scholarly journals A Characterization of Polynomial Density on Curves via Matrix Algebra

Mathematics ◽  
2019 ◽  
Vol 7 (12) ◽  
pp. 1231
Author(s):  
Carmen Escribano ◽  
Raquel Gonzalo ◽  
Emilio Torrano
Keyword(s):  
Matrix Algebra ◽  
Optimization Problems ◽  
Positive Semidefinite ◽  
Point Of View ◽  
Alternative Proof ◽  
General Context ◽  
Positive Semidefinite Matrices ◽  
Jordan Curves ◽  
Point Evaluations

In this work, our aim is to obtain conditions to assure polynomial approximation in Hilbert spaces L 2 ( μ ) , with μ a compactly supported measure in the complex plane, in terms of properties of the associated moment matrix with the measure μ . To do it, in the more general context of Hermitian positive semidefinite matrices, we introduce two indexes, γ ( M ) and λ ( M ) , associated with different optimization problems concerning theses matrices. Our main result is a characterization of density of polynomials in the case of measures supported on Jordan curves with non-empty interior using the index γ and other specific index related to it. Moreover, we provide a new point of view of bounded point evaluations associated with a measure in terms of the index γ that will allow us to give an alternative proof of Thomson’s theorem, by using these matrix indexes. We point out that our techniques are based in matrix algebra tools in the framework of Hermitian positive definite matrices and in the computation of certain indexes related to some optimization problems for infinite matrices.

scholarly journals Moore-Penrose inverse of a hollow symmetric matrix and a predistance matrix

2016 ◽  
Vol 4 (1) ◽  
Author(s):  
Hiroshi Kurata ◽  
Ravindra B. Bapat
Keyword(s):  
Euclidean Distance ◽  
Symmetric Matrix ◽  
Distance Matrix ◽  
Positive Semidefinite ◽  
Complete Characterization ◽  
Symmetric Matrices ◽  
Euclidean Distance Matrix ◽  
Positive Semidefinite Matrices ◽  
Special Cases

AbstractBy a hollow symmetric matrix we mean a symmetric matrix with zero diagonal elements. The notion contains those of predistance matrix and Euclidean distance matrix as its special cases. By a centered symmetric matrix we mean a symmetric matrix with zero row (and hence column) sums. There is a one-toone correspondence between the classes of hollow symmetric matrices and centered symmetric matrices, and thus with any hollow symmetric matrix D we may associate a centered symmetric matrix B, and vice versa. This correspondence extends a similar correspondence between Euclidean distance matrices and positive semidefinite matrices with zero row and column sums.We show that if B has rank r, then the corresponding D must have rank r, r + 1 or r + 2. We give a complete characterization of the three cases.We obtain formulas for the Moore-Penrose inverse D

scholarly journals A Characterization on Singular Value Inequalities of Matrices

2020 ◽  
Vol 2020 ◽  
pp. 1-4
Author(s):  
Wei Dai ◽  
Yongsheng Ye
Keyword(s):  
Singular Values ◽  
Positive Semidefinite ◽  
Singular Value ◽  
Positive Semidefinite Matrices ◽  
Direct Sums ◽  
New Inequalities

We obtain a characterization of pair matrices A and B of order n such that sjA≤sjB, j=1, …, n, where sjX denotes the j-th largest singular values of X. It can imply not only some well-known singular value inequalities for sums and direct sums of matrices but also Zhan’s result related to singular values of differences of positive semidefinite matrices. In addition, some related and new inequalities are also obtained.

scholarly journals On the closure of the completely positive semidefinite cone and linear approximations to quantum colorings

2017 ◽  
Vol 32 ◽  
pp. 15-40 ◽  
Author(s):  
Sabine Burgdorf ◽  
Monique Laurent ◽  
Teresa Piovesan
Keyword(s):  
Optimization Problems ◽  
Positive Semidefinite ◽  
Quantum Correlations ◽  
Positive Semidefinite Matrices ◽  
Completely Positive ◽  
Matrix Algebras ◽  
Positive Semidefinite Cone ◽  
The One ◽  
Graph Parameters ◽  
Semidefinite Cone

We investigate structural properties of the completely positive semidefinite cone $\mathcal{CS}_+$, consisting of all the $n \times n$ symmetric matrices that admit a Gram representation by positive semidefinite matrices of any size. This cone has been introduced to model quantum graph parameters as conic optimization problems. Recently it has also been used to characterize the set $\mathcal Q$ of bipartite quantum correlations, as projection of an affine section of it. We have two main results concerning the structure of the completely positive semidefinite cone, namely about its interior and about its closure. On the one hand we construct a hierarchy of polyhedral cones covering the interior of $\mathcal{CS}_+$, which we use for computing some variants of the quantum chromatic number by way of a linear program. On the other hand we give an explicit description of the closure of the completely positive semidefinite cone by showing that it consists of all matrices admitting a Gram representation in the tracial ultraproduct of matrix algebras.

scholarly journals Markovian lifts of positive semidefinite affine Volterra-type processes

2019 ◽  
Vol 42 (2) ◽  
pp. 407-448 ◽  
Author(s):  
Christa Cuchiero ◽  
Josef Teichmann
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Stochastic Partial Differential Equations ◽  
Positive Semidefinite ◽  
Point Of View ◽  
Type Model ◽  
Volterra Type ◽  
Partial Differential ◽  
Positive Semidefinite Matrices ◽  
Feller Property

Abstract We consider stochastic partial differential equations appearing as Markovian lifts of matrix-valued (affine) Volterra-type processes from the point of view of the generalized Feller property (see, e.g., Dörsek and Teichmann in A semigroup point of view on splitting schemes for stochastic (partial) differential equations, 2010. arXiv:1011.2651). We introduce in particular Volterra Wishart processes with fractional kernels and values in the cone of positive semidefinite matrices. They are constructed from matrix products of infinite dimensional Ornstein–Uhlenbeck processes whose state space is the set of matrix-valued measures. Parallel to that we also consider positive definite Volterra pure jump processes, giving rise to multivariate Hawkes-type processes. We apply these affine covariance processes for multivariate (rough) volatility modeling and introduce a (rough) multivariate Volterra Heston-type model.

scholarly journals APPLICATION OF SEMIDEFINITE PROGRAMMING TO TRUSS DESIGN OPTIMIZATION / SANTVAROS OPTIMIZAVIMO UŽDAVINIŲ SPRENDIMAS TAIKANT PUSIAU APIBRĖŽTĄ PROGRAMAVIMĄ

2015 ◽  
Vol 7 (3) ◽  
pp. 280-284
Author(s):  
Rasa Giniūnaitė
Keyword(s):  
Semidefinite Programming ◽  
Optimization Problems ◽  
Positive Semidefinite ◽  
Algebraic Manipulation ◽  
Truss Structure ◽  
Convex Constraints ◽  
Positive Semidefinite Matrices ◽  
Combinatorial Optimization Problems ◽  
Linear Problems ◽  
The One

Semidefinite Programming (SDP) is a fairly recent way of solving optimization problems which are becoming more and more important in our fast moving world. It is a minimization of linear function over the intersection of the cone of positive semidefinite matrices with an affine space, i.e. non-linear but convex constraints. All linear problems and many engineering and combinatorial optimization problems can be expressed as SDP, so it is highly applicable. There are many packages that use different algorithms to solve SDP problems. They can be downloaded from internet and easily learnt how to use, two of these are SeDuMi and SDPT-3. In this paper truss structure optimization problem with the goal of minimizing the mass of the truss structure was solved. After doing some algebraic manipulation the problem was formulated suitably for Semidefinite Programming. SeDuMi and SDPT-3 packages were used to solve it. The choice of the initial solution had a great impact on the result using SeDuMi. The mass obtained using SDPT-3 was on average smaller than the one obtained using SeDuMi. Moreover, SDPT-3 worked more efficiently. However, the comparison of my approach and two versions of particle swarm optimization algorithm implied that semidefinite programming is in general more appropriate for solving such problems. Pusiau apibrėžtas programavimas yra iškiliojo optimizavimo posritis, kuriame tikslo funkcija tiesinė, o leistinoji sritis – pusiau teigiamai apibrėžtų matricų kūgio ir afininės erdvės sankirta. Tai gana naujas optimizavimo problemų sprendimo būdas, tačiau jau plačiai taikomas sprendžiant inžinerinius bei kombinatorinius optimizavimo uždavinius. Tokiems uždaviniams spręsti yra daug skirtingų paketų, taikančių įvairius algoritmus. Šiame darbe buvo naudojami SeDuMi ir SDPT-3 paketai, kuriuos, kaip ir daugumą kitų, galima parsisiųsti iš interneto. Tikslas buvo rasti minimalią santvaros masę atsižvelgiant į numatytus apribojimus. Naudojant SDPT-3 gauta optimali masė buvo vidutiniškai mažesnė nei naudojant SeDuMi. SDPT-3 veikė efektyviau ir pradinių sąlygų pasirinkimas neturėjo tokios didelės įtakos sprendiniui kaip naudojant SeDuMi paketą. Palyginus rezultatus su sprendiniais, gautais taikant dalelių spiečiaus optimizavimo algoritmą, nustatyta, kad tokio tipo uždaviniams pusiau apibrėžtas programavimas yra tinkamesnis.

The Analyses of Learning Strategies in English as a Second Language: Theoretical Classification and Measurement Test

2020 ◽  
Vol 4 (2) ◽  
pp. 118-129
Author(s):  
Asti Gumartifa ◽  
◽  
Indah Windra Dwie Agustiani
Keyword(s):  
Language Learning ◽  
Learning Outcomes ◽  
Learning Strategies ◽  
Learning Process ◽  
English Learners ◽  
English Language ◽  
Point Of View ◽  
Effective Learning ◽  
The Impact

Gaining English language learning effectively has been discussed all years long. Similarly, Learners have various troubles outcomes in the learning process. Creating a joyful and comfortable situation must be considered by learners. Thus, the implementation of effective learning strategies is certainly necessary for English learners. This descriptive study has two purposes: first, to introduce the classification and characterization of learning strategies such as; memory, cognitive, metacognitive, compensation, social, and affective strategies that are used by learners in the classroom and second, it provides some questionnaires item based on Strategy of Inventory for Language Learning (SILL) version 5.0 that can be used to examine the frequency of students’ learning strategies in the learning process. The summary of this study explains and discusses the researchers’ point of view on the impact of learning outcomes by learning strategies used. Finally, utilizing appropriate learning strategies are certainly beneficial for both teachers and learners to achieve the learning target effectively.

The Algorithm of Characterization of an Action as a Jointly Committed Crime

2018 ◽  
pp. 37-44
Keyword(s):  
Criminal Code ◽  
Point Of View

The article discusses a sequence of activities to identify a crime as jointly committed. The requirements to the algorithm of such activities are formulated. Programme-based and targeted methods applied by the authors allowed detecting a range of stages of the algorithm. The first four stages aim at defining mandatory elements of a crime allowing to characterize it as a jointly committed action. The rest of the stages focus on identifying a type of criminal complicity. In the article, each stage is described. It is emphasized that in each stage there is a special objective. At the same time, all these stages, taken together, constitute a separate module of the program of criminal characterization of an action. From the authors’ point of view, algorithms are necessary not only for detection of crimes and their criminal characterization, but also for answering the question on existence of criminal complicity in each case. Also the authors give their opinions on interpretation of criminal complicity as a legal category. In particular, it is emphasized that not all of crimes merely committed with participation of two or more persons should be understood as jointly committed. It is joint participation that makes a crime jointly committed. Various forms of criminal complicity and types of co-offenders are considered in the article as well. In various crimes, criminal complicity manifests itself differently. Therefore the proposed algorithm can be applied only after identification a specific article of the Russian Criminal Code stipulating the responsibility for the crime committed.

scholarly journals Some algorithms for maximum volume and cross approximation of symmetric semidefinite matrices

2021 ◽  
Author(s):  
Stefano Massei
Keyword(s):  
Computer Science ◽  
Recent Work ◽  
Linear Algebra ◽  
Optimization Problems ◽  
Approximation Error ◽  
Positive Semidefinite ◽  
Numerical Linear Algebra ◽  
Maximum Volume ◽  
Deterministic Algorithms ◽  
Principal Submatrix

AbstractVarious applications in numerical linear algebra and computer science are related to selecting the $$r\times r$$ r × r submatrix of maximum volume contained in a given matrix $$A\in \mathbb R^{n\times n}$$ A ∈ R n × n . We propose a new greedy algorithm of cost $$\mathcal O(n)$$ O ( n ) , for the case A symmetric positive semidefinite (SPSD) and we discuss its extension to related optimization problems such as the maximum ratio of volumes. In the second part of the paper we prove that any SPSD matrix admits a cross approximation built on a principal submatrix whose approximation error is bounded by $$(r+1)$$ ( r + 1 ) times the error of the best rank r approximation in the nuclear norm. In the spirit of recent work by Cortinovis and Kressner we derive some deterministic algorithms, which are capable to retrieve a quasi optimal cross approximation with cost $$\mathcal O(n^3)$$ O ( n 3 ) .

scholarly journals Processing Effect and Characterization of Olive Oils from Spanish Wild Olive Trees (Olea europaea var. sylvestris)

Molecules ◽  
2021 ◽  
Vol 26 (5) ◽  
pp. 1304
Author(s):  
Francisco Espínola ◽  
Alfonso M. Vidal ◽  
Juan M. Espínola ◽  
Manuel Moya
Keyword(s):  
Phenolic Compounds ◽  
Volatile Compounds ◽  
Olive Tree ◽  
Extraction Yield ◽  
Point Of View ◽  
Human Consumption ◽  
Analytical Point ◽  
Wild Olive ◽  
Olive Trees

Wild olive trees have important potential, but, to date, the oil from wild olives has not been studied significantly, especially from an analytical point of view. In Spain, the wild olive tree is called “Acebuche” and its fruit “Acebuchina”. The objective of this work is to optimize the olive oil production process from the Acebuchina cultivar and characterize the oil, which could be marketed as healthy and functional food. A Box–Behnken experimental design with five central points was used, along with the Response Surface Methodology to obtain a mathematical experimental model. The oils from the Acebuchina cultivar meet the requirements for human consumption and have a good balance of fatty acids. In addition, the oils are rich in antioxidants and volatile compounds. The highest extraction yield, 12.0 g oil/100 g paste, was obtained at 90.0 min and the highest yield of phenolic compounds, 870.0 mg/kg, was achieved at 40.0 °C, and 90.0 min; but the maximum content of volatile compounds, 26.9 mg/kg, was obtained at 20 °C and 30.0 min. The oil yield is lower than that of commercial cultivars, but the contents of volatile and phenolic compounds is higher.

scholarly journals Grounding semantic transparency in context

Morphology ◽  
2021 ◽  
Author(s):  
Rossella Varvara ◽  
Gabriella Lapesa ◽  
Sebastian Padó
Keyword(s):  
Large Scale ◽  
Point Of View ◽  
Distributional Semantics ◽  
Semantic Transparency ◽  
Inclusion Measure ◽  
The Difference ◽  
Semantic Point ◽  
The Many ◽  
The Relationship

AbstractWe present the results of a large-scale corpus-based comparison of two German event nominalization patterns: deverbal nouns in -ung (e.g., die Evaluierung, ‘the evaluation’) and nominal infinitives (e.g., das Evaluieren, ‘the evaluating’). Among the many available event nominalization patterns for German, we selected these two because they are both highly productive and challenging from the semantic point of view. Both patterns are known to keep a tight relation with the event denoted by the base verb, but with different nuances. Our study targets a better understanding of the differences in their semantic import.The key notion of our comparison is that of semantic transparency, and we propose a usage-based characterization of the relationship between derived nominals and their bases. Using methods from distributional semantics, we bring to bear two concrete measures of transparency which highlight different nuances: the first one, cosine, detects nominalizations which are semantically similar to their bases; the second one, distributional inclusion, detects nominalizations which are used in a subset of the contexts of the base verb. We find that only the inclusion measure helps in characterizing the difference between the two types of nominalizations, in relation with the traditionally considered variable of relative frequency (Hay, 2001). Finally, the distributional analysis allows us to frame our comparison in the broader coordinates of the inflection vs. derivation cline.

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