Spectroscopic studies of metal complexes

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A discrete least squares collocation method for two-dimensional nonlinear time-dependent partial differential equations

In this paper, we develop regularized discrete least squares collocation and finite volume methods for solving two-dimensional nonlinear time-dependent partial differential equations on irregular domains. The solution is approximated using tensor product cubic spline basis functions defined on a background rectangular (interpolation) mesh, which leads to high spatial accuracy and straightforward implementation, and establishes a solid base for extending the computational framework to three-dimensional problems. A semi-implicit time-stepping method is employed to transform the nonlinear partial differential equation into a linear boundary value problem. A key finding of our study is that the newly proposed mesh-free finite volume method based on circular control volumes reduces to the collocation method as the radius limits to zero. Both methods produce a large constrained least-squares problem that must be solved at each time step in the advancement of the solution. We have found that regularization yields a relatively well-conditioned system that can be solved accurately using QR factorization. An extensive numerical investigation is performed to illustrate the effectiveness of the present methods, including the application of the new method to a coupled system of time-fractional partial differential equations having different fractional indices in different (irregularly shaped) regions of the solution domain

Universal difference? Understanding relationality and difference in transpersonal psychotherapy

As a working class, black, male, who is the son of immigrants who travelled from the Caribbean with the Windrush Generation, I often feel at odds with my psychotherapy profession, dominated as it is by middle class, white, women, who typically have a British family line flowing back generations. My sense of otherness is with me throughout my working day, in my psychotherapy practice, as I sit with a diverse range of clients within the complex context of contemporary ‘multicultural’ Britain. The sense of ‘the other’, the sense of myself as ‘other’ impacts on, and to some degree constitutes therapeutic relationality. Within most styles of psychotherapy difference is mainly understood in terms of the acknowledgement of the various categories, consideration of power imbalances, which we try as therapists to work with, work around, work through. But I am a transpersonal psychotherapist, and within this modality, there is very little consideration of ‘difference’, or otherness, except to highlight the apparent universality of us all. In this paper, we will explore ways of carving out a space within transpersonal ways of thinking to consider the relational context of therapy, and to explore the constitution of ‘othering’ within this transpersonal therapeutic context. This paper outlines how the use of creative techniques common to Transpersonal psychotherapy, such as visualisations, drawing, and Sand Tray work can be used in research on therapy to explore the emotional bodily and relational experience of difference, between therapist and client, and between researcher and researche

On the analysis of mixed-index time fractional differential equation systems

In this paper we study the class of mixed-index time fractional differential equations in which different components of the problem have different time fractional derivatives on the left hand side. We prove a theorem on the solution of the linear system of equations, which collapses to the well-known Mittag-Leffler solution in the case the indices are the same, and also generalises the solution of the so-called linear sequential class of time fractional problems. We also investigate the asymptotic stability properties of this class of problems using Laplace transforms and show how Laplace transforms can be used to write solutions as linear combinations of generalised Mittag-Leffler functions in some cases. Finally we illustrate our results with some numerical simulations.Comment: 21 pages, 6 figures (some are made up of sub-figures - there are 15 figures or sub-figures

Relationships between burley tobacco marketing practice use and Tennessee producersℓ̓personal and farm characteristics : and their contacts with county Extension Agents

The major purpose of this study was to determine the relationships between burley tobacco marketing practice use and Tennessee burley tobacco producers\u27 personal and farm characteristics and their contacts with Agricultural Extension Agents. Data were obtained through personal interviews by county Extension Agents with 1,358 randomly selected burley tobacco producers in 55 Tennessee counties where burley tobacco production was important. Information was obtained about the general production characteristics of burley tobacco producers, their use of recommended burley tobacco production practices in 1983 and the number of contacts they had with Extension Agents over a 12-month period. The data were coded and punched on computer cards and computations were made by The University of Tennessee Computing Center. One way analysis of variance F-test was used to determine strength and significance of the relationships between the dependent and independent variables. Major findings included the following; 1. Only 12 percent of the burley tobacco producers were college graduates and over 50 percent were part-time farmers. 2. Burley tobacco producers had averaged making 8.1 contacts per year with county Extension Agents. They attended on the average 0.5 tobacco meetings, 1.1 other Extension meetings, made 2.0 visits to the Extension office, made 2.7 telephone calls to the Extension office, and received 1.8 farm visits from county Extension Agents. Seventeen percent of the producers had no contact with Extension Agents. 3. Forty-two percent of the producers had no tobacco land in permanent sod during the previous three years. 4. Forty-three percent of the producers fertilized and limed tobacco land according to a soil test recommendation. 5. Thirty-one percent of the producers applied over 200 pounds of nitrogen per acre. 6. The producers made an average of three grades of burley tobacco. Producers hand tied 40 percent of their tobacco, baled 55 percent of their tobacco, and sheeted 6 percent of their tobacco. 7. Producers with larger allotments and more pounds sold hand tied significantly less tobacco than producers with smaller allotments and fewer pounds sold. Producers with larger allotments and more pounds sold baled and sheeted significantly more tobacco than producers with smaller allotments and fewer pounds sold. 8. Younger producers and producers with more formal education hand tied significantly less tobacco than older producers and producers with less formal education. Younger producers and producers with more formal education baled significantly more tobacco than older producers and producers with less formal education. 9. Producers attending more tobacco meetings, attending more other Extension meetings, making more visits to the Extension office, making more telephone calls to the Extension office, receiving more farm visits and having more total Extension contacts hand tied significantly less tobacco than producers having fewer Extension contacts. Producers attending more tobacco meetings, attending more other Extension meetings, making more visits to the Extension office, making more telephone calls to the Extension office, receiving more farm visits and having more total Extension contacts baled and baled and/or sheeted significantly more tobacco than producers having fewer Extension contacts. Implications and recommendations were also made

Efficient multistep methods for tempered fractional calculus: Algorithms and Simulations

In this work, we extend the fractional linear multistep methods in [C. Lubich, SIAM J. Math. Anal., 17 (1986), pp.704--719] to the tempered fractional integral and derivative operators in the sense that the tempered fractional derivative operator is interpreted in terms of the Hadamard finite-part integral. We develop two fast methods, Fast Method I and Fast Method II, with linear complexity to calculate the discrete convolution for the approximation of the (tempered) fractional operator. Fast Method I is based on a local approximation for the contour integral that represents the convolution weight. Fast Method II is based on a globally uniform approximation of the trapezoidal rule for the integral on the real line. Both methods are efficient, but numerical experimentation reveals that Fast Method II outperforms Fast Method I in terms of accuracy, efficiency, and coding simplicity. The memory requirement and computational cost of Fast Method II are $O(Q)$ and $O(Qn_T)$, respectively, where $n_T$ is the number of the final time steps and $Q$ is the number of quadrature points used in the trapezoidal rule. The effectiveness of the fast methods is verified through a series of numerical examples for long-time integration, including a numerical study of a fractional reaction-diffusion model

The West Island Site (41MXI65)

This paper describes a set of artifacts collected from the West Island site, a poorly known Titus phase cemetery in Ellison Creek Reservoir. The site is on a small knoll adjacent to a small spring branch that flows into the now-inundated Ellison Creek, a tributary of Big Cypress Creek. The site knoll is now no more than one foot (30 em) above the normal pool elevation of Ellison Creek Reservoir, and it is usually totally submerged. Up to five feet (1.52 meters) of white sand caps the knoll, and overlies the clay subsoil. Due to continued submergence, the knoll is being eroded by the reservoir, anq. consequently many stone tools and pieces of lithic debris are present along the water\u27s edge. Dart points and arrowpoints have been found at the site, along with some pottery sherds, but no grounds tone implements. Small amounts of charcoal were found around the top of the knoll in pockets of modern mussel shell and gravels, but its association with the site deposits is unknown. No middens are known to be present on the knoll. The West Island site has been previously dug by private collectors sometime before 1965. Turner had examined some of the site collections, and reported that, ceramic vessels of the types Avery Engraved, Bailey Engraved, Bullard Brushed, Cowhide Stamped, Harleton Appliqued, Hodges Engraved, Karnack Brushed-Incised, Maydelle Incised, Ripley Engraved, Simms Engraved, Taylor Engraved, and Wilder Engraved were present in an unknown number of burials. These types of decorated ceramics are characteristic of the Titus phase, which dates from about 1400 to the 1600s