Article
Mathematics, Interdisciplinary Applications
Miguel Vivas-Cortez, Muzammil Mukhtar, Iram Shabbir, Muhammad Samraiz, Muhammad Yaqoob
Summary: In this study, we apply fractional calculus and convexity theory to certain convex functions, deriving novel mean-type inequalities. By establishing an identity, we investigate fractional mean inequalities and estimate the error of the HH inequality using RL-fractional integrals and convex functions. Specific functions are used for validation, and the main results of this study generalize many existing mean-type inequalities in the literature.
FRACTAL AND FRACTIONAL
(2023)
Article
Mathematics, Applied
Ern Gun Kwon, Min Ju Jo
Summary: The continuous version of Holder's inequality provides a new and direct proof for Polya-Knopp type inequalities, and we also obtain a single variable generalization of Polya-Knopp's inequality.
JOURNAL OF MATHEMATICAL INEQUALITIES
(2021)
Article
Mathematics
Asif R. Khan, Hira Nabi, Josip E. Pecaric
Summary: New Ostrowski type inequalities are obtained in this paper by utilizing the extended version of Montgomery identity and Green's functions. Estimations of the difference between two integral means are also provided.
Article
Mathematics
Josip Pecaric, Jurica Peric, Sanja Varosanec
Summary: We provide a refinement of the converse Holder inequality for functionals by using an interpolation result for Jensen's inequality. In addition, we improve the converse of the Beckenbach inequality. We also consider the converse Minkowski inequality for functionals and give refinements of it, along with applications on integral mixed means.
Article
Mathematics, Applied
M. M. Osman, S. H. Saker, D. R. Anderson
Summary: In this paper, new dynamic inequalities of Opial type involving higher-order derivatives of two functions with two different weights on time scales are proven. Special cases are derived and some versions of recent results are improved from these inequalities.
QUALITATIVE THEORY OF DYNAMICAL SYSTEMS
(2022)
Article
Mathematics, Applied
Necmettin Alp, Mehmet Zeki Sarikaya
Summary: The aim of this study is to obtain quantum estimates for q-Hardy type integral inequalities on quantum calculus by establishing new identities and proving a generalized q-Minkowski integral inequality. The results presented are q-extensions and q-generalizations of comparable results in the literature on inequalities, and our findings also provide classical results on the Hardy inequality by taking the limit q -> 1(-).
ADVANCES IN DIFFERENCE EQUATIONS
(2021)
Article
Mathematics, Applied
Limin Yang, Ruiyun Yang
Summary: The paper aims to establish new Hardy-Hilbert-type inequalities with multiparameters and their equivalent forms and variants, generalizing some existing results. Similarly, corresponding Hardy-Hilbert-type integral inequalities are also provided.
Article
Mathematics
Ahmed A. El-Deeb, Jan Awrejcewicz
Summary: This article proves new backward difference dynamic inequalities of Hardy-Hilbert type on time scales, using the Fenchel-Legendre transform and submultiplicative functions. The (gamma,a)-nabla conformable Holder's and Jensen's inequalities on time scales are also proved, along with several inequalities due to Hardy-Hilbert inequalities on time scales. Additionally, continuous inequalities and discrete inequalities are introduced as special cases.
Article
Mathematics, Applied
S. H. Saker, J. Alzabut, D. O'Regan, R. P. Agarwal
Summary: This paper proves the self-improving property of the weighted Gehring class in non-homogeneous spaces, obtaining sharp bounds of exponents and applying it to the self-improving property of the Muckenhoupt class. By utilizing rearrangement of functions and Jensen inequality, the results cover non-monotonic functions and provide a higher integrability theorem. Furthermore, solutions of partial differential equations can be solved in an extended space using this self-improving property, reflecting a different approach to inequalities of Hardy type.
ADVANCES IN DIFFERENCE EQUATIONS
(2021)
Article
Mathematics, Interdisciplinary Applications
Shanhe Wu, Muhammad Samraiz, Sajid Iqbal, Gauhar Rahman
Summary: In this paper, a new class of Hardy-type inequalities involving fractional calculus operators is studied. Hardy-type inequalities are derived for the variant of Riemann-Liouville fractional calculus operators and k-Hilfer fractional derivative operator. The obtained inequalities involving fractional operators are more general as compared to some existing results in the literature.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2022)
Article
Multidisciplinary Sciences
Muzammil Mukhtar, Muhammad Yaqoob, Muhammad Samraiz, Iram Shabbir, Sina Etemad, Manuel De la Sen, Shahram Rezapour
Summary: This study introduces a new class of mean-type inequalities using fractional calculus and convexity theory. The strong correlation between symmetry and convexity increases its significance. The study establishes a crucial identity for investigating fractional mean inequalities and provides main results related to the error estimation of the Hermite-Hadamard inequality for composite convex functions through a generalized Riemann-type fractional integral. These results are verified in specific cases and have the potential to extend known inequalities from other studies.
Article
Mathematics, Interdisciplinary Applications
Soubhagya Kumar Sahoo, Pshtiwan Othman Mohammed, Bibhakar Kodamasingh, Muhammad Tariq, Y. S. Hamed
Summary: In this article, a new approach is presented to derive generalized midpoint-type Hermite-Hadamard inequality and Pachpattetype inequality using a new fractional integral operator related to the Caputo-Fabrizio derivative. A new fractional identity for differentiable convex functions of first order is proved. Utilizing these results and various inequalities, new estimations of the Hermite-Hadamard H-H type inequality as refinements are obtained. Applications to special means and trapezoidal quadrature formula are introduced to verify the accuracy of the results.
FRACTAL AND FRACTIONAL
(2022)
Article
Mathematics, Interdisciplinary Applications
Saad Ihsan Butt, Saba Yousaf, Ahmet Ocak Akdemir, Mustafa Ali Dokuyucu
Summary: The main purpose of this article is to prove a new and general integral identity and derive new integral inequalities of various Hadamard types using this identity. Basic inequalities such as Holder, Young, power-mean, and Jensen inequality were employed, and it was found that the main results are generalizations and repetitions of existing results in the literature. Additionally, a new version of the Atangana-Baleanu integral operator was utilized, and simulations were provided to demonstrate the consistency and harmony of this operator for different parameter values.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Mathematics, Applied
S. H. Saker, J. Alzabut, A. G. Sayed, D. O'Regan
Summary: In this paper, new Opial-type dynamic inequalities on time scales are proved by utilizing convexity property, chain rule, Jensen and Holder inequalities. Some particular Opial-type inequalities reported in the literature are also illustrated for demonstration purpose.
ADVANCES IN DIFFERENCE EQUATIONS
(2021)
Article
Mathematics, Applied
Ying Wu, Feng Qi
Summary: In this paper, the authors demonstrate the errors in the proofs of Theorems 1 and 2 in a previous paper by constructing a counterexample and utilizing Minkowski's inequality. They also present a new integral inequality of the Hermite-Hadamard type for convex functions using an integral identity and Holder's integral inequality.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2022)
Article
Neurosciences
Forooz Shahbazi, Arne Ewald, Guido Nolte
Article
Clinical Neurology
Stefan Haufe, Arne Ewald
Article
Engineering, Biomedical
Arne Ewald, Forooz Shahbazi Avarvand, Guido Nolte
BIOMEDICAL ENGINEERING-BIOMEDIZINISCHE TECHNIK
(2013)
Article
Mathematical & Computational Biology
Forooz Shahbazi Avarvand, Arne Ewald, Guido Nolte
COMPUTATIONAL AND MATHEMATICAL METHODS IN MEDICINE
(2012)
Meeting Abstract
Psychology, Biological
G. Nolte, F. Shahbazi Avarvand, A. Ewald
INTERNATIONAL JOURNAL OF PSYCHOPHYSIOLOGY
(2012)
Article
Neurosciences
Arne Ewald, Laura Marzetti, Filippo Zappasodi, Frank C. Meinecke, Guido Nolte
Article
Neurosciences
Arne Ewald, Forooz Shahbazi Avarvand, Guido Nolte
Article
Engineering, Biomedical
Lyubomir Zagorchev, Matthias Brueck, Nick Flaschner, Fabian Wenzel, Damon Hyde, Arne Ewald, Jurriaan Peters
Summary: The study introduces and validates a new, fully-automatic method for sensor registration which can accurately identify electrode locations in a short amount of time and is expected to be more easily integrated into clinical workflows.
IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING
(2021)
Article
Clinical Neurology
F. U. Hohlefeld, A. Ewald, F. Ehlen, H. O. Tiedt, A. Horn, A. A. Kuehn, G. Curio, F. Klostermann, V. V. Nikulin
CLINICAL NEUROPHYSIOLOGY
(2017)
Article
Ergonomics
Andreas Sonnleitner, Matthias Sebastian Treder, Michael Simon, Sven Willmann, Arne Ewald, Axel Buchner, Michael Schrauf
ACCIDENT ANALYSIS AND PREVENTION
(2014)
Article
Psychology, Multidisciplinary
Arne Ewald, Sabrina Aristei, Guido Nolte, Rasha Abdel Rahman
FRONTIERS IN PSYCHOLOGY
(2012)
Article
Biochemical Research Methods
Aline Silva da Cruz, Maria Margarida Drehmer, Wagner Baetas-da-Cruz, Joao Carlos Machado
Summary: This study quantified microcirculation cerebral blood flow in a rat model of ischemic stroke using ultrasound biomicroscopy and ultrasound contrast agents. The results showed high sensitivity and specificity of this method, making it a valuable tool for preclinical studies.
JOURNAL OF NEUROSCIENCE METHODS
(2024)
Article
Biochemical Research Methods
Christina Dalla, Ivana Jaric, Pavlina Pavlidi, Georgia E. Hodes, Nikolaos Kokras, Anton Bespalov, Martien J. Kas, Thomas Steckler, Mohamed Kabbaj, Hanno Wuerbel, Jordan Marrocco, Jessica Tollkuhn, Rebecca Shansky, Debra Bangasser, Jill B. Becker, Margaret McCarthy, Chantelle Ferland-Beckham
Summary: Many funding agencies have emphasized the importance of considering sex as a biological variable in experimental design to improve the reproducibility and translational relevance of preclinical research. Omitting the female sex from experimental designs in neuroscience and pharmacology can result in biased or limited understanding of disease mechanisms. This article provides methodological considerations for incorporating sex as a biological variable in in vitro and in vivo experiments, including the influence of age and hormone levels, and proposes strategies to enhance methodological rigor and translational relevance in preclinical research.
JOURNAL OF NEUROSCIENCE METHODS
(2024)
Article
Biochemical Research Methods
Wenyu Gu, Dongxu Li, Jia-Hong Gao
Summary: We developed a precise and rapid method for positioning and labelling triaxial OPMs on a wearable magnetoencephalography (MEG) system, improving the efficiency of OPM positioning and labelling.
JOURNAL OF NEUROSCIENCE METHODS
(2024)
Article
Biochemical Research Methods
Kai Lin, Linhang Zhang, Jing Cai, Jiaqi Sun, Wenjie Cui, Guangda Liu
Summary: The article introduces an EEG feature map processing model for emotion recognition, which achieves significantly improved accuracy by fusing EEG information at different spatial scales and introducing a channel attention mechanism.
JOURNAL OF NEUROSCIENCE METHODS
(2024)
Article
Biochemical Research Methods
John E. Parker, Asier Aristieta, Aryn H. Gittis, Jonathan E. Rubin
Summary: This work presents a toolbox that implements a methodology for automated classification of neural responses based on spike train recordings. The toolbox provides a user-friendly and efficient approach to detect various types of neuronal responses that may not be identified by traditional methods.
JOURNAL OF NEUROSCIENCE METHODS
(2024)
Article
Biochemical Research Methods
Yun Liang, Ke Bo, Sreenivasan Meyyappan, Mingzhou Ding
Summary: This study compared the performance of SVM and CNN on the same datasets and found that CNN achieved consistently higher classification accuracies. The classification accuracies of SVM and CNN were generally not correlated, and the heatmaps derived from them did not overlap significantly.
JOURNAL OF NEUROSCIENCE METHODS
(2024)
Article
Biochemical Research Methods
Antonino Visalli, Maria Montefinese, Giada Viviani, Livio Finos, Antonino Vallesi, Ettore Ambrosini
Summary: This study introduces an analytical strategy that allows the use of mixed-effects models (LMM) in mass univariate analyses of EEG data. The proposed method overcomes the computational costs and shows excellent performance properties, making it increasingly important in the field of neuroscience.
JOURNAL OF NEUROSCIENCE METHODS
(2024)
Article
Biochemical Research Methods
Xavier Cano-Ferrer, Alexandra Tran -Van -Minh, Ede Rancz
Summary: This study developed a novel rotation platform for studying neural processes and spatial navigation. The platform is modular, affordable, and easy to build, and can be driven by the experimenter or animal movement. The research demonstrated the utility of the platform, which combines the benefits of head fixation and intact vestibular activity.
JOURNAL OF NEUROSCIENCE METHODS
(2024)