx.doi.org/10.3390/sym12030450.

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In general, the group decompositions are formulated by employing automorphisms and semidirect products to determine continuity and compactification properties. This paper proposes a set of constructions of novel topological decompositions of groups and analyzes the behaviour of group actions under the topological decompositions. The proposed topological decompositions arise in two varieties, such as decomposition based on topological fibers without projections and decomposition in the presence of translated projections in topological spaces. The first variety of decomposition introduces the concepts of topological fibers, locality of group operation and the partitioned local homeomorphism resulting in formulation of transitions and symmetric surjection within the topologically decomposed groups. The reformation of kernel under decomposed homeomorphism and the stability of group action with the existence of a fixed point are analyzed. The first variety of decomposition does not require commutativity maintaining generality. The second variety of projective topological decomposition is formulated considering commutative as well as noncommutative projections in spaces. The effects of finite translations of topologically decomposed groups under projections are analyzed. Moreover, the embedding of a decomposed group in normal topological spaces is formulated in this paper. It is shown that Schoenflies homeomorphic embeddings preserve group homeomorphism in the decomposed embeddings within normal topological spaces. This paper illustrates that decomposed group embedding in normal topological spaces is separable. The applications aspects as well as parametric comparison of group decompositions based on topology, direct product and semidirect product are included in the paper.

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Diestel, Reinhard. "Simplicial minors and decompositions of graphs." Mathematical Proceedings of the Cambridge Philosophical Society 103, no. 3 (May 1988): 409–26. http://dx.doi.org/10.1017/s0305004100065026.

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The purpose of this paper is to give natural characterizations of the countable graphs that admit tree-decompositions or simplicial tree-decompositions into primes. Tree-decompositions were recently introduced by Robertson and Seymour in their series of papers on graph minors [7]. Simplicial tree-decompositions were first considered by Halin[6], being the most typical kind of ‘simplicial decomposition’ as introduced by Halin[5] in 1964. The problem of determining which infinite graphs admit a simplicial decomposition into primes has stood unresolved since then; a first solution for simplicial tree-decompositions was given in [2].

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Mendez, M. A., M. Balabane, and J. M. Buchlin. "Multi-scale proper orthogonal decomposition of complex fluid flows." Journal of Fluid Mechanics 870 (May 15, 2019): 988–1036. http://dx.doi.org/10.1017/jfm.2019.212.

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Data-driven decompositions are becoming essential tools in fluid dynamics, allowing for tracking the evolution of coherent patterns in large datasets, and for constructing low-order models of complex phenomena. In this work, we analyse the main limits of two popular decompositions, namely the proper orthogonal decomposition (POD) and the dynamic mode decomposition (DMD), and we propose a novel decomposition which allows for enhanced feature detection capabilities. This novel decomposition is referred to as multi-scale proper orthogonal decomposition (mPOD) and combines multi-resolution analysis (MRA) with a standard POD. Using MRA, the mPOD splits the correlation matrix into the contribution of different scales, retaining non-overlapping portions of the correlation spectra; using the standard POD, the mPOD extracts the optimal basis from each scale. After introducing a matrix factorization framework for data-driven decompositions, the MRA is formulated via one- and two-dimensional filter banks for the dataset and the correlation matrix respectively. The validation of the mPOD, and a comparison with the discrete Fourier transform (DFT), DMD and POD are provided in three test cases. These include a synthetic test case, a numerical simulation of a nonlinear advection–diffusion problem and an experimental dataset obtained by the time-resolved particle image velocimetry (TR-PIV) of an impinging gas jet. For each of these examples, the decompositions are compared in terms of convergence, feature detection capabilities and time–frequency localization.

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Xu, S. Z., J. L. Chen, and J. Benítez. "Partial orders based on the CS decomposition." Ukrains’kyi Matematychnyi Zhurnal 72, no. 8 (August 18, 2020): 1119–33. http://dx.doi.org/10.37863/umzh.v72i8.6025.

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UDC 512.5 A new decomposition for square matrices is given by using two known matrix decompositions, a new characterization of the core-EP order is obtained by using this new matrix decomposition. Also, we will use a matrix decomposition to investigate the minus, star, sharp and core partial orders in the setting of complex matrices.

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CÂMPEANU, C., K. SALOMAA, and S. VÁGVÖLGYI. "SHUFFLE DECOMPOSITIONS OF REGULAR LANGUAGES." International Journal of Foundations of Computer Science 13, no. 06 (December 2002): 799–816. http://dx.doi.org/10.1142/s0129054102001461.

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We study the shuffle quotient operation and introduce equivalence relations it defines with respect to a (regular) language. Corresponding to an arbitrary shuffle decomposition we construct a normalized decomposition that is defined in terms of maximal languages. Using closure properties of the normalized decompositions we show that for certain subclasses of regular languages we can effectively decide whether or not the language has a non-trivial shuffle decomposition. We show that shuffle decomposition is undecidable for context-free languages.

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Luo, Dijun, Chris Ding, and Heng Huang. "Multi-Level Cluster Indicator Decompositions of Matrices and Tensors." Proceedings of the AAAI Conference on Artificial Intelligence 25, no. 1 (August 4, 2011): 423–28. http://dx.doi.org/10.1609/aaai.v25i1.7933.

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A main challenging problem for many machine learning and data mining applications is that the amount of data and features are very large, so that low-rank approximations of original data are often required for efficient computation. We propose new multi-level clustering based low-rank matrix approximations which are comparable and even more compact than Singular Value Decomposition (SVD). We utilize the cluster indicators of data clustering results to form the subspaces, hence our decomposition results are more interpretable. We further generalize our clustering based matrix decompositions to tensor decompositions that are useful in high-order data analysis. We also provide an upper bound for the approximation error of our tensor decomposition algorithm. In all experimental results, our methods significantly outperform traditional decomposition methods such as SVD and high-order SVD.

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AVGUSTINOVICH, S. V., and A. E. FRID. "A UNIQUE DECOMPOSITION THEOREM FOR FACTORIAL LANGUAGES." International Journal of Algebra and Computation 15, no. 01 (February 2005): 149–60. http://dx.doi.org/10.1142/s0218196705002116.

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We study decompositions of a factorial language to catenations of factorial languages and introduce the notion of a canonical decomposition. Then we prove that for each factorial language, a canonical decomposition exists and is unique.

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Steinbach, Bernd, and Christian Posthoff. "Compact XOR-bi-decomposition for lattices of Boolean functions." Facta universitatis - series: Electronics and Energetics 31, no. 2 (2018): 223–40. http://dx.doi.org/10.2298/fuee1802223s.

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Bi-Decomposition is a powerful approach for the synthesis of multi-level combinational circuits because it utilizes the properties of the given functions to find small circuits, with low power consumption and low delay. Compact bi-decompositions restrict the variables in the support of the decomposition functions as much as possible. Methods to find compact AND-, OR-, or XOR-bi-decompositions for a given completely specified function are well known. Lattices of Boolean Functions significantly increase the possibilities to synthesize a minimal circuit. However, so far only methods to find compact AND- or OR-bi-decompositions for lattices of Boolean functions are known. This gap, i.e., a method to find a compact XOR-bi-decomposition for a lattice of Boolean functions, has been closed by the approach suggested in this paper.

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Broer, Abraham. "Decomposition Varieties in Semisimple Lie Algebras." Canadian Journal of Mathematics 50, no. 5 (October 1, 1998): 929–71. http://dx.doi.org/10.4153/cjm-1998-048-6.

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AbstractThe notion of decompositon class in a semisimple Lie algebra is a common generalization of nilpotent orbits and the set of regular semisimple elements.We prove that the closure of a decomposition class has many properties in common with nilpotent varieties, e.g., its normalization has rational singularities.The famous Grothendieck simultaneous resolution is related to the decomposition class of regular semisimple elements. We study the properties of the analogous commutative diagrams associated to an arbitrary decomposition class.

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Zheng, Yu-Bang, Ting-Zhu Huang, Xi-Le Zhao, Qibin Zhao, and Tai-Xiang Jiang. "Fully-Connected Tensor Network Decomposition and Its Application to Higher-Order Tensor Completion." Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 12 (May 18, 2021): 11071–78. http://dx.doi.org/10.1609/aaai.v35i12.17321.

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The popular tensor train (TT) and tensor ring (TR) decompositions have achieved promising results in science and engineering. However, TT and TR decompositions only establish an operation between adjacent two factors and are highly sensitive to the permutation of tensor modes, leading to an inadequate and inflexible representation. In this paper, we propose a generalized tensor decomposition, which decomposes an Nth-order tensor into a set of Nth-order factors and establishes an operation between any two factors. Since it can be graphically interpreted as a fully-connected network, we named it fully-connected tensor network (FCTN) decomposition. The superiorities of the FCTN decomposition lie in the outstanding capability for characterizing adequately the intrinsic correlations between any two modes of tensors and the essential invariance for transposition. Furthermore, we employ the FCTN decomposition to one representative task, i.e., tensor completion, and develop an efficient solving algorithm based on proximal alternating minimization. Theoretically, we prove the convergence of the developed algorithm, i.e., the sequence obtained by it globally converges to a critical point. Experimental results substantiate that the proposed method compares favorably to the state-of-the-art methods based on other tensor decompositions.

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FOULIS, DAVID J., SYLVIA PULMANNOVÁ, and ELENA VINCEKOVÁ. "TYPE DECOMPOSITION OF A PSEUDOEFFECT ALGEBRA." Journal of the Australian Mathematical Society 89, no. 3 (December 2010): 335–58. http://dx.doi.org/10.1017/s1446788711001042.

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AbstractEffect algebras, which generalize the lattice of projections in a von Neumann algebra, serve as a basis for the study of unsharp observables in quantum mechanics. The direct decomposition of a von Neumann algebra into types I, II, and III is reflected by a corresponding decomposition of its lattice of projections, and vice versa. More generally, in a centrally orthocomplete effect algebra, the so-called type-determining sets induce direct decompositions into various types. In this paper, we extend the theory of type decomposition to a (possibly) noncommutative version of an effect algebra called a pseudoeffect algebra. It has been argued that pseudoeffect algebras constitute a natural structure for the study of noncommuting unsharp or fuzzy observables. We develop the basic theory of centrally orthocomplete pseudoeffect algebras, generalize the notion of a type-determining set to pseudoeffect algebras, and show how type-determining sets induce direct decompositions of centrally orthocomplete pseudoeffect algebras.

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Saad Qassim Fleh. "IMAGE COMPRESSION BASED ON LOSSLESS WAVELET WITH HYBEID 2D_DECOMPOSIYION." Diyala Journal of Engineering Sciences 5, no. 1 (June 1, 2012): 1–12. http://dx.doi.org/10.24237/djes.2012.05101.

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This paper introduces a proposed method for hybrid 2D wavelet transform, and applies this method on the field of lossless image compression method. Wavelets in 2D or higher dimensions are often generated by a decomposition scheme from 1D wavelets. There are two decomposition schemes; the standard (rectangular) and the nonstandard (square) decomposition. A hybrid 2D wavelet transform is a result of mixing these two decompositions in order to improve the compression performance and compression ratio

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Shi, Shuo, and Lin Shuang Zhao. "Effect of Humidity on the Thermal Stability of Red Pyrotechnic Composition." Advanced Materials Research 1030-1032 (September 2014): 52–55. http://dx.doi.org/10.4028/www.scientific.net/amr.1030-1032.52.

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pyrotechnic mixtures are sensitivity with the influence of humidity and are susceptible to explosive decompositions. The aim of this paper is to provide thermal decomposition data under different humidity conditions. The method of TG-DSC simultaneous analysis has been used to study the thermal decomposition mechanism of a typical red pyrotechnic mixture. The kinetic parameters were calculated by kissinger method. The thermal stability is evaluated by decomposition peak temperature (Tm), mass loss (△m) and activation energy (E), which shows that the decomposition peak temperature and activation energy decreased obviously. Therefore, the thermal safety under humidity atmosphere become lower.

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Qiu, Jian, and Ji Jun Chen. "EMD in the Research and Application of Deformation Monitoring in Embankment." Applied Mechanics and Materials 501-504 (January 2014): 1868–72. http://dx.doi.org/10.4028/www.scientific.net/amm.501-504.1868.

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In this paper, the deformation monitoring of empirical mode decomposition method is applied to the embankment, and accordingly to evaluate dike reinforcement effect. Based on empirical mode decompositionof the endpoint effect makes the decomposition results of distortion, put forward to properly control point by using the window function method.effectively ensure the accuracy of the results of decomposition. Reference for peers and staff.

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Kalajdzievski, Timjan, and Nicolás Quesada. "Exact and approximate continuous-variable gate decompositions." Quantum 5 (February 8, 2021): 394. http://dx.doi.org/10.22331/q-2021-02-08-394.

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We gather and examine in detail gate decomposition techniques for continuous-variable quantum computers and also introduce some new techniques which expand on these methods. Both exact and approximate decomposition methods are studied and gate counts are compared for some common operations. While each having distinct advantages, we find that exact decompositions have lower gate counts whereas approximate techniques can cover decompositions for all continuous-variable operations but require significant circuit depth for a modest precision.

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LIU, ZHENXIN, SHUGUAN JI, and MENGLONG SU. "ATTRACTOR–REPELLER PAIR, MORSE DECOMPOSITION AND LYAPUNOV FUNCTION FOR RANDOM DYNAMICAL SYSTEMS." Stochastics and Dynamics 08, no. 04 (December 2008): 625–41. http://dx.doi.org/10.1142/s0219493708002494.

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In the stability theory of dynamical systems, Lyapunov functions play a fundamental role. In this paper, we study the attractor–repeller pair decomposition and Morse decomposition for compact metric space in the random setting. In contrast to [7,17], by introducing slightly stronger definitions of random attractor and repeller, we characterize attractor–repeller pair decompositions and Morse decompositions for random dynamical systems through the existence of Lyapunov functions. These characterizations, we think, deserve to be known widely.

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Theriault, Stephen D. "Homotopy Decompositions Involving the Loops of Coassociative Co-H Spaces." Canadian Journal of Mathematics 55, no. 1 (February 1, 2003): 181–203. http://dx.doi.org/10.4153/cjm-2003-008-5.

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AbstractJames gave an integral homotopy decomposition of ∑Ω∑X, Hilton-Milnor one for Ω(∑X ∨ ∑Y), and Cohen-Wu gave p-local decompositions of Ω∑X if X is a suspension. All are natural. Using idempotents and telescopes we show that the James andHilton-Milnor decompositions have analogues when the suspensions are replaced by coassociative co-H spaces, and the Cohen-Wu decomposition has an analogue when the (double) suspension is replaced by a coassociative, cocommutative co-H space.

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LI, Yong Jia, Ting Lei, and Da Jin Yang. "Radionuclide of Process of Carbon Decomposition and Anneal of Liquor after Desilication from Nepheline." Applied Mechanics and Materials 330 (June 2013): 22–26. http://dx.doi.org/10.4028/www.scientific.net/amm.330.22.

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Carbon decomposition of liquor afger desilication from nephine was investigated, aluminium oxide was prepard by anneal of Al (OH)3 separated out from carbon decompositon, and analysis of radionuclide of both above process was performed. The results show decomposition rate of sodium aluminate can be obtained when experiments of carbon decomposition of liquor after desilication using CO2 of hight concentration, and it is beneifit for the crystal growth of Al (OH)3, filtration and separation. Great mass of nuclide exists in the mother solution of carbon decomposition, and few into Al (OH)3, which could be regarded as wiout radioactive contamination. .

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BIFERALE, LUCA, DETLEF LOHSE, IRENE M. MAZZITELLI, and FEDERICO TOSCHI. "Probing structures in channel flow through SO(3) and SO(2) decomposition." Journal of Fluid Mechanics 452 (February 10, 2002): 39–59. http://dx.doi.org/10.1017/s0022112001006632.

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SO(3) and SO(2) decompositions of numerical channel flow turbulence are performed. The decompositions are used to probe, characterize, and quantify anisotropic structures in the flow. Close to the wall, the anisotropic modes are dominant and reveal the flow structures. The dominance of the (j, m) = (2, 1) mode of the SO(3) decomposition in the buffer layer is associated with hairpin vortices. The SO(2) decomposition in planes parallel to the walls allows us also to access the regions very close to the wall. In those regions we have found that the strong enhancement of intermittency can be explained in terms of streaklike structures and their signatures in the m = 2 and m = 4 modes of the SO(2) decomposition.

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Hernandez, Bryan, Deza Amistas, Ralph John De la Cruz, Lauro Fontanil, Aurelio de los Reyes, and Eduardo Mendoza. "Independent, Incidence Independent and Weakly Reversible Decompositions of Chemical Reaction Networks." MATCH Communications in Mathematical and in Computer Chemistry 87, no. 2 (2021): 367–96. http://dx.doi.org/10.46793/match.87-2.367h.

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Chemical reaction networks (CRNs) are directed graphs with reactant or product complexes as vertices, and reactions as arcs. A CRN is weakly reversible if each of its connected components is strongly connected. Weakly reversible networks can be considered as the most important class of reaction networks. Now, the stoichiometric subspace of a network is the linear span of the reaction vectors (i.e., difference between the product and the reactant complexes). A decomposition of a CRN is independent (incidence independent) if the direct sum of the stoichiometric subspaces (incidence maps) of the subnetworks equals the stoichiometric subspace (incidence map) of the whole network. Decompositions can be used to study relationships between positive steady states of the whole system (induced from partitioning the reaction set of the underlying network) and those of its subsystems. In this work, we revisit our novel method of finding independent decomposition, and use it to expand applicability on (vector) components of steady states. We also explore CRNs with embedded deficiency zero independent subnetworks. In addition, we establish a method for finding incidence independent decomposition of a CRN. We determine all the forms of independent and incidence independent decompositions of a network, and provide the number of such decompositions. Lastly, for weakly reversible networks, we determine that incidence independence is a sufficient condition for weak reversibility of a decomposition, and we identify subclasses of weakly reversible networks where any independent decomposition is weakly reversible.

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GUTIERREZ, MAURICIO, and ADAM PIGGOTT. "RIGIDITY OF GRAPH PRODUCTS OF ABELIAN GROUPS." Bulletin of the Australian Mathematical Society 77, no. 2 (April 2008): 187–96. http://dx.doi.org/10.1017/s0004972708000105.

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AbstractWe show that if G is a group and G has a graph-product decomposition with finitely generated abelian vertex groups, then G has two canonical decompositions as a graph product of groups: a unique decomposition in which each vertex group is a directly indecomposable cyclic group, and a unique decomposition in which each vertex group is a finitely generated abelian group and the graph satisfies the T0 property. Our results build on results by Droms, Laurence and Radcliffe.

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Dai, Shuang Ye, Ge You Ao, and Myung Soo Kim. "Properties of CB/Rubber Composites Filled by Carbon Black Used as Catalysts for Hydrocarbon Decomposition." Advanced Materials Research 26-28 (October 2007): 301–4. http://dx.doi.org/10.4028/www.scientific.net/amr.26-28.301.

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Carbon blacks were used as catalysts for hydrogen production through hydrocarbon decomposition. The aim of this work is to find suitable conditions for decomposition reaction to cut down the net cost of hydrogen production. Carbon blacks after hydrocarbon decomposition under different operation conditions were mixed with NBR rubber. The surface area of carbon black increased with low weight gain in methane decomposition caused by carbon deposits on the surface of carbon black aggregates, and the decrease of surface area with further weight gain might be due to the carbon deposits adhering to each other and forming bigger aggregates. The same results were gotten from decomposition of mixture gas of methane and propane. The surface area of carbon black always decreased with the development of propane decomposition reaction. With the same carbon black loading, the composites filled by carbon blacks with low weight gain in methane and methane-propane mixture gas decompositions showed higher tensile strength than those mixed with raw carbon blacks, but there were no significant differences in 300% modulus. With the increase of carbon blacks loading in all composites, 300% modulus and tensile strength always increased. The surface resistivity of composites showed that it was much easier for carbon blacks with low weight gain in methane and methane-propane mixture gas decompositions to dissipate well in the in rubber system.

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Jing, Yuan-Wei, Jun Zhao, Mile Stankovski, and Georgi Dimirovski. "Three theorems on hierarchical decomposition of similarity linear systems." Facta universitatis - series: Electronics and Energetics 17, no. 2 (2004): 241–49. http://dx.doi.org/10.2298/fuee0402241j.

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In this paper the problem of system decomposition of complex linear dynamical systems biy exploiting the similarity property is studied. System decompositions are sought in terms of similarity hierarchical structures. The method for constructing the transformation is derived. The conditions for such decomposition of complex linear systems are given.

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Batyanovskii, A. V., V. A. Namiot, I. V. Filatov, V. G. Tumanyan, N. G. Esipova, and I. D. Volotovsky. "Fourier transformation in spherical systems as a tool of structural biology." Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series 56, no. 4 (December 31, 2020): 496–503. http://dx.doi.org/10.29235/1561-2430-2020-56-4-496-503.

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Applications of the most common adaptation of Fourier analysis in spherical coordinate systems used to solve a number of problems in structural biology, namely, flat wave decomposition (flat waves are represented as spherical functions decomposition), are herein considered. Arguments in favor of this decomposition are compared with other decompositions in superposition of special functions. A more general justification for the correctness of this decomposition is obtained than that existing today. A method for representing groups of atoms in the form of a Fourier object is proposed. It is also considered what opportunities give such a representation. The prospects for the application of Fourier analysis in structural biophysics are discussed.

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Batyanovskii, A. V., V. A. Namiot, I. V. Filatov, V. G. Tumanyan, N. G. Esipova, and I. D. Volotovsky. "Fourier transformation in spherical systems as a tool of structural biology." Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series 56, no. 4 (December 31, 2020): 496–503. http://dx.doi.org/10.29235/1561-2430-2020-56-4-496-503.

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Applications of the most common adaptation of Fourier analysis in spherical coordinate systems used to solve a number of problems in structural biology, namely, flat wave decomposition (flat waves are represented as spherical functions decomposition), are herein considered. Arguments in favor of this decomposition are compared with other decompositions in superposition of special functions. A more general justification for the correctness of this decomposition is obtained than that existing today. A method for representing groups of atoms in the form of a Fourier object is proposed. It is also considered what opportunities give such a representation. The prospects for the application of Fourier analysis in structural biophysics are discussed.

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Correa, Carlos G., Mark K. Ho, Frederick Callaway, Nathaniel D. Daw, and Thomas L. Griffiths. "Humans decompose tasks by trading off utility and computational cost." PLOS Computational Biology 19, no. 6 (June 1, 2023): e1011087. http://dx.doi.org/10.1371/journal.pcbi.1011087.

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Human behavior emerges from planning over elaborate decompositions of tasks into goals, subgoals, and low-level actions. How are these decompositions created and used? Here, we propose and evaluate a normative framework for task decomposition based on the simple idea that people decompose tasks to reduce the overall cost of planning while maintaining task performance. Analyzing 11,117 distinct graph-structured planning tasks, we find that our framework justifies several existing heuristics for task decomposition and makes predictions that can be distinguished from two alternative normative accounts. We report a behavioral study of task decomposition (N = 806) that uses 30 randomly sampled graphs, a larger and more diverse set than that of any previous behavioral study on this topic. We find that human responses are more consistent with our framework for task decomposition than alternative normative accounts and are most consistent with a heuristic—betweenness centrality—that is justified by our approach. Taken together, our results suggest the computational cost of planning is a key principle guiding the intelligent structuring of goal-directed behavior.

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Dem’yanovich, Yu K., and I. G. Burova. "Properties of Decomposition Operators of Spline-Wavelet Decompositions." Journal of Mathematical Sciences 205, no. 2 (January 20, 2015): 205–21. http://dx.doi.org/10.1007/s10958-015-2242-7.

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Graversen, S. E. "A Riesz decomposition theorem." Nagoya Mathematical Journal 114 (June 1989): 123–33. http://dx.doi.org/10.1017/s0027763000001422.

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The topic of this note is the Riesz decomposition of excessive functions for a “nice” strong Markov process X. I.e. an excessive function is decomposed into a sum of a potential of a measure and a “harmonic” function. Originally such decompositions were studied by G.A. Hunt [8]. In [1] a Riesz decomposition is given assuming that the state space E is locally compact with a countable base and X is a transient standard process in strong duality with another standard process having a strong Feller resolvent. Recently R.K. Getoor and J. Glover extended the theory to the case of transient Borei right processes in weak duality [6].

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JOHANSSON, ÖJVIND. "NLC2-DECOMPOSITION IN POLYNOMIAL TIME." International Journal of Foundations of Computer Science 11, no. 03 (September 2000): 373–95. http://dx.doi.org/10.1142/s0129054100000223.

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NLC k is a family of algebras on vertex-labeled graphs introduced by Wanke. An NLC-decomposition of a graph is a derivation of this graph from single vertices using the operations in question. The width of the decomposition is the number of labels used, and the NLC-width of the graph is the smallest width among its NLC-decompositions. Many difficult graph problems can be solved efficiently with dynamic programming if an NLC-decomposition of low width is given for the input graph. It is unknown, though, whether arbitrary graphs of NLC-width at most k can be decomposed with k labels in polynomial time. So far this has been possible only for k = 1, which corresponds to cographs. In this paper, an algorithm is presented that works for k = 2. It runs in O(n4 log n) time and uses O(n2) space. Related concepts: clique-decomposition, clique-width.

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Cui, Xiaopeng, and Yu Shi. "Trotter errors in digital adiabatic quantum simulation of quantum ℤ2 lattice gauge theory." International Journal of Modern Physics B 34, no. 30 (August 19, 2020): 2050292. http://dx.doi.org/10.1142/s0217979220502926.

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Trotter decomposition is the basis of the digital quantum simulation. Asymmetric and symmetric decompositions are used in our GPU demonstration of the digital adiabatic quantum simulations of (2[Formula: see text]+[Formula: see text]1)-dimensional quantum [Formula: see text] lattice gauge theory. The actual errors in Trotter decompositions are investigated as functions of the coupling parameter and the number of Trotter substeps in each step of the variation of coupling parameter. The relative error of energy is shown to be equal to the Trotter error usually defined in terms of the evolution operators. They are much smaller than the order-of-magnitude estimation. The error in the symmetric decomposition is much smaller than that in the asymmetric decomposition. The features of the Trotter errors obtained here are useful in the experimental implementation of digital quantum simulation and its numerical demonstration.

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Führ, Hartmut, and Azita Mayeli. "Homogeneous Besov Spaces on Stratified Lie Groups and Their Wavelet Characterization." Journal of Function Spaces and Applications 2012 (2012): 1–41. http://dx.doi.org/10.1155/2012/523586.

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We establish wavelet characterizations of homogeneous Besov spaces on stratified Lie groups, both in terms of continuous and discrete wavelet systems. We first introduce a notion of homogeneous Besov spaceB˙p,qsin terms of a Littlewood-Paley-type decomposition, in analogy to the well-known characterization of the Euclidean case. Such decompositions can be defined via the spectral measure of a suitably chosen sub-Laplacian. We prove that the scale of Besov spaces is independent of the precise choice of Littlewood-Paley decomposition. In particular, different sub-Laplacians yield the same Besov spaces. We then turn to wavelet characterizations, first via continuous wavelet transforms (which can be viewed as continuous-scale Littlewood-Paley decompositions), then via discretely indexed systems. We prove the existence of wavelet frames and associated atomic decomposition formulas for all homogeneous Besov spacesB˙p,qswith1≤p,q<∞ands∈ℝ.

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Šiljak, D. D., and A. I. Zečević. "A nested decomposition algorithm for parallel computations of very large sparse systems." Mathematical Problems in Engineering 1, no. 1 (1995): 41–57. http://dx.doi.org/10.1155/s1024123x95000068.

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In this paper we present a generalization of the balanced border block diagonal (BBD) decomposition algorithm, which was developed for the parallel computation of sparse systems of linear equations. The efficiency of the new procedure is substantially higher, and it extends the applicability of the BBD decomposition to extremely large problems. Examples of the decomposition are provided for matrices as large as250,000×250,000, and its performance is compared to other sparse decompositions. Applications to the parallel solution of sparse systems are discussed for a variety of engineering problems.

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Chang, Yi-Jun, Seth Pettie, Thatchaphol Saranurak, and Hengjie Zhang. "Near-optimal Distributed Triangle Enumeration via Expander Decompositions." Journal of the ACM 68, no. 3 (May 13, 2021): 1–36. http://dx.doi.org/10.1145/3446330.

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We present improved distributed algorithms for variants of the triangle finding problem in the model. We show that triangle detection, counting, and enumeration can be solved in rounds using expander decompositions . This matches the triangle enumeration lower bound of by Izumi and Le Gall [PODC’17] and Pandurangan, Robinson, and Scquizzato [SPAA’18], which holds even in the model. The previous upper bounds for triangle detection and enumeration in were and , respectively, due to Izumi and Le Gall [PODC’17]. An -expander decomposition of a graph is a clustering of the vertices such that (i) each cluster induces a subgraph with conductance at least and (ii) the number of inter-cluster edges is at most . We show that an -expander decomposition with can be constructed in rounds for any and positive integer . For example, a -expander decomposition only requires rounds to compute, which is optimal up to subpolynomial factors, and a -expander decomposition can be computed in rounds, for any arbitrarily small constant . Our triangle finding algorithms are based on the following generic framework using expander decompositions, which is of independent interest. We first construct an expander decomposition. For each cluster, we simulate algorithms with small overhead by applying the expander routing algorithm due to Ghaffari, Kuhn, and Su [PODC’17] Finally, we deal with inter-cluster edges using recursive calls.

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Breiding, Paul, and Nick Vannieuwenhoven. "On the average condition number of tensor rank decompositions." IMA Journal of Numerical Analysis 40, no. 3 (June 20, 2019): 1908–36. http://dx.doi.org/10.1093/imanum/drz026.

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Abstract We compute the expected value of powers of the geometric condition number of random tensor rank decompositions. It is shown in particular that the expected value of the condition number of $n_1\times n_2 \times 2$ tensors with a random rank-$r$ decomposition, given by factor matrices with independent and identically distributed standard normal entries, is infinite. This entails that it is expected and probable that such a rank-$r$ decomposition is sensitive to perturbations of the tensor. Moreover, it provides concrete further evidence that tensor decomposition can be a challenging problem, also from the numerical point of view. On the other hand, we provide strong theoretical and empirical evidence that tensors of size $n_1~\times ~n_2~\times ~n_3$ with all $n_1,n_2,n_3 \geqslant 3$ have a finite average condition number. This suggests that there exists a gap in the expected sensitivity of tensors between those of format $n_1\times n_2 \times 2$ and other order-3 tensors. To establish these results we show that a natural weighted distance from a tensor rank decomposition to the locus of ill-posed decompositions with an infinite geometric condition number is bounded from below by the inverse of this condition number. That is, we prove one inequality towards a so-called condition number theorem for the tensor rank decomposition.

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Trisasongko, Bambang H., Dyah R. Panuju, Amy L. Griffin, and David J. Paull. "Fully Polarimetric L-Band Synthetic Aperture Radar for the Estimation of Tree Girth as a Representative of Stand Productivity in Rubber Plantations." Geographies 2, no. 2 (March 24, 2022): 173–85. http://dx.doi.org/10.3390/geographies2020012.

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This article explores a potential exploitation of fully polarimetric radar data for the management of rubber plantations, specifically for predicting tree circumference as a crucial information need for sustainable plantation management. Conventional backscatter coefficients along with Eigen-based and model-based decomposition features served as the predictors in models of tree girth using ten regression approaches. The findings suggest that backscatter coefficients and Eigen-based decomposition features yielded lower accuracy than model-based decomposition features. Model-based decompositions, especially the Singh decomposition, provided the best accuracies when they were coupled with guided regularized random forests regression. This research demonstrates that L-band SAR data can provide an accurate estimation of rubber plantation tree girth, with an RMSE of about 8 cm.

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Paúl, Pedro J., Carmen Sáez, and Juan M. Virués. "Locally Convex Spaces with Toeplitz Decompositions." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 68, no. 1 (February 2000): 19–40. http://dx.doi.org/10.1017/s1446788700001555.

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AbstractA Toeplitz decomposition of a locally convez space E into subspaces (Ek) with continuous projections (Pk) is a decomposition of every x ∈ E as x = ΣkPkx where ordinary summability has been replaced by summability with respect to an infinite and row-finite matrix. We extend to the setting of Toeplitz decompositions a number of results about the locally convex structure of a space with a Schauder decomposition. Namely, we give some necessary or sufficient conditions for being reflexive, a Montel space or a Schwartz space. Roughly speaking, each of these locally convex properties is linked to a property of the convergence of the decomposition. We apply these results to study some structural questions in projective tensor products and spaces with Cesàro bases.

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Goh, Say Song, S. L. Lee, Zuowei Shen, and W. S. Tang. "Construction of Schauder decomposition on banach spaces of periodic functions." Proceedings of the Edinburgh Mathematical Society 41, no. 1 (February 1998): 61–91. http://dx.doi.org/10.1017/s001309150001943x.

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This paper deals with Schauder decompositions of Banach spaces X2π of 2π-periodic functions by projection operators Pk onto the subspaces Vk, k = 0,1,…, which form a multiresolution of X2π,. The results unify the study of wavelet decompositions by orthogonal projections in the Hilbert space on one hand and by interpolatory projections in the Banach space C2π on the other. The approach, using “orthogonal splines”, is constructive and leads to the construction of a Schauder decomposition of X2π and a biorthogonal system for X2π, and its dual X2π. Decomposition and reconstruction algorithms are derived from the construction.

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Journal articles on the topic 'Decomposition'

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