bluuebunny/crossref_metadata_2025_split huggingface dataset:
The rate of convergence of Chebyshev polynomials for functions which have asymptotic power series about one endpoint
Authors: Boyd John P. 
Published: June 2010

The theorem proved here extends Chebyshev theory into what has previously been no man’s land: functions which have an infinite number of bounded derivatives on the expansion interval [a, b] but which are singular at one endpoint. The Chebyshev series in

1

/

x

1/x

for all the familiar special functions fall into this category, so this class of functions is very important indeed. In words, the theorem shows that the more slowly the asymptotic power series about the singular point converges, the slower the convergence of the corresponding Chebyshev series must be. More formally, if

f
(
x
)

f(x)

, analytic on [a, b), is singular at

x
=
b

x = b

in such a way that it has an asymptotic power series

f
(
x
)
∼
Σ

a
n

(
x
−
b

)
n

f(x) \sim \Sigma \,{a_n}{(x - b)^n}

about that endpoint, then, if
\[

lim

n
→
∞

¯

log
⁡

|

a
n

|

n
log
⁡
n

=
r
,

\overline {\lim \limits _{n \to \infty } } \frac {{\log |{a_n}|}}{{n\log n}} = r,

\]
it is proved that the coefficients of the convergent Chebyshev polynomial series on [a, b],

f
(
x
)
∼
Σ

b
n

T
n

(
y
)

f(x) \sim \Sigma \,{b_n}{T_n}(y)

where

y
=
2
[
x
−
0.5
(
b
+
a
)
]

/

(
b
−
a
)

y = 2[x - 0.5(b + a)]/(b - a)

, satisfy the inequality
\[

lim

n
→
∞

¯

log
⁡

|

(
log
⁡

|

b
n

|

)

|

log
⁡
n

⩽

2

r
+
2

\overline {\lim \limits _{n \to \infty } } \frac {{\log |(\log |{b_n}|)|}}{{\log n}} \leqslant \frac {2}{{r + 2}}

\]
.
Integrals of Jacobi functions
Authors: Kalla Shyam L. , Conde Salvador , Luke Yudell L. 
Published: June 2010

In this paper, we study

∫

−
1

1

(
1
−
x

)
a

(
1
+
x

)
b

P
ν

(
α
,
β
)

(
x
)

d
x

\smallint _{ - 1}^1{(1 - x)^a}{(1 + x)^b}P_\nu ^{(\alpha ,\beta )}(x)\,dx

and its partial derivatives with respect to a and b, where

P
ν

(
α
,
β
)

(
x
)

P_\nu ^{(\alpha ,\beta )}(x)

is the Jacobi function. Our expressions generalize the work of Blue, Gautschi and Gatteschi. The results are useful to derive integration formulas for integrands with algebraic and logarithmic singularities.
Strong primality tests that are not sufficient
Authors: Adams William , Shanks Daniel 
Published: June 2010

A detailed investigation is given of the possible use of cubic recurrences in primality tests. No attempt is made in this abstract to cover all of the many topics examined in the paper. Define a doubly infinite set of sequencesA(n)A(n)by\[A(n+3)=rA(n+2)−sA(n+1)+A(n)A(n + 3) = rA(n + 2) - sA(n + 1) + A(n)\]withA(−1)=sA( - 1) = s,A(0)=3A(0) = 3, andA(1)=rA(1) = r. Ifnis prime,A(n)≡A(1)(modn)A(n) \equiv A(1)\;\pmod n. Perrin asked if any composite satisfies this congruence ifr=0r = 0,s=−1s = - 1. The answer is yes, and our first example leads us to strengthen the condition by introducing the "signature" ofn:\[A(−n−1),A(−n),A(−n+1),A(n−1),A(n),A(n+1)A( - n - 1),A( - n),A( - n + 1),A(n - 1),A(n),A(n + 1)\]modn\bmod n. Primes have three types of signatures depending on how they split in the cubic field generated byx3−rx2+sx−1=0{x^3} - r{x^2} + sx - 1 = 0. Composites with "acceptable" signatures do exist but are very rare. TheS-type signature, which corresponds to the completely split primes, has a very special role, and it may even be thatIandQtype composites do not occur in Perrin’s sequence even though theIandQprimes comprise5/65/6ths of all primes.A(n)(modn)A(n)\;\pmod nis easily computable inO(log⁡n)O(\log n)operations. The paper closes with ap-adic analysis. This powerful tool sets the stage for our [12] which will be Part II of the paper.
On the largest zeroes of orthogonal polynomials for certain weights
Authors: Lubinsky D. S. , Sharif A. 
Published: June 2010

The asymptotic growth of the largest zero of the orthogonal polynomials for the weights

W
(
x
)
=

|

x

|

b

exp
⁡
(
−
k

|

log
⁡

|

x

|

|

c

)

W(x) = |x{|^b}\exp ( - k|\log |x|{|^c})

is investigated.
Some extensions of W. Gautschi’s inequalities for the gamma function
Authors: Kershaw D. 
Published: June 2010

It has been shown by W. Gautschi that if

0
>
s
>
1

0 > s > 1

, then for

x
⩾
1

x \geqslant 1

\[

x

1
−
s

>

Γ
(
x
+
1
)

Γ
(
x
+
s
)

>
exp
⁡
[
(
1
−
s
)
ψ
(
x
+
1
)
]
.

{x^{1 - s}} > \frac {{\Gamma (x + 1)}}{{\Gamma (x + s)}} > \exp [(1 - s)\psi (x + 1)].

\]
The following closer bounds are proved:
\[

exp
⁡
[
(
1
−
s
)
ψ
(
x
+

s

1

/

2

)
]
>

Γ
(
x
+
1
)

Γ
(
x
+
s
)

>
exp
⁡

[

(
1
−
s
)
ψ

(

x
+

s
+
1

2

)

]

\exp [(1 - s)\psi (x + {s^{1/2}})] > \frac {{\Gamma (x + 1)}}{{\Gamma (x + s)}} > \exp \left [ {(1 - s)\psi \left ( {x + \frac {{s + 1}}{2}} \right )} \right ]

\]
and
\[

[

x
+

s
2

]

1
−
s

>

Γ
(
x
+
1
)

Γ
(
x
+
s
)

>

[

x
−

1
2

+

(

s
+

1
4

)

1

/

2

]

1
−
s

.

{\left [ {x + \frac {s}{2}} \right ]^{1 - s}} > \frac {{\Gamma (x + 1)}}{{\Gamma (x + s)}} > {\left [ {x - \frac {1}{2} + {{\left ( {s + \frac {1}{4}} \right )}^{1/2}}} \right ]^{1 - s}}.

\]
These are compared with each other and with inequalities given by T. Erber and J. D. Kečkić and P. M. Vasić.
Further inequalities for the gamma function
Authors: Laforgia Andrea 
Published: June 2010

For

λ
>
0

\lambda > 0

and

k
⩾
0

k \geqslant 0

we present a method which permits us to obtain inequalities of the type

(
k
+
α

)

λ
−
1

>
Γ
(
k
+
λ
)

/

Γ
(
k
+
1
)
>

(
k
+
β

)

λ
−
1

{(k + \alpha )^{\lambda - 1}} > \Gamma (k + \lambda )/\Gamma (k + 1) > {(k + \beta )^{\lambda - 1}}

, with the usual notation for the gamma function, where

α
\alpha

and

β
\beta

are independent of k. Some examples are also given which improve well-known inequalities. Finally, we are also able to show in some cases that the values

α
\alpha

and

β
\beta

in the inequalities that we obtain cannot be improved.
Sharp convergence rates for nonlinear product formulas
Authors: Schechter Eric 
Published: June 2010

Nonlinear versions of the Lie-Trotter product formula

exp
⁡
[
t
(
A
+
B
)
]
=

lim

n
→
∞

[
exp
⁡
(
(
t

/

n
)
A
)
exp
⁡
(
(
t

/

n
)
B
)

]
n

\exp [t(A + B)] = {\lim _{n \to \infty }}{[\exp ((t/n)A)\exp ((t/n)B)]^n}

and related formulas are given in this paper. The convergence rates are optimal. The results are applicable to some nonlinear partial differential equations.
Further extensions of a Legendre function integral
Authors: Fettis Henry E. 
Published: June 2010

The integral
\[

∫
z
1

(

1
−
t

2

)

β
−
1

(

1
−
t

1
+
t

)

μ

/

2

ln
⁡

(

1
−
t

2

)

P

ν
−
1

μ

(
t
)

d
t

\int _z^1 {{{\left ( {\frac {{1 - t}}{2}} \right )}^{\beta - 1}}{{\left ( {\frac {{1 - t}}{{1 + t}}} \right )}^{\mu /2}}\ln \left ( {\frac {{1 - t}}{2}} \right )P_{\nu - 1}^\mu (t)\;dt}

\]
is evaluated as a hypergeometric function for arbitrary values of

ν
\nu

,

μ
\mu

,

−
1
⩽
z
⩽
1

- 1 \leqslant z \leqslant 1

, and

Re
⁡
(
β
)
>
0

\operatorname {Re} (\beta ) > 0

.
Fast primality tests for numbers less than 50⋅10⁹
Authors: Kurtz G. C. , Shanks Daniel , Williams H. C. 
Published: June 2010

Consider the doubly infinite set of sequences

A
(
n
)

A(n)

given by
\[

A
(
n
+
3
)
=
r
A
(
n
+
2
)
−
s
A
(
n
+
1
)
+
A
(
n
)

A(n + 3) = rA(n + 2) - sA(n + 1) + A(n)

\]
with

A
(
−
1
)
=
s

A( - 1) = s

,

A
(
0
)
=
3

A(0) = 3

,

A
(
1
)
=
r

A(1) = r

. For a given pair r,s, the "signature" of n is defined to be the sextet
\[

A
(
−
n
−
1
)
,
A
(
−
n
)
,
A
(
−
n
+
1
)
,
A
(
n
−
1
)
,
A
(
n
)
,
A
(
n
+
1
)
,

A( - n - 1),A( - n),A( - n + 1),A(n - 1),A(n),A(n + 1),

\]
each reduced modulo n. Primes have only three types of signatures, depending on how they split in the cubic field generated by

x
3

−
r

x
2

+
s
x
−
1

{x^3} - r{x^2} + sx - 1

. An "acceptable" composite is a composite integer which has the same type of signature as a prime; such integers are very rare. In this paper, a description is given of the results of a computer search for all acceptable composites

⩽
50
⋅

10
9

\leqslant 50 \cdot {10^9}

in the Perrin sequence

(
r
=
0
,
s
=
−
1
)

(r = 0,s = - 1)

. Also, some numbers which are acceptable composites for both the Perrin sequence and the sequence with

r
=
1

r = 1

,

s
=
0

s = 0

are presented.
Hyperelliptic integrals and multiple hypergeometric series
Authors: Loiseau Jean-Francis , Codaccioni Jean-Pierre , Caboz Régis 
Published: June 2010

We consider the complete hyperelliptic integral
\[

J
(
a
)
=

∫

α
(
a
)

β
(
a
)

d
x

a
−

P
n

(
x
)

,

J(a) = \int _{\alpha (a)}^{\beta (a)} {\frac {{dx}}{{\sqrt {a - {P_n}(x)} }},}

\]
where

a
>
0

a > 0

and
\[

P
n

(
x
)
=

∑

k
=
2

n

λ
k

x
k

,

{P_n}(x) = \sum \limits _{k = 2}^n {{\lambda _k}{x^k},}

\]
with

λ
2

>
0
,
[
α
,
β
]

{\lambda _2} > 0,[\alpha ,\beta ]

being the connected component of

{
x

|

P
n

(
x
)
≤
a
}

\{ x|{P_n}(x) \leq a\}

containing the origin. Using a recent result concerning the Taylor expansion of the

δ
\delta

-Dirac function, we write

J
(
a
)

J(a)

as a power series of a parameter involving a and the

λ
k

{\lambda _k}

’s. We prove this series to be a sum of multiple hypergeometric series which reduces to a single term when the number of odd monomial terms in

P
n

{P_n}

is less than or equal to one. The region of convergence is then studied and a few particular cases are detailed.
Some infinite product identities
Authors: Blecksmith Richard , Brillhart John , Gerst Irving 
Published: June 2010

In this paper we derive the power series expansions of four infinite products of the form
\[

∏

n
∈

S
1

(
1
−

x
n

)

∏

n
∈

S
2

(
1
+

x
n

)
,

\prod \limits _{n \in {S_1}} {(1 - {x^n})\;\prod \limits _{n \in {S_2}} {(1 + {x^n}),} }

\]
where the index sets

S
1

{S_1}

and

S
2

{S_2}

are specified with respect to a modulus (Theorems 1, 3, and 4). We also establish a useful formula for expanding the product of two Jacobi triple products (Theorem 2). Finally, we give nonexistence results for identities of two forms.
On the mean iteration (𝑎,𝑏)←((𝑎+3𝑏)/4,(√𝑎𝑏+𝑏)/2)
Authors: Borwein J. M. , Borwein P. B. 
Published: June 2010

The iterative process
\[

a

n
+
1

=
(

a
n

+
3

b
n

)

/

4
,

b

n
+
1

=
(

a
n

b
n

+

b
n

)

/

2

{a_{n + 1}} = ({a_n} + 3{b_n})/4,\quad {b_{n + 1}} = (\sqrt {{a_n}{b_n}} + {b_n})/2

\]
is studied in detail. The limit of this quadratically converging process is explicitly identified, as are the uniformizing parameters. The role of symbolic computation, in discovering these nontrivial identifications, is highlighted.
Factorization tables for trinomials over 𝐺𝐹(𝑞)
Authors: Beard, Jr. Jacob T. B. , West Karen I. 
Published: June 2010

Tables placed in the UMT file give the complete factorization over

GF

(
q
)
,
q
=

p
a

{\text {GF}}(q),q = {p^a}

, of each trinomial

T
(
x
)

T(x)

of degree

n
,
2
⩽
n
⩽
d

n, 2 \leqslant n \leqslant d

, as below, together with the generalized Euler

Φ
\Phi

-function whenever

T
(
x
)

T(x)

is not prime and

Φ
(
T
(
x
)
)
>

10
8

\Phi (T(x)) > {10^8}

. In addition, the numerical exponent and q-polynomial is given for each

T
(
x
)

T(x)

whenever

2
⩽
n
⩽

d
1

2 \leqslant n \leqslant {d_1}

.
\[

q
=
2
:
d
=
20
,

d
1

=
18
,

a
m
p
;

q
=
5
:
d
=
15
,

d
1

=
8
,

q
=

2
2

:
d
=
16
,

d
1

=
10
,

a
m
p
;

q
=
7
:
d
=
10
,

d
1

=
7
,

q
=

2
3

:
d
=
9
,

d
1

=
7
,

a
m
p
;

q
=
11
:
d
=
7
,

q
=

2
4

:
d
=
8
,

a
m
p
;

q
=
13
:
d
=
7
,

q
=
3
:
d
=
18
,

d
1

=
9
,

a
m
p
;

q
=
17
:
d
=
7
,

q
=

3
2

:
d
=
9
,

a
m
p
;

q
=
19
:
d
=
7.

\begin {array}{*{20}{c}} {q = 2:d = 20,{d_1} = 18,} \hfill & {q = 5:d = 15,{d_1} = 8,} \hfill \\ {q = {2^2}:d = 16,{d_1} = 10,} \hfill & {q = 7:d = 10,{d_1} = 7,} \hfill \\ {q = {2^3}:d = 9,{d_1} = 7,} \hfill & {q = 11:d = 7,} \hfill \\ {q = {2^4}:d = 8,} \hfill & {q = 13:d = 7,} \hfill \\ {q = 3:d = 18,{d_1} = 9,} \hfill & {q = 17:d = 7,} \hfill \\ {q = {3^2}:d = 9,} \hfill & {q = 19:d = 7.} \hfill \\ \end {array}

\]
On a microfiche card with this note, selected results from the above appear as Table I-Table IV as follows:
\[

q
=
2
:
d
=
20
,

d
1

=
18
,

a
m
p
;

q
=
3
:
d
=
11
,

d
1

=
9
,

q
=

2
2

:
d
=
8
,

d
1

=
8
,

a
m
p
;

q
=
5
:
d
=
5
,

d
1

=
5.

\begin {array}{*{20}{c}} {q = 2:d = 20,{d_1} = 18,} \hfill & {q = 3:d = 11,{d_1} = 9,} \hfill \\ {q = {2^2}:d = 8,{d_1} = 8,} \hfill & {q = 5:d = 5,{d_1} = 5.} \hfill \\ \end {array}

\]
As evidenced by these tables, there does not necessarily exist a prime trinomial of given degree n over arbitrary

GF

(
q
)

{\text {GF}}(q)

.
Electron back‐scattering diffraction (EBSD) measurements of antigorite lattice‐preferred orientations (LPO)
Authors: VAN DE MOORTÈLE B. , BEZACIER L. , TRULLENQUE G. , REYNARD B. 
Published: June 2010

SummaryLattice preferred orientations of serpentines induce a strong anisotropy of various properties in serpentine bearing‐rocks. Lattice preferred orientations had so far been obtained only by X‐ray diffraction techniques. We have applied electron back‐scattering diffraction to the measurement of the lattice preferred orientations of antigorite in a naturally deformed high‐pressure serpentinite. This technique is very sensitive to sample preparation that can lead to surface amorphization in the case of serpentine. A polishing procedure is described that avoids amorphization and allows accurate electron back‐scattering diffraction measurements with optimized experimental conditions in a variable pressure scanning electron microscope. Results indicate that deformation leads to lattice preferred orientations characterized by extremely strong c‐axis clustering perpendicular to the foliation, as expected for a layered silicate. In the foliation plane, a significant clustering of the a‐axis is observed and tentatively attributed to intracrystalline deformation mechanisms. These data suggest that antigorite deforms mostly by gliding along the basal plane of the layered phyllosilicate structure, but that gliding may occur along directions favouring a‐axis alignment. Electron back‐scattering diffraction appears to be a reliable method for determining phyllosilicate lattice preferred orientations in deformed rocks, with potential applications for determining anisotropy of properties like seismic velocities or thermal and electrical conductivities.
Comparative study of the retinal vessel anatomy of rhesus monkeys and humans
Authors: Kong Xiangmei , Wang Kaidi , Sun Xinghuai , Witt Rachel E 
Published: June 2010

AbstractObjectives:  This study aims to compare retinal vessel anatomy of normal rhesus monkeys and humans and to provide a basis from a structural perspective for the use of rhesus monkey as an experimental model in future studies of retinal vessels.Methods:  The retinas of six normal rhesus monkey eyes and eight human eyecups following corneal transplantation were obtained and stained using adenosine diphosphatase methods. The distributions, orders, layers of the retinal vessels and the perifoveal vascular ring were compared.Results:  With adenosine diphosphatase staining, distinct retinal vessels were fully discernable from the first order surrounding the optic disc to the fifth order. There were no statistically significant differences between rhesus monkeys and humans in the percentages of vessels surrounding the optic disc at the equator and the peripheral region. Vascular networks in both species were arranged in several layers around the optic disc, two anastomotic layers at the equator and one sparse layer peripherally. Capillaries at the macular area were quite dense and an intact perifoveal vascular ring was observed. No differences were observed between rhesus monkeys and humans in the percentage area of the vessels and the area, perimeter and diameter of the perifoveal vascular ring.Conclusions:  The distributions, orders, layers and the perifoveal vascular ring of the retinal vessels of rhesus monkey are quite similar to those of humans. The data suggest that from an anatomical perspective, the rhesus monkey is a good animal model for the study of human retinal vessels, particularly the macular capillaries.
Air pollution impedes plant‐to‐plant communication by volatiles
Authors: Blande James D. , Holopainen Jarmo K. , Li Tao 
Published: June 2010

Ecology Letters (2010) 13: 1172–1181AbstractVolatile organic compounds (VOCs) emitted by damaged plants convey information to undamaged neighbouring plants, and previous research has shown that these signals are effective over short distances in nature. Many herbivore‐induced VOCs react with ozone, which is the most important tropospheric air pollutant in rural areas. We used extrafloral nectar (EFN) secretion as a phenotypic indicator of between‐plant communication in Phaseolus lunatus L. (Lima bean) and show that an ozone‐rich (80 ppb) atmosphere reduces the distance over which signalling occurs. We found that ozone degrades several herbivore‐induced VOCs, a likely mechanism reducing communication distances. Direct exposure to 80‐ppb ozone did not affect the VOC emissions from P. lunatus. In addition, we demonstrated that high ozone concentrations, 120 and 160 ppb, induced EFN secretion in exposed plants, whereas more moderate concentrations, 80 and 100 ppb, did not. This suggests that ozone can play a complex role in the indirect defence of P. lunatus.
Planning changes to health library services on the basis of impact assessment
Authors: Urquhart Christine , Thomas Rhian , Ovens Jason , Lucking Wendy , Villa Jane 
Published: June 2010

AbstractBackground:  Various methods of impact assessment for health library services exist, including a toolkit developed for the UK. The Knowledge, Resource and Information service (KRIS) for health promotion, health service commissioning and public health (Bristol area, UK) commissioned an independent team at Aberystwyth University to provide an impact assessment and evaluation of their services and to provide evidence for future planning.Objective:  The review aimed to provide an action plan for KRIS through assessing the impact of the current service, extent of satisfaction with existing services and views on desirable improvements.Methods:  Existing impact toolkit guidance was used, with an adapted impact questionnaire, which was distributed by the KRIS staff to 244 users (response rate 62.3%) in early 2009. The independent team analysed the questionnaire data and presented the findings.Results:  Users valued the service (93% considered that relevant information was obtained). The most frequent impacts on work were advice to patients, clients or carers, and advice to colleagues. Literature searching and current awareness services saved staff time. Many users were seeking health promotion materials.Conclusion:  The adapted questionnaire worked well in demonstrating the service impacts achieved by KRIS, as well as indicating desirable improvements in service delivery.
Celebrating the role of health information
Authors: Grant Maria J. 
Published: June 2010

AbstractThis inaugural virtual issue of the Health Information and Libraries Journal (HILJ) celebrates the contribution of health information in informing health and social care library and information provision. It has been drawn together to reflect the 2010 biennial Health Libraries Group conference theme of Keeping Information Centre Stage Amid Changing Scenery and includes a series of eleven key papers published in the journal over the last two years. This virtual issue mirrors the usual format of a journal issue with a review article, original articles and regular features on Learning and Teaching in Action, Using Evidence in Practice and International Perspectives and Initiatives. All papers included in this virtual issue of Health Information and Libraries Journal are available free online.
Operations research/management science contributions to peace studies
Authors: Bartolucci Valentina , Gallo Giorgio 
Published: June 2010

AbstractThe discourse on ethics in operations research/management science (OR/MS) has many aspects. Among them there is the ethical responsibility the OR/MS community faces in a world in which the widespread presence of structural violence makes the construction of a peaceful and sustainable social order a very challenging task, and puts at risk the very survival of human kind. In this paper we want to emphasize the role of the systemic approach, which is proper of OR/MS, with respect to the issue of peace, and in particular within the Peace Studies area.
Interproximal periodontal defect model in dogs: a pilot study
Authors: Jung U‐W , Chang Y‐Y , Um Y‐J , Kim C‐S , Cho K‐S , Choi S‐H 
Published: June 2010

Oral Diseases (2010) 17, 26–32Objective:  This study aimed to evaluate the validity of a surgically created interproximal periodontal defect in dogs.Materials and methods:  Surgery was performed in the interproximal area between the maxillary second and third premolars in two beagle dogs. Following an incision and reflection of the gingival flap, a 3‐mm wide and 5‐mm high defect was prepared surgically at the interproximal area. A thorough root planing was performed and the flap was coronally positioned and sutured. The contra‐lateral area was served as the control with no surgical intervention. After 8 weeks of healing, the animals were killed and the defect was analysed histometrically and radiographically.Results:  The interproximal periodontal defect resembled a naturally occurring defect and mimicked a clinical situation. After healing, the defect showed limited bone (0.89 ± 0.02 mm) and cementum regeneration (1.50 ± 0.48 mm).Conclusions:  Within the limitations of this pilot study, the interproximal periodontal defect showed limited bone and cementum regeneration. Thus, it can be considered as a standardized, reproducible defect model for testing new biomaterials.
Smoking and ulcer perforation
Authors: Svanes C , Søreide J A , Skarstein A , Fevang B T , Bakke P , Vollset S E , Svanes K , Søreide O 
Published: June 2010

Background—The use of ulcerogenic drugs is the only well documented risk factor for peptic ulcer perforation, but accounts for only a quarter of the events. Smoking is a well known risk factor for uncomplicated ulcer disease, and patients with ulcer bleeding have increased death rates from smoking related disorders.Aim—To assess the role of smoking in ulcer perforation.Subjects—A total of 168 consecutive patients with gastroduodenal ulcer perforation and 4469 control subjects from a population based health survey.Methods—The association between ulcer perforation and smoking habits was analysed by logistic regression while adjusting for age and sex.Results—Current smoking increased the risk for ulcer perforation 10-fold in the age group 15–74 years (OR 9.7, 95% CI 5.9 to 15.8) and there was a highly significant dose-response relationship (p<0.001). The results were similar in men (OR 9.3, 95% CI 4.9 to 17) and women (OR 11.6, 95% CI 5.3 to 25), and for gastric (OR 10.5, 95% CI 4.5 to 25) and duodenal (OR 8.6, 95% CI 4.9 to 15.4) ulcer perforation. No increase in risk was found in previous smokers (OR 0.8, 95% CI 0.2 to 2.2).Conclusion—Our findings suggest that smoking is a causal factor for ulcer perforation and accounts for a major part of ulcer perforations in the population aged less than 75 years.