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Journal articles on the topic 'Normality conditions'

Author: Grafiati

Published: 3 June 2025

Last updated: 13 July 2025

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1

Liu, Chia-Hsin, and D. S. Passman. "Groups with Certain Normality Conditions." Communications in Algebra 44, no. 8 (2016): 3308–23. http://dx.doi.org/10.1080/00927872.2015.1044104.

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2

MEZIANE, MOHAMMED, and ABDELKADER BENALI. "CONDITIONS IMPLYING NORMALITY AND HYPO-NORMALITY OF OPERATORS IN HILBERT SPACE." Journal of Science and Arts 20, no. 4 (2020): 947–56. http://dx.doi.org/10.46939/j.sci.arts-20.4-a15.

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The aim of this paper is to give sufficient conditions on two normal and hyponormal operators (bounded or not), defined on a Hilbert space, which make their algebraic sum hyponormal (only in bounded case). The results are accompanied by some interesting examples and counter examples.

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3

Moslehian, M. S., and S. M. S. Nabavi Sales. "Some conditions implying normality of operators." Comptes Rendus Mathematique 349, no. 5-6 (2011): 251–54. http://dx.doi.org/10.1016/j.crma.2011.01.018.

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4

Ikramov, Khakim D. "Normality conditions for the BHH matrix operator." Linear and Multilinear Algebra 63, no. 9 (2014): 1901–8. http://dx.doi.org/10.1080/03081087.2014.978254.

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5

Rosenblueth, Javier F. "Conditions for generic normality in optimal control." Systems & Control Letters 9, no. 5 (1987): 433–38. http://dx.doi.org/10.1016/0167-6911(87)90073-9.

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6

Fowler, K. E., and L. R. Sons. "Interaction between coefficient conditions and solution conditions of differential equations in the unit disk." International Journal of Mathematics and Mathematical Sciences 2006 (2006): 1–11. http://dx.doi.org/10.1155/ijmms/2006/52583.

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The influence of the normality of the coefficientA(z)of the differential equationf(k)+A(z)f=0on a solutionfand also the influence of the normality of a solutionfonA(z)are investigated in the unit disk. In particular, an estimate of P. Lappan is used to determine restrictions on the growth of a meromorphic functionA(z)when a solutionfisα-normal.

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7

Zrotowski, R. "Normality and." Journal of Symbolic Logic 56, no. 3 (1991): 1064–67. http://dx.doi.org/10.2307/2275072.

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AbstractThe main result of this paper is that if κ is not a weakly Mahlo cardinal, then the following two conditions are equivalent:1. is κ+-complete.2. is a prenormal ideal.Our result is a generalization of an announcement made in [Z]. We say that is selective iff for every -function f: κ → κ there is a set X ∈ such that f∣(κ − X) is one-to-one. Our theorem provides a positive partial answer to a question of B. Wȩglorz from [BTW, p. 90], viz.: is every selective ideal with κ+-complete, isomorphic to a normal ideal?The theorem is also true for fine ideals on [λ]<κ for any κ ≤ λ, i.e. if κ is not a weakly Mahlo cardinal then the Boolean algebra is λ+-complete iff is a prenormal ideal (in the sense of [λ/<κ).

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8

Singal, M. K., and Asha Rani Singal. "On some pairwise normality conditions in bitopological spaces." Publicationes Mathematicae Debrecen 21, no. 1-2 (2022): 71–81. http://dx.doi.org/10.5486/pmd.1974.21.1-2.11.

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9

De Falco, M., F. de Giovanni, C. Musella, and Y. P. Sysak. "Groups with normality conditions for non-abelian subgroups." Journal of Algebra 315, no. 2 (2007): 665–82. http://dx.doi.org/10.1016/j.jalgebra.2007.01.025.

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10

Maturo, Antonio. "The Shifting Borders of Medicalization: Perspectives and Dilemmas of Human Enhancement." SALUTE E SOCIETÀ, no. 2 (July 2009): 13–30. http://dx.doi.org/10.3280/ses2009-en2003.

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- While medicalization is the process of extending the medical gaze on human conditions through the mechanism of pathologization, human enhancement actions are implemented towards normal conditions. In this sense, human enhancement can not be considered either health care or health promotion because its aim is optimization, not healing nor prevention. As the borders between normality and pathology are blurred, biomedical interventions aiming at improving a normal individual today could be conceived as health care practices directed towards a sick person tomorrow. Therefore, human enhancement actions should be analyzed through the lenses of the medicalization-theory proposed by Conrad - but on a long-term scale. Under an ethical perspective, human enhancement interventions - being very heterogeneous - should be analyzed case-by-case.Keywords: medicalization, human enhancement, medicine, normality, health promotion, disease.Parole chiave: medicalizzazione, miglioramento umano, medicina, normalitÀ, promozione della salute, malattia.

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11

Maturo, Antonio. "I mutevoli confini della medicalizzazione: prospettive e dilemmi del miglioramento umano." SALUTE E SOCIETÀ, no. 2 (July 2009): 17–35. http://dx.doi.org/10.3280/ses2009-002003.

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- While medicalization is the process of extending the medical gaze on human conditions through the mechanism of pathologization, human enhancement actions are implemented towards normal conditions. In this sense, human enhancement can not be considered either health care or health promotion because its aim is optimization, not healing nor prevention. As the borders between normality and pathology are blurred, biomedical interventions aiming at improving a normal individual today could be conceived as health care practices directed towards a sick person tomorrow. Therefore, human enhancement actions should be analyzed through the lenses of the medicalization-theory proposed by Conrad - but on a long-term scale. Under an ethical perspective, human enhancement interventions - being very heterogeneous - should be analyzed case-by-case.Keywords: medicalization, human enhancement, medicine, normality, health promotion, disease.Parole chiave: medicalizzazione, miglioramento umano, medicina, normalitÀ, promozione della salute, malattia.

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12

De Falco, M., F. de Giovanni, and C. Musella. "Groups with normality conditions for subgroups of infinite rank." Publicacions Matemàtiques 58 (July 1, 2014): 331–40. http://dx.doi.org/10.5565/publmat_58214_16.

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13

Ikramov, Kh D. "Normality conditions for matrix equations of the Sylvester type." Doklady Mathematics 90, no. 3 (2014): 727–29. http://dx.doi.org/10.1134/s1064562414070230.

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14

Linke, Yu Yu, and A. I. Sakhanenko. "Conditions of Asymptotic Normality of One-Step M-Estimators." Journal of Mathematical Sciences 230, no. 1 (2018): 95–111. http://dx.doi.org/10.1007/s10958-018-3730-3.

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15

Amiri, Aboubacar. "Asymptotic normality of recursive estimators under strong mixing conditions." Statistical Inference for Stochastic Processes 16, no. 2 (2013): 81–96. http://dx.doi.org/10.1007/s11203-013-9078-x.

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16

WANG, XIAOLING, and WANG ZHOU. "Uniformly bounded components of normality." Mathematical Proceedings of the Cambridge Philosophical Society 143, no. 1 (2007): 85–101. http://dx.doi.org/10.1017/s0305004107000060.

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AbstractSuppose that f(z) is a transcendental entire function and that the Fatou set F(f)≠∅. Set and where the supremum supU is taken over all components of F(f). If B1(f)<∞ or B2(f)<∞, then we say F(f) is strongly uniformly bounded or uniformly bounded respectively. We show that, under some conditions, F(f) is (strongly) uniformly bounded.

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17

Ikramov, Kh D. "Normality conditions for semilinear matrix operators of the Stein type." Numerical Analysis and Applications 8, no. 4 (2015): 299–303. http://dx.doi.org/10.1134/s1995423915040035.

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18

Ikramov, Kh D. "Normality conditions for linear matrix operators of the Stein type." Doklady Mathematics 91, no. 1 (2015): 50–52. http://dx.doi.org/10.1134/s1064562415010159.

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19

Mason, David M., and Galen R. Shorack. "Necessary and Sufficient Conditions for Asymptotic Normality of $L$-Statistics." Annals of Probability 20, no. 4 (1992): 1779–804. http://dx.doi.org/10.1214/aop/1176989529.

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20

Sahaidak, Mykhailo, and Yaroslav Biletskyi. "Business ecosystem management in the conditions new normality and transcendence." Scientific notes, no. 36 (November 6, 2024): 226–41. http://dx.doi.org/10.33111/vz_kneu.36.24.03.20.138.144.

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The article examines the essence of the concept, examines the elements and their inherent features of the business ecosystem, substantiates the approaches to effective management in the conditions of new normality and transcendence. The signs of a business ecosystem presented in the article are at first glance inherent in the characteristics of any enterprise, institution or organization, however, we note that ecosystems or turquoise organizations represent the next stage of consciousness development, where traditional concepts and methods are questioned and the organization is considered as a living organism, not a mechanical system. In the context of the transcendental development of business ecosystems, environmental turbulence and growing uncertainty lead to a decrease in the effectiveness of traditional management tools, at the same time, these characteristics can become a catalyst for new opportunities and non-standard management solutions that can significantly strengthen their position in the market and affect corporate synergistic effects, contribute to the formation of new connections and ideas, which will subsequently lead to the introduction of innovations and the development of business ecosystems. Transcendence in the context of management is considered as a concept that covers aspects that go beyond the established boundaries of existing experience, understanding or perception, standard models, conditions and approaches in managing business ecosystems. Management of the business ecosystem in the conditions of new normality and transcendence requires the use of integrated approaches and strategies that can go beyond traditional tools, methods and models. Envisioning the transcendence of management means changing the way you think and understanding that standard models and methods may become ineffective or insufficient in the new normal. Business ecosystems whose leaders are focused on transcendental development in the conditions of the new normality have the greatest chances for business viability, recovery and success. In this context, the article examines transcendental leadership, which refers to the concept of leadership that goes beyond traditional models and focuses on a deeper understanding and approach to managing people, organizations, and change.

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21

Bai, Kuang, Jane J. Ye, and Jin Zhang. "Directional Quasi-/Pseudo-Normality as Sufficient Conditions for Metric Subregularity." SIAM Journal on Optimization 29, no. 4 (2019): 2625–49. http://dx.doi.org/10.1137/18m1232498.

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22

Boldin, A. Yu, A. A. Bronnikov, V. V. Dmitrieva, and R. A. Sharipov. "Conditions of complete normality for dynamical systems on Riemannian manifolds." Theoretical and Mathematical Physics 103, no. 2 (1995): 550–55. http://dx.doi.org/10.1007/bf02274032.

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23

Pavlova, Natal'ya. "2-regularity and 2-normality conditions for systems with impulsive controls." Yugoslav Journal of Operations Research 17, no. 2 (2007): 149–64. http://dx.doi.org/10.2298/yjor0702149p.

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In this paper a controlled system with impulsive controls in the neighborhood of an abnormal point is investigated. The set of pairs (u,?) is considered as a class of admissible controls, where u is a measurable essentially bounded function and ? is a finite-dimensional Borel measure, such that for any Borel set B, ?(B) is a subset of the given convex closed pointed cone. In this article the concepts of 2-regularity and 2-normality for the abstract mapping ?, operating from the given Banach space into a finite-dimensional space, are introduced. The concepts of 2-regularity and 2-normality play a great role in the course of derivation of the first and the second order necessary conditions for the optimal control problem, consisting of the minimization of a certain functional on the set of the admissible processes. These concepts are also important for obtaining the sufficient conditions for the local controllability of the nonlinear systems. The convenient criterion for 2-regularity along the prescribed direction and necessary conditions for 2-normality of systems, linear in control, are introduced in this article as well.

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24

Griffin, Philip S., and David M. Mason. "On the asymptotic normality of self-normalized sums." Mathematical Proceedings of the Cambridge Philosophical Society 109, no. 3 (1991): 597–610. http://dx.doi.org/10.1017/s0305004100070018.

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AbstractLet X1, …, Xn be a sequence of non-degenerate, symmetric, independent identically distributed random variables, and let Sn(rn) denote their sum when the rn largest in modulus have been removed. We obtain necessary and sufficient conditions for asymptotic normality of the studentized version of Sn(rn), and compare this to the condition for asymptotic normality of the scalar normalized version. In particular, when rn = r these conditions are the same, but when rn → ∞the former holds more generally.

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25

Dyavanal, R. S., and S. B. Kalakoti. "Normality and uniqueness of homogeneous differential polynomials." Matematychni Studii 59, no. 2 (2023): 168–77. http://dx.doi.org/10.30970/ms.59.2.168-177.

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The primary goal of this work is to determine whether the results from [19, 20] still hold true when a differential polynomial is considered in place of a differential monomial. In this perspective, we continue our study to establish the uniqueness theorem for homogeneous differential polynomial of an entire and its higher order derivative sharing two polynomials using normal family theory as well as to obtain normality criteria for a family of analytic functions in a domain concerning homogeneous differential polynomial of a transcendental meromorphic function satisfying certain conditions. Meanwhile, as a result of this investigation, we proved three theorems that provide affirmative responses for the purpose of this study. Several examples are offered to demonstrate that the conditions of the theorem are necessary.

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26

Motta, Monica, Franco Rampazzo, and Richard Vinter. "Normality and gap phenomena in optimal unbounded control." ESAIM: Control, Optimisation and Calculus of Variations 24, no. 4 (2018): 1645–73. http://dx.doi.org/10.1051/cocv/2018069.

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Optimal unbounded control problems with affine control dependence may fail to have minimizers in the class of absolutely continuous state trajectories. For this reason, extended impulsive versions – which cannot be of measure-theoretic type – have been investigated, in which the domain is enlarged to include discontinuous state trajectories of bounded variation, and for which existence of minimizers is guaranteed. It is of interest to know whether the passage from the original optimal control problem to its extension introduces an infimum gap. This paper provides sufficient conditions for the absence of an infimum gap based on normality of extremals. In certain cases, the normality conditions reduce to simple verifiable criteria, which improve on earlier, directly-derived sufficient conditions for no infimum gap.

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27

Виноградова and Natalya Vinogradova. "Primary School Today: Normality and Reality." Primary Education 5, no. 2 (2017): 4–12. http://dx.doi.org/10.12737/article_58f9af2ec82f54.52754499.

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The article considers the key ideas of academic and methodological complex “Primary school of the XXI century”: priority of the development of learning activity, conditions of successful differential training, organization of educational interaction and search activity of schoolchildren on the basis of imaginary situation. The concept of “norm” is considered in respect to the sphere of education from the perspective of ensuring the objective interests of the public, compliance with the requirements of state educational standards, as well as the specifics of the didactic process, which includes objectives, content, methods and tools.

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28

Yuryev, V. M., and V. G. Babayan. "RUSSIA IN 2016: STRATEGY IN THE CONDITIONS OF «THE NEW NORMALITY»." Social - Economic Phenomena and Processes 11, no. 1 (2016): 119–25. http://dx.doi.org/10.20310/1819-8813-2016-11-1-119-125.

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29

Yigitler, Huseyin, Riku Jantti, and Neal Patwari. "On Log-Normality of RSSI in Narrowband Receivers Under Static Conditions." IEEE Signal Processing Letters 24, no. 4 (2017): 367–71. http://dx.doi.org/10.1109/lsp.2017.2657332.

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30

Marinković, Boban. "2-Regularity and 2-Normality Conditions in Discrete Optimal Control Problems." Numerical Functional Analysis and Optimization 29, no. 11-12 (2008): 1286–98. http://dx.doi.org/10.1080/01630560802580836.

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31

Mason, David M., and Galen R. Shorack. "Necessary and sufficient conditions for asymptotic normality of trimmed L-statistics." Journal of Statistical Planning and Inference 25, no. 2 (1990): 111–39. http://dx.doi.org/10.1016/0378-3758(90)90061-x.

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32

Roussas, George G., and Lanh T. Tran. "Asymptotic Normality of the Recursive Kernel Regression Estimate Under Dependence Conditions." Annals of Statistics 20, no. 1 (1992): 98–120. http://dx.doi.org/10.1214/aos/1176348514.

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33

Dudnikova, T. V. "On Mixing Conditions in Proving the Asymptotical Normality for Harmonic Crystals." Lobachevskii Journal of Mathematics 44, no. 7 (2023): 2613–29. http://dx.doi.org/10.1134/s1995080223070119.

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34

Engelmann, Danilo, Yan Zimmerli, Jan Czerwinski, and Peter Bonsack. "Real Driving Emissions in Extended Driving Conditions." Energies 14, no. 21 (2021): 7310. http://dx.doi.org/10.3390/en14217310.

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The real driving emission (RDE) testing for certification of vehicles is performed in conditions that are well defined in legislation. For emissions inventories and for research, the influences of some extended driving conditions on emissions are an interesting issue. In the present work, some examples of RDE results from two common passenger cars with gasoline and diesel propulsion are given. The varying driving conditions were “winter/summer”, “mild/aggressive”, and “higher altitude/slop”. The driving conditions: “winter”, “aggressive”, and “higher slope/altitude” generally require more energy, cause higher fuel consumption, and therefore, higher CO2-emissions. The condition of “winter driving”, especially in the urban type of operation, may cause some longer phases with not enough warmed-up exhaust aftertreatment and consequently some increased gaseous emissions. The DPF eliminates the nanoparticles (PN) independently on the driving conditions. Nevertheless, the DPF regeneration has an influence on the CO2-normality of the trip. The CO2-normality primary tolerance range can also be exceeded with aggressive driving. The elaborated results confirm the usefulness of the existing legal limits for the driving conditions of RDE homologation tests.

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35

Soro, Brahima, and Ouagnina Hili. "Asymptotic normality for kernel weighted averages estimation." Afrika Statistika 17, no. 2 (2022): 3237–57. http://dx.doi.org/10.16929/as/2022.3237.305.

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This paper presents a set of general normality results for kernel weighted averages. We extend existing results in literature for independent data a s in Yao (2017) to stationary dependent longitudinal data. The asymptotic properties of the proposed weighted averages are investigated under \(\alpha\)-mixing conditions. These results are useful for covariance function estimation based on nonparametric kernel method.

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36

Marinkovic, Boban. "First and second order necessary optimality conditions for discrete optimal control problems." Yugoslav Journal of Operations Research 16, no. 2 (2006): 153–60. http://dx.doi.org/10.2298/yjor0602153m.

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37

Masry, Elias, and Dag Tjøstheim. "Nonparametric Estimation and Identification of Nonlinear ARCH Time Series Strong Convergence and Asymptotic Normality: Strong Convergence and Asymptotic Normality." Econometric Theory 11, no. 2 (1995): 258–89. http://dx.doi.org/10.1017/s0266466600009166.

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We consider the estimation and identification of the functional structures of nonlinear econometric systems of the ARCH type. We employ nonparametric kernel estimates for the nonlinear functions characterizing the systems, and we establish strong consistency along with sharp rates of convergence under mild regularity conditions. We also prove the asymptotic normality of the estimates.

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38

Yallaoui, El-Bachir. "On normal and strongly normal lattices." International Journal of Mathematics and Mathematical Sciences 16, no. 2 (1993): 337–44. http://dx.doi.org/10.1155/s0161171293000407.

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In this paper we will investigate the properties of normality and strong normality of lattices and their relationships to zero-one measures. We will eventually establish necessary and sufficient conditions for lattices to be strongly normal. These properties are then investigated in the case of separated lattices.

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39

Correa-Ávarez, Cristian David, Jessica María Rojas-Mora, Antonio Elías Zumaqué Ballesteros, and Osnamir Elias Bru-Cordero. "Simulation Study on the Power and Sensitivity of Sixteen Normality Tests Under Different Non-Normality Scenarios." TecnoLógicas 28, no. 62 (2025): e3293. https://doi.org/10.22430/22565337.3293.

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In data analysis, validating the normality assumption is crucial for determining the suitability of applying parametric methods. The objective of this research was to compare the power and sensitivity of sixteen normality tests, classified according to various aspects. The methodology involved simulating data using the Fleishman contamination system. This approach allowed us to evaluate the tests under non-normality conditions across ten distributions with varying degrees of deviation from normality. The results obtained showed that tests based on correlation and regression, such as Shapiro-Wilk and Shapiro-Francia, outperform the others in power, especially for large samples and substantial deviations from normality. For moderate deviations, the D’Agostino-Pearson and skewness tests performed well, while for low deviations, the Robust Jarque-Bera and Jarque-Bera tests were the most effective. Additionally, some tests exhibited high power across multiple distribution types, such as Snedecor-Cochran and Chen-Ye, which performed well for both symmetric platykurtic and asymmetric leptokurtic distributions. These findings offer valuable insights for selecting appropriate normality tests based on sample characteristics, which improves the reliability of statistical inference. Finally, it is concluded that this research demonstrates scenarios in which the most commonly used statistical tests are not always the most effective.

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40

Boaz, Annette, and Myfanwy Morgan. "Working to establish ‘normality’ post-transplant: A qualitative study of kidney transplant patients." Chronic Illness 10, no. 4 (2013): 247–58. http://dx.doi.org/10.1177/1742395313504789.

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Objectives To explore patients’ perceptions and experiences of ‘normality’ and the influences on this at three time points post-transplant. Methods In-depth interviews with 25 patients at three months, one year and more than three years following kidney transplant. Patients’ accounts were compared with Sanderson et al.’s typology of types of normality. Findings Post-transplant, patients worked hard to re-establish normality, albeit in a ‘reset’ form. This normality was a very personal construct, shaped by a wide range of factors including age, gender and personal circumstances. Some patients encountered significant challenges in regaining normality, both at three months for those experiencing acute and distressing side effects, and later relating to the long-term side effects of transplant medication and co-morbidities. However, the most dramatic threat to normality (disrupted normality) came from episodes of rejection and transplant failure. Conclusions The main types of normality achieved vary for different conditions. Moreover, despite improvements in health post-transplant and opportunities to build a new, reset normality, the participants recognised the need to pay careful attention to the spectre of future ill health and transplant failure. Transplant failure was therefore a source of disruption that was central to their illness narratives and perceived as an ever present risk.

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41

Liang, Han-Ying. "Asymptotic Normality for Regression Function Estimate Under Truncation and α-Mixing Conditions". Communications in Statistics - Theory and Methods 40, № 11 (2011): 1999–2021. http://dx.doi.org/10.1080/03610921003666420.

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42

Bierens, Herman J. "CONSISTENCY AND ASYMPTOTIC NORMALITY OF SIEVE ML ESTIMATORS UNDER LOW-LEVEL CONDITIONS." Econometric Theory 30, no. 5 (2014): 1021–76. http://dx.doi.org/10.1017/s0266466614000036.

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This paper considers sieve maximum likelihood estimation of seminonparametric (SNP) models with an unknown density function as non-Euclidean parameter, next to a finite-dimensional parameter vector. The density function involved is modeled via an infinite series expansion, so that the actual parameter space is infinite-dimensional. It will be shown that under low-level conditions the sieve estimators of these parameters are consistent, and the estimators of the Euclidean parameters are$\sqrt N$asymptotically normal, given a random sample of sizeN. The latter result is derived in a different way than in the sieve estimation literature. It appears that this asymptotic normality result is in essence the same as for the finite dimensional case. This approach is motivated and illustrated by an SNP discrete choice model.

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43

Ralescu, Stefan S., and Shan Sun. "Necessary and sufficient conditions for the asymptotic normality of perturbed sample quantiles." Journal of Statistical Planning and Inference 35, no. 1 (1993): 55–64. http://dx.doi.org/10.1016/0378-3758(93)90067-g.

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44

Arutyunov, Aram, and Fernando Lobo Pereira. "Second-Order Necessary Optimality Conditions for Problems Without A Priori Normality Assumptions." Mathematics of Operations Research 31, no. 1 (2006): 1–12. http://dx.doi.org/10.1287/moor.1050.0172.

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45

Ribeiro Neto, Homero, Marciel Lelis Duarte, and Nerilson Terra Santos. "Evaluation of empirical type I error rates of F and normality tests under different variance and mean conditions in multi-treatment CRDs." Multi-Science Journal 8, no. 1 (2025): 1–9. https://doi.org/10.33837/msj.v8i1.1719.

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Hypothesis tests, such as normality tests, are extensively employed in Agricultural Sciences to evaluate the normality assumption of the F test in the Analysis of Variance (ANOVA) when large sample sizes are unavailable. Nonetheless, researchers conducting these tests are exposed to the risk of committing type I or type II errors, with probabilities that are influenced by different experimental conditions. This study assesses the empirical type I error rate of hypothesis tests by considering the equality (inequality) of treatment means, the homogeneity (heterogeneity) of variances, and different numbers of repetitions per treatment. Applying Completely Randomized Designs (CRD), sub-scenarios were simulated for each experimental scenario, with 10,000 iterations performed for each sub-scenario. Response variable values and experimental residuals were generated and subjected to appropriate tests. The results demonstrate that when the assumption of homogeneity of variances is violated, both the F and normality tests (excluding the Kolmogorov-Smirnov test) exhibit higher empirical type I error rates. Additionally, for normality tests, these error rates increase with the number of repetitions. Conversely, without such violations, the error rates remain stable and closely approximate the theoretical significance level for all analyzed hypothesis tests.

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46

PÉREZ-DÍAZ, S., J. R. SENDRA, and C. VILLARINO. "A FIRST APPROACH TOWARDS NORMAL PARAMETRIZATIONS OF ALGEBRAIC SURFACES." International Journal of Algebra and Computation 20, no. 08 (2010): 977–90. http://dx.doi.org/10.1142/s0218196710005972.

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In this paper we analyze the problem of deciding the normality (i.e. the surjectivity) of a rational parametrization of a surface [Formula: see text]. The problem can be approached by means of elimination theory techniques, providing a proper close subset [Formula: see text] where surjectivity needs to be analyzed. In general, these direct approaches are unfeasible because [Formula: see text] is very complicated and its elements computationally hard to manipulate. Motivated by this fact, we study ad hoc computational alternative methods that simplifies [Formula: see text]. For this goal, we introduce the notion of pseudo-normality, a concept that provides necessary conditions for a parametrization for being normal. Also, we provide an algorithm for deciding the pseudo-normality. Finally, we state necessary and sufficient conditions on a pseudo-normal parametrization to be normal. As a consequence, certain types of parametrizations are shown to be always normal. For instance, pseudo-normal polynomial parametrizations are normal. Moreover, for certain class of parametrizations, we derive an algorithm for deciding the normality.

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Yang, Q., R. K. Wang, and L. J. Xue. "Normality Structures With Thermodynamic Equilibrium Points." Journal of Applied Mechanics 74, no. 5 (2007): 965–71. http://dx.doi.org/10.1115/1.2722772.

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Enriched by the nonlinear Onsager reciprocal relations and thermodynamic equilibrium points (Onsager, Phys. Rev., 37, pp. 405–406; 38, pp. 2265–2279), an extended normality structure by Rice (1971, J. Mech. Phys. Solids, 19, pp. 433–455) is established in this paper as a unified nonlinear thermodynamic theory of solids. It is revealed that the normality structure stems from the microscale irrotational thermodynamic fluxes. Within the extended normality structure, this paper focuses on the microscale thermodynamic mechanisms and significance of the convexity of flow potentials and yield surfaces. It is shown that the flow potential is convex if the conjugate force increment cannot not oppose the increment of the rates of local internal variables. For the Rice fluxes, the convexity condition reduces to the local rates being monotonic increasing functions with respect to their conjugate forces. The convexity of the flow potential provides the thermodynamic system a capability against the disturbance of the thermodynamic equilibrium point. It is proposed for time-independent behavior that the set of plastically admissible stresses determined by yield conditions corresponds to the set of thermodynamic equilibrium points. Based on that viewpoint, the intrinsic dissipation inequality is just the thermodynamic counterpart of the principle of maximum plastic dissipation and requires the convexity of the yield surfaces.

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Kim, Jae-Young. "Bayesian Asymptotic Theory in a Time Series Model with a Possible Nonstationary Process." Econometric Theory 10, no. 3-4 (1994): 764–73. http://dx.doi.org/10.1017/s0266466600008768.

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Asymptotic normality of the Bayesian posterior is a well-known result for stationary dynamic models or nondynamic models. This paper extends the analysis to a time series model with a possible nonstationary process. We spell out conditions under which asymptotic normality of the posterior is obtained even if the true data-generation process is a nonstationary process.

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Avarucci, Marco, Eric Beutner, and Paolo Zaffaroni. "ON MOMENT CONDITIONS FOR QUASI-MAXIMUM LIKELIHOOD ESTIMATION OF MULTIVARIATE ARCH MODELS." Econometric Theory 29, no. 3 (2012): 545–66. http://dx.doi.org/10.1017/s0266466612000473.

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This paper questions whether it is possible to derive consistency and asymptotic normality of the Gaussian quasi-maximum likelihood estimator (QMLE) for possibly the simplest multivariate GARCH model, namely, the multivariate ARCH(1) model of the Baba, Engle, Kraft, and Kroner form, under weak moment conditions similar to the univariate case. In contrast to the univariate specification, we show that the expectation of the log-likelihood function is unbounded, away from the true parameter value, if (and only if) the observable has unbounded second moment. Despite this nonstandard feature, consistency of the Gaussian QMLE is still warranted. The same moment condition proves to be necessary and sufficient for the stationarity of the score when evaluated at the true parameter value. This explains why high moment conditions, typically bounded sixth moment and above, have been used hitherto in the literature to establish the asymptotic normality of the QMLE in the multivariate framework.

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Gouet, Raul, F. Javier López, and Gerardo Sanz. "Asymptotic normality for the number of records from general distributions." Advances in Applied Probability 43, no. 2 (2011): 422–36. http://dx.doi.org/10.1239/aap/1308662486.

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We provide necessary and sufficient conditions for the asymptotic normality of Nn, the number of records among the first n observations from a sequence of independent and identically distributed random variables, with general distribution F. In the case of normality we identify the centering and scaling sequences. Also, we characterize distributions for which the limit is not normal in terms of their discrete and continuous components.

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