LEADER 05164nam 2200601 450 001 9910585774303321 005 20230718113645.0 010 $a3-031-05296-X 035 $a(MiAaPQ)EBC7052881 035 $a(Au-PeEL)EBL7052881 035 $a(CKB)24286023400041 035 $a(PPN)263896986 035 $a(EXLCZ)9924286023400041 100 $a20230106h20222022 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aConvolution-like structures, differential operators and diffusion processes /$fRu?ben Sousa, Manuel Guerra, Semyon Yakubovich 210 1$aCham, Switzerland :$cSpringer,$d[2022] 210 4$d©2022 215 $a1 online resource (269 pages) 225 1 $aLecture notes in mathematics ;$vVolume 2315 311 08$aPrint version: Sousa, Rúben Convolution-Like Structures, Differential Operators and Diffusion Processes Cham : Springer International Publishing AG,c2022 9783031052958 320 $aIncludes bibliographical references and index. 327 $aIntro -- Preface -- Contents -- List of Symbols -- 1 Introduction -- 1.1 Motivation and Scope -- 1.2 Organization of the Book -- 2 Preliminaries -- 2.1 Continuous-Time Markov Processes -- 2.2 Sturm-Liouville Theory -- 2.2.1 Solutions of the Sturm-Liouville Equation -- 2.2.2 Eigenfunction Expansions -- 2.2.3 Diffusion Semigroups Generated by Sturm-Liouville Operators -- 2.2.4 Remarkable Particular Cases -- 2.3 Generalized Convolutions and Hypergroups -- 2.4 Harmonic Analysis with Respect to the Kingman Convolution -- 3 The Whittaker Convolution -- 3.1 A Special Case: The Kontorovich-Lebedev Convolution -- 3.2 The Product Formula for the Whittaker Function -- 3.3 Whittaker Translation -- 3.4 Index Whittaker Transforms -- 3.5 Whittaker Convolution of Measures -- 3.5.1 Infinitely Divisible Distributions -- 3.5.2 Lévy-Khintchine Type Representation -- 3.6 Lévy Processes with Respect to the Whittaker Convolution -- 3.6.1 Convolution Semigroups -- 3.6.2 Lévy and Gaussian Processes -- 3.6.3 Some Auxiliary Results on the Whittaker Translation -- 3.6.4 Moment Functions -- 3.6.5 Lévy-Type Characterization of the Shiryaev Process -- 3.7 Whittaker Convolution of Functions -- 3.7.1 Mapping Properties in the Spaces Lp(r?) -- 3.7.2 The Convolution Banach Algebra L?,? -- 3.8 Convolution-Type Integral Equations -- 4 Generalized Convolutions for Sturm-Liouville Operators -- 4.1 Known Results and Motivation -- 4.2 Laplace-Type Representation -- 4.3 The Existence Theorem for Sturm-Liouville Product Formulas -- 4.3.1 The Associated Hyperbolic Cauchy Problem -- 4.3.2 The Time-Shifted Product Formula -- 4.3.3 The Product Formula for w? as the Limit Case -- 4.4 Sturm-Liouville Transform of Measures -- 4.5 Sturm-Liouville Convolution of Measures -- 4.5.1 Infinite Divisibility and Lévy-Khintchine Type Representation -- 4.5.2 Convolution Semigroups. 327 $a4.5.3 Additive and Lévy Processes -- 4.6 Sturm-Liouville Hypergroups -- 4.6.1 The Nondegenerate Case -- 4.6.2 The Degenerate Case: Degenerate Hypergroups of Full Support -- 4.7 Harmonic Analysis on Lp Spaces -- 4.7.1 A Family of L1 Spaces -- 4.7.2 Application to Convolution-Type Integral Equations -- 5 Convolution-Like Structures on Multidimensional Spaces -- 5.1 Convolutions Associated with Conservative Strong Feller Semigroups -- 5.2 Nonexistence of Convolutions: Diffusion Processes on Bounded Domains -- 5.2.1 Special Cases and Numerical Examples -- 5.2.2 Some Auxiliary Results -- 5.2.3 Eigenfunction Expansions, Critical Points and Nonexistence Theorems -- 5.3 Nonexistence of Convolutions: One-Dimensional Diffusions -- 5.4 Families of Convolutions on Riemannian Structures with Cone-Like Metrics -- 5.4.1 The Eigenfunction Expansion of the Laplace-Beltrami Operator -- 5.4.2 Product Formulas and Convolutions -- 5.4.3 Infinitely Divisible Measures and Convolution Semigroups -- 5.4.4 Special Cases -- 5.4.5 Product Formulas and Convolutions Associated with Elliptic Operators on Subsets of R2 -- A Some Open Problems -- References -- Index. 410 0$aLecture notes in mathematics (Springer-Verlag) ;$vv. 2315. 606 $aConvolutions (Mathematics) 606 $aDifferential operators 606 $aDiffusion processes 606 $aConvolucions (Matemàtica)$2thub 606 $aOperadors diferencials$2thub 606 $aProcessos de difusió$2thub 608 $aLlibres electrònics$2thub 615 0$aConvolutions (Mathematics) 615 0$aDifferential operators. 615 0$aDiffusion processes. 615 7$aConvolucions (Matemàtica) 615 7$aOperadors diferencials 615 7$aProcessos de difusió 676 $a512.86 700 $aSousa$b Ru?ben$c(Mathematician),$01252162 702 $aGuerra$b Manuel$g(Manuel Cidraes Castro), 702 $aYakubovich$b S. B$g(Semen B.),$f1961- 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910585774303321 996 $aConvolution-like structures, differential operators and diffusion processes$92999680 997 $aUNINA LEADER 05300nam 2200469z- 450 001 9910261144103321 005 20210211 035 $a(CKB)4100000002484651 035 $a(oapen)https://directory.doabooks.org/handle/20.500.12854/40310 035 $a(oapen)doab40310 035 $a(EXLCZ)994100000002484651 100 $a20202102d2016 |y 0 101 0 $aeng 135 $aurmn|---annan 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 00$aAdvances in Microalgae Biology and Sustainable Applications 210 $cFrontiers Media SA$d2016 215 $a1 online resource (152 p.) 225 1 $aFrontiers Research Topics 311 08$a2-88945-014-7 330 $aIt has become more evident that many microalgae respond very differently than land plants to diverse stimuli. Therefore, we cannot reduce microalgae biology to what we have learned from land plants biology. However, we are still at the beginning of a comprehensive understanding of microalgae biology. Microalgae have been posited several times as prime candidates for the development of sustainable energy platforms, making thus the in-depth understanding of their biological features an important objective. Thus, the knowledge related to the basics of microalgae biology must be acquired and shared rapidly, fostering the development of potential applications. Microalgae biology has been studied for more than forty years now and more intensely since the 1970's, when genetics and molecular biology approaches were integrated into the research programs. Recently, studies on the molecular physiology of microalgae have provided evidences on the particularities of these organisms, mainly in model species, such as Chlamydomonas reinhardtii. Of note, cellular responses in microalgae produce very interesting phenotypes, such as high lipid content in nitrogen deprived cells, increased protein content in cells under high CO2 concentrations, the modification of flagella structure and motility in basal body mutant strains, the different ancient proteins that microalgae uses to dissipate the harmful excess of light energy, the hydrogen production in cells under sulfur deprivation, to mention just a few. Moreover, several research groups are using high-throughput and data-driven technologies, including "omics" approaches to investigate microalgae cellular responses at a system-wide level, revealing new features of microalgae biology, highlighting differences between microalgae and land plants. It has been amazing to observe the efforts towards the development and optimization of new technologies required for the proper study of microalgae, including methods that opened new paths to the investigation of important processes such as regulatory mechanisms, signaling crosstalk, chemotactic mechanisms, light responses, chloroplast controlled mechanisms, among others. This is an exciting moment in microalgae research when novel data are been produced and applied by research groups from different areas, such as bioprocesses and biotechnology. Moreover, there has been an increased amount of research groups focused in the study of microalgae as a sustainable source for bioremediation, synthesis of bioproducts and development of bioenergy. Innovative strategies are combining the knowledge of basic sciences on microalgae into their applied processes, resulting in the progression of many applications that hopefully, will achieve the necessary degree of optimization for economically feasible large-scale applications. Advances on the areas of basic microalgae biology and novelties on the essential cellular processes were revealed. Progress in the applied science showed the use of the basic science knowledge into fostering translational research, proposing novel strategies for a sustainable world scenario. In this present e-book, articles presented by research groups from different scientific areas showed, successfully, the increased development of the microalgae research. Herewith, you will find articles ranging from bioprospecting regional microalgae species, through advances in microalgae molecular physiology to the development of techniques for characterization of biomass and the use of biomass into agriculture and bioenergy production. This e-book is an excellent source of knowledge for those working with microalgae basic and applied sciences, and a great opportunity for researchers from both areas to have an overview of the amazing possibilities we have for building an environmentally sustainable future once the knowledge is translated into novel applications. 606 $aHistory of engineering and technology$2bicssc 610 $abioenergy 610 $aBiofuels 610 $abiomass 610 $aBiotechnology 610 $aCarbon Dioxide 610 $aHydrogen 610 $aLipids 610 $aMicroalgae 610 $aNutrients 610 $asustainability 615 7$aHistory of engineering and technology 700 $aDiego Mauricio Riano-Pachon$4auth$01332412 702 $aFlavia Vischi Winck$4auth 702 $aTelma Teixeira Franco$4auth 906 $aBOOK 912 $a9910261144103321 996 $aAdvances in Microalgae Biology and Sustainable Applications$93040954 997 $aUNINA