The objective of Ibis paper is to establish precise characterizations of scaling functions which are orthonormal or fundamental.A criterion for the corresponding wavelets is also given.
There are several examples of spaces of univariate functions for which we have a characterization of all sets of knots which are poised for the interpolation problem. For the standard spaces of univariate polynomials,...There are several examples of spaces of univariate functions for which we have a characterization of all sets of knots which are poised for the interpolation problem. For the standard spaces of univariate polynomials, or spline functions the mentioned results are well-known. In contrast with this, there are no such results in the bivariate case. As an exception, one may consider only the Pascal classic theorem, in the interpolation theory interpretation. In this paper, we consider a space of bivariate piecewise linear functions, for which we can readily find out whether the given node set is poised or not. The main tool we use for this purpose is the reduction by a basic subproblem, introduced in this paper.展开更多
A fundamental solution was obtained for an infinite plane bonded by two dissimilar isotropic semi-planes by employing plane elastic complex variable method and theory of boundary value problems for analytic functions....A fundamental solution was obtained for an infinite plane bonded by two dissimilar isotropic semi-planes by employing plane elastic complex variable method and theory of boundary value problems for analytic functions.Fundamental solution was prepared for solving these types of problems with boundary element method.展开更多
In this note, we establish a companion result to the theorem of J. Szabados on the maximum of fundamental functions of Lagrange interpolation based on Chebyshev nodes.
Let D={z∈C: │z│【1} be the unit disk in the finite complex plane C and Г a Fuchsiangroup consisting of Mbius maps from D to itself. Also, let Ω={z∈D:│z│【│γz│, id≠γ∈Г}be the fundamental region unde Г. ...Let D={z∈C: │z│【1} be the unit disk in the finite complex plane C and Г a Fuchsiangroup consisting of Mbius maps from D to itself. Also, let Ω={z∈D:│z│【│γz│, id≠γ∈Г}be the fundamental region unde Г. Put Ω=D when Г={id}. If we denote by Ω andΩ the closure and boundary of Ω on D, respectively, then we know that Ω has展开更多
In this note, we estimate the maximum amplitude for the Solar Cycle 25. We use the curvature technique presented for earlier cycles by Verdes and coworkers. We further extrapolate the location of the solar maximum num...In this note, we estimate the maximum amplitude for the Solar Cycle 25. We use the curvature technique presented for earlier cycles by Verdes and coworkers. We further extrapolate the location of the solar maximum number of Sunspots, of which the prediction made is about 115 in the year 2025 and identify the arrival to the minimum in the year 2031, forecasting the main characteristics for the current Solar Cycle 25 and list a short comparison with a few other predictions.展开更多
In this paper,the fundamental thermodynamic functions of six important uranyl carbonate minerals,rou-baultite,fontanite,widenmannite,grimselite,čejkaite and bayleyite,are computed using first principles solid-state me...In this paper,the fundamental thermodynamic functions of six important uranyl carbonate minerals,rou-baultite,fontanite,widenmannite,grimselite,čejkaite and bayleyite,are computed using first principles solid-state methods based on Periodic Density Functional Theory,from their energy-optimized crystal structures determined in previous works.These properties are obtained within a wide range of tempera-ture(250–800 K)and are employed in order to derive the thermodynamic functions of formation of these minerals in terms of the elements.The resulting temperature-dependent functions of formation are merged with the thermodynamic functions of other prominent uranyl-containing minerals,also deter-mined using theoretical methods,to determine a rich set of thermodynamic functions of reaction for a series of chemical reactions relating these mineral phases.The influence of the presence of hydrogen peroxide in many of these reactions is also investigated.These additional minerals include uranyl oxide hydrates,hydroxides,peroxides,silicates,sulfates and another uranyl carbonate mineral(rutherfordine)and,therefore,a detailed and wide-ranging view of the relative thermodynamic stability of uranyl minerals is afforded.Unexpectedly,the uranyl tricarbonate minerals,grimselite,čejkaite and bayleyite,are shown to be by far the most stable phases within the full range of temperature considered and under the pres-ence and absence of hydrogen peroxide.Furthermore,the analysis of the solubility products of the con-sidered uranyl carbonate minerals,obtained from the Gibbs free energies of the dissolution reactions,reveals that the widespread belief of the great solubility of these minerals is not supported.Except for rou-baultite and widenmannite,all these minerals are sparingly soluble.As a consequence,the development of accurate temperature-dependent thermodynamic functions of an even larger number of uranyl car-bonate minerals is mandatory for the simulation of the migration of uranium from nuclear waste reposi-tories,uraninite deposits and uranium contaminated sites,as well as for the study of the paragenetic sequence of uranyl minerals arising from the oxidative dissolution processes occurring in uraninite ore deposits and corrosion of spent nuclear fuel.展开更多
基金NSF Grant #DMS-89-01345ARO Contract DAAL 03-90-G-0091
文摘The objective of Ibis paper is to establish precise characterizations of scaling functions which are orthonormal or fundamental.A criterion for the corresponding wavelets is also given.
文摘There are several examples of spaces of univariate functions for which we have a characterization of all sets of knots which are poised for the interpolation problem. For the standard spaces of univariate polynomials, or spline functions the mentioned results are well-known. In contrast with this, there are no such results in the bivariate case. As an exception, one may consider only the Pascal classic theorem, in the interpolation theory interpretation. In this paper, we consider a space of bivariate piecewise linear functions, for which we can readily find out whether the given node set is poised or not. The main tool we use for this purpose is the reduction by a basic subproblem, introduced in this paper.
文摘A fundamental solution was obtained for an infinite plane bonded by two dissimilar isotropic semi-planes by employing plane elastic complex variable method and theory of boundary value problems for analytic functions.Fundamental solution was prepared for solving these types of problems with boundary element method.
文摘In this note, we establish a companion result to the theorem of J. Szabados on the maximum of fundamental functions of Lagrange interpolation based on Chebyshev nodes.
文摘Let D={z∈C: │z│【1} be the unit disk in the finite complex plane C and Г a Fuchsiangroup consisting of Mbius maps from D to itself. Also, let Ω={z∈D:│z│【│γz│, id≠γ∈Г}be the fundamental region unde Г. Put Ω=D when Г={id}. If we denote by Ω andΩ the closure and boundary of Ω on D, respectively, then we know that Ω has
文摘In this note, we estimate the maximum amplitude for the Solar Cycle 25. We use the curvature technique presented for earlier cycles by Verdes and coworkers. We further extrapolate the location of the solar maximum number of Sunspots, of which the prediction made is about 115 in the year 2025 and identify the arrival to the minimum in the year 2031, forecasting the main characteristics for the current Solar Cycle 25 and list a short comparison with a few other predictions.
文摘In this paper,the fundamental thermodynamic functions of six important uranyl carbonate minerals,rou-baultite,fontanite,widenmannite,grimselite,čejkaite and bayleyite,are computed using first principles solid-state methods based on Periodic Density Functional Theory,from their energy-optimized crystal structures determined in previous works.These properties are obtained within a wide range of tempera-ture(250–800 K)and are employed in order to derive the thermodynamic functions of formation of these minerals in terms of the elements.The resulting temperature-dependent functions of formation are merged with the thermodynamic functions of other prominent uranyl-containing minerals,also deter-mined using theoretical methods,to determine a rich set of thermodynamic functions of reaction for a series of chemical reactions relating these mineral phases.The influence of the presence of hydrogen peroxide in many of these reactions is also investigated.These additional minerals include uranyl oxide hydrates,hydroxides,peroxides,silicates,sulfates and another uranyl carbonate mineral(rutherfordine)and,therefore,a detailed and wide-ranging view of the relative thermodynamic stability of uranyl minerals is afforded.Unexpectedly,the uranyl tricarbonate minerals,grimselite,čejkaite and bayleyite,are shown to be by far the most stable phases within the full range of temperature considered and under the pres-ence and absence of hydrogen peroxide.Furthermore,the analysis of the solubility products of the con-sidered uranyl carbonate minerals,obtained from the Gibbs free energies of the dissolution reactions,reveals that the widespread belief of the great solubility of these minerals is not supported.Except for rou-baultite and widenmannite,all these minerals are sparingly soluble.As a consequence,the development of accurate temperature-dependent thermodynamic functions of an even larger number of uranyl car-bonate minerals is mandatory for the simulation of the migration of uranium from nuclear waste reposi-tories,uraninite deposits and uranium contaminated sites,as well as for the study of the paragenetic sequence of uranyl minerals arising from the oxidative dissolution processes occurring in uraninite ore deposits and corrosion of spent nuclear fuel.
