Pub Date : 2021-02-24DOI: 10.2174/1877946810999200831101239
H. Sharma, Y. Sharma
Thermoelectric material with high performance and low cost is the basic need of today. Bismuth selenide is a thermoelectric material. A set of bismuth selenide thin films having different stoichiometry ratios varying Bi/Se ratio from 0.123 to 0.309 have been prepared. The present work deals with the synthesis and characterization of various thin films of bismuth selenide. The thermoelectric properties of thin films were also investigated. The aim of this work is to investigate the effect of composition ratio on the structural and thermoelectric properties and to find out the best stoichiometry ratio of bismuth selenide thin films that can be used in the application of thermoelectric devices. A set of bismuth selenide thin films having different elemental compositions were prepared by employing the thermal evaporation technique. The crystal structure and elemental composition of thin films were investigated by XRD and EDAX, respectively. The roughness of films was analyzed by AFM. The thermoelectric properties of various thin films were also measured. XRD spectrum confirms the formation of phases formed in thin films which slightly matched with standard data. AFM results indicated that the surface of films was smooth and nanoparticles were generated on the surface. AFM results indicated that the surfaces of annealed thin films were smoother than as-deposited thin films. Seebeck coefficient was found negative throughout the temperature range. The power factor was also calculated by the Seebeck coefficient and results revealed the effect of composition ratio on Seebeck coefficient, electrical conductivity, and power factor. Thin films having a composition ratio of 0.182 exhibited the highest power factor. This study provides relevant basic information on the thermoelectric property of thin films, as well as presents the effect of compositional variation on thermoelectric measurements. From the application point of view in the thermoelectric devices, the best stoichiometric thin films out of four prepared thin films have been presented.
{"title":"Investigation of Structural and Thermoelectric Properties of Bismuth Selenide Thin Films","authors":"H. Sharma, Y. Sharma","doi":"10.2174/1877946810999200831101239","DOIUrl":"https://doi.org/10.2174/1877946810999200831101239","url":null,"abstract":"\u0000\u0000Thermoelectric material with high performance and low cost is\u0000the basic need of today. Bismuth selenide is a thermoelectric material. A set of bismuth\u0000selenide thin films having different stoichiometry ratios varying Bi/Se ratio from 0.123 to\u00000.309 have been prepared.\u0000\u0000\u0000\u0000The present work deals with the synthesis and characterization of various thin\u0000films of bismuth selenide. The thermoelectric properties of thin films were also investigated.\u0000The aim of this work is to investigate the effect of composition ratio on the structural\u0000and thermoelectric properties and to find out the best stoichiometry ratio of bismuth selenide\u0000thin films that can be used in the application of thermoelectric devices.\u0000\u0000\u0000\u0000A set of bismuth selenide thin films having different elemental compositions\u0000were prepared by employing the thermal evaporation technique. The crystal structure and\u0000elemental composition of thin films were investigated by XRD and EDAX, respectively.\u0000The roughness of films was analyzed by AFM. The thermoelectric properties of various\u0000thin films were also measured.\u0000\u0000\u0000\u0000XRD spectrum confirms the formation of phases formed in thin films which\u0000slightly matched with standard data. AFM results indicated that the surface of films was\u0000smooth and nanoparticles were generated on the surface. AFM results indicated that the\u0000surfaces of annealed thin films were smoother than as-deposited thin films. Seebeck coefficient\u0000was found negative throughout the temperature range. The power factor was also\u0000calculated by the Seebeck coefficient and results revealed the effect of composition ratio\u0000on Seebeck coefficient, electrical conductivity, and power factor. Thin films having a\u0000composition ratio of 0.182 exhibited the highest power factor.\u0000\u0000\u0000\u0000This study provides relevant basic information on the thermoelectric property\u0000of thin films, as well as presents the effect of compositional variation on thermoelectric\u0000measurements. From the application point of view in the thermoelectric devices, the best\u0000stoichiometric thin films out of four prepared thin films have been presented.\u0000","PeriodicalId":10513,"journal":{"name":"Combinatorics, Probability & Computing","volume":"11 1","pages":"58-68"},"PeriodicalIF":0.9,"publicationDate":"2021-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48930853","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 : 2021-02-19DOI: 10.1017/S096354832200030X
James Foster, Karen Habermann
We study approximations for the Lévy area of Brownian motion which are based on the Fourier series expansion and a polynomial expansion of the associated Brownian bridge. Comparing the asymptotic convergence rates of the Lévy area approximations, we see that the approximation resulting from the polynomial expansion of the Brownian bridge is more accurate than the Kloeden–Platen–Wright approximation, whilst still only using independent normal random vectors. We then link the asymptotic convergence rates of these approximations to the limiting fluctuations for the corresponding series expansions of the Brownian bridge. Moreover, and of interest in its own right, the analysis we use to identify the fluctuation processes for the Karhunen–Loève and Fourier series expansions of the Brownian bridge is extended to give a stand-alone derivation of the values of the Riemann zeta function at even positive integers.
{"title":"Brownian bridge expansions for Lévy area approximations and particular values of the Riemann zeta function","authors":"James Foster, Karen Habermann","doi":"10.1017/S096354832200030X","DOIUrl":"https://doi.org/10.1017/S096354832200030X","url":null,"abstract":"\u0000 We study approximations for the Lévy area of Brownian motion which are based on the Fourier series expansion and a polynomial expansion of the associated Brownian bridge. Comparing the asymptotic convergence rates of the Lévy area approximations, we see that the approximation resulting from the polynomial expansion of the Brownian bridge is more accurate than the Kloeden–Platen–Wright approximation, whilst still only using independent normal random vectors. We then link the asymptotic convergence rates of these approximations to the limiting fluctuations for the corresponding series expansions of the Brownian bridge. Moreover, and of interest in its own right, the analysis we use to identify the fluctuation processes for the Karhunen–Loève and Fourier series expansions of the Brownian bridge is extended to give a stand-alone derivation of the values of the Riemann zeta function at even positive integers.","PeriodicalId":10513,"journal":{"name":"Combinatorics, Probability & Computing","volume":"11 1","pages":"370-397"},"PeriodicalIF":0.9,"publicationDate":"2021-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84253468","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 : 2021-02-10DOI: 10.1017/S0963548322000050
Freddie Illingworth
The classical Andrásfai-Erdős-Sós theorem considers the chromatic number of $K_{r + 1}$ -free graphs with large minimum degree, and in the case, $r = 2$ says that any n-vertex triangle-free graph with minimum degree greater than $2/5 cdot n$ is bipartite. This began the study of the chromatic profile of triangle-free graphs: for each k, what minimum degree guarantees that a triangle-free graph is k-colourable? The chromatic profile has been extensively studied and was finally determined by Brandt and Thomassé. Triangle-free graphs are exactly those in which each neighbourhood is one-colourable. As a natural variant, Luczak and Thomassé introduced the notion of a locally bipartite graph in which each neighbourhood is 2-colourable. Here we study the chromatic profile of the family of graphs in which every neighbourhood is b-colourable (locally b-partite graphs) as well as the family where the common neighbourhood of every a-clique is b-colourable. Our results include the chromatic thresholds of these families (extending a result of Allen, Böttcher, Griffiths, Kohayakawa and Morris) as well as showing that every n-vertex locally b-partite graph with minimum degree greater than $(1 - 1/(b + 1/7)) cdot n$ is $(b + 1)$ -colourable. Understanding these locally colourable graphs is crucial for extending the Andrásfai-Erdős-Sós theorem to non-complete graphs, which we develop elsewhere.
{"title":"The chromatic profile of locally colourable graphs","authors":"Freddie Illingworth","doi":"10.1017/S0963548322000050","DOIUrl":"https://doi.org/10.1017/S0963548322000050","url":null,"abstract":"\u0000 The classical Andrásfai-Erdős-Sós theorem considers the chromatic number of \u0000 \u0000 \u0000 \u0000$K_{r + 1}$\u0000\u0000 \u0000 -free graphs with large minimum degree, and in the case, \u0000 \u0000 \u0000 \u0000$r = 2$\u0000\u0000 \u0000 says that any n-vertex triangle-free graph with minimum degree greater than \u0000 \u0000 \u0000 \u0000$2/5 cdot n$\u0000\u0000 \u0000 is bipartite. This began the study of the chromatic profile of triangle-free graphs: for each k, what minimum degree guarantees that a triangle-free graph is k-colourable? The chromatic profile has been extensively studied and was finally determined by Brandt and Thomassé. Triangle-free graphs are exactly those in which each neighbourhood is one-colourable. As a natural variant, Luczak and Thomassé introduced the notion of a locally bipartite graph in which each neighbourhood is 2-colourable. Here we study the chromatic profile of the family of graphs in which every neighbourhood is b-colourable (locally b-partite graphs) as well as the family where the common neighbourhood of every a-clique is b-colourable. Our results include the chromatic thresholds of these families (extending a result of Allen, Böttcher, Griffiths, Kohayakawa and Morris) as well as showing that every n-vertex locally b-partite graph with minimum degree greater than \u0000 \u0000 \u0000 \u0000$(1 - 1/(b + 1/7)) cdot n$\u0000\u0000 \u0000 is \u0000 \u0000 \u0000 \u0000$(b + 1)$\u0000\u0000 \u0000 -colourable. Understanding these locally colourable graphs is crucial for extending the Andrásfai-Erdős-Sós theorem to non-complete graphs, which we develop elsewhere.","PeriodicalId":10513,"journal":{"name":"Combinatorics, Probability & Computing","volume":"78 1","pages":"976-1009"},"PeriodicalIF":0.9,"publicationDate":"2021-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76062182","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 : 2021-02-08DOI: 10.1017/s0963548321000389
Andrea Freschi, Joseph Hyde, Andrew Treglown
<jats:p>Motivated by analogous questions in the setting of Steiner triple systems and Latin squares, Nenadov, Sudakov and Wagner [Completion and deficiency problems, Journal of Combinatorial Theory Series B, 2020] recently introduced the notion of <jats:italic>graph deficiency</jats:italic>. Given a global spanning property <jats:inline-formula>