bluuebunny/crossref_metadata_2025 huggingface dataset:
Turn design and progression
Authors: Wu Ruey-Jiuan Regina
Published: December 2016

The temporal character of talk is one fundamental feature of languagein situ. As interaction unfolds, participants need to not only monitor the temporal progression of talk toward a completion, but also attend to how the current turn ties back to the preceding turns. Whereas such dual-directional consideration is often a latent aspect of turn construction, at times efforts to clear up possible ambiguity are in order. This article introduces a Mandarin practice,aiyou-preface, which seems to be used just to this end, and demonstrates an intimate relationship between the prosodic design ofaiyou-preface and the displayed orientation to the intended directionality of the talk. The analysis draws upon a corpus of 35 hours of conversations collected in China.
Solutions in Constructive Field Theory
Authors: Hancox-Li Leif
Published: December 2016

Constructive field theory aims to rigorously construct concrete, nontrivial solutions to Lagrangians used in particle physics. I examine the relationship of solutions in constructive field theory to both axiomatic and Lagrangian quantum field theory (QFT). I argue that Lagrangian QFT provides conditions for what counts as a successful constructive solution and other information that guides constructive field theorists to solutions. Solutions matter because they describe the behavior of QFT systems and thus what QFT says the world is like. Constructive field theory clarifies existing disputes about which parts of QFT are philosophically relevant and how rigor relates to these disputes.
On an initial value problem concerning Taylor instability of incompressible fluids
Authors: Carrier G. F. , Chang C. T.
Published: December 2016

By taking the effect of surface tension and viscosity into consideration, Bellman and Pennington [2] have generalized the original treatment of the problem of Taylor instability [1]. They claim, however, that a problem in which the motion starts from rest cannot be treated with their linearized formulation. In this paper, the initial value problem is treated and, although the algebra becomes more complicated, the linearized analysis suffices. In particular, the cut-off wave number as found in [2] is not modified.
Folding of a layered viscoelastic medium derived from an exact stability theory of a continuum under initial stress
Authors: Biot M. A.
Published: December 2016

A layer of viscoelastic material embedded in an infinite medium also viscoelastic tends to fold through instability when the system is compressed in a direction parallel with the layer. This phenomenon which was treated previously by using an approximate plate theory, [1, 2], is analyzed here by using an exact theory for the deformation of a continuum under prestress [3, 4, 5, 6], The effect of the compressive prestress in the embedding medium is taken into account, and it is found that although it is not always negligible, it tends to be very small under conditions where the instability of the layer is strong. The same conclusion holds for the error involved in the use of a plate theory for the layer instead of the exact equations for a prestressed continuum. In the course of the analysis we have also treated the problem of a semi-infinite viscoelastic half space subject to a uniform internal compression parallel with the boundary and a surface load normal to this boundary. The compressive load produces an increase of the surface deflection under the normal load. This effect appears through an amplification factor which is evaluated numerically for the particular example of an elastic body. It is shown that under certain conditions the free surface of the compressed semi-infinite medium may become unstable and will tend to wrinkle. This is suggested as a probable explanation for the wrinkles which appear on the surface of a body subjected to a plastic compression.
Approximate distributions of noise power measurements
Authors: Freiberger Walter , Grenander Ulf
Published: December 2016

The frequency functions of certain spectral estimates are studied analytically and numerically. An approximation is obtained for the case of a Poisson weight function and compared to the true distribution. The eigenvalues of products of Toeplitz matrices play a crucial role in the sampling theory of quadratic forms; an approximation to their distribution is discussed and its accuracy studied numerically. This leads to approximate probability densities which are thought to be valid for moderate or even small sample sizes.
Shape-preserving solutions of the time-dependent diffusion equation
Authors: Ham Frank S.
Published: December 2016

Exact solutions to the time-dependent diffusion equation are exhibited which correspond to the diffusion-limited growth of ellipsoidal precipitate particles with constant shape and dimensions proportional to the square root of the time. The asymmetry of the diffusion field in these solutions is consistent with the preservation of the particle’s shape during growth even if the diffusivity is anisotropic. Limiting cases for simpler geometries are derived and shown to be in agreement with previously known results for radially symmetric particles and isotropic diffusion. Similar solutions for hyperboloidal surfaces are exhibited and generalizations are considered analogous to those discussed by Danckwerts for one-dimensional diffusion.
Plate design for minimum weight
Authors: Shield R. T.
Published: December 2016

A discussion of the equations determining the minimum weight design of transversely loaded sandwich plates is given. By means of an inverse method, the solution for an elliptical plate clamped around its edge is derived.
Transient motion of a line load on the surface of an elastic half-space
Authors: Ang Dang Dinh
Published: December 2016

The present paper studies the wave patterns generated in an elastic half-space by a line load moving on its surface with a velocity varying as a step function of time. The solution given in closed form is obtained by means of Fourier integral equations techniques following a Laplace transformation with respect to the time variable. The inversion of the Laplace transforms is based on a trick due to Cagniard and De Hoop.
The Mises yield condition for rotationally symmetric shells
Authors: Hodge P. G.
Published: December 2016

The stress state in a rotationally symmetric shell under small displacements is characterized by the direct stresses and moments in the circumferential and longitudinal directions. If the shell material is perfectly plastic, it is desirable to express the material yield condition in terms of these stress resultants. Previous investigations have obtained this yield condition in certain special cases and for the maximum shear stress criterion in the general case.
On the one-dimensional flow of a conducting gas in crossed fields
Authors: Dahlberg Erling
Published: December 2016

The equations governing the quasi-one-dimensional steady flow of a conducting perfect gas in crossed, transverse electric and magnetic fields are treated under the assumptions that the electric conductivity is a scalar, that the wall drag is small and that the magnetic field due to the currents in the gas is negligible. The equations are normalized and different flow situations are illustrated by means of phase diagrams (drawn for a gas of constant specific heats,

γ
=
1.33

\gamma = 1.33

). The possibility of a smooth transition from supersonic to subsonic motion is pointed out and the phenomena of standing shock fronts and choking are surveyed for constant-area, small-friction, power-yielding flow. The appendix contains some general remarks on the system of non-linear differential equations:

x
′

=
P

(

x
,
y

)

/

R

(

x
,
y

)

x’ = P\left ( {x,y} \right )/R\left ( {x,y} \right )

;

y
′

=
Q
(
x
,
y
)

/

R
(
x
,
y
)

y’ = Q(x,y)/R(x,y)

.
Steady spheroidal vortices—More exact solutions to the Navier-Stokes equation
Authors: O’Brien Vivian
Published: December 2016

The vorticity equation, the curl of the Navier-Stokes equation, is considered in ellipsoidal coordinates. The steady spheroidal vortex solutions are demonstrated as examples of a class of exact flow solutions characterized by a simple linear vorticity distribution.
The 𝐴𝑡𝑒𝑏(ℎ)-functions and their properties
Authors: Rosenberg R. M.
Published: December 2016

The Ateb(h)-functions are inversions of incomplete Beta-functions. They are the solutions of normal mode vibrations of certain nonlinear multi-degree-of-freedom systems just as the trigonometric functions yield the normal mode vibrations of the corresponding linear systems. Like elliptic functions, the Ateb(h)-functions depend on a parameter. The Ateb-functions reduce to trigonometric functions, and the Atebh-functions to hyperbolic functions when the parameter is 1. When the parameter is 2, the Ateb-functions become elliptic functions. A number of properties of the Ateb(h)-functions, such as identities, derivatives, integrals, differential equations satisfied by them, etc., are given.
Function-theoretic solution to a class of dual integral equations and an application to diffraction theory
Authors: Schmeltzer Robert A. , Lewin Myrna
Published: December 2016

Dual integral equations of the type
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="integral Subscript 0 Superscript normal infinity Baseline u Superscript lamda Baseline f left-parenthesis u right-parenthesis upper J Subscript mu Baseline left-parenthesis r u right-parenthesis d u equals g left-parenthesis r right-parenthesis comma 0 greater-than r greater-than 1 comma integral Subscript 0 Superscript normal infinity Baseline u left-parenthesis u squared plus a squared right-parenthesis Superscript negative 1 slash 2 Baseline f left-parenthesis u right-parenthesis upper J Subscript v Baseline left-parenthesis r u right-parenthesis d u equals h left-parenthesis r right-parenthesis comma 1 greater-than r greater-than normal infinity comma">

∫
0
∞

u
λ

f

(
u
)

J
μ

(

r
u

)

d
u
=
g

(
r
)

,
0
>
r
>
1
,

∫
0
∞

u

(

u
2

+

a
2

)

−
1

/

2

f

(
u
)

J
v

(

r
u

)

d
u
=
h

(
r
)

,

1
>
r
>
∞
,

\int _0^\infty {{u^\lambda }f\left ( u \right ){J_\mu }\left ( {ru} \right )du = g\left ( r \right ),0 > r > 1, \\ \int _0^\infty u {{\left ( {{u^2} + {a^2}} \right )}^{ - 1/2}}f\left ( u \right ){J_v}\left ( {ru} \right )du = h\left ( r \right ),} 1 > r > \infty ,

\]
where

g

(
r
)

g\left ( r \right )

,

h

(
r
)

h\left ( r \right )

are prescribed functions and

f

(
u
)

f\left ( u \right )

is to be found, are solved exactly by the application of function-theoretic methods. As an example, a closed-form solution is obtained for the diffraction of an electromagnetic wave by a plane slit.
The associated elastic problems in dynamic visco-elasticity
Authors: Tao L. N.
Published: December 2016

The paper is concerned with the associated elastic problems of linear visco-elastic bodies under dynamic conditions. By the introduction of an adjunct problem and the use of Laplace transforms, an associated elastic problem is established. This includes the quasi-static study of Lee as a special case. Also, a modification of the adjunct problem leads to a second associated elastic problem, which is in agreement with the correspondence principle.
Plastic plate theory
Authors: Hodge Philip G.
Published: December 2016

It is shown that the governing equations for perfectly plastic flow of plates are generally elliptic, the only exceptions being certain piecewise linear yield conditions and corners of the yield curve.
Temperature distributions in rotating flows normal to a flat surface
Authors: Lugt Hans J. , Schwiderski Ernst W.
Published: December 2016

The temperature fields of rotating laminar flows over a flat surface are investigated. Dissipation is considered, whereas free convection effects are neglected. The calculation is based on the knowledge of the flow fields, which have been studied in previous papers by the authors. In these papers first order approximations reduce the Navier-Stokes equations to ordinary differential equations. The basic ideas of this method are applied to the energy equation. In the special case of negligible dissipation the heat transfer of von Kármán type flows can be compared with existing experimental data. The agreement is satisfactory.
Transient solutions for a class of diffraction problems
Authors: Felsen L. B.
Published: December 2016

The study of the fields excited by impulsive sources in layered media has been facilitated by a technique employed originally by Cagniard and Pekeris, and simplified subsequently by de Hoop. The procedure involves a reformulation of the time-harmonic solution so as to permit the explicit recovery of the transient result by inspection. In the present paper, it is shown that this method may be applied conveniently to the inversion of a certain Sommerfeld-type integral which occurs frequently in diffraction theory, thereby unifying the analysis of a class of pulse diffraction problems. Illustrative examples include the transient response to a line source in the presence of a dielectric half space, a perfectly absorbing and perfectly reflecting wedge, and a unidirectionally conducting infinite and semi-infinite screen. The latter applications illuminate the role of surface waves in the impulsive solution. It is found, in contrast to the time-harmonic case, that a different behavior characterizes the surface waves excited on a unidirectionally conducting half plane by the incident field and by the edge discontinuity, respectively.
On certain relaxation oscillations: Confining regions
Authors: Ponzo Peter J. , Wax Nelson
Published: December 2016

Relaxation oscillations described by the generalized Liénard equation,

d
2

x

/

d

t
2

+
μ
f
(
x
)
d
x

/

d
t
+
g
(
x
)
=
0

{d^2}x/d{t^2} + \mu f(x)dx/dt + g(x) = 0

, with

μ
≫
1

\mu \gg 1

, are investigated in the phase and Liénard planes. When

f
(
x
)

f(x)

,

g
(
x
)

g(x)

, and

F

(
x
)

=

∫
0
x

f

(
u
)

d
u

F\left ( x \right ) = \int _0^x {f\left ( u \right )du}

are subject to certain restrictions, a number of analytic curves can be obtained in these planes which serve as bounds on solution trajectories. Piece-wise connection of such bounding curves provide explicit annular regions with the property that solution trajectories on the boundary of an annulus move to the interior with increasing time,

t
t

. The Poincaré—Bendixson theorem then guarantees at least one periodic orbit within such an annulus. It is shown that the periodic orbits which are isolated by this means are unique within the annulus, hence orbitally stable. The maximum width of the annulus is of order

μ

−
4

/

3

{\mu ^{ - 4/3}}

, and the amplitude bounds obtained for the periodic solution agree favorably with the known amplitude for the specific case of the van der Pol equation

d
2

x

/

d

t
2

+
μ

(

x
2

−
1

)

d
x

/

d
t
+
x
=
0

{d^2}x/d{t^2} + \mu \left ( {{x^2} - 1} \right )dx/dt + x = 0

. The results are generalized to less restrictive

f
(
x
)

f(x)

,

g
(
x
)

g(x)

, and

F
(
x
)

F(x)

than those first considered.
Buckling of an elastic membrane on a surface of revolution
Authors: Schechter Murray
Published: December 2016

This paper is concerned with a generalization of the following problem in nonlinear membrane theory studied by S. Lubkin [1] and C. Sensenig [2]: a membrane in the shape of an annulus is deformed by the application of a hydrostatic pressure to the outer boundary while the inner boundary remains stress free. The membrane is constrained to lie between two lubricated plates, so that no work is done at these surfaces during the deformation. The deformation is rotationally symmetric, each point on the membrane moving along a radius so that the deformed membrane is still in the shape of an annulus. What is to be determined is the stability of this deformation with respect to asymmetric disturbances satisfying the same stress conditions at the two boundaries and the same constraint imposed by the plates.
A nonlinear theory of plasticity for plane strain
Authors: Shoemaker E. M.
Published: December 2016

A nonlinear theory of plasticity is proposed which facilitates the solution of a restricted class of plane strain problems. An anisotropic approximation to a real material is utilized with the characteristic directions chosen a priori. The formulation is in terms of displacements and sufficient displacement boundary conditions must be prescribed in order to solve the resulting classical wave equation. Subsequently, the stress field is determined, corresponding to any nonlinear monotonic relation between shear stress and strain, by direct integration of the equilibrium equations. Uniqueness restricts the class of problems suitable to the theory. Classical isotropic theory will be closely approximated in problems where the deviatoric stress field is predominantly uniform. The theory is illustrated by the solution of an indentation problem.
Linearization based upon differential approximation and Galerkin’s method
Authors: Bellman R. , Richardson J. M.
Published: December 2016

We present a new linearization technique based upon differential approximation which is considerably simpler and more flexible than those used in our previous work.
A new perturbation technique for differential equations with small parameters
Authors: Brull M. A. , Soler A. I.
Published: December 2016

Ordinary linear differential equations containing small parameter

ϵ
\epsilon

are investigated in regard to the existence of solutions in power series of the parameter. A new perturbation technique is developed which yields solutions more convenient for computation than comparable solutions obtained by making the usual series expansion in the small parameter. The new method is applied to second and fourth order differential equations in normal form and it is shown that the method yields asymptotic solution for small

ϵ
\epsilon

. Conditions needed for successful application of the method are discussed and a typical solution is obtained. Comparison of numerical results with an exact solution and with an ordinary perturbation solution indicates the usefulness of the technique.
Pseudo-similarity solutions of the one-dimensional diffusion equation with applications to the phase change problem
Authors: Langford David
Published: December 2016

New solutions of the diffusion equation may be used to prescribe both the diffusion potential and the diffusional flow rate, along the moving curve

X
=
α

(

1
+
β
⋅
T

)

1

/

2

X = \alpha {\left ( {1 + \beta \cdot T} \right )^{1/2}}

, as arbitrary power series in the variable

(

α

(

1
+
β
⋅
T

)

1

/

2

)

\left ( {\alpha {{\left ( {1 + \beta \cdot T} \right )}^{1/2}}} \right )

, where

α
\alpha

and

β
\beta

are arbitrary constants and

T
T

is time.
On the distance between polytopes
Authors: Willner Leopold B.
Published: December 2016

This paper is written to fill an apparent gap in the literature in connection with some elementary problems of distance in finite dimensional normed linear spaces. In particular the problem of determining the distance between two polytopes in a normed

n
n

-dimensional real vector space is considered. Special consideration is given to the case in which the norm is a twice differentiable function of its arguments and for this case a convex programming algorithm is presented. In addition several other cases are considered including the well known discrete Tchebycheff approximation. The results should find application in approximation theory.
Motion in the neighborhood of a stationary point
Authors: Morrison J. A.
Published: December 2016

A perturbed system of differential equations is considered, wherein the zero order rate of change of one variable, which depends on the other, slowly changing, variables, vanishes at a particular point. A detailed analysis of the motions in certain close neighborhoods of the stationaiy point of the perturbed system is given, the method of averaging being applied, after some preliminary transformations have been made. It is found that the motions corresponding to the averaged equations are damped under the stability conditions given in [1] by Volosov and Morgunov, who considered a more general problem. However, our analysis reveals the nature of the motion in the neighborhood of the stationary point, and, moreover, our results are valid for a time interval of the order of the reciprocal of the perturbation parameter, rather than the reciprocal of just its square root.
Series representations of Fourier integrals
Authors: Levey H. C. , Mahony J. J.
Published: December 2016

General series representations, valid at least for small values of

x
x

, are obtained for the representative Fourier integral

∫
0
∞

A

(
k
)

exp
⁡

(

i
k
x

)

d
k

\int _0^\infty {A\left ( k \right ) \exp \left ( {ikx} \right ) dk}

for a variety of asymptotic forms of behaviour of the function

A

(
k
)

A\left ( k \right )

, assumed bounded and integrable in any finite range. The results obtained should be of value in the numerical evaluation of such integrals as well as in the determination of their analytic properties.
On some inverse problems in dynamics
Authors: Klamkin M. S. , Newman D. J.
Published: December 2016

It is known that the time of traverse of a freely falling body through a straight tunnel connecting any two points of the surface of a uniform spherical planet is isochronous. We show here that if the isochronous property is to hold for any planet with a spherical symmetric density, then the density must be constant. Also it is shown that if the isochronous property is to hold for any uniform spherical planet subject to a central force law, then the force law must be inverse square. However, the isochronous property can hold for one uniform spherical planet with a different force law of attraction.
Uniqueness theorem for a multi-mode surface wave diffraction problem.
Authors: Morgan R. C.
Published: December 2016

Uniqueness is demonstrated for the solution to the reduced wave equation subject to a mixed boundary value condition that excites two surface wave modes. The configuration is taken as a right-angled wedge and the edge condition assumed has the form
The oscillating rectangular airfoil at supersonic speeds
Authors: Miles John W.
Published: December 2016

The pressure distribution on a quarter infinite, zero thickness airfoil having a prescribed distribution of downwash (on the wing only), which exhibits a harmonic time dependence, is determined by a Fourier transform solution of the linearized, potential equation for supersonic flow. The solution is effected with the aid of the Wiener-Hopf technique and leads to a Green’s function, which may be expressed either as a finite, definite integral or as an expansion in powers of a dimensionless frequency parameter. It is shown that the results are applicable to the calculation of the forces and moments on rectangular airfoils of effective aspect ratio (

A
cot
⁡
θ

A\cot \theta

, where

θ
\theta

is the Mach angle) greater than unity. It appears that the force and moment coefficients of practical interest may be expressed in terms of known functions, including certain integrals which have been calculated for the two-dimensional, oscillating airfoil. The extension of the two-dimensional results to rectangular wings for which the prescribed downwash is constant along the span is particularly simple. The extension of the results for harmonic time dependence to the step function (Heaviside) case is indicated.
A boundary value problem in the theory of plastic wave propagation
Authors: Lee E. H.
Published: December 2016

In the analysis of boundary value problems in the theory of plasticity, the general situation arises that different partial differential equations are to be satisfied depending on whether the material is in the plastic or elastic state. The criterion determining the state at any material point depends on the dependent variables and their derivatives with respect to time. Thus the regions of application of the different differential equations must be determined from the boundary and initial conditions as the solution is developed. The theory of the propagation of plastic waves in one dimension is a case in which the solution, including the determination of the unknown plastic-elastic boundaries, can be treated. An example is presented in this paper which illustrates the many types of boundary determination conditions which must be used. The method is based on the numerical integration along the characteristics of the hyperbolic equations arising, one linear and one quasi-linear. The development is possible since forward integration along characteristics enables the unknown boundaries to be determined independently of the subsequent solution. This situation is contrasted with other problems in the theory of plasticity. The complexity of the procedure indicates the difficulty to be anticipated with analytical treatment of such problems, and with the numerical treatment of problems involving more extensive plastic flow.
Reflection of waves from varying media
Authors: Hines C. O.
Published: December 2016

Formulae are found for the coefficient of reflection from varying media of a type encountered in physics. These are applied approximately for some general classes of media, and exactly for some specific cases. Many media which would normally be expected to be highly reflecting are shown to be completely transparent to certain waves at least and, in some cases, to a whole spectrum of waves. The results are considered both for electromagnetic (or other classical) waves and for mass waves.
Stress functions of Maxwell and Morera
Authors: Ornstein Wilhelm
Published: December 2016

A systematic process is devised for the derivation of the stress functions of Maxwell and Morera by the application of the theorem that a vector whose divergence vanishes is solenoidal. Symmetric and anti-symmetric matrices are established, and the elements of these matrices represent the stress functions of Maxwell and Morera respectively.
On the transformation of the linearized equation of unsteady supersonic flow
Authors: Miles John W.
Published: December 2016

The linearized potential equation for unsteady motion in frictionless, supersonic flow is transformed from the classical wave equation to the canonical form

ϕ

x
x

−

ϕ

y
y

−

ϕ

z
z

=

ϕ

τ
τ

{\phi _{xx}} - {\phi _{yy}} - {\phi _{zz}} = {\phi _{\tau \tau }}

with the aid of a modified Lorentz transformation. Possible invariant transformations of the latter, including the classical Lorentz transformation, are discussed. Eleven coordinate systems (each of which has its counterpart in the classical theory of the wave equation) permitting separation of variables are set forth, their derivation being based on the analogy between the hyperbolic metric defined by

(

d
s

)

2

=

(

d
x

)

2

−

(

d
y

)

2

−

(

d
z

)

2

{\left ( {ds} \right )^2} = {\left ( {dx} \right )^2} - {\left ( {dy} \right )^2} - {\left ( {dz} \right )^2}

and the Euclidean (Cartesian) metric. A few practical applications are indicated.
Heat transfer by free convection across a closed cavity between vertical boundaries at different temperatures
Authors: Batchelor G. K.
Published: December 2016

The two-dimensional convective motion generated by buoyancy forces on the fluid in a long rectangle, of which the two long sides are vertical boundaries held at different temperatures, is considered with a view to the determination of the rate of transfer of heat between the two vertical boundaries. The governing equations are set up; they reveal that the flow is determined uniquely by the Prandtl number

σ
\sigma

, the Rayleigh number

A
=
g

(

T
1

−

T
0

)

d
3

/

(

T
0

κ
ν

)

A = g\left ( {{T_1} - {T_0}} \right ){d^3}/\left ( {{T_0}\kappa \nu } \right )

, and the ratio of the sides of the rectangle

l

/

d

l/d

. In the case of cavities used for thermal insulation of buildings, which is kept specially in mind throughout the paper,

A
A

is usually about 1000 d

3

^{3}

(where

d
d

is in centimeters), and

l

/

d

l/d

takes values between about 5 and 200.
A note on laminar axially symmetric jets
Authors: Beran Mark
Published: December 2016

It is shown that there is no stream function of the form

ψ
=
r
f

(
θ
)

\psi = rf\left ( \theta \right )

, that is compatible with the complete Navier-Stokes equations, which represents a jet issuing from a small circular hole in an axially symmetric cone.
A method for the construction of Green’s functions
Authors: Boley Bruno A.
Published: December 2016

A method is outlined for the determination of the Green’s function associated with any partial differential equation for arbitrary domains. The Green’s function is obtained as the solution of an integral equation. A method of solution of this equation is discussed which yields the Green’s function as the limit of an infinite sequence of functions. Convergence of this sequence is proved for the case of Helmholtz’ equation. An example from the theory of heat conduction is solved in detail.
On the steady-state thermoelastic problem for the half-space
Authors: Sternberg E. , McDowell E. L.
Published: December 2016

This paper deals with the determination of the steady-state thermal stresses and displacements in a semi-infinite elastic medium which is bounded by a plane. The problem is treated within the classical theory of elasticity and is approached by the method of Green. It is shown that the stress field induced by an arbitrary distribution of surface temperatures is plane and parallel to the boundary. If the surface temperature is prescribed arbitrarily over a bounded “region of exposure” and is otherwise constant, the problem reduces to the determination of Boussinesq’s three-dimensional logarithmic potential for a disk in the shape of the region of exposure, whose mass density is equal to the given temperature. Moreover, it is found that there exists a useful connection between the solutions to Boussinesq’s and to the present problem for the half-space. An exact closed solution, in terms of complete and incomplete elliptic integrals of the first and second kind, is given for a circular region of exposure at uniform temperature. Exact solutions in terms of elementary functions are presented for a hemispherical distribution of temperature over a circular region, as well as for a rectangle at constant temperature.
Heat flow in a cylinder
Authors: Reid Walter P.
Published: December 2016

A formal, analytical solution is given to the problem of finding the temperature in a cylinder which is gaining or losing heat by radiation exchange with a concentric, thin-walled metal tube. The tube in turn is radiating to, or receiving radiation from, its surroundings. A general treatment of systems with this type of boundary condition is presented first, and then the given problem is solved as a particular case.
Stability limits for a clamped spherical shell segment under uniform pressure
Authors: Archer Robert R.
Published: December 2016

An integration procedure for the differential equations for the finite deflections of clamped shallow spherical shells under uniform pressure is developed. Stability limits for the clamped shell are obtained for a range of the central height to thickness ratio from about 1 to 35. This serves to correct and extend previously known stability limits for this problem.
Torsion of a finite elastic cylindrical rod partially bonded to an elastic half space
Authors: Keer L. M. , Freeman N. J.
Published: December 2016

A solution is given for the problem of axially symmetric torsion of a finite elastic cylindrical rod partially bonded to an elastic half space. The problem is formulated in a manner that involves coupling between dual Dini series and dual integral equations. Auxiliary functions are introduced and the problem is reduced to the solution of a Fredholm integral equation of the second kind. Approximate closed-form results are obtained when the radius of the bonded region is less than one-half the radius of the cylinder. Fractional order singularities in the stress are noted and calculated for the case when the crack vanishes.
Parameter values excluded by existence conditions for buoyant dissipative motions in vertical channels
Authors: Joseph D. D. , Warner W. H.
Published: December 2016

The nonexistence of steady, fully-developed solutions for frictionally-heated buoyant flow in vertical channels is established analytically. Explicit bounds on the values of parameters beyond which solutions to this nonlinear problem cannot exist are derived by integral estimation and by a priori comparison methods. The a priori bound shows that no solution exists if a linear combination of the pressure gradient, constant heat source and wall temperature difference is larger than a specific number proportional to the lowest eigenvalue of a linear comparison equation. The integral estimation procedure leads to the delineation of excluded regions in a parameter space; for parameter values in these regions, no solution exists. For boundary conditions permitting a symmetric solution, the integral estimates exclude further regions in the parameter space, while the power series solution leads to an excluded line of values.
An integral equation approach to boundary value problems of classical elastostatics
Authors: Rizzo Frank J.
Published: December 2016

The analogy between potential theory and classical elasticity suggests an extension of the powerful method of integral equations to the boundary value problems of elasticity. A vector boundary formula relating the boundary values of displacement and traction for the general equilibrated stress state is derived. The vector formula itself is shown to generate integral equations for the solution of the traction, displacement, and mixed boundary value problems of plane elasticity. However, an outstanding conceptual advantage of the formulation is that it is not restricted to two dimensions. This distinguishes it from the methods of Muskhelishvili and most other familiar integral equation methods. The presented approach is a real variable one and is applicable, without inherent restriction, to multiply connected domains. More precisely, no difficulty of the order of determining a mapping function is present and unwanted Volterra type dislocation solutions are eliminated a priori. An indication of techniques necessary to effect numerical solution of the resulting integral equations is presented with numerical data from a set of test problems.
Dynamic snap-through of a simple viscoelastic truss
Authors: Nachbar W. , Huang N. C.
Published: December 2016

In order to understand the behavior of shallow structures in dynamic snap-through or buckling, a detailed study has been made for a plane, viscoelastic, three-hinged truss with a concentrated mass at the central hinge, and with a normal load of constant magnitude applied suddenly at this hinge. The dynamic buckling criterion is found to correspond to values of the parameters for which the solution goes into the saddle point of a two-dimensional autonomous system. It is shown that another dynamic buckling criterion, based upon the asymptotic behavior of solutions in time, can give incorrect results in certain cases. Two methods to compute buckling loads are investigated with the aid of a phase plane diagram and potential curves. Approximations to the buckling load, including an upper bound, are computed by means of an energy integral method. The exact buckling loads are computed by numerical integration of the governing differential equation.
Use of classical variational principles to determine bounds for the effective bulk modulus in heterogeneous media
Authors: Beran M. , Molyneux J.
Published: December 2016

Bounds are here derived for the effective bulk modulus in heterogeneous media, denoted by

k
∗

k*

, using the two standard variational principles of elasticity. As trial functions for the stress and strain fields we use perturbation expansions that have been modified by the inclusion of a set of multiplicative constants. The first order perturbation effect is explicitly calculated and bounds for

k
∗

k*

are derived in terms of the correlation functions

⟨

μ
′

(
0
)

k
′

(
r
)

k
′

(
s
)

⟩

\left \langle {\mu ’(0)k’(r)k’(s)} \right \rangle

and

⟨

[

k
′

(
r
)

k
′

(
s
)

/

μ
(
0
)

]

⟩

\left \langle {\left [ {k’(r)k’(s)/\mu (0)} \right ]} \right \rangle

where

μ
′

\mu ’

and

k
′

k’

are the fluctuating parts of the shear modulus

μ
\mu

and the bulk modulus,

k
k

, respectively. Explicit calculations are given for two phase media when

μ
′

(
x
)
=
0

\mu ’(x) = 0

and when the media are symmetric in the two phases. Results are also included for the dielectric problem when the media are composed of two symmetric phases.
Generalized aerodynamic forces on an oscillating cylindrical shell
Authors: Dowell Earl H. , Widnall Sheila E.
Published: December 2016

The present paper presents a mathematical and numerical solution for the problem of determining the aerodynamic forces on a harmonically oscillating cylindrical shell at supersonic speeds within the framework of the classical, linearized, potential flow theory. The method of solution is given in detail and extensive numerical results are presented to indicate the nature of the aerodynamic forces. Comparisons of the present results are made with those of simpler, but more approximate theories, such as the quasi-steady, two-dimensional theory and a (generalized) “slender-body” theory, to indicate where these may be used with confidence.
Stress distribution around a hole in an ellipsoidal shell
Authors: De Silva C. N. , Cohen H
Published: December 2016

This paper treats the stress distribution in an ellipsoidal shell of revolution with a hole. The problem is reduced to the solution of sets of eight simultaneous equations. If interest is restricted to the neighborhood of the hole, a simplification occurs requiring the solution of sets of four simultaneous equations.
Distributions involving norms of correlated Gaussian vectors
Authors: Miller K. S.
Published: December 2016

The norm of a Gaussian vector is called a Rayleigh random variable. We compute various first and higher order probability density functions of products and quotients of correlated Rayleigh variates. Moments of these distributions are also calculated. The main results are summarized in Section 2 below. Extensive use is made of formulas involving special functions. These identities enable us to obtain the desired results directly and efficiently.
A continuum model for two-directional traffic flow
Authors: Bick J. H. , Newell G. F.
Published: December 2016

The flow of traffic in two directions of an undivided highway is investigated using the equations of continuity and assumed empirical relations between the average velocities and densities in both lanes. These lead to a pair of quasi-linear partial differential equations. Even if the velocity in one lane depends only very weakly on the density in the other lane, it is found that for a certain small range of densities the equations are of elliptic rather than the expected hyperbolic type. For densities outside this range, solutions of the equations can be found for various special types of initial conditions.
A general framework for association analysis of microbial communities on a taxonomic tree
Authors: Tang Zheng-Zheng , Chen Guanhua , Alekseyenko Alexander V , Li Hongzhe
Published: December 2016

Motivation

Association analysis of microbiome composition with disease-related outcomes provides invaluable knowledge towards understanding the roles of microbes in the underlying disease mechanisms. Proper analysis of sparse compositional microbiome data is challenging. Existing methods rely on strong assumptions on the data structure and fail to pinpoint the associated microbial communities.

Results

We develop a general framework to: (i) perform robust association tests for the microbial community that exhibits arbitrary inter-taxa dependencies; (ii) localize lineages on the taxonomic tree that are associated with covariates (e.g. disease status); and (iii) assess the overall association of the whole microbial community with the covariates. Unlike existing methods for microbiome association analysis, our framework does not make any distributional assumptions on the microbiome data; it allows for the adjustment of confounding variables and accommodates excessive zero observations; and it incorporates taxonomic information. We perform extensive simulation studies under a wide-range of scenarios to evaluate the new methods and demonstrate substantial power gain over existing methods. The advantages of the proposed framework are further demonstrated with real datasets from two microbiome studies. The relevant R package miLineage is publicly available.

Availability and Implementation

miLineage package, manual and tutorial are available at https://medschool.vanderbilt.edu/tang-lab/software/miLineage.

Supplementary information

Supplementary data are available at Bioinformatics online.
Openness and Closure in the Later Medieval Village*
Authors: Mileson Stephen
Published: December 2016

There is a growing scholarly interest in the daily life and perceptions of ordinary medieval people, yet there has been little attempt to conceptualise the social space of the rural settlements in which the great majority of the population lived. This article examines how a village or hamlet in England might have been used and perceived in the later Middle Ages (c.1200 to 1500), especially in terms of access and permeability—in other words how open or closed (or, more crudely, ‘public’ or ‘private’) the components of a settlement were, and how the spatial relationships between these components affected their use and social significance. The data are drawn mainly from lowland England, with a special focus on Ewelme hundred in Oxfordshire, an area of mixed countryside including open-field villages and dispersed wood-pasture settlements. It will be argued that differences in openness and closure across space and time supply a guide to rural social interaction as a whole.
Local Zinc Chloride Release From a Calcium Sulfate Carrier Enhances Fracture Healing
Authors: Krell Ethan S. , Ippolito Joseph A. , Montemurro Nicholas J. , Lim Phillip H. , Vincent Richard A. , Hreha Jeremy , Cottrell Jessica , Sudah Suleiman Y. , Muñoz Maximilian F. , Pacific Kristen P. , Benevenia Joseph , O'Connor J. Patrick , Lin Sheldon S.
Published: December 2016

Background:

This study examined the efficacy of calcium sulfate (CaSO4) as a carrier for intramedullary delivery of zinc chloride (ZnCl2) to treat fracture healing in a BB Wistar rat model. A non–carrier-mediated injection of 3.0 mg/kg of ZnCl2 has previously been shown to enhance fracture healing.

Methods:

A heterogeneous mixture of ZnCl2 and CaSO4 was administered into the intramedullary femoral canal and a mid-diaphyseal femur fracture was created unilaterally. Early and late parameters of fracture healing were assessed using biomechanical testing, radiographic scoring, quantitative histomorphometry (for percentage of new cartilage and bone within the fracture callus), and long-term histologic evaluation.

Results:

Fractures treated with 1.0 mg/kg of ZnCl2/CaSO4 demonstrated a significantly higher maximum torque to failure compared with both CaSO4 (P = 0.048) and saline (P = 0.005) controls at 4 weeks postfracture (396.4 versus 251.3 versus 178.7 N mm, respectively). Statistically significant increases in torsional rigidity, effective shear modulus, and effective shear stress were also found, as well as a 3.5 times increase in radiographic score (based on bone union). Histologic examination of the fracture callus indicated enhanced chondrogenesis at day 14 postfracture, with increased percent cartilage for the ZnCl2/CaSO4 group compared with saline (P = 0.0004) and CaSO4 (P = 0.0453) controls. Long-term radiographic and histologic evaluation revealed no abnormal bone formation or infection up to 12 weeks postoperatively.

Conclusions:

The effective dose of ZnCl2 augmentation for the enhancement of fracture healing in rats was reduced 3-fold in this study compared with previous findings. Furthermore, CaSO4 acted synergistically with ZnCl2 to increase the mechanical strength and stability at the fracture site.
A Novel Reconstructive Procedure for the Divided Nevus of the Eyelids Using a Tissue Expander
Authors: Yamamichi Kosaku , Kosaka Masaaki
Published: December 2016

Expanded local flaps and skin grafts (expanded/nonexpanded) are a common approach for reconstructing medium (1.5–20 cm) and large (>20 cm) divided nevi of the eyelids. However, this approach does not often provide a satisfactory cosmetic result, particularly in Asian patients, because of different skin types. We recently devised a new surgical procedure using an extended cheek flap and tissue expander for the medium-sized divided nevus of the eyelids. The upper and lower eyelids are concurrently reconstructed by divided flaps. This method is an effective treatment method for the medium-sized divided nevus of the eyelids and can be applied in total reconstruction of the eyelids in the future. This article presents our novel technique and is illustrated using a brief case report.
Novel Therapy for the Treatment of Early-Onset Preeclampsia
Authors: ORNAGHI SARA , PAIDAS MICHAEL J.
Published: December 2016

Preeclampsia is a multisystem disorder affecting 2% to 8% of pregnancies and a leading cause of maternal and perinatal morbidity and mortality worldwide. Recent investigations have improved our understanding of the pathogenesis of this potentially life-threatening disease, especially in its early-onset form of manifestation. Despite these advances, therapeutic options are still limited and no effective pharmacologic interventions are currently available. Ongoing lines of research indicate some potential novel treatments targeting specific pathogenic steps. In this article we provide an updated overview of the multiple therapeutic approaches under preclinical and clinical assessment for the treatment of early-onset preeclampsia.
STRUCTURAL AND FUNCTIONAL MONITORING OF EXTRAMACULAR CYSTOID SPACES IN A CASE OF X-LINKED RETINOSCHISIS TREATED WITH ACETAZOLAMIDE
Authors: Collison Frederick T. , Fishman Gerald A.
Published: December 2016

Background:

Carbonic anhydrase inhibitors (CAIs) have been shown to have a beneficial effect on cystoid macular edema in X-linked retinoschisis (XLRS) and other inherited retinal conditions. The effect of CAIs outside the macula has been less well studied.

Methods:

Snellen visual acuity, spectral-domain optical coherence tomography (SD-OCT), kinetic visual field, and dark-adapted single-flash full-field electroretinogram (ERG) testing were all done at baseline and at least one follow-up visit. A 55-year-old male diagnosed with XLRS exhibited extensive macular and extramacular cystoid splitting in the right eye and was treated with oral extended-release acetazolamide 500 mg/day.

Results:

By 6 months of follow-up on acetazolamide treatment, SD-OCT demonstrated resolution of cystoid spaces both within the macula and out to the midperiphery. Visual acuity improved from 20/70 to 20/30. The full-field ERG was distinctly electronegative at both baseline and at a follow-up visit, with oscillatory potentials becoming more apparent at the follow-up visit. Peripheral visual field boundaries did not change significantly.

Conclusion:

This report demonstrates structural resolution of cystoid spaces throughout much of the retina in a patient with XLRS, adding to a published case report in which we first noted that extramacular cystoid spaces observed in XLRS may respond to CAI treatment. To our knowledge, this is the first reported study of follow-up functional studies (ERG and perimetry) in a CAI treatment responder with XLRS.