S. Cazzato, M. G. Izzo, T. Bryk, T. Scopigno, G. Ruocco
Density fluctuations in simple liquids are analysed in the context of three different and widely used formalisms, whose equivalence in the hydrodynamic limit is shown. We, furthermore, address the issue of the dispersion of the propagating modes outside the hydrodynamics, by comparing three different definitions of the generalized sound velocity. The first definition is standard in statistical mechanics. It relates the sound velocity to the imaginary part of the complex conjugate poles of the so-called intermediate scattering function. Other definitions, frequently used in the literature, identify the characteristic frequencies of the inelastic excitations with the maxima of the inelastic features of the dynamic structure factor, or with the maxima of the current function. The behaviour of these three quantities in the hydrodynamic limit is discussed. Deviations from hydrodynamic dispersion law are also considered with particular emphasis given to the analysis of different sound propagation regimes related to different density fluctuations decay channels.
{"title":"Propagating density fluctuations in hydrodynamics and beyond","authors":"S. Cazzato, M. G. Izzo, T. Bryk, T. Scopigno, G. Ruocco","doi":"10.1478/AAPP.98S1A2","DOIUrl":"https://doi.org/10.1478/AAPP.98S1A2","url":null,"abstract":"Density fluctuations in simple liquids are analysed in the context of three different and widely used formalisms, whose equivalence in the hydrodynamic limit is shown. We, furthermore, address the issue of the dispersion of the propagating modes outside the hydrodynamics, by comparing three different definitions of the generalized sound velocity. The first definition is standard in statistical mechanics. It relates the sound velocity to the imaginary part of the complex conjugate poles of the so-called intermediate scattering function. Other definitions, frequently used in the literature, identify the characteristic frequencies of the inelastic excitations with the maxima of the inelastic features of the dynamic structure factor, or with the maxima of the current function. The behaviour of these three quantities in the hydrodynamic limit is discussed. Deviations from hydrodynamic dispersion law are also considered with particular emphasis given to the analysis of different sound propagation regimes related to different density fluctuations decay channels.","PeriodicalId":43431,"journal":{"name":"Atti Accademia Peloritana dei Pericolanti-Classe di Scienze Fisiche Matematiche e Naturali","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44965556","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The aim of this work is to review the main results about the vibrational dynamics of glasses and to clarify the effect induced by changes of the mass density on their thermal properties. In particular, we present the temperature dependence of the specific heat of permanently densified silica glass in comparison to that of crystalline alpha-quartz. We propose a very simple and schematic model to interpret the experimental results.
{"title":"On the Debye-like behaviour of the specific heat of permanently densified silica glass","authors":"G. Baldi, A. Fontana, F. Rossi","doi":"10.1478/AAPP.98S1A3","DOIUrl":"https://doi.org/10.1478/AAPP.98S1A3","url":null,"abstract":"The aim of this work is to review the main results about the vibrational dynamics of glasses and to clarify the effect induced by changes of the mass density on their thermal properties. In particular, we present the temperature dependence of the specific heat of permanently densified silica glass in comparison to that of crystalline alpha-quartz. We propose a very simple and schematic model to interpret the experimental results.","PeriodicalId":43431,"journal":{"name":"Atti Accademia Peloritana dei Pericolanti-Classe di Scienze Fisiche Matematiche e Naturali","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47770738","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The versatile behaviour of poly-vinylbutyral (PVB) and its ability to form quasi-solid polymer electrolytes (SPE) with reliable ionic mobility, has been investigated over the temperature range from 120 K to 350 K, by mechanical and dielectric spectroscopic measurements. Enhancements in the polymer chain flexibility, due to the addition of low molar mass organic liquid plasticizers (acetonitrile, AcN, and methoxy-propionitrile, MPN) favouring the long-range motion of charge carriers, give rise to a room temperature ionic conductivity which in the hybrid PVB/MPN/LiI system increases of about 3 and 9 orders of magnitude with respect to the counterparts PVB/LiI and pure dry-PVB system, respectively. This result proves the existence of coupling between cooperative segmental motion and ion dynamics in such kind of materials.
{"title":"Rising the molecular mobility of polyvinyl butyral by plasticizers: towards energy storage applications","authors":"A. Bartolotta, G. Marco, M. Federico, G. Carini","doi":"10.1478/AAPP.98S1A6","DOIUrl":"https://doi.org/10.1478/AAPP.98S1A6","url":null,"abstract":"The versatile behaviour of poly-vinylbutyral (PVB) and its ability to form quasi-solid polymer electrolytes (SPE) with reliable ionic mobility, has been investigated over the temperature range from 120 K to 350 K, by mechanical and dielectric spectroscopic measurements. Enhancements in the polymer chain flexibility, due to the addition of low molar mass organic liquid plasticizers (acetonitrile, AcN, and methoxy-propionitrile, MPN) favouring the long-range motion of charge carriers, give rise to a room temperature ionic conductivity which in the hybrid PVB/MPN/LiI system increases of about 3 and 9 orders of magnitude with respect to the counterparts PVB/LiI and pure dry-PVB system, respectively. This result proves the existence of coupling between cooperative segmental motion and ion dynamics in such kind of materials.","PeriodicalId":43431,"journal":{"name":"Atti Accademia Peloritana dei Pericolanti-Classe di Scienze Fisiche Matematiche e Naturali","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49368392","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Preface to the AAPP special issue gathering the proceedings of the international workshop on Glasses and Polymers: the Science of Disorder , held in Messina, Italy, on 15-16 November 2018.
2018年11月15日至16日在意大利墨西拿举行的眼镜和聚合物：无序科学国际研讨会的前言。
{"title":"Introducing “Glasses and Polymers: The Science of Disorder”","authors":"G. D’Angelo, U. Wanderlingh, C. Branca","doi":"10.1478/AAPP.98S1E1","DOIUrl":"https://doi.org/10.1478/AAPP.98S1E1","url":null,"abstract":"Preface to the AAPP special issue gathering the proceedings of the international workshop on Glasses and Polymers: the Science of Disorder , held in Messina, Italy, on 15-16 November 2018.","PeriodicalId":43431,"journal":{"name":"Atti Accademia Peloritana dei Pericolanti-Classe di Scienze Fisiche Matematiche e Naturali","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48686816","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The inelastic light scattering of the acoustic vibration of spherical nanoparticles is reviewed. For particles much smaller than the wavelength of the exciting light (λ), with a diameter ( d ) smaller than about 20 nm, the dominant physical mechanism, called Raman, is the polarizability fluctuation due to dipole dipole or bond polarizability induced effects. Only spheroidal modes with l = 0 and l = 2 are Raman active. For particles of size comparable with λ ( d larger than about 100 nm) a different physical mechanism is dominant, the mass displacement and relative polarization associated with the vibration, as for the usual Brillouin scattering of liquid and solids. As the size increases, higher and higher l modes with higher and higher n, the index that labels the radial wavevector, become important and many dozen of peaks appear for d > 500 nm. A simple model allows to reproduce the main features of the observed spectra. A more precise agreement is obtained by a refinement that considers the interaction among the particles in a phononic crystals. The interaction produces broadening and shift of the lines and accounts for the presence of a very low frequency broad band, attributed to the density of states of the modes of the sound propagation in the crystal. The analysis of the spectra allows to obtain information on the dynamics of the single free sphere and on the strength of the interaction. By measuring the temperature-dependence of the Brillouin spectra in clusters of polystyrene nanoparticles during the sintering process, it is possible to identify the glass- transition temperature and calculate the elastic modulus of individual nanoparticles as a function of particle size and chemistry. Surface mobility is evidenced by a size dependence of the interaction among the particles and of the glass transition temperature.
{"title":"Raman and Brillouin scattering of spherical nanoparticles and their clusters","authors":"M. Secchi, M. Montagna","doi":"10.1478/AAPP.98S1A5","DOIUrl":"https://doi.org/10.1478/AAPP.98S1A5","url":null,"abstract":"The inelastic light scattering of the acoustic vibration of spherical nanoparticles is reviewed. For particles much smaller than the wavelength of the exciting light (λ), with a diameter ( d ) smaller than about 20 nm, the dominant physical mechanism, called Raman, is the polarizability fluctuation due to dipole dipole or bond polarizability induced effects. Only spheroidal modes with l = 0 and l = 2 are Raman active. For particles of size comparable with λ ( d larger than about 100 nm) a different physical mechanism is dominant, the mass displacement and relative polarization associated with the vibration, as for the usual Brillouin scattering of liquid and solids. As the size increases, higher and higher l modes with higher and higher n, the index that labels the radial wavevector, become important and many dozen of peaks appear for d > 500 nm. A simple model allows to reproduce the main features of the observed spectra. A more precise agreement is obtained by a refinement that considers the interaction among the particles in a phononic crystals. The interaction produces broadening and shift of the lines and accounts for the presence of a very low frequency broad band, attributed to the density of states of the modes of the sound propagation in the crystal. The analysis of the spectra allows to obtain information on the dynamics of the single free sphere and on the strength of the interaction. By measuring the temperature-dependence of the Brillouin spectra in clusters of polystyrene nanoparticles during the sintering process, it is possible to identify the glass- transition temperature and calculate the elastic modulus of individual nanoparticles as a function of particle size and chemistry. Surface mobility is evidenced by a size dependence of the interaction among the particles and of the glass transition temperature.","PeriodicalId":43431,"journal":{"name":"Atti Accademia Peloritana dei Pericolanti-Classe di Scienze Fisiche Matematiche e Naturali","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47324926","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this work we investigate, from both a macroscopic and a microscopic point of view, the fragility degree of complex material systems. In particular, we integrate a microscopic and a macroscopic approach. The former is formulated in the framework of non-equilibrium thermodynamics in order to obtain the phenomenological equations for the heat flux and viscous pressure tensor, as functions of the absolute temperature T and of the small strain tensor, in the isotropic case, where the shear viscosity is supposed to depend on T g /T . The latter is connected with a macroscopic definition of fragility, operatively introduced by Angell for glass-forming systems, and with the definition of thermal restraint, based on elastic incoherent neutron scattering data. On that score literature data of viscosity, as a function of concentration and temperature, and literature data of elastic intensity data are correlated with the system fragility and with the system thermal restraint. The obtained results are of interest for a wide range of innovative materials, such as, for example, carbon nanotubes and bioprotectant systems.
在这项工作中，我们从宏观和微观的角度研究了复杂材料系统的脆弱程度。特别是，我们结合了微观和宏观的方法。前者是在非平衡热力学的框架下表述的，目的是在各向同性的情况下，得到热流和粘性压力张量的现象学方程，作为绝对温度T和小应变张量的函数，其中剪切粘度应该取决于T g /T。后者与脆性的宏观定义(由Angell为玻璃形成系统引入)以及基于弹性非相干中子散射数据的热约束定义有关。在这一点上，粘度的文献数据作为浓度和温度的函数，弹性强度的文献数据与系统脆弱性和系统热约束相关。获得的结果对广泛的创新材料感兴趣，例如，碳纳米管和生物保护剂系统。
{"title":"On the fragility of complex material systems","authors":"M. T. Caccamo, S. Magazù, L. Restuccia","doi":"10.1478/AAPP.981A4","DOIUrl":"https://doi.org/10.1478/AAPP.981A4","url":null,"abstract":"In this work we investigate, from both a macroscopic and a microscopic point of view, the fragility degree of complex material systems. In particular, we integrate a microscopic and a macroscopic approach. The former is formulated in the framework of non-equilibrium thermodynamics in order to obtain the phenomenological equations for the heat flux and viscous pressure tensor, as functions of the absolute temperature T and of the small strain tensor, in the isotropic case, where the shear viscosity is supposed to depend on T g /T . The latter is connected with a macroscopic definition of fragility, operatively introduced by Angell for glass-forming systems, and with the definition of thermal restraint, based on elastic incoherent neutron scattering data. On that score literature data of viscosity, as a function of concentration and temperature, and literature data of elastic intensity data are correlated with the system fragility and with the system thermal restraint. The obtained results are of interest for a wide range of innovative materials, such as, for example, carbon nanotubes and bioprotectant systems.","PeriodicalId":43431,"journal":{"name":"Atti Accademia Peloritana dei Pericolanti-Classe di Scienze Fisiche Matematiche e Naturali","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2020-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44004674","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The propagation of a computer virus is expressed as a stochastic differential game based on the two-dimensional Kermack-McKendrick model for the spread of epidemics. One optimizer tries to maximize the expected value of a cost function with quadratic control costs, while the other one wants to minimize this expected value. A particular problem is solved explicitly by making use of the method of similarity solutions to obtain the solution to the partial differential equation satisfied by the value function, subject to the appropriate conditions.
{"title":"Computer virus propagation modelled as a stochastic differential game","authors":"M. Lefebvre","doi":"10.1478/AAPP.981A3","DOIUrl":"https://doi.org/10.1478/AAPP.981A3","url":null,"abstract":"The propagation of a computer virus is expressed as a stochastic differential game based on the two-dimensional Kermack-McKendrick model for the spread of epidemics. One optimizer tries to maximize the expected value of a cost function with quadratic control costs, while the other one wants to minimize this expected value. A particular problem is solved explicitly by making use of the method of similarity solutions to obtain the solution to the partial differential equation satisfied by the value function, subject to the appropriate conditions.","PeriodicalId":43431,"journal":{"name":"Atti Accademia Peloritana dei Pericolanti-Classe di Scienze Fisiche Matematiche e Naturali","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2020-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43350059","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
An updated catalogue of the Sicilian species of the weevil subfamily Curculioninae is proposed on the basis of revised bibliographical data and new Sicilian material collected by the authors and other entomologists in the last decades. A total of 167 species is reported with certainty from the main island and surrounding isles, five of them new for Sicily: Anthonomus conspersus (Desbrochers des Loges, 1868), Bradybatus fallax Gerstaecker, 1860, Dorytomus rubrirostris (Gravenhorst, 1807), Gymnetron stimulosum (Germar, 1821) and Tychius longicollis C.N.F. Brisout de Barneville, 1863. Detailed data for Anthonomus incurvus (Panzer, 1795), A. ulmi (DeGeer, 1775), Bradybatus elongatulus (Boheman, 1843), Curculio propinquus (Desbrochers des Loges, 1868), Archarius troglodytes (Jekel, 1861), Derelomus subcostatus Boheman, 1844, Pachytychius discithorax Desbrochers des Loges, 1873, and Sibinia arenariae Stephens, 1831 are quoted for the first time, being these species previously reported generically from Sicily. The presence of 14 taxa formerly indicated from Sicily is considered as doubtful, whereas for other 16 taxa it is excluded.
根据作者和其他昆虫学家在过去几十年中收集的修订后的目录数据和新的西西里材料，提出了一份更新的象甲亚科西西里物种目录。据报道，主岛和周围岛屿共有167种物种，其中5种是西西里岛的新物种：Anthonomus consolesus（Desbrochers des Loges，1868）、Bradybatus fallax Gerstaecker，1860、Dorytomus rubrirostris（Gravenhorst，1807）、Gymnetron stimulosum（Germar，1821）和Tychius longicolis C.N.F.Brisout de Barneville，1863。首次引用了Anthonomus incavus（Panzer，1795）、A.ulmi（DeGeer，1775）、Bradybatus elongatulus（Bohman，1843）、Curculio propincus（Desbrochers des Loges，1868）、Archarius troglodytes（Jekel，1861）、Derelomus subcostatus Bohman（1844）、Pachytychius discithorax Desbrocheers des Loges（1873）和Sibinia arenariae Stephens（1831）的详细数据，这些物种以前一般来自西西里岛。西西里岛以前指示的14个分类群的存在被认为是可疑的，而其他16个分类群则被排除在外。
{"title":"The Curculioninae (Coleoptera: Curculionidae) of Sicily: recent records and updated catalogue","authors":"C. Baviera, R. Caldara","doi":"10.1478/AAPP.981A1","DOIUrl":"https://doi.org/10.1478/AAPP.981A1","url":null,"abstract":"An updated catalogue of the Sicilian species of the weevil subfamily Curculioninae is proposed on the basis of revised bibliographical data and new Sicilian material collected by the authors and other entomologists in the last decades. A total of 167 species is reported with certainty from the main island and surrounding isles, five of them new for Sicily: Anthonomus conspersus (Desbrochers des Loges, 1868), Bradybatus fallax Gerstaecker, 1860, Dorytomus rubrirostris (Gravenhorst, 1807), Gymnetron stimulosum (Germar, 1821) and Tychius longicollis C.N.F. Brisout de Barneville, 1863. Detailed data for Anthonomus incurvus (Panzer, 1795), A. ulmi (DeGeer, 1775), Bradybatus elongatulus (Boheman, 1843), Curculio propinquus (Desbrochers des Loges, 1868), Archarius troglodytes (Jekel, 1861), Derelomus subcostatus Boheman, 1844, Pachytychius discithorax Desbrochers des Loges, 1873, and Sibinia arenariae Stephens, 1831 are quoted for the first time, being these species previously reported generically from Sicily. The presence of 14 taxa formerly indicated from Sicily is considered as doubtful, whereas for other 16 taxa it is excluded.","PeriodicalId":43431,"journal":{"name":"Atti Accademia Peloritana dei Pericolanti-Classe di Scienze Fisiche Matematiche e Naturali","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2020-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41316218","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper examines the consequences of including distributed delays in an energy model. The stability behaviour of the resulting equilibrium for our dynamic system is analysed, including models with Dirac, weak and strong kernels. Applying the Hopf bifurcation theorem we determine conditions under which limit cycle motion is born in such models. The results indicate that distributed delays have an ambivalent impact on the dynamical behaviour of systems, either stabilizing or destabilizing them.
{"title":"Stability and Hopf bifurcation analysis of a distributed time delay energy model for sustainable economic growth","authors":"M. Ferrara, M. Gangemi, L. Guerrini, B. Pansera","doi":"10.1478/AAPP.981A2","DOIUrl":"https://doi.org/10.1478/AAPP.981A2","url":null,"abstract":"This paper examines the consequences of including distributed delays in an energy model. The stability behaviour of the resulting equilibrium for our dynamic system is analysed, including models with Dirac, weak and strong kernels. Applying the Hopf bifurcation theorem we determine conditions under which limit cycle motion is born in such models. The results indicate that distributed delays have an ambivalent impact on the dynamical behaviour of systems, either stabilizing or destabilizing them.","PeriodicalId":43431,"journal":{"name":"Atti Accademia Peloritana dei Pericolanti-Classe di Scienze Fisiche Matematiche e Naturali","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2020-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48821182","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The theory of set-valued mappings has grown with the development of modern variational analysis. It is a key in convex and non-smooth analysis, in game theory, in mathematical economics and in control theory. The concepts of nearness and orthogonality have been known for functions since the pioneering works of Campanato, Birkhoff and James. In a recent paper Barbagallo et al. [J. Math. Anal. Appl., 484 (1), (2020)] a connection between these two concepts has been made. This note is mainly devoted to introduce nearness and orthogonality between set-valued mappings with the goal to study the solvability of generalized equations involving set-valued mappings.
{"title":"SET-VALUED ORTHOGONALITY AND NEARNESS","authors":"A. Barbagallo, Octavian-Emil Ernst, Michel Théra","doi":"10.1478/AAPP.98S2A2","DOIUrl":"https://doi.org/10.1478/AAPP.98S2A2","url":null,"abstract":"The theory of set-valued mappings has grown with the development of modern variational analysis. It is a key in convex and non-smooth analysis, in game theory, in mathematical economics and in control theory. The concepts of nearness and orthogonality have been known for functions since the pioneering works of Campanato, Birkhoff and James. In a recent paper Barbagallo et al. [J. Math. Anal. Appl., 484 (1), (2020)] a connection between these two concepts has been made. This note is mainly devoted to introduce nearness and orthogonality between set-valued mappings with the goal to study the solvability of generalized equations involving set-valued mappings.","PeriodicalId":43431,"journal":{"name":"Atti Accademia Peloritana dei Pericolanti-Classe di Scienze Fisiche Matematiche e Naturali","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2020-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46578199","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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