bluuebunny/crossref_metadata_2025_split huggingface dataset:
Phospholipase D1 deficiency in mice causes nonalcoholic fatty liver disease via an autophagy defect
Authors: Hur Jang Ho , Park Shi-Young , Dall’Armi Claudia , Lee Jae Sung , Di Paolo Gilbert , Lee Hui-Young , Yoon Mee-Sup , Min Do Sik , Choi Cheol Soo 
Published: December 2016

AbstractNonalcoholic fatty liver disease (NAFLD) is characterized by the accumulation of triglycerides (TG) as lipid droplets in the liver. Although lipid-metabolizing enzymes are considered important in NAFLD, the involvement of phospholipase D1 (PLD1) has not yet been studied. Here, we show that the genetic ablation of PLD1 in mice induces NAFLD due to an autophagy defect. PLD1 expression was decreased in high-fat diet-induced NAFLD. Subsequently, PLD1 deficiency led to an increase in hepatic TGs and liver weight. Autophagic flux was blocked in Pld1−/− hepatocytes, with decreased β-oxidation rate, reduced oxidation-related gene expression, and swollen mitochondria. The dynamics of autophagy was restored by treatment with the PLD product, phosphatidic acid (PA) or adenoviral PLD1 expression in Pld1−/− hepatocytes, confirming that lysosomal PA produced by PLD1 regulates autophagy. Notably, PLD1 expression in Pld1−/− liver significantly reduced hepatic lipid accumulation, compared with Pld1−/− liver. Thus, PLD1 plays an important role in hepatic steatosis via the regulation of autophagy.
Vocal sequences suppress spiking in the bat auditory cortex while evoking concomitant steady-state local field potentials
Authors: Hechavarría Julio C. , Beetz M. Jerome , Macias Silvio , Kössl Manfred 
Published: December 2016

AbstractThe mechanisms by which the mammalian brain copes with information from natural vocalization streams remain poorly understood. This article shows that in highly vocal animals, such as the bat species Carollia perspicillata, the spike activity of auditory cortex neurons does not track the temporal information flow enclosed in fast time-varying vocalization streams emitted by conspecifics. For example, leading syllables of so-called distress sequences (produced by bats subjected to duress) suppress cortical spiking to lagging syllables. Local fields potentials (LFPs) recorded simultaneously to cortical spiking evoked by distress sequences carry multiplexed information, with response suppression occurring in low frequency LFPs (i.e. 2–15 Hz) and steady-state LFPs occurring at frequencies that match the rate of energy fluctuations in the incoming sound streams (i.e. >50 Hz). Such steady-state LFPs could reflect underlying synaptic activity that does not necessarily lead to cortical spiking in response to natural fast time-varying vocal sequences.
Efficacy of Two Techniques in Anterior Cruciate Ligament Reconstruction
Authors: Hurt James , Berry John , Replogle William , Thibodeaux Kasey , Hydrick Josie , Barrett Austin , Barrett Gene 
Published: December 2016

AbstractThe purpose of this study is to compare failure rate and functional outcome in young, active patients (< 25 years) with two-incision (rear-entry) versus transtibial (all-endoscopic) anterior cruciate ligament (ACL) reconstructions.Utilizing a computerized relational database (Access 2007, Microsoft Inc., Redmond, WA), 480 patients were identified that underwent ACL reconstruction, using a bone-patellar-tendon-bone autograft, by a single surgeon between January 2000 and December 2010 via a transtibial or two-incision technique. Totally, 377 (78.6%) of these patients were less than 25 years of age. Data for each patient were collected at their initial clinic visit, at the time of surgery, and at each follow-up clinic visit and entered into the computerized relational database. Overall, 274 patients (72.7%) underwent ACL reconstruction with a transtibial technique, and 103 patients (27.3%) underwent reconstruction with a two-incision technique. Failures were identified as a 2+ Lachman, 1+ or greater pivot shift, or a KT-1000 arthrometer difference of five or more.In patients < 25 years of age, there were 10 failures (9.7%) out of 103 patients undergoing a two-incision reconstruction and 28 failures (10.2%) out of 274 patients undergoing a transtibial reconstruction (p = 1.000). There was no statistical significance between the failure rate in the two different groups in regards to gender, meniscal tear, activity level, or any other factor that was analyzed.Our study showed no statistical difference between the two-incision technique and the transtibial technique for ACL reconstruction using bone-patellar-tendon-bone autograft with an overall 10.1% failure rate in young, active patients (< 25 years of age). The level of evidence is level IV.
Resting-state hemodynamics are spatiotemporally coupled to synchronized and symmetric neural activity in excitatory neurons
Authors: Ma Ying , Shaik Mohammed A. , Kozberg Mariel G. , Kim Sharon H. , Portes Jacob P. , Timerman Dmitriy , Hillman Elizabeth M. C. 
Published: December 2016

SignificanceResting-state functional connectivity mapping exploits correlations in the functional magnetic resonance imaging (fMRI) blood oxygen level-dependent (BOLD) signal across the brain. However, results are difficult to interpret without an understanding of the neural correlates of these hemodynamic fluctuations. This work uses mice in which neural activity and brain hemodynamics can be mapped simultaneously. We show that resting-state hemodynamics can be predicted from spontaneous neural activity and correspond to a series of driven increases in local blood volume, coupled with spontaneous, bilaterally symmetric fluctuations in excitatory neural activity. This result provides reassurance that resting-state functional connectivity has neural origins. The network-like spontaneous neural activity visualized here represents an underexplored feature of neural activity in the awake brain.
Comparison principle for some nonlocal problems
Authors: Deng Keng 
Published: December 2016

In this paper, for the parabolic equation

u
t

=
Δ
u
+
g

(

x
,
u

)

,

(

x
,
t

)

∈

Ω
×

(

0
,
T

)

{u_t} = \Delta u + g\left ( {x, u} \right ), \left ( {x, t} \right ) \in \\ \Omega \times \left ( {0, T} \right )

, with nonlocal boundary conditions

u

|

∂
Ω

=

∫

Ω

f

(

x
,
y

)

u

(

y
,
t

)

d
y

u\left | {_{\partial \Omega }} \right . = \int _{\Omega } f\left ( {x, y} \right )u\left ( {y, t} \right )dy

, we establish the comparison theorem and local existence of the solution. We also discuss its long time behavior.
Unstable simple modes of the nonlinear string
Authors: Cazenave Thierry , Weissler Fred B. 
Published: December 2016

We prove instability of high-energy simple modes for the nonlinear vibrating string equation
\[

{

u

|

∂
Ω

=
0
,

u

t
t

−

(

a
+
b

∫
0
π

u
x
2

(

t
,
x

)

d
x

)

u

x
x

=
0
,

\left \{ {_{u\left | {_{\partial \Omega } = 0,} \right .}^{{u_{tt}} - \left ( {a + b \int _0^\pi {u_x^2 \left ( {t, x} \right ) dx} } \right ) {u_{xx}} = 0,}} \right .

\]
in

Ω
=

(

0
,
π

)

\Omega = \left ( {0, \pi } \right )

, where

a
≥
0
,
b
>
0

a \ge 0, b > 0

.
Existence and nonexistence of global solutions of the wave equation with a nonlinear boundary condition
Authors: Ackleh Azmy S. , Deng Keng 
Published: December 2016

We study the initial-boundary value problem
\[

u

t
t

=

u

x
x

,

0
>
x
>
∞
,

t
>
0
,

{u_{tt}} = {u_{xx}}, \qquad 0 > x > \infty , \qquad t > 0,

\]

\[

−

u
x

(
0
,
t
)

=
h

(
u

(
0
,
t
)

)

,

t
>
0
,

- {u_x}\left ( 0, t \right ) = h\left ( u\left ( 0, t \right ) \right ), \qquad t > 0,

\]

\[

u

(
x
,
0
)

=
f

(
x
)

,

u
t

(
x
,
0
)

=
g

(
x
)

,

0
>
x
>
∞
.

u\left ( x, 0 \right ) = f\left ( x \right ), \qquad {u_t}\left ( x, 0 \right ) = g\left ( x \right ), \qquad 0 > x > \infty .

\]
We establish criteria for existence and nonexistence of global solutions, and we present the growth rate at blow-up.
Conical quantum billiard revisited
Authors: Liboff Richard L. 
Published: December 2016

Eigenstates of a particle confined to a cone of finite length capped by a spherical surface element are derived. A countable infinite set of solutions is obtained corresponding to integer azimuthal and orbital quantum numbers

(
m
,
l
)

\left ( m, l \right )

. These solutions apply to a discrete subset of the domain of half vertex angles,

0
≤

θ
0

≤
π

/

2

0 \le {\theta _0} \le \pi /2

. For arbitrary real orbital quantum numbers,

l
→
ν

l \to \nu

, solutions are given in terms of the hypergeometric function, with

ν
=
ν

(

θ
0

)

\nu = \nu \left ( {\theta _0} \right )

, and are valid in the

θ
0

{\theta _0}

domain,

0
≤

θ
0

>
π

/

2

0 \le {\theta _0} > \pi /2

. Eigenstates are either nondegenerate or two-fold degenerate. Numerical examples of both classes of solutions are included. For the case

μ
=
cos
⁡
π

/

4

\mu = \cos \pi /4

, the ground-state wavefunction and eigenenergy are
\[

φ
G

=

P
ν

(
μ
)

j
ν

(

x

ν
1

r

/

a
)

,

E
G

=

ℏ
2

(
6.4387
)

2

/

(
2
M

a
2

)

{\varphi _G} = {P_\nu }\left ( \mu \right ){j_\nu }\left ( {x_{\nu 1}}r/a \right ), \qquad {E_G} = {\hbar ^2}{\left ( 6.4387 \right )^2}/\left ( 2M{a^2} \right )

\]
where

ν
=
2.54791
,

P
ν

(
μ
)

\nu = 2.54791, {P_\nu }\left ( \mu \right )

are Legendre functions,

x

ν
1

{x_{\nu 1}}

is the first finite zero of the spherical Bessel function

j
ν

(
x
)

{j_\nu }\left ( x \right )

,

M
M

is the mass of the confined particle and

a
a

is the edgelength of the cone. Solutions constructed also represent the scalar

r
^

⋅
E

\hat r \cdot E

electric field, where

r
^

\hat r

is the unit radius from the vertex of the cone. The first excited state of the conical quantum billiard has the nodal surface

μ
=
1

\mu = 1

for all

0
≤

μ
0

≤
1

0 \le {\mu _0} \le 1

.
A singular perturbation solution to a problem of extreme temperatures imposed at the surface of a variable-conductivity halfspace: small surface conductivity
Authors: Cooper Leonard Y. 
Published: December 2016

The transient temperature field resulting from a constant and uniform temperature

T
s

{T_s}

(or time-dependent heat flux

H
=
h

t

−
1

/

2

H = h{t^{ - 1/2}}

) imposed at the surface of a halfspace initially at uniform temperature

T
0

{T_0}

is considered. A temperature-dependent thermal conductivity variation,

k

(
T
)

=

k
0

exp
⁡

[

λ
(
T
−

T
0

)

/

T
0

]

k\left ( T \right ) = {k_0}\exp \left [ {\lambda (T - {T_0})/{T_0}} \right ]

, and a constant product of density and specific heat,

ρ
C

\rho C

, are assumed to be accurate models for the halfspace for some useful temperature range. The problem is initially formulated in terms of the dimensionless conductivity

ϕ
=
k

(
T
)

/

k
0

\phi = k\left ( T \right )/{k_0}

. Attention is then focused on the singular problem resulting from the limits

ϕ
s

=
ϕ

(

T
s

)

↓
0

{\phi _s} = \phi \left ( {{T_s}} \right ) \downarrow 0

and

ϕ
s

→
∞

{\phi _s} \to \infty

. This work considers the use of matched asymptotic expansions to solve the problem under the first of these limits. In particular, Fraenkel’s interpretation [5] of Van Dyke’s method of inner and outer expansions [6] is carefully applied to the problem under consideration. Besides obtaining a uniformly valid solution to the problem, a particularly interesting explicit result is deduced, namely
\[

lim

ϕ
s

↓
0

h
=
−
(
1.182754
⋅
⋅
⋅
)
(

T
0

/

λ
)

[
ρ
C

k
0

/

2

]

1

/

2

+
O
(

ϕ
s

l
n

ϕ
s

)

\lim \limits _{{\phi _s} \downarrow 0} h = - (1.182754 \cdot \cdot \cdot )({T_0}/\lambda ){[\rho C{k_0}/2]^{1/2}} + O({\phi _s}ln{\phi _s})

\]
On some problems of homogenization
Authors: Burgers J. M. 
Published: December 2016

This article concerns a type of partial differential equations in which coefficients occur that are periodic functions of the basic independent variables or coordinates

x
1

{x_1}

,

x
2

{x_2}

(we restrict ourselves to two-dimensional problems). The period length

H
H

, here assumed to be the same in both directions, is supposed to be small in comparison with the scale of the general field, and interest is directed to what happens when

H
→
0

H \to 0

. An example is the equation
\[

Σ

∂

∂

x
j

(

a

i
j

∂
u

∂

x
i

)

=
f

(

x
1

,

x
2

)

\Sigma \frac {\partial }{{\partial {x_j}}}\left ( {{a_{ij}}\frac {{\partial u}}{{\partial {x_i}}}} \right ) = f\left ( {{x_1},{x_2}} \right )

\]
with the boundary condition

u
=
0

u = 0

on a given closed curve

C
C

in the

X
1

{X_1}

,

x
2

{x_2}

-plane. Size and shape of

C
C

are independent of

H
H

, while the coefficients

a

11

{a_{11}}

,

a

12

{a_{12}}

,

a

21

{a_{21}}

,

a

22

{a_{22}}

are periodic functions of auxiliary variables

ξ
i

=

x
1

/

H

{\xi _i} = {x_1}/H

with period 1 in

ξ
1

{\xi _1}

,

ξ
2

{\xi _2}

. The problem of interest is whether the unknown function

u
u

, which must react upon all the fluctuations of the

a

i
j

{a_{ij}}

, can be related to a function

U

(

x
1

,

x
2

)

U\left ( {{x_1}, {x_2}} \right )

which is determined by a partial differential equation with constant coefficients, and how these coefficients can be obtained from the

a

i
j

{a_{ij}}

. This is called the problem of "homogenization".
Some functional differential equations
Authors: Chambers Ll. G. 
Published: December 2016

Sufficient conditions are given for the solution of the functional differential equations with associated boundary conditions
\[

d
y

/

d
x
=

∑

n
=
0

∞

a
n

y

(

μ
n

x

)

,

y

(
0
)

=
1
,

d
y

/

d
x
=

∫
0
∞

a

(
u
)

y

(

μ
u

x

)

d
u

,

y

(
0
)

=
1

dy/dx = \sum \limits _{n = 0}^\infty {{a_n}y\left ( {{\mu ^n}x} \right ),\qquad y\left ( 0 \right ) = 1, \\ dy/dx = \int _0^\infty {a\left ( u \right )y\left ( {{\mu ^u}x} \right )du},\qquad y\left ( 0 \right ) = 1}

\]
A discussion is also given of some possible solutions to the differential equations which do not satisfy the boundary conditions.
Asymptotic properties of best 𝐿₂[0,1] approximation by splines with variable knots
Authors: Barrow D. L. , Smith P. W. 
Published: December 2016

Let

S
N
k

S_N^k

be the set of

k
k

th-order splines on

[

0
,
1

]

\left [ {0, 1} \right ]

having at most

N
−
1

N - 1

interior knots, counting multiplicities. We prove the following sharp asymptotic behavior of the error for the best

L
2

[

0
,
1

]

{L_2}\left [ {0, 1} \right ]

approximation of a sufficiently smooth function

f
f

by the set

S
N
k

S_N^k

:
\[

lim

N
→
∞

N
k

d
i
s
t

(

f
,

S
N
k

)

=

(

|

B

2
k

|

/

(

2
K

)

!

)

1

/

2

(

∫
0
1

|

f

(
k
)

(
τ
)

|

σ

d
τ

)

1

/

σ

\lim \limits _{N \to \infty } {N^k}dist\left ( {f, S_N^k} \right ) = {\left ( {\left | {{B_{2k}}} \right |/\left ( {2K} \right )!} \right )^{1/2}}{\left ( {{{\int _0^1 {\left | {{f^{\left ( k \right )}}\left ( \tau \right )} \right |} }^\sigma }d\tau } \right )^{1/\sigma }}

\]
, where

σ
=

(

k
+
1

/

2

)

−
1

\sigma = {\left ( {k + 1/2} \right )^{ - 1}}

and

B

2
k

{B_{2k}}

is the

2
k

2k

th Bernoulli number. Similar results have previously been obtained for piecewise polynomial (i.e., with no continuity constraints) approximation, but with different constant before the integral term. The approach we use is first to study the asymptotic behavior of dist(

f
f

,

S
N
k

(
t
)

S_N^k\left ( t \right )

), where

S
N
k

(
t
)

S_N^k\left ( t \right )

is the linear space of

k
k

th-order splines having simple knots determined from the fixed function

t
t

by the rule

t
i

=
t

(

i

/

N

)

,
i
=
0
,
.
.
.
,
N

{t_i} \\ = t\left ( {i/N} \right ),i = 0,...,N

.
On optimal strain paths in linear viscoelasticity
Authors: Gurtin Morton E. , MacCamy Richard C. , Murphy Lea F. 
Published: December 2016

For a viscoelastic material the work

W

(
e
)

W\left ( e \right )

needed to produce a given strain

e
0

{e_0}

in a given time

T
T

depends on the strain path

e

(
t
)

,
0
≤
t
≤
T

e\left ( t \right ), 0 \le t \le T

, connecting the unstrained state with

e
0

{e_0}

. We here ask the question: Of all strain paths of this type, is there one which is optimal,

1

^{1}

that is, one which renders

W
W

a minimum? In answer to this question we show that: (i) There is no smooth optimal strain path. (ii) There exists a unique optimal path in

L
2

(

0
,
T

)

{L_2}\left ( {0,T} \right )

; this path is smooth on the open interval

(

0
,
T

)

\left ( {0,T} \right )

, but suffers jump discontinuities

2

^{2}

at the end points 0 and

T

(

i
.
e
.
,
e

(

0
+

)

≠
0
,

e

(

T
−

)

≠

e
0

)

T\left ( {i.e.,e\left ( {{0^ + }} \right ) \ne 0, \\ e\left ( {{T^ - }} \right ) \ne {e_0}} \right )

. (iii) For a Maxwell material the optimal path is linear on

(

0
,
T

)

\left ( {0,T} \right )

.
Stability conditions for linear nonautonomous delay differential equations
Authors: Busenberg Stavros N. , Cooke Kenneth L. 
Published: December 2016

We derive new sufficient conditions for uniform asymptotic stability of the zero solution of linear non-autonomous delay differential equations. The equations considered include scalar equations of the form
\[

x
′

(
t
)

=
−
c

(
t
)

x

(
t
)

+

∑

i
=
1

n

b
i

(
t
)

x

(

t
−

T
i

)

x’\left ( t \right ) = - c\left ( t \right )x\left ( t \right ) + \sum \limits _{i = 1}^n {{b_i}\left ( t \right )x\left ( {t - {T_i}} \right )}

\]
where

c

(
t
)

c\left ( t \right )

,

b
i

(
t
)

{b_i}\left ( t \right )

are continuous for

t
≥
0

t \ge 0

and

T
i

{T_i}

is a positive number

(
i
=
1
,
2
,
.
.
.
,
n
)

(i = 1, 2,...,n)

, and also systems of the form
\[

x
′

(
t
)
=
B
(
t
)
x
(
t
−
T
)
−
C
(
t
)
x
(
t
)

x’(t) = B(t)x(t - T) - C(t)x(t)

\]
where

B
(
t
)

B(t)

) and

C
(
t
)

C(t)

are

n
×
n

n \times n

matrices. The results are found by using the method of Lyapunov functionals.
Laplace type integrals: transformation to standard form and uniform asymptotic expansions
Authors: Temme N. M. 
Published: December 2016

Integrals are considered which can be transformed into the Laplace integral
\[

F
λ

(
z
)

=

1

Γ

(
λ
)

∫
0
∞

t

λ
−
1

e

−
z
t

f

(
t
)

d
t

{F_\lambda } \left ( z \right ) = \frac {1}{{\Gamma \left ( \lambda \right )}}\int _0^\infty {{t^{\lambda - 1}}{e^{ - zt}}f\left ( t \right )dt}

\]
, where

f
f

is holomorphic,

z
z

is a large parameter,

μ
=
λ

/

z

\mu = \lambda /z

is a uniformity parameter,

μ
≥
0

\mu \ge 0

. A uniform asymptotic expansion is given with error bounds for the remainders. Applications are given for special functions, with a detailed analysis for a ratio of gamma functions. Further applications are mentioned for Bessel functions and parabolic cylinder functions. Analogue results are given for loop integrals in the complex plane.
Oscillations of the sunflower equation
Authors: Kulenović M. R. S. , Ladas G. 
Published: December 2016

Consider the delay differential equation
\[

y
¨

(
t
)

+
α

y
˙

(
t
)

+
β
f

(

y

(

t
−
r

)

)

=
0
,

(
∗
)

\ddot y\left ( t \right ) + \alpha \dot y\left ( t \right ) + \beta f\left ( {y\left ( {t - r} \right )} \right ) = 0, \qquad \left ( * \right )

\]
where

α
,
β

\alpha , \beta

, and

r
r

are positive constants and

f
f

is a continuous function such that
\[

u
f

(
u
)

>
0

f
o
r
u
∈

[

−
A
,
B

]

,
u
≠
0
,
a
n
d

lim

u
→
0

f

(
u
)

u

=
1
,

uf\left ( u \right ) > 0 \qquad for u \in \left [ { - A, B} \right ], u \ne 0, and \lim \limits _{u \to 0} \frac {{f\left ( u \right )}}{u} = 1,

\]
where

A
A

and

B
B

are positive numbers. When

f

(
u
)

=
sin
⁡
u
,

(
∗
)

f\left ( u \right ) = \sin u, \left ( * \right )

is the so-called “sunflower” equation, which describes the motion of the tip of the sunflower plant.
Oscillation and nonoscillation in a nonautonomous delay-logistic equation
Authors: Zhang B. G. , Gopalsamy K. 
Published: December 2016

Sufficient conditions are obtained for the delay-logistic equation

x
˙

(
t
)

=

r

(
t
)

x

(
t
)

[

1
−
x

(

t
−
τ

(
t
)

)

/

K

]

\dot x\left ( t \right ) = \\ r\left ( t \right )x\left ( t \right )\left [ {1 - x\left ( {t - \tau \left ( t \right )} \right )/K} \right ]

to be respectively oscillatory and nonoscillatory.
Energy methods for the Cahn-Hilliard equation
Authors: Novick-Cohen Amy 
Published: December 2016

The Cahn-Hilliard equation, which is important in the context of first-order phase transition, has frequently been studied in its simplified form,
\[

c
t

=
Δ

[

h

(
c
)

−
K
Δ
c

]

,

{c_t} = \Delta \left [ {h\left ( c \right ) - K\Delta c} \right ],

\]
where

c

(

x
,
t

)

c\left ( {x, t} \right )

is a concentration,

h

(
c
)

h\left ( c \right )

is a nonmonotone chemical potential, and

K
K

, the coefficient of gradient energy, is a positive constant. In this paper we consider the Cahn-Hilliard equation with nonconstant mobility and gradient energy coefficients,
\[

c
t

=
∇
⋅

[

M

(
c
)

∇

{

h

(
c
)

−
K

(
c
)

Δ
c

}

]

,

{c_t} = \nabla \cdot \left [ {M\left ( c \right )\nabla \left \{ {h\left ( c \right ) - K\left ( c \right )\Delta c} \right \}} \right ],

\]
where

M

(
c
)

M\left ( c \right )

and

K

(
c
)

K\left ( c \right )

are assumed to be positive. When

K
K

is constant, the free energy functional
\[

F

(
t
)

=

∫
Ω

{

∫

c

h

(

c
¯

)

d

c
¯

+

1
2

K

|

∇
c

|

2

}

d
x

F\left ( t \right ) = \int _\Omega {\left \{ {\int ^{c} {h\left ( {\bar c} \right )d\bar c + \frac {1}{2}K{{\left | {\nabla c} \right |}^2}} } \right \}dx}

\]
acts as a Liapounov functional for the Cahn-Hilliard equation. However, when

K
K

is nonconstant

F

(
t
)

F\left ( t \right )

no longer acts as a Liapounov functional, and it becomes relevant to examine an alternative energy. In this paper the stability of spatially homogeneous states is studied in terms of the energy
\[

E

(
t
)

=

∫
Ω

∫
0

c
−

c
0

∫
0

c
~

M

−
1

(

c
¯

+

c
0

)

d

c
¯

d

c
~

d
x
.

E\left ( t \right ) = \int _\Omega {\int _0^{c - {c_0}} {\int _0^{\tilde c} {{M^{ - 1}}\left ( {\bar c + {c_0}} \right )d\bar c} d\tilde c} } dx.

\]
The possibility of dependence of

h

(
c
)

h\left ( c \right )

,

M

(
c
)

M\left ( c \right )

, and

K

(
c
)

K\left ( c \right )

on a spatially uniform temperature is also considered and the physical implications of the location of the limit of monotonic global stability in the average concentration-temperature plane is discussed. In particular, this limit is shown to lie below the critical temperature.
Further observations on a problem of constant surface heating of a variable-conductivity halfspace
Authors: Cooper Leonard Y. 
Published: December 2016

A solution to the problem of constant surface heating of an initially constant-temperature,

T
0
∗

T_0^*

, halfspace where the material in question has a temperature-dependent thermal conductivity is obtained. The thermal conductivity,

k
∗

{k^ * }

, is specifically given by

k
∗

=

k
0
∗

exp
⁡

[

λ

(

T
∗

−

T
0
∗

)

/

T
0
∗

]

{k^ * } = k_0^ * \exp \left [ {\lambda \left ( {{T^ * } - T_0^ * } \right )/T_0^ * } \right ]

. The solution is valid for both heating and cooling of the material where

λ
\lambda

and

k
0
∗

k_0^ *

are arbitrary in magnitude, and

λ
\lambda

can be either positive or negative in sign.
Pandemics: A Very Short Introduction
Authors: McMillen Christian W. 
Published: December 2016

Abstract
The 2014 Ebola epidemic demonstrated the power of pandemics and their ability not only to destroy lives locally but also to capture imaginations worldwide. Pandemics: A Very Short Introduction provides a concise yet comprehensive account of pandemics throughout human history, illustrating the ways in which pandemic disease—including plague, tuberculosis, malaria, smallpox, cholera, influenza, and HIV/AIDS—has shaped history and how human history has shaped pandemic disease. By considering the explosion of medical research and the varying state responses, such as quarantine and travel restrictions, this Very Short Introduction shows why pandemics are both interesting from a medical standpoint and provide insight into the culture and politics of their time.