bluuebunny/crossref_metadata_2025_split huggingface dataset:
On uniqueness of 𝑝-adic meromorphic functions
Authors: Boutabaa Abdelbaki , Escassut Alain 
Published: July 2002

Let

K
K

be a complete ultrametric algebraically closed field of characteristic zero, and let

M

(
K
)

{\mathcal {M}} (K)

be the field of meromorphic functions in

K
K

. For all set

S
S

in

K
K

and for all

f
∈

M

(
K
)

f\in {\mathcal {M}}(K)

we denote by

E
(
f
,
S
)

\displaystyle E(f,S)

the subset of

K

×

N

∗

K {\times } {\mathbb {N}}^{*}

:

⋃

a
∈
S

{
(
z
,
q
)
∈
K

×

N

∗

|
z

{\bigcup _{ a\in S}}\{(z,q)\in K {\times } \mathbb {N}^{*} \vert z

zero of order

q
of
f
(
z
)
−
a
}
.

q \text { of} f(z)-a\}.

After studying unique range sets for entire functions in

K
K

in a previous article, here we consider a similar problem for meromorphic functions by showing, in particular, that, for every

n
≥
5

n\geq 5

, there exist sets

S
S

of

n
n

elements in

K
K

such that, if

f
,
g
∈

M

(
K
)

f, g\in {\mathcal {M}} (K)

have the same poles (counting multiplicities), and satisfy

E
(
f
,
S
)
=
E
(
g
,
S
)

E(f,S)=E(g,S)

, then

f
=
g

f=g

. We show how to construct such sets.
Weighted integrability of double trigonometric series
Authors: Chen Chang-Pao , Huang Xin-Rong 
Published: July 2002

We study the double trigonometric series whose coefficients

c

j
k

c_{jk}

are such that

∑

j
=
−
∞

∞

∑

k
=
−
∞

∞

|

c

j
k

|

>
∞
.

\sum _{j=-\infty }^\infty \sum _{k=-\infty }^\infty |c_{jk}|>\infty .

Then its rectangular partial sums converge uniformly to some

f
∈
C
(

T
2

)

f\in C(T^2)

. We give sufficient conditions for the Lebesgue integrability of

{
f
(
x
,
y
)
−
f
(
x
,
0
)
−
f
(
0
,
y
)
+
f
(
0
,
0
)
}
ϕ
(
x
,
y
)

\{f(x,y)-f(x,0)-f(0,y)+f(0,0)\}\phi (x,y)

, where

ϕ
(
x
,
y
)
=
1

/

x
y
,
1

/

x

\phi (x,y)=1/xy, 1/x

, or

1

/

y

1/y

. For certain cases, they are also necessary conditions. Our results extend those of Boas and Móricz from the one-dimensional to the two-dimensional series.
The groups of quasiconformal homeomorphisms on Riemann surfaces
Authors: Yagasaki Tatsuhiko 
Published: July 2002

Suppose

M
M

is a connected Riemann surface. Let

H

(
M
)

{\mathcal H}(M)

denote the homeomorphism group of

M
M

with the compact-open topology, and

H

Q
C

(
M
)

{\mathcal H}^{\mathrm {QC}}(M)

denote the subgroup of quasiconformal mappings of

M
M

onto itself, and let

H

(
M

)
0

{\mathcal H}(M)_0

and

H

Q
C

(
M

)
0

{\mathcal H}^{\mathrm {QC}}(M)_0

denote the identity components of

H

(
M
)

{\mathcal H}(M)

and

H

Q
C

(
M
)

{\mathcal H}^{\mathrm {QC}}(M)

respectively. In this paper we show that the pair

(

H

(
M

)
0

,

H

Q
C

(
M

)
0

)

({\mathcal H}(M)_0, {\mathcal H}^{\mathrm {QC}}(M)_0)

is an

(
s
,
Σ
)

(s, \Sigma )

-manifold, and determine their topological types.
A mean value theorem on bounded symmetric domains
Authors: Engliš Miroslav 
Published: July 2002

LetΩ\Omegabe a Cartan domain of rankrrand genusppandBνB_\nu,ν>p−1\nu >p-1, the Berezin transform onΩ\Omega; the numberBνf(z)B_{\nu }f(z)can be interpreted as a certain invariant-mean-value of a functionffaround zz. We show that a Lebesgue integrable function satisfyingf=Bνf=Bν+1f=⋯=Bν+rff=B_\nu f=B_{\nu +1}f=\dots =B_{\nu +r}f,ν≥p\nu \ge p, must beM\mathcal {M}-harmonic. In a sense, this result is reminiscent of Delsarte’s two-radius mean-value theorem for ordinary harmonic functions on the complexnn-spaceCn\mathbf {C}^{n}, but with the role of radiusrrplayed by the quantity 1/ν1/\nu.
Weighted inequalities for iterated convolutions
Authors: Andersen Kenneth 
Published: July 2002

Given a fixed exponentpp,1≤p>∞1\le p>\infty, and suitable nonnegative weight functionsvjv_j,j=1,…,mj=1,\dots ,m, an optimal associated weight functionωm\omega _mis constructed for which the iterated convolution product satisfies\[∫0∞|[∏j=1m∗Fj](x)|pdxωm(x)≤∏j=1m∫0∞|Fj(t)|pdtvj(t)\int _0^{\infty }\bigg |\bigg [\prod _{j=1}^m*F_j\bigg ](x)\bigg |^p\, \dfrac {dx}{\omega _m(x)}\le \prod _{j=1}^m\int _0^{\infty }|F_j(t)|^p\, \dfrac {dt}{v_j(t)}\]for all complex valued measurable functionsFjF_jwith∫0∞|Fj(t)|pdt/vj(t)>∞\int _0^{\infty }|F_j(t)|^p\,dt/v_j(t)>\infty. Here[∏j=12∗Fj](x)=[F1∗F2](x)=∫0xF1(t)F2(x−t)dt[\prod _{j=1}^2*F_j](x)=[F_1*F_2](x)= \int _0^xF_1(t)F_2(x-t)\,dtand for eachm>2m>2,∏j=1m∗Fj=[∏j=1m−1∗Fj]∗Fm\prod _{j=1}^m*F_j=\bigg [\prod _{j=1}^{m-1}*F_j \bigg ]*F_m. Analogous results are given whenR+=(0,∞)R^+=(0,\infty )is replaced byRnR^nand also when the convolutionF1∗F2F_1*F_2onR+R^+is taken instead to be∫0∞F(t)G(x/t)dt/t\int _0^{\infty }F(t)G(x/t)\,dt/t. The extremal functions are also discussed.
A global approach to fully nonlinear parabolic problems
Authors: Kartsatos Athanassios , Skrypnik Igor 
Published: July 2002

We consider the general initial-boundary value problem (1)

∂
u

∂
t

−
F
(
x
,
t
,
u
,

D

1

u
,

D

2

u
)
=
f
(
x
,
t
)
,

(
x
,
t
)
∈

Q

T

≡
Ω
×
(
0
,
T
)
,

\displaystyle {\frac {\partial u}{\partial t}-F(x,t,u,\mathcal {D}^{1}u, \mathcal {D}^{2}u)=f(x,t),\quad (x,t)\in Q_{T}\equiv \Omega \times (0,T),}

(2)

G
(
x
,
t
,
u
,

D

1

u
)
=
g
(
x
,
t
)
,

(
x
,
t
)
∈

S

T

≡
∂
Ω
×
(
0
,
T
)
,

\displaystyle {G(x,t,u,\mathcal {D}^{1}u)=g(x,t),\quad (x,t)\in S_{T}\equiv \partial \Omega \times (0,T),}

(3)

u
(
x
,
0
)
=
h
(
x
)
,

x
∈
Ω
,

\displaystyle {u(x,0)=h(x),\quad x\in \Omega ,}

where

Ω
\Omega

is a bounded open set in

R

n

\mathcal {R}^{n}

with sufficiently smooth boundary. The problem (1)-(3) is first reduced to the analogous problem in the space

W

p

(
4
)
,
0

(

Q

T

)

W^{(4),0}_{p}(Q_{T})

with zero initial condition and
\[

f
∈

W

p

(
2
)
,
0

(

Q

T

)
,

g
∈

W

p

(
3
−

1
p

)
,
0

(

S

T

)
.

f\in W^{(2),0}_{p}(Q_{T}),~g \in W^{(3-\frac {1}{p}),0}_{p}(S_{T}).

\]
The resulting problem is then reduced to the problem

A
u
=
0
,

Au=0,

where the operator

A
:

W

p

(
4
)
,
0

(

Q

T

)
→

[

W

p

(
4
)
,
0

(

Q

T

)
]

∗

A:W^{(4),0}_{p}(Q_{T})\to \left [W^{(4),0}_{p}(Q_{T})\right ]^{*}

satisfies Condition

(
S

)

+

.

(S)_{+}.

This reduction is based on a priori estimates which are developed herein for linear parabolic operators with coefficients in Sobolev spaces. The local and global solvability of the operator equation

A
u
=
0

Au=0

are achieved via topological methods developed by I. V. Skrypnik. Further applications are also given involving relevant coercive problems, as well as Galerkin approximations.
The problem of lacunas and analysis on root systems
Authors: Berest Yuri 
Published: July 2002

A lacuna of a linear hyperbolic differential operator is a domain inside its propagation cone where a proper fundamental solution vanishes identically. Huygens’ principle for the classical wave equation is the simplest important example of such a phenomenon. The study of lacunas for hyperbolic equations of arbitrary order was initiated by I. G. Petrovsky (1945). Extending and clarifying his results, Atiyah, Bott and Gårding (1970–73) developed a profound and complete theory for hyperbolic operators with constant coefficients. In contrast, much less is known about lacunas for operators with variable coefficients. In the present paper we study this problem for one remarkable class of partial differential operators with singular coefficients. These operators stem from the theory of special functions in several variables related to finite root systems (Coxeter groups). The underlying algebraic structure makes it possible to extend many results of the Atiyah-Bott-Gårding theory. We give a generalization of the classical Herglotz-Petrovsky-Leray formulas expressing the fundamental solution in terms of Abelian integrals over properly constructed cycles in complex projective space. Such a representation allows us to employ the Petrovsky topological condition for testing regular (strong) lacunas for the operators under consideration. Some illustrative examples are constructed. A relation between the theory of lacunas and the problem of classification of commutative rings of partial differential operators is discussed.
Optimal factorization of Muckenhoupt weights
Authors: Korey Michael 
Published: July 2002

Peter Jones’ theorem on the factorization of

A
p

A_p

weights is sharpened for weights with bounds near

1
1

, allowing the factorization to be performed continuously near the limiting, unweighted case. When

1
>
p
>
∞

1>p>\infty

and

w
w

is an

A
p

A_p

weight with bound

A
p

(
w
)
=
1
+
ε

A_p(w)=1+\varepsilon

, it is shown that there exist

A
1

A_1

weights

u
,
v

u,v

such that both the formula

w
=
u

v

1
−
p

w=uv^{1-p}

and the estimates

A
1

(
u
)
,

A
1

(
v
)
=
1
+

O

(

ε

)

A_1(u), A_1(v)=1+\mathcal O(\sqrt \varepsilon )

hold. The square root in these estimates is also proven to be the correct asymptotic power as

ε
→
0

\varepsilon \to 0

.
Drinfel´d algebra deformations, homotopy comodules and the associahedra
Authors: Markl Martin , Shnider Steve 
Published: July 2002

The aim of this work is to construct a cohomology theory controlling the deformations of a general Drinfel′d algebra

A
A

and thus finish the program which began in [M. Markl and J.D. Stasheff, Deformation theory via deviations, Journal of Algebra, 70 (1994), 122–155], [S. Shnider and S. Sternberg, The cobar construction and a restricted deformation theory for Drinfeld algebras, Journal of Algebra, 169 (1994), 343–366]. The task is accomplished in three steps. The first step, which was taken in the aforementioned articles, is the construction of a modified cobar complex adapted to a non-coassociative comultiplication. The following two steps each involves a new, highly non-trivial, construction. The first construction, essentially combinatorial, defines a differential graded Lie algebra structure on the simplicial chain complex of the associahedra. The second construction, of a more algebraic nature, is the definition of a map of differential graded Lie algebras from the complex defined above to the algebra of derivations on the bar resolution. Using the existence of this map and the acyclicity of the associahedra we can define a so-called homotopy comodule structure (Definition 3.3 below) on the bar resolution of a general Drinfel′d algebra. This in turn allows us to define the desired cohomology theory in terms of a complex which consists, roughly speaking, of the bimodule and bicomodule maps from the bar resolution to the modified cobar resolution. The complex is bigraded but not a bicomplex as in the Gerstenhaber-Schack theory for bialgebra deformations. The new components of the coboundary operator are defined via the constructions mentioned above. The results of the paper were announced in [12].
Homology and some homotopy decompositions for the James filtration on spheres
Authors: Selick Paul 
Published: July 2002

The filtrations on the James construction on spheres,

J

k

(

S

2
n

)

J_{k}\left (S^{2n}\right )

, have played a major role in the study of the double suspension

S

2
n
−
1

→

Ω
2

S

2
n
+
1

S^{2n-1}\to \Omega ^2 S^{2n+1}

and have been used to get information about the homotopy groups of spheres and Moore spaces and to construct product decompositions of related spaces. In this paper we calculate

H
∗

(
Ω

J

k

(

S

2
n

)

;

Z

/

p

Z

)

H_*\left ( \Omega J_{k}\left (S^{2n}\right ); {\mathbb {Z}}/p{\mathbb {Z}}\right )

for odd primes

p
p

. When

k
k

has the form

p
t

−
1

p^t-1

, the result is well known, but these are exceptional cases in which the homology has polynomial growth. We find that in general the homology has exponential growth and in some cases also has higher

p
p

-torsion. The calculations are applied to construct a

p
p

-local product decomposition of

Ω

J

k

(

S

2
n

)

\Omega J_{k}\left (S^{2n}\right )

for

k
>

p
2

−
p

k>p^2-p

which demonstrates a mod

p
p

homotopy exponent in these cases.
Functorial structure of units in a tensor product
Authors: Jaffe David 
Published: July 2002

The behavior of units in a tensor product of rings is studied, as one factor varies. For example, let

k
k

be an algebraically closed field. Let

A
A

and

B
B

be reduced rings containing

k
k

, having connected spectra. Let

u
∈
A

⊗
k

B

u\in A\otimes _k\,B

be a unit. Then

u
=
a
⊗
b

u=a\otimes b

for some units

a
∈
A

a\in A

and

b
∈
B

b\in B

.

Here is a deeper consequence, stated for simplicity in the affine case only. Let

k
k

be a field, and let

φ
:
R
→
S

\varphi :R\to S

be a homomorphism of finitely generated

k
k

-algebras such that

Spec
⁡
(
φ
)

\operatorname {Spec}(\varphi )

is dominant. Assume that every irreducible component of

Spec
⁡
(

R

red

)

\operatorname {Spec}(R_{\operatorname {red}})

or

Spec
⁡
(

S

red

)

\operatorname {Spec}(S_{\operatorname {red}})

is geometrically integral and has a rational point. Let

B
→
C

B\to C

be a faithfully flat homomorphism of reduced

k
k

-algebras. For

A
A

a

k
k

-algebra, define

Q
(
A
)

Q(A)

to be

(
S

⊗
k

A

)
∗

/

(
R

⊗
k

A

)
∗

(S\otimes _k\,A)^*/(R\otimes _k\,A)^*

. Then

Q
Q

satisfies the following sheaf property: the sequence
\[

0
→
Q
(
B
)
→
Q
(
C
)
→
Q
(
C

⊗
B

C
)

0\to Q(B)\to Q(C)\to Q(C\otimes _B\,C)

\]
is exact. This and another result are used to prove (5.2) of [R. Guralnick, D. B. Jaffe, W. Raskind and R. Wiegand, On the Picard group: torsion and the kernel induced by a faithfully flat map, J. of Algebra (to appear)].
Virtually free groups with finitely many outer automorphisms
Authors: Pettet Martin 
Published: July 2002

Let

G
G

be a finitely generated virtually free group. From a presentation of

G
G

as the fundamental group of a finite graph of finite-by-cyclic groups, necessary and sufficient conditions are derived for the outer automorphism group of

G
G

to be finite. Two versions of the characterization are given, both effectively verifiable from the graph of groups. The more purely group theoretical criterion is expressed in terms of the structure of the normalizers of the edge groups (Theorem 5.10); the other version involves certain finiteness conditions on the associated

G
G

-tree (Theorem 5.16). Coupled with an earlier result, this completes a description of the finitely generated groups whose full automorphism groups are virtually free.
Twin trees and 𝜆_{Λ}-gons
Authors: Bennett Curtis 
Published: July 2002

We define a natural generalization of generalized

n
n

-gons to the case of

Λ
\Lambda

-graphs (where

Λ
\Lambda

is a totally ordered abelian group and

0
>
λ
∈
Λ

0>\lambda \in \Lambda

). We term these objects

λ

Λ

\lambda _{\Lambda }

-gons. We then show that twin trees as defined by Ronan and Tits can be viewed as

(
1
,
0

)

Λ

(1,0)_{\Lambda }

-gons, where

Λ
=
Z
×
Z

\Lambda = Z \times Z

is ordered lexicographically. This allows us to then generalize twin trees to the case of

Λ
\Lambda

-trees. Finally, we give a free construction of

λ

Λ

\lambda _{\Lambda }

-gons in the cases where

Λ
\Lambda

is discrete and has a subgroup of index

2
2

that does not contain the minimal element of

Λ
\Lambda

.
On the rational homotopy type of function spaces
Authors: Brown Edgar , Szczarba Robert 
Published: July 2002

The main result of this paper is the construction of a minimal model for the function space

F

(
X
,
Y
)

\mathcal {F}(X,Y)

of continuous functions from a finite type, finite dimensional space

X
X

to a finite type, nilpotent space

Y
Y

in terms of minimal models for

X
X

and

Y
Y

. For the component containing the constant map,

π

∗

(

F

(
X
,
Y
)
)
⊗
Q
=

π

∗

(
Y
)
⊗

H

−
∗

(
X
;
Q
)

\pi _{*}(\mathcal {F}(X,Y))\otimes Q =\pi _{*}(Y)\otimes H^{-*}(X;Q)

in positive dimensions. When

X
X

is formal, there is a simple formula for the differential of the minimal model in terms of the differential of the minimal model for

Y
Y

and the coproduct of

H

∗

(
X
;
Q
)

H_{*}(X;Q)

. We also give a version of the main result for the space of cross sections of a fibration.
Lower bounds for derivatives of polynomials and Remez type inequalities
Authors: Erdélyi Tamás , Nevai Paul 
Published: July 2002

P. Turán [Über die Ableitung von Polynomen, Comositio Math. 7 (1939), 89–95] proved that if all the zeros of a polynomial

p
p

lie in the unit interval

I

=
def

[
−
1
,
1
]

I \overset {\text {def}}{=} [-1,1]

, then

‖

p
′

‖

L

∞

(
I
)

≥

deg
⁡
(
p
)

/

6

‖
p

‖

L

∞

(
I
)

\|p’\|_{L^{\infty }(I)}\ge {\sqrt {\deg (p)}}/{6}\; \|p\|_{L^{\infty }(I)}\;

. Our goal is to study the feasibility of

lim

n
→
∞

‖

p

n

′

‖

X

/

‖

p

n

‖

Y

=
∞

\lim _{{n\to \infty } }{\|p_{n}’\|_{X}} / {\|p_{n}\|_{Y}} =\infty

for sequences of polynomials

{

p

n

}

n
∈

N

\{p_{n}\}_{n\in \mathbb N }

whose zeros satisfy certain conditions, and to obtain lower bounds for derivatives of (generalized) polynomials and Remez type inequalities for generalized polynomials in various spaces.
Tessellations of solvmanifolds
Authors: Witte Dave 
Published: July 2002

Let

A
A

be a closed subgroup of a connected, solvable Lie group

G
G

, such that the homogeneous space

A
∖
G

A\backslash G

is simply connected. As a special case of a theorem of C. T. C. Wall, it is known that every tessellation

A
∖
G

/

Γ

A\backslash G/\Gamma

of

A
∖
G

A\backslash G

is finitely covered by a compact homogeneous space

G
′

/

Γ
′

G’/\Gamma ’

. We prove that the covering map can be taken to be very well behaved — a “crossed" affine map. This establishes a connection between the geometry of the tessellation and the geometry of the homogeneous space. In particular, we see that every geometrically-defined flow on

A
∖
G

/

Γ

A\backslash G/\Gamma

that has a dense orbit is covered by a natural flow on

G
′

/

Γ
′

G’/\Gamma ’

.
Witten-Helffer-Sjöstrand theory for 𝑆¹-equivariant cohomology
Authors: Wai Hon-kit 
Published: July 2002

Given an

S
1

S^1

-invariant Morse function

f
f

and an

S
1

S^1

-invariant Riemannian metric

g
g

, a family of finite dimensional subcomplexes

(

Ω
~

i
n
v
,
s
m

∗

(
M
,
t
)
,
D
(
t
)
)

(\widetilde \Omega ^*_{inv,sm}(M,t), D(t))

,

t
∈
[
0
,
∞
)

t\in [0,\infty )

, of the Witten deformation of the

S
1

S^1

-equivariant de Rham complex is constructed, by studying the asymptotic behavior of the spectrum of the corresponding Laplacian

Δ
~

k

(
t
)
=

D
k
∗

(
t
)

D
k

(
t
)
+

D

k
−
1

(
t
)

D

k
−
1

∗

(
t
)

\widetilde \Delta ^k(t)=D^*_k(t)D_k(t)+D_{k-1}(t)D^*_{k-1}(t)

as

t
→
∞

t\to \infty

. In fact the spectrum of

Δ
~

k

(
t
)

\widetilde \Delta ^k(t)

can be separated into the small eigenvalues, finite eigenvalues and the large eigenvalues. Then one obtains

(

Ω
~

i
n
v
,
s
m

∗

(
M
,
t
)
,
D
(
t
)
)

( \widetilde \Omega ^*_{inv,sm}(M,t),D(t))

as the complex of eigenforms corresponding to the small eigenvalues of

Δ
~

(
t
)

\widetilde \Delta (t)

. This permits us to verify the

S
1

S^1

-equivariant Morse inequalities. Moreover suppose

f
f

is self-indexing and

(
f
,
g
)

(f,g)

satisfies the Morse-Smale condition, then it is shown that this family of subcomplexes converges as

t
→
∞

t\to \infty

to a geometric complex which is induced by

(
f
,
g
)

(f,g)

and calculates the

S
1

S^1

-equivariant cohomology of

M
M

.
Criteria of algebraic independence with multiplicities and interpolation determinants
Authors: Laurent Michel , Roy Damien 
Published: July 2002

We generalize Gel’fond’s criterion of algebraic independence by taking into account the values of the derivatives of the polynomials, and show how the new criterion applies to proving results of algebraic independence using interpolation determinants. We also establish a new result of approximation of a transcendental number by algebraic numbers of bounded degree and size. It contains an earlier result of E. Wirsing and also a result announced by A. Durand.
Random intersections of thick Cantor sets
Authors: Kraft Roger 
Published: July 2002

Let

C

1

C_{1}

,

C

2

C_{2}

be Cantor sets embedded in the real line, and let

τ

1

\tau _{1}

,

τ

2

\tau _{2}

be their respective thicknesses. If

τ

1

τ

2

>
1

\tau _{1}\tau _{2}>1

, then it is well known that the difference set

C

1

−

C

2

C_{1}-C_{2}

is a disjoint union of closed intervals. B. Williams showed that for some

t
∈
int
⁡
(

C

1

−

C

2

)

t\in \operatorname {int} (C_{1}-C_{2})

, it may be that

C

1

∩
(

C

2

+
t
)

C_{1}\cap (C_{2}+t)

is as small as a single point. However, the author previously showed that generically, the other extreme is true;

C

1

∩
(

C

2

+
t
)

C_{1}\cap (C_{2}+t)

contains a Cantor set for all

t
t

in a generic subset of

C

1

−

C

2

C_{1}-C_{2}

. This paper shows that small intersections of thick Cantor sets are also rare in the sense of Lebesgue measure; if

τ

1

τ

2

>
1

\tau _{1}\tau _{2}>1

, then

C

1

∩
(

C

2

+
t
)

C_{1}\cap (C_{2}+t)

contains a Cantor set for almost all

t
t

in

C

1

−

C

2

C_{1}-C_{2}

.
Petrogenesis and Implications of Calc-Alkaline Cryptic Hybrid Magmas from Washburn Volcano, Absaroka Volcanic Province, USA
Authors: FEELEY T. C. , COSCA M. A. , LINDSAY C. R. 
Published: July 2002

AbstractThe petrogenesis of calc-alkaline magmatism in the Eocene Absaroka Volcanic Province (AVP) is investigated at Washburn volcano, a major eruptive center in the low-K western belt of the AVP. New 40Ar/39Ar age determinations indicate that magmatism at the volcano commenced as early as 55 Ma and continued until at least 52 Ma. Although mineral and whole-rock compositional data reflect near equilibrium crystallization of modal phenocrysts, petrogenetic modeling demonstrates that intermediate composition magmas are hybrids formed by mixing variably fractionated and contaminated mantle-derived melts and heterogeneous silicic crustal melts. Nd and Sr isotopic compositions along with trace element data indicate that silicic melts in the Washburn system are derived from deep-crustal rocks broadly similar in composition to granulite-facies xenoliths in the Wyoming Province. Our preferred explanation for these features is that mantle-derived basaltic magma intruded repeatedly in the deep continental crust leading to fractional crystallization, silicic melt production, and homogenization of magmas, followed by ascent to shallow reservoirs and crystallization of new plagioclase-rich mineral assemblages in equilibrium with the intermediate hybrid liquids. The implications of this process are that (1) some calc-alkaline magmas may only be recognized as hybrids on purely chemical grounds, particularly in systems where mixing precedes and is widely separated from crystallization in space and time, and (2) given the role ascribed to crustal processes at Washburn volcano, the variation between rocks that follow calc-alkaline trends in the western AVP and those that follow shoshonitic trends in the east cannot simply reflect higher pressures of fractionation to the east in Moho-level magma chambers in the absence of crustal interaction.
Hygroscopic‐Microgels‐Enabled Rapid Water Extraction from Arid Air
Authors: Guan Weixin , Lei Chuxin , Guo Youhong , Shi Wen , Yu Guihua 
Published: October 2022

AbstractSorbent‐based atmospheric water harvesting (AWH) has emerged as a promising decentralized water‐production technology to mitigate the freshwater crisis in arid areas. Hydrogels have been regarded as attractive sorbents due to their high water retention and tailorable polymer–water interactions. Yet, the kinetics of water sorption and desorption at low relative humidity (RH) shall be improved for their practical implementation. Here, hygroscopic microgels (HMGs) composed of hydroxypropyl cellulose (HPC) and hygroscopic salt are reported, which achieve a water uptake of ca. 0.5–0.8 g g−1 at 15–30% RH. HMGs enable rapid sorption–desorption kinetics owing to the short‐distance diffusion in the microgels and hydrophilicity–hydrophobicity switching of the thermoresponsive HPC. To validate the feasibility of HMGs for moisture extraction, a potential daily water collection of up to equivalent 7.9–19.1 L kg−1 at low RH is demonstrated, enabled by 24–36 operation cycles per day based on the material‐level experiments. With renewable raw materials and superior performance, HMGs provide a sustainable approach for rapid moisture extraction in arid climates.