Researches and investigations involving the theory and applications of integral transforms and operational calculus are remarkably wide-spread in many diverse areas of the mathematical, physical, ...chemical, engineering and statistical sciences.
As a much-enriched supplement to the previous review paper entitled the “Effective work functions for ionic and electronic emissions from mono- and polycrystalline surfaces” Prog. Surf. Sci. 83 ...(2008) 1–165, the present monograph summarizes a comprehensive and up-to-date database in Table 1, which includes more than ten thousands of experimental and theoretical data accumulated mainly during the last half century on the work functions (ϕ+, ϕe and ϕ−) effective for positive-ionic, electronic and negative-ionic emissions from mono- and polycrystalline surfaces of 88 kinds of chemical elements (1H–99Es), and also which includes the main experimental condition and method employed for each sample specimen (bulk or film) together with 490 footnotes. From the above database originating from 4461 references published to date in the fields of both physics and chemistry, the most probable values of ϕ+, ϕe and ϕ− for substantially clean surfaces are statistically estimated for about 600 surface species of mono- and polycrystals. The values recommended for ϕe together with ϕ+ and ϕ− in Table 2 are much more abundant in both surface species and data amount, and also they may be more reliable and convenient than those in popular handbooks and reviews consulted widely still today by great many workers, because the latter is based on less-plentiful data on ϕe published generally before ∼1980 and also because it covers no value recommended for ϕ+ and ϕ−. Consequently, Table 1 may be more advantageous as the latest and most abundant database on work functions (especially ϕe) for quickly referring to a variety of data obtained under specified conditions. Comparison of the most probable values of ϕe recommended for each surface species between this article and other literatures listed in Tables 2 and 3 indicates that consideration of the recent work function data accumulated particularly during the last ∼40 years is very important for correct analysis of these surface phenomena or processes concerned with either work function or its changes. On the basis of our simple model about the work function of polycrystal consisting of a number of patchy faces (1–i) having each a fractional area (Fi) and a local work function (ϕi), its values of both ϕ+ and ϕe are theoretically calculated and also critically compared with a plenty of experimental data. In addition, the “polycrystalline thermionic work function contrast” (Δϕ∗≡ϕ+−ϕe) well-known as the thermionic peculiarity inherent in every polycrystal is carefully analyzed as a function of the degree of monocrystallization (δm) corresponding to the largest (Fm) among Fi’s (Tables 4–6 and Fig. 1), thereby yielding the conclusions as follows: (1) Δϕ∗≃ const (>0) holds for the generally called “polycrystalline” surfaces (usually δm < 50%), (2) Δϕ∗ ranges from ∼0.3 eV (Pt) to 0.7 eV (Nb) depending upon the polycrystalline surface species, (3) in the case of the “submonocrystal” (50 <δm < 100%) tentatively named here, Δϕ∗ decreases parabolically down to zero as δm increases from ∼50% up to 100% (monocrystal), (4) Δϕ∗=0.0eV applies to a clean and smooth monocrystalline surface (δm≈ 100%) alone, (5) regarding negative ion emission, on the other hand, our theoretical prediction of Δϕ∗∗≡ϕ−−ϕe=0.0eV is experimentally verified to hold for any surface species under any surface conditions (Table 7), (6) every polycrystal (usually, δm < 50%) may be concluded in general to have a unique value of ϕe characteristic of its species with little dependence upon δm, (7) this conclusion affords us first a sound basis for supporting theoretically the experimental fact (Table 2) that every species of polycrystal has a nearly constant value of ϕe as well as ϕ+ (usually within the uncertainty of ±0.1 eV) depending little upon the difference in the surface components (Fi and ϕi) among specimens so long as δm < 50%, (8) on the contrary to polycrystal (δm < 50%), any submonocrystal (50 <δm < 100%) has such an anomaly that it does not possess the unique value of work function characteristic of the surface species itself, because its ϕe as well as ϕ+ changes considerably depending upon δm, (9) consequently, submonocrystal must be taken as another type (category) different from both poly- and monocrystals, (10) in this way, δm acts as the key factor mainly governing the work functions in the different mode between poly- and submonocrystals with δm lower and higher than the “critical point” of 50%, respectively, (11) on the contrary to δm, ϕm belonging to δm has a differential effect on both ϕ+ and ϕe, but their values remain nearly constant so long as δm < 50% and, thus interestingly, (12) the complicate governance of ϕ+ and ϕe by both δm and ϕm and also the anomaly of submonocrystal (cf. (8) above) observed first by our theoretical analysis may be considered as a new contribution to the work function studies developed to date. Together with brief comments and experimental conditions, typical data on ϕe and/or ϕ+ are summarized from the various aspects of (1) examination of the work function dependence upon the surface atom density of low-Miller-index monocrystals of typical metals such as Al, Ni, W and Re (Table 8), (2) demonstration of the above dependence usually called the “anisotropic work function dependence sequences” of both ϕe(110) >ϕe(100) >ϕe(111) and ϕ+(110) >ϕ+(100) >ϕ+(111) for various bcc-metals (e.g., Nb, Mo, Ta and W) exactly obeying the Smoluchowski rule (Table 9), (3) substantiation of both ϕe(111) >ϕe(100) >ϕe(110) for a variety of fcc-metals (except Al and Pb) and ϕ+(111) >ϕ+(100) >ϕ+(110) for Ni strictly following the above rule (Table 10), (4) verification of the quantitative relations between work function and surface energy and also melting point of the three low index planes of several metals (typically, Ni), (5) examination of the work function change (Δϕe) due to allotropic transformation from α to β or β to γ phase (Table 11) together with a concise outline of the Burgers orientation relationship, (6) evaluation of Δϕe due to liquefying (Table 12), (7) estimation of Δϕe due to transformation from ferro- to paramagnetic state (Table 13) in addition to a brief description of the Curie point dependence upon metastable metal film thickness above one monolayer, (8) estimation of Δϕe due to transition from normal to superconducting state (Table 14), (9) study of the work function dependence on the Wigner–Seitz radius and also comparison between its theoretical values (by Kohn) and experimental data (Fig. 2), (10) inspection of the annealing effect on work function for layers or films, (11) verification of the coincidence of work function values among different experimental methods, and (12) inquisition of the work function dependence upon the size of fine particles (∼20–100 Å in radius) studied by theory and experiment.
•Ten thousands of work function data are summarized together with methods and conditions.•Most probable work function values are listed for 600 surface species of 88 elements.•The above values are discussed comparatively with data recommended previously.•Three kinds of effective work functions are examined by theory and experiment.•Work function changes at various critical temperatures are analyzed critically.
This book focuses on applications of the theory of fractional calculus in numerical analysis and various fields of physics and engineering. Inequalities involving fractional calculus operators ...containing the Mittag–Leffler function in their kernels are of particular interest. Special attention is given to dynamical models, magnetization, hypergeometric series, initial and boundary value problems, and fractional differential equations, among others.
This volume is dedicated to the memory of Björn Jawerth. It contains original research contributions and surveys in several of the areas of mathematics to which Björn made important contributions. ...Those areas include harmonic analysis, image processing, and functional analysis, which are of course interrelated in many significant and productive ways.Among the contributors are some of the world's leading experts in these areas. With its combination of research papers and surveys, this book may become an important reference and research tool.This book should be of interest to advanced graduate students and professional researchers in the areas of functional analysis, harmonic analysis, image processing, and approximation theory. It combines articles presenting new research with insightful surveys written by foremost experts.
This issue is a continuation of the previous successful Special Issue “Mathematical Analysis and Applications” <https://www.mdpi.com/journal/axioms/special_issues/mathematical_analysis>. ...Investigations involving the theory and applications of mathematical analytical tools and techniques are remarkably widespread in many diverse areas of the mathematical, physical, chemical, engineering and statistical sciences. In this Special Issue, we invite and welcome review, expository and original research articles dealing with the recent advances in mathematical analysis and its multidisciplinary applications.
This book explores the most recent developments in the theory of planar quasiconformal mappings with a particular focus on the interactions with partial differential equations and nonlinear analysis. ...It gives a thorough and modern approach to the classical theory and presents important and compelling applications across a spectrum of mathematics: dynamical systems, singular integral operators, inverse problems, the geometry of mappings, and the calculus of variations. It also gives an account of recent advances in harmonic analysis and their applications in the geometric theory of mappings.The book explains that the existence, regularity, and singular set structures for second-order divergence-type equations--the most important class of PDEs in applications--are determined by the mathematics underpinning the geometry, structure, and dimension of fractal sets; moduli spaces of Riemann surfaces; and conformal dynamical systems. These topics are inextricably linked by the theory of quasiconformal mappings. Further, the interplay between them allows the authors to extend classical results to more general settings for wider applicability, providing new and often optimal answers to questions of existence, regularity, and geometric properties of solutions to nonlinear systems in both elliptic and degenerate elliptic settings.
Heat shock protein 90 (Hsp90) is an ATP-dependent molecular chaperone which is essential in eukaryotes. It is required for the activation and stabilization of a wide variety of client proteins and ...many of them are involved in important cellular pathways. Since Hsp90 affects numerous physiological processes such as signal transduction, intracellular transport, and protein degradation, it became an interesting target for cancer therapy. Structurally, Hsp90 is a flexible dimeric protein composed of three different domains which adopt structurally distinct conformations. ATP binding triggers directionality in these conformational changes and leads to a more compact state. To achieve its function, Hsp90 works together with a large group of cofactors, termed co-chaperones. Co-chaperones form defined binary or ternary complexes with Hsp90, which facilitate the maturation of client proteins. In addition, posttranslational modifications of Hsp90, such as phosphorylation and acetylation, provide another level of regulation. They influence the conformational cycle, co-chaperone interaction, and inter-domain communications. In this review, we discuss the recent progress made in understanding the Hsp90 machinery.
Habitat‐selection analyses allow researchers to link animals to their environment via habitat‐selection or step‐selection functions, and are commonly used to address questions related to wildlife ...management and conservation efforts. Habitat‐selection analyses that incorporate movement characteristics, referred to as integrated step‐selection analyses, are particularly appealing because they allow modelling of both movement and habitat‐selection processes.
Despite their popularity, many users struggle with interpreting parameters in habitat‐selection and step‐selection functions. Integrated step‐selection analyses also require several additional steps to translate model parameters into a full‐fledged movement model, and the mathematics supporting this approach can be challenging for many to understand.
Using simple examples, we demonstrate how weighted distribution theory and the inhomogeneous Poisson point process can facilitate parameter interpretation in habitat‐selection analyses. Furthermore, we provide a ‘how to’ guide illustrating the steps required to implement integrated step‐selection analyses using the amt package
By providing clear examples with open‐source code, we hope to make habitat‐selection analyses more understandable and accessible to end users.
Habitat‐selection analyses allow researchers to link animals to their environment in support of wildlife management and conservation efforts. We provide a ‘how to' guide for correctly interpreting parameters in habitat‐ and step‐selection functions and for implementing integrated step‐selection analyses using the amt package for program R.
The importance and usefulness of subjects and topics involving integral transformations and operational calculus are becoming widely recognized, not only in the mathematical sciences but also in the ...physical, biological, engineering and statistical sciences. This book contains invited reviews and expository and original research articles dealing with and presenting state-of-the-art accounts of the recent advances in these important and potentially useful subjects.
ABSTRACT
We explore the assumption, widely used in many astrophysical calculations, that the stellar initial mass function (IMF) is universal across all galaxies. By considering both a canonical ...broken-power-law IMF and a non-universal IMF, we are able to compare the effect of different IMFs on multiple observables and derived quantities in astrophysics. Specifically, we consider a non-universal IMF that varies as a function of the local star formation rate, and explore the effects on the star formation rate density (SFRD), the extragalactic background light, the supernova (both core-collapse and thermonuclear) rates, and the diffuse supernova neutrino background. Our most interesting result is that our adopted varying IMF leads to much greater uncertainty on the SFRD at $z \approx 2-4$ than is usually assumed. Indeed, we find an SFRD (inferred using observed galaxy luminosity distributions) that is a factor of $\gtrsim 3$ lower than canonical results obtained using a universal IMF. Secondly, the non-universal IMF we explore implies a reduction in the supernova core-collapse rate of a factor of $\sim 2$, compared against a universal IMF. The other potential tracers are only slightly affected by changes to the properties of the IMF. We find that currently available data do not provide a clear preference for universal or non-universal IMF. However, improvements to measurements of the star formation rate and core-collapse supernova rate at redshifts $z \gtrsim 2$ may offer the best prospects for discernment.
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