Singular Solutions and Potentials in Complex Form

2002 ◽  
pp. 31-49
Author(s):  
A. M. Linkov
Keyword(s):  
Complex Form ◽  
Singular Solutions

Singular Solutions to the Shallow Shell Equations

1970 ◽  
Vol 37 (2) ◽  
pp. 361-366 ◽  
Author(s):  
J. Lyell Sanders
Keyword(s):  
Closed Form ◽  
Theoretical Investigation ◽  
Shallow Shell ◽  
Fourier Transforms ◽  
Complex Form ◽  
Middle Surface ◽  
Singular Solutions ◽  
Concentrated Loads ◽  
Shell Equations ◽  
Complete Solutions

The paper contains a theoretical investigation of those multivalued singular solutions to the shallow shell equations which correspond physically to concentrated loads and dislocations. Use of the shell equations in complex form permits a unified treatment of the load and dislocation problems. The analysis is limited to the case of shells with a quadratic middle surface, and Fourier transforms of the solutions are obtained. Complete solutions in closed form in the case of a shallow sphere are given in the Appendix, including some results not previously published.

Kramers-Kronig Relation in Complex Form

2004 ◽  
Vol 124 (12) ◽  
pp. 1121-1128 ◽  
Author(s):  
Hiroyuki Hosono ◽  
Toshio Hosono
Keyword(s):  
Complex Form ◽  
Kronig Relation

New singular solutions for the (3+1)-D Protter problem

2018 ◽  
Vol 91 (3) ◽  
pp. 61-68 ◽  
Author(s):  
T.P. Popov ◽  
Keyword(s):  
Singular Solutions

Finite Element Method for Solving Problems with Singular Solutions.

1995 ◽  
Author(s):  
I. Babuska ◽  
B. Andersson ◽  
B. Guo ◽  
H. S. Oh ◽  
J. M. Melenk
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Singular Solutions ◽  
Element Method

A new algorithm for finding CRM-model coefficients

2019 ◽  
Vol 5 (3) ◽  
pp. 164-185 ◽  
Author(s):  
Alexander D. Bekman ◽  
Sergey V. Stepanov ◽  
Alexander A. Ruchkin ◽  
Dmitry V. Zelenin
Keyword(s):  
Approximate Solution ◽  
Optimization Problem ◽  
Optimal Solution ◽  
Complex Form ◽  
Approximate Solutions ◽  
The Other ◽  
Programming Algorithm ◽  
Stochastic Algorithms ◽  
Large Set ◽  
Flow Rates

The quantitative evaluation of producer and injector well interference based on well operation data (profiles of flow rates/injectivities and bottomhole/reservoir pressures) with the help of CRM (Capacitance-Resistive Models) is an optimization problem with large set of variables and constraints. The analytical solution cannot be found because of the complex form of the objective function for this problem. Attempts to find the solution with stochastic algorithms take unacceptable time and the result may be far from the optimal solution. Besides, the use of universal (commercial) optimizers hides the details of step by step solution from the user, for example&nbsp;— the ambiguity of the solution as the result of data inaccuracy.<br> The present article concerns two variants of CRM problem. The authors present a new algorithm of solving the problems with the help of “General Quadratic Programming Algorithm”. The main advantage of the new algorithm is the greater performance in comparison with the other known algorithms. Its other advantage is the possibility of an ambiguity analysis. This article studies the conditions which guarantee that the first variant of problem has a unique solution, which can be found with the presented algorithm. Another algorithm for finding the approximate solution for the second variant of the problem is also considered. The method of visualization of approximate solutions set is presented. The results of experiments comparing the new algorithm with some previously known are given.

Injectable in-situ Forming Depot Of Doxycycline Hyclate/α-Cyclodextrin Complex using PLGA for Periodontitis Treatment: Preparation, Charac-terization, and In-Vitro Evaluation

2020 ◽  
Vol 17 ◽  
Author(s):  
Elham Khodaverdi ◽  
Farhad Eisvand ◽  
Mohammad Sina Nezami ◽  
Seyedeh Nesa Rezaeian Shiadeh ◽  
Hossein Kamali ◽  
...  
Keyword(s):  
Complex Form ◽  
Docking Studies ◽  
Morphological Properties ◽  
Burst Release ◽  
Cyclodextrin Complex ◽  
Doxycycline Hyclate ◽  
Scanning Calorimetry ◽  
In Situ Forming

Background:: Doxycycline (DOX) is used in treating a bacterial infection, especially for periodontitis treatment. Objective: To reduce irritation of DOX for subgingival administration and increase the chemical stability and against enzy-matic, the complex of α-cyclodextrin with DOX was prepared and loaded into injectable in situ forming implant based on PLGA. Methods:: FTIR, molecular docking studies, X-ray diffraction, and differential scanning calorimetry was performed to char-acterize the DOX/α-cyclodextrin complex. Finally, the in-vitro drug release and modeling, morphological properties, and cellular cytotoxic effects were also evaluated. Results:: The stability of DOX was improved with complex than pure DOX. The main advantage of the complex is the al-most complete release (96.31 ± 2.56 %) of the drug within 14 days of the implant, whereas in the formulation containing the pure DOX and the physical mixture the DOX with α-cyclodextrin release is reached to 70.18 ± 3.61 % and 77.03 ± 3.56 %, respectively. This trend is due to elevate of DOX stability in the DOX/ α-cyclodextrin complex form within PLGA implant that confirmed by the results of stability. Conclusion:: Our results were indicative that the formulation containing DOX/α-cyclodextrin complex was biocompatible and sustained-release with minimum initial burst release.

scholarly journals Polymer Composites with 0.98 Transparencies and Small Optical Energy Band Gap Using a Promising Green Methodology: Structural and Optical Properties

Polymers ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1648
Author(s):  
Muaffaq M. Nofal ◽  
Shujahadeen B. Aziz ◽  
Jihad M. Hadi ◽  
Wrya O. Karim ◽  
Elham M. A. Dannoun ◽  
...  
Keyword(s):  
Refractive Index ◽  
Optical Properties ◽  
Polymer Composites ◽  
Amorphous Phase ◽  
Absorption Edge ◽  
Complex Form ◽  
Bandgap Energy ◽  
Optical Parameters ◽  
Visible Spectroscopy ◽  
Uv Visible

In this work, a green approach was implemented to prepare polymer composites using polyvinyl alcohol polymer and the extract of black tea leaves (polyphenols) in a complex form with Co2+ ions. A range of techniques was used to characterize the Co2+ complex and polymer composite, such as Ultraviolet–visible (UV-Visible) spectroscopy, Fourier transform infrared spectroscopy (FTIR), and X-ray diffraction (XRD). The optical parameters of absorption edge, refractive index (n), dielectric properties including real and imaginary parts (εr, and εi) were also investigated. The FRIR and XRD spectra were used to examine the compatibility between the PVA polymer and Co2+-polyphenol complex. The extent of interaction was evidenced from the shifts and change in the intensity of the peaks. The relatively wide amorphous phase in PVA polymer increased upon insertion of the Co2+-polyphenol complex. The amorphous character of the Co2+ complex was emphasized with the appearance of a hump in the XRD pattern. From UV-Visible spectroscopy, the optical properties, such as absorption edge, refractive index (n), (εr), (εi), and bandgap energy (Eg) of parent PVA and composite films were specified. The Eg of PVA was lowered from 5.8 to 1.82 eV upon addition of 45 mL of Co2+-polyphenol complex. The N/m* was calculated from the optical dielectric function. Ultimately, various types of electronic transitions within the polymer composites were specified using Tauc’s method. The direct bandgap (DBG) treatment of polymer composites with a developed amorphous phase is fundamental for commercialization in optoelectronic devices.

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