Pub Date : 2020-11-05DOI: 10.1017/s0963548320000565
P. Lehre, C. Witt
Drift analysis is one of the state-of-the-art techniques for the runtime analysis of randomized search heuristics (RSHs) such as evolutionary algorithms (EAs), simulated annealing, etc. The vast majority of existing drift theorems yield bounds on the expected value of the hitting time for a target state, for example the set of optimal solutions, without making additional statements on the distribution of this time. We address this lack by providing a general drift theorem that includes bounds on the upper and lower tail of the hitting time distribution. The new tail bounds are applied to prove very precise sharp-concentration results on the running time of a simple EA on standard benchmark problems, including the class of general linear functions. On all these problems, the probability of deviating by an r-factor in lower-order terms of the expected time decreases exponentially with r. The usefulness of the theorem outside the theory of RSHs is demonstrated by deriving tail bounds on the number of cycles in random permutations. All these results handle a position-dependent (variable) drift that was not covered by previous drift theorems with tail bounds. Finally, user-friendly specializations of the general drift theorem are given.
{"title":"Tail bounds on hitting times of randomized search heuristics using variable drift analysis","authors":"P. Lehre, C. Witt","doi":"10.1017/s0963548320000565","DOIUrl":"https://doi.org/10.1017/s0963548320000565","url":null,"abstract":"Drift analysis is one of the state-of-the-art techniques for the runtime analysis of randomized search heuristics (RSHs) such as evolutionary algorithms (EAs), simulated annealing, etc. The vast majority of existing drift theorems yield bounds on the expected value of the hitting time for a target state, for example the set of optimal solutions, without making additional statements on the distribution of this time. We address this lack by providing a general drift theorem that includes bounds on the upper and lower tail of the hitting time distribution. The new tail bounds are applied to prove very precise sharp-concentration results on the running time of a simple EA on standard benchmark problems, including the class of general linear functions. On all these problems, the probability of deviating by an r-factor in lower-order terms of the expected time decreases exponentially with r. The usefulness of the theorem outside the theory of RSHs is demonstrated by deriving tail bounds on the number of cycles in random permutations. All these results handle a position-dependent (variable) drift that was not covered by previous drift theorems with tail bounds. Finally, user-friendly specializations of the general drift theorem are given.","PeriodicalId":10513,"journal":{"name":"Combinatorics, Probability & Computing","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2020-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89653627","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-11-04DOI: 10.2174/1877946810666200221122053
Vandana Sukhadia, Rashmi Sharma, Asha Meena
The aim of this research work is to synthesise, study and analyse photocatalytic degradation, kinetics. Copper(II) mustard thio urea complex has been synthesized and characterized through FT-IR, NMR, ESR studies. Photocatalytic degradation of copper(II) mustard thio urea complex was studied in the presence of ZnO as a catalyst in the solution form, using a non polar solvent benzene and a polar solvent methanol with different compositions. Antibacterial activities of copper(II) complex have also been studied against Staphylococcus aureus. O.D. was measured after different time intervals spectrophotometrically to measure the degradation of the complex. Plot of 2+ log O.D. (absorbance) versus time was plotted and found to be linear. The heterogeneous photocatalysis followed pseudo-first-order reaction kinetics. The present study suggests that the CMT complex shows antibacterial activity at different concentrations. The rate of photocatalytic degradation of CMT complex was studied and analyzed. It has been found that the rate of degradation varies with different parameters like the concentration of complex, the amount of catalyst, light intensity, solvent polarity etc. The CMT complex derived from natural mustard oil has shown an inhibitory effect on the growth of S. aureus which may cause skin diseases.
{"title":"Photocatalytic Degradation and Antibacterial Study of Copper(II) Mustard Thiourea Complex","authors":"Vandana Sukhadia, Rashmi Sharma, Asha Meena","doi":"10.2174/1877946810666200221122053","DOIUrl":"https://doi.org/10.2174/1877946810666200221122053","url":null,"abstract":"\u0000\u0000The aim of this research work is to synthesise, study and analyse\u0000photocatalytic degradation, kinetics.\u0000\u0000\u0000\u0000Copper(II) mustard thio urea complex has been synthesized and\u0000characterized through FT-IR, NMR, ESR studies.\u0000\u0000\u0000\u0000Photocatalytic degradation of copper(II) mustard thio urea complex was studied\u0000in the presence of ZnO as a catalyst in the solution form, using a non polar solvent benzene\u0000and a polar solvent methanol with different compositions. Antibacterial activities of\u0000copper(II) complex have also been studied against Staphylococcus aureus.\u0000\u0000\u0000\u0000O.D. was measured after different time intervals spectrophotometrically to\u0000measure the degradation of the complex.\u0000\u0000\u0000\u0000Plot of 2+ log O.D. (absorbance) versus time was plotted and found to be linear.\u0000The heterogeneous photocatalysis followed pseudo-first-order reaction kinetics. The present\u0000study suggests that the CMT complex shows antibacterial activity at different concentrations.\u0000\u0000\u0000\u0000The rate of photocatalytic degradation of CMT complex was studied and analyzed.\u0000It has been found that the rate of degradation varies with different parameters like\u0000the concentration of complex, the amount of catalyst, light intensity, solvent polarity etc.\u0000The CMT complex derived from natural mustard oil has shown an inhibitory effect on the\u0000growth of S. aureus which may cause skin diseases.\u0000","PeriodicalId":10513,"journal":{"name":"Combinatorics, Probability & Computing","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2020-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44898689","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-11-04DOI: 10.2174/1877946809666191011162351
H. Kumar, Tilak Dhanda
Pitting corrosion is a very serious problem for mild steel when it comes in contact with the dilute sulfuric acid medium. Specialized corrosion inhibitors are essentially required to minimize pitting and uniform types of corrosion in mild steel. Most of the corrosion inhibitors discovered so far protects the mild steel from uniform type of corrosion. But pitting corrosion is more fatal than a uniform type of corrosion because it immediately makes mild steel unfit for use as leakage starts from the pit. The objective was to protect the mild steel alloys from pitting corrosion when comes in contact with dilute sulfuric acid by the use of organic corrosion inhibitor. Cetyl Trimethyl Ammonium Bromide (CTAB) is tested as a corrosion inhibitor for mild steel in 0.1 N H2SO4 as corroding medium at 25.0, 30.0 and 35.0°C by weight loss, electrochemical polarization, and Impedance spectroscopy methods. Surface study of corroded and un-corroded specimens of mild steel was carried out by Metallurgical Research Microscopy (MRM) and Scanning Electron Microscopy (SEM) techniques. Surface study confirms that the adsorption of CTAB takes place through nitrogen atom resulting in the formation of uniform, nonporous, passive film confirmed by decrease in Warburg Impedance (Zw), decrease in Faradaic current, increase in Capacitive current, an increase in charge transfer resistance, Rct (41 to 401 Ω cm2) and significant increase in capacitive loop in Nyquist plot with increase in concentration of CTAB which results in significant decrease in corrosion rate of mild steel in 0.1N H2SO4 medium (percentage corrosion inhibition efficiency: 95.0%) especially eradicating pitting type of corrosion. CTAB was proved to be a very good anti-pit agent for mild steel in 0.1N sulfuric acid medium. Pitting and uniform type of corrosion was significantly reduced by the use of CTAB as corrosion inhibitor for mild steel in the dilute sulfuric acid medium at 25.0, 30.0 and 35.0°C.
{"title":"Cetyl Trimethyl Ammonium Bromide as Anti-Pit Agent for Mild Steel in Sulfuric Acid Medium","authors":"H. Kumar, Tilak Dhanda","doi":"10.2174/1877946809666191011162351","DOIUrl":"https://doi.org/10.2174/1877946809666191011162351","url":null,"abstract":"\u0000\u0000Pitting corrosion is a very serious problem for mild steel when it comes in\u0000contact with the dilute sulfuric acid medium. Specialized corrosion inhibitors are essentially\u0000required to minimize pitting and uniform types of corrosion in mild steel.\u0000\u0000\u0000\u0000Most of the corrosion inhibitors discovered so far protects the mild steel from\u0000uniform type of corrosion. But pitting corrosion is more fatal than a uniform type of corrosion\u0000because it immediately makes mild steel unfit for use as leakage starts from the pit.\u0000\u0000\u0000\u0000The objective was to protect the mild steel alloys from pitting corrosion when\u0000comes in contact with dilute sulfuric acid by the use of organic corrosion inhibitor.\u0000\u0000\u0000\u0000 Cetyl Trimethyl Ammonium Bromide (CTAB) is tested as a corrosion inhibitor\u0000for mild steel in 0.1 N H2SO4 as corroding medium at 25.0, 30.0 and 35.0°C by weight\u0000loss, electrochemical polarization, and Impedance spectroscopy methods. Surface study of\u0000corroded and un-corroded specimens of mild steel was carried out by Metallurgical Research\u0000Microscopy (MRM) and Scanning Electron Microscopy (SEM) techniques.\u0000\u0000\u0000\u0000Surface study confirms that the adsorption of CTAB takes place through nitrogen\u0000atom resulting in the formation of uniform, nonporous, passive film confirmed by decrease\u0000in Warburg Impedance (Zw), decrease in Faradaic current, increase in Capacitive current,\u0000an increase in charge transfer resistance, Rct (41 to 401 Ω cm2) and significant increase in\u0000capacitive loop in Nyquist plot with increase in concentration of CTAB which results in\u0000significant decrease in corrosion rate of mild steel in 0.1N H2SO4 medium (percentage corrosion\u0000inhibition efficiency: 95.0%) especially eradicating pitting type of corrosion.\u0000\u0000\u0000\u0000 CTAB was proved to be a very good anti-pit agent for mild steel in 0.1N sulfuric\u0000acid medium. Pitting and uniform type of corrosion was significantly reduced by the\u0000use of CTAB as corrosion inhibitor for mild steel in the dilute sulfuric acid medium at\u000025.0, 30.0 and 35.0°C.\u0000","PeriodicalId":10513,"journal":{"name":"Combinatorics, Probability & Computing","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2020-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2174/1877946809666191011162351","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41293755","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-11-04DOI: 10.2174/1877946809666191115120147
D. Rajaniverma, D. J. Rao, S. R. Begum, V. Seetaramaiah, Yajjala Ramakrishna, Poonam Tondon, K. Thangavel
Non-Covalent Interactions (NCIs) play a vital role in the chemical process. Certain Experimental and theoretical approaches provide information about the stronger and weaker interactions. In the present work, we have implemented Hirshfeld charges based surface mapping to find the weaker interactions between the molecules of busulfan. The main objective of this work is to recognize the non-covalent interactions which are not simply drawn from the experimental and conventional theoretical approach. It aims to provide more insightful information into the crystallographic structure. In the present work, we have implemented a Hirshfeld surface mapping which incorporates periodic boundary conditions of the crystalline geometry. Each point of the isosurface is defined by two distances i.e. de, the distance from the point to the nearest atom outside to the surface and di, the distance to the nearest atom inside the surface. Also, for precise identification of intermolecular interactions, mapping by normalized contact distance dnorm is also considered. Fingerprint plot di vs de for various types of interactions were also provided. The Hirshfeld surface and fingerprint plot show the very weak H···H interactions in addition to the O···H interactions. This enables the visualization of very weak interactions. This proposed work on Hirschfeld surface analysis accounts for the solidstate environment of the busulfan, crystallographic parameters and packing information. Hence, the interactions obtained for monomer and extended molecular framework in this work are more reliable to study the intermolecular interactions. The 2D finger print plots revealed the predominant O⋅⋅⋅H interactions within the crystal packing. In addition to O⋅⋅⋅H interactions, H⋅⋅⋅H interaction were also identified.
{"title":"Molecular Interactions within the Crystal Packing of Busulfan (DNA Cross-Linking Agent) by Hirshfeld Surface Analysis","authors":"D. Rajaniverma, D. J. Rao, S. R. Begum, V. Seetaramaiah, Yajjala Ramakrishna, Poonam Tondon, K. Thangavel","doi":"10.2174/1877946809666191115120147","DOIUrl":"https://doi.org/10.2174/1877946809666191115120147","url":null,"abstract":"\u0000\u0000Non-Covalent Interactions (NCIs) play a vital role in the chemical\u0000process. Certain Experimental and theoretical approaches provide information about the\u0000stronger and weaker interactions. In the present work, we have implemented Hirshfeld\u0000charges based surface mapping to find the weaker interactions between the molecules of\u0000busulfan.\u0000\u0000\u0000\u0000The main objective of this work is to recognize the non-covalent interactions\u0000which are not simply drawn from the experimental and conventional theoretical approach.\u0000It aims to provide more insightful information into the crystallographic structure.\u0000\u0000\u0000\u0000In the present work, we have implemented a Hirshfeld surface mapping which\u0000incorporates periodic boundary conditions of the crystalline geometry. Each point of the\u0000isosurface is defined by two distances i.e. de, the distance from the point to the nearest atom\u0000outside to the surface and di, the distance to the nearest atom inside the surface. Also,\u0000for precise identification of intermolecular interactions, mapping by normalized contact\u0000distance dnorm is also considered. Fingerprint plot di vs de for various types of interactions\u0000were also provided.\u0000\u0000\u0000\u0000The Hirshfeld surface and fingerprint plot show the very weak H···H interactions in\u0000addition to the O···H interactions. This enables the visualization of very weak interactions.\u0000\u0000\u0000\u0000 This proposed work on Hirschfeld surface analysis accounts for the solidstate\u0000environment of the busulfan, crystallographic parameters and packing information.\u0000Hence, the interactions obtained for monomer and extended molecular framework in this\u0000work are more reliable to study the intermolecular interactions. The 2D finger print plots\u0000revealed the predominant O⋅⋅⋅H interactions within the crystal packing. In addition to O⋅⋅⋅H\u0000interactions, H⋅⋅⋅H interaction were also identified.\u0000","PeriodicalId":10513,"journal":{"name":"Combinatorics, Probability & Computing","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2020-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2174/1877946809666191115120147","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42180930","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Understanding the interaction between different organic dyes and carbon quantum dots helps us to understand several photo physical processes like electron transfer, energy transfer, molecular sensing, drug delivery and dye degradation processes etc. The primary objective of this study is to whether the carbon quantum dots can act as an electron donor and can participate in the different photo physical processes. In this work, Carbon Quantum Dots (CQDLs) are synthesized in most economical and simple carbonization method where petals of Nelumbo nucifera L. are used as a carbon precursor. The synthesized CQDLs were characterized by using experimental techniques like UV−Vis absorption, FT-IR, Transmission Electron Microscopy (TEM), steadystate and time-resolved fluorescence spectroscopy. The spectral analysis shows that the so synthesized CQDLs are spherical in shape and its diameter is around 4.2 nm. It shows the fluorescence emission maximum at 495 nm with a quantum yield of 4%. In this work the interaction between Carbon Quantum Dots (CQDLs) and an organic dye Malachite Green (MG) is studied using fluorescence spectroscopic technique under ambient pH condition (At pH 7). The quenching mechanism of CQDLs with MG was investigated using Stern-Volmer equation and time-resolved fluorescence lifetime studies. The results show that the dominant process of fluorescence quenching is attributed to Forster Resonance Energy Transfer (FRET) having a donor acceptor distance of 53 Å where CQDLs act as a donor and MG acts as an acceptor. This work has a consequence that CQDLs can be used as a donor species for different photo physical processes such as photovoltaic cell, dye sensitized solar cell, and also for antioxidant activity study.
{"title":"FRET Study Between Carbon Quantum Dots and Malachite Green by Steady-State and Time-Resolved Fluorescence Spectroscopy","authors":"Bipin Rooj, Ankita Dutta, Debojyoti Mukherjee, Sahidul Islam, Ujjwal Mandal","doi":"10.2174/1877946809666191114143123","DOIUrl":"https://doi.org/10.2174/1877946809666191114143123","url":null,"abstract":"\u0000\u0000Understanding the interaction between different organic dyes and\u0000carbon quantum dots helps us to understand several photo physical processes like electron\u0000transfer, energy transfer, molecular sensing, drug delivery and dye degradation processes\u0000etc.\u0000\u0000\u0000\u0000The primary objective of this study is to whether the carbon quantum dots can\u0000act as an electron donor and can participate in the different photo physical processes.\u0000\u0000\u0000\u0000In this work, Carbon Quantum Dots (CQDLs) are synthesized in most economical\u0000and simple carbonization method where petals of Nelumbo nucifera L. are used as a\u0000carbon precursor. The synthesized CQDLs were characterized by using experimental techniques\u0000like UV−Vis absorption, FT-IR, Transmission Electron Microscopy (TEM), steadystate\u0000and time-resolved fluorescence spectroscopy.\u0000\u0000\u0000\u0000The spectral analysis shows that the so synthesized CQDLs are spherical in shape\u0000and its diameter is around 4.2 nm. It shows the fluorescence emission maximum at 495 nm\u0000with a quantum yield of 4%. In this work the interaction between Carbon Quantum Dots\u0000(CQDLs) and an organic dye Malachite Green (MG) is studied using fluorescence spectroscopic\u0000technique under ambient pH condition (At pH 7). The quenching mechanism of\u0000CQDLs with MG was investigated using Stern-Volmer equation and time-resolved fluorescence\u0000lifetime studies. The results show that the dominant process of fluorescence\u0000quenching is attributed to Forster Resonance Energy Transfer (FRET) having a donor acceptor\u0000distance of 53 Å where CQDLs act as a donor and MG acts as an acceptor.\u0000\u0000\u0000\u0000This work has a consequence that CQDLs can be used as a donor species for\u0000different photo physical processes such as photovoltaic cell, dye sensitized solar cell, and\u0000also for antioxidant activity study.\u0000","PeriodicalId":10513,"journal":{"name":"Combinatorics, Probability & Computing","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2020-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2174/1877946809666191114143123","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48483537","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-11-04DOI: 10.2174/1877946810666200212094533
V. Padmanabhan, M. Madhu, S. M. Hariharan
To study the temperature stability of TGS doped with ZnSO4, CdCl2, BaCl2, and compare it with that of pure TGS. Synthesizing pure and doped TGS and studying their temperature dependence using TGA, DTA, and DSC analysis. Slow cooling solution growth was used to grow single crystals of pure and doped TGS. The TGA, DTA and DSC analysis was conducted for determining the temperature stability. The thermal analysis of pure and doped TGS shows that the doped samples show a similar dependence on temperature as pure TGS. The temperature of decomposition of pure and doped samples (BTGS, ZTGS, CdTGS) was 226.60°C, 228.38°C, 229.13°C, and 239.13°C respectively. The melting onset of these samples was 214.51°C, 216.04°C, 217.69°C and 216.04°C respectively. The study shows that doping TGS with the above three described materials did not alter their temperature stability considerably. It is a good result as doping TGS, for varying its characteristics like absorbance, reflectance, bandgap energy, etc., which did not alter its temperature stability. Therefore, TGS doped with the above three dopants can be used at the same temperature ranges as of pure TGS but with much-improved efficiency.
{"title":"Studies on the Temperature Stability of Pure and Doped Triglycine Sulphate Crystals Using TGA/DTA","authors":"V. Padmanabhan, M. Madhu, S. M. Hariharan","doi":"10.2174/1877946810666200212094533","DOIUrl":"https://doi.org/10.2174/1877946810666200212094533","url":null,"abstract":"\u0000\u0000To study the temperature stability of TGS doped with ZnSO4, CdCl2,\u0000BaCl2, and compare it with that of pure TGS.\u0000\u0000\u0000\u0000 Synthesizing pure and doped TGS and studying their temperature dependence\u0000using TGA, DTA, and DSC analysis.\u0000\u0000\u0000\u0000Slow cooling solution growth was used to grow single crystals of pure and\u0000doped TGS. The TGA, DTA and DSC analysis was conducted for determining the temperature\u0000stability.\u0000\u0000\u0000\u0000 The thermal analysis of pure and doped TGS shows that the doped samples show\u0000a similar dependence on temperature as pure TGS. The temperature of decomposition of\u0000pure and doped samples (BTGS, ZTGS, CdTGS) was 226.60°C, 228.38°C, 229.13°C, and\u0000239.13°C respectively. The melting onset of these samples was 214.51°C, 216.04°C,\u0000217.69°C and 216.04°C respectively.\u0000\u0000\u0000\u0000The study shows that doping TGS with the above three described materials\u0000did not alter their temperature stability considerably. It is a good result as doping TGS, for\u0000varying its characteristics like absorbance, reflectance, bandgap energy, etc., which did not\u0000alter its temperature stability. Therefore, TGS doped with the above three dopants can be\u0000used at the same temperature ranges as of pure TGS but with much-improved efficiency.\u0000","PeriodicalId":10513,"journal":{"name":"Combinatorics, Probability & Computing","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2020-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41831628","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-11-04DOI: 10.2174/1877946809666191129110018
M. G. Gomes, N. Rocha, A. A. Moura, Nadine P. Merlo, Moilton R. Franco Júnior, P. O. Rodrigues
The liquid molar volume (V) and the heat of vaporization (ΔHVAP) of four fatty acids (n-Heptanoic acid, Hexadecanoic acid, n-Hexanoic acid and n- Dodecanoic acid) have been estimated. This paper aims to calculate the liquid molar volume and the heat of vaporization of four fatty acids under the critical point using two traditional equations of state: Peng-Robinson (PR) [21] and Soave-Redlich-Kwong. The area rules method applicable to obtaining the saturation pressure of the compounds has been used. The properties of the acids investigated in this work have been compared with those provided by literature. For molar volumes, the equations of state have given improved predictions when compared to traditional equations such as Rackett equation and so on. According to the vapor enthalpy calculations, no reference value was required. In general, the Clausius-Clapeyron equation provides a better estimation of the vaporization enthalpy of fatty acids when Soave-Redlich-Kwong (SRK) equation was used. The heat of vaporization for fatty acids can be calculated with good reliability in comparison with the Watson equation if suitable equation of state is used. Accurate results for heat of vaporization can be reached in comparison with the Watson equation if the reliable equation of state is used.
{"title":"Prediction of Liquid Molar Volume and Heat of Vaporization of Fatty Acids Using an Equation of State","authors":"M. G. Gomes, N. Rocha, A. A. Moura, Nadine P. Merlo, Moilton R. Franco Júnior, P. O. Rodrigues","doi":"10.2174/1877946809666191129110018","DOIUrl":"https://doi.org/10.2174/1877946809666191129110018","url":null,"abstract":"\u0000\u0000The liquid molar volume (V) and the heat of vaporization (ΔHVAP) of four fatty acids (n-Heptanoic acid, Hexadecanoic acid, n-Hexanoic acid and n-\u0000Dodecanoic acid) have been estimated.\u0000\u0000\u0000\u0000This paper aims to calculate the liquid molar volume and the heat of vaporization\u0000of four fatty acids under the critical point using two traditional equations of state:\u0000Peng-Robinson (PR) [21] and Soave-Redlich-Kwong.\u0000\u0000\u0000\u0000The area rules method applicable to obtaining the saturation pressure of the\u0000compounds has been used. The properties of the acids investigated in this work have been\u0000compared with those provided by literature. For molar volumes, the equations of state have\u0000given improved predictions when compared to traditional equations such as Rackett equation\u0000and so on. According to the vapor enthalpy calculations, no reference value was required.\u0000\u0000\u0000\u0000 In general, the Clausius-Clapeyron equation provides a better estimation of the\u0000vaporization enthalpy of fatty acids when Soave-Redlich-Kwong (SRK) equation was\u0000used. The heat of vaporization for fatty acids can be calculated with good reliability in\u0000comparison with the Watson equation if suitable equation of state is used.\u0000\u0000\u0000\u0000Accurate results for heat of vaporization can be reached in comparison with\u0000the Watson equation if the reliable equation of state is used.\u0000","PeriodicalId":10513,"journal":{"name":"Combinatorics, Probability & Computing","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2020-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46020516","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-11-03DOI: 10.1017/s0963548321000511
Vishesh Jain, A. Sah, Mehtaab Sawhney
We show that for an $ntimes n$ random symmetric matrix $A_n$ , whose entries on and above the diagonal are independent copies of a sub-Gaussian random variable $xi$ with mean 0 and variance 1, begin{equation*}mathbb{P}[s_n(A_n) le epsilon/sqrt{n}] le O_{xi}(epsilon^{1/8} + exp(!-Omega_{xi}(n^{1/2}))) quad text{for all } epsilon ge 0.end{equation*} This improves a result of Vershynin, who obtained such a bound with $n^{1/2}$ replaced by $n^{c}$ for a small constant c, and $1/8$ replaced by $(1/8) - eta$ (with implicit constants also depending on $eta > 0$ ). Furthermore, when $xi$ is a Rademacher random variable, we prove that begin{equation*}mathbb{P}[s_n(A_n) le epsilon/sqrt{n}] le O(epsilon^{1/8} + exp(!-Omega((!log{n})^{1/4}n^{1/2}))) quad text{for all } epsilon ge 0.end{equation*} The special case $epsilon = 0$ improves a recent result of Campos, Mattos, Morris, and Morrison, which showed that $mathbb{P}[s_n(A_n) = 0] le O(exp(!-Omega(n^{1/2}))).$ Notably, in a departure from the previous two best bounds on the probability of singularity of symmetric matrices, which had relied on somewhat specialized and involved combinatorial techniques, our methods fall squarely within the broad geometric framework pioneered by Rudelson and Vershynin, and suggest the possibility of a principled geometric approach to the study of the singular spectrum of symmetric random matrices. The main innovations in our work are new notions of arithmetic structure – the Median Regularized Least Common Denominator (MRLCD) and the Median Threshold, which are natural refinements of the Regularized Least Common Denominator (RLCD)introduced by Vershynin, and should be more generally useful in contexts where one needs to combine anticoncentration information of different parts of a vector.
我们表明，对于$ntimes n$随机对称矩阵$A_n$，其对角线上和上面的条目是亚高斯随机变量$xi$的独立副本，平均值为0，方差为1,begin{equation*}mathbb{P}[s_n(A_n) le epsilon/sqrt{n}] le O_{xi}(epsilon^{1/8} + exp(!-Omega_{xi}(n^{1/2}))) quad text{for all } epsilon ge 0.end{equation*}，这改进了Vershynin的结果，Vershynin得到了这样一个界，$n^{1/2}$被$n^{c}$代替了一个小常数c，并将$1/8$替换为$(1/8) - eta$(隐式常数也取决于$eta > 0$)。此外，当$xi$是Rademacher随机变量时，我们证明begin{equation*}mathbb{P}[s_n(A_n) le epsilon/sqrt{n}] le O(epsilon^{1/8} + exp(!-Omega((!log{n})^{1/4}n^{1/2}))) quad text{for all } epsilon ge 0.end{equation*}特殊情况$epsilon = 0$改进了Campos, Mattos, Morris和Morrison最近的结果，该结果表明$mathbb{P}[s_n(A_n) = 0] le O(exp(!-Omega(n^{1/2}))).$值得注意的是，与前两个关于对称矩阵奇点概率的最佳边界不同，这依赖于一些专门的和涉及组合技术，我们的方法完全符合Rudelson和Vershynin开创的广泛几何框架，并提出了一种研究对称随机矩阵奇异谱的原则性几何方法的可能性。我们工作中的主要创新是算法结构的新概念-中位数正则化最小公分母(MRLCD)和中位数阈值，它们是Vershynin引入的正则化最小公分母(RLCD)的自然改进，在需要组合向量不同部分的反集中信息的情况下应该更普遍有用。
{"title":"On the smallest singular value of symmetric random matrices","authors":"Vishesh Jain, A. Sah, Mehtaab Sawhney","doi":"10.1017/s0963548321000511","DOIUrl":"https://doi.org/10.1017/s0963548321000511","url":null,"abstract":"\u0000 We show that for an \u0000 \u0000 \u0000 \u0000$ntimes n$\u0000\u0000 \u0000 random symmetric matrix \u0000 \u0000 \u0000 \u0000$A_n$\u0000\u0000 \u0000 , whose entries on and above the diagonal are independent copies of a sub-Gaussian random variable \u0000 \u0000 \u0000 \u0000$xi$\u0000\u0000 \u0000 with mean 0 and variance 1, \u0000 \u0000 \u0000 \u0000begin{equation*}mathbb{P}[s_n(A_n) le epsilon/sqrt{n}] le O_{xi}(epsilon^{1/8} + exp(!-Omega_{xi}(n^{1/2}))) quad text{for all } epsilon ge 0.end{equation*}\u0000\u0000 \u0000 This improves a result of Vershynin, who obtained such a bound with \u0000 \u0000 \u0000 \u0000$n^{1/2}$\u0000\u0000 \u0000 replaced by \u0000 \u0000 \u0000 \u0000$n^{c}$\u0000\u0000 \u0000 for a small constant c, and \u0000 \u0000 \u0000 \u0000$1/8$\u0000\u0000 \u0000 replaced by \u0000 \u0000 \u0000 \u0000$(1/8) - eta$\u0000\u0000 \u0000 (with implicit constants also depending on \u0000 \u0000 \u0000 \u0000$eta > 0$\u0000\u0000 \u0000 ). Furthermore, when \u0000 \u0000 \u0000 \u0000$xi$\u0000\u0000 \u0000 is a Rademacher random variable, we prove that \u0000 \u0000 \u0000 \u0000begin{equation*}mathbb{P}[s_n(A_n) le epsilon/sqrt{n}] le O(epsilon^{1/8} + exp(!-Omega((!log{n})^{1/4}n^{1/2}))) quad text{for all } epsilon ge 0.end{equation*}\u0000\u0000 \u0000 The special case \u0000 \u0000 \u0000 \u0000$epsilon = 0$\u0000\u0000 \u0000 improves a recent result of Campos, Mattos, Morris, and Morrison, which showed that \u0000 \u0000 \u0000 \u0000$mathbb{P}[s_n(A_n) = 0] le O(exp(!-Omega(n^{1/2}))).$\u0000\u0000 \u0000 Notably, in a departure from the previous two best bounds on the probability of singularity of symmetric matrices, which had relied on somewhat specialized and involved combinatorial techniques, our methods fall squarely within the broad geometric framework pioneered by Rudelson and Vershynin, and suggest the possibility of a principled geometric approach to the study of the singular spectrum of symmetric random matrices. The main innovations in our work are new notions of arithmetic structure – the Median Regularized Least Common Denominator (MRLCD) and the Median Threshold, which are natural refinements of the Regularized Least Common Denominator (RLCD)introduced by Vershynin, and should be more generally useful in contexts where one needs to combine anticoncentration information of different parts of a vector.","PeriodicalId":10513,"journal":{"name":"Combinatorics, Probability & Computing","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2020-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74117595","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-11-02DOI: 10.1017/S0963548321000146
Asaf Ferber, Matthew Kwan, Lisa Sauermann
Consider a random $ntimes n$ zero-one matrix with ‘sparsity’ p, sampled according to one of the following two models: either every entry is independently taken to be one with probability p (the ‘Bernoulli’ model) or each row is independently uniformly sampled from the set of all length-n zero-one vectors with exactly pn ones (the ‘combinatorial’ model). We give simple proofs of the (essentially best-possible) fact that in both models, if $min(p,1-p)geq (1+varepsilon)log n/n$ for any constant $varepsilon>0$ , then our random matrix is nonsingular with probability $1-o(1)$ . In the Bernoulli model, this fact was already well known, but in the combinatorial model this resolves a conjecture of Aigner-Horev and Person.
{"title":"Singularity of sparse random matrices: simple proofs","authors":"Asaf Ferber, Matthew Kwan, Lisa Sauermann","doi":"10.1017/S0963548321000146","DOIUrl":"https://doi.org/10.1017/S0963548321000146","url":null,"abstract":"\u0000 Consider a random \u0000 \u0000 \u0000 $ntimes n$\u0000 \u0000 zero-one matrix with ‘sparsity’ p, sampled according to one of the following two models: either every entry is independently taken to be one with probability p (the ‘Bernoulli’ model) or each row is independently uniformly sampled from the set of all length-n zero-one vectors with exactly pn ones (the ‘combinatorial’ model). We give simple proofs of the (essentially best-possible) fact that in both models, if \u0000 \u0000 \u0000 $min(p,1-p)geq (1+varepsilon)log n/n$\u0000 \u0000 for any constant \u0000 \u0000 \u0000 $varepsilon>0$\u0000 \u0000 , then our random matrix is nonsingular with probability \u0000 \u0000 \u0000 $1-o(1)$\u0000 \u0000 . In the Bernoulli model, this fact was already well known, but in the combinatorial model this resolves a conjecture of Aigner-Horev and Person.","PeriodicalId":10513,"journal":{"name":"Combinatorics, Probability & Computing","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2020-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75218824","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Г.М. Наурзбаева, Ш.Т. Сұлтахан, М. Нажипкызы, Дж.Р. Митчелл
Соңғы жылдары аддитивті өндіріс (АӨ) деп аталатын 3D-басып шығару әдістері өнеркәсіптік өндіріс және прототиптеу салаларында дәстүрлі қолданулар шеңберінен асып шықты. Бұл мақалада энергия сыйымды (энергетикалық) материалдарға қысқаша шолу жасалады, сондай-ақ аддитивті өндіріс технологиялары үшін жиі қолданылатын материалдарға қысқаша талқылау берілді. Эксперимент барысында біз 3D басып шығару ыңғайлы энергия сыйымды материал термит алынды, ал байланыстырғыш ретінде нитроцеллюлоза таңдалынды. TERRA әмбебап бағдарламасы арқылы газдандыру үрдістеріне термодинамикалық талдау жүргізілді. Сонымен қатар, әр түрлі қатынастағы энергия сыйымды материалдар зерттелді. Біздің мақсатымыз 3D басып шығаруға лайықты энергия сыйымдылығы жоғары материалды таңдау.
{"title":"3D басып шығару материалдары: энергия сыйымды материалдарды таңдау","authors":"Г.М. Наурзбаева, Ш.Т. Сұлтахан, М. Нажипкызы, Дж.Р. Митчелл","doi":"10.18321/CPC354","DOIUrl":"https://doi.org/10.18321/CPC354","url":null,"abstract":"Соңғы жылдары аддитивті өндіріс (АӨ) деп аталатын 3D-басып шығару әдістері өнеркәсіптік өндіріс және прототиптеу салаларында дәстүрлі қолданулар шеңберінен асып шықты. Бұл мақалада энергия сыйымды (энергетикалық) материалдарға қысқаша шолу жасалады, сондай-ақ аддитивті өндіріс технологиялары үшін жиі қолданылатын материалдарға қысқаша талқылау берілді. Эксперимент барысында біз 3D басып шығару ыңғайлы энергия сыйымды материал термит алынды, ал байланыстырғыш ретінде нитроцеллюлоза таңдалынды. TERRA әмбебап бағдарламасы арқылы газдандыру үрдістеріне термодинамикалық талдау жүргізілді. Сонымен қатар, әр түрлі қатынастағы энергия сыйымды материалдар зерттелді. Біздің мақсатымыз 3D басып шығаруға лайықты энергия сыйымдылығы жоғары материалды таңдау.","PeriodicalId":10513,"journal":{"name":"Combinatorics, Probability & Computing","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2020-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47661830","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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