Статті в журналах: "Unique norm"

1

Aron, R., C. Boyd, and Y. S. Choi. "Unique Hahn-Banach theorems for spaces of homogeneous polynomials." Journal of the Australian Mathematical Society 70, no. 3 (June 2001): 387–400. http://dx.doi.org/10.1017/s1446788700002408.

Повний текст джерела

Анотація:

AbstractWe investigate certain norm and continuity conditions that provide us with ‘uniqe Hahn-Banch Theorems’ from (nc0) to (nℓ∞) and from N(nE) to N(nE″). We show that there is a unique norm-preserving extension for norm-attaining 2-homogeneous polynomials on complex c0 to ℓ∈ but there is no unique norm-preserving extension from (3c0) to (3ℓ∈).

Стилі APA, Harvard, Vancouver, ISO та ін.

2

Bhatt, S. J., and H. V. Dedania. "Banach algebras with unique uniform norm." Proceedings of the American Mathematical Society 124, no. 2 (1996): 579–84. http://dx.doi.org/10.1090/s0002-9939-96-03063-8.

Повний текст джерела

Стилі APA, Harvard, Vancouver, ISO та ін.

3

Bhatt, S. J., and H. V. Dedania. "Banach algebras with unique uniform norm II." Studia Mathematica 147, no. 3 (2001): 211–35. http://dx.doi.org/10.4064/sm147-3-2.

Повний текст джерела

Стилі APA, Harvard, Vancouver, ISO та ін.

4

Bou Akl, Ziad. "From Norm Evaluation to Norm Construction." Journal of Arabic and Islamic Studies 21 (January 4, 2022): 141–58. http://dx.doi.org/10.5617/jais.9373.

Повний текст джерела

Анотація:

This study examines the issue of norm construction in al-Ghazālī’s thought focusing on the grounds advanced to support his radical infallibilist position. To fulfill such end, al-Ghazālī, I explain, relies on two types of arguments, the first one relates to the presumptive nature of legal texts in order to highlight their fundamental indeterminacy and the second links to the interpreter to show the impossibility to fall into error. To buttress these arguments, al-Ghazālī both draws on epistemological principles and metaethical ones. As it will be shown in the study, al-Ghazālī ultimately explains the divergence in interpretation of norms using the concept of ṭabʿ (nature, disposition or appetitive self) drawing on his well-known relativist ethical theory concerning norm evaluation and therefore brings in a unique way this typical feature of Ashʿarism within his own radical infallibilist theory of norm construction. The concept of ṭabʿ allows to bridge the gap between the ambiguity in the revealed text and the mujtahid’s interpretation in the norm construction process, and ultimately serves to justify ex post the choices made by the mujtahid. In doing so, al-Ghazālī assigns to theology a critical role in revealing the origin of the illusion of the jurists who naively think that licit and illicit are qualities of things themselves.

Стилі APA, Harvard, Vancouver, ISO та ін.

5

Protasov, Vladimir Y. "The Barabanov Norm is Generically Unique, Simple, and Easily Computed." SIAM Journal on Control and Optimization 60, no. 4 (July 28, 2022): 2246–67. http://dx.doi.org/10.1137/21m1426821.

Повний текст джерела

Стилі APA, Harvard, Vancouver, ISO та ін.

6

Ojha, Bhuwan Prasad, Prakash Muni Bajracharya, and Vishnu Narayan Mishra. "On Uniqueness of New Orthogonality via 2-HH Norm in Normed Linear Space." Journal of Function Spaces 2020 (November 20, 2020): 1–6. http://dx.doi.org/10.1155/2020/8835492.

Повний текст джерела

Анотація:

This paper generalizes the special case of the Carlsson orthogonality in terms of the 2-HH norm in real normed linear space. Dragomir and Kikianty (2010) proved in their paper that the Pythagorean orthogonality is unique in any normed linear space, and isosceles orthogonality is unique if and only if the space is strictly convex. This paper deals with the complete proof of the uniqueness of the new orthogonality through the medium of the 2-HH norm. We also proved that the Birkhoff and Robert orthogonality via the 2-HH norm are equivalent, whenever the underlying space is a real inner-product space.

Стилі APA, Harvard, Vancouver, ISO та ін.

7

Yin, Feng, and Guang-Xin Huang. "An Iterative Algorithm for the Least Squares Generalized Reflexive Solutions of the Matrix Equations." Abstract and Applied Analysis 2012 (2012): 1–18. http://dx.doi.org/10.1155/2012/857284.

Повний текст джерела

Анотація:

The generalized coupled Sylvester systems play a fundamental role in wide applications in several areas, such as stability theory, control theory, perturbation analysis, and some other fields of pure and applied mathematics. The iterative method is an important way to solve the generalized coupled Sylvester systems. In this paper, an iterative algorithm is constructed to solve the minimum Frobenius norm residual problem: min over generalized reflexive matrix . For any initial generalized reflexive matrix , by the iterative algorithm, the generalized reflexive solution can be obtained within finite iterative steps in the absence of round-off errors, and the unique least-norm generalized reflexive solution can also be derived when an appropriate initial iterative matrix is chosen. Furthermore, the unique optimal approximate solution to a given matrix in Frobenius norm can be derived by finding the least-norm generalized reflexive solution of a new corresponding minimum Frobenius norm residual problem: with , . Finally, several numerical examples are given to illustrate that our iterative algorithm is effective.

Стилі APA, Harvard, Vancouver, ISO та ін.

8

Nagashima, Jennifer B., and Nucharin Songsasen. "Canid Reproductive Biology: Norm and Unique Aspects in Strategies and Mechanisms." Animals 11, no. 3 (March 1, 2021): 653. http://dx.doi.org/10.3390/ani11030653.

Повний текст джерела

Анотація:

The reproductive physiology of canids is unique compared to other mammalian species. Specifically, the reproductive cycle of female canids is characterized by extended periods of proestrus and estrus followed by obligatory diestrus and protracted ovarian inactivity (anestrus). Although canid reproduction follows this general pattern, studies have shown variations in reproductive biology among species and geographic regions. Understanding of these differences is critical to the development of assisted reproductive technologies including estrus induction, gamete rescue, and embryo production techniques for canid conservation efforts. This review summarizes current knowledge of canid reproduction, including estrus cyclicity, seasonality, and seminal traits, with the emphasis on species diversity. The application of reproductive technologies in wild canid conservation will also be discussed.

Стилі APA, Harvard, Vancouver, ISO та ін.

9

Callejo, Alfonso, Farnood Gholami, Andreas Enzenhöfer, and József Kövecses. "Unique minimum norm solution to redundant reaction forces in multibody systems." Mechanism and Machine Theory 116 (October 2017): 310–25. http://dx.doi.org/10.1016/j.mechmachtheory.2017.06.001.

Повний текст джерела

Стилі APA, Harvard, Vancouver, ISO та ін.

10

Dimant, Verónica, Daniel Galicer, and Ricardo García. "Geometry of integral polynomials, M-ideals and unique norm preserving extensions." Journal of Functional Analysis 262, no. 5 (March 2012): 1987–2012. http://dx.doi.org/10.1016/j.jfa.2011.12.021.

Повний текст джерела

Стилі APA, Harvard, Vancouver, ISO та ін.

11

Sze, Chet Lee, Keat Ng Chun, Mohd Amiruddin Mohd Kassim, and Nicholas Tze Ping Pang. "Unique Challenges for Mental Health in Inpatient Settings Amid the COVID-19 Pandemic: Perspective from Sabah." Borneo Epidemiology Journal 1, no. 1 (June 24, 2020): 79–87. http://dx.doi.org/10.51200/bej.v1i1.2439.

Повний текст джерела

Анотація:

COVID-19 has impacted the world in many ways due to fears of contracting the pandemic, social distancing, and large-scale movement control rules. These have especially grave consequences for inpatient psychiatry. This article reviews measures taken to adapt to the new norm in inpatient care, both for standalone psychiatry units and consultation-liaison units. For inpatient units, changes have been made for personal protective equipment usage, screening and triaging policies, and training and educational policies. Consultation liaison units together with inpatient units have been required to expand the scope of coverage and difficulties by providing certain teleconsultation services. As the new norm takes precedence, Sabah has to embrace and empower community-based psychiatry services for better outreach and coverage. This article discusses the issues underlying the new norm in the management of inpatient psychiatry patients in both units and presents some points and practical solutions on the ground to instil hope.

Стилі APA, Harvard, Vancouver, ISO та ін.

12

Mu, Yan, Shinobu Kitayama, Shihui Han, and Michele J. Gelfand. "How culture gets embrained: Cultural differences in event-related potentials of social norm violations." Proceedings of the National Academy of Sciences 112, no. 50 (November 30, 2015): 15348–53. http://dx.doi.org/10.1073/pnas.1509839112.

Повний текст джерела

Анотація:

Humans are unique among all species in their ability to develop and enforce social norms, but there is wide variation in the strength of social norms across human societies. Despite this fundamental aspect of human nature, there has been surprisingly little research on how social norm violations are detected at the neurobiological level. Building on the emerging field of cultural neuroscience, we combine noninvasive electroencephalography (EEG) with a new social norm violation paradigm to examine the neural mechanisms underlying the detection of norm violations and how they vary across cultures. EEG recordings from Chinese and US participants (n = 50) showed consistent negative deflection of event-related potential around 400 ms (N400) over the central and parietal regions that served as a culture-general neural marker of detecting norm violations. The N400 at the frontal and temporal regions, however, was only observed among Chinese but not US participants, illustrating culture-specific neural substrates of the detection of norm violations. Further, the frontal N400 predicted a variety of behavioral and attitudinal measurements related to the strength of social norms that have been found at the national and state levels, including higher culture superiority and self-control but lower creativity. There were no cultural differences in the N400 induced by semantic violation, suggesting a unique cultural influence on social norm violation detection. In all, these findings provided the first evidence, to our knowledge, for the neurobiological foundations of social norm violation detection and its variation across cultures.

Стилі APA, Harvard, Vancouver, ISO та ін.

13

Puzzuoli, Daniel. "Characterization of linear maps onMnwhose multiplicity maps have maximal norm, with an application in quantum information." Quantum 2 (February 5, 2018): 51. http://dx.doi.org/10.22331/q-2018-02-05-51.

Повний текст джерела

Анотація:

Given a linear mapΦ:Mn→Mm, its multiplicity maps are defined as the family of linear mapsΦ⊗idk:Mn⊗Mk→Mm⊗Mk, whereidkdenotes the identity onMk. Let‖⋅‖1denote the trace-norm on matrices, as well as the induced trace-norm on linear maps of matrices, i.e.‖Φ‖1=max{‖Φ(X)‖1:X∈Mn,‖X‖1=1}. A fact of fundamental importance in both operator algebras and quantum information is that‖Φ⊗idk‖1can grow withk. In general, the rate of growth is bounded by‖Φ⊗idk‖1≤k‖Φ‖1, and matrix transposition is the canonical example of a map achieving this bound. We prove that, up to an equivalence, the transpose is the unique map achieving this bound. The equivalence is given in terms of complete trace-norm isometries, and the proof relies on a particular characterization of complete trace-norm isometries regarding preservation of certain multiplication relations.We use this result to characterize the set of single-shot quantum channel discrimination games satisfying a norm relation that, operationally, implies that the game can be won with certainty using entanglement, but is hard to win without entanglement. Specifically, we show that the well-known example of such a game, involving the Werner-Holevo channels, is essentially the unique game satisfying this norm relation. This constitutes a step towards a characterization of single-shot quantum channel discrimination games with maximal gap between optimal performance of entangled and unentangled strategies.

Стилі APA, Harvard, Vancouver, ISO та ін.

14

Martsinkevitš, Julia, and Märt Põldvere. "Uniqueness of norm-preserving extensions of functionals on the space of compact operators." MATHEMATICA SCANDINAVICA 125, no. 1 (August 29, 2019): 67–83. http://dx.doi.org/10.7146/math.scand.a-112071.

Повний текст джерела

Анотація:

Godefroy, Kalton, and Saphar called a closed subspace $Y$ of a Banach space $Z$ an ideal if its annihilator $Y^\bot $ is the kernel of a norm-one projection $P$ on the dual space $Z^\ast $. If $Y$ is an ideal in $Z$ with respect to a projection on $Z^\ast $ whose range is norming for $Z$, then $Y$ is said to be a strict ideal. We study uniqueness of norm-preserving extensions of functionals on the space $\mathcal{K}(X,Y) $ of compact operators between Banach spaces $X$ and $Y$ to the larger space $\mathcal{K}(X,Z) $ under the assumption that $Y$ is a strict ideal in $Z$. Our main results are: (1) if $y^\ast $ is an extreme point of $B_{Y^{\ast} }$ having a unique norm-preserving extension to $Z$, and $x^{\ast\ast} \in B_{X^{\ast\ast} }$, then the only norm-preserving extension of the functional $x^{\ast\ast} \otimes y^\ast \in \mathcal {K}(X,Y)^\ast $ to $\mathcal {K}(X,Z)$ is $x^{\ast\ast} \otimes z^\ast $ where $z^\ast \in Z^\ast $ is the only norm-preserving extension of $y^\ast $ to $Z$; (2) if $\mathcal{K}(X,Y) $ is an ideal in $\mathcal{K}(X,Z) $ and $Y$ has Phelps' property $U$ in its bidual $Y^{\ast\ast} $ (i.e., every bounded linear functional on $Y$ admits a unique norm-preserving extension to $Y^{\ast\ast} $), then $\mathcal{K}(X,Y) $ has property $U$ in $\mathcal{K}(X,Z) $ whenever $X^{\ast\ast} $ has the Radon-Nikodým property.

Стилі APA, Harvard, Vancouver, ISO та ін.

15

Polat, Faruk. "Approximate Riesz Algebra-Valued Derivations." Abstract and Applied Analysis 2012 (2012): 1–5. http://dx.doi.org/10.1155/2012/240258.

Повний текст джерела

Анотація:

Let be a Riesz algebra with an extended norm such that is complete. Also, let be another extended norm in weaker than such that whenever (a) and in , then ; (b) and in , then . Let and be two nonnegative real numbers. Assume that a map satisfies and for all . In this paper, we prove that there exists a unique derivation such that , (). Moreover, for all .

Стилі APA, Harvard, Vancouver, ISO та ін.

16

Nisya, Chairun, and Dwi Ardhanariswari Sundrijo. "Indigenisation of Global Norms: Norm Localization Analysis on LGBTQ+ Acceptance in Surabaya, Indonesia." SALASIKA: Indonesian Journal of Gender, Women, Child, and Social Inclusion's Studies 5, no. 1 (November 20, 2022): 33–49. http://dx.doi.org/10.36625/sj.v5i1.90.

Повний текст джерела

Анотація:

In the era of globalisation, norms can easily travel and transfer worldwide; they can also be adapted into certain local norms. Indonesian public acceptance of global norms is heavily affected by religious norms, which are deeply conservative. The acceptance of the LGBTQ+ community by the Indonesian public has been its hard case for that reason. However, in Surabaya, one of the biggest cities in Indonesia, religious norms have been utilised by GayA Nusantara (GN), a local NGO advocating for the acceptance of the LGBTQ+, as an effective tool to reconstruct public perception towards the LGBTQ+ community. This research explains how the GN approach helped the Surabayan accept the LGBTQ+ community. This research highlights the importance of the history of local culture and local wisdom that proves that Indonesian society – to certain degrees – has long been relatively accepting of gender diversity as part of their day-to-day life. However, when it comes to accepting LGBTQ+ as part of global norms, Indonesian still seems reluctant to be open to it. Within this unique context, this research aims to explain the localisation process of the global norms on LGBTQ+ as part of the advocacy strategy conducted by GN. Applying the interpretative research method allows the researcher to interpret the result based on the data without letting the theory and/or indicators shape the research outcome.

Стилі APA, Harvard, Vancouver, ISO та ін.

17

Bojeldain, Abdussalam A. "the Existence of A Unique Solution for Nonlinear Ordinary Differential Equations of Order m." Al-Mukhtar Journal of Sciences 30, no. 1 (June 30, 2015): 10–17. http://dx.doi.org/10.54172/mjsc.v30i1.44.

Повний текст джерела

Анотація:

In this work I state and prove a theorem for local existence of a unique solution for the Nonlinear Ordinary Differential Equations (NODE): (1) of order m; where m is a positive integer; having the initial conditions: , (2) Since the (NODE) (1) with the initial conditions (2) is equivalent to the Integral Equation: (3) We denote the right hand side (r.h.s.) of (3) by the nonlinear operator; then prove that this operator is contractive in a metric space E subset of the Banach space B of the class of continuous bounded functions defined by: (4) and B is equipped with the weighted norm: (5) which is known as Bielescki's type norm. , are finite real numbers, where is the Lipschitz coefficient of the r.h.s. of (1) in B1(a subset of the Banach space B given by (4)) defined by: (6) Where for ,and are finite real numbers.

Стилі APA, Harvard, Vancouver, ISO та ін.

18

Escassut, Alain. "The Ultrametric Corona Problem and spherically complete fields." Proceedings of the Edinburgh Mathematical Society 53, no. 2 (April 30, 2010): 353–71. http://dx.doi.org/10.1017/s0013091508000837.

Повний текст джерела

Анотація:

AbstractLet K be a complete ultrametric algebraically closed field and let A be the Banach K-algebra of bounded analytic functions in the ‘open’ unit disc D of K provided with the Gauss norm. Let Mult(A,‖ · ‖) be the set of continuous multiplicative semi-norms of A provided with the topology of simple convergence, let Multm(A, ‖ · ‖) be the subset of the φ ∈ Mult(A, ‖ · ‖) whose kernel is a maximal ideal and let Multa(A, ‖ · ‖) be the subset of the φ ∈ Mult(A, ‖ · ‖) whose kernel is a maximal ideal of the form (x − a)A with a ∈ D. We complete the characterization of continuous multiplicative norms of A by proving that the Gauss norm defined on polynomials has a unique continuation to A as a norm: the Gauss norm again. But we find prime closed ideals that are neither maximal nor null. The Corona Problem on A lies in two questions: is Multa(A, ‖ · ‖) dense in Multm(A, ‖ · ‖)? Is it dense in Multm(A, ‖ · ‖)? In a previous paper, Mainetti and Escassut showed that if each maximal ideal of A is the kernel of a unique φ ∈ Mult(m(A, ‖ · ‖), then the answer to the first question is affirmative. In particular, the authors showed that when K is strongly valued each maximal ideal of A is the kernel of a unique φ ∈ Mult(m(A, ‖ · ‖). Here we prove that this uniqueness also holds when K is spherically complete, and therefore so does the density of Multa(A, ‖ · ‖) in Multm(A, ‖ · ‖).

Стилі APA, Harvard, Vancouver, ISO та ін.

19

Eisenstein, Marie A., and April K. Clark. "Explaining Differing Democratic Norm Commitment: Rethinking the Religion-Psychological Security-Democratic Norm Support Connection." Politics and Religion 10, no. 04 (May 8, 2017): 753–85. http://dx.doi.org/10.1017/s175504831700030x.

Повний текст джерела

Анотація:

AbstractThe psychological security index is an important predictor of democratic norm support. However, insufficient attention has been paid to the separate but independent contributions of dogmatism, self-esteem, and trust, the three components typically combined to create that index. Thus, we do not know the unique influence of these components on democratic norm commitment. We also do not know the exact nature of the influence of the multiple dimensions of religion (belief, belonging, behavior) on the separate psychological security components. Using structural equation modeling and two national surveys, we examine the religion-psychological security-democratic norm support relationship. Our findings do not fully support a negative association between religion and democratic values. In fact, no matter the influence of religious belief, belonging, or behavior on psychological security, the mediating link of psychological security to democratic norm support is what is most important. Indeed, any differences that manifest as a consequence of the various dimensions of religion disappear in the religion-psychological security-democratic norm support linkage. As such, anti-democratic values are a product of one's psychological attributes and are almost entirely unrelated to one's religion. Further, our findings challenge the theoretical underpinnings of the psychological security index, as we find little evidence that the separate components used to construct the composite measure, particularly trust, are an appropriate proxy for authoritarianism.

Стилі APA, Harvard, Vancouver, ISO та ін.

20

GAO, WEIDONG, ALFRED GEROLDINGER, and QINGHONG WANG. "A QUANTITATIVE ASPECT OF NON-UNIQUE FACTORIZATIONS: THE NARKIEWICZ CONSTANTS." International Journal of Number Theory 07, no. 06 (September 2011): 1463–502. http://dx.doi.org/10.1142/s1793042111004721.

Повний текст джерела

Анотація:

Let K be an algebraic number field with non-trivial class group G and let [Formula: see text] be its ring of integers. For k ∈ ℕ and some real x ≥ 1, let Fk (x) denote the number of non-zero principal ideals [Formula: see text] with norm bounded by x such that a has at most k distinct factorizations into irreducible elements. It is well known that Fk (x) behaves, for x → ∞, asymptotically like x( log x)-1+1/|G|( log log x) N k(G). We study N k (G) with new methods from Combinatorial Number Theory.

Стилі APA, Harvard, Vancouver, ISO та ін.

21

Kocak, Huseyin, Atalay Caglar, and Gulin Zeynep Oztas. "Euclidean Best–Worst Method and Its Application." International Journal of Information Technology & Decision Making 17, no. 05 (September 2018): 1587–605. http://dx.doi.org/10.1142/s0219622018500323.

Повний текст джерела

Анотація:

In this study, we propose Euclidean best–worst method (Euclidean BWM), which does not require any other extra calculations and analysis compared to nonlinear Chebyshev BWM. Using numerical examples, we illustrate and discuss the efficiency of the Euclidean BWM based on minimizing Euclidean norm instead of Chebyshev norm and using the consistency index matrix. Obtained results show that Euclidean BWM is an efficient tool resulting in reliable unique solutions, regardless of the number of the criteria, comparing with the linear and nonlinear model of the Chebyshev BWM. Moreover, we develop a MAPLE package “BWM” using only pairwise comparison vectors as the arguments to obtain the unique solution of a given problem by both the Euclidean BWM and linear model of Chebyshev BWM.

Стилі APA, Harvard, Vancouver, ISO та ін.

22

Slabospitsky, A. "Recurrent algorithm for non-stationary parameter estimation by least squares method with least deviations from ‘attraction’ points for bilinear discrete dynamic systems." Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics, no. 3 (2018): 71–74. http://dx.doi.org/10.17721/1812-5409.2018/3.10.

Повний текст джерела

Анотація:

The estimation problem of slowly time-varying parameter matrices is considered for bilinear discrete dynamic system in the presence of disturbances. The least squares estimate with variable forgetting factor is investigated for this object in non-classical situation when this estimate may be not unique and additionally ‘attraction’ points for unknown parameter matrices are given at any moment. The set of all above-mentioned estimates of these unknown matrices is defined through the Moore-Penrose pseudo-inverse operator. The least squares estimate with variable forgetting factor and least deviation norm from given ‘attraction’ point at any moment is proposed as unique estimate on this set of all estimates. The explicit form of representation is obtained for this unique estimate of the parameter matrices by the least squares method with variable forgetting factor and least deviation norm from given ‘attraction’ points under non-classical assumptions. The recurrent algorithm for this estimate is also derived which does not require the usage of the matrix pseudo-inverse operator.

Стилі APA, Harvard, Vancouver, ISO та ін.

23

RESCORLA, MICHAEL. "A DUTCH BOOK THEOREM AND CONVERSE DUTCH BOOK THEOREM FOR KOLMOGOROV CONDITIONALIZATION." Review of Symbolic Logic 11, no. 4 (May 28, 2018): 705–35. http://dx.doi.org/10.1017/s1755020317000296.

Повний текст джерела

Анотація:

AbstractThis article discusses how to update one’s credences based on evidence that has initial probability 0. I advance a diachronic norm, Kolmogorov Conditionalization, that governs credal reallocation in many such learning scenarios. The norm is based upon Kolmogorov’s theory of conditional probability. I prove a Dutch book theorem and converse Dutch book theorem for Kolmogorov Conditionalization. The two theorems establish Kolmogorov Conditionalization as the unique credal reallocation rule that avoids a sure loss in the relevant learning scenarios.

Стилі APA, Harvard, Vancouver, ISO та ін.

24

McLean, W., and D. Elliott. "On the p-norm of the truncated Hilbert transform." Bulletin of the Australian Mathematical Society 38, no. 3 (December 1988): 413–20. http://dx.doi.org/10.1017/s0004972700027799.

Повний текст джерела

Анотація:

The p-norm of the Hilbert transform is the same as the p-norm of its truncation to any Lebesgue measurable set with strictly positive measure. This fact follows from two symmetry properties, the joint presence of which is essentially unique to the Hilbert transform. Our result applies, in particular, to the finite Hilbert transform taken over (−1, 1), and to the one-sided Hilbert transform taken over (0, ∞). A related weaker property holds for integral operators with Hardy kernels.

Стилі APA, Harvard, Vancouver, ISO та ін.

25

Li, Yuanqing, Andrzej Cichocki, and Shun-ichi Amari. "Analysis of Sparse Representation and Blind Source Separation." Neural Computation 16, no. 6 (June 1, 2004): 1193–234. http://dx.doi.org/10.1162/089976604773717586.

Повний текст джерела

Анотація:

In this letter, we analyze a two-stage cluster-then-l1-optimization approach for sparse representation of a data matrix, which is also a promising approach for blind source separation (BSS) in which fewer sensors than sources are present. First, sparse representation (factorization) of a data matrix is discussed. For a given overcomplete basis matrix, the corresponding sparse solution (coefficient matrix) with minimum l1 norm is unique with probability one, which can be obtained using a standard linear programming algorithm. The equivalence of the l1—norm solution and the l0—norm solution is also analyzed according to a probabilistic framework. If the obtained l1—norm solution is sufficiently sparse, then it is equal to the l0—norm solution with a high probability. Furthermore, the l1—norm solution is robust to noise, but the l0—norm solution is not, showing that the l1—norm is a good sparsity measure. These results can be used as a recoverability analysis of BSS, as discussed. The basis matrix in this article is estimated using a clustering algorithm followed by normalization, in which the matrix columns are the cluster centers of normalized data column vectors. Zibulevsky, Pearlmutter, Boll, and Kisilev (2000) used this kind of two-stage approach in underdetermined BSS. Our recoverability analysis shows that this approach can deal with the situation in which the sources are overlapped to some degree in the analyzed

Стилі APA, Harvard, Vancouver, ISO та ін.

26

Pawłow, Irena, and Wojciech M. Zajączkowski. "Unique solvability of a nonlinear thermoviscoelasticity system in Sobolev space with a mixed norm." Discrete & Continuous Dynamical Systems - S 4, no. 2 (2011): 441–66. http://dx.doi.org/10.3934/dcdss.2011.4.441.

Повний текст джерела

Стилі APA, Harvard, Vancouver, ISO та ін.

27

Domínguez-Vázquez, Miguel, and Olga Pérez-Barral. "Existence and uniqueness of inhomogeneous ruled hypersurfaces with shape operator of constant norm in the complex hyperbolic space." International Journal of Mathematics 32, no. 08 (May 12, 2021): 2150049. http://dx.doi.org/10.1142/s0129167x2150049x.

Повний текст джерела

Анотація:

We complete the classification of ruled real hypersurfaces with shape operator of constant norm in nonflat complex space forms by showing the existence of a unique inhomogeneous example in the complex hyperbolic space.

Стилі APA, Harvard, Vancouver, ISO та ін.

28

T, Thakshna Moorthy. "The Devotional Norm of the Siddharthas." International Research Journal of Tamil 4, SPL 2 (February 28, 2022): 247–50. http://dx.doi.org/10.34256/irjt22s239.

Повний текст джерела

Анотація:

This is the time when the Tamil community is being studied globally. The reason is that the multi-purpose talents of the Tamils who have lived in every age are astonishing to many. These skills have been documented in the literature over time. One of them is Siddharth literature. It is no exaggeration to say that the Siddhars who originated in the Tamil tradition have a unique place in India and in the world. Those who have attained the eight types of Siddhas are generally called Siddhas. The Siddhas realized the instability of the yajna and subjected their body to their enlightenment, knowing the way to live with their body without dying for a long time. Needless to say, there is no such thing as a field that the Siddhars who have lived for a long time have not studied. Atheists have the argument that atheists are supernaturalists. Some may have defined themselves as atheists because they hate idolatry and say it in their songs. This article is designed to illustrate the point that the Siddhas are of the opinion that they should have a united mind and worship by removing the hypocrisy of paganism and how they have visualized the forms of the Lord in their songs.

Стилі APA, Harvard, Vancouver, ISO та ін.

29

Tarantino, Nicholas, Catherine Matthews, Shufang Sun, Lindsay Orchowski, Abigail Harrison, Naeemah Abrahams, Alan Berkowitz, Morayo Akande, and Caroline Kuo. "Unique and Shared Correlates of Sexual Violence Perpetration and Sexual Risk Behavior Among South African Adolescent Boys." AIDS Education and Prevention 33, no. 5 (October 2021): 424–38. http://dx.doi.org/10.1521/aeap.2021.33.5.424.

Повний текст джерела

Анотація:

Associations between sexual risk behavior (SRB) and sexual violence perpetration (SVP) contribute to the intersecting HIV and sexual violence epidemics in South Africa. We examined SVP and SRB, and their potential correlates among South African boys (N = 80; ages 15–17). Fifty-one percent endorsed SVP in the past year; 61% engaged in past-3-month SRB. Whereas most unique correlates were socio-structural, family, or community factors, correlates shared across behaviors were behavior-specific social norm perceptions and cognitive factors. In final multivariate models, food insecurity and positive attitudes toward delaying sex were associated with SVP (odds ratios [ORs] = 3.05 and 0.37, respectively), and community violence exposure, gender equitable social norm perceptions, positive attitudes toward delaying sex, and intentions to obtain sexual consent were associated with SRBs (ORs = 1.56–1.57, 0.90–0.38, 0.58–0.60, respectively). Interventions to address HIV/sexual violence risk among adolescents in South Africa should be integrated and multilevel.

Стилі APA, Harvard, Vancouver, ISO та ін.

30

Heydari, Mohammad Taghi. "Numerical Range on Weighted Hardy Spaces as Semi Inner Product Spaces." Analele Universitatii "Ovidius" Constanta - Seria Matematica 25, no. 1 (January 26, 2017): 87–98. http://dx.doi.org/10.1515/auom-2017-0008.

Повний текст джерела

Анотація:

AbstractThe semi-inner product, in the sense of Lumer, on weighted Hardy space which generate the norm is unique. Also we will discuss some properties of the numerical range of bounded linear operators on weighted Hardy spaces.

Стилі APA, Harvard, Vancouver, ISO та ін.

31

Childs, A. M., and R. Kothari. "Limitations on the simulation of non-sparse Hamiltonians." Quantum Information and Computation 10, no. 7&8 (July 2010): 669–84. http://dx.doi.org/10.26421/qic10.7-8-7.

Повний текст джерела

Анотація:

The problem of simulating sparse Hamiltonians on quantum computers is well studied. The evolution of a sparse $N \times N$ Hamiltonian $H$ for time $t$ can be simulated using $\O(\norm{Ht} \poly(\log N))$ operations, which is essentially optimal due to a no--fast-forwarding theorem. Here, we consider non-sparse Hamiltonians and show significant limitations on their simulation. We generalize the no--fast-forwarding theorem to dense Hamiltonians, ruling out generic simulations taking time $\o(\norm{Ht})$, even though $\norm{H}$ is not a unique measure of the size of a dense Hamiltonian $H$. We also present a stronger limitation ruling out the possibility of generic simulations taking time $\poly(\norm{Ht},\log N)$, showing that known simulations based on discrete-time quantum walk cannot be dramatically improved in general. On the positive side, we show that some non-sparse Hamiltonians can be simulated efficiently, such as those with graphs of small arboricity.

Стилі APA, Harvard, Vancouver, ISO та ін.

32

Koliev, Faradj. "Shaming and democracy: Explaining inter-state shaming in international organizations." International Political Science Review 41, no. 4 (October 7, 2019): 538–53. http://dx.doi.org/10.1177/0192512119858660.

Повний текст джерела

Анотація:

Why do some states name and shame norm-violating states while other states abstain? Inter-state naming and shaming is typically viewed as a political tool to punish adversaries and reward allies. In this study, I propose a regime-type explanation for inter-state shaming in international politics. I pose two interrelated questions. First, are democracies more prone to condemn norm violations than non-democratic countries? Second, are democracies likely to shame each other in cases of norm violations? In search of answers to these questions, I use a unique dataset on inter-state shaming the International Labour Organization (ILO) for the period 1991–2011. In line with my main argument, the results suggest that democracies are more likely than non-democracies to engage in the shaming of norm violators, while providing no evidence for special relations between democracies. In addition, this study unpacks other factors influencing the inter-state shaming. The findings have implications for how we understand state interactions in international politics.

Стилі APA, Harvard, Vancouver, ISO та ін.

33

Li, Lifeng, and Qinjun Luo. "Sufficient Conditions for Triangular Norms Preserving ⊗-Convexity." Symmetry 10, no. 12 (December 7, 2018): 729. http://dx.doi.org/10.3390/sym10120729.

Повний текст джерела

Анотація:

The convexity in triangular norm (for short, ⊗−convexity) is a generalization of Zadeh’s quasiconvexity. The aggregation of two ⊗−convex sets is under the aggregation operator ⊗ is also ⊗−convex, but the aggregation operator ⊗ is not unique. To solve it in complexity, in the present paper, we give some sufficient conditions for aggregation operators preserve ⊗−convexity. In particular, when aggregation operators are triangular norms, we have that several results such as arbitrary triangular norm preserve ⊗ D − convexity and ⊗ a − convexity on bounded lattices, ⊗ M preserves ⊗ H − convexity in the real unite interval [ 0 , 1 ] .

Стилі APA, Harvard, Vancouver, ISO та ін.

34

Yu, Xin, and Liang Zhang. "The bang-bang property of time and norm optimal control problems for parabolic equations with time-varying fractional Laplacian." ESAIM: Control, Optimisation and Calculus of Variations 25 (2019): 7. http://dx.doi.org/10.1051/cocv/2017075.

Повний текст джерела

Анотація:

In this paper, we establish the bang-bang property of time and norm optimal control problems for parabolic equations governed by time-varying fractional Laplacian, evolved in a bounded domain of ℝd. We firstly get a quantitative unique continuation at one point in time for parabolic equations governed by time-varying fractional Laplacian. Then, we establish an observability inequality from measurable sets in time for solutions of the above-mentioned equations. Finally, with the aid of the observability inequality, the bang-bang property of time and norm optimal control problems can be obtained.

Стилі APA, Harvard, Vancouver, ISO та ін.

35

Merle, F., and L. A. Peletier. "Positive solutions of elliptic equations involving supercritical growth." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 118, no. 1-2 (1991): 49–62. http://dx.doi.org/10.1017/s0308210500028882.

Повний текст джерела

Анотація:

SynopsisPositive radial solutions of elliptic equation involving supercritical growth are analysed as their supremum norm tends to infinity. It is shown that they converge, uniformly away from the origin, as well as in H1, to the unique singular solution.

Стилі APA, Harvard, Vancouver, ISO та ін.

36

Martínez, Servet, Jaime San Martín, and Denis Villemonais. "Existence and Uniqueness of a Quasistationary Distribution for Markov Processes with Fast Return from Infinity." Journal of Applied Probability 51, no. 3 (September 2014): 756–68. http://dx.doi.org/10.1239/jap/1409932672.

Повний текст джерела

Анотація:

We study the long-time behaviour of a Markov process evolving in N and conditioned not to hit 0. Assuming that the process comes back quickly from ∞, we prove that the process admits a unique quasistationary distribution (in particular, the distribution of the conditioned process admits a limit when time goes to ∞). Moreover, we prove that the distribution of the process converges exponentially fast in the total variation norm to its quasistationary distribution and we provide a bound for the rate of convergence. As a first application of our result, we bring a new insight on the speed of convergence to the quasistationary distribution for birth-and-death processes: we prove that starting from any initial distribution the conditional probability converges in law to a unique distribution ρ supported in N* if and only if the process has a unique quasistationary distribution. Moreover, ρ is this unique quasistationary distribution and the convergence is shown to be exponentially fast in the total variation norm. Also, considering the lack of results on quasistationary distributions for nonirreducible processes on countable spaces, we show, as a second application of our result, the existence and uniqueness of a quasistationary distribution for a class of possibly nonirreducible processes.

Стилі APA, Harvard, Vancouver, ISO та ін.

37

David, Joseph E. "The One Who Is More Violent Prevails—Law and Violence from a Talmudic Legal Perspective." Canadian Journal of Law and Jurisprudence 19, no. 02 (July 2006): 385–406. http://dx.doi.org/10.1017/s0841820900004161.

Повний текст джерела

Анотація:

How are we to distinguish between law and violence? On what grounds is the former legitimized while the latter is condemned? This modern question sheds light on the essential concepts of law and order and their social value. My task in this paper is to trace the roots of this question in the Jewish jurisprudential tradition by focusing on a unique norm, established sometime during the 5th to the 6th century, in which violence become a legitimized norm when a case could not be determined by means of official legal procedure. This survey shows that while ancient sources legitimized this norm of extra-legal violence, medieval thinkers redefined it and neutralized it, reduced it to an economic procedure or even explicated interesting stances regarding the honor and stability of legal institutions.

Стилі APA, Harvard, Vancouver, ISO та ін.

38

Manerova, K. V. "Variation of Pronunciation Norm and Meaning in Light of Semantic-Cognitive Analysis: german Idiom <i>das A und O</i>." Nauchnyi dialog 11, no. 7 (September 30, 2022): 74–98. http://dx.doi.org/10.24224/2227-1295-2022-11-7-74-98.

Повний текст джерела

Анотація:

A unique example for the German language of the divergent development of the pronunciation norm and frame semantics in the phraseological unit das A und O and variants das Alpha und Omega / das Alpha und O / A und O. The interpretation of the pronunciation norm from the theoretical works of L. A. Verbitskaya is used. Observations on the development of semantic frames are presented on the basis of semantic-cognitive analysis and sociophonetic analysis of the pronunciation norm of a grapheme phraseological unit. The loss of religious connotation during the transition of the phrase into profane discourse in the course of discursive secularization is noted. The influence of the written norm on the oral norm is established as the reason for the emergence of the variance of the phraseological unit in diachrony. The emergence of variance of a grapheme formula in the direction of reduction of its components is studied. Mechanisms for modeling the meaning of idiom variants by means of four cognitive operations are disclosed. The study of formula norm dynamics is confirmed by examples of codification in nine German dictionaries. The relevance of the study is due to the application of corpus analysis to 14743 contextual uses of the formula das A und O in texts from the digital corpus of the German language DWDS. It is concluded that the pronunciation norm in its dynamics regulates the functioning of this phraseological unit in literary German.

Стилі APA, Harvard, Vancouver, ISO та ін.

39

Wang, Hongxing, and Xiaoyan Zhang. "The core inverse and constrained matrix approximation problem." Open Mathematics 18, no. 1 (July 6, 2020): 653–61. http://dx.doi.org/10.1515/math-2020-0178.

Повний текст джерела

Анотація:

Abstract In this article, we study the constrained matrix approximation problem in the Frobenius norm by using the core inverse: ||Mx-b|{|}_{F}=\hspace{.25em}\min \hspace{1em}\text{subject}\hspace{.25em}\text{to}\hspace{1em}x\in {\mathcal R} (M), where M\in {{\mathbb{C}}}_{n}^{\text{CM}} . We get the unique solution to the problem, provide two Cramer’s rules for the unique solution and establish two new expressions for the core inverse.

Стилі APA, Harvard, Vancouver, ISO та ін.

40

Ramm, Alexander G. "Estimates of Solutions to Nonlinear Evolution Equations." JOURNAL OF ADVANCES IN MATHEMATICS 14, no. 2 (July 3, 2018): 7812–17. http://dx.doi.org/10.24297/jam.v14i2.7445.

Повний текст джерела

Анотація:

Consider the equation u’(t) = A (t, u (t)), u(0)= U0 ; u' := du/dt (1). Under some assumptions on the nonlinear operator A(t,u) it is proved that problem (1) has a unique global solution and this solution satisfies the following estimate ||u (t)|| < µ (t) -1 for every t belongs to R+ = [0,infinity). Here µ(t) > 0, µ belongs to C1 (R+), is a suitable function and the norm ||u || is the norm in a Banach space X with the property ||u (t) ||’ <= ||u’ (t) ||.

Стилі APA, Harvard, Vancouver, ISO та ін.

41

ANTONIOU, IOANNIS, COSTAS KARANIKAS, and STANISLAV SHKARIN. "DECOMPOSITIONS OF SPACES OF MEASURES." Infinite Dimensional Analysis, Quantum Probability and Related Topics 11, no. 01 (March 2008): 119–26. http://dx.doi.org/10.1142/s0219025708003014.

Повний текст джерела

Анотація:

Let 𝔐 be the Banach space of σ-additive complex-valued measures on an abstract measurable space. We prove that any closed, with respect to absolute continuity norm-closed, linear subspace L of 𝔐 is complemented and describe the unique complement, projection onto L along which has norm 1. Using this fact we prove a decomposition theorem, which includes the Jordan decomposition theorem, the generalized Radon–Nikodým theorem and the decomposition of measures into decaying and non-decaying components as particular cases. We also prove an analog of the Jessen–Wintner purity theorem for our decompositions.

Стилі APA, Harvard, Vancouver, ISO та ін.

42

Martínez, Servet, Jaime San Martín, and Denis Villemonais. "Existence and Uniqueness of a Quasistationary Distribution for Markov Processes with Fast Return from Infinity." Journal of Applied Probability 51, no. 03 (September 2014): 756–68. http://dx.doi.org/10.1017/s0021900200011657.

Повний текст джерела

Анотація:

We study the long-time behaviour of a Markov process evolving inNand conditioned not to hit 0. Assuming that the process comes back quickly from ∞, we prove that the process admits a uniquequasistationary distribution(in particular, the distribution of the conditioned process admits a limit when time goes to ∞). Moreover, we prove that the distribution of the process converges exponentially fast in the total variation norm to its quasistationary distribution and we provide a bound for the rate of convergence. As a first application of our result, we bring a new insight on the speed of convergence to the quasistationary distribution for birth-and-death processes: we prove that starting from any initial distribution the conditional probability converges in law to a unique distribution ρ supported inN*if and only if the process has a unique quasistationary distribution. Moreover, ρ is this unique quasistationary distribution and the convergence is shown to be exponentially fast in the total variation norm. Also, considering the lack of results on quasistationary distributions for nonirreducible processes on countable spaces, we show, as a second application of our result, the existence and uniqueness of a quasistationary distribution for a class of possibly nonirreducible processes.

Стилі APA, Harvard, Vancouver, ISO та ін.

43

Zhou, Zhongli, and Guangxin Huang. "An Iterative Algorithm for the Reflexive Solution of the General Coupled Matrix Equations." Scientific World Journal 2013 (2013): 1–15. http://dx.doi.org/10.1155/2013/952974.

Повний текст джерела

Анотація:

The general coupled matrix equations (including the generalized coupled Sylvester matrix equations as special cases) have numerous applications in control and system theory. In this paper, an iterative algorithm is constructed to solve the general coupled matrix equations over reflexive matrix solution. When the general coupled matrix equations are consistent over reflexive matrices, the reflexive solution can be determined automatically by the iterative algorithm within finite iterative steps in the absence of round-off errors. The least Frobenius norm reflexive solution of the general coupled matrix equations can be derived when an appropriate initial matrix is chosen. Furthermore, the unique optimal approximation reflexive solution to a given matrix group in Frobenius norm can be derived by finding the least-norm reflexive solution of the corresponding general coupled matrix equations. A numerical example is given to illustrate the effectiveness of the proposed iterative algorithm.

Стилі APA, Harvard, Vancouver, ISO та ін.

44

Alvarez-Pardo, Edgardo, and Carlos Lizama. "The Maximal Subspace for Generation of(a,k)-Regularized Families." Abstract and Applied Analysis 2012 (2012): 1–14. http://dx.doi.org/10.1155/2012/683021.

Повний текст джерела

Анотація:

LetAbe a linear operator in a Banach spaceX. We define a subspace ofXand a norm such that the part ofAin such subspace generates an (a,k)-regularized resolvent family. This space is maximal-unique in a suitable sense and nontrivial, under certain conditions on the kernelsaandk.

Стилі APA, Harvard, Vancouver, ISO та ін.

45

Wofford, Mary Claire, Jessica Cano, J. Marc Goodrich, and Lisa Fitton. "Tell or Retell? The Role of Task and Language in Spanish–English Narrative Microstructure Performance." Language, Speech, and Hearing Services in Schools 53, no. 2 (April 11, 2022): 511–31. http://dx.doi.org/10.1044/2021_lshss-21-00055.

Повний текст джерела

Анотація:

Purpose: This study examined performance of dual language learners (DLLs) on Spanish- and English-language narrative story retells and unique tells. Transcription and analysis focused on comparisons of common microstructural language sample measures in Spanish and English across tasks. Each language sample measure was evaluated for its possible convergence with norm-referenced standardized assessments for DLL children. Method: Spanish–English DLLs ( N = 133) enrolled in English-only kindergarten or first-grade classrooms completed two-language sample tasks (one in each language), which were transcribed and analyzed using Systematic Analysis of Language Transcripts (Miller & Iglesias, 2017) for measures of syntactic complexity (mean length of utterance [MLU] in words), lexical diversity (number of different words [NDW]), and grammaticality (percent grammatical utterances [PGU]). Students also completed a norm-referenced sentence repetition task (Peña et al., 2014) and expressive vocabulary assessment (Martin, 2013). Results: Comparison of story retells and unique stories revealed similar performance on MLU, NDW, and PGU across elicitation techniques, with one exception: NDW in Spanish was higher in the story retell condition. Predictive models revealed several differences in the relations between the microstructure measures and norm-referenced language measures by elicitation technique, although neither context demonstrated a consistent advantage across all metrics. Conclusions: Measures derived from story retells and unique tells offer practical findings for speech-language pathologists and other educators to use in assessment of early grade DLLs. This work increases knowledge of procedural differences across narrative assessments and their influence on language variables, supporting school-based speech-language pathologists in making assessment decisions for DLLs on their caseload. Supplemental Material: https://doi.org/10.23641/asha.19191278

Стилі APA, Harvard, Vancouver, ISO та ін.

46

Tallberg, Jonas, Magnus Lundgren, Thomas Sommerer, and Theresa Squatrito. "Why International Organizations Commit to Liberal Norms." International Studies Quarterly 64, no. 3 (July 13, 2020): 626–40. http://dx.doi.org/10.1093/isq/sqaa046.

Повний текст джерела

Анотація:

Abstract Recent decades have witnessed the emergence and spread of a broad range of liberal norms in global governance, among them sustainable development, gender equality, and human security. While existing scholarship tells us a lot about the trajectories of particular norms, we know much less about the broader patterns and sources of commitments to liberal norms by international organizations (IOs). This article offers the first comparative large-N analysis of such commitments, building on a unique dataset on IO policy decisions over the time period 1980–2015. Distinguishing between deep norm commitment and shallow norm recognition, the analysis produces several novel findings. We establish that IOs’ deeper commitments to liberal norms primarily are driven by internal conditions: democratic memberships and institutional designs more conducive to norm entrepreneurship. In contrast, legitimacy standards in the external environment of IOs, often invoked in existing research, mainly account for shallower recognition or “talk” of norms.

Стилі APA, Harvard, Vancouver, ISO та ін.

47

Brunnée, Jutta, and Stephen Toope. "The Responsibility to Protect and the Use of Force: Building Legality?" Global Responsibility to Protect 2, no. 3 (2010): 191–212. http://dx.doi.org/10.1163/187598410x500354.

Повний текст джерела

Анотація:

AbstractThe rapid rise of the responsibility to protect provides us with a unique opportunity to consider the impact of a decade or so of determined norm entrepreneurship. The responsibility to protect has not yet become a binding norm of international law, and in this article we examine what factors are holding back or promoting this development. We draw on an 'interactional' account of international law, which focuses on three inter-locking elements. First, legal norms are social norms and as such they are connected to social practice – they must be grounded in shared understandings. Second, what distinguishes law from other types of social ordering is not so much form or pedigree, as adherence to specific criteria of legality. When norm creation meets these criteria and, third, is matched with norm application that also satisfies the legality requirements, international law will have legitimacy and generate a sense of commitment among those to whom it is addressed. After highlighting key steps in the norm building process so far, from the 2001 report of the International Commission on Intervention and State Sovereignty to the General Assembly debate in 2009, we offer a brief sketch of our theoretical framework, and employ it to examine the trajectory of the responsibility to protect norm, concluding with an assessment of its current and potential status as binding law. Although the responsibility to protect, including its potential for the collectively authorized use of force, is increasingly supported by globally shared understandings, the norm falls short on several of the legality criteria. Furthermore, given the inconsistent practice on protective use of force, no practice of legality can be said to have evolved. Proponents of the norm face a lot of hard work ahead.

Стилі APA, Harvard, Vancouver, ISO та ін.

48

Mecheri, Salah. "AN EXTENSION OF PENROSE’S INEQUALITY ON GENERALIZED INVERSES TO THE SCHATTEN p-CLASSES." Annals of the Alexandru Ioan Cuza University - Mathematics 60, no. 1 (January 1, 2014): 77–84. http://dx.doi.org/10.2478/v10157-012-0036-5.

Повний текст джерела

Анотація:

Abstract Let B(H) be the algebra of all bounded linear operators on a complex separable infinite dimensional Hilbert space H. In this paper we minimize the Schatten Cp-norm of suitable affine mappings from B(H) to Cp, using convex and differential analysis (Gâteaux derivative) as well as input from operator theory. The mappings considered generalize Penrose’s inequality which asserts that if A+ and B+ denote the Moore-Penrose inverses of the matrices A and B, respectively, then ||AXB − C||2 ≥ ||AA+CB+B − C||2, with A+CB+ being the unique minimizer of minimal ||:||2 norm. The main results obtained characterize the best Cp-approximant of the operator AXB.

Стилі APA, Harvard, Vancouver, ISO та ін.

49

Livadiotis, George. "General Fitting Methods Based on Lq Norms and their Optimization." Stats 3, no. 1 (January 6, 2020): 16–31. http://dx.doi.org/10.3390/stats3010002.

Повний текст джерела

Анотація:

The widely used fitting method of least squares is neither unique nor does it provide the most accurate results. Other fitting methods exist which differ on the metric norm can be used for expressing the total deviations between the given data and the fitted statistical model. The least square method is based on the Euclidean norm L2, while the alternative least absolute deviations method is based on the Taxicab norm, L1. In general, there is an infinite number of fitting methods based on metric spaces induced by Lq norms. The most accurate, and thus optimal method, is the one with the (i) highest sensitivity, given by the curvature at the minimum of total deviations, (ii) the smallest errors of the fitting parameters, (iii) best goodness of fitting. The first two cases concern fitting methods where the given curve functions or datasets do not have any errors, while the third case deals with fitting methods where the given data are assigned with errors.

Стилі APA, Harvard, Vancouver, ISO та ін.

50

Courtney, Dennis, and Donald Sarason. "A mini-max problem for self-adjoint Toeplitz matrices." MATHEMATICA SCANDINAVICA 110, no. 1 (March 1, 2012): 82. http://dx.doi.org/10.7146/math.scand.a-15198.

Повний текст джерела

Анотація:

We study a minimum problem and associated maximum problem for finite, complex, self-adjoint Toeplitz matrices. If $A$ is such a matrix, of size $(N+1)$-by-$(N+1)$, we identify $A$ with the operator it represents on ${\mathcal P}_N$, the space of complex polynomials of degrees at most $N$, with the usual Hilbert space structure it inherits as a subspace of $L^2$ of the unit circle. The operator $A$ is the compression to ${\mathcal P}_N$ of the multiplication operator on $L^2$ induced by any function in $L^{\infty}$ whose Fourier coefficients of indices between $-N$ and $N$ match the matrix entries of $A$. Our minimum problem is to minimize the $L^{\infty}$ norm of such inducers. We show there is a unique one of minimum norm, and we describe it. The associated maximum problem asks for the maximum of the ratio of the preceding minimum to the operator norm. That problem remains largely open. We present some suggestive numerical evidence.

Стилі APA, Harvard, Vancouver, ISO та ін.

Статті в журналах з теми "Unique norm"

Оформте джерело за APA, MLA, Chicago, Harvard та іншими стилями