Article ID Research Articles

The least gradient problem with Dirichlet and Neumann boundary conditions

Abstract In this paper, we consider the BV least gradient problem with Dirichlet condition on a part Γ ⊂ ∂ ⁡ Ω {\Gamma\subset\partial\Omega} and Neumann boundary condition on its complementary part ∂ ⁡ Ω \ Γ {\partial\Omega\backslash\Gamma} . We will show that in the plane this problem is equivalent to an optimal transport problem with import/export taxes on ∂ ⁡ Ω \ Γ {\partial\Omega\backslash\Gamma} . Thanks to this equivalence, we will be able to show existence and uniqueness of a solution to this mixed least gradient problem and we will also prove some Sobolev regularity on this solution. We note that these results generalize those in [S. Dweik, W 1 , p W^{1,p} regularity on the solution of the BV least gradient problem with Dirichlet condition on a part of the boundary, Nonlinear Anal. 223 2022, Article ID 113012], where we studied the pure Dirichlet version of this problem.

Analysis of a Combined Spherical Harmonics and Discontinuous Galerkin Discretization for the Boltzmann Transport Equation

Abstract In [L. Bourhrara, A new numerical method for solving the Boltzmann transport equation using the PN method and the discontinuous finite elements on unstructured and curved meshes, J. Comput. Phys. 397 2019, Article ID 108801], a numerical scheme based on a combined spherical harmonics and discontinuous Galerkin finite element method for the resolution of the Boltzmann transport equation is proposed. One of its features is that a streamline weight is added to the test function to obtain the variational formulation. In the present paper, restricting our attention to the advective part of the Boltzmann equation, we prove the convergence and provide error estimates of this numerical scheme. To this end, the original variational formulation is restated in a broken functional space. The use of broken functional spaces enables to build a conforming approximation, that is the finite element space is a subspace of the broken functional space. The setting of a conforming approximation simplifies the numerical analysis, in particular the error estimates, for which a Céa’s type lemma and standard interpolation estimates are sufficient for our analysis. For our numerical scheme, based on ℙ k {\mathbb{P}^{k}} discontinuous Galerkin finite elements (in space) on a mesh of size h and a spherical harmonics approximation of order N (in the angular variable), the convergence rate is of order 𝒪 ⁢ ( N - t + h k ) {\mathcal{O}(N^{-t}+h^{k})} for a smooth solution which admits partial derivatives of order k + 1 {k+1} and t with respect to the spatial and angular variables, respectively. For k = 0 {k=0} (piecewise constant finite elements) we also obtain a convergence result of order 𝒪 ⁢ ( N - t + h 1 2 ) {\mathcal{O}(N^{-t}+h^{\frac{1}{2}})} . Numerical experiments in one, two and three dimensions are provided, showing a better convergence behavior for the L 2 {L^{2}} -norm, typically of one more order, 𝒪 ⁢ ( N - t + h k + 1 ) {\mathcal{O}(N^{-t}+h^{k+1})} .

Investigation of solution behavior of Differential Equations by Sumudu methods of random complex Partial Differential Equations

In this study, solutions of random complex partial differential equations were found using the two-dimensional Sumudu transformation method(STM). The initial conditions of a deterministic equation or the non-homogeneous part of the equation are transformed into random variables to obtain a random complex partial differential equation. With the help of the properties of two-dimensional Sumudu and inverse Sumudu transformation, an approximate analytical solution of a complex partial differential equation with random constant coefficients was obtained by selecting a random variable with an initial condition of Normal and Gamma distribution. The probability characteristics of the resulting solutions, such as expected value and variance, were obtained and graphically shown with the help of the Maple package program.

YOLO V3 AND CCN FOR THE TRACKING AND CLASSIFICATION OF AERIAL OBJECT AND DRONES

The goal of this study is to give headways in aeronautical article ID that will help with making recognitions that are both more exact and more precise. Specifically, we revamp the meaning of the article recognition anchor enclose request to remember turns for expansion to level and width, and besides, we make it conceivable to have erratic four corner point structures. Furthermore, the consideration of new anchor boxes gives the model additional adaptability to address protests that are focused at a pivot of turn that gives a 45-degree point. By accomplishing these results, we can make an organization that considers negligible tradeoffs about speed and unwavering quality, while likewise giving more exact restrictions. The latest ways to deal with PC vision and article acknowledgment are for the most part dependent on brain organizations and different advances that utilize profound learning. This powerful field of study is utilized in various applications, including military and observation, aeronautical photography, independent driving, and airborne perception. To precisely locate the location of an item, contemporary object identification techniques make use of bounding boxes that are drawn over the object and have a rectangular form (horizontal and vertical). These orthogonal bounding boxes do not consider the posture of the object, which leads to a decrease in the amount of object localization and restricts subsequent tasks such as object comprehension and tracking. We have used the DOTA dataset to present all of the results, demonstrating the value of flexible object boundaries, particularly with rotated and non-rectangular objects. We have also achieved an accuracy of 98.47% for the detection and classification of aerial objects, with forty percent of the data being used for training and the remaining twenty percent being used for testing. There was a minimum of 2.8 seconds of processing time required for the whole program to be executed to categorize all of the aerial items that were parked on the base.

A doubly robust estimator for the Mann Whitney Wilcoxon rank sum test when applied for causal inference in observational studies

ABSTRACT The Mann–Whitney–Wilcoxon rank sum test (MWWRST) is a widely used method for comparing two treatment groups in randomized control trials, particularly when dealing with highly skewed data. However, when applied to observational study data, the MWWRST often yields invalid results for causal inference. To address this limitation, Wu et al. (Causal inference for Mann–Whitney–Wilcoxon rank sum and other nonparametric statistics, Stat. Med. 33 (2014), pp. 1261–1271) introduced an approach that incorporates inverse probability weighting (IPW) into this rank-based statistic to mitigate confounding effects. Subsequently, Mao (On causal estimation using U-statistics, Biometrika 105 (2018), pp. 215–220), Zhang et al. (Estimating Mann Whitney-type causal effects, J. Causal Inference 7 (2019), ARTICLE ID 20180010), and Ai et al. (A Mann–Whitney test of distributional effects in a multivalued treatment, J. Stat. Plan. Inference 209 (2020), pp. 85–100) extended this IPW estimator to develop doubly robust estimators. Nevertheless, each of these approaches has notable limitations. Mao's method imposes stringent assumptions that may not align with real-world study data. Zhang et al.'s (Estimating Mann Whitney-type causal effects, J. Causal Inference 7 (2019), ARTICLE ID 20180010) estimators rely on bootstrap inference, which suffers from computational inefficiency and lacks known asymptotic properties. Meanwhile, Ai et al. (A Mann–Whitney test of distributional effects in a multivalued treatment, J. Stat. Plan. Inference 209 (2020), pp. 85–100) primarily focus on testing the null hypothesis of equal distributions between two groups, which is a more stringent assumption that may not be well-suited to the primary practical application of MWWRST. In this paper, we aim to address these limitations by leveraging functional response models (FRM) to develop doubly robust estimators. We demonstrate the performance of our proposed approach using both simulated and real study data.

Flat flow solution to the mean curvature flow with volume constraint

Abstract In this paper I will revisit the construction of a global weak solution to the volume preserving mean curvature flow via discrete minimizing movement scheme by Mugnai, Seis and Spadaro [L. Mugnai, C. Seis and E. Spadaro, Global solutions to the volume-preserving mean-curvature flow, Calc. Var. Partial Differential Equations 55 2016, 1, Article ID 18]. This method is based on the gradient flow approach due to Almgren, Taylor and Wang [F. Almgren, J. E. Taylor and L. Wang, Curvature-driven flows: a variational approach, SIAM J. Control Optim. 31 1993, 2, 387–438] and Luckhaus and Sturzenhecker [S. Luckhaus and T. Sturzenhecker, Implicit time discretization for the mean curvature flow equation, Calc. Var. Partial Differential Equations 3 1995, 2, 253–271] and my aim is to replace the volume penalization with the volume constraint directly in the discrete scheme, which from practical point of view is perhaps more natural. A technical novelty is the proof of the density estimate which is based on second variation argument.

The high-order estimate of the entire function associated with inverse Sturm–Liouville problems

Abstract The inverse Sturm–Liouville problem with smooth potentials is considered. The high-order estimate of the entire function associated with two Sturm–Liouville problems is established. Applying this estimate expression to inverse Sturm–Liouville problems, we proved that the conclusion in [L. Amour, J. Faupin and T. Raoux, Inverse spectral results for Schrödinger operators on the unit interval with partial information given on the potentials, J. Math. Phys. 50 2009, 3, Article ID 033505] remains true for more general case.

Least energy solutions for affine p-Laplace equations involving subcritical and critical nonlinearities

Abstract The paper is concerned with Lane–Emden and Brezis–Nirenberg problems involving the affine p-Laplace nonlocal operator Δ p 𝒜 {\Delta_{p}^{\cal A}} , which has been introduced in [J. Haddad, C. H. Jiménez and M. Montenegro, From affine Poincaré inequalities to affine spectral inequalities, Adv. Math. 386 2021, Article ID 107808] driven by the affine L p {L^{p}} energy ℰ p , Ω {{\cal E}_{p,\Omega}} from convex geometry due to [E. Lutwak, D. Yang and G. Zhang, Sharp affine L p L_{p} Sobolev inequalities, J. Differential Geom. 62 2002, 1, 17–38]. We are particularly interested in the existence and nonexistence of positive C 1 {C^{1}} solutions of least energy type. Part of the main difficulties are caused by the absence of convexity of ℰ p , Ω {{\cal E}_{p,\Omega}} and by the comparison ℰ p , Ω ⁢ ( u ) ≤ ∥ u ∥ W 0 1 , p ⁢ ( Ω ) {{\cal E}_{p,\Omega}(u)\leq\|u\|_{W^{1,p}_{0}(\Omega)}} generally strict.

Comments on the paper ‘A new contribution to best proximity point theory on quasi metric spaces and an application to nonlinear integral equations’

Just recently M. Aslantas [A new contribution to best proximity point theory on quasi metric spaces and an application to nonlinear integral equations. Optimization. 2022] established a new best proximity point theorem multivalued non-self mappings which satisfy an appropriate contractive condition in the framework of quasi metric spaces. Then he applied the existing result to present an application to the solvability of a class of nonlinear integral equations. In this short note, we show that the best proximity point theorem proved in the aforesaid article is a special case of a fixed point theorem for multivalued contraction type mappings which was studied by J. Marin et al. [Q-functions on quasimetric spaces and fixed points for multivalued maps. Fixed Point Theory Appl. 2011:Article ID 603861].

Multilinear commutators of multilinear strongly singular integral operators with generalized kernels

Abstract In [S. Yang and Y. Lin, Multilinear strongly singular integral operators with generalized kernels and applications, AIMS Math. 6 2021, 12, 13533–13551], the authors of the present paper further weaken the smoothness condition of kernel functions with multilinear strongly singular Calderón–Zygmund operators of [Y. Lin, Multilinear theory of strongly singular Calderón–Zygmund operators and applications, Nonlinear Anal. 192 2020, Article ID 111699]. They defined a new class of multilinear strongly singular integral operators, and studied its weighted L p {L^{p}} boundedness, variable exponent L p ⁢ ( ⋅ ) {L^{p(\cdot)}} boundedness and endpoint estimates. In this paper, we naturally consider the boundedness of multilinear commutators and multilinear iterated commutators, which are generated by multilinear strongly singular integral operators with generalized kernels and Lipschitz functions. Our results include the corresponding results of multilinear strongly singular Calderón–Zygmund operators and classical multilinear Calderón–Zygmund operators, respectively.

Positive solutions for Kirchhoff equation in exterior domains with small Sobolev critical perturbation

ABSTRACT The paper concerns with the existence of positive solutions for the following Kirchhoff problem { − ( a + b ∫ Ω | ∇u | 2 d x ) Δu + u = | u | p − 2 u + ε | u | 4 u in Ω , u ∈ H 0 1 ( Ω ) , where a, b>0, 4<p<6, 0 $ ]]> ε > 0 is a parameter and Ω ⊂ R 3 is an exterior domain, that is, Ω is an unbounded domain with R 3 ∖Ω nonempty and bounded. After showing the nonexistence of ground state solutions, we prove the existence of one positive solution with higher energy when R 3 ∖Ω is contained in a small ball and 0 $ ]]> ε > 0 is sufficiently small. The novelty of this paper is that we extend the result obtained in Alves and de Freitas [Existence of a positive solution for a class of elliptic problems in exterior domains involving critical growth. Milan J Math. 2017;85:309–330] to nonlocal case and generalize the subcritical nonlinearity discussed in Chen and Liu [Positive solutions for Kirchhoff equation in exterior domains. J Math Phys. 2021;62:Article ID 041510] to small critical perturbation.

PubExN: An Automated PubMed Bulk Article Extractor with Affiliation Normalization Package.

Biomedical article extraction is the preliminary step for every biomedical application. These applications are helpful in finding the gene, disease, chemical, drugs, protein entities. Finding entities relation such as gene-gene entities, drug-disease interaction, and chemical protein relation the PubExN can be helpful for these types of biomedical applications. In most cases, domain experts do this extraction process on their own. Human interference makes this process time-consuming and there is a high probability, that documents can be missed during the extraction process. To get rid of these complicated processes a python package is introduced to automate the process of bulk extraction from the PubMed database. The extraction process covers all the citation information with the associated abstract. The batch approach is used to extract the bulk extraction. The motivation for the development of PubExN was to provide flexibility for the extraction process of biomedical article's text data from NCBI's PubMed database. Basically, NCBI's PubMed database article contains the article id or can say PubMed-id (PMID), the title of the article, abstract, authors information, etc. This package will benefit many biomedical texts mining research including biomedical named entity recognition, biomedical relation extraction, literature discovery, knowledgebase creation, and various biomedical Natural Language Processing (NLP) tasks. In addition, it could be used in the author name disambiguation problems and new drug discoveries. This package will help save time and extra effort for the extraction and normalization process of PubMed articles.

Reconstruction of modified transmission eigenvalues using Cauchy data

Abstract The modified transmission eigenvalue (MTE) problem was introduced in [S. Cogar, D. Colton, S. Meng and P. Monk, Modified transmission eigenvalues in inverse scattering theory, Inverse Problems 33 2017, 12, Article ID 125002] and used as a target signature for nondestructive testing. In this paper, we study the inverse spectral problem to reconstruct the modified transmission eigenvalues using Cauchy data. We propose a reciprocity gap functional method and show that the MTEs can be determined by solving some linear ill-posed integral equations. Numerical examples for both absorbing and non-absorbing media are presented to validate the effectiveness and robustness of the proposed method.

Erratum: Curvature inheritance symmetry on M-projectively flat spacetimes

International Journal of Geometric Methods in Modern PhysicsOnline Ready No AccessErratum: Curvature inheritance symmetry on M-projectively flat spacetimesis erratum ofCurvature inheritance symmetry on M-projectively flat spacetimesAbsos Ali Shaikh, Musavvir Ali, Mohammad Salman, and Füsun Özen ZenginAbsos Ali ShaikhDepartment of Mathematics, University of Burdwan, Golapbag, Burdwan, 713104 West Bengal, IndiaE-mail Address: [email protected], Musavvir AliDepartment of Mathematics, Aligarh Muslim University, Aligarh 202002, IndiaE-mail Address: [email protected], Mohammad SalmanDepartment of Mathematics, Aligarh Muslim University, Aligarh 202002, India, and Füsun Özen ZenginDepartment of Mathematics, Istanbul Technical University, Istanbul 34469, Turkeyhttps://doi.org/10.1142/S0219887823920019Cited by:0 PreviousNext AboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack CitationsRecommend to Library ShareShare onFacebookTwitterLinked InRedditEmail [Int. J. Geom. Methods Mod. Phys., Vol. 20, No. 2 (2023), Article ID: 2350088, DOI: 10.1142/S0219887823500883] Remember to check out the Most Cited Articles! Check out new Mathematical Physics books in our Mathematics 2021 catalogue Featuring authors Bang-Yen Chen, John Baez, Matilde Marcolli and more! FiguresReferencesRelatedDetailsRelated articlesCurvature inheritance symmetry on M-projectively flat spacetimes6 Feb 2023International Journal of Geometric Methods in Modern Physics Recommended Online Ready Metrics History Published: 20 April 2023 PDF download

A pipeline for medical literature search and its evaluation

One database commonly used by clinicians for searching the medical literature and practicing evidence-based medicine is PubMed. As the literature grows, it has become challenging for users to find the relevant material quickly because most of the time the relevant results are not on the top. In this article, we propose a search and ranking pipeline to improve the search results based on relevancy. We first propose an ensemble model consisting of three classifiers: bidirectional long-short-term memory conditional random field (bi-LSTM-CRF), support vector machine and naive Bayes to recognise PICO (patient, intervention, comparison, outcome) elements from abstracts. The ensemble was trained on an annotated corpus consisting of 5000 abstracts split into 4000 and 1000 training and testing data, respectively. The ensemble recorded an accuracy of 93%. We then retrieved around 927,000 articles from PubMed for the years 2017–2021 (access date 16 April 2021). For every abstract, we extracted and grouped all P, I and O terms, and stored these groups along with the article ID in a separate database. During the search, every P, I and O term of the query is searched only in its corresponding group of every abstract. The scoring method simply counts the number of matches between the query’s P, I and O elements and the words in P, I and O groups, respectively. The abstracts are sorted by the number of matches and the top five abstracts are listed using their pre-stored abstract IDs. A comprehensive user study was conducted where 60 different queries were formulated and used to generate ranked search results using both PubMed and our proposed model. Five medical professionals assessed the ranked search results and marked every item as relevant or non-relevant. Both models were compared using precision@K and mean-average-precision@K metrics where K is 5. For most of the queries, our model produced higher precision@K values than PubMed. The mean-average-precision@K value of our model is also higher than PubMed (0.83 versus 0.67).

Notice of Retraction: Radiation reaction force on an accelerating point charge

International Journal of Modern Physics AVol. 38, No. 01, 2393001 (2023) RetractionFree AccessNotice of Retraction: Radiation reaction force on an accelerating point chargeOriginal articleRadiation reaction force on an accelerating point chargeJerrold FranklinJerrold FranklinDepartment of Physics, Temple University, Philadelphia, PA 19122, USAE-mail Address: [email protected] Search for more papers by this author https://doi.org/10.1142/S0217751X23930016Cited by:0 Previous AboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack CitationsRecommend to Librarian ShareShare onFacebookTwitterLinked InRedditEmail [International Journal of Modern Physics A, Vol. 37, No. 15 (2022), Article ID: 2250096, https://doi.org/10.1142/S0217751X22500968]This article has been retracted due to an error that invalidated the result. A new version of this article is now published: J. Franklin, “Radiation reaction on an accelerating point charge”, Int. J. Mod. Phys. A 38, 2350005 (2023). The new article corrects the error in the original article and derives a correct and reasonable result. You currently do not have access to the full text article. Recommend the journal to your library today! FiguresReferencesRelatedDetailsRelated articlesRadiation reaction force on an accelerating point charge9 Jun 2022International Journal of Modern Physics A Recommended Vol. 38, No. 01 Metrics History Published: 25 February 2023 PDF download

ТОРГОВО-ЭКОНОМИЧЕСКИЕ ОТНОШЕНИЯ РЕСПУБЛИКИ ИНДОНЕЗИЯ И КОРОЛЕВСТВА ТАИЛАНД

The article id devoted to the problems of bilateral trade and economic cooperation of two ASEAN country-members, Indonesia and Thailand. The main attention is paid to the bilateral trade, the problems of mutual investments and cooperation in the field of tourism are also regarded as well as a cooperation in the field of banking for organizing cross border payments using digital technologies, a cooperation for stabilizing rubber prices and for prevention of illegal fishing.

ТОРГОВО-ЭКОНОМИЧЕСКИЕ ОТНОШЕНИЯ РЕСПУБЛИКИ ИНДОНЕЗИЯ И СОЦИАЛИСТИЧЕСКОЙ РЕСПУБЛИКИ ВЬЕТНАМ

The article id devoted to the problems of bilateral trade and economic cooperation of two ASEAN country-members, Indonesia and Vietnam. The main attention is paid to the bilateral trade, the problems of mutual investments and cooperation in the field of tourism are also regarded as well as a cooperation for prevention of illegal fishing.

Extremal problems of Turán-type involving the location of all zeros of a polynomial

If P ( z ) = a n ∏ v = 1 n ( z − z v ) is a polynomial of degree n having all its zeros in | z | ≤ k , k ≥ 1 then Aziz [Inequalities for the derivative of a polynomial. Proc Am Math Soc. 1983;89(2):259–266] proved that max | z | = 1 | P ′ ( z ) | ≥ 2 1 + k n ∑ v = 1 n k k + | z v | max | z | = 1 | P ( z ) | . Recently, Kumar [On the inequalities concerning polynomials. Complex Anal Oper Theory. 2020;14(6):1–11 (Article ID 65)] established a generalization of this inequality and proved under the same hypothesis for a polynomial P ( z ) = a 0 + a 1 z + a 2 z 2 + ⋯ + a n z n = a n ∏ v = 1 n ( z − z v ) , that max | z | = 1 | P ′ ( z ) | ≥ ( 2 1 + k n + ( | a n | k n − | a 0 | ) ( k − 1 ) ( 1 + k n ) ( | a n | k n + k | a 0 | ) ) ∑ v = 1 n k k + | z v | max | z | = 1 | P ( z ) | . In this paper, we sharpen the above inequalities and further extend the obtained results to the polar derivative of a polynomial. As a consequence, our results also sharpens considerably some results of Dewan and Upadhye [Inequalities for the polar derivative of a polynomial. J Ineq Pure Appl Math. 2008;9:1–9 (Article ID 119)].

On the convex components of a set in ℝ n

Abstract We prove a lower bound on the number of the convex components of a compact set with non-empty interior in ℝ n {\mathbb{R}^{n}} for all n ≥ 2 {n\geq 2} . Our result generalizes and improves the inequalities previously obtained in [M. Carozza, F. Giannetti, F. Leonetti and A. Passarelli di Napoli, Convex components, Commun. Contemp. Math. 21 2019, 6, Article ID 1850036] and [M. La Civita and F. Leonetti, Convex components of a set and the measure of its boundary, Atti Semin. Mat. Fis. Univ. Modena Reggio Emilia 56 2008/09, 71–78].