bluuebunny/crossref_metadata_2025 huggingface dataset:
Blocking Soluble Tumor Necrosis Factor Signaling with Dominant-Negative Tumor Necrosis Factor Inhibitor Attenuates Loss of Dopaminergic Neurons in Models of Parkinson's Disease
Authors: McCoy Melissa K. , Martinez Terina N. , Ruhn Kelly A. , Szymkowski David E. , Smith Christine G. , Botterman Barry R. , Tansey Keith E. , Tansey Malú G.
Published: September 2006

The mechanisms that trigger or contribute to loss of dopaminergic (DA) neurons in Parkinson's disease (PD) remain unclear and controversial. Elevated levels of tumor necrosis factor (TNF) in CSF and postmortem brains of PD patients and animal models of PD implicate this proinflammatory cytokine in the pathophysiology of the disease; but a role for TNF in mediating loss of DA neurons in PD has not been clearly demonstrated. Here, we report that neutralization of soluble TNF (solTNF)in vivowith the engineered dominant-negative TNF compound XENP345 (a PEGylated version of the TNF variant A145R/I97T) reduced by 50% the retrograde nigral degeneration induced by a striatal injection of the oxidative neurotoxin 6-hydroxydopamine (6-OHDA). XENP345 was neuroprotective only when infused into the nigra, not the striatum. XENP345/6-OHDA rats displayed attenuated amphetamine-induced rotational behavior, indicating preservation of striatal dopamine levels. Similar protective effects were observed with chronicin vivocoinfusion of XENP345 with bacterial lipopolysaccharide (LPS) into the substantia nigra, confirming a role for solTNF-dependent neuroinflammation in nigral degeneration. In embryonic rat midbrain neuron/glia cell cultures exposed to LPS, even delayed administration of XENP345 prevented selective degeneration of DA neurons despite sustained microglia activation and secretion of solTNF. XENP345 also attenuated 6-OHDA-induced DA neuron toxicityin vitro. Collectively, our data demonstrate a role for TNFin vitroandin vivoin two models of PD, and raise the possibility that delaying the progressive degeneration of the nigrostriatal pathway in humans is therapeutically feasible with agents capable of blocking solTNF in early stages of PD.
Homeostatic Regulation of Sleep: A Role for Preoptic Area Neurons
Authors: Gvilia Irma , Xu Feng , McGinty Dennis , Szymusiak Ronald
Published: September 2006

The median preoptic nucleus (MnPN) and the ventrolateral preoptic area (vlPOA) contain putative sleep-regulatory neurons that exhibit elevated discharge rates during sleep compared with waking. Expression of c-Fos protein immunoreactivity (IR) in GABAergic neurons in the MnPN and the vlPOA is high in spontaneously sleeping rats and in rats undergoing recovery sleep after sleep deprivation. However, it is unclear whether c-Fos-IR in these neurons is evoked by increases in sleep pressure or by increases in sleep amount. We examined c-Fos-IR in MnPN and vlPOA neurons under experimental conditions that dissociated homeostatic sleep pressure, sleep amount, and time of day. Groups of rats with strong diurnal rhythms in sleep-wake organization were killed after (1) spontaneous sleep in the light, (2) spontaneous sleep in the dark, (3) sleep deprivation (SLD) in the light and (4) recovery sleep after SLD in the light. Numbers of GABAergic neurons expressing c-Fos-IR in the MnPN were significantly higher after SLD in the light compared with spontaneous sleep and recovery sleep in the light. In contrast, Fos-IR in vlPOA GABAergic neurons was most prevalent after spontaneous sleep and recovery sleep in the light. No light–dark differences in Fos-IR were observed in the MnPN after SLD in groups of rats with weak or absent diurnal sleep-waking rhythms. Our findings define potential roles for MnPN and vlPOA GABAergic neurons in homeostatic aspects of sleep regulation.
Suppressor of Cytokine Signaling-3 Suppresses the Ability of Activated Signal Transducer and Activator of Transcription-3 to Stimulate Neurite Growth in Rat Primary Sensory Neurons
Authors: Miao Tizong , Wu Dongsheng , Zhang Yi , Bo Xuenong , Subang Maria Cristina , Wang Ping , Richardson Peter M.
Published: September 2006

The actions of the neuropoietic cytokines are mediated by the gp130 receptor, which activates several signaling molecules including the transcription factor STAT3 (signal transducer and activator of transcription), which, in turn, is subject to feedback inhibition by SOCS3 (suppressor of cytokine signaling). Activation of the gp130 receptor has been implicated in axonal growth particularly during regeneration, but the specific contribution of STAT3 is the subject of conflicting reports. Measurements of SOCS3 mRNA in rat dorsal root ganglia showed a significant induction in this inhibitory molecule after peripheral nerve injury. The functions of STAT3 and SOCS3 in adult rat primary sensory neurons were investigatedin vitrothrough transduction of lentiviruses yielding a conditionally activated STAT3, native SOCS3, or a mutant SOCS3 with dominant-negative actions. The SOCS3 construct was effective in inhibiting tyrosine phosphorylation of STAT3 in a neuroblastoma cell line and in blocking nuclear accumulation of endogenous STAT3 or of the conditionally activated STAT3 chimera in primary sensory neurons. In such neurons, transduction and activation of STAT3 enhanced neurite growth, transduction with SOCS3 reduced neurite outgrowth, and transduction with mutant SOCS3 enhanced neurite growth, at least under basal conditions. In conclusion, STAT3 signaling is beneficial to axonal growth through activating transcription of unidentified genes, and SOCS3 is detrimental to axonal growth through inhibition of STAT3 and/or other transcription factors.
Regulation of Store-Operated Calcium Entry by Calcium-Independent Phospholipase A2in Rat Cerebellar Astrocytes
Authors: Singaravelu Karthika , Lohr Christian , Deitmer Joachim W.
Published: September 2006

We have studied store-operated Ca2+entry (SOCE) in Bergmann glia and granule cell layer astrocytes in acute brain slices of the rat cerebellum, using the Ca2+-sensitive fluorescent dye Fluo-4 and confocal laser scanning microscopy. Astrocytes were identified by their morphology, location, and their Ca2+response in K+-free solution. Depletion of Ca2+stores by cyclopiazonic acid (CPA) (20 μm) induced SOCE in both types of astrocyte. A similar Ca2+influx was elicited by the calmodulin antagonist calmidazolium (CMZ) (1 μm). The SOCE channel blocker 2-aminoethoxy-diphenylborate (2-APB) (100 μm) and the Ca2+release-activated channel blocker 3,5-bistrifluoromethyl pyrazole derivative (BTP2) (20 μm) suppressed the CPA- and the CMZ-induced Ca2+influx. Pretreatment of acute slices with the specific Ca2+-independent phospholipase A2(iPLA2) inhibitor bromoenol lactone (BEL) (25 μm) blocked the CPA- and the CMZ-induced Ca2+influx. The lysophospholipid products of iPLA2, lysophosphatidylcholine (250 nm) and lysophosphatidylinositol (250 nm), but not lysophosphatidic acid (250 nm), induced a BTP2- and 2-APB-sensitive, but BEL-insensitive, Ca2+influx. CPA or CMZ enhanced the BEL-sensitive enzymatic activity of iPLA2in cerebellar astrocyte culture. Inhibition of iPLA2expression by specific antisense oligodeoxynucleotide of iPLA2reduced the SOCE and the Ca2+store refilling in cultured astrocytes. Spontaneous Ca2+oscillations in astrocytesin situwere reduced after inhibiting SOCE channels or iPLA2activity. The results suggest that the depletion of Ca2+stores activates iPLA2to open Ca2+channels in the plasma membrane by the formation of lysophospholipids in astrocytes, presumably to refill the stores and allow normal Ca2+signaling.
Activated c-Jun N-Terminal Kinase Is Required for Axon Formation
Authors: Oliva Anthony A. , Atkins Coleen M. , Copenagle Lily , Banker Gary A.
Published: September 2006

A critical transition in neuron development is formation of the axon, which establishes the polarized structure of the neuron that underlies its entire input and output capabilities. The morphological events that occur during axonogenesis have long been known, yet the molecular determinants underlying axonogenesis remain poorly understood. We demonstrate here that axonogenesis requires activated c-Jun N-terminal kinase (JNK). JNK is expressed throughout the neuron, but its phosphorylated, activated form is highly enriched in the axon. In young axons, activated JNK forms a proximodistal gradient of increasing intensity, beginning at about the point where the axon exceeds the lengths of the other neurites (minor processes). Treatment with SP600125, a specific inhibitor of JNK, reversibly inhibits axonogenesis but does not prevent the formation of minor processes or their differentiation into dendrites (based on their immunostaining with marker proteins). Expression of a dominant-negative construct against JNK similarly prevents axonogenesis. Investigation of JNK targets revealed that activating transcription factor-2 is phosphorylated under normal conditions in neurons, and its phosphorylation is significantly attenuated after JNK inhibition. These results demonstrate that activated JNK is required for axonogenesis but not formation of minor processes or development of dendrites.
Dissociable Systems for Gain- and Loss-Related Value Predictions and Errors of Prediction in the Human Brain
Authors: Yacubian Juliana , Gläscher Jan , Schroeder Katrin , Sommer Tobias , Braus Dieter F. , Büchel Christian
Published: September 2006

Midbrain dopaminergic neurons projecting to the ventral striatum code for reward magnitude and probability during reward anticipation and then indicate the difference between actual and predicted outcome. It has been questioned whether such a common system for the prediction and evaluation of reward exists in humans. Using functional magnetic resonance imaging and a guessing task in two large cohorts, we are able to confirm ventral striatal responses coding both reward probability and magnitude during anticipation, permitting the local computation of expected value (EV). However, the ventral striatum only represented the gain-related part of EV (EV+). At reward delivery, the same area shows a reward probability and magnitude-dependent prediction error signal, best modeled as the difference between actual outcome and EV+. In contrast, loss-related expected value (EV−) and the associated prediction error was represented in the amygdala. Thus, the ventral striatum and the amygdala distinctively process the value of a prediction and subsequently compute a prediction error for gains and losses, respectively. Therefore, a homeostatic balance of both systems might be important for generating adequate expectations under uncertainty. Prevalence of either part might render expectations more positive or negative, which could contribute to the pathophysiology of mood disorders like major depression.
Neumatizing the Sequence: Special Performances of Sequences in the Central Middle Ages
Authors: KRUCKENBERG LORI
Published: September 2006

In his liturgical commentary Rationale divinorum officiorum, the thirteenthcentury writer Guillaume Durand describes a special, “antique” way of singing sequences called “neumatizing” (“neumatizare”). According to Durand, a sequence could be neumatized either by singing certain phrases melismatically or by vocalizing the entire sequence without words. The chief focus of this investigation is the identification of which sequences were still being neumatized after the decline of that practice around 1100, where and at which feasts they were sung, and why. The evidence suggests that neumatizing was especially cultivated in northern France during the twelfth and thirteenth centuries, especially in the cathedral towns of Rouen, Laon, Cambrai, and Amiens, as well as at various religious institutions in Metz, Andenne, Chichester, and Bamberg. The liturgical period of Advent, Christmas Eve, the Feast of John the Evangelist, and masses celebrating patron saints were the most typical liturgical occasions where neumatizing took place. The rationales for the singing practice appear to have been manifold, ranging from the practical and mundane to the spiritual and sacred. Motives for neumatizing include improving preexisting structures for purposes of fulfilling expectations about genre; using musical responses to highlight poetic topoi; lending solemnity and symbolic meaning to important liturgical feasts; and honoring ancient traditions while resisting some of the newer trends found with late examples of the genre.
Making History at the Frontier
Authors: Wasson Christina
Published: September 2006

This volume presents the stories of 11 women anthropologists whose career paths have successfully navigated the terrain of practice. Its overall goal is to help future generations of anthropologists who are initiating careers in practice, both women and men. Students in applied anthropology programs, and others considering careers in practice, are hungry for such information. A second goal is to highlight the contributions and concerns of women practitioners from the perspective of feminist anthropology. Three common threads run across the life histories of these authors: an integrated scholar‐practitioner identity; improvisation; and a shared set of building blocks for constructing their lives. Brief histories of four forerunners are provided to provide historical depth. They illustrate the continuing importance of persistence and determination, as well as the possibility of having meaningful and satisfying careers by approaching life and work creatively in the face of various obstacles.
An Interim Story of a Career as an Applied Anthropologist
Authors: Iris Madelyn
Published: September 2006

Every life has a story, constructed out of realities we cannot change, events that form a backdrop, and the choices and decisions we make as we move through time and space. This chapter describes my own life story. My character is grounded in the affects of my birth, the values I was taught as a child, and the paths I was encouraged to pursue. But my emergence as a woman, a wife, and a mother, and as an anthropologist, came out of a desire to pursue new ways of looking at the world and studying it, as well as a series of events that shaped, defined, and redefined the pathways I felt were open to me. Along the way to today, I have been helped by many people, taken some chances, and confronted a number of challenges. I hope this narrative reveals to the reader something about the possibilities of life, both personal and professional, and the ways in which these have melded in my own life to create my story about a career as an applied anthropologist.
Bushwhacking a Career
Authors: Sachs Patricia
Published: September 2006

Patricia Sachs describes the "bushwhacking" nature of her career in becoming a professional anthropologist and operating a business and work anthropology consulting firm. She discusses the influences of her family in the shaping of her decisions, and the challenge of creating anthropological practice and influence among clients who face transformation in what, where, and how they do business.
Seeing Double
Authors: Copeland‐Carson Jacqueline
Published: September 2006

This chapter is an autoethnographic account of Copeland‐Carson's lifelong effort to create a hybrid identity that integrates theory, practice, and lived experience from multiple fields, including anthropology, evaluation, community development, and philanthropy. Building on Abu‐Lughod's (1991) privileging of women's individual life stories as a lens for understanding society's power dynamics, she recounts how her early life cultivated a proto‐ethnographic ability for self‐reflection from both insider (emic) and outsider (etic) perspectives, eventually evolving into an anthropological career. Copeland‐Carson suggests that women of color applied anthropologists often experience a kind of double, "double consciousness" (Du Bois 1990) as they traverse multiple cultural worlds, struggle against racism and sexism, and cope with the discipline's subordination of practice. With growing interest in ethnography in various fields and industries, she argues that there may be an emerging feminization of practicing or applied anthropology affecting both men and women. This feminization can position applied ethnography (practice) as "soft" (women's) work, leaving analyzing and theorizing (scholarship) to the 'hard" (men's) social sciences such as economics. Copeland‐Carson concludes with some suggested tactics for empowering practicing careers and proposes a scholarship‐practitioner vision of anthropology that uses data from applied practice to inform publicly relevant scholarship.
Vibration serviceability for pedestrian bridges
Authors: Kasperski M.
Published: September 2006

The response of pedestrians to lively bridges is one of the problems that has to be addressed in the scope of analysing serviceability. The excitation process by walking and/or running and the sensitivity of the human receiver both have to be understood as random variables. The present paper analyses the expected scatter of the response of pedestrians based on today's available information. A discussion is then presented on a method of correlating observed reactions of pedestrians and measured vertical vibration amplitudes, which allow a serviceability criterion to be developed. A tentative limit value for serviceability is proposed based on the observations so far.
Vibration control of ultra-sensitive facilities
Authors: Brownjohn J. , Pavic A.
Published: September 2006

Feature sizes continue to decrease in computer processors, display units and media, while experimental facilities demand ever increasing measurement resolution. As a result, the requirements for controlling vibration levels in the structures of factories and laboratories become more severe and govern structural design more frequently. Design guidance in the UK and elsewhere is so far limited and vibration control exercises are presently case specific. Vibration control is a process by which simulated or measured vibration response of a vibration-sensitive facility can be managed and mitigated, before it is too late and the experiment or industrial process has failed (at great cost). Vibration control, as defined here, involves establishment of acceptance standards (vibration norms), measurement or estimation of inputs, simulation of structures and foundations with design iterations, study of vibration propagation mechanisms and finally comparison with vibration norms. The present paper distils experiences in vibration control of vibration-sensitive facilities, drawing attention to the major difficulties in the process and to some of the acceptable procedures for analysis, design and measurement.
Hopf Bifurcation and Stability of a Competition Diﬀusion System with Distributed Delay
Authors: Tang Yanbin , Zhou Li
Published: September 2006

In this paper we investigate the eﬀects of time delay and diffusion rate on the stability of the positive steady state for a competition diffusion system with distributed delay. We obtain the condition of instability of the positive uniform steady state. Regarding the time delay as bifurcation parameter, we reduce the original system on the center manifold and get the stability of the Hopf bifurcation periodic solutions. Finally, regarding the diﬀusion rate as a bifurcation parameter, we show that the onedimensional competition diﬀusion system with inﬁnite delay and Dirichlet boundary condition exhibits the spatiotemporal structures near the steady state of the system.
Higher Arithmetic $K$-Theory
Authors: Takeda Yuichiro
Published: September 2006

A concrete deﬁnition of higher

K

-theory in Arakelov geometry is given. The

K

-theory deﬁned in this paper is a higher extension of the arithmetic

K_0

-group of an arithmetic variety deﬁned by Gillet and Soulé. Products and direct images in this

K

-theory are discussed.
Approximate Conjugacy and Full Groups of Cantor Minimal Systems
Authors: Matui Hiroki
Published: September 2006

H. Lin and the author introduced the notion of approximate conjugacy of dynamical systems. In this paper, we will discuss the relationship between approximate conjugacy and full groups of Cantor minimal systems. An analogue of Glasner–Weiss’s theorem will be shown. Approximate conjugacy of dynamical systems on the product of the Cantor set and the circle will also be studied.
Weak Solution of a Singular Semilinear Elliptic Equation in a Bounded Domain
Authors: Dalmasso Robert
Published: September 2006

We study the singular semilinear elliptic equation

∆u + f(., u) = 0

in

\mathcal D'(Ω)

, where

Ω ⊂ ℝ^n

(

n ≥ 1

) is a bounded domain of class

C^{1,1}. f : Ω × (0, ∞) → [0, ∞)

is such that

f(., u) \in L^1(Ω)

for

u > 0

and

u → f(x, u)

is continuous and nonincreasing for a.e.

x

in

Ω

. We assume that there exists a subset

Ω' ⊂ Ω

with positive measure such that

f(x, u) > 0

for

x\in Ω'

and

u > 0

and that

∫_Ω f(x, cd(x, ∂Ω))dx < ∞

for all

c > 0

. Then we show that there exists a unique solution

u

in

W_0^{1,1}(Ω)

such that

∆u\in L^1(Ω)

,

u > 0

a.e. in

Ω

.
On Termination of 4-fold Semi-stable Log Flips
Authors: Fujino Osamu
Published: September 2006

In this paper, we prove the termination of 4-fold semi-stable log ﬂips under the assumption that there always exist 4-fold (semi-stable) log ﬂips.
Uniqueness and Existence of the Integrated Density of States for Schrödinger Operators with Magnetic Field and Electric Potential with Singular Negative Part
Authors: Iftimie Viorel
Published: September 2006

We prove the coincidence of the two deﬁnitions of the integrated density of states (IDS) for Schrödinger operators with strongly singular magnetic ﬁelds and scalar potentials: the ﬁrst one using the counting function of eigenvalues of the induced operator on a bounded open set with Dirichlet boundary conditions, the second one using the spectral projections of the whole space operator. Thus we generalize a result of [5], where the scalar potential was non-negative. Moreover, we prove the existence of IDS for the case of periodical magnetic ﬁeld and scalar potential.
Conditionally Positive Deﬁnite Hyperfunctions
Authors: Chung Jaeyoung , Kim Dohan
Published: September 2006

Making use of the heat kernel method we deﬁne a conditionally positive deﬁnite hyperfunction and obtain a Bochner–Schwartz type theorem for hyperfunctions which generalizes both the Bochner–Schwartz type theorem for distributions of Gelfand-Vilenkin in [GV] and our version of Bochner–Schwartz theorem for (Fourier) hyperfunctions in [CCK2, CK1].
Explicit Formulation of the Solution of Hamada–Leray–Wagschal’s Theorem
Authors: Camalès Renaud
Published: September 2006

In this paper, an explicit formula of the solution of Hamada–Leray–Wagschal’s theorem is given. For this, only structure’s theorem of ﬁnite dimensional determination’s function and linear algebra technics developped in [1] are used.
The $b$-functions for Prehomogeneous Vector Spaces of Commutative Parabolic Type and Universal Generalized Verma Modules
Authors: Kamita Atsushi
Published: September 2006

We shall give a new elementary proof of the uniform expression for the
b
-functions of prehomogeneous vector spaces of commutative parabolic type obtained by Muller, Rubenthaler and Schiffmann [5] by using micro-local analysis. Our method is similar to Kashiwara’s approach using the universal Verma modules. We shall also give a new proof for the criterion of the irreducibility of the generalized Verma module in terms of
b
-functions due to Suga [10], Gyoja [1], Wachi [13].
Microlocal Riemann–Hilbert Correspondence
Authors: Waschkies Ingo
Published: September 2006

We construct the global microlocal Riemann–Hilbert correspondence as an explicit equivalence between the abelian stack of microlocal perverse sheaves deﬁned in [W] and the abelian stack of regular holonomic microdiﬀerential modules of [KK]. The theory of analytic ind-sheaves and its microlocalization is crucial for our construction since it allows us to deﬁne solution complexes with values in the (ind-)ring of microlocal holomorphic functions (resp. microlocal tempered holomorphic functions).
Some Continuous Field Quantizations, Equivalent to the C*-Weyl Quantization
Authors: Honegger Reinhard , Rieckers Alfred
Published: September 2006

Starting from a (possibly inﬁnite dimensional) pre-symplectic space

(E, σ)

, we study a class of modiﬁed Weyl quantizations. For each value of the real Planck parameter

ℏ

, we have a C*-Weyl algebra

\mathcal W(E,ℏ_σ)

, which altogether constitute a continuous ﬁeld of C*-algebras, as discussed in previous works. For

ℏ = 0

, we construct a Fréchet–Poisson algebra, densely contained in

\mathcal W(E, 0)

, as the classical observables to be quantized. The quantized Weyl elements are decorated by so-called quantization factors, indicating the kind of normal ordering in speciﬁc cases. Under some assumptions on the quantization factors, the quantization map may be extended to the Fréchet–Poisson algebra. It is demonstrated to constitute a strict and continuous deformation quantization, equivalent to the Weyl quantization, in the sense of Rieffel and Landsman. Realizing the C*-algebraic quantization maps in regular and faithful Hilbert space representations leads to quantizations of the unbounded ﬁeld expressions.
Shift Operator for Nonabelian Lattice Current Algebra
Authors: Faddeev Ludvig , Volkov Alexander Yu.
Published: September 2006

The shift operator for a quantum lattice current algebra associated with

sl(2)

is produced in the form of product of local factors. This gives a natural deformation of the Sugawara construction for discrete space-time.
Cyclotomic Completions of Polynomial Rings
Authors: Habiro Kazuo
Published: September 2006

For a subset

S ⊂ ℕ = \{1, 2, . . . \}

and a commutative ring

R

with unit, let

R[q]^S

denote the completion

\varprojlim{}_{f(q)} R[q]/(f(q))

, where

f(q)

runs over all the products of the powers of cyclotomic polynomials

Φ_n(q)

with

n\in S

. We will show that under certain conditions the completion

R[q]^S

can be regarded as a “ring of analytic functions” deﬁned on the set of roots of unity of order in

S

. This means that an element of

R[q]^S

vanishes if it vanishes on a certain type of inﬁnite set of roots of unity, or if its power series expansion at one root of unity vanishes. In particular, the completion

ℤ[q]^{ℕ} \simeq \varprojlim{}_nℤ[q]/((1 −q)(1 −q^2 ) \cdots (1 − q^n))

enjoys this property.
Temperature as Order Parameter of Broken Scale Invariance
Authors: Ojima Izumi
Published: September 2006

In algebraic quantum ﬁeld theory the (inverse) temperature is shown to be a macroscopic
order parameter
to parametrize mutually disjoint thermal
sectors
arising from the
broken scale invariance
under renormalization-group transformations.

This is accomplished in a mathematical formalism for the consistent treatment of
explicitly broken symmetries
such as broken scale invariance, on the basis of a clearcut criterion for the symmetry breakdown in a uniﬁed scheme for sectors proposed recently by the author.
Functional Equations and Fusion Matrices for the Eight Vertex Model
Authors: Fabricius Klaus , McCoy Barry M.
Published: September 2006

We derive sets of functional equations for the eight vertex model by exploiting an analogy with the functional equations of the chiral Potts model. From these equations we show that the fusion matrices have special reductions at certain roots of unity. We explicitly exhibit these reductions for the 3, 4 and 5 order fusion matrices and compare our formulation with the algebra of Sklyanin.
From Exact-WKB towards Singular Quantum Perturbation Theory
Authors: Voros André
Published: September 2006

We use exact WKB analysis to derive some concrete formulae in singular quantum perturbation theory, for Schrödinger eigenvalue problems on the real line with polynomial potentials of the form

(q^M + gq^N)

, where

N > M > 0

even, and

g > 0

. Mainly, we establish the

g → 0

limiting forms of global spectral functions such as the zeta-regularized determinants and some spectral zeta functions.
The Second Painlevé Hierarchy and the Stationary KdV Hierarchy
Authors: Joshi Nalini
Published: September 2006

It is well known that soliton equations such as the Korteweg–de Vries equation are members of inﬁnite sequences of PDEs known as hierarchies. Here we consider inﬁnite sequences of ODEs associated with the Painlevé equations. We review methods of constructing such hierarchies, speciﬁcally the second Painlevé hierarchy, as reductions of PDE hierarchies. We also show that in the large-parameter limit, the solutions of the second Painlevé hierarchy are given by the periodic solutions of the stationary KdV hierarchy.
On Theorems of Hardy, Gelfand–Shilov and Beurling for Semisimple Groups
Authors: Thangavelu Sundaram
Published: September 2006

In this paper we prove a strong version of Hardy’s theorem for the group Fourier transform on semisimple Lie groups which characterises the Fourier transforms of all functions satisfying Hardy type conditions. In the particular case of

\mathit{SL}(2, ℝ)

we characterise all such functions and conjecture that the same is true for all rank one semisimple groups. We also establish an analogue of a theorem of Gelfand and Shilov in the context of semisimple groups. A version of Beurling’s theorem which assumes a Cowling–Price condition on the function is also proved. We show that these results yield most of the earlier results as corollaries.
On the Stokes Equation with the Leak and Slip Boundary Conditions of Friction Type: Regularity of Solutions
Authors: Saito Norikazu
Published: September 2006

We consider the Stokes equations under some nonlinear boundary conditions, which are described in terms of subdifferentials of maximal monotone graphs and are called leak and slip boundary conditions of friction type. The main objective is to show the existence of strong solutions, say

u ∈ H^2

and

p ∈ H^1

, to these problems. We start with weak solutions to variational inequalities, and then study the regularity of weak solutions. Our main theorems imply the maximality of Stokes operators with such nonlinear boundary conditions in a suitable Hilbert space and they are of use in analysis of time-dependent problems. Linear boundary conditions of Neumann type, such as slip and penetration conditions, are also discussed.
Distributions of Exponential Growth with Support in a Proper Convex Cone
Authors: Suwa Masanori
Published: September 2006

In this paper we will characterize the spaces of distributions of exponential growth with support in a proper convex cone by the heat kernel method. As application we can obtain the Paley–Wiener theorem for distributions of exponential growth supported by a proper convex cone and Edge-of-the-Wedge theorem for the space of the image by the Fourier–Laplace transform of them.
A Note on the Intersection of Banach Subspaces
Authors: Chacón Gerardo , Montesinos Vicente , Octavio Alfredo
Published: September 2006

We show that reﬂexivity of a Banach space can be characterized by a simple property formulated in terms of the distance to the intersection of a decreasing countable family of closed subspaces. We provide some explicit examples of the failure of the property in the non-reﬂexive case.
Q-reﬂexive Locally Convex Spaces
Authors: Boyd Christopher , Dineen Seán , Venkova Milena
Published: September 2006

For a locally convex space

E

, we use the Aron–Berner extension to deﬁne canonical mappings from

\widehat\otimes_{s,n,π} E''e

into different duals of

\mathcal P({}^n E)

. We investigate necessary and suffcient conditions for the continuity of these mappings, paying particular attention to three special cases — Fréchet spaces, DF spaces and reﬂexive A-nuclear spaces. We deﬁne Q-reﬂexive spaces as spaces where a certain canonical mapping can be extended to an isomorphism between

\widehat\otimes_{s,n,π} E''e

and

\overline{(\mathcal P({}^nE), τ_b)'_i}

. We ﬁnd examples of such spaces.
On the General Hodge Conjecture for Abelian Varieties of CM-type
Authors: Hazama Fumio
Published: September 2006

The General Hodge Conjecture for abelian varieties of CM-type is shown to be implied by the usual Hodge Conjecture for those up to codimension two.
Integral Representation for Borel Sum of Divergent Solution to a Certain Non-Kowalevski Type Equation
Authors: Ichinobe Kunio
Published: September 2006

We shall develop the theory of Borel summability or
k
-summability for a divergent solution of the Cauchy problem for non-Kowalevskian equations of quasihomogeneous type. Precisely, we ﬁrst establish necessary and sufficient conditions for the Borel summability in terms of the Cauchy data (cf. Theorem 2.1), and next we give an integral representation of the Borel sum by using kernel functions which are given by Meijer
G
-function or the generalized hypergeometric functions of conﬂuent type (cf. Theorems 2.3 and 2.6).
Uhlenbeck Spaces for $\mathbb A^2$ and Affine Lie Algebra $\widehat{\mathfrak{sl}}_n$
Authors: Finkelberg Michael , Gaitsgory Dennis , Kuznetsov Alexander
Published: September 2006

We introduce an Uhlenbeck closure of the space of based maps from projective line to the Kashiwara ﬂag scheme of an untwisted affine Lie algebra. For the algebra

\widehat{\mathfrak{sl}}_n

this space of based maps is isomorphic to the moduli space of locally free parabolic sheaves on

P^1 × P^1

trivialized at inﬁnity. The Uhlenbeck closure admits a resolution of singularities: the moduli space of torsion free parabolic sheaves on

P^1 × P^1

trivialized at inﬁnity. We compute the Intersection Cohomology sheaf of the Uhlenbeck space using this resolution of singularities. The moduli spaces of parabolic sheaves of various degrees are connected by certain Hecke correspondences. We prove that these correspondences deﬁne an action of

\widehat{\mathfrak{sl}}_n

in the cohomology of the above moduli spaces.
A Maillet Type Theorem for First Order Singular Nonlinear Partial Differential Equations
Authors: Shirai Akira
Published: September 2006

We shall study the ﬁrst order singular nonlinear partial diﬀerential equation of the form

f(x, u(x), ∂_xu(x)) = 0

with

u(0) = 0

, where

x \in ℂ^n

and

f(x, u, ξ)

is holomorphic in a neighborhood of the origin. This equation is said to be singular if

f(0, 0, ξ) ≡ 0

for all

ξ \in ℂ^n

. The purpose of this paper is to study the Maillet type theorem which means to determine the Gevrey order of a formal power series solution which may diverge.
The Heat Semigroup on Configuration Spaces
Authors: Kondratiev Yuri , Lytvynov Eugene , Röckner Michael
Published: September 2006

In this paper, we study properties of the heat semigroup of configuration space analysis. Using a natural “Riemannian-like” structure of the configuration space

Γ_X

over a complete, connected, oriented, and stochastically complete Riemannian manifold

X

of infinite volume, the heat semigroup

(e^{-tH^Γ})_{t\in ℝ_+}

was introduced and studied in [J. Funct. Anal.
154
(1998), 444-500]. Here,

H^Γ

is the Dirichlet operator of the Dirichlet form

\mathcal E^Γ

over the space

L^2(Γ_X, π_m)

, where

π_m

is the Poisson measure on

Γ_X

with intensity

m

—the volume measure on

X

. We construct a metric space

Γ_∞

that is continuously embedded into

Γ_X

. Under some conditions on the manifold

X

, we prove that

Γ_∞

is a set of full

π_m

measure and derive an explicit formula for the heat semigroup:

(e^{-tH^Γ} F)(γ) = ∫_{Γ_∞} F(ξ) \mathbf P_{t,γ}(dξ)

, where

\mathbf P_{t,γ}

is a probability measure on

Γ_∞

for all

t > 0

,

γ \in Γ_∞

. The central results of the paper are two types of Feller properties for the heat semigroup. The first one is a kind of strong Feller property with respect to the metric on the space

Γ_∞

. The second one, obtained in the case

X=ℝ^d

, is the Feller property with respect to the intrinsic metric of the Dirichlet form

\mathcal E^Γ

. Next, we give a direct construction of the independent infinite particle process on the manifold

X

, which is a realization of the Brownian motion on the configuration space. The main point here is that we prove that this process can start in every

γ \in Γ_∞

, will never leave

Γ_∞

, and has continuous sample path in

Γ_∞

, provided

\dim X ≥ 2

. In this case, we also prove that this process is a strong Markov process whose transition probabilities are given by the

\mathbf P_{t,γ}(\cdot)

above. Furthermore, we discuss the necessary changes to be done for constructing the process in the case

\dim X=1

. Finally, as an easy consequence we get a “path-wise” construction of the independent particle process on

Γ_∞

from the underlying Brownian motion.
Principal Bundle Maps via Rational Homotopy Theory
Authors: Shiga Hiroo , Yamaguchi Toshihiro
Published: September 2006

Let

P

be a finite complex on which

S^1

acts freely. In this paper, we shall give a sufficient condition that the kernel of the natural map (forgetful map)

\mathrm{Aut}_{S^1} P → \mathrm{Aut} P

is a finite group.
Form Factors of $\textit{SU}(N)$ Invariant Thirring Model
Authors: Takeyama Yoshihiro
Published: September 2006

We obtain a new integral formula for solutions of the rational quantum Knizhnik–Zamolodchikov equation associated with Lie algebra

\textit{sl}_N

at level zero. Our formula contains the integral representation of form factors of

\textit{SU}(N)

invariant Thirring model constructed by F. Smirnov. We write down recurrence relations arising from the construction of the form factors. We check that the recurrence relations hold for the form factors of the energy momentum tensor.
Group Actions on Spaces of Rational Functions
Authors: Ono Yohei , Yamaguchi Kohhei
Published: September 2006

Let

\mathrm{Hol}_d

be the space consisting of all holomorphic maps

f : S^2 → S^2

of degree

d

. The group

\mathrm{Hol}_1 = \mathrm{PSL}_2(ℂ)

acts on

\mathrm{Hol}_d

freely by the post-composition and we shall study the orbit space

X_d = \mathrm{Hol}_1\backslash \mathrm{Hol}_d

. As an application, we shall determine the homotopy types of the universal covering spaces of

\mathrm{Hol}_d

and

X_d

explicitly.
Hukuhara’s Topological Degree for non Compact Valued Multifunctions
Authors: De Blasi Francesco S. , Georgiev Pando Gr.
Published: September 2006

We present a direct construction of a topological degree for multivalued vector ﬁelds

I

-

F

in a Banach space, where

F

takes closed, bounded, convex (or non convex) values and the set-valued range of

F

is precompact in the Pompeiu–Hausdorff metric. Some useful properties of our topological degree are established. Applications to ﬁxed point theory including a Borsuk’s type result are considered.
Multiplicity of Filtered Rings and Simple K3 Singularities of Multiplicity Two
Authors: Tomari Masataka
Published: September 2006

Given a filtered ring, we give bounds of its multiplicity in terms of the data of the tangent cone using the technique of the filtered blowing-up. Applying it to each simple K3 singularity of multiplicity two, we find a good coordinate where the Newton boundary of the defining equation contains the point

(1,1,1,1) \in \mathbf R^4

. In the course of the proof, we classify simple K3 singularities of multiplicity two into 48 weight types. Furthermore we prove that the weight type of the singularity stays the same under arbitrary one-parameter (FG)-deformations.
Quasianalyticity of Positive Definite Continuous Functions
Authors: Chung Soon-Yeong
Published: September 2006

It is shown that for a positive definite continuous function

f(x)

on

ℝ^n

the followings are equivalent:

Moreover, an analogue for the analyticity is also given as a corollary.
An Integral PBW Basis of the Quantum Affine Algebra of Type $A_2^{(2)}$
Authors: Akasaka Tatsuya
Published: September 2006

We construct an integral PBW basis and an integral crystal basis of the quantum affine algebra of type

A_2^{(2)}

.
On Inner Characterizations of Pseudo-Krein and Pre-Krein Spaces
Authors: Hofmann Gerald
Published: September 2006

For developing a theory of

^*

-representations of

^*

-algebras

\mathcal A

on (indefinite) inner product spaces

E,(\cdot, \cdot)

, the classes of pseudo-Krein and pre-Krein spaces which admit a Hilbert space structure and exactly one maximal Hilbert space structure, respectively, are introduced. Inner characterizations for the topological structure of

E,(\cdot, \cdot)

to be a pseudo-Krein and pre-Krein space, respectively, are given. The results are illustrated by some examples.
The Uniqueness of the Integrated Density of States for the Schrödinger Operators for the Robin Boundary Conditions
Authors: Mine Takuya
Published: September 2006

The integrated density of states (IDS) for the Schrödinger operators is deﬁned by using the eigenvalue counting function of the operator restricted to bounded regions with appropriate boundary conditions. Two sufficient conditions for the coincidence of the IDS for the Dirichlet boundary conditions and the IDS for the Robin boundary conditions are given. The proofs of some fundamental formulas, e.g. the change of variables, the chain rule and the divergence formula, for Lipschitz domains are given for the completeness.
Invariants of Fold-maps via Stable Homotopy Groups
Authors: Ando Yoshifumi
Published: September 2006

In the 2-jet space

J^2(n, p)

of smooth map germs

(\mathbf R^n, 0) → (\mathbf R^p, 0)

with

n ≥ p ≥ 2

, we consider the subspace

Ω^{n−p_+1,0}(n, p)

consisting of all 2-jets of regular germs and map germs with fold singularities. In this paper we determine the homotopy type of the space

Ω^{n−p_+1,0}(n, p)

. Let

N

and

P

be smooth (

C^∞

) manifolds of dimensions

n

and

p

. A smooth map

f : N→ P

is called a fold-map if

f

has only fold singularities. We will prove that this homotopy type is very useful in ﬁnding invariants of fold-maps. For instance, by applying the homotopy principle for fold-maps in [An3] and [An4] we prove that if

n − p + 1

is odd and

P

is connected, then there exists a surjection of the set of cobordism classes of fold-maps into

P

to the stable homotopy group

\lim_{k,l →∞} π_{n+k+l}(T(ν_P^k) \wedge T_(\widehat γ^l_{G_{n−p_+1,l}}))

. Here,

ν_P^k

is the normal bundle of

P

in

\mathbf R^{p+k}

and

\widehat γ^l_{G_{n−p_+1,l}}

denote the canonical vector bundles of dimension

l

over the grassman manifold

G_{n−p+1,l}

. We also prove the oriented version.
$L_2$ and $L_∞$ Estimates of the Solutions for the Compressible Navier–Stokes Equations in a 3D Exterior Domain
Authors: Kobayashi Takayuki
Published: September 2006

We consider the boundary value problem of the equation of motion of viscous compressible ﬂuid in a 3D exterior domain. We shall give the

L_∞

estimates of the solutions and

L_2

estimates of the derivative with respect to space variable of the solutions.
Longo–Rehren Subfactors Arising from $α$-induction
Authors: Böckenhauer Jens , Evans David E. , Kawahigashi Yasuyuki
Published: September 2006

We study (dual) Longo–Rehren subfactors

M\otimes M^{\mathrm{opp}} ⊂ R

arising from various systems of endomorphisms of

M

obtained from

α

-induction for some braided subfactor

N ⊂ M

. Our analysis provides useful tools to determine the systems of

R

-

R

morphisms associated with such Longo–Rehren subfactors, which constitute the “quantum double” systems in an appropriate sense. The key to our analysis is that

α

-induction produces half-braidings in the sense of Izumi, so that his general theory can be applied. Nevertheless,

α

-induced systems are in general not braided, and thus our results allow to compute the quantum doubles of (certain) systems without braiding. We illustrate our general results by several examples, including the computation of the quantum double systems for the asymptotic inclusion of the E8 subfactor as well as its three analogues arising from conformal inclusions of

\textit{SU}(3)_k

.
The $q$-twisted Cohomology and the $q$-hypergeometric Function at $|q|=1$
Authors: Takeyama Yoshihiro
Published: September 2006

We construct the

q

-twisted cohomology associated with the

q

-multiplicative function of Jordan–Pochhammer type at

|q|=1

. In this framework, we prove the Heine's relations and a connection formula for the

q

-hypergeometric function of the Barnes type. We also prove an orthogonality relation of the

q

-little Jacobi polynomials at

|q|=1

.
Propagation of the Irregularity of a Microdifferential System
Authors: Monteiro Fernandes Teresa
Published: September 2006

We construct the functor of microlocal analytic irregularity

Iμ\mathrm{hom}(\cdot, \mathcal O_X)

which gives a natural third term of a distinguished triangle associated to the transformation

t_μ\mathrm{hom}(\cdot, \mathcal O_X) → μ \mathrm{hom}(\cdot, \mathcal O_X)

of functors on the derived category of

ℝ

-constructible sheaves. When restricting to

ℂ

-constructible objects we prove that the microlocal irregularity of a microdifferential system propagates along non 1-microcharacteristic directions, as a consequence of the propagation for

tμ\mathrm{hom}(\cdot, \mathcal O_X)

and

μ\mathrm{hom}(\cdot, \mathcal O_X

).
Analytic Representation of Generalized Tempered Distributions by Wavelets
Authors: Sohn Byung Keun , Pahk Dae Hyeon
Published: September 2006

The analytic representation of the generalized tempered distributions of exponential growth,

\mathcal K_p^{r'}

, is given in terms of series of analytic wavelets. These series converge uniformly on compact subsets of the upper and lower half planes.
On a Conjecture of Kac–Wakimoto
Authors: Xu Feng
Published: September 2006

We prove a conjecture about mininmal index of certain representations of Coset Algebraic Conformal Field Theories under certain conditions as formulated previously by us. As a by-product, the Kac–Wakimoto Conjecture (KWC) which is related to the asympotics of the coset characters is true under the same conditions. The same idea in the proof also proves a recent conjecture related to subfactors from conformal inclusions.
Asymptotic Exponential Stability for Diffusion Processes Driven by Stochastic Differential Equations in Duals of Nuclear Spaces
Authors: Liu Kai , Caraballo Tomás
Published: September 2006

The main objective of this paper is to investigate the asymptotic stability for diffusion processes driven by a class of Itô stochastic differential equations in duals of nuclear spaces. A coercivity condition imposed on this sort of equation plays the role of an exponential stability criterion. An example is studied to illustrate our theory.
The Cauchy Problem for Nonlinear Klein–Gordon Equations in the Sobolev Spaces
Authors: Nakamura Makoto , Ozawa Tohru
Published: September 2006

The local and global well-posedness for the Cauchy problem for a class of nonlinear Klein–Gordon equations is studied in the Sobolev space

H^s = H^s(ℝ^n)

with

s ≥ n/2

. The global well-posedness of the problem is proved under the following assumptions: (1) Concerning the nonlinearity

f

,

f(u)

behaves as a power

u^{1+4/n}

near zero. At infinity

f(u)

has an exponential growth rate such as

\exp(κ|u|^ν)

with

κ > 0

and

0 < ν ≤ 2

if

s = n/2

, and has an arbitrary growth rate if

s > n/2

. (2) Concerning the Cauchy data

(\phi,ψ) \in \mathcal H^s ≡ H^s \oplus H^{s-1}

,

‖(\phi,ψ);\mathcal H^{1/2}‖

is relatively small with respect to

(\phi, ψ); \mathcal H^{s^∗}

, where

s^∗

is a number with

s^∗ = n/2

if

s = n/2

,

n/2 < s^∗ ≤ s

if

s > n/2

, and the smallness of

‖(\phi, ψ);\.{\mathcal H}^{n/2}‖

is also needed when

s = n/2

and

ν = 2

.