bluuebunny/crossref_metadata_2025 huggingface dataset:
Rumen-buffering capacity using dietary sources and in vitro gas fermentation
Authors: Kang Sungchhang , Wanapat Metha
Published: December 2016

The present study aimed to compare the effect of the rumen-buffering capacity of dietary sources and urea supplementation on ruminal kinetic gas production, rumen pH and fermentation efficiency and degradability, using in vitro gas-production techniques. The treatments were arranged according to a 4 × 3 factorial arrangement in a completely randomised design. The first factor was a rumen-buffering source, including the following: no buffering, and supplementation of 2% of sodium bicarbonate (NaHCO3), 2% of banana flower powder I (BAFLOP-I; Musa (AAA group)) or 2% of BAFLOP-II (Musa sapientum L.) in total substrate. The second factor was urea supplementation at 0, 3% or 6% of total substrate, as a non-protein nitrogen source. Dietary substrate was provided by roughage–concentrate fed at a ratio of 30 : 70 and two rumen-fistulated dairy steers were used as rumen-fluid donors. The chemical compositions and mineral element contents of both BAFLOP-I and BAFLOP-II were similar. The pH declined below 6.0 as a result of using a high concentrate ratio; however, inclusion of buffering sources increased the pH, which led to an improvement of efficiency of rumen fermentation, microbial protein synthesis, microbial growth and nutrient digestibility. The intercept values for the different treatments representing gas production from soluble fractions, gas production from the insoluble fraction, gas production rate, potential extent of gas production and cumulative gas production (120 h of incubation) were significantly different between no buffering and buffering groups (P < 0.05) and increased with an increasing level of urea supplementation. Moreover, in vitro true and neutral detergent fibre digestibility as well as the number of ruminal microorganisms by direct counts (protozoa, fungi and bacteria) were higher with supplementation of buffering sources and increased linearly with an increasing supplementation level of urea. However, under the present study, there were no differences among the effects of the three buffering agents (NaHCO3, BAFLOP-I and BAFLOP-II) on ruminal kinetic gas production, rumen pH and fermentation efficiency, and digestibility (P > 0.05). In addition, the concentration of ruminal ammonia-nitrogen increased with an increasing level of urea supplementation. On the basis of the present experiment, it can be concluded that supplementation of BAFLOP either with or without urea as non-protein nitrogen could enhance rumen ecology and digestibility. The present study suggested that either BAFLOP-I or BAFLOP-II could be used as a dietary rumen-buffering agent supplemented at 2%, together with urea at up to 6% of total diet substrate, when animals are fed a diet of roughage–concentrate at an ratio of 30 : 70, with rice straw as the main roughage source.
Complex language, complex thought?
Authors: Bogaerds-Hazenberg Suzanne T.M. , Hendriks Petra
Published: December 2016

It has been argued (e.g., by De Villiers and colleagues) that the acquisition of sentence embedding is necessary for the development of first-order Theory of Mind (ToM): the ability to attribute beliefs to others. This raises the question whether the acquisition of double embedded sentences is related to, and perhaps even necessary for, the development of second-order ToM: the ability to attribute beliefs about beliefs to others. This study tested 55 children (aged 7-10) on their ToM understanding in a false-belief task and on their elicited production of sentence embeddings. We found that second-order ToM passers produced mainly double embeddings, whereas first-order ToM passers produced mainly single embeddings. Furthermore, a better performance on second-order ToM predicted a higher rate of double embeddings and a lower rate of single embeddings in the production task. We conclude that children’s ability to produce double embeddings is related to their development of second-order ToM.
Organizing TCUs in a turn
Authors: Zhang Wei
Published: December 2016

This paper examines two self-initiated same-turn repair operations, namely reordering and parenthesizing, in Mandarin conversation. Although both are initiated within a TCU, they often operate on global trouble sources instead of local ones internal to that TCU. On the surface, the two operations seem to share a similar formal pattern in which a TCU is first self-interrupted, and non-projected clausal materials are then produced before the interrupted TCU is resumed. What differentiate the two operations are their distinct roles in organizing TCUs in multi-unit turns. Reordering addresses the tension between the temporal sequence of the events being recounted and the temporal arrangement of the recounting. The clausal material added through reordering becomes an integral part in the rearrangement of the TCUs in that turn. Parenthesizing addresses the tension between the linearity of speech production and information management. It also addresses potential interactional problems to maintain intersubjectivity.
Investigating the parent-child interactive behavior of autistic children by using composite light-emitting or reflective toys
Authors: Lee Ya-Hsueh , Ma Min-Yuan
Published: December 2016

A toy is a valuable medium for promoting parent-child interaction. This study selected six light-emitting or reflective materials to produce composite toy balls, and conducted tests on 15 families with preschool-aged high-functioning autistic children. Quantification method I analysis was employed in the study, and the experimental results indicated that (a) the metal ball (reflective and dynamic light) was the representative sample that elicited many smiles or laughs and much finger pointing as well as high levels of pleasure and activeness.; (b) the mitball (static light) was the representative sample that provoked much eye contact, produced satisfactory reactions to activities,; (c) the quality of fluorescence enhanced the levels of pleasure and the reactions to the activity. We propose that dynamic and reflective materials can be adopted to divert the attention of children, and fluorescent toys can then employed to sustain parent-child interaction.
Emotion-related musical variables affect person perception
Authors: Franco Fabia , Angelova Stanislava
Published: December 2016

This study investigated person perception in respect of variables associated with affect in music (tempo and mode) following motor synchronization to music. Participants (n = 128, 50% female) were tested in a task involving stepping with a researcher to the beat of slow or fast music in major or minor mode, following which measures concerning the synchronised partner were collected (incidental memory, likeability of, similarity to and prosocial attitude towards). Significant effects were found only for the ‘likeability’ measure, modulated by gender, suggesting that variables associated with affect perception in music, such as mode and tempo appear relevant for person perception in a synchronization task in ways that differ for men and women. The results of this ‘proof of concept’ study indicate the need for further research on the effect of motor synchronization based on ecologically valid musical interaction tasks.
Graded Incoherence for Accuracy-Firsters
Authors: De Bona Glauber , Staffel Julia
Published: December 2016

This article investigates the relationship between two evaluative claims about agents’ degrees of belief: (i) that it is better to have more rather than less accurate degrees of belief and (ii) that it is better to have less rather than more probabilistically incoherent degrees of belief. We show that, for suitable combinations of inaccuracy measures and incoherence measures, both claims are compatible, although not equivalent; moreover, certain ways of becoming less incoherent always guarantee improvements in accuracy. Incompatibilities between particular incoherence and inaccuracy measures can be exploited to argue against particular ways of measuring either inaccuracy or incoherence.
In Epistemic Networks, Is Less Really More?
Authors: Rosenstock Sarita , Bruner Justin , O’Connor Cailin
Published: December 2016

We show that previous results from epistemic network models by Kevin J. S. Zollman and Erich Kummerfeld showing the benefits of decreased connectivity in epistemic networks are not robust across changes in parameter values. Our findings motivate discussion about whether and how such models can inform real world epistemic communities.
Explicating Top-Down Causation Using Networks and Dynamics
Authors: Bechtel William
Published: December 2016

In many fields in the life sciences investigators refer to downward or top-down causal effects. Craver and I defended the view that such cases should be understood in terms of a constitution relation between levels in a mechanism and intralevel causal relations (occurring at any level). We did not, however, specify when entities constitute a higher-level mechanism. In this article I appeal to graph-theoretic representations of networks, now widely employed in systems biology and neuroscience, and associate mechanisms with modules that exhibit high clustering. As a result of interconnections within clusters, mechanisms often exhibit complex dynamic behaviors that constrain how individual components respond to external inputs, a central feature of top-down causation.
On limit analysis of plates
Authors: Schumann Walter
Published: December 2016

The bending of thin perfectly plastic plates of arbitrary shape under transverse load is studied. The collapse load for a concentrated force on such a plate is found to be

2
π

2\pi

times the yield moment.
The conservation equations for independent coexistent continua and for multicomponent reacting gas mixtures
Authors: Nachbar W. , Williams F. , Penner S. S.
Published: December 2016

The equations for conservation of mass, momentum, and energy are derived for a set of independent, coexistent continua obeying the laws of dynamics and thermodynamics. The idea of a control volume and a control surface for each continuum is used in the analysis. The derived results are practically identical with relations obtained previously by Th. von Kármán.
Effects of gravitational or electromagnetic fields on fluid motion.
Authors: Yih Chia-Shun
Published: December 2016

It is shown in this paper that the effect of gravity on a stratified fluid is to inhibit steady motion in the direction of gravity; that, for small values of the magnetic viscosity, the effect of a main magnetic field is to make steady weak motions of a fluid independent of the distance along the lines of force; and that, again for small values of the magnetic viscosity, the effect of a uniform electric field is to make steady weak motions of a fluid rotationally symmetric with respect to an axis in the direction of the field. These results, together with a similar one of Proudman (1916) [1] for a fluid with general rotation, enable one to state that the effects of rotation, gravity, and electromagnetic fields (for small magnetic viscosity) are to endow the fluid with a certain anisotropic rigidity by “stiffening” it along the vorticity lines, the isopycnic surfaces or lines, or the lines of force, as the case may be. In the case of a weak steady motion or relative motion, this “stiffening” has the effect of reducing the a priori number of physical or at least mathematical dimensions of the motion by one.
Variational principles for guided electromagnetic waves in anisotropic materials
Authors: Hauser Walter
Published: December 2016

It is the purpose of this paper to develop a general method for obtaining approximate solutions to the problems of the propagation of waves in a guide which may only be partially filled with material having tensor electromagnetic properties. With the introduction of an appropriate dyadic Green’s function we are able to obtain a formal solution to the problem in terms of an integral involving the field vectors in the perturbing rod. The reformulation of the original problem in terms of an integral equation enables us to construct a variational principle whose extremal value is insensitive to a great range of trial functions. The extremal value of the variational expression from which the integral equations for the field are derivable is shown to be proportional to

(

γ
0
2

−

γ
2

)

(\gamma _0^2 - {\gamma ^2})

, the difference between the square of the propagation constant of the wave in the empty and loaded guide. Normal modes in terms of which an expansion of the dyadic Green’s function is obtained are defined. In the last section we demonstrate the ability of the variational method to improve the results obtained by perturbation methods obtaining a first order approximation for the propagation constant of a wave in a rectangular guide containing an infinite ferrite slab.
Diffraction of a dipole field by a unidirectionally conducting semi-infinite screen
Authors: Radlow James
Published: December 2016

An exact solution is obtained for the diffraction of a dipole field by a unidirectionally conducting semi-infinite plane screen. Double Laplace transforms are applied to Maxwell’s equations, and the defining conditions of the unidirectionality lead to an equation between two complex functions of two complex variables. This equation is solved by an extension of the usual function-theoretical method, and we can then express the electro-magnetic field in terms of certain complex triple integrals. These are transformed into real integrals, so that it is possible to discuss the field behavior in the neighborhood of the diffracting edge. The variation of singularity along the edge of the screen is given.
Further properties of certain classes of transfer functions
Authors: Zemanian Armen H.
Published: December 2016

Some previously defined classes of rational transfer functions are extended to transfer functions that need not be rational. Several additional properties of these types of functions are then developed. Finally, bounds on certain derivatives of the unit impulse responses corresponding to such functions are shown to exist.
A note on the minimal representation of triggering matrices
Authors: Gill Arthur
Published: December 2016

A triggering matrix is an array of numbers in which each row represents an actuating input of a data-processing system. In this note, upper and lower bounds are given to the minimal form of such a matrix.
Wave refraction at an interface
Authors: Ablow C. M.
Published: December 2016

A plane wave in one of two perfect gases moves toward the parallel plane interface between the gases. The wave is either continuous or headed by a shock front weak enough that entropy changes may be neglected. Using Riemann’s solution of the appropriate hyperbolic partial differential equation, four equations are derived giving the details of the reflected and refracted wave motions. The equations are of first order integro-differential or implicit functional form depending on the boundary conditions and must be solved simultaneously for four functions of a single independent variable. The equations are suitable for numerical step-by-step solution.
On a problem of minimum weight design
Authors: Mróz Zenon
Published: December 2016

A problem of optimal design for perfectly plastic, isotropic structures is analyzed. It is shown that for such structures as plates or shells, an extremum of the volume, if it exists, is either a local maximum or a minimum.
A duality theorem for non-linear programming
Authors: Wolfe Philip
Published: December 2016

A dual problem is formulated for the mathematical programming problem of minimizing a convex function under convex constraints which reduces to the classical dual problem in the case of linear programming problems. Duality theorems are proved regarding the relationship between the problem and its dual.
An application of the dynamic Betti-Rayleigh reciprocal theorem to moving-point loads in elastic media
Authors: Payton R. G.
Published: December 2016

Two problems connected with the transient motion of an elastic body acted upon by a moving-point force are solved by an application of the dynamic Betti-Rayleigh reciprocal theorem. This theorem, which is the analogue of Green’s theorem for the scalar wave equation, permits the solution to be written as a single expression, irrespective of the value of the (constant) moving-force velocity

v
v

. In particular, the displacement field in an infinite elastic body, due to a transient-point body force moving, in a straight line, is given in a simple form. Next the surface motion of an elastic half-space acted upon by a transient pressure spot moving in a straight line is analyzed for a material for which Poisson’s ratio is one-fourth. The normal displacement is expressed in a simple manner, but the tangential displacement is quite complicated and is not fully expressible in terms of elementary functions. Singularities of the displacement fields are identified and discussed.
On the optimal design of a vibrating beam
Authors: Niordson Frithiof I.
Published: December 2016

This paper deals with the problem of finding the best possible tapering of a simply supported beam, which for a given volume would have the highest possible value of the natural frequency for the lowest mode of lateral vibrations. The differential equation governing the deflection is given and a procedure to solve this non-linear equation by successive iterations is presented.
Existence of conditionally periodic orbits for the motion of a satellite around the oblate earth
Authors: Barrar Richard
Published: December 2016

The author’s previous results on the convergence of the Poincaré-von Zeipel procedure in celestial mechanics are applied to the problem of the motion of a satellite around the oblate earth. The investigation concerns a potential that can vary both longitudinally and latitudinally, and also includes behavior near the critical angle. The existence of conditionally periodic orbits in all these cases is established.
Some solutions of a nonlinear differential equation of high order
Authors: Grensted P. E. W.
Published: December 2016

Some exact monotonic, and approximate oscillatory, solutions of the nonlinear equation

d
n

y

/

d

x
n

=
K

|
y
|

r

sgn
⁡
y

{d^n}y/d{x^n} = K{\left | y \right |^r} \operatorname {sgn} y

,

0
≤
r

0 \le r

, are derived. The coefficient

K
K

may be positive or negative,

r
r

may be non-integral and

n
n

is any positive integer. For the case

r
=
0

r = 0

, exact solutions in closed form are obtained. The conditions under which the approximate solutions will be highly accurate are discussed. Every component of the general solution of the linear equation

d
n

y

/

d

x
n

=
K
y

{d^n}y/d{x^n} = Ky

is shown to be analogous to a corresponding solution of the given nonlinear equation.
Bifurcation of periodic solutions in a nonlinear difference-differential equations of neutral type
Authors: Brayton Robert K.
Published: December 2016

The existence of a self-sustained periodic solution in the autonomous equation
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="u prime left-parenthesis tau right-parenthesis minus alpha u prime left-parenthesis tau minus h right-parenthesis plus beta u left-parenthesis tau right-parenthesis plus alpha gamma u left-parenthesis tau minus h right-parenthesis equals epsilon f left-parenthesis u left-parenthesis tau right-parenthesis right-parenthesis">

u
′

(
τ
)

−
α

u
′

(

τ
−
h

)

+
β
u

(
τ
)

+
α
γ
u

(

τ
−
h

)

=
ϵ
f

(

u

(
τ
)

)

u’\left ( \tau \right ) - \alpha u’\left ( {\tau - h} \right ) + \beta u\left ( \tau \right ) + \alpha \gamma u\left ( {\tau - h} \right ) = \epsilon f\left ( {u\left ( \tau \right )} \right )

\]
is proved under appropriate assumptions on

α
,
β
,
γ
,
f

\alpha ,\beta ,\gamma ,f

and

h
h

. The method of proof consists in converting this equation into an equivalent nonlinear integral equation and demonstrating the convergence of an appropriate iteration scheme.
Slightly damped librations
Authors: Morrison J. A.
Published: December 2016

The application of a generalized method of averaging to the problem of slightly damped librations in a perturbed one degree of freedom system is considered. The librations are those arising in the critical case in which the rate of change of the phase in the unperturbed system has a zero. The perturbed system is reduced to a form suitable for the application of the generalized method of averaging, and the first order averaged equation is derived for the slow rate of change of the amplitude of the librations, due to the damping.
Coupled pairs of dual integral equations
Authors: Keer L. M.
Published: December 2016

Using the operator techniques as introduced by Erdélyi and Sneddon, solutions are obtained for two simultaneous pairs of dual integral equations of the Titchmarsh type. It is found that use of these operators exposes the important features of analysis and allows the solutions to be expressed in a compact form. The methods of Copson and Lowengrub and Sneddon form the basis for the solutions derived.
Diffraction of elastic waves by a penny-shaped crack
Authors: Mal A. K.
Published: December 2016

The diffraction of axisymmetric, harmonic elastic waves by a circular crack is considered. It is shown that the potential functions for the diffracted waves can be obtained from the solution of a pair of dual integral equations. The dual equations are transformed into integral equations of the second kind suitable for iteration at low frequencies. The principle of contraction mapping is used to discuss the convergence of the iteration scheme. The solution satisfies an edge condition.
Parametric analysis of statistical communication nets
Authors: Frank H. , Hakimi S. L.
Published: December 2016

The existing traffic within the branches of a communication net can often be assumed to be normally distributed random variables. A natural problem is to determine the probability that a particular flow rate between a pair of stations can be attained. If this probability is too small, it is necessary to improve the net with minimum cost. In this paper, analysis techniques on which effective synthesis procedures can be based are developed. An exact method for evaluating the flow rate probability is obtained as well as upper and lower bounds. Monte Carlo techniques are applied and the flow rate is seen to be approximately normally distributed. A method of finding the approximate mean and variance of the flow rate is given, as well as a Uniformly Most Powerful Invariant Statistical test.
The approximate numerical solution of the non-homogeneous linear Fredholm integral equation by relaxation methods
Authors: Shaw F. S.
Published: December 2016

Relaxation methods are applied to the problem of finding an approximate numerical solution to the non-homogeneous linear Fredholm integral equation. As an illustration of the technique the deflection of a simply supported single span beam subjected to both normal and end loads is found.
The diffraction of a plane wave through a grating
Authors: Miles John W.
Published: December 2016

The problem of diffraction and scattering of a normally incident plane wave of sound by an infinite plane grating consisting of infinitely thin, coplanar, equally spaced (b apart) strips with parallel edges is solved. The potentials on the two sides of the screen are written as Fourier expansions in terms of the velocity in the aperture, and an integral equation for this velocity is determined. An impedance parameter

Z
Z

whose real part is the transmission coefficient, is defined, and it is shown that the real and imaginary parts of the reciprocal of this parameter may both be specified by variational expressions, which are absolute minima for the solution to the aforementioned integral equation. An alternative formulation, in terms of the pressure discontinuity across the screen, is given, leading to an integral equation and to variational expressions for the real and imaginary parts of

(

1
−
Z

)

−
1

{\left ( {1 - Z} \right )^{ - 1}}

A solution to the integral equation is given which reduces the problem to the solution of an infinite number of simultaneous equations. It is shown that solving only one of these equations gives a solution which is essentially a solution to Laplace’s equation, while if

N
N

equations are solved the terms neglected are of the order

N

−
1

[

(

1
−
4

b
2

/

N
2

λ
2

)

−
1

/

2

−
1

]

{N^{ - 1}}\left [ {{{\left ( {1 - 4{b^2}/{N^2}{\lambda ^2}} \right )}^{ - 1/2}} - 1} \right ]

or less, where

λ
\lambda

is the wave length. The solution is extended to the case of a vertically polarized electromagnetic incident wave by direct analogy and to the case of a horizontally polarized electromagnetic wave by a transformation which is a special case of Babinet’s principle. The integral equations for an aperture of finite thickness are set up, and an approximate solution including only first order terms in thickness/wavelength is given. Results are given in the form of curves for the transmission coefficient vs. aperture opening for several ratios of grating spacing to wave length less than unity. For the special case of a half open grating the transmission coefficient is plotted out to that value of spacing/wavelength at which the results agree with Kirchhoff’s theory.
Separation of Laplace’s equation
Authors: Levinson N. , Bogert B. , Redheffer R. M.
Published: December 2016

The following results are established in this paper: (I)

∗
∗

^{**}

For the Laplace equation

Δ
θ
=
0

\Delta \theta = 0

in curvilinear co-ordinates

(

u
,
v
,
w

)

\left ( {u,v,w} \right )

in Euclidean space to be directly separable†into two equations, one for

S
S

and one for

Z
Z

, when the solution is

θ
=
R

(

u
,
v
,
w

)

S

(

u
,
v

)

Z

(
w
)

\theta = R\left ( {u,v,w} \right )S\left ( {u,v} \right )Z\left ( w \right )

with fixed

R
R

, it is necessary and sufficient that the surfaces

w

{w}

= constant (1) be orthogonal to the surfaces

u

{u}

= constant,

v

{v}

= constant and (2) be parallel planes, planes with a common axis, concentric spheres, spheres tangent at a common point, or one of the two sets of spheres generated by the co-ordinate lines when bicircular co-ordinates are rotated about the line joining the poles or about its perpendicular bisector. (II) We have

R
=
1

R = 1

always and only in the first three cases, namely, when the surfaces

w

{w}

= constant are parallel planes, planes with a common axis, or concentric spheres. (III) In these three cases, but only these, the wave equation separates in the sense

R
S
Z

RSZ

, and hence, for the wave equation,

R
=
1

R = 1

automatically. (IV) For further separation of the equation found above for

S
S

, when

S
=
X

(
u
)

Y

(
v
)

S = X\left ( u \right )Y\left ( v \right )

so that the solution is now

R
X
Y
Z

RXYZ

, it is necessary and sufficient that the co-ordinates be toroidal, or such that the wave equation so separates, or any inversions of these. (V) The co-ordinates where the wave equation so separates, that is, admits solutions

R
X

(
u
)

Y

(
v
)

Z

(
w
)

RX\left ( u \right )Y\left ( v \right )Z\left ( w \right )

, are only the well-known cases where this happens with

R
=
1

R = 1

, namely, degenerate ellipsoidal or paraboloidal co-ordinates (but see Sec. 8.2). (VI). In these cases, but only these,

R
=
1

R = 1

for the Laplace equation too. (VII) Co-ordinates for

R
S
Z

RSZ

or

R
X
Y
Z

RXYZ

separation of the Laplace equation have the group property under inversion. (VIII) In all cases

R
R

can be found by inspection of the linear element.
On heat transfer problems in viscous flow
Authors: Carrier G. F. , Lewis J. A.
Published: December 2016

Many problems of physical interest which are associated with the flow of a viscous fluid through a narrow channel require the determination of the temperature distribution throughout the field of flow. In general, such problems may be separated into one of three classifications. The first of these is characterized by the existence of a thermal boundary layer, the second by a temperature distribution independent of the coordinate across the channel, and the third by an intermediate type of temperature distribution. In the present paper a simple method for the classification of such problems is given, and techniques for solving some of the problems which arise in practice are discussed.
Plastic design of beams and plane frames for minimum material consumption
Authors: Heyman Jacques
Published: December 2016

This paper is concerned with the design of plane frames in such a way that the material consumption is a minimum. The method of solution is to set up linear inequalities for the variables involved, and to solve these inequalities by the Dines

1

^{1}

method. Three slightly different classes of problem are treated; collapse design under fixed loads, collapse design under varying loads, and shakedown design under varying loads. Illustrative examples of each are given.
A general solution for the rectangular airfoil in supersonic flow
Authors: Miles John W.
Published: December 2016

The potential on a rectangular airfoil due to an arbitrarily prescribed motion at its surface is obtained by an operational solution of the linearized equations and subsequent comparison with the known solution in steady flow. It is shown that the result can be extended to more general planforms with the aid of the Lorentz transformation. Other methods of solution are noted.
A note on subsonic edges in unsteady supersonic flow
Authors: Miles John W.
Published: December 2016

The pressure distribution due to the unsteady motion of a wing having a supersonic leading edge and a subsonic trailing edge is determined by applying a Lorentz transformation to the corresponding result for a rectangular wing. This result, valid as it stands for a subsonic leading edge, is then modified by the addition of an eigensolution in order to satisfy the Kutta condition.
Connection formulas between the solutions of Mathieu’s equation
Authors: Wannier Gregory H.
Published: December 2016

The problem of connecting the various types of solutions of Mathieu’s equation is solved by the introduction of a new parameter

Φ
\Phi

which is a function of the the two equation parameters

a
a

and

q
q

. This quantity

Φ
\Phi

is introduced and enclosed between two very close analytic limits in section 2. In sections 3, 4, 5 precise definitions are given and information is collected for the three main types of functions which are to be connected. Section 6 contains the connection formulas. Section 7 reviews the status of knowledge achieved. Section 8 is an appendix on integral equations which are more general than those developed earlier in the text, but which appear to be of no use for the main purpose of this paper.
A random walk related to the capacitance of the circular plate condenser
Authors: Reich E.
Published: December 2016

It is shown that the solution of Love’s equation for the capacitance of the circular plate condenser can be expressed in terms of the mean duration of a certain one-dimensional random walk with absorbing barriers. The interpretation as a random walk makes it possible to confirm the fact that the actual capacitance of the condenser is always larger than the value given by the standard approximation for small separations, and yields an upper bound as well. In addition to its theoretical interest, the random walk appears to provide a practical means for the calculation of the capacitance by a Monte Carlo technique.
Addition theorems for spherical waves
Authors: Friedman Bernard , Russek Joy
Published: December 2016

Expansions or “addition theorems” for the spherical wave functions

j
n

(

k
R

)

P
n
m

(

cos
⁡
θ

)

exp
⁡

(

i
m
ϕ

)

{j_n}\left ( {kR} \right )P_n^m\left ( {\cos \theta } \right )\exp \left ( {im\phi } \right )

,
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="h Subscript n Superscript left-parenthesis 1 right-parenthesis Baseline left-parenthesis k upper R right-parenthesis upper P Subscript n Superscript m Baseline left-parenthesis cosine theta right-parenthesis exp left-parenthesis i m phi right-parenthesis">

h
n

(
1
)

(

k
R

)

P
n
m

(

cos
⁡
θ

)

exp
⁡

(

i
m
ϕ

)

h_n^{\left ( 1 \right )}\left ( {kR} \right )P_n^m\left ( {\cos \theta } \right )\exp \left ( {im\phi } \right )

, and
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="h Subscript n Superscript left-parenthesis 2 right-parenthesis Baseline left-parenthesis k upper R right-parenthesis upper P Subscript n Superscript m Baseline left-parenthesis cosine theta right-parenthesis exp left-parenthesis i m phi right-parenthesis">

h
n

(
2
)

(

k
R

)

P
n
m

(

cos
⁡
θ

)

exp
⁡

(

i
m
ϕ

)

h_n^{\left ( 2 \right )}\left ( {kR} \right )P_n^m\left ( {\cos \theta } \right )\exp \left ( {im\phi } \right )

, with reference to the origin

O
O

, have been obtained in terms of spherical wave functions with reference to the origin

O
′

O’

, where

O
′

O’

, has the coordinates

(

r
0

,

θ
0

,

ϕ
0

)

\left ( {{r_0},{\theta _0},{\phi _0}} \right )

with respect to

O
O

.
Equilibrium of membranes elastically supported at the edges
Authors: Hart V. G.
Published: December 2016

The problem considered is that of finding the statical deflection of a stretched membrane, subjected to a uniform pressure on one side and elastically supported at the edges. The deflection of the membrane is supposed small and the problem reduces to solving Laplace’s equation with mixed boundary conditions. Solutions are given for the cases where the bounding curve of the membrane is (i) an equilateral triangle, and (ii) a rectangle.
The plastic indentation of a layer by a flat punch
Authors: Shield R. T.
Published: December 2016

Upper and lower bounds for the average pressure in the indentation by a flat, smooth punch of the plane surface of a layer of elastic-perfectly plastic material resting on a rough, rigid base are obtained by the application of the limit-design theorems. The material of the layer is assumed to obey Tresca’s yield criterion of constant maximum shearing stress during plastic deformation. The square punch problem is considered in detail for layers whose thickness is greater than one-fourteenth of the width of the punch. For thinner layers, reasonably close upper and lower bounds for the average pressure over the square punch are obtained as functions of the relative thickness of the layer. The circular punch is considered briefly, and the bounds obtained determine the indentation force with sufficient accuracy for layers which are not too thick compared with the width of the punch.
The design of two-dimensional aerofoils with mixed boundary conditions
Authors: Woods L. C.
Published: December 2016

A method is given of designing two-dimensional symmetrical aerofoils in subsonic compressible flow when the boundary conditions are mixed. The aerofoil surface is divided into three parts such that the shape is prescribed in the first and third and the pressure distribution is specified in the second. The method has the advantage over the usual method of aerofoil design (pressure distribution given over the whole aerofoil surface) of giving the designer direct control of the nose shape and the trailing edge angle.
Axial displacement dislocations for the hollow cone and the hollow sphere
Authors: Goodier J. N. , Wilhoit J. C.
Published: December 2016

Simple solutions in closed form are given for the dislocational states of stress in a hollow cone (Fig. 3) or a hollow sphere (Fig. 5) induced by making an axial cut, and imposing a rigid-body displacement of one face of the cut relative to the other, in the axial direction. The problems are solved by adaptations of the Saint-Venant torsion theory, and of J. H. Michell’s theory of torsion of non-uniform shafts.
The free oscillations of a buckled panel
Authors: Hayes W. D. , Miles J. W.
Published: December 2016

The non-linear equations of motion of a buckled, two-dimensional panel are formulated in dimensionless form. A Fourier expansion in the space variable is introduced and an approximate solution is obtained for the period of free oscillation on the assumption of only two degrees of freedom, one of which is eliminated by the buckling constraint. The periods of the simplest asymmetric and symmetric modes are plotted as a function of the energy level. It is found that for very small energy levels the period of the buckled panel lies between the periods of the (two) unbuckled degrees of freedom. As the energy is increased the period approaches infinity at some critical energy level and thereafter decreases monotonically.
The torsion of a hollow square
Authors: Synge J. L. , Cahill W. F.
Published: December 2016

SEAC‡ is used to give an approximate solution to the torsion problem for a hollow square, with accurate determination of lower and upper bounds for torsional rigidity.
Waves produced by a pulsating source travelling beneath a free surface
Authors: Tan H. S.
Published: December 2016

The propagation of surface waves induced by a pulsating source travelling beneath a free surface is investigated by introducing Rayleigh’s dissipative force. By defining a disturbance velocity potential

R
φ

(

x
,
y

)

e
x
p

(

i
ω
t

)

R\varphi \left ( {x,y} \right ) exp \left ( {i\omega t} \right )

, it is shown that

φ

(

x
,
y

)

\varphi \left ( {x,y} \right )

has to satisfy throughout the flow field not only the Laplace equation, but also a differential equation resulting from the analytic extension of the free surface boundary condition. The solution is obtained in the form
\[

φ

(

x
,
y

)

=
f

(
z
)

+
g

(

z
¯

)

,

z
=
x
+
i
y

\varphi \left ( {x,y} \right ) = f\left ( z \right ) + g\left ( {\bar z} \right ),\qquad z = x + iy

\]
, i.e.,

φ

(

x
,
y

)

\varphi \left ( {x,y} \right )

is a complex harmonic function of

x
x

,

y
y

but is not an analytic function of

z
z

. The wave propagation is found to depend on a parameter

τ
\tau

, which is the ratio of the pulsation frequency

ω
\omega

of the source strength to the fundamental frequency

ω
0

{\omega _0}

of the surface wave produced by a constant strength source travelling at the same speed. The case

τ
=
0

\tau = 0

, corresponding to the travelling source of constant strength, does give a single undamped harmonic wave train on the downstream side, of wave length

2
π

c
2

/

g

2\pi {c^2}/g

, (or frequency

ω
0

{\omega _0}

), as is expected. For

0
>
τ
>
1

/

4

0 > \tau > 1/4

, there are four, and for

τ
>
1

/

4

\tau > 1/4

, two undamped harmonic wave trains of different wave lengths on the downstream side. It is further observed that there exists a critical frequency at

τ
=
1

/

4

\tau = 1/4

, at which frequency resonance phenomena occur. Thus violent disturbance is predicted at

τ
=
1

/

4

\tau = 1/4

by the present analysis. No disturbance is found to propagate infinitely upstream. This result evidently justifies the imposition of an asymptotic upstream condition of “vanishing disturbance at infinity” to replace the effect of the dissipative force in rendering the solution unique.

1

^{1}
Bounds on minimum weight design
Authors: Drucker D. C. , Shield R. T.
Published: December 2016

A somewhat limited design procedure for elastic-perfectly plastic structures was developed previously [1]

∗
∗

^{**}

. It is extended here to provide upper and lower bounds on the minimum weight of three dimensional structures and is specialized to safe one and two dimensional structures in which either direct stresses or bending stresses are negligible. The generalization also includes the influence of body forces. In principle, therefore, such troublesome factors as the weight of the structure itself or centrifugal “forces” may be designed for in a direct manner. Radially symmetric plane stress and plate bending examples are solved to demonstrate direct design procedures.
Some aspects of three-dimensional boundary layer flows
Authors: Sedney R.
Published: December 2016

The equations for laminar boundary layer flow over a general smooth surface in three dimensions are analyzed in a normal coordinate system. The invariance properties of these equations are found using the concept of subtensors. The boundary layer equations are not tensor equations but subtensor equations. Conditions for the Cartesian form of the equations are given and a criterion for no secondary flow is found in terms of the geodesies of the body surface. The displacement effect of the boundary layer is also discussed.
On local stability of a finitely deformed solid subjected to follower type loads
Authors: Nemat-Nasser S.
Published: December 2016

In this study the problem of the local stability (stability in the small) of a finitely deformed solid subjected to a set of follower type surface loads is analyzed, and a necessary, and a sufficient condition for asymptotic stability is established. Certain implications of the commonly used modal analysis are also investigated, and necessary and sufficient conditions for stability are formulated.
A singular perturbation method. Part II
Authors: Fowkes N. D.
Published: December 2016

This paper extends the work of Part I to the partial differential equation
\[

ϵ
3

∇
2

ψ
−
g

(
x
)

ψ
=
0

{\epsilon ^3}{\nabla ^2}\psi - g\left ( x \right )\psi = 0

\]
where

ϵ
\epsilon

is a small positive parameter and

g

(
x
)

g\left ( x \right )

is a bounded function of

x
x

which vanishes along simple closed surfaces in the solution domain. In particular, the eigenproblem corresponding to the case in which

g

(
x
)

g\left ( x \right )

is positive at infinity and in which the boundary condition

ψ
→
0

\psi \to 0

as

|
x
|

→
∞

\left | x \right | \to \infty

is imposed, is considered. One class of eigensolutions is extracted.
Rolling contact between dissimilar viscoelastic cylinders
Authors: Morland L. W.
Published: December 2016

This paper treats the plane problem of rolling contact between linear viscoelastic cylinders with different radii and different quantitative mechanical response. The analysis is an extension of that previously given for the simpler problem of rolling contact between two identical cylinders (or equivalently one cylinder and a rigid half-plane), for which a singular integral equation was derived connecting pressure and normal displacement in the contact region. The present problem is shown to lead to an integral equation of identical form but containing further parameters which reflect the difference in the properties of the two cylinders. A neater construction of the closed form solution of the integral equation is presented and the final formulae are expressed in terms of tabulated functions. An illustration is given for a viscoelastic model with two characteristic times.
An exact general solution for the temperature distribution and the composite radiation convection heat exchange along a constant cross-sectional area fin
Authors: Shouman A. R.
Published: December 2016

An exact general solution is obtained for the nonlinear differential equation governing the one-dimensional steady-state heat exchange by composite radiation and convection along constant area fins with uniform temperature at the base and an arbitrary temperature gradient at the other end. The fin can dissipate or receive energy. The fin is assumed to have constant thermal properties, and the radiant interaction between the fin and the base surfaces is neglected.
Directivity for one-dimensional scalar raciation
Authors: Synge J. L.
Published: December 2016

This is an elementary contribution to the theory of directivity for scalar radiation. An infinite string is made to vibrate by application of external force to a finite portion of it. It is shown how this force may be applied so that all the energy travels off to the right and none to the left.
A note on singularities in a Cosserat continuum
Authors: Weitsman Yechiel
Published: December 2016

This paper is concerned with the singularities that are due to concentrated couples in an infinite linear, elastic, isotropic Cosserat continuum. The solution to the problem of a concentrated couple, acting within an infinite region, may be obtained as a limiting case of the solution to the problem of body moments acting within a finite portion of the infinite medium. Alternatively, the solution to the problem of the concentrated couple can be constructed from the solution to the case of a concentrated force acting within an infinite body, by combining two double-forces with moments to form a center of rotation.
Nonlinear oscillations in a distributed network
Authors: Brayton Robert K.
Published: December 2016

The oscillations of small amplitude in a lossless transmission line terminated with a nonlinear circuit are studied by perturbation theory. The equations describing this system are reduced to a difference-differential equation with one delay. A general procedure is given for equations of this type for finding the expansion of the oscillation to any order in terms of the coefficient of the fundamental frequency. The frequency-amplitude relations are obtained to second order and compared with results found on the computer. Both the autonomous and forced cases are studied. It is indicated in the forced case that the frequency-amplitude relation gives approximately the range of “locking in".
Dispersion of small amplitute stress waves in pre-stressed elastic, visco-plastic cylindrical bars
Authors: Bejda Jozef , Wierzbicki Tomasz
Published: December 2016

The effect of geometrical dispersion on the propagation of longitudinal harmonic stress waves in prestressed elastic, visco-plastic bars is investigated. The solution involves the Hunter and Johnson approximation in which radial and axial displacements and all components of stress tensor are expanded as power series in the radial coordinate. It is shown that the dispersion of the sinusoidal waves is generated by the two simultaneously acting phenomena. These are the purely geometrical dispersion produced by the influence of a free boundary of the bar and the viscous dispersion caused by the viscous properties of material. The obtained solution embraces the combined effect of the phenomena mentioned above. A numerical example is presented in which constants of material characteristic for mild steel were used. The result of the computations provides a plot of phase and group velocities and damping coefficient against the frequency of harmonic waves. The present solution has been compared with the Hunter and Johnson solution for strain-hardening elastic-plastic material and with the exact Pochhammer-Chree solution for elastic rods.
The resistance on a circular cylinder in an oscillating stream
Authors: Wang Chang-Yi
Published: December 2016

The boundary layer equations, formulated in cylindrical polar coordinates, are applied to a circular cylinder in a slightly viscous stream which is oscillating with a high reduced frequency. The resistance is correctly calculated to the second order. The first order part,

45
∘

45^\circ

out of phase, is due to the interaction of viscosity with acceleration. The second order part,

−

90
∘

-90^\circ

out of phase, is due to the interaction of viscosity with curvature. The interaction of viscosity with inertia, which is of second order also, contributes no resistance.
Corrections in hot-wire correlation measurements
Authors: Pearson Carl E.
Published: December 2016

Particularly in small-scale turbulence, hot-wire correlation measurements must be corrected for the effect of finite wire length. End effects, imperfect velocity correlation along the length of the wire and transient longitudinal heat conduction must be considered. An integral equation for these corrections is obtained; with appropriate experimental procedure, this equation may be solved explicitly.