Relationship between thirty post-thaw spermatozoal characteristics and the field fertility of 11 high-use Australian dairy AI sires

This study determined the relationship between two measures of field fertility of I I high-use Australian artificial insemination (AI) dairy bulls and thirty standard laboratory assessments of spermatozoal post-thaw viability. The two measures of field fertility used, conception rates (cCR) and non-return rates (cNRR), were both corrected for all major non-bull variables. Sperm viability assessments were conducted on semen collected within the same season as that used to derive the field fertility estimates. These assessments measured sperm concentration, motility, morphology and membrane integrity at thawing, after 2 h incubation and after the swim-up sperm selection procedure. Derivations of these measures and in vitro embryo fertilizing and developmental capacity were also determined. The Genstat Statistical Package [Genstat 5 Release 4.2 Reference Manual, VSN International, Oxford, 20001 was used to conduct an analysis of variance on the viability parameters across semen straws and bulls, and to calculate the strength of correlation between each semen parameter, cNRR and cCR in a correlation matrix. Step forward multiple regression identified the combination of semen parameters that were most highly correlated with cCR and with cNRR. The sperm parameters identified as being most predictive of cCR were the percentage of morphologically normal sperm immediately post-thaw (zeroNorm), the number of morphologically normal sperm after the swim-up procedure (nSuNorm), and the rate of zygote cleavage in vitro (Clv); the predictive equation formed by these parameters accounted for 70% of variance. The predictive equation produced for cNRR contained the variables zeroNorm, the proportion of membrane intact sperm after 2 h incubation at 37 degreesC (twoMem) and Clv and accounted for 76.5% of the variation. ZeroNorm was found to be consistent across straws and semen batches within-bull and the sperm parameter with the strongest individual predictive capacity for both cCR (P = 0.1) and cNRR (P = 0.001). Post-thaw sperm parameters can be used to predict field fertility of Australian dairy sires; the calculated predictive equations are particularly useful for identifying and monitoring bulls of very high and very low potential fertility within a group. (C) 2003 Elsevier B.V. All rights reserved.

Mine waste beach profile and flow resistance equations

Four mine waste beach longitudinal profile equations are compared theoretically and in statistical analyses of profile data from 64 field and laboratory beaches formed by mine tailings, co-disposed coal mine wastes, and sand. All four equations fit the profile data well. The best performing equation both accounts for particle sorting and satisfies hydraulic constraints, and the combination of assumptions underlying it is considered to best represent the processes occurring on mine waste beaches. Combining these assumptions with the Lacey normal equation leads to a variant of the Manning resistance equation. Features that it is desirable to incorporate in theoretical and numerical models of mine waste beaches are listed.

On the Schrodinger equation involving a critical Sobolev exponent and magnetic field

We consider the semilinear Schrodinger equation -Delta(A)u + V(x)u = Q(x)vertical bar u vertical bar(2* -2) u. Assuming that V changes sign, we establish the existence of a solution u not equal 0 in the Sobolev space H-A,V(1) + (R-N). The solution is obtained by a min-max type argument based on a topological linking. We also establish certain regularity properties of solutions for a rather general class of equations involving the operator -Delta(A).

Field observations of instantaneous water slopes and horizontal pressure gradients in the swash-zone

Field observations of instantaneous water surface slopes in the swash zone are presented. For free-surface flows with a hydrostatic pressure distribution the surface slope is equivalent to the horizontal pressure gradient. Observations were made using a novel technique which in its simplest form consists of a horizontal stringline extending seaward from the beach face. Visual observation, still photography or video photography is then sufficient to determine the surface slope where the free-surface cuts the line or between reference points in the image. The method resolves the mean surface gradient over a cross-shore distance of 5 m or more to within +/- 0.001, or 1/20th -1/100th of typical beach gradients. In addition, at selected points and at any instant in time during the swash cycle, the water surface slope can be determined exactly to be dipping either seaward or landward. Close to the location of bore collapse landward dipping water surface slopes of order 0.05-0.1 occur over a very small region (order 0.5 m) at the blunt or convex leading edge of the swash. In the middle and upper swash the water surface slope at this leading edge is usually very close to horizontal or slightly seaward. Behind the leading edge, the water surface slope was observed to be very close to horizontal or dipping seaward at all times throughout the swash uprush. During the backwash the water surface slope was observed to be always dipping seaward, approaching the beach slope, and remained seaward until a new uprush edge or incident bore passed any particular cross-shore location of interest. The observations strongly Suggest that the swash boundary layer is subject to an adverse pressure gradient during uprush and a favourable pressure gradient during the backwash. Furthermore, assuming Euler's equations are a good approximation in the swash, the observations also show that the total fluid acceleration is negative (offshore) for almost the whole of the uprush and for the entire backwash. The observations are contrary to recent work suggesting significant shoreward directed accelerations and pressure gradients occur in the swash (i.e., delta u/delta t > 0 similar to delta p/delta x < 0), but consistent with analytical and numerical solutions for swash uprush and backwash. The results have important implications for sediment transport modelling in the swash zone.

Geodesics without differential equations: general relativistic calculations for introductory modern physics classes

Introductory courses covering modem physics sometimes introduce some elementary ideas from general relativity, though the idea of a geodesic is generally limited to shortest Euclidean length on a curved surface of two spatial dimensions rather than extremal aging in spacetime. It is shown that Epstein charts provide a simple geometric picture of geodesics in one space and one time dimension and that for a hypothetical uniform gravitational field, geodesics are straight lines on a planar diagram. This means that the properties of geodesics in a uniform field can be calculated with only a knowledge of elementary geometry and trigonometry, thus making the calculation of some basic results of general relativity accessible to students even in an algebra-based survey course on physics.

Optical Bloch equations and enhanced decay of Rabi oscillations in strong driving fields

Optical Bloch equations are widely used for describing dynamics in a system consisting molecules, electromagnetic waves, and a thermal bath. We analyze applicability of these equations to a single molecule imbedded in a solid matrix. Classical Bloch equations and the limits of their applicability are derived from more general master equations. Simple and intuitively appealing picture based on stochastic Bloch equations shows that at low temperatures, contrary to common believes, a strong driving field can not only suppress but can also increase decay rates of Rabi oscillations. A physical system where predicted effects can be observed experimentally is suggested. (c) 2005 Elsevier B.V. All rights reserved.

A mean field theory of coded CDMA systems

We present a mean field theory of code-division multiple access (CDMA) systems with error-control coding. On the basis of the relation between the free energy and mutual information, we obtain an analytical expression of the maximum spectral efficiency of the coded CDMA system, from which a mean field description of the coded CDMA system is provided in terms of a bank of scalar Gaussian channels whose variances in general vary at different code symbol positions. Regular low-density parity-check (LDPC)-coded CDMA systems are also discussed as an example of the coded CDMA systems.

Developments and extensions of Roth's method of double Fourier series with applications to the solution of electromagnetic field problems

The first part of the thesis compares Roth's method with other methods, in particular the method of separation of variables and the finite cosine transform method, for solving certain elliptic partial differential equations arising in practice. In particular we consider the solution of steady state problems associated with insulated conductors in rectangular slots. Roth's method has two main disadvantages namely the slow rate of con­vergence of the double Fourier series and the restrictive form of the allowable boundary conditions. A combined Roth-separation of variables method is derived to remove the restrictions on the form of the boundary conditions and various Chebyshev approximations are used to try to improve the rate of convergence of the series. All the techniques are then applied to the Neumann problem arising from balanced rectangular windings in a transformer window. Roth's method is then extended to deal with problems other than those resulting from static fields. First we consider a rectangular insulated conductor in a rectangular slot when the current is varying sinusoidally with time. An approximate method is also developed and compared with the exact method.The approximation is then used to consider the problem of an insulated conductor in a slot facing an air gap. We also consider the exact method applied to the determination of the eddy-current loss produced in an isolated rectangular conductor by a transverse magnetic field varying sinusoidally with time. The results obtained using Roth's method are critically compared with those obtained by other authors using different methods. The final part of the thesis investigates further the application of Chebyshdev methods to the solution of elliptic partial differential equations; an area where Chebyshev approximations have rarely been used. A poisson equation with a polynomial term is treated first followed by a slot problem in cylindrical geometry.

Resonant gradient force on atom interacting with laser field

The gradient force, as a function of position and velocity, is derived for a two-level atom interacting with a standing-wave laser field. Basing on optical Bloch equations, the numerical solutions for the gradient force f_(|_;n) (n = 0, 1, 2, 3, 4, ...) pointing in the direction of the transverse of the laser beam are given. It is shown the higher order gradient force plays important role at strong intensity (G = 64), the contribution of them can not be neglected.

Gravity field recovery using two low satellites in different orbital planes

This study is concerned with gravity field recovery from low-low satellite to satellite range rate data. An improvement over a coplanar mission is predicted in the errors associated with certain parts of the geopotential by the separation of the orbital planes of the two satellites. Using Hill's equations an analytical scheme to model the range rate residuals is developed. It is flexible enough to model equally well the residuals between pairs of satellites in the same orbital plane or whose planes are separated in right ascension. The possible benefits of such an orientation to gravity field recovery from range rate data can therefore be analysed, and this is done by means of an extensive error analysis. The results of this analysis show that for an optimal planar mission improvements can be made by separating the satellites in right ascension. Gravity field recoveries are performed in order to verify and gauge the limitations of the analytical model, and to support the results of the error analysis. Finally the possible problem of the differential decay rates of two satellites due to the diurnal bulge are evaluated.

Boundary integral equations for acoustical inverse sound-soft scattering

The shape of a plane acoustical sound-soft obstacle is detected from knowledge of the far field pattern for one time-harmonic incident field. Two methods based on solving a system of integral equations for the incoming wave and the far field pattern are investigated. Properties of the integral operators required in order to apply regularization, i.e. injectivity and denseness of the range, are proved.

The single-phase induction motor:a critical appraisal of the rotating-field and cross-field theories with particular reference to skin effect

The purpose of this thesis is twofold: to examine the validity of the rotating-field and cross-field theories of the single-phase induction motor when applied to a cage rotor machine; and to examine the extent to which skin effect is likely to modify the characteristics of a cage rotor machine. A mathematical analysis is presented for a single-phase induction motor in which the rotor parameters are modified by skin effect. Although this is based on the usual type of ideal machine, a new form of model rotor allows approximations for skin effect phenomena to be included as an integral part of the analysis. Performance equations appropriate to the rotating-field and cross-field theories are deduced, and the corresponding explanations for the steady-state mode of operation are critically examined. The evaluation of the winding currents and developed torque is simplified by the introduction of new dimensionless factors which are functions of the resistance/reactance ratios of the rotor and the speed. Tables of the factors are included for selected numerical values of the parameter ratios, and these are used to deduce typical operating characteristics for both cage and wound rotor machines. It is shown that a qualitative explanation of the mode of operation of a cage rotor machine is obtained from either theory; but the operating characteristics must be deduced from the performance equations of the rotating-field theory, because of the restrictions on the values of the rotor parameters imposed by skin effect.

Practical Stability and Vector-Lyapunov Functions for Impulsive Differential Equations with "Supremum"

Stability of nonlinear impulsive differential equations with "supremum" is studied. A special type of stability, combining two different measures and a dot product on a cone, is defined. Perturbing cone-valued piecewise continuous Lyapunov functions have been applied. Method of Razumikhin as well as comparison method for scalar impulsive ordinary differential equations have been employed.

On the Operational Solution of a System of Fractional Differential Equations

MSC 2010: 26A33, 44A45, 44A40, 65J10

Stability in Terms of Two Measures for Differential Equations with “Maxima”

Атанаска Георгиева, Стела Глухчева, Снежана Христова - Изследвана е устойчивостта на нелинейни диференциални уравнения с “максимуми” по отношение на две мерки. Приложени са две различни мерки за началните условия и за решението. Използван е методът на Разумихин, а също така и методът на сравнението на обикновени скаларни диференциални уравнения. Приложението на получените резултати и достатъчни условия за устойчивост е илюстрирано с пример.