bluuebunny/crossref_metadata_2025 huggingface dataset:
What Motivates Managers to Coordinate the Learning Experience of Interprofessional Student Teams in Service Delivery Settings?
Authors: Kipp Jean , McKim Bob , Zieber Colin , Neumann Iris
Published: June 2010

This article addresses the realities of providing interdisciplinary student team placements (i.e., experiential team learning for students) in healthcare settings. Three site coordinators from different clinical settings in Alberta (a geriatric assessment unit, a geriatric dementia care unit, and a primary healthcare centre), who facilitated Student Team Placements from the University of Alberta (UofA) in 2004, comment on their experiences and incentives for participating in interdisciplinary teamwork with students. The coordinators suggest that students provide input into the sites' continuous quality improvement cycle, contribute to host organizations, and confer benefits for the student preceptors, the staff and the patients who participate. The site coordinators also recognize and accept the responsibility common to all service providers, to model a unique site culture that promotes learning/teaching of team skills for health science students. The experience of others in the literature supports our findings that two systems — the system to educate health professionals and the system that influences the health of the community — can interact so that each realizes a mutual benefit.
New Graph Polynomials from the Bethe Approximation of the Ising Partition Function
Authors: WATANABE Y. , FUKUMIZU K.
Published: June 2010

We introduce two graph polynomials and discuss their properties. One is a polynomial of two variables whose investigation is motivated by the performance analysis of the Bethe approximation of the Ising partition function. The other is a polynomial of one variable that is obtained by the specialization of the first one. It is shown that these polynomials satisfy deletion–contraction relations and are new examples of the V-function, which was introduced by Tutte (Proc. Cambridge Philos. Soc.43, 1947, p. 26). For these polynomials, we discuss the interpretations of special values and then obtain the bound on the number of sub-coregraphs,i.e., spanning subgraphs with no vertices of degree one. It is proved that the polynomial of one variable is equal to the monomer–dimer partition function with weights parametrized by that variable. The properties of the coefficients and the possible region of zeros are also discussed for this polynomial.
Forgers of Law and Their Readers: The Crafting of English Political Identities between the Norman Conquest and the Magna Carta
Authors: O'Brien Bruce R.
Published: June 2010

A short time after 1206 and before 1215, a Londoner assembled a massive collection of older and near contemporary English laws, called theLeges Anglorumby historians, and inserted long interpolations and spurious codes that enunciated many of the principles that guided the baronial opposition to King John and later became part of the Magna Carta. To those familiar with the struggle leading up to the creation of the Magna Carta, these principles should cause no surprise. These ancient laws were made to proclaim that “in the kingdom right and justice ought to reign more than perverse will” (ECf4, 11.1.A.6; Liebermann 1903, 635). In another part of the collection, King Arthur, making his first appearance in English law, is credited with establishing as law the requirement that all nobles, knights, and freemen of the whole kingdom of Britain swear “to defend the kingdom against foreigners and enemies” (ECf4, 32.A.5–7; Liebermann 1903, 655). More surprising is the attribution of the regularly assembled Hustings court in London to the Trojans (who became the Britons). The seventh-century West Saxon king, Ine, suddenly looms large in the ranks of Britain's lawmakers; he not only reigns for the good of all, but is also given the lordly virtues of twelfth-century chivalric romance: he is “generous, wise, prudent, moderate, strong, just, spirited, and warlike” (as was appropriate for the time and place) (ECf4, 32.C.2, 32.C.8; Liebermann 1903, 658–59). A confection of bits of other law, attributed here to King Alfred, orders an end to vice, national education for freemen, and unity for all “as if sworn brothers for the utility of the kingdom” (Leges Angl, Pseudo-Alfred 1–6; Liebermann 1894, 19–20). Finally, in the grandest statement of English political ambition, Arthur appears again as the great conqueror, whose spirit was not satisfied by Britain alone: “Courageously and speedily he subjugated all Scandinavia, which is now called Norway, and all the islands beyond, namely Iceland and Greenland, which belong to Norway, Sweden, Ireland, Gotland, Denmark, Samland, Vinland, Curland, Runoe, Finland, Wirland, Estland, Karelien,Lapland, and all other lands and islands of the eastern Ocean as far as Russia” (ECf4, 32.E; Liebermann 1903, 659).
Slavery and the Magna Carta in the Development of Anglo-American Constitutionalism
Authors: Dyer Justin Buckley
Published: June 2010

If English and American constitutional thought rests on one shared foundation, it is the principle that executive power, in order to be legitimate, must be subject to law. In the thirteenth century, the English jurist Henry de Bracton declared that “the law makes the King”—rather than the King makes the law—and urged, “Let the King … bestow upon the law what the law bestows upon him, namely dominion and power, for there is no King where will rules and not law” (White 1908, 268). Bracton no doubt had in mind some of the recent provisions of the Magna Carta (1215), which provided a formal codification of this principle. The rebel barons who imposed the Magna Carta on King John were animated by a desire to limit arbitrary executive power, and, in Article 39, they secured a promise from the monarchy that “no free man shall be arrested or imprisoned, or disseised or outlawed or exiled or in any way victimised, neither will we attack him or send anyone to attack him, except by the lawful judgment of his peers or by the law of the land” (Turner 2003, 231). In the fourteenth century, Article 39 was redrafted by Parliament to apply not only to free men but also to any man “of whatever estate or condition he may be,” and this process of reinterpretation continued throughout the next several centuries as Parliament expanded “the Charter's special ‘liberties’ for the privileged classes to general guarantees of ‘liberty’ for all the king's subjects” (Turner 2003, 3).
The Legacy of the Magna Carta in Recent Supreme Court Decisions on Detainees' Rights
Authors: Pallitto Robert
Published: June 2010

The legacy of the Magna Carta is apparent in the Supreme Court's recent decisions regarding detainees' rights. Asked to evaluate strong claims of executive power, the Court has had occasion to consider the origin and scope of habeas corpus, which many scholars see as a product of the Magna Carta. The majority opinion in Boumediene v. Bush (2008) traced the history of the writ of habeas corpus back to the Magna Carta and relied on that lineage to rule that Guantanamo detainees were entitled to petition for habeas corpus, even though Congress had explicitly denied them that right in the 2006 Military Commissions Act (MCA) and the 2005 Detainee Treatment Act (DTA).
Terrorism and Human Rights
Authors: Piazza James A. , Walsh James Igoe
Published: June 2010

The articles in this symposium explore the relationships between terrorism and government respect for human rights. These relationships have wide-ranging implications for the study of politics. Terrorism is seen as a major threat to political stability in many countries. Respect for internationally recognized human rights is a fundamental responsibility of national governments. Can governments prevent terrorism while also respecting human rights, or must authorities trade off some human rights to reduce terrorism? If the latter is the case, which human rights can or should be sacrificed for the goal of stopping terrorism?
J. DAVID SINGER
Authors: Morrow James D. , Clark William , Diehl Paul F. , Ray James Lee , Sarkees Meredith Reid , Walker Thomas C.
Published: June 2010

J. David Singer, a globally recognized scholar of international politics, died Monday, December 28, 2009, in Ann Arbor, Michigan. He was involved in an auto accident on September 22 and had been hospitalized since. At the time of his death, Singer was Professor Emeritus at the University of Michigan, where he'd been on the faculty from 1958 until retiring in 2002. He was 84 years old.
TRIBUTES TO JOHN HOPE FRANKLIN
Authors: Savage Barbara D.
Published: June 2010

Like many people, I knew John Hope Franklin long before we ever met. During an age when the disjuncture between public personal and private persona is usually jarring, part of the honor of being in his presence was the seamlessness between the man he presented himself to be and the man he was. Erudite and exacting yet gracious and generous in his writings and public appearances, Franklin brought those same virtues to the private gatherings I was privileged to witness and share with him.
THE POLITICS OF RACE-BLINDNESS
Authors: Keaton Trica Danielle
Published: June 2010

The discourse of “race-blindness” in contemporary France cannot help but engender what it seeks to evade, “race” consciousness. Nowhere, is this dynamic better illustrated than by the current public debate on “Black” consciousness, “Black” identity discourses, and “French Black” activism that have emerge in response to an avoided “race” question in hexagonal France where “Blacks” have now reached a critical mass. In examining these issues, I argue that “French Black” activists are, however, limiting their own effectiveness when its adherents also retreat from a critical concept of “race” in their anti-black struggles. While the potent ideals of French republicanism are intrinsic to “race” avoidance, this stance unwittingly contributes to the prevalent practice of camouflaging the very discrimination and racism that such activists seek to document through controversial ethno-racial statistics, presently proscribed in France. Negated with “race” is the under-stated significance of the semantic particularity of the notion of “black” and its relevance in anti-black discrimination, also explored in this essay. By this, I am referring to those stigmatizing meanings of “black” prior to its incorporation into social categories used to designate and rank people so-perceived and so-denoted in Europe where those meanings crystallized and migrated beyond its shores. The critical use of “race” by these activists, then, would force the recognition, presently occulted, that this construct has played a fundamental role in structuring belonging and opportunity in France, and thereby buttress demands for statistics to demonstrate and analyze that lived reality towards its undoing. Ultimately, the existence of anti-blackness and anti-black struggles serve to illustrate that France has not escaped its “race” question or fulfilled it promises of “race-blind” equality.
Intrinsic properties and external factors determine the differentiation bias of human embryonic stem cell lines
Authors: Mehta Ashish , Mathew Sheena , Viswanathan Chandra , Majumdar Sen Anish
Published: June 2010

A major goal of human embryonic stem cell (hESC) research is to regulate differentiation through external means to generate specific cell types with high purity for regenerative medicine applications. Although all hESC lines express pluripotency‐associated genes, their differentiation ability to various lineages differs considerably. We have compared spontaneous differentiation propensity of the two hESC lines, RelicellhES1 and BG01. Spontaneous differentiation of hESC lines grown in different media conditions was followed by differentiation using two methods. Kinetic data generated by real‐time gene expression studies for differentiated cell types were analyzed, and confirmed at protein levels. Both cell lines showed upregulation of genes associated with the 3 germ layers, although stark contrast was evident in the magnitude of upregulation of lineage specific genes. A distinct difference was also found in the rate at which the pluripoteny factors, Oct‐4 and Nanog, were downregulated during differentiation. Once differentiation was initiated, both Oct‐4 and Nanog gene expression was drastically reduced in RelicellhES1, whereas a gradual decrease was observed in BG01. A clear trend is seen in RelicellhES1 to differentiate into neuroectodermal and mesenchymal lineages, whereas BG01 cells are more prone to mesoderm and endoderm development. In addition, suspension versus plated methods of cell culture significantly influenced the outcome of differentiation of certain types of cells. Results obtained by spontaneous differentiation of hESCs were also amplified by induced differentiation. Thus, differential rates of downregulation of pluripotency markers along with culture conditions seem to play an important role in determining the developmental bias of human ES cell lines.
From productivism to multi-functionality in the Gascoyne - Murchison Rangelands of Western Australia
Authors: Hughes Michael , Jones Roy
Published: June 2010

A sustainability assessment of the Western Australian (WA) rangelands identified a range of issues associated with regional economic decline typical of many marginal rangeland regions in Australia. As part of a regional rejuvenation strategy, the WA state government purchased selected pastoral lease properties for incorporation into the conservation estate. It was intended as a means of land-use transition from mono-functional productivism to multi-functionality incorporating protection of significant rangeland bioregions and development of tourism.
A 1-year project was conducted to assess the issues relating to this transition. Archived information was obtained from government relating to the characteristics of the lease properties at the time they were purchased. Site visits were undertaken to purchased leases acquired by the government as well as neighbouring leases. During site visits, interviews with pastoralists and purchased lease managers were conducted. A series of facilitated community discussion groups in the region was held to ascertain the views of landholders and managers, government representatives, indigenous interests and commercial operators in the region.
This paper describes how the transition to a combination of protection and consumption exchanged one set of problems for another. This was due partly to the intrinsic character of the land, in terms of previous overgrazing, isolation, large distances, and limited infrastructure and services. More importantly, the top-down approach to land transition failed to allocate adequate management resources to replace those lost when the former pastoral leaseholders left. The consequences of inadequate management included theft and rapid degradation of assets, inadequate control of pests and weeds; inadequate fire prevention management and poor communication between the government and other stakeholders over management decisions. This paper discusses the dynamics of this WA rangeland transition with reference to the multi-functional rural transition concept.
Spatial and temporal variation in precipitation at the start of the rainy season in tropical Australia
Authors: Garnett S. T. , Williamson G.
Published: June 2010

The patterns of rainfall early in the rainy season vary substantially across northern Australia, even in sites with the same annual average. This has biophysical and economic implications in terms of land and infrastructure management, resource availability and capacity, and access. Daily patterns in long-term rainfall records in Australia north of 23°S subject to regular monsoonal rainfall were compared with threshold levels for dryland and wetland seed germination, initiation of the growing season, patterns of gaps between early storms and the heaviness of the first falls, correlations between thresholds, spatial variation in correlation with the Southern Oscillation Index (SOI) and temporal trends in mean threshold dates. The earliest rains sufficient to cause seed germination or generate fresh fodder occur in the north-west of the Northern Territory with the average date being later to the south, east and west. Initial falls of the rainy season are heaviest, however, on Cape York Peninsula so that the time between first falls and saturation is shortest in the east. The probability of extended gaps between rainfall events increased from north to south. When the SOI is taken into account, no change in timing could be detected at the few sites with records of sufficient duration. However, because of changes in SOI frequency, rains are tending to start earlier in the drier parts of the north and north-west and later in the east. This may be because anthropogenic climate change is resulting in fewer classical El Niño Southern Oscillation events and more frequent El Niño Modoki climate anomalies.
Rangeland governance in China: overview, impacts on Sunan County in Gansu Province and future options
Authors: Wang M. P. , Zhao C. Z. , Long R. J. , Yang Y. H.
Published: June 2010

The development of the current regulatory framework for management of rangeland resources in China began in 1949. Prior to this, there were family, tribal and other traditional systems of grazing management. The emphasis in government policy since 1949 has been to increase livestock production and economic output from the rangelands. The operations of these policies and regulations in Sunan County, a typical rangeland county in Gansu Province, are examined. The existing laws, policies, and regulations related to rangeland management in Sunan County and elsewhere are identified and described. It is argued that a policy based on rational processes should lead to desired outcomes. Therefore, emphasis needs to be placed on processes that facilitate the development and implementation of policies at every level of government to promote sustainable use and management of natural resources and to secure sustainable livelihoods. It is concluded that the rangeland policies have been rarely integrated with the concept of sustainable development. This is now changing. Sustainable development philosophy needs to be further incorporated into the developmental processes for rangeland policies. Until now processes have focused predominantly on economic performance.
RNA-mediated
trans
-communication can establish paramutation at the
b1
locus in maize
Authors: Arteaga-Vazquez Mario , Sidorenko Lyudmila , Rabanal Fernando A. , Shrivistava Roli , Nobuta Kan , Green Pamela J. , Meyers Blake C. , Chandler Vicki L.
Published: June 2010

Paramutation is the epigenetic transfer of information between alleles that leads to the heritable change of expression of one allele. Paramutation at the
b1
locus in maize requires seven noncoding tandem repeat (
b1TR
) sequences located ∼100 kb upstream of the transcription start site of
b1
, and mutations in several genes required for paramutation implicate an RNA-mediated mechanism. The
mediator of paramutation
(
mop1
) gene, which encodes a protein closely related to RNA-dependent RNA polymerases, is absolutely required for paramutation. Herein, we investigate the potential function of
mop1
and the siRNAs that are produced from the
b1TR
sequences. Production of siRNAs from the
b1TR
sequences depends on a functional
mop1
gene, but transcription of the repeats is not dependent on
mop1
. Further nuclear transcription assays suggest that the
b1TR
sequences are likely transcribed predominantly by RNA polymerase II. To address whether production of
b1TR
-siRNAs correlated with paramutation, we examined siRNA production in alleles that cannot undergo paramutation. Alleles that cannot participate in paramutation also produce
b1TR
-siRNAs, suggesting that
b1TR
-siRNAs are not sufficient for paramutation in the tissues analyzed. However, when
b1TR
-siRNAs are produced from a transgene expressing a hairpin RNA,
b1
paramutation can be recapitulated. We hypothesize that either the
b1TR
-siRNAs or the dsRNA template mediates the
trans
-communication between the alleles that establishes paramutation. In addition, we uncovered a role for
mop1
in the biogenesis of a subset of microRNAs (miRNAs) and show that it functions at the level of production of the primary miRNA transcripts.
Magnetic and magnetocaloric properties of Ce1−xRxFe2 and Ce(Fe1−xMx)2 compounds
Authors: Haldar Arabinda , Suresh K G , Nigam A K
Published: June 2010

We have studied selected rare-earth doped and transition-metal doped CeFe2 compounds by examining their structural, magnetic and magneto-thermal properties. With substitution of Ce by 5% and 10% Gd and 10% Ho, the Curie temperature can be tuned to the range 267–318 K. Localization of Ce 4f electronic state with rare earth substitutions is attributed for the enhancement of Curie temperature. On the other hand, with Ga and Al substitution at the Fe site, the system undergoes paramagnetic to ferromagnetic transition and then to an antiferromagnetic phase on cooling. The magnetocaloric effect across the transitions has been studied from both magnetization isotherms and heat capacity data. It is shown that by choosing the appropriate dopant and its concentration, the magnetocaloric effect around room temperature can be tuned.
Representation of 0 as ∑^{𝑁}_{𝐾=-𝑁}𝜖_{𝑘}𝑘
Authors: van Lint J. H.
Published: June 2010

If

ε
k

{\varepsilon _k}

are independent identically distributed random variables with values

0
0

and

1
1

, each with probability

1
2

\tfrac {1} {2}

then
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper P left-parenthesis sigma-summation Underscript k equals negative upper N Overscript plus upper N Endscripts epsilon Subscript k Baseline k equals 0 right-parenthesis tilde left-parenthesis StartFraction 3 Over pi EndFraction right-parenthesis Superscript 1 slash 2 Baseline upper N Superscript negative 3 slash 2 Baseline period">

P

(

∑

k
=
−
N

+
N

ε
k

k
=
0

)

∼

(

3
π

)

1

/

2

N

−
3

/

2

.

P\left ( {\sum \limits _{k = - N}^{ + N} {{\varepsilon _k}k = 0} } \right ) \sim {\left ( {\frac {3} {\pi }} \right )^{1/2}}{N^{ - 3/2}}.

\]
Positive operators on 𝐶(𝑋)
Authors: Foguel S. R.
Published: June 2010

Conditions for the existence of finite and

σ
\sigma

finite invariant measures for a Markov operator on

C
(
X
)

C(X)

are studied.
A representation for the solution of Fredholm integral equations
Authors: Kagiwada H. H. , Kalaba R. E. , Schumitzky A.
Published: June 2010

This paper provides a new representation formula for the solution of Fredholm integral equations of the second kind. The formula has certain computational advantages over the usual representation involving the resolvent or the representation formula of Krein. As an application, the Bellman-Krein partial differential equation for the resolvent is derived.
The 𝑛-separated-arc property for homeomorphisms
Authors: Belna C. L.
Published: June 2010

Let

f
f

be a function defined in the open unit disk

D
D

whose range is in the Riemann sphere

W
W

, and let

C
C

denote the unit circle. We show that if

f
f

is a homeomorphism of

D
D

onto a Jordan domain, then the set of points

p
∈
C

p \in C

at which

f
f

has the

n
n

-separated-arc property

(
n
≧
2
)

(n \geqq 2)

is a subset of the set of ambiguous points of

f
f

and is thus countable.
Cancellation of groups with maximal condition
Authors: Hirshon R.
Published: June 2010

It is not true that a group which obeys the maximal condition for normal subgroups may always be cancelled in direct products. However, we show the following Theorem. Let

C
C

be a group which obeys the maximal condition for normal subgroup. Suppose further that if

C

∗

{C_{\ast }}

is an arbitrary homomorphic image of

C
C

, then

C

∗

{C_{\ast }}

is not isomorphic to a proper normal subgroup of itself. Then

C
C

may be cancelled in direct products. Some generalizations of this result are indicated.
Some regularity conditions for the (𝑓,𝑑_{𝑛},𝑧₁) summability method
Authors: Jakimovski A. , Skerry H.
Published: June 2010

Regularity conditions for the generalized Lototsky summability method

(
f
,

d
n

,

z
1

)

(f,\;{d_n},\;{z_1})

are derived which do not restrict the Taylor coefficients of

f
f

. Some examples are given.
On the factorization of integrers
Authors: Duncan R. L.
Published: June 2010

The order of magnitude of the average of the exponents in the canonical factorization of an integer is discussed. In particular, it is shown that this average has normal order one and a result which implies that the average order is one is also derived.
Commutative 𝑄𝐹-1 artinian rings are 𝑄𝐹
Authors: Dickson S. E. , Fuller K. R.
Published: June 2010

In a recent paper, D. R. Floyd proved several results on algebras, each of whose faithful representations is its own bicommutant ( = R. M. Thrall’s

QF - 

1

{\text {QF - }}1

algebras, a generalization of

QF

{\text {QF}}

-algebras) among which was the theorem in the title for algebras. We obtain our extension of Floyd’s result by use of interlacing modules, replacing his arguments involving the representations themselves.
Radical and semisimple classes with specified properties
Authors: Leavitt W. G.
Published: June 2010

Conditions are given on a radical (semisimple) property to ensure the existence of a construction for the smallest radical (semisimple) class with the property, containing a given class of rings. This generalizes earlier results on smallest hereditary or strongly hereditary radical classes, and hereditary semisimple classes. In the last section certain classes of rings are shown to admit a construction for the largest radical (semisimple) class contained in the given class. This leads to theorems on largest radical (semisimple) classes dual to the already established smallest theorems.
An inequality for rational functions
Authors: Widom Harold
Published: June 2010

An inequality of A. A. Gončar concerning the relative sizes of rational functions on different sets is reinterpreted. This allows a very simple proof of a more general inequality.
Oscillation theorems for second order nonlinear differential equations.
Authors: Erbe Lynn
Published: June 2010

The oscillatory and nonoscillatory behavior of the nonlinear second order differential equation

(
1
)

x
+
p
(
t
)
f
(
x
)
=
0

(1)\;x + p(t)f(x) = 0

is related to that of

(
2

)
λ

x
+
λ
p
(
t
)
x
=
0
,

λ
>
0

{(2)_\lambda }\;x + \lambda p(t)x = 0,\;\lambda > 0

. Under certain conditions on

p
(
t
)

p(t)

and

f
(
x
)

f(x)

it is shown that all solutions of

(
1
)

(1)

are oscillatory if

(
2

)
λ

{(2)_\lambda }

is oscillatory for all

λ
>
0

\lambda > 0

. In contrast to most of the literature on this subject, no sign or integrability conditions on

p
(
t
)

p(t)

are explicitly assumed.
On the asymptotic behavior of linear systems
Authors: Locke Phil
Published: June 2010

The purpose of this paper is to establish a necessary and sufficient condition for the vector-matrix system

x
˙

=
[
A
(
t
)
+
B
(
t
)
]
x

\dot x = [A(t) + B(t)]x

to have solutions of the form

Y
(
t
)
c
(
t
)

Y(t)c(t)

where

Y
(
t
)

Y(t)

is a fundamental matrix of solutions of

y
˙

=
A
(
t
)
y

\dot y = A(t)y

.
Barbier’s theorem in the Lobachevski plane
Authors: Fillmore Jay P.
Published: June 2010

In the Lobachevski plane, horocycles with the same center are geodesic parallels and are natural replacements for the lines used in defining the support function of a convex curve and the notion of constant width in the Euclidean plane. In this paper, analogs based on horocycles are obtained for Christoffel’s formula, which expresses the radius of curvature of a convex curve in terms of its support function, and Barbier’s theorem, which relates the length and width of a convex curve of constant width.
Applications of stereographic projections to submanifolds in 𝐸^{𝑚} and 𝑆^{𝑚}
Authors: Reilly Robert C.
Published: June 2010

In this paper we give a criterion for a compact minimal submanifold of

S
m

{S^m}

to lie in a given great hypersphere in terms of an integral over the stereographic image in

E
m

{E^m}

of the submanifold. We also show that if all the points a certain normal distance

C
C

from a compact hypersurface

M
M

in

E
m

{E^m}

lie on a sphere of radius

D
>
C

D > C

then

M
M

is a hypersphere. This generalizes a classical result on parallel hypersurfaces. We prove this theorem by showing it to be equivalent, via stereographic projection, to a recent result of Nomizu and Smyth concerning the gauss map for hypersurfaces of

S
m

{S^m}

.
Bounds for zeros of some special functions
Authors: Hethcote Herbert W.
Published: June 2010

For

n
≧
1

n \geqq 1

let

b
n

{b_n}

and

c
n

{c_n}

be zeros (ordered by increasing values) of

u
(
x
)

u(x)

and

v
(
x
)

v(x)

, respectively, which are non-trivial solutions of

u
+
p
(
x
)
u
=
0

u + p(x)u = 0

and

v
+
q
(
x
)
v
=
0

v + q(x)v = 0

with continuous

p
(
x
)

p(x)

and

q
(
x
)

q(x)

. It is shown that if

b
n

−

c
n

→
0

{b_n} - {c_n} \to 0

as

n
→
∞
,

p
(
x
)
≧
q
(
x
)

n \to \infty ,\;p(x) \geqq q(x)

, and either

p
(
x
)

p(x)

or

q
(
x
)

q(x)

is nonincreasing, then

b
n

≧

c
n

{b_n} \geqq {c_n}

for

n
≧
1

n \geqq 1

. Inequalities related to asymptotic expansions are obtained for the negative zeros

a
n

{a_n}

of the Airy function

A
i
(
z
)

Ai(z)

and the zeros

j

v
,
n

{j_{v,n}}

of the Bessel function

J
v

(
x
)

{J_v}(x)

.
A generalization of Sturm’s separation theorem
Authors: Allegretto W.
Published: June 2010

A Sturmian separation theorem is established for elliptic-parabolic equations with minimal assumptions on the coefficients and none on the regularity of the domain. A comparison theorem for linear equations and a separation theorem for quasi-linear equations are then obtained as applications.
Fourier-Stieltjes transforms tending to zero
Authors: Wallen Lawrence J.
Published: June 2010

Let

μ
\mu

be a Borel measure on the circle,

μ
^

\hat \mu

its Fourier transform. It is shown that a certain thinness condition on the positive part of the support of

μ
^

\hat \mu

forces a power of

μ
\mu

(in the sense of convolution) to be absolutely continuous.
On the algebraic independence of symmetric functions
Authors: Haeuslein G. K.
Published: June 2010

The purpose of this note is to establish a necessary and sufficient condition for the algebraic independence of certain sets of homogeneous symmetric polynomials which is used in 2. to solve a problem proposed by L. Flatto [2].
Note on nonnegative matrices
Authors: Djoković D. Ž.
Published: June 2010

Let

A
A

be a nonnegative square matrix and

B
=

D
1

A

D
2

B = {D_1}A{D_2}

where

D
1

{D_1}

and

D
2

{D_2}

are diagonal matrices with positive diagonal entries. Several proofs are known for the following theorem: If

A
A

is fully indecomposable then

D
1

{D_1}

and

D
2

{D_2}

can be chosen so that

B
B

is doubly stochastic. Moreover,

D
1

{D_1}

and

D
2

{D_2}

are unique up to a scalar factor. It is shown that these results can be easily obtained by considering a minimum of a certain rational function of several variables.
The conjugacy function
Authors: Leighton Walter
Published: June 2010

The conjugacy function

δ
(
x
)

\delta (x)

of the differential equation

y
+
p
(
x
)
y
=
0

y + p(x)y = 0

is defined as the distance from a point

x
x

to its first conjugate point. Conditions that

δ
(
x
)

\delta (x)

be convex or concave are given, as well as conditions that

δ
(
x
)

\delta (x)

be an increasing or decreasing function. The lemma provides a novel type of comparison theorem.
A closed subspace of 𝒟(Ω) which is not an ℒℱ-space
Authors: Kascic M. J. , Roth B.
Published: June 2010

With proper choice of region

Ω
⊆

R
n

\Omega \subseteq {R^n}

and constant coefficient linear partial differential operator

P
P

, namely

Ω
\Omega

being

P
P

-convex but not strong

P
P

-convex, the range of

P
P

in

D

(
Ω
)

\mathcal {D}(\Omega )

is a closed subspace of

D

(
Ω
)

\mathcal {D}(\Omega )

whose subspace topology differs from its canonical

LF

{\text {LF}}

-topology. In the present paper this result is proved and an example of a pair

Ω
,

P

\Omega ,\;P

satisfying the above hypotheses is presented.
Common eigenvectors for commutative positive linear operators
Authors: Huff Robert E.
Published: June 2010

The purpose of this note is to point out an extension of the Markov-Kakutani fixed-point theorem to a result on the existence of a common eigenvector in a cone with a compact base when acted upon by a commutative family of operators. As an application, an extension is given of a result of Kreĭn and Rutman on characteristic functionals.
Free coalgebras in a category of rings
Authors: Davis Robert
Published: June 2010

Let

R

\mathcal {R}

be the category of commutative rings with unity and unity-preserving homomorphisms, and let

Π
\Pi

be a small algebraic theory, i.e., an algebraic theory with a rank in the sense of Linton. The category

A

\mathcal {A}

of

Π
\Pi

-coalgebras in

R

\mathcal {R}

is the category of coproduct-preserving functors

Π

∗

→

R

{\Pi ^{\ast }} \to \mathcal {R}

. We prove that the standard forgetful functor

U
:

A

→

R

U:\mathcal {A} \to \mathcal {R}

has a right adjoint

V
V

.
Injective endormorphisms of finitely generated modules
Authors: Vasconcelos Wolmer V.
Published: June 2010

Let

R
R

be a commutative ring. Then any infective endomorphism of a finitely generated

R
R

-module is always an isomorphism if and only if

R
R

is

0
0

-dimensional, that is, if every prime ideal is maximal.
Direct product decomposition of commutative semi-simple rings
Authors: Abian Alexander
Published: June 2010

In this paper it is shown that a commutative semisimple ring is isomorphic to a direct product of fields if and only if it is hyperatomic and orthogonally complete.
𝔉-projective objects
Authors: Hall C. E.
Published: June 2010

Previously, projective abelian topological groups were defined based upon the requirement that free abelian topological groups be projective. In the present paper it is observed that a similar definition of projective relative to a functor which has a right adjoint leads to equivalent results in a much more general setting. These results are then specialized to the category of topological groups (with Markov’s free functor) for a detailed example.
Closed Baire sets are (sometimes) zero-sets
Authors: Comfort W. W.
Published: June 2010

It is a theorem essentially due to Paul Halmos [H, 51.D] that each compact Baire set is a zero-set. Kenneth A. Ross and Karl Stromberg [RS] have shown (a bit more than the fact that) if

X
X

is a completely regular Hausdorff space which is locally compact and

σ
\sigma

-compact, then each closed Baire set in

X
X

is a zero-set; the same conclusion is known to hold in case

X
X

is Lindelöf and a

G
δ

{G_\delta }

in

β
X

\beta X

. In the present paper we prove the following theorem, and we show how the “closed Baire set” theorems of Ross and Stromberg emerge as corollaries: If

X
X

is Baire in

β
X

\beta X

and

A
A

is a closed Baire set in

X
X

, then

A
A

is a zero-set in

X
X

. Finally, we indicate how our theorem, and hence those of Ross and Stromberg, can be derived from early and forthcoming work of Frolík.
Nonoscillation theorems for a nonlinear differential equation
Authors: Gollwitzer H. E.
Published: June 2010

This paper is concerned with the problem of specifying growth conditions on the positive function

q
(
t
)

q(t)

which imply that all solutions of the nonlinear second order ordinary differential equation

y
+
q
(
t
)

|

y

|

α

sgn
⁡
y
=
0
,
α
>
0

y + q(t)|y{|^\alpha }\operatorname {sgn} y = 0,\alpha > 0

, are nonoscillatory on a half line. Several different results are given, and the usual explicit monotonicity condition on

q
q

has been avoided to a certain degree.
Oscillatory criteria for nonlinear matrix differential inequalities.
Authors: Swanson C. A.
Published: June 2010

Oscillation criteria are established for nonlinear matrix differential equations of the form

[
A
(
x
)

V
′

]
′

+
B
(
x
,

V
,

V
′

)
V
=
0

[A(x)V’]’ + B(x,\;V,\;V’)V = 0

and associated differential inequalities. The hypothesis used recently by E. C. Tomastik, that

A
A

and

B
B

are positive definite, is weakened to the following:

A
A

is positive semidefinite.
Some oscillation properties of selfadjoint elliptic equations
Authors: Headley V. B.
Published: June 2010

In this paper a method is given for generalizing to partial differential equations known nonoscillation theorems for second order ordinary differential equations. As illustrations, two theorems of Hille (one of integral type and one of limit type) are generalized to obtain nonoscillation criteria for second order linear elliptic differential equations on unbounded domains

G
G

in

n
n

-dimensional Euclidean space

R
n

{R^n}

.
Solutions of 𝑓(𝑥)=𝑓(𝑎)+(𝑅𝐿)∫ₐ^{𝑥}(𝑓𝐻+𝑓𝐺) for rings
Authors: Helton Burrell W.
Published: June 2010

We show that there is a solution

f
f

of the equation
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="f left-parenthesis x right-parenthesis equals f left-parenthesis a right-parenthesis plus left-parenthesis upper R upper L right-parenthesis integral Subscript a Superscript x Baseline left-parenthesis f upper H plus f upper G right-parenthesis">

f
(
x
)
=
f
(
a
)
+
(
R
L
)

∫
a
x

(
f
H
+
f
G
)

f(x) = f(a) + (RL)\int _a^x {(fH + fG)}

\]
such that

f
(
p
)
=
0

f(p) = 0

and

f
(
q
)
≠
0

f(q) \ne 0

for some pair

p
,
q
∈
[
a
,
b
]

p,q \in [a,b]

iff there is a number

t
∈
[
a
,
b
]

t \in [a,b]

such that one of
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="1 minus upper H left-parenthesis t Superscript minus Baseline comma t right-parenthesis comma 1 minus upper H left-parenthesis t comma t Superscript plus Baseline right-parenthesis comma 1 plus upper G left-parenthesis t Superscript minus Baseline comma t right-parenthesis">

1
−
H
(

t
−

,
t
)
,
1
−
H
(
t
,

t
+

)
,
1
+
G
(

t
−

,
t
)

1 - H({t^ - },t),1 - H(t,{t^ + }),1 + G({t^ - },t)

or

1
+
G
(
t
,

t
+

)

1 + G(t,{t^ + })

is zero or a right divisor of zero, where

f
,
G

f,G

and

H
H

are functions of bounded variation with ranges in a normed ring

N
N

. Furthermore, if

N
N

is a field, then for each discontinuity of

H
H

on

[
a
,
b
]

[a,b]

there exists

λ
∈
N

\lambda \in N

and a finite set of linearly independent nonzero solutions on

[
a
,
b
]

[a,b]

of the equation
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="f left-parenthesis x right-parenthesis equals f left-parenthesis a right-parenthesis plus left-parenthesis upper R upper L right-parenthesis integral Subscript a Superscript x Baseline left-parenthesis f upper H plus f upper G right-parenthesis lamda">

f
(
x
)
=
f
(
a
)
+
(
R
L
)

∫
a
x

(
f
H
+
f
G
)
λ

f(x) = f(a) + (RL)\int _a^x {(fH + fG)\lambda }

such that if

f
f

is a solution and has bounded variation on

[
a
,
b
]

[a,b]

, then

f
f

is a linear combination of this set of solutions. Product integrals are used extensively in the proofs.
Decomposable compact convex sets and peak sets for function spaces.
Authors: Asimow Leonard
Published: June 2010

Geometric conditions are known under which a closed face of a compact convex set is a peak set with respect to the space of continuous affine (real-valued) functions. The purpose of this note is to give an application of this “abstract-geometric” set-up to the problem of finding peak sets (or points) in a compact Hausdorff space with respect to a closed subspace of continuous complex-valued functions. In this fashion we obtain the strong hull criteria of Curtis and Figá-Talamanca and in particular the Bishop peak point theorem for function algebras.
Properties Γ and 𝐿 for type 𝐼𝐼₁ factors
Authors: Willig Paul
Published: June 2010

Using the new concept of central sequences introduced by Dixmier and Lance, it is proved that for a type

II
1

{\operatorname {II} _1}

factor on a separable Hilbert space properties

Γ
\Gamma

and

L
L

are equivalent.
A sufficient condition that the limit of a sequence of continuous functions be an embedding
Authors: Edwards J. R.
Published: June 2010

Suppose

X
X

is a metric space, and

Y
Y

is a complete metric space. In this paper a sufficient condition is given to insure that a sequence of continuous functions from

X
X

into

Y
Y

converge to an embedding from

X
X

into

Y
Y

.
A duality between spheres and spheres with arcs
Authors: Sikkema Carl D.
Published: June 2010

The purpose of this paper is to extend the authors duality between nearly tame spheres and nearly tame arcs to a duality between wild spheres and tame spheres with nearly tame arcs properly attached, one arc for each wild point of the wild sphere.
Cup product in projective spaces
Authors: Lam Kee Yuen
Published: June 2010

Cup product in projective spaces is computed by an elementary method.
On a hierarchy of generalized diagonal dominance properties for complex matrices
Authors: Brenner J. L. , Brown W. G.
Published: June 2010

This article concerns dominance conditions for an

n
×
m

n \times m

matrix. In the simplest kind of dominance, the (absolute) value of the diagonal element exceeds the sum of the absolute values of the nondiagonal elements on the same row. This condition has been generalized in the literature in several ways, of which we consider ways in which the rows of the matrix cooperate. Our work amounts to a sorting out of certain dominance conditions that belong to a class

C

\mathcal {C}

of dominance conditions. We prove a theorem characterizing all true statements of the form
\[

C
1

,

C
2

,
⋯
,

C
s

⇒

C
0

{C_1},{C_2}, \cdots ,{C_s} \Rightarrow {C_0}

\]
where

C
i

∈

C

(
i
=
0
,
1
,
⋯
,
s
)

{C_i} \in \mathcal {C}(i = 0,1, \cdots ,s)

.
Irreducible polynomial identities in anticommutative algebras
Authors: Kass Seymour , Witthoft William G.
Published: June 2010

The methods introduced by J. M. Osborn for isolating those polynomial identities worth studying in commutative algebras are here modified to yield three theorems for anticommutative algebras. The first establishes a practical criterion for the irreducibility of polynomial identities; the others list all canonical polynomials of low degree that are irreducible relative to anticommutativity.
On a conjecture of E. Granirer concerning the range of an invariant mean
Authors: Chou Ching
Published: June 2010

The purpose of this paper is to prove the following conjecture of E. Granirer: if

S
S

is an infinite right cancellation left amenable semigroup then for each left invariant mean

ϕ
\phi

of

S
S

.
Regularity of Baire measures
Authors: Dinculeanu N. , Lewis Paul W.
Published: June 2010

In a recent paper N. Dinculeanu and I. Kluvánek showed that any Baire measure with values in a locally convex topological vector space is regular. Their construction depended heavily on the regularity of nonnegative Baire measures. In the present paper, a proof of the regularity is given which holds at once for the nonnegative case and the vector case.
An approximate solution of the Riccati matrix equation
Authors: Henry M. S. , Stein F. M.
Published: June 2010

The Riccati matrix equation has been the subject of several recent papers. In the present paper, the solution to this equation is approximated by a sequence of matrices whose elements are rational functions. It is shown that the sequence converges uniformly to the solution. Furthermore, each element of the sequence is constructed from a matrix polynomial which is in a sense the best approximation to the solution of the linear system associated with the Riccati matrix equation.
On multipliers and order-bounded operators in 𝐶*-algebras
Authors: Andersen Tage Bai
Published: June 2010

It is shown that the selfadjoint multipliers from a sub-

C

∗

{C^{\ast }}

-algebra to the bigger

C

∗

{C^{\ast }}

-algebra are exactly the order-bounded operators. As a corollary we get a characterization of the relative commutant of a sub-

C

∗

{C^{\ast }}

-algebra with unit.
The automorphism group of a product of graphs
Authors: Miller Donald J.
Published: June 2010

In a recent paper we showed that every connected graph can be written as a weak cartesian product of a family of indecomposable rooted graphs and that this decomposition is unique to within isomorphisms. Using this unique prime factorization theorem we prove that if a graph

X
X

can be written as a product of connected rooted graphs, which are pairwise relatively prime, then the automorphism group of

X
X

is isomorphic to the restricted direct product of the automorphism groups of the factors with prescribed subgroups the isotropy groups of the factors at the roots. This is a generalization of Sabidussi’s theorem for cartesian multiplication.
On 𝔉-normalizers
Authors: Yen Ti
Published: June 2010

The concept of system normalizers of a finite solvable group is generalized to any saturated formation

F

\mathfrak {F}

. Given a Sylow system

Σ
\Sigma

of the finite solvable group

G
G

and an

F

\mathfrak {F}

-projector

V
V

of

G
G

reducing

Σ
\Sigma

, a sequence

{

H
i

}

\{ {H_i}\}

of subgroups

H
i

{H_i}

, is constructed such that (i) each

H
i

{H_i}

reduces

Σ
\Sigma

, and (ii) the

F

\mathfrak {F}

-normalizers of

Σ
∩

H
i

\Sigma \cap {H_i}

in

H
i

{H_i}

converge to

V
V

.
Subsemigroups of an amenable group
Authors: Jenkins Joe W.
Published: June 2010

The following example is presented.

G
G

is a nondiscrete locally compact amenable group.

H
H

is a subgroup of

G
G

with zero Haar measure such that if

g
∈
G
∼
H

g \in G \sim H

then (i) there is a subsemigroup

S
=

⋃

n
=
0

∞

I
n

S = \bigcup \nolimits _{n = 0}^\infty {{I_n}}

of

G
G

where the

I
n

′

s

{I_n}’s

are open pairwise disjoint ideals of

S
S

(all right- or all left-ideals) and (ii)

g
∈

I
0

g \in {I_0}

.
Strongly branched coverings of closed Riemann surfaces
Authors: Accola Robert D. M.
Published: June 2010

Let

b
:

W
1

→

W
2

b:{W_1} \to {W_2}

be a

B
B

-sheeted covering of closed Riemann surfaces of genera

p
1

{p_1}

and

p
2

{p_2}

respectively.

b
b

is said to be strongly branched if

p
1

>

B
2

p
2

+

(
B
−
1

)
2

{p_1} > {B^2}{p_2} + {(B - 1)^2}

. If

M
2

{M_2}

is the function field on

W
1

{W_1}

obtained by lifting the field from

W
2

{W_2}

to

W
1

{W_1}

, then

M
2

{M_2}

is said to be a emphstrongly branched subfield if the same condition holds. If

M
1

{M_1}

admits a strongly branched subfield, then there is a unique maximal one. If

M
2

{M_2}

is this unique one and

f
f

is a function in

M
1

{M_1}

so that
\[

(
B
−
1
)
o
(
f
)
>
(

p
1

−
B

p
2

)
+
(
B
−
1
)

(B - 1)o(f) > ({p_1} - B{p_2}) + (B - 1)

\]
then

f
∈

M
2

f \in {M_2}

, where

o
(
f
)

o(f)

is the order of

f
f

. (This is a generalization of the hyperelliptic situation.) These results are applied to groups of automorphisms of

W
1

{W_1}

to obtain another generalization of the hyperelliptic case.
On the growth of certain meromorphic solutions of arbitrary second order algebraic differential equations
Authors: Bank Steven
Published: June 2010

In this note, we present two results concerning meromorphic functions on the whole finite plane, which are solutions of algebraic differential equations (i.e., equations of the form

Ω
(
z
,
y
,
d
y

/

d
z
,
⋯
,

d
n

y

/

d

z
n

)
=
0

\Omega (z,y,dy/dz, \cdots ,{d^n}y/d{z^n}) = 0

, where

Ω
\Omega

is a polynomial in

z
,
y
,
d
y

/

d
z
,
⋯
,

d
n

y

/

d

z
n

)

z,y,dy/dz, \cdots ,{d^n}y/d{z^n})

.
A note on subparacompact spaces
Authors: Hodel R. E.
Published: June 2010

The main result in this paper states that every metacompact space in which every closed set is a

G
δ

{G_\delta }

is subparacompact. The class of countably subparacompact spaces is introduced and several results about such spaces are proved.