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Fourier Spectral Method for Higher Order Space Fractional Reaction–Diffusion Equations for Eliminating Artificial Boundary Conditions in Time-Dependent Density Functional Theory (Dft) Using Response Functions from Fourier Component Variational Pertur

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Mini-Review | DOI: https://doi.org/10.31579/2834-5134/032

Fourier Spectral Method for Higher Order Space Fractional Reaction–Diffusion Equations for Eliminating Artificial Boundary Conditions in Time-Dependent Density Functional Theory (Dft) Using Response Functions from Fourier Component Variational Pertur

  • Alireza Heidari 1234

1 Faculty of Chemistry, California South University, 14731 Comet St. Irvine, CA 92604, USA

2 BioSpectroscopy Core Research Laboratory (BCRL), California South University, 14731 Comet St. Irvine, CA 92604, USA 

3 Cancer Research Institute (CRI), California South University, 14731 Comet St. Irvine, CA 92604, USA

4 American International Standards Institute (AISI), Irvine, CA 3800, USA

*Corresponding Author: Alireza Heidari1, American International Standards Institute (AISI), Irvine, CA 3800, USA.

Citation: Alireza Heidari, (2023). Fourier Spectral Method for Higher Order Space Fractional Reaction–Diffusion Equations for Eliminating Artificial Boundary Conditions in Time-Dependent Density Functional Theory (Dft) Using Response Functions from Fourier Component Variational Perturbation Theory Applied to A Time‐Averaged Quasienergy and Fourier Contour Deformation, Journal of Clinical Anatomy, 2(5) DOI:10.31579/2834-5134/032

Copyright: © 2023 Alireza Heidari, this is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Received: 31 August 2023 | Accepted: 05 September 2023 | Published: 15 September 2023

Keywords:

Abstract

Time-resolved digital spectra can be received/be gotten as the Fourier change of a special type of time mathematical dating-related function referred to as loyalty extent/size, which, in flip, can be (discovered the worth, amount, or excellent of) approximately and (in a manner that produces lots with very little waste) with the dephasing illustration. right here we improve both the (great of being very near the reality or real number) of this near guess--with a quantity/length correction came/coming from the section-space propagator--and its (losing little or no whilst operating or generating something)--with an advanced cellular huge plan/layout/cheating plan employing inverse Weierstrass trade and great scaling of the cell size. We (show or show) the benefits of the new way(s) of doing matters by figuring out/calculating broke up and moved away time-resolved stimulated emission spectra within the harmonic possible, pyrazine, and the NCO molecule. In evaluation, we show that in strongly noisy and loopy systems inclusive of the quartic oscillator the unique dephasing illustration is greater suitable than both the cellular or prefactor-corrected techniques [1-114].

Acknowledgement:

This study was supported by the Cancer Research Institute (CRI) Project of Scientific Instrument and Equipment Development, the National Natural Science Foundation of the United Sates, the International Joint BioSpectroscopy Core Research Laboratory (BCRL) Program supported by the California South University (CSU), and the Key project supported by the American International Standards Institute (AISI), Irvine, California, USA.

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  71. A.Heidari, (2018), “Gamma Linolenic Methyl Ester, 5–Heptadeca–5,8,11–Trienyl 1,3,4–Oxadiazole–2–Thiol, Sulphoquinovosyl Diacyl Glycerol, Ruscogenin, Nocturnoside B, Protodioscine B, Parquisoside–B, Leiocarposide, Narangenin, 7–Methoxy Hespertin, Lupeol, Rosemariquinone, Rosmanol and Rosemadiol Nano Molecules Incorporation into the Nano Polymeric Matrix (NPM) by Immersion of the Nano Polymeric Modified Electrode (NPME) as Molecular Enzymes and Drug Targets for Human Cancer Cells, Tissues and Tumors Treatment under Synchrotron and Synchrocyclotron Radiations”, Int J Pharma Anal Acta, 2 (1): 007–014.
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  72. A.Heidari, (2018), “Fourier Transform Infrared (FTIR) Spectroscopy, Attenuated Total Reflectance Fourier Transform Infrared (ATR–FTIR) Spectroscopy, Micro–Attenuated Total Reflectance Fourier Transform Infrared (Micro–ATR–FTIR) Spectroscopy, Macro–Attenuated Total Reflectance Fourier Transform Infrared (Macro–ATR–FTIR) Spectroscopy, Two–Dimensional Infrared Correlation Spectroscopy, Linear Two–Dimensional Infrared Spectroscopy, Non–Linear Two–Dimensional Infrared Spectroscopy, Atomic Force Microscopy Based Infrared (AFM–IR) Spectroscopy, Infrared Photodissociation Spectroscopy, Infrared Correlation Table Spectroscopy, Near–Infrared Spectroscopy (NIRS), Mid–Infrared Spectroscopy (MIRS), Nuclear Resonance Vibrational Spectroscopy, Thermal Infrared Spectroscopy and Photothermal Infrared Spectroscopy Comparative Study on Malignant and Benign Human Cancer Cells and Tissues under Synchrotron Radiation with the Passage of Time”, Glob Imaging Insights, Volume 3 (2): 1–14.
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  73. A.Heidari, (2018), “Heteronuclear Single–Quantum Correlation Spectroscopy (HSQC) and Heteronuclear Multiple–Bond Correlation Spectroscopy (HMBC) Comparative Study on Malignant and Benign Human Cancer Cells, Tissues and Tumors under Synchrotron and Synchrocyclotron Radiations”, Chronicle of Medicine and Surgery 2.3: 144–156.
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  74. A.Heidari, (2018), “Tetrakis [3, 5–bis (Trifluoromethyl) Phenyl] Borate (BARF)–Enhanced Precatalyst Preparation Stabilization and Initiation (EPPSI) Nano Molecules”, Medical Research and Clinical Case Reports 2.1: 113–126.
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  75. A.Heidari, (2018), “Sydnone, Münchnone, Montréalone, Mogone, Montelukast, Quebecol and Palau’amine–Enhanced Precatalyst Preparation Stabilization and Initiation (EPPSI) Nano Molecules”, Sur Cas Stud Op Acc J. 1 (3).
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  76. A.Heidari, (2018), “Fornacite, Orotic Acid, Rhamnetin, Sodium Ethyl Xanthate (SEX) and Spermine (Spermidine or Polyamine) Nanomolecules Incorporation into the Nanopolymeric Matrix (NPM)”, International Journal of Biochemistry and Biomolecules, Vol. 4: Issue 1, Pages 1–19.
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  77. A.Heidari, R. Gobato, (2018), “Putrescine, Cadaverine, Spermine and Spermidine–Enhanced Precatalyst Preparation Stabilization and Initiation (EPPSI) Nano Molecules”, Parana Journal of Science and Education (PJSE)–v.4, n.5, (1–14) July 1.
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  78. A.Heidari, (2018), “Cadaverine (1,5–Pentanediamine or Pentamethylenediamine), Diethyl Azodicarboxylate (DEAD or DEADCAT) and Putrescine (Tetramethylenediamine) Nano Molecules Incorporation into the Nano Polymeric Matrix (NPM) by Immersion of the Nano Polymeric Modified Electrode (NPME) as Molecular Enzymes and Drug Targets for Human Cancer Cells, Tissues and Tumors Treatment under Synchrotron and Synchrocyclotron Radiations”, Hiv and Sexual Health Open Access Open Journal. 1 (1): 4–11.
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  79. A.Heidari, (2018), “Improving the Performance of Nano–Endofullerenes in Polyaniline Nanostructure–Based Biosensors by Covering Californium Colloidal Nanoparticles with Multi–Walled Carbon Nanotubes”, Journal of Advances in Nanomaterials, Vol. 3, No. 1, Pages 1–28.
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  80. R.Gobato, A. Heidari, (2018), “Molecular Mechanics and Quantum Chemical Study on Sites of Action of Sanguinarine Using Vibrational Spectroscopy Based on Molecular Mechanics and Quantum Chemical Calculations”, Malaysian Journal of Chemistry, Vol. 20 (1), 1–23.
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  81. A.Heidari, (2018), “Vibrational Biospectroscopic Studies on Anti–Cancer Nanopharmaceuticals (Part I)”, Malaysian Journal of Chemistry, Vol. 20 (1), 33–73.
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  82. A.Heidari, (2018), “Vibrational Biospectroscopic Studies on Anti–Cancer Nanopharmaceuticals (Part II)”, Malaysian Journal of Chemistry, Vol. 20 (1), 74–117.
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  83. A.Heidari, (2018), “Uranocene (U(C8H8)2) and Bis(Cyclooctatetraene)Iron (Fe(C8H8)2 or Fe(COT)2)–Enhanced Precatalyst Preparation Stabilization and Initiation (EPPSI) Nano Molecules”, Chemistry Reports, Vol. 1, Iss. 2, Pages 1–16.
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  84. A.Heidari, (2018), “Biomedical Systematic and Emerging Technological Study on Human Malignant and Benign Cancer Cells and Tissues Biospectroscopic Analysis under Synchrotron Radiation”, Glob Imaging Insights, Volume 3 (3): 1–7.
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  85. A.Heidari, (2018), “Deep–Level Transient Spectroscopy and X–Ray Photoelectron Spectroscopy (XPS) Comparative Study on Malignant and Benign Human Cancer Cells and Tissues with the Passage of Time under Synchrotron Radiation”, Res Dev Material Sci. 7(2). RDMS.000659.
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  86. A.Heidari, (2018), “C70–Carboxyfullerenes Nano Molecules Incorporation into the Nano Polymeric Matrix (NPM) by Immersion of the Nano Polymeric Modified Electrode (NPME) as Molecular Enzymes and Drug Targets for Human Cancer Cells, Tissues and Tumors Treatment under Synchrotron and Synchrocyclotron Radiations”, Glob Imaging Insights, Volume 3 (3): 1–7.
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  87. A.Heidari, (2018), “The Effect of Temperature on Cadmium Oxide (CdO) Nanoparticles Produced by Synchrotron Radiation in the Human Cancer Cells, Tissues and Tumors”, International Journal of Advanced Chemistry, 6 (2) 140–156.
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  88. A.Heidari, (2018), “A Clinical and Molecular Pathology Investigation of Correlation Spectroscopy (COSY), Exclusive Correlation Spectroscopy (ECOSY), Total Correlation Spectroscopy (TOCSY), Heteronuclear Single–Quantum Correlation Spectroscopy (HSQC) and Heteronuclear Multiple–Bond Correlation Spectroscopy (HMBC) Comparative Study on Malignant and Benign Human Cancer Cells, Tissues and Tumors under Synchrotron and Synchrocyclotron Radiations Using Cyclotron versus Synchrotron, Synchrocyclotron and the Large Hadron Collider (LHC) for Delivery of Proton and Helium Ion (Charged Particle) Beams for Oncology Radiotherapy”, European Journal of Advances in Engineering and Technology, 5 (7): 414–426.
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  89. A.Heidari, (2018), “Nano Molecules Incorporation into the Nano Polymeric Matrix (NPM) by Immersion of the Nano Polymeric Modified Electrode (NPME) as Molecular Enzymes and Drug Targets for Human Cancer Cells, Tissues and Tumors Treatment under Synchrotron and Synchrocyclotron Radiations”, J Oncol Res; 1 (1): 1–20.
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  90. A.Heidari, (2018), “Use of Molecular Enzymes in the Treatment of Chronic Disorders”, Canc Oncol Open Access J. 1 (1): 12–15.
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  91. A.Heidari, (2018), “Vibrational Biospectroscopic Study and Chemical Structure Analysis of Unsaturated Polyamides Nanoparticles as Anti–Cancer Polymeric Nanomedicines Using Synchrotron Radiation”, International Journal of Advanced Chemistry, 6 (2) 167–189.
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  92. A.Heidari, (2018), “Adamantane, Irene, Naftazone and Pyridine–Enhanced Precatalyst Preparation Stabilization and Initiation (PEPPSI) Nano Molecules”, Madridge J Nov Drug Res. 2 (1): 61–67.
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  93. A.Heidari, (2018), “Heteronuclear Single–Quantum Correlation Spectroscopy (HSQC) and Heteronuclear Multiple–Bond Correlation Spectroscopy (HMBC) Comparative Study on Malignant and Benign Human Cancer Cells and Tissues with the Passage of Time under Synchrotron Radiation”, Madridge J Nov Drug Res, 2 (1): 68–74.
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  94. A.Heidari, R. Gobato, (2018), “A Novel Approach to Reduce Toxicities and to Improve Bioavailabilities of DNA/RNA of Human Cancer Cells–Containing Cocaine (Coke), Lysergide (Lysergic Acid Diethyl Amide or LSD), Δ⁹–Tetrahydrocannabinol (THC) [(–)–trans–Δ⁹–Tetrahydrocannabinol], Theobromine (Xantheose), Caffeine, Aspartame (APM) (NutraSweet) and Zidovudine (ZDV) [Azidothymidine (AZT)] as Anti–Cancer Nano Drugs by Coassembly of Dual Anti–Cancer Nano Drugs to Inhibit DNA/RNA of Human Cancer Cells Drug Resistance”, Parana Journal of Science and Education (PJSE), v. 4, n. 6, pp. 1–17.
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  95. A.Heidari, R. Gobato, (2018), “Ultraviolet Photoelectron Spectroscopy (UPS) and Ultraviolet–Visible (UV–Vis) Spectroscopy Comparative Study on Malignant and Benign Human Cancer Cells and Tissues with the Passage of Time under Synchrotron Radiation”, Parana Journal of Science and Education (PJSE), v. 4, n. 6, pp. 18–33.
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  96. R.Gobato, A. Heidari, A. Mitra, (2018), “The Creation of C13H20BeLi2SeSi. The Proposal of a Bio–Inorganic Molecule, Using Ab Initio Methods for the Genesis of a Nano Membrane”, Arc Org Inorg Chem Sci 3 (4). AOICS.MS.ID.000167.
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  97. R.Gobato, A. Heidari, (2018), “Using the Quantum Chemistry for Genesis of a Nano Biomembrane with a Combination of the Elements Be, Li, Se, Si, C and H”, J Nanomed Res.7 (4): 241‒252.
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  98. A.Heidari, (2018), “Bastadins and Bastaranes–Enhanced Precatalyst Preparation Stabilization and Initiation (EPPSI) Nano Molecules”, Glob Imaging Insights, Volume 3 (4): 1–7.
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  99. A.Heidari, (2018), “Fucitol, Pterodactyladiene, DEAD or DEADCAT (DiEthyl AzoDiCArboxylaTe), Skatole, the NanoPutians, Thebacon, Pikachurin, Tie Fighter, Spermidine and Mirasorvone Nano Molecules Incorporation into the Nano Polymeric Matrix (NPM) by Immersion of the Nano Polymeric Modified Electrode (NPME) as Molecular Enzymes and Drug Targets for Human Cancer Cells, Tissues and Tumors Treatment under Synchrotron and Synchrocyclotron Radiations”, Glob Imaging Insights, Volume 3 (4): 1–8.
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  100. E.Dadvar, A. Heidari, (2018), “A Review on Separation Techniques of Graphene Oxide (GO)/Base on Hybrid Polymer Membranes for Eradication of Dyes and Oil Compounds: Recent Progress in Graphene Oxide (GO)/Base on Polymer Membranes–Related Nanotechnologies”, Clin Med Rev Case Rep 5: 228.
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  101. A.Heidari, R. Gobato, (2018), “First–Time Simulation of Deoxyuridine Monophosphate (dUMP) (Deoxyuridylic Acid or Deoxyuridylate) and Vomitoxin (Deoxynivalenol (DON)) ((3α,7α)–3,7,15–Trihydroxy–12,13–Epoxytrichothec–9–En–8–One)–Enhanced Precatalyst Preparation Stabilization and Initiation (EPPSI) Nano Molecules Incorporation into the Nano Polymeric Matrix (NPM) by Immersion of the Nano Polymeric Modified Electrode (NPME) as Molecular Enzymes and Drug Targets for Human Cancer Cells, Tissues and Tumors Treatment under Synchrotron and Synchrocyclotron Radiations”, Parana Journal of Science and Education (PJSE), Vol. 4, No. 6, pp. 46–67.
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  102. A.Heidari, (2018), “Buckminsterfullerene (Fullerene), Bullvalene, Dickite and Josiphos Ligands Nano Molecules Incorporation into the Nano Polymeric Matrix (NPM) by Immersion of the Nano Polymeric Modified Electrode (NPME) as Molecular Enzymes and Drug Targets for Human Hematology and Thromboembolic Diseases Prevention, Diagnosis and Treatment under Synchrotron and Synchrocyclotron Radiations”, Glob Imaging Insights, Volume 3 (4): 1–7.
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  103. A.Heidari, (2018), “Fluctuation X–Ray Scattering (FXS) and Wide–Angle X–Ray Scattering (WAXS) Comparative Study on Malignant and Benign Human Cancer Cells and Tissues under Synchrotron Radiation”, Glob Imaging Insights, Volume 3 (4): 1–7.
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  104. A.Heidari, (2018), “A Novel Approach to Correlation Spectroscopy (COSY), Exclusive Correlation Spectroscopy (ECOSY), Total Correlation Spectroscopy (TOCSY), Incredible Natural–Abundance Double–Quantum Transfer Experiment (INADEQUATE), Heteronuclear Single–Quantum Correlation Spectroscopy (HSQC), Heteronuclear Multiple–Bond Correlation Spectroscopy (HMBC), Nuclear Overhauser Effect Spectroscopy (NOESY) and Rotating Frame Nuclear Overhauser Effect Spectroscopy (ROESY) Comparative Study on Malignant and Benign Human Cancer Cells and Tissues under Synchrotron Radiation”, Glob Imaging Insights, Volume 3 (5): 1–9.
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  105. A.Heidari, (2018), “Terphenyl–Based Reversible Receptor with Rhodamine, Rhodamine–Based Molecular Probe, Rhodamine–Based Using the Spirolactam Ring Opening, Rhodamine B with Ferrocene Substituent, Calix[4]Arene–Based Receptor, Thioether + Aniline–Derived Ligand Framework Linked to a Fluorescein Platform, Mercuryfluor–1 (Flourescent Probe), N,N’–Dibenzyl–1,4,10,13–Tetraraoxa–7,16–Diazacyclooctadecane and Terphenyl–Based Reversible Receptor with Pyrene and Quinoline as the Fluorophores–Enhanced Precatalyst Preparation Stabilization and Initiation (EPPSI) Nano Molecules”, Glob Imaging Insights, Volume 3 (5): 1–9.
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  106. A.Heidari, (2018), “Small–Angle X–Ray Scattering (SAXS), Ultra–Small Angle X–Ray Scattering (USAXS), Fluctuation X–Ray Scattering (FXS), Wide–Angle X–Ray Scattering (WAXS), Grazing–Incidence Small–Angle X–Ray Scattering (GISAXS), Grazing–Incidence Wide–Angle X–Ray Scattering (GIWAXS), Small–Angle Neutron Scattering (SANS), Grazing–Incidence Small–Angle Neutron Scattering (GISANS), X–Ray Diffraction (XRD), Powder X–Ray Diffraction (PXRD), Wide–Angle X–Ray Diffraction (WAXD), Grazing– Incidence X–Ray Diffraction (GIXD) and Energy–Dispersive X–Ray Diffraction (EDXRD) Comparative Study on Malignant and Benign Human Cancer Cells and Tissues under Synchrotron Radiation”, Glob Imaging Insights, Volume 3 (5): 1–10.
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  107. A.Heidari, (2018), “Nuclear Resonant Inelastic X–Ray Scattering Spectroscopy (NRIXSS) and Nuclear Resonance Vibrational Spectroscopy (NRVS) Comparative Study on Malignant and Benign Human Cancer Cells and Tissues under Synchrotron Radiation”, Glob Imaging Insights, Volume 3 (5): 1–7.
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  108. A.Heidari, (2018), “Small–Angle X–Ray Scattering (SAXS) and Ultra–Small Angle X–Ray Scattering (USAXS) Comparative Study on Malignant and Benign Human Cancer Cells and Tissues under Synchrotron Radiation”, Glob Imaging Insights, Volume 3 (5): 1–7.
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  109. A.Heidari, (2018), “Curious Chloride (CmCl3) and Titanic Chloride (TiCl4)–Enhanced Precatalyst Preparation Stabilization and Initiation (EPPSI) Nano Molecules for Cancer Treatment and Cellular Therapeutics”, J. Cancer Research and Therapeutic Interventions, Volume 1, Issue 1, Pages 01–10.
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  110. R.Gobato, M. R. R. Gobato, A. Heidari, A. Mitra, (2018), “Spectroscopy and Dipole Moment of the Molecule C13H20BeLi2SeSi via Quantum Chemistry Using Ab Initio, Hartree–Fock Method in the Base Set CC–pVTZ and 6–311G**(3df, 3pd)”, Arc Org Inorg Chem Sci 3 (5), Pages 402–409.
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  111. A.Heidari, (2018), “C60 and C70–Encapsulating Carbon Nanotubes Incorporation into the Nano Polymeric Matrix (NPM) by Immersion of the Nano Polymeric Modified Electrode (NPME) as Molecular Enzymes and Drug Targets for Human Cancer Cells, Tissues and Tumors Treatment under Synchrotron and Synchrocyclotron Radiations”, Integr Mol Med, Volume 5 (3): 1–8.
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  112. A.Heidari, (2018), “Two–Dimensional (2D) 1H or Proton NMR, 13C NMR, 15N NMR and 31P NMR Spectroscopy Comparative Study on Malignant and Benign Human Cancer Cells and Tissues under Synchrotron Radiation with the Passage of Time”, Glob Imaging Insights, Volume 3 (6): 1–8.
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  113. A.Heidari, (2018), “FT–Raman Spectroscopy, Coherent Anti–Stokes Raman Spectroscopy (CARS) and Raman Optical Activity Spectroscopy (ROAS) Comparative Study on Malignant and Benign Human Cancer Cells and Tissues with the Passage of Time under Synchrotron Radiation”, Glob Imaging Insights, Volume 3 (6): 1–8.
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  114. A.Heidari, (2018), “A Modern and Comprehensive Investigation of Inelastic Electron Tunneling Spectroscopy (IETS) and Scanning Tunneling Spectroscopy on Malignant and Benign Human Cancer Cells, Tissues and Tumors through Optimizing Synchrotron Microbeam Radiotherapy for Human Cancer Treatments and Diagnostics: An Experimental Biospectroscopic Comparative Study”, Glob Imaging Insights, Volume 3 (6): 1–8.
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Clinical Trials and Clinical Research: I am delighted to provide a testimonial for the peer review process, support from the editorial office, and the exceptional quality of the journal for my article entitled “Effect of Traditional Moxibustion in Assisting the Rehabilitation of Stroke Patients.” The peer review process for my article was rigorous and thorough, ensuring that only high-quality research is published in the journal. The reviewers provided valuable feedback and constructive criticism that greatly improved the clarity and scientific rigor of my study. Their expertise and attention to detail helped me refine my research methodology and strengthen the overall impact of my findings. I would also like to express my gratitude for the exceptional support I received from the editorial office throughout the publication process. The editorial team was prompt, professional, and highly responsive to all my queries and concerns. Their guidance and assistance were instrumental in navigating the submission and revision process, making it a seamless and efficient experience. Furthermore, I am impressed by the outstanding quality of the journal itself. The journal’s commitment to publishing cutting-edge research in the field of stroke rehabilitation is evident in the diverse range of articles it features. The journal consistently upholds rigorous scientific standards, ensuring that only the most impactful and innovative studies are published. This commitment to excellence has undoubtedly contributed to the journal’s reputation as a leading platform for stroke rehabilitation research. In conclusion, I am extremely satisfied with the peer review process, the support from the editorial office, and the overall quality of the journal for my article. I wholeheartedly recommend this journal to researchers and clinicians interested in stroke rehabilitation and related fields. The journal’s dedication to scientific rigor, coupled with the exceptional support provided by the editorial office, makes it an invaluable platform for disseminating research and advancing the field.

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Dr Shiming Tang

Clinical Reviews and Case Reports, The comment form the peer-review were satisfactory. I will cements on the quality of the journal when I receive my hardback copy

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Hameed khan