Статті в журналах: "Quasi-Kernel"

1

Wang, Dongdong, and Pengjie Chen. "Quasi-convex reproducing kernel meshfree method." Computational Mechanics 54, no. 3 (April 19, 2014): 689–709. http://dx.doi.org/10.1007/s00466-014-1022-4.

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2

Yreux, Edouard, and Jiun-Shyan Chen. "A quasi-linear reproducing kernel particle method." International Journal for Numerical Methods in Engineering 109, no. 7 (July 14, 2016): 1045–64. http://dx.doi.org/10.1002/nme.5319.

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3

Ai, Jiangdong, Stefanie Gerke, Gregory Gutin, Anders Yeo, and Yacong Zhou. "Results on the small quasi-kernel conjecture." Discrete Mathematics 346, no. 7 (July 2023): 113435. http://dx.doi.org/10.1016/j.disc.2023.113435.

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4

Wegkamp, Marten H. "Quasi-universal bandwidth selection for kernel density estimators." Canadian Journal of Statistics 27, no. 2 (June 1999): 409–20. http://dx.doi.org/10.2307/3315649.

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5

Qinghui, Hu, Wei Shiwei, Li Zhiyuan, and Liu Xiaogang. "Quasi-newton method for L multiple kernel learning." Neurocomputing 194 (June 2016): 218–26. http://dx.doi.org/10.1016/j.neucom.2016.01.079.

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6

Wang, Jiecheng, Yantong Liu, and Jincai Chang. "An Improved Model for Kernel Density Estimation Based on Quadtree and Quasi-Interpolation." Mathematics 10, no. 14 (July 8, 2022): 2402. http://dx.doi.org/10.3390/math10142402.

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There are three main problems for classical kernel density estimation in its application: boundary problem, over-smoothing problem of high (low)-density region and low-efficiency problem of large samples. A new improved model of multivariate adaptive binned quasi-interpolation density estimation based on a quadtree algorithm and quasi-interpolation is proposed, which can avoid the deficiency in the classical kernel density estimation model and improve the precision of the model. The model is constructed in three steps. Firstly, the binned threshold is set from the three dimensions of sample number, width of bins and kurtosis, and the bounded domain is adaptively partitioned into several non-intersecting bins (intervals) by using the iteration idea from the quadtree algorithm. Then, based on the good properties of the quasi-interpolation, the kernel functions of the density estimation model are constructed by introducing the theory of quasi-interpolation. Finally, the binned coefficients of the density estimation model are constructed by using the idea of frequency replacing probability. Simulation of the Monte Carlo method shows that the proposed non-parametric model can effectively solve the three shortcomings of the classical kernel density estimation model and significantly improve the prediction accuracy and calculation efficiency of the density function for large samples.

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7

Mazzoni, Thomas, and Elmar Reucher. "Quasi-continuous maximum entropy distribution approximation with kernel density." International Journal of Information and Decision Sciences 3, no. 4 (2011): 335. http://dx.doi.org/10.1504/ijids.2011.043026.

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8

Winnewisser, Manfred, Brenda P. Winnewisser, Ivan R. Medvedev, Frank C. De Lucia, Stephen C. Ross, and Larry M. Bates. "The hidden kernel of molecular quasi-linearity: Quantum monodromy." Journal of Molecular Structure 798, no. 1-3 (October 2006): 1–26. http://dx.doi.org/10.1016/j.molstruc.2006.06.036.

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9

Yam, Wun Kwan, Kin Long Fong, Juntao Wang, Siew Ann Cheong, and K. Y. Michael Wong. "Intrinsic Quasi-Periodicity in Hong Kong Housing Price and Its Prediction." New Mathematics and Natural Computation 16, no. 03 (November 2020): 645–55. http://dx.doi.org/10.1142/s1793005720500398.

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Housing price time series is worth studying as it is closely related to the well-being of society. In the Hong Kong housing market from 1992 to 2010, signs of quasi-periodicity in housing price and transaction volume can be observed. We find that there is an overall periodicity of approximately 30 months in housing price changes and a strong lead–lag relationship between housing price and transaction volume. Analysis of the cross-covariance of the housing price, transaction volume and prime lending rate reveals that this quasi-periodicity is potentially driven by prime lending rates. Incorporation of quasi-periodicity into the kernel of Gaussian processes further enables us to construct a predictive model of the Hong Kong housing price trends that outperforms other traditional kernel functions.

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10

Matsutani, Shigeki. "On Time Development of a Quasi-Quantum Particle in Quartic Potential (x2-a2)2/2g." Reviews in Mathematical Physics 09, no. 08 (November 1997): 943–91. http://dx.doi.org/10.1142/s0129055x97000336.

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In this article, I have precisely considered the time development of a quantum particle (of excited states) in the quartic potential (x2-a2)2/2g by means of the semiclassical path integral method. Using the elliptic functions, I have evaluated the tunneling phenomena and the quasi-quantum fluctuation around the quasi-classical paths. I found that the quasi-quantum fluctuation is expressed by the Lamé equation and was exactly solved. Then I have shown that the obtained kernel function is in agreement with exact solutions of the linear potential and the quadratic potential under certain limits as no time-development kernel function of the quartic potential has ever been found which contains the exact solution of the linear and the quadratic potential. It is natural because the classical motion in the quartic potential becomes those of the linear and the quadratic potential under the limits. Thus the obtained time-development kernel function also consists of the energy representation of the Green function of the quartic potential in the semiclassical path integral method given by Carlitz and Nicole (Ann. Phys.164 (1985) 411), which agrees with that of the WKB method in the operator formalism.

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11

Volkmer, Hans. "Addition Formula and Related Integral Equations for Heine—Stieltjes Polynomials." Symmetry 11, no. 10 (October 2, 2019): 1231. http://dx.doi.org/10.3390/sym11101231.

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It is shown that symmetric products of Heine–Stieltjes quasi-polynomials satisfy an addition formula. The formula follows from the relationship between Heine–Stieltjes quasi-polynomials and spaces of generalized spherical harmonics, and from the known explicit form of the reproducing kernel of these spaces. In special cases, the addition formula is written out explicitly and verified. As an application, integral equations for Heine–Stieltjes quasi-polynomials are found.

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12

Tsionas, Efthymios G. "Bayesian inference in time series models using kernel quasi likelihoods." Statistica Neerlandica 56, no. 3 (August 2002): 285–94. http://dx.doi.org/10.1111/1467-9574.04800.

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13

Olshanski, Grigori. "The quasi-invariance property for the Gamma kernel determinantal measure." Advances in Mathematics 226, no. 3 (February 2011): 2305–50. http://dx.doi.org/10.1016/j.aim.2010.09.015.

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14

Collier, Nathan, and Daniel Craig Simkins. "The quasi-uniformity condition for reproducing kernel element method meshes." Computational Mechanics 44, no. 3 (March 3, 2009): 333–42. http://dx.doi.org/10.1007/s00466-009-0379-2.

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15

Alves, A. C. B., R. P. Marinho, G. A. A. Brigatto, and L. P. Garces. "Multilayer Stratification Earth by Kernel Function and Quasi-Newton Method." IEEE Latin America Transactions 14, no. 1 (January 2016): 225–34. http://dx.doi.org/10.1109/tla.2016.7430083.

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16

Moret, I., and P. Novati. "Interpolating functions of matrices on zeros of quasi-kernel polynomials." Numerical Linear Algebra with Applications 12, no. 4 (2005): 337–53. http://dx.doi.org/10.1002/nla.393.

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17

Huban, Birgül, Mehmet Gürdal, and Havva Tilki. "Some classical inequalities and their applications." Filomat 35, no. 7 (2021): 2165–73. http://dx.doi.org/10.2298/fil2107165h.

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In this paper, we define analogies of classical H?lder-McCarthy and Young type inequalities in terms of the Berezin symbols of operators on a reproducing kernel Hilbert space H = H (?). These inequalities are applied in proving of some new inequalities for the Berezin number of operators. We also define quasi-paranormal and absolute-k-quasi paranormal operators and study their properties by using the Berezin symbols.

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18

Freund, Roland W. "Quasi-kernel polynomials and their use in non-Hermitian matrix iterations." Journal of Computational and Applied Mathematics 43, no. 1-2 (November 1992): 135–58. http://dx.doi.org/10.1016/0377-0427(92)90263-w.

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19

Schlinkman, Ryan T., Jonghyuk Baek, Frank N. Beckwith, Stacy M. Nelson, and J. S. Chen. "A quasi-conforming embedded reproducing kernel particle method for heterogeneous materials." Computer Methods in Applied Mechanics and Engineering 416 (November 2023): 116363. http://dx.doi.org/10.1016/j.cma.2023.116363.

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20

Li, Ruijuan, Yanqin Cao, and Xinhong Zhang. "On kernels by rainbow paths in arc-coloured digraphs." Open Mathematics 19, no. 1 (January 1, 2021): 268–83. http://dx.doi.org/10.1515/math-2021-0019.

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Abstract In 2018, Bai, Fujita and Zhang [Discrete Math. 341 (2018), no. 6, 1523–1533] introduced the concept of a kernel by rainbow paths (for short, RP-kernel) of an arc-coloured digraph D D , which is a subset S S of vertices of D D such that ( a a ) there exists no rainbow path for any pair of distinct vertices of S S , and ( b b ) every vertex outside S S can reach S S by a rainbow path in D D . They showed that it is NP-hard to recognize whether an arc-coloured digraph has an RP-kernel and it is NP-complete to decide whether an arc-coloured tournament has an RP-kernel. In this paper, we give the sufficient conditions for the existence of an RP-kernel in arc-coloured unicyclic digraphs, semicomplete digraphs, quasi-transitive digraphs and bipartite tournaments, and prove that these arc-coloured digraphs have RP-kernels if certain “short” cycles and certain “small” induced subdigraphs are rainbow.

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21

Ling, Leevan, and Qi Ye. "On meshfree numerical differentiation." Analysis and Applications 16, no. 05 (August 30, 2018): 717–39. http://dx.doi.org/10.1142/s021953051850001x.

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We combine techniques in meshfree methods and Gaussian process regressions to construct kernel-based estimators for numerical derivatives from noisy data. Specially, we construct meshfree estimators from normal random variables, which are defined by kernel-based probability measures induced from symmetric positive definite kernels, to reconstruct the unknown partial derivatives from scattered noisy data. Our developed theories give rise to Tikhonov regularization methods with a priori parameter, but the shape parameters of the kernels remain tunable. For that, we propose an error measure that is computable without the exact values of the derivative. This allows users to obtain a quasi-optimal kernel-based estimator by comparing the approximation quality of kernel-based estimators. Numerical examples in two dimensions and three dimensions are included to demonstrate the convergence behavior and effectiveness of the proposed numerical differentiation scheme.

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22

Rovenski, Vladimir, Sergey Stepanov, and Irina Tsyganok. "The Bourguignon Laplacian and Harmonic Symmetric Bilinear Forms." Mathematics 8, no. 1 (January 3, 2020): 83. http://dx.doi.org/10.3390/math8010083.

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In this paper, we study the kernel and spectral properties of the Bourguignon Laplacian on a closed Riemannian manifold, which acts on the space of symmetric bilinear forms (considered as one-forms with values in the cotangent bundle of this manifold). We prove that the kernel of this Laplacian is an infinite-dimensional vector space of harmonic symmetric bilinear forms, in particular, such forms on a closed manifold with quasi-negative sectional curvature are zero. We apply these results to the description of surface geometry.

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23

Zhu, Hui, Jing Niu, Ruimin Zhang, and Yingzhen Lin. "A New Approach for Solving Nonlinear Singular Boundary Value Problems." Mathematical Modelling and Analysis 23, no. 1 (February 12, 2018): 33–43. http://dx.doi.org/10.3846/mma.2018.003.

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In this paper, an efficient method based on Quasi-Newton's method and the simpliffied reproducing kernel method is proposed for solving nonlinear singular boundary value problems. For the Quasi-Newton's method the convergence order is studied. The uniform convergence of the numerical solution as well as its derivatives are also proved. Numerical examples are given to demonstrate the efficiency and stability of the proposed method. The numerical results are compared with exact solutions and the outcomes of other existing numerical methods.

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24

Bachir, Ahmed, and Abdelkader Segres. "Asymmetric Putnam-Fuglede Theorem for (n,k)-Quasi-∗-Paranormal Operators." Symmetry 11, no. 1 (January 8, 2019): 64. http://dx.doi.org/10.3390/sym11010064.

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T ∈ B ( H ) is said to be ( n , k ) -quasi-∗-paranormal operator if, for non-negative integers k and n, ∥ T ∗ ( T k x ) ∥ ( 1 + n ) ≤ ∥ T ( 1 + n ) ( T k x ) ∥ ∥ T k x ∥ n ; for all x ∈ H . In this paper, the asymmetric Putnam-Fuglede theorem for the pair ( A , B ) of power-bounded operators is proved when (i) A and B ∗ are n-∗-paranormal operators (ii) A is a ( n , k ) -quasi-∗-paranormal operator with reduced kernel and B ∗ is n-∗-paranormal operator. The class of ( n , k ) -quasi-∗-paranormal operators properly contains the classes of n-∗-paranormal operators, ( 1 , k ) -quasi-∗-paranormal operators and k-quasi-∗-class A operators. As a consequence, it is showed that if T is a completely non-normal ( n , k ) -quasi-∗-paranormal operator for k = 0 , 1 such that the defect operator D T is Hilbert-Schmidt class, then T ∈ C 10 .

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25

Jeong, Byeongseon, Scott N. Kersey, and Jungho Yoon. "Approximation of Multivariate Functions on Sparse Grids By Kernel-Based Quasi-Interpolation." SIAM Journal on Scientific Computing 43, no. 2 (January 2021): A953—A979. http://dx.doi.org/10.1137/20m1318055.

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26

Di, Qianli. "Quasi-Monte Carlo Approximations for Exponentiated Quadratic Kernel in Latent Force Models." Open Journal of Modelling and Simulation 10, no. 04 (2022): 349–90. http://dx.doi.org/10.4236/ojmsi.2022.104021.

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27

LI, Weite, Bo ZHOU, Benhui CHEN, and Jinglu HU. "A Deep Neural Network Based Quasi-Linear Kernel for Support Vector Machines." IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E99.A, no. 12 (2016): 2558–65. http://dx.doi.org/10.1587/transfun.e99.a.2558.

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28

CHEN, LI. "QUASI RIESZ TRANSFORMS, HARDY SPACES AND GENERALISED SUB-GAUSSIAN HEAT KERNEL ESTIMATES." Bulletin of the Australian Mathematical Society 92, no. 3 (August 10, 2015): 508–10. http://dx.doi.org/10.1017/s0004972715000714.

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29

Fan, Jianqing, Nancy E. Heckman, and M. P. Wand. "Local Polynomial Kernel Regression for Generalized Linear Models and Quasi-Likelihood Functions." Journal of the American Statistical Association 90, no. 429 (March 1995): 141–50. http://dx.doi.org/10.1080/01621459.1995.10476496.

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30

Jinyuan, Du. "Quadrature Formulas of Quasi-Interpolation Type for Singular Integrals with Hilbert Kernel." Journal of Approximation Theory 93, no. 2 (May 1998): 231–57. http://dx.doi.org/10.1006/jath.1998.3166.

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31

Drnovšek, Roman, Nika Novak, and Vladimir Müller. "An operator is a product of two quasi-nilpotent operators if and only if it is not semi-Fredholm." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 136, no. 5 (October 2006): 935–44. http://dx.doi.org/10.1017/s0308210500004819.

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Анотація:

We prove that a (bounded, linear) operator acting on an infinite-dimensional, separable, complex Hilbert space can be written as a product of two quasi-nilpotent operators if and only if it is not a semi-Fredholm operator. This solves the problem posed by Fong and Sourour in 1984. We also consider some closely related questions. In particular, we show that an operator can be expressed as a product of two nilpotent operators if and only if its kernel and co-kernel are both infinite dimensional. This answers the question implicitly posed by Wu in 1989.

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32

Jiang, Qinhui, and Changguo Shao. "Finite groups with three conjugacy class sizes of certain elements." Publications de l'Institut Math?matique (Belgrade) 98, no. 112 (2015): 265–70. http://dx.doi.org/10.2298/pim140905006j.

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Let G be a finite group. Let m and n be two positive coprime integers. We prove that the set of conjugacy class sizes of primary and biprimary elements of G is {1,m,n} if and only if G is quasi-Frobenius with abelian kernel and complement.

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33

Daoudi, Hamza, Zouaoui Chikr Elmezouar, and Fatimah Alshahrani. "Asymptotic Results of Some Conditional Nonparametric Functional Parameters in High-Dimensional Associated Data." Mathematics 11, no. 20 (October 14, 2023): 4290. http://dx.doi.org/10.3390/math11204290.

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In this paper, we propose to study the asymptotic properties of some conditional functional parameters, such as the distribution function, the density, and the hazard function, for an explanatory variable with values in a Hilbert space (infinite dimension) and a response variable real in a quasi-associated dependency framework. We consider the non parametric estimation of the conditional distribution function by the kernel method in the presence of the quasi-associated dependence, and we establish under general hypotheses the almost complete convergence with speed of the estimator built in the associated case. The estimation of the conditional hazard function will be conducted by utilizing the two outcomes of the conditional distribution function and the conditional density. We establish the asymptotic normality of the kernel estimator as the conditional risk function of a properly normalized functional. We explicitly give the asymptotic variance. Simulation studies were conducted to investigate the behavior of the asymptotic property in the context of finite sample data. All the statistical analyses were performed using R software.

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34

Marius, Arghirescu. "Analogies and differences between the particle’ model used in a Cold Genesis Theory and those used in the Standard Model." Physics & Astronomy International Journal 5, no. 2 (August 16, 2021): 60–71. http://dx.doi.org/10.15406/paij.2021.05.00235.

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The main particularities of the vortexial model of particles resulted in a cold genesis theory of the author (CGT) are compared by those corresponding to the Standard Model of particles. It is argued that the interaction mechanism by intermediary Z–boson and respective– by ‘color’ charges and gluons, considered by the Standard Model for the weak and the strong and nuclear interactions, is semi–formal, a more natural explanation for these interactions being given in CGT by a multi–vortexial model of proton– resulted in CGT as non– destructive collapsed clusters of paired quasi electrons (e*−e*+ ) and by its resulted vortexial field, which imply also a specific “bag” model of inter–quarks interaction, a “dynamide” model of neutron, with degenerate negatron rotated around the protonic center and a preonic model of quark, with quasi–crystalline kernel formed by kerneloids of –preons of 34 . A vortexial potential with repulsive kernel of ‘sombrero’ type can be proposed as general genesic potential, which can explain also the cold genesis by chiral quantum fluctuations.

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35

Li, You Sheng. "A Fast Point-Sampled Model Denoising Algorithm for Product Design." Advanced Materials Research 605-607 (December 2012): 392–96. http://dx.doi.org/10.4028/www.scientific.net/amr.605-607.392.

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Denoising is an essential step in creating perfect point-sampled models, which are widly used in the field of product Design. As the bilateral mesh deoising method by Fleishman has been extended to 3D point-sampled model, which is not efficient enough. For the reason, a method is proposed that using the quasi-Cauchy kernel to replace the Gauss kernel used in the bilateral filtering algorithm, so that the efficiency of the algorithm is improved. Experiments show that the method can eliminate the noise on the surface of the point-sampled model effectively and meanwhile the sharp features of the surface are preserved well．

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36

Zhang, Zhongqing, Chenhui Zhou, Jingmin Yang, Bingjian Yan, Jinhua Liu, Sinan Wang, Qi Li, and Mengmeng Zhou. "Preparation and Characterization of Apricot Kernel Shell Biochar and Its Adsorption Mechanism for Atrazine." Sustainability 14, no. 7 (March 30, 2022): 4082. http://dx.doi.org/10.3390/su14074082.

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In this study, the preparation of apricot kernel shell biochar by a hydrothermal method and its adsorption mechanism for atrazine was studied by scanning electron microscopy (SEM) and infrared spectrum (FTIR) analytical techniques. The results show that the biochar prepared from the apricot kernel shell has an evenly distributed, nonaggregated carbon microsphere structure and contains a large number of oxygen-containing groups. The higher the preparation temperature is, the more functional groups exist and the better the potential adsorption performance is. The adsorption kinetics of atrazine on apricot kernel shell biochar were fitted with a quasi-second-order kinetic equation (R2 ≥ 0.995, p < 0.05). The isothermal adsorption data were in accordance with the Freundlich model (R2 ≥ 0.911, p < 0.05). The adsorption of atrazine on apricot kernel shell biochar includes two processes: surface adsorption and diffusion. The adsorption capacity of apricot kernel shell biochar for atrazine increases with increasing preparation temperature and decreases with increasing pH and Ca2+ concentration. The adsorption mechanism includes hydrogen bonding and hydrophobic interactions. Therefore, biochar prepared from apricot shells, an agricultural waste, exhibits good adsorption performance for atrazine and has a good application prospect in addressing agricultural non-point source pollution, especially in pesticide residue pollution control.

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37

Móricz, F., and B. E. Rhoades. "Approximation by weighted means of Walsh-Fourier series." International Journal of Mathematics and Mathematical Sciences 19, no. 1 (1996): 1–8. http://dx.doi.org/10.1155/s0161171296000014.

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Анотація:

We study the rate of approximation to functions inLpand, in particular, inLip(α,p)by weighted means of their Walsh-Fourier series, whereα>0and1≤p≤∞. For the casep=∞,Lpis interpreted to beCW, the collection of uniformlyWcontinuous functions over the unit interval[0,1). We also note that the weighted mean kernel is quasi-positive, under fairly general conditions.

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38

Hajjej, Zayd, and Menglan Liao. "General stability for a system of coupled quasi-linear and linear wave equations and with memory term." AIMS Mathematics 8, no. 12 (2023): 30668–82. http://dx.doi.org/10.3934/math.20231567.

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Анотація:

<abstract><p>In this paper, a system of coupled quasi-linear and linear wave equations with a finite memory term is concerned. By constructing an appropriate Lyapunov function, we prove that the total energy associated with the system is stable under suitable conditions on memory kernel.</p></abstract>

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39

Vainikko, Eero, and Gennadi Vainikko. "PRODUCT QUASI-INTERPOLATION IN LOGARITHMICALLY SINGULAR INTEGRAL EQUATIONS." Mathematical Modelling and Analysis 17, no. 5 (November 1, 2012): 696–714. http://dx.doi.org/10.3846/13926292.2012.736089.

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Анотація:

A discrete high order method is constructed and justified for a class of Fredholm integral equations of the second kind with kernels that may have boundary and logarithmic diagonal singularities. The method is based on the improving the boundary behaviour of the kernel with the help of a change of variables, and on the product integration using quasi-interpolation by smooth splines of order m. Properties of different proposed calculation schemes are compared through numerical experiments using, in particular, variable precision interval arithmetics.

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40

H, Uguru, Akpokodje OI, and Ijabo OJ. "Fracture Resistance of Groundnut (cv. SAMNUT 11) Kernel under Quasi-Static Compression Loading." Scholars Journal of Engineering and Technology 08, no. 01 (January 25, 2020): 1–8. http://dx.doi.org/10.36347/sjet.2020.v08i01.001.

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41

Baudoin, Fabrice, Maria Gordina, and Tai Melcher. "Quasi-invariance for heat kernel measures on sub-Riemannian infinite-dimensional Heisenberg groups." Transactions of the American Mathematical Society 365, no. 8 (December 27, 2012): 4313–50. http://dx.doi.org/10.1090/s0002-9947-2012-05778-3.

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42

Alzghool, Raed, Yan-Xia Lin, and Song Xi Chen. "Asymptotic Quasi-Likelihood Based on Kernel Smoothing for Multivariate Heteroschedastic Models with Correlation." American Journal of Mathematical and Management Sciences 30, no. 1-2 (January 2010): 147–77. http://dx.doi.org/10.1080/01966324.2010.10737782.

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43

Chen, Yanping, and Zihua Guo. "Generalized singular integral with rough kernel and approximation of surface quasi-geostrophic equation." Journal of Differential Equations 346 (February 2023): 205–28. http://dx.doi.org/10.1016/j.jde.2022.11.035.

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44

Driver, Bruce K. "Integration by Parts and Quasi-Invariance for Heat Kernel Measures on Loop Groups." Journal of Functional Analysis 149, no. 2 (October 1997): 470–547. http://dx.doi.org/10.1006/jfan.1997.3103.

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Garibaldi, R. S. "The Rost invariant has trivial kernel for quasi-split groups of low rank." Commentarii Mathematici Helvetici 76, no. 4 (December 1, 2001): 684–711. http://dx.doi.org/10.1007/s00014-001-8325-8.

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46

Liang, Peifeng, Weite Li, Hao Tian, and Jinglu Hu. "One‐class classification using a support vector machine with a quasi‐linear kernel." IEEJ Transactions on Electrical and Electronic Engineering 14, no. 3 (October 17, 2018): 449–56. http://dx.doi.org/10.1002/tee.22826.

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47

Laouar, M., M. Brahimi, and I. E. Lakhdari. "Kernel function with BFGS quasi-newton methods for solving nonlinear semi-definite problems." Journal of Mathematics and Computer Science 33, no. 01 (November 16, 2023): 1–16. http://dx.doi.org/10.22436/jmcs.033.01.01.

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In this paper, we will improve the practical performance of an interior points algorithm for convex nonlinear semi-definite optimization, where to minimize a nonlinear convex objective function subject to nonlinear convex constraints. We will propose a new method for solving this kind of problem by using a straightforward kernel function and the iterative Newton directions combined with the Broyden-Fletcher-Goldfarb-Shanno (BFGS in short) quasi-Newton method. Further, a best polynomial complexity for solving nonlinear convex problems will be found until now.

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Cho, Minsung, Seth Hoisington, Roger Nichols, and Brian Udall. "The Krein-von Neumann extension of a regular even order quasi-differential operator." Opuscula Mathematica 41, no. 6 (2021): 805–41. http://dx.doi.org/10.7494/opmath.2021.41.6.805.

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We characterize by boundary conditions the Krein-von Neumann extension of a strictly positive minimal operator corresponding to a regular even order quasi-differential expression of Shin-Zettl type. The characterization is stated in terms of a specially chosen basis for the kernel of the maximal operator and employs a description of the Friedrichs extension due to Möller and Zettl.

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49

SHIRAISHI, HIROSHI, and MASANOBU TANIGUCHI. "STATISTICAL ESTIMATION OF OPTIMAL PORTFOLIOS FOR LOCALLY STATIONARY RETURNS OF ASSETS." International Journal of Theoretical and Applied Finance 10, no. 01 (February 2007): 129–54. http://dx.doi.org/10.1142/s0219024907004093.

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This paper discusses the asymptotic property of estimators for optimal portfolios when the returns are vector-valued locally stationary processes. First, we derive the asymptotic distribution of a nonparametric portfolio estimator based on the kernel method. Optimal bandwidth and kernel function are given by minimizing the mean squares error of it. Next, assuming parametric models for non-Gaussian locally stationary processes, we prove the LAN theorem, and propose a parametric portfolio estimator ĝ based on a quasi-maximum likelihood estimator. Then it is shown that ĝ is asymptotically efficient based on the LAN. Numerical studies are provided to investigate the accuracy of the portfolio estimators parametrically and nonparametrically. They illuminate some interesting features of them.

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Baek, Jonghyuk, Jiun-Shyan Chen, Guohua Zhou, Kevin P. Arnett, Michael C. Hillman, Gilbert Hegemier, and Scott Hardesty. "A semi-Lagrangian reproducing kernel particle method with particle-based shock algorithm for explosive welding simulation." Computational Mechanics 67, no. 6 (April 27, 2021): 1601–27. http://dx.doi.org/10.1007/s00466-021-02008-2.

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AbstractThe explosive welding process is an extreme-deformation problem that involves shock waves, large plastic deformation, and fragmentation around the collision point, which are extremely challenging features to model for the traditional mesh-based methods. In this work, a particle-based Godunov shock algorithm under a semi-Lagrangian reproducing kernel particle method (SL-RKPM) is introduced into the volumetric strain energy to accurately embed the key shock physics in the absence of a mesh or grid, which is shown to also ensure the conservation of linear momentum. For kernel stability, a deformation-dependent anisotropic kernel support update algorithm is proposed, which is shown to capture excessive plastic flow and material separation. A quasi-conforming nodal integration is adopted to avoid the need of updating conforming cells which is tedious in extreme deformations. It is shown that the proposed formulation effectively captures shocks, jet formation, and smooth-to-wavy interface morphology transition with good agreement with experimental results.

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