Parkinson's Law Quantified: Three Investigations on Bureaucratic Inefficiency

We formulate three famous, descriptive essays of C.N. Parkinson on bureaucratic inefficiency in a quantifiable and dynamical socio-physical framework. In the first model we show how the use of recent opinion formation models for small groups can be used to understand Parkinson's observation that decision making bodies such as cabinets or boards become highly inefficient once their size exceeds a critical 'Coefficient of Inefficiency', typically around 20. A second observation of Parkinson - which is sometimes referred to as Parkinson's Law - is that the growth of bureaucratic or administrative bodies usually goes hand in hand with a drastic decrease of its overall efficiency. In our second model we view a bureaucratic body as a system of a flow of workers, which enter, become promoted to various internal levels within the system over time, and leave the system after having served for a certain time. Promotion usually is associated with an increase of subordinates. Within the proposed model it becomes possible to work out the phase diagram under which conditions bureaucratic growth can be confined. In our last model we assign individual efficiency curves to workers throughout their life in administration, and compute the optimum time to send them to old age pension, in order to ensure a maximum of efficiency within the body - in Parkinson's words we compute the 'Pension Point'.Comment: 15 pages, 5 figure

Fractional variational calculus of variable order

We study the fundamental problem of the calculus of variations with variable order fractional operators. Fractional integrals are considered in the sense of Riemann-Liouville while derivatives are of Caputo type.Comment: Submitted 26-Sept-2011; accepted 18-Oct-2011; withdrawn by the authors 21-Dec-2011; resubmitted 27-Dec-2011; revised 20-March-2012; accepted 13-April-2012; to 'Advances in Harmonic Analysis and Operator Theory', The Stefan Samko Anniversary Volume (Eds: A. Almeida, L. Castro, F.-O. Speck), Operator Theory: Advances and Applications, Birkh\"auser Verlag (http://www.springer.com/series/4850

Family studies of somatic and functional characteristics in the polish rural population

In the present investigation we were trying to determine the genetic and environmental conditioning of the chosen somatic and functional traits in Polish rural population during ontogenesis. In order to find out interactions between environmental and genetic conditions of the studied traits, classical methods of quantitative features were applied: correlation coefficients corrected by assortative mating in the chosen types of heritability were evaluated on their base, heritability coefficients of analyzed features were assessed. The biggest stability of the correlation coefficients was observed for the length-parameters. We did not noticed stronger genetic control of functional features in men. Mean-strong genetic control among analyzed traits was observed in: reaction time, space orientation and static strength expressed as relative and absolute strength

Stationarity-conservation laws for certain linear fractional differential equations

The Leibniz rule for fractional Riemann-Liouville derivative is studied in algebra of functions defined by Laplace convolution. This algebra and the derived Leibniz rule are used in construction of explicit form of stationary-conserved currents for linear fractional differential equations. The examples of the fractional diffusion in 1+1 and the fractional diffusion in d+1 dimensions are discussed in detail. The results are generalized to the mixed fractional-differential and mixed sequential fractional-differential systems for which the stationarity-conservation laws are obtained. The derived currents are used in construction of stationary nonlocal charges.Comment: 28 page

Comments on discrete time in quantum mechanics

The possibility that time can be regarded as a discrete parameter is re-examined. We study the dynamics of the free particle and find in some cases superluminal propagation

Principles of Discrete Time Mechanics: II. Classical field Theory

We apply the principles discussed in an earlier paper to the construction of discrete time field theories. We derive the discrete time field equations of motion and Noether's theorem and apply them to the Schrodinger equation to illustrate the methodology. Stationary solutions to the discrete time Schrodinger wave equation are found to be identical to standard energy eigenvalue solutions except for a fundamental limit on the energy. Then we apply the formalism to the free neutral Klein Gordon system, deriving the equations of motion and conserved quantities such as the linear momentum and angular momentum. We show that there is an upper bound on the magnitude of linear momentum for physical particle-like solutions. We extend the formalism to the charged scalar field coupled to Maxwell's electrodynamics in a gauge invariant way. We apply the formalism to include the Maxwell and Dirac fields, setting the scene for second quantisation of discrete time mechanics and discrete time Quantum Electrodynamics.Comment: 23 pages, LateX, To be published in J.Phys.A: Math.Gen: contact email address: [email protected]

Logical independence and quantum randomness

We propose a link between logical independence and quantum physics. We demonstrate that quantum systems in the eigenstates of Pauli group operators are capable of encoding mathematical axioms and show that Pauli group quantum measurements are capable of revealing whether or not a given proposition is logically dependent on the axiomatic system. Whenever a mathematical proposition is logically independent of the axioms encoded in the measured state, the measurement associated with the proposition gives random outcomes. This allows for an experimental test of logical independence. Conversely, it also allows for an explanation of the probabilities of random outcomes observed in Pauli group measurements from logical independence without invoking quantum theory. The axiomatic systems we study can be completed and are therefore not subject to Goedel's incompleteness theorem.Comment: 9 pages, 4 figures, published version plus additional experimental appendi

Principles of Discrete Time Mechanics: I. Particle Systems

We discuss the principles to be used in the construction of discrete time classical and quantum mechanics as applied to point particle systems. In the classical theory this includes the concept of virtual path and the construction of system functions from classical Lagrangians, Cadzow's variational principle applied to the action sum, Maeda-Noether and Logan invariants of the motion, elliptic and hyperbolic harmonic oscillator behaviour, gauge invariant electrodynamics and charge conservation, and the Grassmannian oscillator. First quantised discrete time mechanics is discussed via the concept of system amplitude, which permits the construction of all quantities of interest such as commutators and scattering amplitudes. We discuss stroboscopic quantum mechanics, or the construction of discrete time quantum theory from continuous time quantum theory and show how this works in detail for the free Newtonian particle. We conclude with an application of the Schwinger action principle to the important case of the quantised discrete time inhomogeneous oscillator.Comment: 35 pages, LateX, To be published in J.Phys.A: Math.Gen. Basic principles stated: applications to field theory in subsequent papers of series contact email address: [email protected]

Morphological-developmental reaction and productivity of plants and canopy of semileafless pea (Pisum sativum L.) after seed vaccination with Rhizobium and foliar micronutrient fertilization

The determinants of semileafless peas (Pisum sativum> L., cv. Tarchalska) crop productivity were studied during two vegetative seasons: cool 2010 and warm 2011 in south part of Poland (Modzurów 50°09’N 18°07’E; 274 m. a.s.l.. Peas was treated either with seed vaccine (NitraginaTM) containing Rhizobium bacteria or foliar micronutrient fertilizer (PhotrelTM) or both of them. The range of peas response to treatments included biometrical measurements and also the measurements of vegetation indices namely, green area index (GAI), normalized difference vegetation index (NDVI) and relative chlorophyll content (SPAD), carried out in the specific stages of development, which for the compared objects were generally insignifi cant. In the warmer growing season, pea plants grew better, what resulted in a very high yield of seeds per plant, determined by a greater number of large seeds. It was shown that the length and weight of pea pod and the number of seeds formed in the pod depends on its position on the particular node. The longest pods, characterized by the greatest weight and number of seeds, developed on the lower nodes: 1st and 2nd one. The pea pods forming on higher nodes, from the 3rd, had reduced number of fruits and the weight of a single seed. The shortest pods were growing out of the 5th and 6th nodes, at the top of the stem. Analysis of the single pea seed mass shows a highly significant effect of its position in the fruit on pod productivity. Seeds located in the central part of the pod had the greatest mass, and this accuracy, as highly significant, was found for the pods containing from 3 to 8 seeds. The tested agrochemical treatments did not differentiate the chemical composition of seeds