Papers by Nguyên Hoàng thảo
Photocatalytic Disinfection of E. coli Using Silver-Doped TiO2 Coated on Cylindrical Cordierite Honeycomb Monolith Photoreactor Under Artificial Sunlight Irradiation
Topics in Catalysis
This study analyzes the border disputes of Cambodia, Laos, and Vietnam, respectively. Both settle... more This study analyzes the border disputes of Cambodia, Laos, and Vietnam, respectively. Both settled and unsettled disputes are encompassed. The study outlines the settlements reached and the remaining unsettled disputes. Furthermore, the broader trends in managing the border disputes are analyzed and remaining challenges, both in implementing agreements and in managing the unsettled disputes, are addressed. So are the implications for regional conflict management. The study displays that both Laos and Vietnam have made considerable progress in both managing and settling their existing border disputes, whereas Cambodia has thus far been less successful.
New dimension for the phase retrieval problem
Imaging and Applied Optics Congress, 2020
We consider the extension of the traditional projection-based phase retrieval algorithms by incre... more We consider the extension of the traditional projection-based phase retrieval algorithms by increasing the problem dimensionality and introducing novel projection operators. The approach is demonstrated on an example of phase retrieval for the high-NA case.
ArXiv, 2021
We propose and study the single-frame anisoplanatic deconvolution problem associated with image c... more We propose and study the single-frame anisoplanatic deconvolution problem associated with image classification using machine learning algorithms, named the nonuniform defocus removal (NDR) problem. Mathematical analysis of the NDR problem is done and the so-called defocus removal (DR) algorithm for solving it is proposed. Global convergence of the DR algorithm is established without imposing any unverifiable assumption. Numerical results on simulation data show significant features of DR including solvability, noise robustness, convergence, model insensitivity and computational efficiency. Physical relevance of the NDR problem and practicability of the DR algorithm are tested on experimental data. Back to the application that originally motivated the investigation of the NDR problem, we show that the DR algorithm can improve the accuracy of classifying distorted images using convolutional neural networks. The key difference of this paper compared to most existing works on single-fra...
Advances in Computational Mathematics, 2021
We present the convergence analysis of convex combination of the alternating projection and Dougl... more We present the convergence analysis of convex combination of the alternating projection and Douglas–Rachford operators for solving the phase retrieval problem. New convergence criteria for iterations generated by the algorithm are established by applying various schemes of numerical analysis and exploring both physical and mathematical characteristics of the phase retrieval problem. Numerical results demonstrate the advantages of the algorithm over the other widely known projection methods in practically relevant simulations.
SIAM Journal on Mathematics of Data Science, 2020
In this paper, we propose and investigate the phase retrieval problem with the a priori constrain... more In this paper, we propose and investigate the phase retrieval problem with the a priori constraint that the phase is sparse (SPR), which encompasses a number of practical applications, for instance, in characterizing phase-only objects such as microlenses, in phase-contrast microscopy, in optical path difference microscopy, and in Fourier ptychography, where the phase object occupies a small portion of the whole field. The considered problem is strictly more general than the sparse signal recovery problem, which assumes the sparsity of the signal because the sparsity of the signal trivially implies the sparsity of the phase, but the converse is not true. As a result, existing solution algorithms in the literature of sparse signal recovery cannot be applied to SPR and there is an appeal for developing new solution methods for it. In this paper, we propose a new regularization scheme which efficiently captures the sparsity constraint of SPR. The idea behind the proposed approach is to perform a metric projection of the current estimated signal onto the set of all the signals whose phase satisfies the sparsity constraint. The main challenge here is that the latter set is not convex and its associated projector in general does not admit a closed form. One novelty of our analysis is to establish an explicit form of that projector when restricted to those points which are relevant to the solutions of SPR. Note that this result is fundamentally different from the widely known calculation form for projections onto intensity constraint sets. Based on this new result, we propose an efficient solution method, named the sparsity regularization on phase (SROP) algorithm, for the SPR problem in the challenging setting where only one point-spread-function image is given, and we analyze its convergence. The algorithm is the combination of the Gerchberg-Saxton (GS) algorithm with the projection step described above. In view of the GS algorithm being equivalent to the alternating projection for an associated two-set feasibility, the SROP algorithm is shown to be the cyclic projection for an associated three-set feasibility, one of the sets being analyzed in this paper for the first time. Analyzing regularity properties of the involved sets, we obtain convergence results for the SROP algorithm based on our recent convergence theory for the cyclic projection method. Numerical results show clear effectiveness and efficiency of the proposed solution approach for the SPR problem.
South China Sea
Asia-Pacific Journal of Ocean Law and Policy, 2021
Malaysia’s partial submission to the United Nations Commission on the Limits of the Continental S... more Malaysia’s partial submission to the United Nations Commission on the Limits of the Continental Shelf on its extended continental shelf beyond 200 nm limit made in December 2019 sparked a new legal battle of diplomatic notes on the South China Sea (scs) from claimant States (Brunei, China, Malaysia, the Philippines and Viet Nam) and non-claimant States (Australia, Germany, France, Japan, Indonesia, New Zealand, the United Kingdom and the United States). It has greater volume and significance compared to the first exchange of notes in 2009 – 2011. This article examines the impact of diplomatic notes among claimants on the prospect for the peaceful settlement of the maritime disputes in the scs.
Asian Yearbook of International Law, Volume 8 (1998-1999), 2003
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Set-Valued and Variational Analysis, 2020
Motivated by a number of questions concerning transversality-type properties of pairs of sets rec... more Motivated by a number of questions concerning transversality-type properties of pairs of sets recently raised by Ioffe and Kruger, this paper reports several new characterizations of the intrinsic transversality property in Hilbert spaces. New results in terms of normal vectors clarify the picture of intrinsic transversality, its variants and sufficient conditions for subtransversality, and unify several of them. For the first time, intrinsic transversality is characterized by an equivalent condition which does not involve normal vectors. This characterization offers another perspective on intrinsic transversality. As a consequence, the obtained results allow us to answer a number of important questions about transversality-type properties.
Journal of the Optical Society of America A, 2019
We present an efficient phase retrieval approach for imaging systems with high numerical aperture... more We present an efficient phase retrieval approach for imaging systems with high numerical aperture based on the vectorial model of the point spread function. The algorithm is in the class of alternating minimization methods and can be adjusted for applications with either known or unknown amplitude of the field in the pupil. The algorithm outperforms existing solutions for high-numerical-aperture phase retrieval: (1) the generalization of the method of Hanser et al., based on extension of the scalar diffraction theory by representing the out-of-focus diversity applied to the image by a spherical cap, and (2) the method of Braat et al., which assumes through the use of extended Nijboer–Zernike expansion the phase to be smooth. The former is limited in terms of accuracy due to model deviations, while the latter is of high computational complexity and excludes phase retrieval problems where the phase is discontinuous or sparse. Extensive numerical results demonstrate the efficiency, rob...
VNU Journal of Science: Legal Studies, 2019
In the twenty-first century, before the revolution of science and technology 4.0 and 5.0, environ... more In the twenty-first century, before the revolution of science and technology 4.0 and 5.0, environmental protection and sustainable development are increasingly becoming a great concern of humanity as well as of each country. Among the components of the environment, the marine environment plays an important role with 71% of the Earth's surface covered with water and 90% of the biosphere is the ocean. Along with the development of the sea direction of mankind - the cradle of Earth's life - the sea is also facing serious challenges of pollution, over-fishing of marine resources. Marine environmental protection is not limited to a single country. Due to the uniformity of the marine environment, the spread of transboundary agents in the marine environment and climate change, this task requires cooperation between countries. Regional international treaties serve as a basis for cooperation in marine environmental protection. The paper will focus on analyzing and assessing regional ...
Vietnam Journal of Mathematics, 2018
We investigate the role of error bounds, or metric subregularity, in the convergence of Picard it... more We investigate the role of error bounds, or metric subregularity, in the convergence of Picard iterations of nonexpansive maps in Hilbert spaces. Our main results show, on one hand, that the existence of an error bound is sufficient for strong convergence and, on the other hand, that an error bound exists on bounded sets for nonexpansive mappings possessing a fixed point whenever the space is finite dimensional. In a Hilbert space setting, we show that a monotonicity property of the distances of the Picard iterations is all that is needed to guarantee the existence of an error bound. The same monotonicity assumption turns out also to guarantee that the distance of Picard iterates to the fixed point set converges to zero. Our results provide a quantitative characterization of strong convergence as well as new criteria for when strong, as opposed to just weak, convergence holds.
Mathematical Programming, 2018
We present necessary conditions for monotonicity, in one form or another, of fixed point iteratio... more We present necessary conditions for monotonicity, in one form or another, of fixed point iterations of mappings that violate the usual nonexpansive property. We show that most reasonable notions of linear-type monotonicity of fixed point sequences imply metric subregularity. This is specialized to the alternating projections iteration where the metric subregularity property takes on a distinct geometric characterization of sets at points of intersection called subtransversality. Our more general results for fixed point iterations are specialized to establish the necessity of subtransversality for consistent feasibility with a number of reasonable types of sequential monotonicity, under varying degrees of assumptions on the regularity of the sets.
Mathematics of Operations Research, 2018
We develop a framework for quantitative convergence analysis of Picard iterations of expansive se... more We develop a framework for quantitative convergence analysis of Picard iterations of expansive set-valued fixed point mappings. There are two key components of the analysis. The first is a natural generalization of single-valued averaged mappings to expansive set-valued mappings that characterizes a type of strong calmness of the fixed point mapping. The second component to this analysis is an extension of the well-established notion of metric subregularity—or inverse calmness—of the mapping at fixed points. Convergence of expansive fixed point iterations is proved using these two properties, and quantitative estimates are a natural by-product of the framework. To demonstrate the application of the theory, we prove, for the first time, a number of results showing local linear convergence of nonconvex cyclic projections for inconsistent (and consistent) feasibility problems, local linear convergence of the forward-backward algorithm for structured optimization without convexity, stro...
Bulletin of the Australian Mathematical Society, 2016
Mathematical Programming, 2016
We synthesize and unify notions of regularity, both of individual sets and of collections of sets... more We synthesize and unify notions of regularity, both of individual sets and of collections of sets, as they appear in the convergence theory of projection methods for consistent feasibility problems. Several new characterizations of regularities are presented which shed light on the relations between seemingly different ideas and point to possible necessary conditions for local linear convergence of fundamental algorithms.
Set-Valued and Variational Analysis, 2017
We provide dual sufficient conditions for subtransversality of collections of sets in an Asplund ... more We provide dual sufficient conditions for subtransversality of collections of sets in an Asplund space setting. For the convex case, we formulate a necessary and sufficient dual criterion of subtransversality in general Banach spaces. Our more general results suggest an intermediate notion of subtransversality, what we call weak intrinsic subtransversality, which lies between intrinsic transversality and subtransversality in Asplund spaces.
Nuclear Physics B, 2017
The lepton flavor violating decay of the Standard Model-like Higgs boson (LFVHD), h → µτ , is dis... more The lepton flavor violating decay of the Standard Model-like Higgs boson (LFVHD), h → µτ , is discussed in seesaw models at the one-loop level. Based on particular analytic expressions of Passarino-Veltman functions, the two unitary and 't Hooft Feynman gauges are used to compute the branching ratio of LFVHD and compare with results reported recently. In the minimal seesaw (MSS) model, the branching ratio was investigated in the whole valid range 10 −9 −10 15 GeV of new neutrino mass scale m n 6. Using the Casas-Ibarra parameterization, this branching ratio enhances with large and increasing m n 6. But the maximal value can reach only order of 10 −11. Interesting relations of LFVHD predicted by the MSS and inverse seesaw (ISS) model are discussed. The ratio between two LFVHD branching ratios predicted by the ISS and MSS is simply m 2 n 6 µ −2 X , where µ X is the small neutrino mass scale in the ISS. The consistence between different calculations is shown precisely from analytical approach.
SIAM Journal on Optimization, 2015
A general nonlinear regularity model for a set-valued mapping F : X × R + ⇒ Y , where X and Y are... more A general nonlinear regularity model for a set-valued mapping F : X × R + ⇒ Y , where X and Y are metric spaces, is studied using special iteration procedures, going back to Banach, Schauder, Lyusternik and Graves. Namely, we revise the induction theorem from Khanh, J. Math. Anal. Appl., 118 (1986) and employ it to obtain basic estimates for exploring regularity/openness properties. We also show that it can serve as a substitution of the Ekeland variational principle when establishing other regularity criteria. Then, we apply the induction theorem and the mentioned estimates to establish criteria for both global and local versions of regularity/openness properties for our model and demonstrate how the definitions and criteria translate into the conventional setting of a set-valued mapping F : X ⇒ Y. An application to second-order necessary optimality conditions for a nonsmooth set-valued optimization problem with mixed constraints is provided.
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Papers by Nguyên Hoàng thảo