A numerical method to compute derivatives of functions of large complex matrices and its application to the overlap Dirac operator at finite chemical potential

We present a method for the numerical calculation of derivatives of functions of general complex matrices. The method can be used in combination with any algorithm that evaluates or approximates the desired matrix function, in particular with implicit Krylov-Ritz-type approximations. An important use case for the method is the evaluation of the overlap Dirac operator in lattice Quantum Chromodynamics (QCD) at finite chemical potential, which requires the application of the sign function of a non-Hermitian matrix to some source vector. While the sign function of non-Hermitian matrices in practice cannot be efficiently approximated with source-independent polynomials or rational functions, sufficiently good approximating polynomials can still be constructed for each particular source vector. Our method allows for an efficient calculation of the derivatives of such implicit approximations with respect to the gauge field or other external parameters, which is necessary for the calculation of conserved lattice currents or the fermionic force in Hybrid Monte-Carlo or Langevin simulations. We also give an explicit deflation prescription for the case when one knows several eigenvalues and eigenvectors of the matrix being the argument of the differentiated function. We test the method for the two-sided Lanczos approximation of the finite-density overlap Dirac operator on realistic $SU(3)$ gauge field configurations on lattices with sizes as large as $14\times14^3$ and $6\times18^3$.Comment: 26 pages elsarticle style, 5 figures minor text changes, journal versio

The skills debate in the context of a pandemic: Are students prepared for the workplace?

This paper explores the preparation of hospitality management students for the workplace in the context of a global health crisis. In an intrinsic mixed methods case study, student perspectives are used to problematize and evaluate conceptualizations and terminologies. The study recommends that employability, a dualistic and politicised term, be replaced by the intrinsic construct of work readiness and finds that competencies, work integrated learning and perceived relevance of the degree play instrumental roles in delivering work readiness. Context-specific and regularly updated competency frameworks are recommended. Capability emerges as a powerful and often overlooked construct

Soil Changes as Influenced by Cropping and Fertilizer Treatment

Yields of crops are dependent in a large measure on the supply of plant food in the soil. Although many of our soils had a high virgin fertility, past soil management practices have not included adequate provisions for the return to the soil of a substantial portion of the plant food removed by crops. Specific knowledge concerning the rate of depletion of our soils with respect to soil organic matter, nitrogen, and phosphorus is imperative to sound recommendations regarding crop rotations, fertilizer application, and other soil-building practices. This investigation is concerned with soil fertility changes which are the result of cropping practices and fertilizer treatment on plots at the Agronomy Farm of the South Dakota Agricultural Experiment Station

Fielding\u27s Clergymen

Henry Fielding presented more clergymen in his fiction than any other major novelist except Trollope, and his non-fictional writings--notably articles in his journal, The Champion--also reflect his interest in the status of the clergy in eighteenth-century England. In his series of articles entitled “An Apology for the Clergy,” Fielding establishes the criteria by which he feels clergymen should be judged and lists the qualities of the “true” and “false” clergymen. This study reveals that while Fielding in his non-fictional works clearly explains the traits of the true clergyman, his fiction does not contain a clergyman measuring up to his standards. The study consists of a detailed examination of the clergymen in Fielding\u27s five works of fiction--Shamela, Joseph Andrews, Jonathan Wild, Tom Jones, and Amelia--an assessment of their character traits, and an indication of their shortcomings when compared with the true clergyman defined in his journal articles. The opening sections of this study explain Fielding\u27s views about religion and the clergy, and discuss Fielding\u27s satiric technique, since satire is the vehicle he uses to demolish clerical pretenders and to accentuate the flaws of more sincere or “almost true” clergymen--notably Parson Adams in Joseph Andrews and Dr. Harrison in Amelia. The longest section discusses the false clergymen in the novels and the kinds of behavior that earn them Fielding\u27s contempt. His obviously flawed false clergymen are guilty of vices such as perverted reasoning, exhibited by Parson Tickletext and Parson Williams in Shamela; uncharitable hypocrisy, shown by Parsons Trulliber and Barnabas in Joseph Andrews; vanity, seen in the Ordinary of Newgate in Jonathan Wild and in the young clergyman in Amelia; malevolence, peculiar to Parson Thwackum in Tom Jones; parasitical behavior, Parson Supple\u27s mode of conduct in Tom Jones; and manipulation and duplicity--especially by those adhering to the detested sect of Methodism--exhibited by Williams in particular as well as by other false clerics. The last section examines the two superior--though still flawed--clergymen, Parson Adams and Dr. Harrison. While Fielding is unquestionably successful in presenting the false clergyman--in his numerous incarnations--whom he describes in “An Apology for the Clergy,” the study establishes that he does not present a true clergyman. Parson Adams is deficient because of naivete and the inability to be a dignified leader; Dr. Harrison is overly suspicious, impatient, vain, and unable to inspire his parishioners to follow his example of kindness and charity. Thus even these two “good” clergymen are inferior when compared with Fielding\u27s non-fictional model

Catchment afforestation, surface water acidification, and salmonid populations in Galloway, South West Scotland.

SIGLEAvailable from British Library Document Supply Centre-DSC:DXN014108 / BLDSC - British Library Document Supply CentreGBUnited Kingdo

Fielding\u27s Clergymen

Henry Fielding presented more clergymen in his fiction than any other major novelist except Trollope, and his non-fictional writings--notably articles in his journal, The Champion--also reflect his interest in the status of the clergy in eighteenth-century England. In his series of articles entitled “An Apology for the Clergy,” Fielding establishes the criteria by which he feels clergymen should be judged and lists the qualities of the “true” and “false” clergymen. This study reveals that while Fielding in his non-fictional works clearly explains the traits of the true clergyman, his fiction does not contain a clergyman measuring up to his standards. The study consists of a detailed examination of the clergymen in Fielding\u27s five works of fiction--Shamela, Joseph Andrews, Jonathan Wild, Tom Jones, and Amelia--an assessment of their character traits, and an indication of their shortcomings when compared with the true clergyman defined in his journal articles. The opening sections of this study explain Fielding\u27s views about religion and the clergy, and discuss Fielding\u27s satiric technique, since satire is the vehicle he uses to demolish clerical pretenders and to accentuate the flaws of more sincere or “almost true” clergymen--notably Parson Adams in Joseph Andrews and Dr. Harrison in Amelia. The longest section discusses the false clergymen in the novels and the kinds of behavior that earn them Fielding\u27s contempt. His obviously flawed false clergymen are guilty of vices such as perverted reasoning, exhibited by Parson Tickletext and Parson Williams in Shamela; uncharitable hypocrisy, shown by Parsons Trulliber and Barnabas in Joseph Andrews; vanity, seen in the Ordinary of Newgate in Jonathan Wild and in the young clergyman in Amelia; malevolence, peculiar to Parson Thwackum in Tom Jones; parasitical behavior, Parson Supple\u27s mode of conduct in Tom Jones; and manipulation and duplicity--especially by those adhering to the detested sect of Methodism--exhibited by Williams in particular as well as by other false clerics. The last section examines the two superior--though still flawed--clergymen, Parson Adams and Dr. Harrison. While Fielding is unquestionably successful in presenting the false clergyman--in his numerous incarnations--whom he describes in “An Apology for the Clergy,” the study establishes that he does not present a true clergyman. Parson Adams is deficient because of naivete and the inability to be a dignified leader; Dr. Harrison is overly suspicious, impatient, vain, and unable to inspire his parishioners to follow his example of kindness and charity. Thus even these two “good” clergymen are inferior when compared with Fielding\u27s non-fictional model