W.T. Coffey, C. Rybarschry and W. SCHRÖER
The Debye theory of dielectric relaxation as corrected for inertial effects has as yet been only considered in the linear approximation. There, the rise and decay transients are…
Abstract
The Debye theory of dielectric relaxation as corrected for inertial effects has as yet been only considered in the linear approximation. There, the rise and decay transients are identical. Here a method recently developed for the treatment of a rotator in a periodic potential is applied to calculate the transient behaviour when the linear approximation is discarded. The Kramers equation for the problem is expanded in a set of orthogonal functions which lead to a set of linear differential difference equations giving the relaxation behaviour. It is shown that the Mori formalism for the problem leads to the same set of differential difference equations as the Kramers equation.
Iqbal M. Batiha, Adel Ouannas, Ramzi Albadarneh, Abeer A. Al-Nana and Shaher Momani
This paper aims to investigate the existence and uniqueness of solution for generalized Sturm–Liouville and Langevin equations formulated using Caputo–Hadamard fractional…
Abstract
Purpose
This paper aims to investigate the existence and uniqueness of solution for generalized Sturm–Liouville and Langevin equations formulated using Caputo–Hadamard fractional derivative operator in accordance with three nonlocal Hadamard fractional integral boundary conditions. With regard to this nonlinear boundary value problem, three popular fixed point theorems, namely, Krasnoselskii’s theorem, Leray–Schauder’s theorem and Banach contraction principle, are employed to theoretically prove and guarantee three novel theorems. The main outcomes of this work are verified and confirmed via several numerical examples.
Design/methodology/approach
In order to accomplish our purpose, three fixed point theorems are applied to the problem under consideration according to some conditions that have been established to this end. These theorems are Krasnoselskii's theorem, Leray Schauder's theorem and Banach contraction principle.
Findings
In accordance to the applied fixed point theorems on our main problem, three corresponding theoretical results are stated, proved, and then verified via several numerical examples.
Originality/value
The existence and uniqueness of solution for generalized Sturm–Liouville and Langevin equations formulated using Caputo–Hadamard fractional derivative operator in accordance with three nonlocal Hadamard fractional integral boundary conditions are studied. To the best of the authors’ knowledge, this work is original and has not been published elsewhere.
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Mostafa Abbaszadeh, Hossein Pourbashash and Mahmood Khaksar-e Oshagh
This study aims to propose a new numerical method for solving non-linear partial differential equations on irregular domains.
Abstract
Purpose
This study aims to propose a new numerical method for solving non-linear partial differential equations on irregular domains.
Design/methodology/approach
The main aim of the current paper is to propose a local meshless collocation method to solve the two-dimensional Klein-Kramers equation with a fractional derivative in the Riemann-Liouville sense, in the time term. This equation describes the sub-diffusion in the presence of an external force field in phase space.
Findings
First, the authors use two finite difference schemes to discrete temporal variables and then the radial basis function-differential quadrature method has been used to estimate the spatial direction. To discrete the time-variable, the authors use two different strategies with convergence orders
Originality/value
The proposed numerical technique is flexible for different computational domains.
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In this study, the authors introduce a solvability of special type of Langevin differential equations (LDEs) in virtue of geometric function theory. The analytic solutions of the…
Abstract
Purpose
In this study, the authors introduce a solvability of special type of Langevin differential equations (LDEs) in virtue of geometric function theory. The analytic solutions of the LDEs are considered by utilizing the Caratheodory functions joining the subordination concept. A class of Caratheodory functions involving special functions gives the upper bound solution.
Design/methodology/approach
The methodology is based on the geometric function theory.
Findings
The authors present a new analytic function for a class of complex LDEs.
Originality/value
The authors introduced a new class of complex differential equation, presented a new technique to indicate the analytic solution and used some special functions.
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Qualitative data analysis requires methodological knowledge and intellectual competence. Analysis is not about adhering to any one correct approach or set of right techniques; it…
Abstract
Qualitative data analysis requires methodological knowledge and intellectual competence. Analysis is not about adhering to any one correct approach or set of right techniques; it is imaginative, artful, flexible, and reflexive. It should also be methodical, scholarly, and intellectually rigorous. (Coffey and Atkinson, 1996, p.1.
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We have before us the recently‐issued Annual Report of the Local Government Board on the work done by the Local Authorities under the Sale of Food and Drugs Acts. While preserving…
Abstract
We have before us the recently‐issued Annual Report of the Local Government Board on the work done by the Local Authorities under the Sale of Food and Drugs Acts. While preserving the general form and arrangement of its predecessors, it shows that not only the Board itself, but the local authorities also, are coming to an increasing realisation of the importance of the subject. Six years ago we had occasion to point out some of the defects attaching to these reports, and to suggest various improvements that might be made in them. We felt, and expressed at the time our belief, that the Board was much handicapped by the form of quarterly reports imposed on the Public Analyst by the Food and Drugs Acts, and by the non‐existence of any machinery by which it could get together and collate the vast amount of information which those reports ought to, but do not, yield. Until the law is altered the present system must continue, but it is striking evidence of the lack of serious study spent on the matter that for want of effective coordination and control more than one‐half of what may be considered the real and permanent value of the Public Analyst's work goes into the waste‐paper basket. The work done by most Public Analysts as individuals is limited to some few hundreds of samples of any one article of food, but the combined expeperience of them all would in most cases — assuming it could be accurately ascertained—go far towards settling in a single year many of the thorny questions relative to standards and limits which are fought out at such great length and still greater cost to the community in the courts of law.
The study aimed to identify occupational stressors and measure experiences of clinical burn‐out among a group of mental health nurses and occupational therapists in a medium…
Abstract
The study aimed to identify occupational stressors and measure experiences of clinical burn‐out among a group of mental health nurses and occupational therapists in a medium secure service. All the nursing staff (n=115) and occupational therapists (n=9) on three wards in a medium secure hospital were asked to partake in the study, and to complete a modified version of the Psychiatric Nurse Occupational Stress Scale (PNOSS), the Maslach Burnout Inventory (MBI) and a demographic questionnaire designed for the study.Results from the PNOSS revealed that organisational issues elicited the greatest stress and were most strongly related to high burn‐out scores, identified by the MBI. Limited resource and staff conflict were also associated with stress and burn‐out. Patient care had a relatively small impact. MBI findings were that a substantial proportion (54%) were experiencing high burn‐out in relation to emotional exhaustion.
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Month after month we bring forward additional evidence of the injury resulting from the use of chemical “preservatives” in food, while the Authorities feebly hesitate to give…
Abstract
Month after month we bring forward additional evidence of the injury resulting from the use of chemical “preservatives” in food, while the Authorities feebly hesitate to give specific legal effect to the recommendations of the Departmental Committee which made such a complete inquiry into this question. The evidence upon which those recommendations were based has been fully corroborated by a number of different observers. FERE and others have shown that, as regards boric acid and borax, even when administered in the smallest medicinal doses, there is always the risk that these drugs may aggravate, or even produce, renal diseases. These observations have been confirmed by the work of Dr. CHARLES HARRINGTON, an account of which has been recently published. Twelve cats were fed on the same food; six were treated with borax, one had no preservative, and five were given a preservative which had no apparent effect. The experiment extended over a period of 133 days, the quantity of borax given averaging about 0.5 grms, per diem. Three of the borated cats soon became ill, and one died at the end of six weeks. On the termination of the experiment the cats were all killed, and upon examination it was found that the organs of the six cats which had not taken borax were in perfectly sound and healthy condition, while the others, with one exception, were all suffering from nephritis. Of course, instances are recorded in which patients have been treated with borax and boracic acid with apparently no injurious result, but as a general rule these experiments have been of too short duration to allow of the desired information being arrived at, and the results must therefore be regarded as inconclusive and unreliable. It is perfectly evident that the kidneys may be for a short time quite capable of eliminating many objectionable substances, but the long‐continued use of such bodies, as Dr. HARRINGTON'S researches clearly indicate, sets up an inflammatory condition of the kidneys which, of course, interferes with the effective performance of their proper functions, and lays the foundations for complications of the most serious nature.
Of milk alone no less than 36,000 samples were purchased during 1904, almost as many as the total for all articles 10 years ago. Of these 4,031 (or 11.1 per cent.) were returned…
Abstract
Of milk alone no less than 36,000 samples were purchased during 1904, almost as many as the total for all articles 10 years ago. Of these 4,031 (or 11.1 per cent.) were returned as adulterated. In the previous year 10.4 per cent. were condemned. The difference is not of necessity due to any increase in adulteration, as the figures are admittedly inaccurate owing to the differences of procedure on the part of Public Analysts in making out their reports. In support of this view it is mentioned that in 14 Metropolitan Districts where 6,270 milks were examined, 4.9 per cent. were reported as containing percentages of added water under 5 per cent., while in 15 other districts, where 3,205 samples were submitted, only 0.56 per cent. were returned as being adulterated to this extent. The explanation is that in the former case the Public Analyst adhered more or less rigidly to the standard fixed by the “Sale of Milk Regulations,” while in the latter, in most instances, where the amount of adulteration was under 5 per cent., the samples were reported as genuine. Here the Report takes what is a more or less new and certainly welcome departure, in definitely expressing an opinion for the guidance of those in doubt, and stating that so long as the “Sale of Milk Regulations” remains in force, “Public Analysts have no warrant for the adoption of a still lower standard.”