Second-Order Composed Contingent Derivative of the Perturbation Map in Multiobjective Optimization

2020 ◽  
Vol 37 (02) ◽  
pp. 2050002
Author(s):  
Zhenhua Peng ◽  
Zhongping Wan
Keyword(s):  
Second Order ◽  
Contingent Derivative ◽  
Lipschitz Property ◽  
Dini Derivative ◽  
New Concepts ◽  
Locally Lipschitz ◽  
Perturbation Maps ◽  
Perturbation Map ◽  
First Time ◽  
Derivatives Of

In view of the structural advantage of second-order composed derivatives, the purpose of this paper is to analyze quantitatively the behavior of perturbation maps for the first time by using this concept. First, new concepts of the second-order composed adjacent derivative and the second-order composed lower Dini derivative are introduced. Some relationships among the second-order composed contingent derivative, the second-order composed adjacent derivative and the second-order composed lower Dini derivative are discussed. Second, the relationships between second-order composed lower Dini derivable and Aubin property are provided. Third, by virtue of second-order composed contingent derivatives and the above relationships, some results concerning second-order sensitivity analysis are established without the assumption of the locally Lipschitz property or the locally Hölder continuity. Finally, we give some complete characterizations of second-order composed contingent derivatives of the perturbation maps.

Second-order sensitivity analysis for parametric equilibrium problems in set-valued optimization

2019 ◽  
Vol 53 (4) ◽  
pp. 1245-1260
Author(s):  
Nguyen Le Hoang Anh
Keyword(s):  
Sensitivity Analysis ◽  
Equilibrium Problems ◽  
Second Order ◽  
Weak Perturbation ◽  
Parametric Equilibrium Problems ◽  
Perturbation Map ◽  
Derivatives Of

In the paper, we first establish relationships between second-order contingent derivatives of a given set-valued map and that of the weak perturbation map. Then, these results are applied to sensitivity analysis for parametric equilibrium problems in set-valued optimization.

scholarly journals The second-order contingent derivative of generalized perturbation maps

2018 ◽  
Vol 1 (T5) ◽  
pp. 203-213
Author(s):  
Anh Le Hoang Nguyen
Keyword(s):  
Sensitivity Analysis ◽  
Second Order ◽  
Contingent Derivative ◽  
Sum Rule ◽  
Perturbation Maps ◽  
Better Than

In the paper, we give some remarks on [1]. Then, we modify main results concerning the sum rule of second-order contingent derivatives for set-valued maps and its application to the sensitivity analysis of generalized perturbation maps. The obtained results are new and better than those in [1]. Some examples are proposed to illustrate our results.

Second-Order Composed Radial Derivatives of the Benson Proper Perturbation Map for Parametric Multi-Objective Optimization Problems

2020 ◽  
Vol 37 (04) ◽  
pp. 2040011
Author(s):  
Qilin Wang ◽  
Xiaoyan Zhang
Keyword(s):  
Lipschitz Continuity ◽  
Optimization Problems ◽  
Second Order ◽  
Proper Efficiency ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Benson Proper Efficiency ◽  
Perturbation Map ◽  
Derivatives Of ◽  
Cone Convexity

In this paper, we introduce second-order composed radial derivatives of set-valued maps and establish some of its properties. By applying this second-order derivative, we obtain second-order sensitivity results for parametric multi-objective optimization problems under the Benson proper efficiency without assumptions of cone-convexity and Lipschitz continuity. Some of our results improve and derive the recent corresponding ones in the literature.

scholarly journals Second-order neutrosophic boundary-value problem

2021 ◽  
Author(s):  
Sandip Moi ◽  
Suvankar Biswas ◽  
Smita Pal(Sarkar)
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Differential Calculus ◽  
Boundary Value ◽  
Second Order ◽  
Numerical Examples ◽  
Different Types ◽  
First Time

AbstractIn this article, some properties of neutrosophic derivative and neutrosophic numbers have been presented. This properties have been used to develop the neutrosophic differential calculus. By considering different types of first- and second-order derivatives, different kind of systems of derivatives have been developed. This is the first time where a second-order neutrosophic boundary-value problem has been introduced with different types of first- and second-order derivatives. Some numerical examples have been examined to explain different systems of neutrosophic differential equation.

scholarly journals Pioneer Legislation on Second Order of Sexual Harassment: Sociolegal Innovation in Addressing Sexual Harassment

2021 ◽  
Author(s):  
Ana Vidu ◽  
Gema Tomás ◽  
Ramon Flecha
Keyword(s):  
Sexual Harassment ◽  
Women's Studies ◽  
Legal System ◽  
Scientific Evidence ◽  
Second Order ◽  
Bystander Intervention ◽  
Policy Implications ◽  
Women’S Studies ◽  
Key Innovation ◽  
First Time

Abstract Backgroud Countless efforts to combat sexual harassment have been proposed, and for the first time in history, the second order of sexual harassment (SOSH) has been legislated under the term second-order violence (SOV) by a unanimous vote of the Catalan Parliament. Advances in preventing and responding to sexual harassment contribute to highlighting the intervention as being crucial to supporting survivors against retaliation. A lack of support provides a general explanation on why bystanders tend not to intervene and highlights the reality that reprisals are suffered by those who support victims. Methods From the existing knowledge about sexual harassment prevention and response mechanisms, this paper analyzes scientific evidence through a review of the literature published in databases, as well as legislation, reports, and other materials. Results The context that enables SOV legislation is grounded in three realms: (1) bystander intervention and protection, (2) the role of support networks in protecting survivors, and (3) awareness and legislation of SOSH. An active bystander refers to the involvement of someone who is aware of potential sexual harassment situations. Conclusions The lack of legislation against SOSH limits bystander intervention and support; therefore, legislating protection for supporters has become urgent and necessary. Legislating SOSH has great social implications because gender equality cannot be fully achieved if bystander protection is not legally considered. Policy Implications: As no legal system has previously contemplated SOSH, its pioneering parliamentarian approval and establishment by Catalan law constitute a legal key innovation for the field of gender and women’s studies. In fact, evidence reported here are important in developing further regulations and policy. Policy Implications As no legal system has previously contemplated SOSH, its pioneering parliamentarian approval and establishment by Catalan law constitute a legal key innovation for the field of gender and women’s studies. In fact, evidence reported here are important in developing further regulations and policy.

scholarly journals Insight into the Secondary Metabolites of Geum urbanum L. and Geum rivale L. Seeds (Rosaceae)

Plants ◽  
2021 ◽  
Vol 10 (6) ◽  
pp. 1219
Author(s):  
Marek Bunse ◽  
Peter Lorenz ◽  
Florian C. Stintzing ◽  
Dietmar R. Kammerer
Keyword(s):  
Fatty Acids ◽  
Phenolic Compounds ◽  
Unsaturated Fatty Acids ◽  
Asiatic Acid ◽  
Cosmetic Products ◽  
Nutritional Properties ◽  
First Time ◽  
Derivatives Of ◽  
Geum Urbanum ◽  
Insight Into

The present study aimed at the identification and quantitation of phenolic compounds, fatty acids, and further characteristic substances in the seeds of Geum urbanum L. and Geum rivale L. For this purpose, individual components of extracts recovered with MeOH, CH2Cl2, and by cold-pressing, respectively, were characterized by HPLC-DAD/ESI-MSn and GC/MS and compared with reference compounds. For both Geum species, phenolic compounds, such as flavonoids and gallic acid derivatives, and triterpenes, such as saponins and their aglycones, were detected. Surprisingly, both Geum species revealed the presence of derivatives of the triterpenoid aglycons asiatic acid and madecassic acid, which were characterized for the first time in the genus Geum. Furthermore, the fatty acids of both species were characterized by GC–MS after derivatization. Both species showed a promising fatty-acid profile in terms of nutritional properties because of high proportions of unsaturated fatty acids. Linoleic acid and linolenic acid were most abundant, among other compounds such as palmitic acid and stearic acid. In summary, the present study demonstrates the seeds of G. urbanum and G. rivale to be a valuable source of unsaturated fatty acids and bioactive phenolics, which might be exploited for nutritional and cosmetic products and for phytotherapeutic purposes.

scholarly journals Identification of pigments in artworks by inverse tangent derivative of spectrum and a new filtering method

2020 ◽  
Vol 8 (1) ◽  
Author(s):  
F. Fazlali ◽  
S. Gorji Kandi
Keyword(s):  
Reflectance Spectrum ◽  
Practical Method ◽  
Chemical Methods ◽  
Munk Function ◽  
Absorption Of Light ◽  
Spectrophotometric Data ◽  
First Time ◽  
Non Destructive ◽  
Derivatives Of

Abstract Employing an economical and non-destructive method for identifying pigments utilized in artworks is a significant aspect for preserving their antiquity value. One of the non-destructive methods for this purpose is spectrophotometry, which is based on the selected absorption of light. Mathematical descriptive methods such as derivatives of the reflectance spectrum, the Kubelka–Munk function and logarithm have been employed for the characterization of the peak features corresponding to the spectrophotometric data. In the present study, the mentioned mathematical descriptive methods were investigated with the aim to characterize the constituents of an Iranian artwork but were not efficient for the samples. Therefore, inverse tangent derivative equation was developed on spectral data for the first time, providing considerable details in the profile of reflectance curves. In the next part, to have a simpler and more practical method it was suggested to use filters made up of pure pigments. By using these filters and placing them on the samples, imaging was done. Then, images of samples with and without filter were evaluated and pure pigments were distinguished. The mentioned methods were also used to identify pigments in a modern Iranian painting specimen. The results confirmed these methods with reliable answers indicating that physical methods (alongside chemical methods) can also be effective in determining the types of pigments.

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