On the Complex Form of the Poincare Lemma

1958 ◽  
Vol 9 (2) ◽  
pp. 183
Author(s):  
H. K. Nickerson
Keyword(s):  
Complex Form ◽  
Poincaré Lemma

Some Remarks on the Nijenhuis Tensor

1973 ◽  
Vol 25 (5) ◽  
pp. 903-907 ◽  
Author(s):  
A. P. Stone
Keyword(s):  
Differential Form ◽  
Complex Form ◽  
Exact Form ◽  
Nijenhuis Tensor ◽  
Positive Degree ◽  
Poincaré Lemma

A differential form α of degree r on an n-manifold is exact if there exists a form β of degree r — 1 such that α = dβ and is closed if dα = 0. Since d-d = 0 any exact form is closed. The Poincaré lemma asserts that a closed differential form of positive degree is locally exact. There is also a complex form, proved by Cartan-Grothendieck, of the Poincaré lemma in which the operator d has a decomposition into components and .

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

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.

scholarly journals The effect of the outlet angle β2 on the thermomechanical behavior of a centrifugal compressor blade

2020 ◽  
Vol 29 (1) ◽  
pp. 1-8
Author(s):  
Ahmed Allali ◽  
Sadia Belbachir ◽  
Ahmed Alami ◽  
Belhadj Boucham ◽  
Abdelkader Lousdad
Keyword(s):  
Mechanical Behavior ◽  
Centrifugal Compressor ◽  
Three Dimensional ◽  
Complex Form ◽  
Compressor Blade ◽  
Stress Fields ◽  
The Finite Element Method ◽  
Mechanical Fatigue ◽  
Outlet Angle ◽  
The Impact

AbstractThe objective of this work lies in the three-dimensional study of the thermo mechanical behavior of a blade of a centrifugal compressor. Numerical modeling is performed on the computational code "ABAQUS" based on the finite element method. The aim is to study the impact of the change of types of blades, which are defined as a function of wheel output angle β2, on the stress fields and displacements coupled with the variation of the temperature.This coupling defines in a realistic way the thermo mechanical behavior of the blade where one can note the important concentrations of stresses and displacements in the different zones of its complex form as well as the effects at the edges. It will then be possible to prevent damage and cracks in the blades of the centrifugal compressor leading to its failure which can be caused by the thermal or mechanical fatigue of the material with which the wheel is manufactured.

scholarly journals When Figurative Language Goes off the Rails and under the Bus: Fluid Intelligence, Openness to Experience, and the Production of Poor Metaphors

2021 ◽  
Vol 9 (1) ◽  
pp. 2
Author(s):  
Paul J. Silvia ◽  
Roger E. Beaty
Keyword(s):  
Figurative Language ◽  
Fluid Intelligence ◽  
Complex Form ◽  
Semantic Distance ◽  
Openness To Experience ◽  
Creative Thought ◽  
Basic Task ◽  
Task Requirements ◽  
Dead Metaphor ◽  
Metaphor Production

The present research examined the varieties of poor metaphors to gain insight into the cognitive processes involved in generating creative ones. Drawing upon data from two published studies as well as a new sample, adults’ open-ended responses to different metaphor prompts were categorized. Poor metaphors fell into two broad clusters. Non-metaphors—responses that failed to meet the basic task requirements—consisted of “adjective slips” (describing the topic adjectivally instead of figuratively), “wayward attributes” (attributing the wrong property to the topic), and “off-topic idioms” (describing the wrong topic). Bad metaphors—real metaphors that were unanimously judged as uncreative—consisted of “exemplary exemplars” (vehicles that lacked semantic distance and thus seemed trite) and “retrieved clichés” (pulling a dead metaphor from memory). Overall, people higher in fluid intelligence (Gf) were more likely to generate a real metaphor, and their metaphor was less likely to be a bad one. People higher in Openness to Experience, in contrast, were more likely to generate real metaphors but not more or less likely to generate bad ones. Scraping the bottom of the response barrel suggests that creative metaphor production is a particularly complex form of creative thought.

scholarly journals Information Length as a Useful Index to Understand Variability in the Global Circulation

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 299 ◽  
Author(s):  
Eun-jin Kim ◽  
James Heseltine ◽  
Hanli Liu
Keyword(s):  
Climate Model ◽  
Traditional Approach ◽  
Essential Feature ◽  
Complex Form ◽  
Time Dependent ◽  
Spatial Gradient ◽  
Mean Values ◽  
Global Circulation ◽  
New Perspective ◽  
Non Gaussian

With improved measurement and modelling technology, variability has emerged as an essential feature in non-equilibrium processes. While traditionally, mean values and variance have been heavily used, they are not appropriate in describing extreme events where a significant deviation from mean values often occurs. Furthermore, stationary Probability Density Functions (PDFs) miss crucial information about the dynamics associated with variability. It is thus critical to go beyond a traditional approach and deal with time-dependent PDFs. Here, we consider atmospheric data from the Whole Atmosphere Community Climate Model (WACCM) and calculate time-dependent PDFs and the information length from these PDFs, which is the total number of statistically different states that a system evolves through in time. Specifically, we consider the three cases of sampling data to investigate the distribution of information (information budget) along the altitude and longitude to gain a new perspective of understanding variabilities, correlation among different variables and regions. Time-dependent PDFs are shown to be non-Gaussian in general; the information length tends to increase with the altitude albeit in a complex form; this tendency is more robust for flows/shears than temperature. Much similarity among flows and shears in the information length is also found in comparison with the temperature. This means a strong correlation among flows/shears because of their coupling through gravity waves in this particular WACCM model. We also find the increase of the information length with the latitude and interesting hemispheric asymmetry for flows/shears/temperature, with the tendency of anti-correlation (correlation) between flows/shears and temperature at high (low) latitude. These results suggest the importance of high latitude/altitude in the information budget in the Earth’s atmosphere, the spatial gradient of the information length being a useful proxy for information flow.

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