bluuebunny/crossref_metadata_2025 huggingface dataset:
Heat Kernel Estimates and Parabolic Harnack Inequalities on Graphs and Resistance Forms
Authors: Kumagai Takashi
Published: September 2006

We summarize recent work on heat kernel estimates and parabolic Harnack inequalities for graphs, where the time scale is the

β

-th power of the space scale for some

β ≥ 2

. We then discuss self-adjoint operators induced by resistance forms. Using a resistance metric, we give a simple condition for detailed heat kernel estimates and parabolic Harnack inequalities. As an application, we show that on trees a detailed two-sided heat kernel estimate is equivalent to some volume growth condition.
Correspondence and Analyticity
Authors: Stapp Henry P.
Published: September 2006

The analyticity properties of the S-matrix in the physical region are determined by the correspondence principle, which asserts that the predictions of classical physics are generated by taking the classical limit of the predictions of quantum theory. The analyticity properties deducible in this way from classical properties include the locations of the singularity surfaces, the rules for analytic continuation around these singularity surfaces, and the analytic character (e.g., pole, logarithmic, etc.) of these singularities. These important properties of the S-matrix are thus derived without using stringent locality assumptions, or the Schrödinger equation for temporal evolution, except for freely moving particles. Sum-over-all-paths methods that emphasize paths of stationary action tend to produce the quantum analogs of the contributions from classical paths. These quantum analogs are derived directly from the associated classical properties by reverse engineering the correspondence-principle connection.
Filtrations on Chow Groups and Transcendence Degree
Authors: Saito Morihiko
Published: September 2006

For a smooth complex projective variety
X
deﬁned over a number ﬁeld, we have ﬁltrations on the Chow groups depending on the choice of realizations. If the realization consists of mixed Hodge structure without any additional structure, we can show that the obtained ﬁltration coincides with the ﬁltration of Green and Griﬃths, assuming the Hodge conjecture. In the case the realizations contain Hodge structure and etale cohomology, we prove that if the second graded piece of the ﬁltration does not vanish, it contains a nonzero element which is represented by a cycle deﬁned over a ﬁeld of transcendence degree one. This may be viewed as a reﬁnement of results of Nori, Schoen, and Green–Griffiths–Paranjape. For higher graded pieces we have a similar assertion assuming a conjecture of Beilinson and Grothendieck’s generalized Hodge conjecture.
The Uniformity Principle on Traced Monoidal Categories
Authors: Hasegawa Masahito
Published: September 2006

The uniformity principle for traced monoidal categories has been introduced as a natural generalization of the uniformity principle (Plotkin’s principle) for ﬁxpoint operators in domain theory. We show that this notion can be used for constructing new traced monoidal categories from known ones. Some classical examples like the Scott induction principle are shown to be instances of these constructions. We also characterize some speciﬁc cases of our constructions as suitable enriched limits.
Applications of Discrete Convex Analysis to Mathematical Economics
Authors: Tamura Akihisa
Published: September 2006

Discrete convex analysis, which is a uniﬁed framework of discrete optimization, is being recognized as a basic tool for mathematical economics. This paper surveys the recent progress in applications of discrete convex analysis to mathematical economics.
On Twisted Microdifferential Modules I. Non-existence of Twisted Wave Equations
Authors: D'Agnolo Andrea , Schapira Pierre
Published: September 2006

Using the notion of subprincipal symbol, we give a necessary condition for the existence of twisted
D
-modules simple along a smooth involutive submanifold of the cotangent bundle to a complex manifold. As an application, we prove that there are no generalized massless ﬁeld equations with non-trivial twist on grassmannians, and in particular that the Penrose transform does not extend to the twisted case.
Sample Path Large Deviations for Diffusion Processes on Conﬁguration Spaces over a Riemannian Manifold
Authors: Röckner Michael , Zhang Tusheng S.
Published: September 2006

In this paper, we establish a sample path large deviation principle for a class of diffusion processes on conﬁguration spaces over a Riemannian manifold. The rate functional turns out to be the energy of the paths associated to the _L_2-Wasserstein distance.
Poles and α-points of Meromorphic Solutions of the First Painlevé Hierarchy
Authors: Shimomura Shun
Published: September 2006

The ﬁrst Painlevé hierarchy, which is a sequence of higher order analogues of the ﬁrst Painlevé equation, follows from the singular manifold equations for the mKdV hierarchy. For meromorphic solutions of the ﬁrst Painlevé hierarchy, we give a lower estimate for the number of poles; which is regarded as an extension of one corresponding to the ﬁrst Painlevé equation, and which indicates a conjecture on the growth order. From our main result, two corollaries follow: one is the transcendency of meromorphic solutions, and the other is a lower estimate for the frequency of α-points. An essential part of our proof is estimation of certain sums concerning the poles of each meromorphic solution.
A BPE Model for the Burgers Equation
Authors: Ogawa Shigeyoshi , Kohatsu-Higa Arturo
Published: September 2006

We study the BPE (Brownian particle equation) model of the Burgers equation presented in the preceding article [6]. More precisely, we are interested in establishing the existence and uniqueness properties of solutions using probabilistic techniques.
An Inverse Problem for an Elliptic Equation
Authors: Dalmasso Robert
Published: September 2006

We consider the following overdetermined boundary value problem:

∆u = λu−µ

in

Ω

,

u = 0

on

∂Ω

and

\frac{∂u}{∂n} = ψ

on

∂Ω

, where

λ

and

µ

are real constants and

Ω

is a smooth bounded planar domain. A very interesting problem is to examine whether ∂_u_ one can identify the constants

λ

and

µ

from knowledge of the normal ﬂux

\frac{∂u}{∂n}

on

∂Ω

corresponding to some nontrivial solution. It is well known that if

Ω

is a disk then such identiﬁcation of

(λ, µ)

is completely impossible. Some partial results have already been obtained. The purpose of this paper is to extend and to improve these results. Moreover we also examine the interesting case where

ψ

is constant.
Existence of Solutions with Asymptotic Expansion of Linear Partial Differential Equations in the Complex Domain
Authors: Ōuchi Sunao
Published: September 2006

Consider the linear partial differential equation

P(z, ∂_z)u(z) = f(z)

in

ℂ^{d+1}

, where

f(z)

is not holomorphic on

K = \{z_0 = 0\}

, but it has an asymptotic expansion with respect to

z_0

as

z_0 → 0

in some sectorial region. We show under some conditions on

P(z, ∂_z)

that there exists a solution

u(z)

which has an asymptotic expansion of the same type as that of

f(z)

.
The Multiple Zeta Value Algebra and the Stable Derivation Algebra
Authors: Furusho Hidekazu
Published: September 2006

The MZV algebra is the graded algebra over

\mathbf Q

generated by all multiple zeta values. The stable derivation algebra is a graded Lie algebra version of the Grothendieck–Teichmüller group. We shall show that there is a canonical surjective

\mathbf Q

-linear map from the graded dual vector space of the stable derivation algebra over

\mathbf Q

to the new-zeta space, the quotient space of the sub-vector space of the MZV algebra whose grade is greater than 2 by the square of the maximal ideal. As a corollary, we get an upper-bound for the dimension of the graded piece of the MZV algebra at each weight in terms of the corresponding dimension of the graded piece of the stable derivation algebra. If some standard conjectures by Y. Ihara and P. Deligne concerning the structure of the stable derivation algebra hold, this will become a bound conjectured in Zagier’s talk at 1st European Congress of Mathematics. Via the stable derivation algebra, we can compare the new-zeta space with the l-adic Galois image Lie algebra which is associated with the Galois representation on the pro-
l
fundamental group of

\mathbf P\frac 1 {\mathbf Q} − \{0, 1, ∞\}

.
Spiral Traveling Wave Solutions of Nonlinear Diﬀusion Equations Related to a Model of Spiral Crystal Growth
Authors: Ogiwara Toshiko , Nakamura Ken-Ichi
Published: September 2006

This paper is concerned with nonlinear diﬀusion equations related to a model of the motion of screw dislocations on crystal surfaces. We prove the existence, uniqueness and asymptotic stability of a rotating and growing solution with a timeindependent proﬁle, which we call a spiral traveling wave solution.
A Remark on the Fast Gauss Transform
Authors: Kobayashi Kenta
Published: September 2006

We propose an improvement on the Fast Gauss Transform which was presented by Greengard and Sun [Documenta Mathematica, Extra volume ICM 1998, III, pp.575-584(1998)]. In their method, plane waves are used to approximate the Gauss kernel. Plane waves they used were generated by the Fourier integral and the trapezoidal rule. We propose diﬀerent plane waves, which enables us to calculate the Fast Gauss Transform more efficiently.
Bernstein Polynomials of a Smooth Function Restricted to an Isolated Hypersurface Singularity
Authors: Torrelli Tristan
Published: September 2006

Let

f, g

be two germs of holomorphic functions on

\mathbf C^n

such that

f

is smooth at the origin and

(f, g)

deﬁnes an analytic complete intersection

(Z, 0)

of codimension two. We study Bernstein polynomials of

f

associated with sections of the local cohomology module with support in

X = g^{−1}(0)

, and in particular some sections of its minimal extension. When

(X, 0)

and

(Z, 0)

have an isolated singularity, this may be reduced to the study of a minimal polynomial of an endomorphism on a ﬁnite dimensional vector space. As an application, we give an effective algorithm to compute those Bernstein polynomials when

f

is a coordinate and

g

is non-degenerate with respect to its Newton boundary.
A New Technique in Nonlinear Singularity Analysis
Authors: Gordoa Pilar R. , Joshi Nalini , Pickering Andrew
Published: September 2006

The test for singularity structure proposed by Ablowitz, Ramani and Segur (1980) has been widely used to obtain necessary conditions for non-linear ordinary diﬀerential equations (ODEs) to have the Painlevé property. In this paper, we proe vide an example of an ODE for which this standard test breaks down in a new and surprising way. We show how to overcome the problems presented by this equation by developing a new technique based on regular singular points of bilinear equations.
Conﬁguration Space Models for Spaces of Maps from a Riemann Surface to Complex Projective Space
Authors: Yamaguchi Kohhei
Published: September 2006

Let

\mathrm{Map}_d^∗(\mathrm M_g, ℂ\mathrm{P}^{n−1})

denote the space consisting of all basepoint preserving continuous maps of degree
d
from a compact Riemann surface

\mathrm M_g

of genus

g

into an

(n − 1)

-dimensional complex projective space

ℂ\mathrm{P}^{n−1}

. In this paper, we construct a ﬁnite dimensional conﬁguration space model

\mathrm{SP}_n^d(\mathrm M'_g)

for the inﬁnite dimensional space

\mathrm{Map}_d^∗(\mathrm M_g, ℂ\mathrm{P}^{n−1})

and show that the Atiyah–Jones type theorem (cf. [1], [12]) holds for this model.
Lie Subalgebras of Differential Operators on the Super Circle
Authors: Cheng Shun-Jen , Wang Weiqiang
Published: September 2006

We classify anti-involutions of Lie superalgebra

\widehat{\mathcal{SD}}

preserving the principal gradation, where

\widehat{\mathcal{SD}}

is the central extension of the Lie superalgebra of differential operators on the super circle

S^{1\mid 1}

. We clarify the relations between the corresponding subalgebras ﬁxed by these anti-involutions and subalgebras of

\widehat{gl}_{∞|∞}

of types
OSP
and
P
. We obtain a criterion for an irreducible highest weight module over these subalgebras to be quasiﬁnite and construct free ﬁeld realizations of a distinguished class of these modules. We further establish dualities between them and certain ﬁnite-dimensional classical Lie groups on Fock spaces.
Problème de Cauchy Analytique I
Authors: Hamada Yûsaku
Published: September 2006

In this article, we study singularities and analytic continuations of the solution of the Cauchy problem in the complex domain.
Carleman Inequalities for Parabolic Equations in Sobolev Spaces of Negative Order and Exact Controllability for Semilinear Parabolic Equations
Authors: Imanuvilov Oleg Yu. , Yamamoto Masahiro
Published: September 2006

We prove Carleman inequalities for a second order parabolic equation when the coeffcients are not bounded and norms of right hand sides are taken in the Sobolev space

L^2(0, T; W_2^{-ℓ}(Ω))

,

ℓ \in [0, 1]

. Our Carleman inequality yields the unique continuation for

L^2

-solutions. We further apply these inequalities to the global exact zero controllability of a semilinear parabolic equation whose semilinear term also contains derivatives of ﬁrst order of solutions and is of sub-linear growth at the inﬁnity.
Noncommutative Sobolev Spaces, $C^∞$ Algebras and Schwartz Distributions Associated with Semicircular Systems
Authors: Mizuo Masaru
Published: September 2006

When the

C^∗

-algebra and the

W^∗

-algebra generated by a semicircular system are viewed from the viewpoints of noncommutative topology and noncommutative probability theory, we may consider the

C^∗

-algebra as a certain kind of a “noncommutative cubic space” and the

W^∗

-algebra as a “noncommutative cubic measure space.” In this paper we introduce the Sobolev spaces

W_n^p

associated with the

W^∗

-algebra generated by a semicircular system, and the

C^∞

algebra

\mathcal S

is deﬁned as the projective limit of

W_n^p

. The Schwartz distribution space is then deﬁned as the dual space of

\mathcal S

and the Fourier representation theorem is obtained for Schwartz distributions. We furthermore discuss vector ﬁelds on the

C^∞

algebra

\mathcal S

. Appendix treats the

K

-theory of the noncommutative cubic space.
Backward Global Solutions Characterizing Annihilation Dynamics of Travelling Fronts
Authors: Yagisita Hiroki
Published: September 2006

We consider a reaction-diffusion equation

u_t = u_{xx} + f(u)

, where

f

has exactly three zeros

0

,

α

and

1

(0 < α < 1)

,

f_u(0) < 0

,

f_u(1) < 0

and

\int_0^1 f(u) du ≥ 0

. Then, the equation has a travelling wave solution

u(x, t) = \phi(x − ct)

with

\phi(−∞) = 0

and

\phi(+∞) = 1

. Known results suggest that for an initial state

u_0(x)

with

\underline{\lim}_{x→±∞} u_0(x) > α

having two interfaces at a large distance,

u(x, t)

approaches a pair of travelling wave solutions

\phi(x − p_1(t)) + \phi(−x + p_2(t))

for a long time, and then the travelling fronts eventually disappear by colliding with each other. While our results establish this process, they show that
there is a (backward) global solution

ψ(x, t)

and that
the annihilation process is approximated by a solution

ψ(x−x_0, t−t_0)

.
On Norm Attaining Polynomials
Authors: Aron Richard M. , García Domingo , Maestre Manuel
Published: September 2006

We show that for every Banach space

X

the set of 2-homogeneous continuous polynomials whose canonical extension to

X^{∗∗}

attain their norm is a dense subset of the space of all 2-homogeneous continuous polynomials

\mathcal P({}^2X)

.
Operators with Symbol Hierarchies and Iterated Asymptotics
Authors: Schulze B.-Wolfgang
Published: September 2006

Ellipticity of (pseudo-differential) operators on a manifold with geometric singularities gives rise to a hierarchy of symbols, associated with the system of lower-dimensional strata of the configuration. Classical examples are boundary value problems with interior and boundary symbols (the latter ones describe Shapiro–Lopatinskij ellipticity of boundary conditions), or operators on manifolds with conical singularities with interior and conormal symbols. Ellipticity on a manifold with smooth edges may be investigated by a suitable combination of ideas from boundary value problems and cone calculus. The present article studies another typical case, namely ellipticity on a manifold that has edges with conical singularities. Locally, we may talk about cones, where the base is a manifold with smooth edges. Parametrices and iterated asymptotics of solutions to elliptic equations are determined by a three-component symbolic hierarchy, with interior, edge and conormal symbols. We construct an operator algebra of 2 × 2-block matrices, where the upper left corners contain the interior operators, together with so-called Green and Mellin operators (caused by analogues of Green's function in boundary value problems as well as by asymptotic phenomena), while the other entries contain trace and potential conditions with respect to the edge and pseudo-differential operators on the edge itself that are of Fuchs type with respect to the conical points. The calculus is organized in an iterative way and can be viewed as a starting point for constructing similar operator algebras with asymptotics for higher polyhedral singularities.
Global Structure of an Elliptic Fibration
Authors: Nakayama Noboru
Published: September 2006

∂

-étale topology is introduced for analytic spaces with boundary as an analog of étale topology for schemes. A locally projective elliptic fibration is bimeromorphically considered as a torsor in the

∂

-étale topology of the associated basic elliptic fibration. The related

∂

-étale cohomology groups have much information on the structure of elliptic fibrations. In particular, an answer to Ueno's extension problem, a relation to Tate–Shafarevich groups and their finiteness properties, characterizations of projective and Kähler elliptic fibrations, and a generalization of logarithmic transformation to arbitrary dimension are obtained. This article is a revised version of [N5].
Contractions of Angles in Symmetric Cones
Authors: Koufany Khalid
Published: September 2006

For a symmetric cone

Ω

, we compute its Riemannian distance in terms of the singular values of a generalized cross-ratio and prove that the semigroup of the compressions of

Ω

decreases the compounds distance.
Crystal Bases, Path Models, and a Twining Character Formula for Demazure Modules
Authors: Sagaki Daisuke
Published: September 2006

We give a combinatorial proof of a twining character formula for Demazure modules, by combining the isomorphism theorem between path models and crystal bases with our previous result about Lakshmibai-Seshadri paths ﬁxed by a diagram automorphism.
Non-isotropic Gevrey Hypoellipticity for Grushin Operators
Authors: Hashimoto Yoshiaki , Hoshino Takaaki , Matsuzawa Tadato
Published: September 2006

We shall determine non-isotropic Gevrey exponents for general Grushin operators based on the results given in the paper [26], where a method to determine isotropic (worst) Gevrey exponents was given. The ideas of the bracket calculus given in the paper [2] and FBI-transformation given in the paper [5] are also useful.
Asymptotic Distribution of Negative Eigenvalues for Three Dimensional Pauli Operators with Nonconstant Magnetic Fields
Authors: Shimomura Akihiro
Published: September 2006

We study the asymptotic distribution of negative eigenvalues of three dimensional Pauli operators with a two dimensional magnetic ﬁeld and a three dimensional potential which decay to zero at inﬁnity. For

λ > 0

suffciently small, we estimate the number of eigenvalues less than

-λ

of such Pauli operators.
The Second Bounded Cohomology of 3-manifolds
Authors: Fujiwara Koji , Ohshika Ken’ichi
Published: September 2006

Let

G

be the fundamental group of a compact, orientable 3-manifold

M

. We show that if each piece of the canonical decomposition of

M

has a geometric structure (e.g. when

G

contains

ℤ^2

), then either

G

has inﬁnite dimensional second bounded cohomology or

G

is virtually solvable.
Inverse Problem for Interior Spectral Data of the Dirac Operator on a Finite Interval
Authors: Mochizuki Kiyoshi , Trooshin Igor
Published: September 2006

In this paper the inverse problems for the Dirac operator on a ﬁnite interval are studied. A set of values of eigenfunctions in some internal point and spectrum are taken as a data. Uniqueness theorems are obtained. The approach that was used in the investigation of inverse problems for interior spectral data of the Sturm-Liouville operator is employed.
Couplings to Classical and Non-Classical Squeezed White Noise as Stationary Markov Processes
Authors: Hellmich Jürgen , Honegger Reinhard , Köstler Claus , Kümmerer Burkhard , Rieckers Alfred
Published: September 2006

The squeezed white noise states of the quantum optics literature are identiﬁed with speciﬁc quasifree states on the bosonic
C
*-Weyl (resp. CCR) algebra, which are not gauge invariant. Their properties are discussed, and concrete realizations of their GNS-representations are given. The squeezed white noise states are obtained from the chaotic temperature (or white noise states) by the application of squeezing Bogoliubov transformations, which may lead to a noise reduction in selected modes. A squeezing strength is determined, below which the squeezed white noise states remain classical and above which they are rendered non-classical. We further couple additional systems to the squeezed white noise, the quantum character of which are leading to a large class of stationary quantum Markov processes with related quantum stochastic calculus. Their interactions are described in terms of unitary cocycles, which arise from adapted additive cocycles by means of solutions of stochastic differential equations resp. by stochastic Itô integrals. The restriction of the Markovian dynamics to the sub-system leads to a quantum semi-group, for which the Lindblad generator is of detailed balance type. Finally the stochastic Itô table for squeezed white noise is derived. From the latter non-classicality of the squeezed white noise process can now be checked by inspection.
Endomorphisms of Smooth Projective 3-Folds with Non-Negative Kodaira Dimension
Authors: Fujimoto Yoshio
Published: September 2006

Let

X

be a nonsingular projective 3-fold with non-negative Kodaira dimension

κ(X) ≥ 0

which admits a nonisomorphic surjective morphism

f : X → X

onto itself. If

κ(X) = 0

or

2

, a suitable ﬁnite étale covering

\tilde X

of

X

is isomorphic to an abelian 3-fold or the direct product

E × S

of an elliptic curve

E

and a nonsingular algebraic surface

S

with

κ(S) = κ(X)

.
On a Discrete Analogue of the Two-Dimensional Toda Lattice Hierarchy
Authors: Tsujimoto Satoshi
Published: September 2006

A discrete analogue of the two-dimensional Toda lattice hierarchy, which includes the discrete analogue of the two-dimensional Toda lattice equation, is obtained by extending the theory of the Toda lattice hierarchy. Special solutions and bilinear equations for the discrete analogue of the two-dimensional Toda lattice hierarchy are presented. It is shown that the subjects originated from the Sato theory are useful for the discrete-time integrable systems.
Cuntz–Krieger–Pimsner Algebras Associated with Amalgamated Free Product Groups
Authors: Okayasu Rui
Published: September 2006

We give a construction of a nuclear

C^∗

-algebra associated with an amalgamated free product of groups, generalizing Spielberg’s construction of a certain Cuntz–Krieger algebra associated with a ﬁnitely generated free product of cyclic groups. Our nuclear

C^∗

-algebras can be identiﬁed with certain Cuntz–Krieger–Pimsner algebras. We will also show that our algebras can be obtained by the crossed product construction of the canonical actions on the hyperbolic boundaries, which proves a special case of Adams’ result about amenability of the boundary action for hyperbolic groups. We will also give an explicit formula of the

K

-groups of our algebras. Finally we will investigate a relationship between the KMS states of the generalized gauge actions on our

C^∗

-algebras and random walks on the groups.
The Borel Sum of Divergent Barnes Hypergeometric Series and its Application to a Partial Differential Equation
Authors: Ichinobe Kunio
Published: September 2006

An explicit form and its analytic continuation around the origin of the Borel sum of the Barnes generalized hypergeometric series

{}_qF_{p-1}

of divergent type (

q> p

) is obtained. As an application we give an integral representation of the Borel sum of the formal solution to the Cauchy problem of a certain partial differential equation of non-Kowalevski type.
$G$-surgery on 3-dimensional Manifolds for Homology Equivalences
Authors: Morimoto Masaharu
Published: September 2006

For a finite group

G

and a

G

-map

f :X → Y

of degree one, where

X

and

Y

are compact, connected, oriented, 3-dimensional, smooth

G

-manifolds, we give an obstruction element

σ(f)

in a

K

-theoretic group called the Bak group, with the property:

σ(f) = 0

guarantees that one can perform

G

-surgery on

X

so as to convert

f

to a homology equivalence

f': X' → Y

. Using this obstruction theory, we determine the

G

-homeomorphism type of the singular set of a smooth action of

A_5

on a 3-dimensional homology sphere having exactly one fixed point, where

A_5

is the alternating group on five letters.
Some Absolute Continuity Relationships for Certain Anticipative Transformations of Geometric Brownian Motions
Authors: Donati-Martin Catherine , Matsumoto Hiroyuki , Yor Marc
Published: September 2006

We present some absolute continuity relationships between the probability laws of a geometric Brownian motion

e^{(μ)} = \{e_t^{(μ)}, t ≧ 0\}

and its images by certain transforms

T_α

involving

e^{(μ)}

and its quadratic variation

\{\langle e^{(μ)}\rangle_t, t ≧ 0\}

. These results are derived from, and shown to be closely related to, our previous results about the generalized Dufresne’s identity and the exponential type extensions of Pitman’s

2M−X

theorem for

X

, a Brownian motion with constant drift

μ

, and its one-sided supremum

M

. These absolute continuity results are then shown to be particular cases of those by Ramer–Kusuoka for non-linear transformations of the Wiener space and by Buckdahn–Föllmer for solutions of certain stochastic differential equations with anticipative drifts.
Theta Constants Associated with the Cyclic Triple Coverings of the Complex Projective Line Branching at Six Points
Authors: Matsumoto Keiji
Published: September 2006

Let

ψ

be the period map for a family of the cyclic triple coverings of the complex projective line branching at six points. The symmetric group

S_6

acts on this family and on its image under

ψ

. In this paper, we give an

S_6

-equivariant expression of

ψ^{−1}

in terms of fifteen theta constants.
The Asymptotic Behavior of Eisenstein Series and a Comparison of the Weil–Petersson and the Zograf–Takhtajan Metrics
Klein-Gordon equations is studied in the Sobolev space Hs = Hs(
Authors: Obitsu Kunio
Published: September 2006

The asymptotic behavior of Eisenstein series for degenerating hyperbolic surfaces with cusps is of interest to us. In order to investigate it we use integral representations of eigenfunctions for the Laplacian, the collar lemma, the interior Schauder estimates, the maximum principles for subharmonic functions and the Harnack Inequalities. As an application, we will compare the Weil–Petersson and the Zograf–Takhtajan metrics near the boundary of moduli spaces.
Geometric Bäcklund–Darboux Transformations for the KP Hierarchy
Klein-Gordon equations is studied in the Sobolev space Hs = Hs(
Authors: Helminck Gerard F. , van de Leur Johan W.
Published: September 2006

In this paper it is shown that, if you have two planes in the Sato Grassmannian that have an intersection of finite codimension, then the corresponding solutions of the KP hierarchy are linked by Bäcklund–Darboux (shortly BD-)transformations. The pseudodifferential operator that performs this transformation is shown to be built up in a geometric way from so-called elementary BD-transformations and is given here in a closed form. The corresponding action on the tau-function, associated to a plane in the Grassmannian, is also determined.
The tide is turning on decriminalization: Saved from the brink of drowning?
Authors: Knopf Alison
Published: March 2024

Recent news from Oregon and California indicate that decriminalization has failed and encouraging public drug use isn't actually a success either. Measure 110, passed in Oregon three years ago, decriminalized possession of small amounts of all illegal drugs. Overdose rates went up, as more drug users were attracted to the state. The streets of San Francisco and Oakland, California, just for example, have been populated by out‐of‐state drug users looking for cheap fentanyl, government hand‐outs, and most recently, free housing.
Enzyme‐Immobilized Surface‐Catalyzed Cross‐Linking: Creating Multifunctional Double Network Hydrogel Coatings on Diverse Substrates
Authors: Ren Xingrong , Zhang Jiayi , Yang Fan , Xu Hong , Guo Gaoyang , Wang Yunbing
Published: March 2024

Hydrogel coatings, with natural tissue‐like mechanical and biological compatibility, demonstrate promise for bulk material applications. However, existing coating methods lack efficiency and control, especially when dealing with complex geometries, diverse substrate materials, and varying sizes. In this study, an enzyme‐immobilized surface‐catalyzed cross‐link approach is proposed for the growth of hydrogel coatings on multiple substrates, accommodating various materials and shapes. The hydrogel coating is formed through the catalytic action of interface‐immobilized enzymes, which induce the crosslinking of hyaluronic acid, and its mechanical properties are further enhanced by introducing a secondary polyacrylamide network. This approach enables the controlled growth of conformal double network hydrogel coatings with a desired thickness on a wide range of substrate surfaces and devices. Notably, the hydrogel coating exhibits remarkable lubricity and anti‐thrombotic properties, especially desire for medical intervention devices. This advancement offers a universal route to impart biocompatible soft interfaces to bulk materials or devices.
Single‐Layer Carbon Nitride as an Efficient Metal‐Free Organic Electron‐Transport Material with a Tunable Work Function
Authors: Saboor Abdus , Stroyuk Oleksandr , Raievska Oleksandra , Liu Chao , Hauch Jens , Brabec Christoph J.
Published: March 2024

Single‐layer carbon nitride (SLCN) is introduced as a metal‐free organic electron transport material (ETL) for organic solar cells, delivering a performance comparable to that of the benchmark nanocrystalline ZnO. SLCN is produced in the form of stable aqueous inks and can serve as an efficient electron transport layer for three different types of active layers, showing high stability to photodegradation. A lower conductivity of SLCN films as compared to ZnO is counter‐balanced by their higher transparency and lower light scattering losses. The SLCN ETL provides a unique opportunity to tune the work function from ca. −4.1 to −4.6 eV by varying the annealing temperature due to partial thermal oxidation of the SLCN film. The PL band position follows the oxidation‐induced changes of the work function allowing PL properties of SLCN to be used to predict the PV efficiency. The 2D structure of SLCN coupled with unique structural and compositional variability, and tunability of the work function show a high promise for emerging organic PV devices.
Multiscale Interfacial Regulation of Zn‐V2O5 Pouch Cell via Ultrathin Molecular‐Engineered Separator
Authors: Xue Rongrong , Wang Zhiqiao , Yao Ning , Liu Yuyao , Wang Helin , Zhang Min , Shao Ahu , Tang Xiaoyu , Liu Jiacheng , Tang Jiawen , Wang Zhaohui , Ma Yue
Published: March 2024

Rechargeable aqueous zinc batteries (RAZBs) suffer from the structural degradation of the layered oxide cathode, parasitic side reaction on the Zn foil as well as often‐overlooked self‐discharge phenomenon at the elevated temperatures. Herein, this study presents a thin‐layer (9 µm) molecular‐engineered separator strategy to achieve the concurrent shelf life, cycling endurance, as well as the practical energy density for the RAZBs prototype. On the face‐to‐cathode side, the biphthalic anhydride is anchored onto the polyethylene separator substrate (PE) via a robotic arm‐controlled spray‐coating method, inhibiting the spontaneous vanadium dissolution and shuttle at both the dynamic cycling or static high‐temperature storage; meanwhile the 3,3′‐diamino‐4,4′‐dihydroxydiphenyl sulfone molecular tailoring on the face‐to‐anode side provides ion‐sieving capability to repel detrimental SO42−, yet guiding uniform Zn2+ influx and preferential deposits accumulation along the (002) crystallographic orientation even at the extreme deposition scenario (20 mA cm−2, 20 mAh cm−2). Upon the layer‐stacked assembly of the V2O5 cathode (2.0 mAh cm−2), molecular‐engineered separator as well as the Zn foil (20 µm), the 0.78 Ah pouch‐format prototype exhibits the superior volumetric/gravimetric energy densities of 133.3 Wh L−1/71.4 Wh kg−1 and extreme power output (444.3 W L−1/238.0 W kg−1).
Synergistic Entropy Engineering with Vacancies: Unraveling the Cocktail Effect for Extraordinary Thermoelectric Performance in SnTe‐Based Materials
Authors: Xia Junchao , Yang Jianmin , Wang Yan , Jia Baohai , Li Shangyang , Sun Kaitong , Zhao Qian , Mao Dasha , Li Hai‐Feng , He Jiaqing
Published: March 2024

The pursuit of high‐power factor and low lattice thermal conductivity simultaneously in thermoelectric research is longstanding. Herein, great success has been achieved in SnTe‐based materials by employing a proposed strategy of entropy engineering involving vacancies, thus leveraging the promising cocktail effect. Significant band convergence and flatness effects have given rise to exceptionally high density of state carrier effective mass and Seebeck coefficients. These effects have also led to the theoretical optimal carrier concentration closely aligning with the actual carrier concentration. Furthermore, the entropy engineering involving vacancies has induced pronounced lattice disorder and a wealth of nanostructures, facilitating multi‐scale phonon scattering. Consequently, impressive thermoelectric performance is realized in AgSb3Pb2Ge2Sn6Te15: room‐temperature ZT of ≈0.4, peak ZT of ≈1.3 at 623 K, and average ZT of ≈1.0 (300–773 K). A thermoelectric module, comprising this p‐type material and the homemade n‐type PbTe, is assembled, demonstrating a competitive conversion efficiency of 9.3% at a temperature difference of 478 K. This work not only provides valuable insights into the modulation of electron/phonon transports but also establishes an effective paradigm of entropy engineering involving vacancies.
Afterglow of Dual‐Confined Carbon Dots Ranging from Blue to Near‐Infrared
Authors: Sun Wenxuan , Zhang Yongqiang , Yin Guangchao , Lu Siyu
Published: March 2024

Comprehensive research into afterglow emission in the near‐infrared (NIR) region of carbon dots (CDs) is currently lacking. In this study, highly efficient multicolor CDs are synthesized with fluorescence from blue to NIR using Rhodamine 6G. Boron oxide (B2O3) is employed as a matrix for encapsulating and confining the CDs, inhibiting triplet exciton quenching. Furthermore, structural rigidity is enhanced due to the formation of carbon‐boron (C─B) covalent bonds between CDs and B2O3, achieving tunable afterglow emission ranging from 463 to 722 nm with lifetimes up to 801 ms. The green–yellow afterglow composite exhibits an impressive quantum yield up to 37.67% while demonstrating thermally activated delayed fluorescence (TADF). Thus, this composite is coated onto a blue alternating‐current light‐emitting diode (BAC‐LED) to fabricate a white AC‐LED, which is successfully prepared with Commission Internationale de L'Eclairage (CIE) at coordinates of (0.32, 0.34), accompanied by the color rendering index (CRI) reaching 81.1. The bright afterglow compensates for zero‐point flickering in the BAC‐LED, resulting in stable and gentle emission. The potential applications of these luminescent materials in optoelectronic devices are undoubtedly widened by this remarkable advancement.
Phospholipid Membranes as Chemically and Functionally Tunable Materials
Authors: Huster Daniel , Maiti Sudipta , Herrmann Andreas
Published: March 2024

The sheet‐like lipid bilayer is the fundamental structural component of all cell membranes. Its building blocks are phospholipids and cholesterol. Their amphiphilic structure spontaneously leads to the formation of a bilayer in aqueous environment. Lipids are not just structural elements. Individual lipid species, the lipid membrane structure, and lipid dynamics influence and regulate membrane protein function. An exciting field is emerging where the membrane‐associated material properties of different bilayer systems are used in designing innovative solutions for widespread applications across various fields, such as the food industry, cosmetics, nano‐ and biomedicine, drug storage and delivery, biotechnology, nano‐ and biosensors, and computing. Here, the authors summarize what is known about how lipids determine the properties and functions of biological membranes and how this has been or can be translated into innovative applications. Based on recent progress in the understanding of membrane structure, dynamics, and physical properties, a perspective is provided on how membrane‐controlled regulation of protein functions can extend current applications and even offer new applications.
Long‐Range Atomic Order on Double‐Stepped Al2O3(0001) Surfaces
Authors: Smink Sander , Majer Lena N. , Boschker Hans , Mannhart Jochen , Braun Wolfgang
Published: March 2024

The deterministic preparation of highly ordered single‐crystalline surfaces is a key step for studying and utilizing the physical properties of various advanced materials. This paper presents the fast and straightforward preparation of vicinal Al2O3(0001) surfaces with micrometer‐scale atomic order. Crisp electron‐diffraction spots up to at least 20th order evidence atomic coherence on terraces with widths exceeding 1 μm. The unique combination of three properties of Al2O3(0001) underlie this remarkable coherence: its high‐temperature stability; the differences in the ionic bonding systems of the surface as compared to the bulk; and the fact that the terraces are non‐polar whereas the step edges have a polar character. The step edges are furthermore found to have alternating configurations, which drive a step‐doubling transition. On double‐stepped surfaces, the Al‐rich ° surface reconstruction attains a singular in‐plane orientation. These results set a benchmark for high‐quality surface preparation and thus expand the scope for both fundamental studies on and the technological utilization of exciting material systems.
Understanding Advanced Transition Metal‐Based Two Electron Oxygen Reduction Electrocatalysts from the Perspective of Phase Engineering
Authors: Yang Hongyuan , An Na , Kang Zhenhui , Menezes Prashanth W. , Chen Ziliang
Published: March 2024

Non‐noble transition metal (TM)‐based compounds have recently become a focal point of extensive research interest as electrocatalysts for the two electron oxygen reduction (2e− ORR) process. To efficiently drive this reaction, these TM‐based electrocatalysts must bear unique physiochemical properties, which are strongly dependent on their phase structures. Consequently, adopting engineering strategies toward the phase structure has emerged as a cutting‐edge scientific pursuit, crucial for achieving high activity, selectivity, and stability in the electrocatalytic process. This comprehensive review addresses the intricate field of phase engineering applied to non‐noble TM‐based compounds for 2e− ORR. First, the connotation of phase engineering and fundamental concepts related to oxygen reduction kinetics and thermodynamics are succinctly elucidated. Subsequently, the focus shifts to a detailed discussion of various phase engineering approaches, including elemental doping, defect creation, heterostructure construction, coordination tuning, crystalline design, and polymorphic transformation to boost or revive the 2e− ORR performance (selectivity, activity, and stability) of TM‐based catalysts, accompanied by an insightful exploration of the phase‐performance correlation. Finally, the review proposes fresh perspectives on the current challenges and opportunities in this burgeoning field, together with several critical research directions for the future development of non‐noble TM‐based electrocatalysts.
The Energy Level Alignment at the Buffer/Cu(In,Ga)Se2 Thin‐Film Solar Cell Interface for CdS and GaOx
Authors: Valenta Donald , Yetkin Hasan Arif , Kodalle Tim , Bombsch Jakob , Garcia‐Diez Raul , Hartmann Claudia , Ueda Shigenori , Félix Roberto , Frisch Johannes , Bodenstein‐Dresler Lucas , Wilks Regan G. , Kaufmann Christian A. , Bär Marcus
Published: March 2024

Sputter‐deposited GaOx (i.e., oxygen‐deficient gallium oxide) films are evaluated as a potential replacement for the standard CdS buffer layers in Cu(In,Ga)Se2 (CIGSe) based thin‐film photovoltaics. The energy level alignment at the GaOx/CIGSe and CdS/CIGSe interfaces are compared by means of direct and inverse photoemission. For the GaOx/CIGSe a (0.04 ± 0.07) eV (i.e., a small spike‐like) conduction band offset (CBO) and a (−3.21 ± 0.19) eV (i.e., a large cliff‐like) valence band offset (VBO) are found, which suggests a nearly ideal charge‐selective contact. The derived GaOx band gap of (4.80 ± 0.25) eV confirms its utility as a highly transparent buffer layer. However, the GaOx (with x derived to be 1.1 ± 0.1) exhibits considerable (presumably) defect‐related occupied states above the valence band maximum. It is proposed that these states may increase charge carrier recombination and decrease open circuit voltage in respective devices; also explaining why solar cells with standard CdS buffer outperform devices with GaOx buffer, despite less ideal electronic interface properties (CBO: (−0.18 ± 0.07) eV, VBO: (−0.98 ± 0.15) eV) and the smaller CdS band gap of (2.35 ± 0.22) eV.
Mechatronic Spatial Atomic Layer Deposition for Closed‐Loop and Customizable Process Control
Authors: Penley Daniel , Cho Tae H. , Brooks Andre J. , Ransohoff Lauren , Park Hyunwoo , Herman Ellis , Zhao Enpei , Trejo Orlando , Barton Kira , Dasgupta Neil P.
Published: March 2024

A customized atmospheric‐pressure spatial atomic layer deposition (AP‐SALD) system is designed and implemented, which enables mechatronic control of key process parameters, including gap size and parallel alignment. A showerhead depositor delivers precursors to the substrate while linear actuators and capacitance probe sensors actively maintain gap size and parallel alignment through multiple‐axis tilt and closed‐loop feedback control. Digital control of geometric process variables with active monitoring is facilitated with a custom software control package and user interface. AP‐SALD of TiO2 is performed to validate self‐limiting deposition with the system. A novel multi‐axis printing methodology is introduced using x‐y position control to define a customized motion path, which enables an improvement in the thickness uniformity by reducing variations from 8% to 2%. In the future, this mechatronic system will enable experimental tuning of parameters that can inform multi‐physics modeling to gain a deeper understanding of AP‐SALD process tolerances, enabling new pathways for non‐traditional SALD processing that can push the technology towards large‐scale manufacturing.
Regio‐ and Enantioselective Synthesis of Succinimides Bearing All‐Carbon Quaternary Centers Using a Chiral Phenanthroline‐Palladium Catalyst
Authors: Kuroiwa Yudai , Tamura Masafumi
Published: March 2024

The synthesis of chiral succinimides bearing all‐carbon quaternary stereocenters at the C3 position is important, but remains challenging. The present work demonstrates conjugate additions with catalysis by a chiral 1,10‐phenanthroline‐Pd complex (L1‐PdCl2) that exhibit complete regioselectivity with a high degree of enantioselectivity. These reactions afford chiral 3,3‐disubstituted succinimides having all‐carbon quaternary stereocenters with 40–99% ee. Importantly, chiral 3,3‐diaryl succinimides could also be obtained in 35–98% yields and 40–99% ee. Moreover, the present L1‐PdCl2‐catalyzed asymmetric conjugate addition could be performed on the gram scale and was also used to introduce such stereocenters into bioactive molecules.
Formal Insertion of a Metal Carbene Complex into a σ‐Carbon‐Carbon Bond. Gold‐Catalyzed Synthesis of 3H‐Indoles
Authors: Allegue Darío , Sampedro Diego , Ballesteros Alfredo , Santamaría Javier
Published: March 2024

We report here a formal insertion of a metal carbene complex in a single carbon‐carbon bond. This behavior occurs with the participation of an α‐imino gold carbene complex, generated from benzofused triazapentalenes or, in a one‐pot procedure, from their 1‐propargyl‐1H‐benzotriazole precursors, and gold‐catalytically activated ynamides. As the result, 3H‐indole derivatives were obtained, with formation of a quaternary center. A computational analysis carried out on the reaction mechanism indicates that the bulkiness of the gold ligand plays a key role forcing a conformation, which includes aromatic interactions, that favors the approximation of the carbenic carbon to the reactive site. In addition, a negative crossover experiment rules out a cationic arene migration pathway.
Stable Cycling of Mg Metal Anodes by Regulating the Reactivity of Mg2+ Solvation Species
Authors: Li Zheng , Nguyen Dan‐Thien , Bazak J. David , Han Kee Sung , Chen Ying , Prabhakaran Venkateshkumar , Le Thuy Thanh , Cheng Zezhen , Song Minyung , Pol Vilas G. , Mueller Karl T. , Murugesan Vijayakumar
Published: March 2024

Rationally designing stable nonaqueous electrolytes for Mg metal anodes demands a thorough understanding of their interfacial behaviors. Here, the critical role of cation–anion pairing in improving the cathodic stabilities of amine‐based electrolytes against solvent reduction and H2 evolution is identified. It is demonstrated that strong coordination between solvating amine groups and the Mg2+ cation facilitates the dehydrogenation of the ─NH2 group, which is mainly responsible for low reversibility during Mg metal plating and stripping. Introducing ion‐pairing into the primary solvation shell can effectively weaken the amine coordination such that its reduction is suppressed. A novel interfacial behavior regarding parasitic reaction product dissolution is also identified, which is responsible for the failure of interfacial passivation. An ion‐pairing electrolyte is developed based on a weakly‐solvated amine molecule and strongly coordinating Mg2+ salt. This electrolyte composition delivers long‐term Mg metal anode cycling with 99.6% Coulombic efficiency for 800 cycles.