bluuebunny/crossref_metadata_2025_split huggingface dataset:
Effect of chromium dinicocysteinate supplementation on circulating levels of insulin, TNF‐α, oxidative stress, and insulin resistance in type 2 diabetic subjects: Randomized, double‐blind, placebo‐controlled study
Authors: Jain Sushil K. , Kahlon Gunjan , Morehead Lester , Dhawan Richa , Lieblong Benjamin , Stapleton Tommie , Caldito Gloria , Hoeldtke Robert , Levine Steven N. , Bass Pat Farrington 
Published: June 2012

ScopeChromium and cysteine supplementation have been shown to improve glucose metabolism in animal studies. This study examined the hypothesis that chromium dinicocysteinate (CDNC), a complex of chromium and l‐cysteine, is beneficial in lowering oxidative stress, vascular inflammation, and glycemia in type 2 diabetic subjects.Methods and resultsType 2 diabetic subjects enrolled in this study were given placebo for 1 month for stabilization and then randomized into one of three groups: placebo (P), chromium picolinate (CP), or CDNC, after which they received daily oral supplementation for 3 months. Of the 100 patients enrolled in the study, 74 patients completed it. There were 25 patients in the P supplemented group, 25 in the CP supplemented and 24 in the CDNC supplemented group who completed the study. Blood markers of glycemia, vascular inflammation, HOMA insulin resistance, and oxidative stress were determined at randomization and after 3 months of supplementation with P, CP, or CDNC. There was a significant decrease at 3 months in insulin resistance (p = 0.02) and in the levels of protein oxidation (p = 0.02) and TNF‐α (p = 0.01) in the CDNC supplemented cohort compared to baseline. However, there was no statistically significant change in these markers in the CP supplemented group compared to baseline. Insulin levels significantly decreased (p = 0.01) for subjects receiving CDNC but not CP. There was no significant impact of supplementation on HbA1c or glucose levels in either of the groups.ConclusionCDNC supplementation lowers insulin resistance by reducing blood levels of TNF‐α, insulin, and oxidative stress in type 2 diabetic subjects. Therefore, CDNC supplementation has potential as an adjunct therapy for individuals with type 2 diabetes.
Boundary elements solution of stokes flow between curved surfaces with nonlinear slip boundary condition
Authors: Nieto Cesar , Power Henry , Giraldo Mauricio 
Published: June 2012

AbstractThis work presents a boundary integral equation formulation for Stokes nonlinear slip flows based on the normal and tangential projection of the Green's integral representational formulae for the velocity field. By imposing the surface tangential velocity discontinuity (slip velocity) in terms of the nonlinear slip flow boundary condition, a system of nonlinear boundary integral equations for the unknown normal and tangential components of the surface traction is obtained. The Boundary Element Method is used to solve the resulting system of integral equations using a direct Picard iteration scheme to deal with the resulting nonlinear terms. The formulation is used to study flows between curved rotating geometries: i.e., concentric and eccentric Couette flows and single rotor mixers, under nonlinear slip boundary conditions. The numerical results obtained for the concentric Couette flow is validated again a semianalytical solution of the problem, showing excellent agreements. The other two cases, eccentric Couette and single rotor mixers, are considered to study the effect of different nonlinear slip conditions in these flow configurations. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013
Dynamic vibrations of a damageable viscoelastic beam in contact with two stops
Authors: Campo Marco , Copetti Maria I.M. , Fernández José R. 
Published: June 2012

AbstractA model for the material damage, due to dynamic vibrations of a Kelvin‐Voigt viscoelastic beam whose tip is constrained to move between two stops, is presented and numerically analyzed. The contact of the free tip with the stops is described by the normal compliance condition. The evolution of damage of the beam's material, which measures the reduction of its load carrying capacity, is modeled with a parabolic inclusion. The existence of the unique local solution is stated. A numerical algorithm is presented, in which spatially it is approximated by finite elements, and the time derivatives are discretized with the Euler scheme. Error estimates are derived for sufficiently regular solutions, and four numerical simulations are shown. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013
Angiotensin‐converting enzyme inhibitors or angiotensin II receptor blockers and the risk of developing rheumatoid arthritis in antihypertensive drug users
Authors: de Jong Hilda J. I. , Vandebriel Rob J. , Saldi Siti R. F. , van Dijk Liset , van Loveren Henk , Cohen Tervaert Jan Willem , Klungel Olaf H. 
Published: June 2012

ABSTRACTPurposeAngiotensin‐converting enzyme (ACE) inhibitors and angiotensin II receptor blockers (ARBs) are effective in the treatment of cardiovascular disease. Next to effects on hypertension and cardiac function, these drugs have anti‐inflammatory and immunomodulating properties which may either facilitate or protect against the development of autoimmunity, potentially resulting in autoimmune diseases. Therefore, we determined in the current study the association between ACE inhibitor and ARB use and incident rheumatoid arthritis (RA).MethodsA matched case–control study was conducted among patients treated with antihypertensive drugs using the Netherlands Information Network of General Practice (LINH) database in 2001–2006. Cases were patients with a first‐time diagnosis of RA. Each case was matched to five controls for age, sex, and index date, which was selected 1 year before the first diagnosis of RA. ACE inhibitor and ARB exposure was considered to be any prescription issued in the period before index date. Logistic regression analysis was used to estimate odds ratios (ORs) and their 95% confidence intervals (CI).ResultsOur study included 211 cases and 667 matched controls. After controlling for potential confounders, ever use of ACE inhibitors or ARBs was not associated with incident RA (adjusted ORs [95%CI], 0.99 [0.55–1.79] and 1.02 [0.67–1.56], respectively). The adjusted ORs (95%CI) for current and past use of ACE inhibitors were 1.18 (0.75–1.85) and 0.61 (0.28–1.35). For current and past use of ARBs, these adjusted ORs (95%CI) were 1.40 (0.80–2.45) and 0.29 (0.05–1.67), respectively. No duration and dose–effect relationship was observed.ConclusionsACE inhibitor or ARB use is not associated with incident RA. Copyright © 2012 John Wiley & Sons, Ltd.
Synthesis and characterization of monomeric and polymeric pyridinylimine‐based Ni(II) complexes and their catalytic activities in ethylene oligomerization
Authors: Ahamad Tansir , Alshehri Saad M 
Published: June 2012

AbstractA new polymeric ligand was synthesized through the reaction of 4‐(pyridinylimine)phenol and formaldehyde in a basic medium, and its corresponding polymer–nickel complexes were formed in a 1:1 molar ratio. The synthesized compounds were characterized using elemental and spectral analyses. The monomeric and polymeric Ni(II) complexes (C1 and C2, respectively) were evaluated as catalyst precursors for ethylene oligomerization, using methylaluminoxane as an activator at two different ethylene pressures. C2 was found to be a more effective pre‐catalyst than C1, with the co‐catalyst having a similar effect in both cases. C2 exhibited an activity of 1.282 × 106 g (mol Ni)−1 h−1 bar−1, with an Al:Ni ratio of 2000:1 at room temperature and 1 atm ethylene pressure. Meanwhile C1 exhibited an activity of 1.126 × 106 g (mol Ni)−1 h−1 bar−1 under similar experimental conditions. At 5 atm ethylene pressure, C1 favoured the formation of high‐density polyethylene, whereas C2 favoured the formation of branched low‐density polyethylene. Copyright © 2012 Society of Chemical Industry
Kältemittel‐Leckschnüffler
Authors: Jitschin Wolfgang , Reinl Friedrich 
Published: June 2012

AbstractKühlschränke, Klimaanlagen, Luftentfeuchter, Wasserrückkühler und andere kühlende Maschinen erzeugen die Kälte durch Zirkulieren eines Kältemittels in einem geschlossenen Kreislauf. Als Kältemittel kommen meist halogenierte Kohlenwasserstoffe wegen ihrer guten thermophysikalischen Eigenschaften zum Einsatz. Leider sind diese Kältemittel umweltschädlich, weil sie zum Abbau der Ozonschicht und damit zum Treibhaus‐Effekt beitragen. Um eine Freisetzung der Kältemittel in die Atmosphäre zu vermeiden, müssen die Kreisläufe dicht sein. Der Gesetzgeber fordert, dass die Leckagerate des gesamten Kreislaufs kleiner sein muss als wenige Gramm pro Jahr. Zur Dichtheitsprüfung von Geräten und Anlagen werden in der Praxis mobile Kältemittel‐Detektoren eingesetzt. Der Anwender muss sicherstellen, dass sein Leckschnüffler die spezifizierte Nachweisgrenze einhält. Im vorliegenden Artikel wird die Prüfung dieser Geräte nach genormten Verfahren diskutiert.
Hochselektive Absorberschichten für thermische Sonnenkollektoren
Authors: Pavić Davorin 
Published: June 2012

AbstractFür die effektive Wirkungsweise von modernen thermischen Sonnenkollektoren ist eine hochselektive Absorberbeschichtung notwendig. Aufgebaut als dünnes optisches Gradientenschichtsystem verfügt die Absorberschicht über strahlungsselektive Eigenschaften, ausgedrückt im hohen solaren Absorptions‐ und niedrigem thermischen Emissiongrad. Solche komplexen Mehrschichtsysteme werden in modularen Vakuumbeschichtungsverfahren hergestellt. Industrielle Air‐to‐air Bandbeschichtungsanlagen erlauben das kontinuierliche Beschichten von Metallbändern im Durchlaufprozesss und ermöglichen die Herstellung von Absorbern, die höchsten Ansprüchen an Effizienz, Beständigkeit und Ästhetik genügen.
Hydrophobe Grenzflächenmodifikationen
Authors: Fliedner Michael , Chavez Ricardo 
Published: June 2012

AbstractDurch Aufbringen hydrophoben und oleophoben Nanoschichten lassen sich Grenzflächen modifizieren, ohne die ursprünglichen funktionellen Eigenschaften der Grenzfläche zu beeinflussen. Nasschemisch hergestellte Nanoschichten haben üblicherweise eine irreguläre, aus vielen unterschiedlichen Bausteinen zusammengesetzte Struktur, die auch polare und damit hydrophile Komponenten enthält. Im Gegensatz dazu lassen sich bei der Gasphasenabscheidung unter Vakuum durch entsprechende Prozessführung die Grenzflächen der zu beschichtenden Objekte den Anforderungen einer selbstorganisierenden hydrophoben Nanostruktur optimal anpassen. Die Gebrauchseigenschaften von Grenzflächen mit reflexmindernden, reflektierenden oder funktionellen Schichten werden durch Auftragen einer Nanoschicht im praktischen Gebrauch mit geringem Verfahrens‐ und Maschinenaufwand erheblich verbessert.
Anforderungen an Beschichtungen für den optischen Gerätebau
Authors: Pulker Hans Karl 
Published: June 2012

AbstractOptische Technologien zeigen starkes Wachstum. Die zur praktischen Durchführung erforderlichen optischen Geräte sind, in wichtigen Teilen, mit unterschiedlichen optischen Komponenten aus hochwertigen dünnen Schichten aufgebaut. Die Qualität der Beschichtungen ist dabei von außerordentlich großer Bedeutung für zuverlässige, optimale Funktionstüchtigkeit und gute Umweltbeständigkeit der Geräte. Entwicklungen von neuen / hybriden Schichtherstellungstechniken für industriellen Einsatz und Suche nach neuen Materialien sowie neuen Schichtsystem‐Design sind fortdauernde, herausfordernde Notwendigkeiten.
Syntheses and Fluorescence Properties of New Coordination Polymers Containing 4, 4′‐Dinitrostilbene‐2, 2′‐Disulfonate Building Unit Supported by Rigid Auxiliary Ligands
Authors: Ji Shu‐Ying , Liu Lu , Mu Ya‐Juan , Jia Yan‐Yuan , Hou Hong‐Wei , Mi Li‐Wei 
Published: June 2012

AbstractTwo new coordination polymers, [Pb(phen)2(dans)]n (1) and [Pb(4, 4′‐bipy)(dans)]n (2) (dans = disodium 4, 4′‐dinitrostilbene‐2, 2′‐disulfonate, phen = 1, 10‐phenanthroline and 4, 4′‐bipy = 4, 4′‐bipyridyl) were synthesized and characterized by elemental analysis, thermogravimetry, IR spectroscopy, and X‐ray single crystal diffraction. Compound 1 is a 1D chain with Pb–O bond lengths in the range of 2.76 to 2.90 Å,. The structure of 2 is a three‐dimensional (3D) framework with (44·610·8)(3·43·52)(43·63) topology.
Prise en charge de la cryptorchidie au centre hospitalier et universitaire de Brazzaville
Authors: Bouya P. A. , Odzébé A. W. S. , Avala P. P. , Ondongo Atipo M. , Koutaba E. , Cardorelle Mbika A. I. 
Published: June 2012

Résumé

But
contribuer à l’amélioration de la prise en charge de la cryptorchidie en milieu hospitalier.

Patients et méthodes
il s’agit une étude rétrospective descriptive réalisée dans les services de chirurgie pédiatrique et d’urologie-andrologie du centre hospitalier et universitaire de Brazzaville concernant les patients opérés pour cryptorchidie du 1er janvier 2000 au 31 décembre 2009. Les paramètres étudiés ont été: la fréquence, l’âge au moment du diagnostic et du traitement, les renseignements de l’examen physique, les données chirurgicales et évolutives.

Résultats
sur 8100 patients hospitalisés dans les deux services, 163 (2,7 %) l’étaient pour cryptorchidie dont 2,6 % chez les patients de 1 à 16 ans et 0,8 % chez les patients de 19 à 36 ans. L’âge moyen était de 9,6 ans avec des extrêmes de 1 à 36 ans. Les circonstances de découverte étaient: la vacuité de la bourse (77,3 %), la hernie inguinale étranglée (13,5 %), la hernie ombilicale étranglée (3,1 %), l’infertilité (3,1 %), les douleurs abdominales (1,8 %) et l’hypospadias (1,2 %). L’atteinte était unilatérale gauche (82 cas), droite (70 cas) et bilatérale dans 11 cas. À l’exploration chirurgicale, le testicule était intra-abdominal (26,5 %), inguinal profond (62 %), inguinal superficiel (11,5 %). Les testicules étaient d’aspect normal en peropératoire dans 129 cas, atrophiques dans neuf cas et d’aspect non précisé dans 25 cas. Les résultats du traitement après orchidopexie en un temps étaient bons dans 139 cas (92,6) et mauvais dans deux cas (1,3 %); pour l’orchidopexie en deux temps, les résultats étaient bon dans un cas et mauvais dans trois cas.

Conclusion
la cryptorchidie est encore diagnostiquée et traitée tardivement dans notre milieu hospitalier. Une prise en charge thérapeutique entre l’âge d’un et deux an(s) est nécessaire pour l’amélioration du pronostic fonctionnel.
THE UK BRIBERY ACT 2010 AND ACCOMPANYING GUIDANCE: BELATED IMPLEMENTATION OF THE OECD ANTI-BRIBERY CONVENTION
Authors: Rose Cecily 
Published: June 2012

AbstractOn 1 July 2011 the UK Bribery Act 2010 and accompanying guidance finally came into force, marking the end of years of controversy about how and when the United Kingdom would implement the OECD Anti-Bribery Convention. The United Kingdom's very delayed implementation of the Convention provoked an increasingly threatening response from the OECD Working Group on Bribery, and highlighted this body's lack of binding enforcement procedures. By contrast, the OECD's reliance on non-binding guidelines has proved successful in that the UK Guidance draws heavily upon the OECD's guidance on how corporations should prevent the bribery of foreign public officials.
‘SEIZING’ PHARMACEUTICALS IN TRANSIT: ANALYSING THE WTO DISPUTE THAT WASN'T
Authors: Mercurio Bryan 
Published: June 2012

AbstractSeveral recent detentions of generic pharmaceutical products transiting through the European Union (EU) for suspected infringements of intellectual property rights raised serious concerns for public health advocates and threatened to expose systemic problems existing in the World Trade Organization's (WTO) Agreement on Trade-Related Aspects of Intellectual Property Rights (TRIPS). The detentions not only garnered international attention, but India and Brazil formally began WTO dispute settlement proceedings against the EU. The parties recently reached a mutually agreed solution to the matter and the proceedings have been halted, leaving unanswered the complex legal and technical questions raised by the detentions of pharmaceuticals in transit. Despite a solution being reached in this dispute, the matter will undoubtedly resurface in the near future for a number of reasons. For instance, the EU is attempting to export its laws to its trading partners through the negotiation of free trade agreements and in other forums such as the recently concluded Anti-Counterfeiting Trade Agreement which increases the likelihood that similar detentions will occur at some point in the future. Moreover, recent trends in international intellectual property law indicate a move towards increased protection and enforcement in at least the short and medium term. The issue therefore offers the opportunity for rich legal analysis into an underexplored, yet increasingly important, aspect of WTO law.
Homogeneous continua in Euclidean (𝑛+1)-space which contain an 𝑛-cube are 𝑛-manifolds
Authors: Prajs Janusz R. 
Published: June 2012

Let

X
X

be a homogeneous continuum and let

E
n

{E^n}

be Euclidean

n
n

-space. We prove that if

X
X

is properly contained in a connected

(
n
+
1
)

(n + 1)

-manifold, then

X
X

contains no

n
n

-dimensional umbrella (i.e. a set homeomorphic to the set

{
(

x
1

,
…
,

x

n
+
1

)
∈

E

n
+
1

:

x
1
2

+
⋯
+

x

n
+
1

2

≤
1

\{ ({x_1}, \ldots ,{x_{n + 1}}) \in {E^{n + 1}}:x_1^2 + \cdots + x_{n + 1}^2 \leq 1

and

x

n
+
1

≤
0

{x_{n + 1}} \leq 0

and either

x
1

=
⋯
=

x
n

=
0

{x_1} = \cdots = {x_n} = 0

or

x

n
+
1

=
0
}

{x_{n + 1}} = 0\}

). Combining this fact with an earlier result of the author we conclude that if

X
X

lies in

E

n
+
1

{E^{n + 1}}

and topologically contains

E
n

{E^n}

, then

X
X

is an

n
n

-manifold.
Centers of generic Hecke algebras
Authors: Jones Lenny K. 
Published: June 2012

Let

W
W

be a Weyl group and let

W
′

W’

be a parabolic subgroup of

W
W

. Define

A
A

as follows:
\[

A
=
R

⊗

Q

[
u
]

A

(
W
)

A = R{ \otimes _{{\mathbf {Q}}[u]}}\mathcal {A}(W)

\]
where

A

(
W
)

\mathcal {A}(W)

is the generic algebra of type

A
n

{A_n}

over

Q

[
u
]

{\mathbf {Q}}[u]

an indeterminate, associated with the group

W
W

, and

R
R

is a

Q

[
u
]

{\mathbf {Q}}[u]

-algebra, possibly of infinite rank, in which

u
u

is invertible. Similarly, we define

A
′

A’

associated with

W
′

W’

. Let

M
M

be an

A
−
A

A - A

bimodule, and let

b
∈
M

b \in M

. Define the relative norm [14]
\[

N

W
,

W
′

(
b
)
=

∑

t
∈
T

u

−
l
(
t
)

a

t

−
1

b

a
t

{N_{W,W’}}(b) = \sum \limits _{t \in T} {{u^{ - l(t)}}{a_{{t^{ - 1}}}}b{a_t}}

\]
where

T
T

is the set of distinguished right coset representives for

W
′

W’

in

W
W

. We show that if

b
∈

Z
M

(

A
′

)
=
{
m
∈
M

|

m

a
′

=

a
′

m

∀

a
′

∈

A
′

}

b \in {Z_M}(A’) = \{ m \in M|ma’ = a’m\quad \forall a’ \in A’\}

, then

N

W
,

W
′

(
b
)
∈

Z
M

(
A
)

{N_{W,W’}}(b) \in {Z_M}(A)

. In addition, other properties of the relative norm are given and used to develop a theory of induced modules for generic Hecke algebras including a Markey decomposition. This section of the paper is previously unpublished work of P. Hoefsmit and L. L. Scott. Let

α
=
(

k
1

,

k
2

,
…
,

k
z

)

\alpha = ({k_1},{k_2}, \ldots ,{k_z})

be a partition of

n
n

and let

S
α

=

Π

i
=
1

Z

S

k
i

{S_\alpha } = \Pi _{i = 1}^Z{S_{{k_i}}}

be a "left-justified" parabolic subgroup of

S
n

{S_n}

of shape

α
\alpha

. Define
\[

b
α

=

N

S
n

,

S
α

(

N

α

)

{b_\alpha } = {N_{{S_n},{S_\alpha }}}({\mathcal {N}_\alpha })

\]
, where
\[

N

α

=

∏

i
=
1

z

N

S

k
i

−
1

,

S
1

(

a

w
i

)

{\mathcal {N}_\alpha } = \prod \limits _{i = 1}^z {{N_{{S_{{k_i} - 1}},{S_1}}}({a_{{w_i}}})}

\]
with

w
i

{w_i}

a

k
i

{k_i}

-cycle of length

k
i

−
1

{k_i} - 1

in

S

k
i

{S_{{k_i}}}

. Then the main result of this paper is Theorem. The set

{

b
α

|

α
⊢
n
}

\{ {b_\alpha }|\alpha \vdash n\}

is a basis for

Z

A
(

S
n

)

(
A
(

S
n

)
)

{Z_{A({S_n})}}(A({S_n}))

over

Q

[
u
,

u

−
1

]

{\mathbf {Q}}[u,{u^{ - 1}}]

. Remark. The norms

b
α

{b_\alpha }

in

Z

A
(

S
n

)

(
A
(

S
n

)
)

{Z_{A({S_n})}}(A({S_n}))

are analogs of conjugacy class sums in the center of

Q

S
n

{\mathbf {Q}}{S_n}

and, in fact, specialization of these norms at

u
=
1

u = 1

gives the standard conjugacy class sum basis of the center of

Q

S
n

{\mathbf {Q}}{S_n}

up to coefficients from

Q

{\mathbf {Q}}

.
𝐿^{𝑝} inequalities for entire functions of exponential type
Authors: Rahman Qazi I. , Schmeisser G. 
Published: June 2012

Let

f
f

be an entire function of exponential type

τ
\tau

belonging to

L
p

{L^p}

on the real line. It has been known since a long time that
\[

∫

−
∞

∞

|

f
′

(
x
)

|

p

d
x
≤

τ
p

∫

−
∞

∞

|

f
(
x
)

|

p

d
x

if

p
≥
1.

\int _{ - \infty }^\infty {{{\left | {f’(x)} \right |}^p}dx \leq {\tau ^p}\int _{ - \infty }^\infty {{{\left | {f(x)} \right |}^p}dx\quad {\text {if}}\;p \geq 1.} }

\]
We prove that the same inequality holds also for

0
>
p
>
1

0 > p > 1

. Various other estimates of the same kind have been obtained.
The Schrödinger equation with a quasi-periodic potential
Authors: Surace Steve 
Published: June 2012

We consider the Schràdinger equation
\[

−

d
2

d

x
2

ψ
+
ε
(
cos
⁡
x
+
cos
⁡
(
α
x
+
ϑ
)
)
ψ
=
E
ψ

- \frac {{{d^2}}} {{d{x^2}}}\psi + \varepsilon (\cos x + \cos (\alpha x + \vartheta ))\psi = E\psi

\]
where

ε
\varepsilon

is small and

σ
\sigma

satisfies the Diophantine inequality
\[

|

p
+
q
α

|

≥
C

/

q
2

for

p

,

q
∈

Z

,
q
≠
0.

|p + q\alpha | \geq C/{q^2}{\text {for}}p{\text {,}}q \in {\mathbf {Z}},q \ne 0.

\]
. We look for solutions of the form
\[

ψ
(
x
)
=

e

i
K
x

q
(
x
)
=

e

i
K
x

∑

ψ

m
n

e

i
n
x

e

i
m
(
α
x
+
ϑ
)

\psi (x) = {e^{iKx}}q(x) = {e^{iKx}}\sum {{\psi _{mn}}{e^{inx}}} {e^{im(\alpha x + \vartheta )}}

\]
. If we try to solve for

ψ
=

ψ

m
n

\psi = {\psi _{mn}}

we are led to the Schràdinger equation on the lattice

Z

2

{{\mathbf {Z}}^2}

\[

H
(
K
)
ψ
=
(
ε
Δ
+
V
(
K
)
)
ψ
=
E
ψ

H(K)\psi = (\varepsilon \Delta + V(K))\psi = E\psi

\]
where

Δ
\Delta

is the discrete Laplacian (without diagonal terms) and

V
(
K
)

V(K)

is some potential on

Z

2

{{\mathbf {Z}}^2}

. We have two main results: (1) For

ε
\varepsilon

sufficiently small,

H
(
K
)

H(K)

has pure point spectrum for almost every

K
K

. (2) For

ε
\varepsilon

sufficiently small, the operator
\[

−

d
2

/

d

x
2

+
ε
(
cos
⁡
x
+
cos
⁡
(
α
x
+
ϑ
)
)

- {d^2}/d{x^2} + \varepsilon (\cos x + \cos (\alpha x + \vartheta ))

\]
has no point spectrum. To prove our results, we must get decay estimates on the Green’s function

(
E
−
H

)

−
1

{(E - H)^{ - 1}}

. The decay of the eigenfunction follows from this. In general, we must keep track of small divisors which can make the Green’s function large. This is accomplished by a KAM (Kolmogorov, Arnold, Moser) type of multiscale perturbation analysis.