bluuebunny/crossref_metadata_2025_split huggingface dataset:
Multiplicative convolution of real asymmetric and real anti-symmetric matrices
Authors: Kieburg Mario , Forrester Peter J. , Ipsen Jesper R. 
Published: January 2019

AbstractThe singular values of products of standard complex Gaussian random matrices, or sub-blocks of Haar distributed unitary matrices, have the property that their probability distribution has an explicit, structured form referred to as a polynomial ensemble.
It is furthermore the case that the corresponding bi-orthogonal system can be determined in terms of Meijer G-functions, and the correlation kernel given as an explicit double contour integral.
It has recently been shown that the Hermitised product {X_{M}\cdots X_{2}X_{1}AX_{1}^{T}X_{2}^{T}\cdots X_{M}^{T}}, where each {X_{i}} is a standard real Gaussian matrix and A is real anti-symmetric, exhibits analogous properties.
Here we use the theory of spherical functions and transforms to present a theory which, for even dimensions, includes these properties of the latter product as a special case.
As an example we show that the theory also allows for a treatment of this class of Hermitised product when the {X_{i}} are chosen as sub-blocks of Haar distributed real orthogonal matrices.
Inversion of the Initial Value for a Time-Fractional Diffusion-Wave Equation by Boundary Data
Authors: Jiang Suzhen , Liao Kaifang , Wei Ting 
Published: January 2019

Abstract
In this study, we consider an inverse problem of recovering the initial value for a multi-dimensional time-fractional diffusion-wave equation.
By using some additional boundary measured data, the uniqueness of the inverse initial value problem is proven by the Laplace transformation and the analytic continuation technique.
The inverse problem is formulated to solve a Tikhonov-type optimization problem by using a finite-dimensional approximation.
We test four numerical examples in one-dimensional and two-dimensional cases for verifying the effectiveness of the proposed algorithm.
A New Probabilistic Interpretation of the Bramble–Hilbert Lemma
Authors: Chaskalovic Joël , Assous Franck 
Published: January 2019

Abstract
The aim of this paper is to provide new perspectives on relative finite element accuracy which is usually based on the asymptotic speed of convergence comparison when the mesh size h goes to zero. Starting from a geometrical reading of the error estimate due to the Bramble–Hilbert lemma, we derive two probability distributions that estimate the relative accuracy, considered as a random variable, between two Lagrange finite elements

P
k

{P_{k}}

and

P
m

{P_{m}}

(

k
<
m

{k<m}

). We establish mathematical properties of these probabilistic distributions and we get new insights which, among others, show that

P
k

{P_{k}}

or

P
m

{P_{m}}

is more likely accurate than the other, depending on the value of the mesh size h.
Structure theorems for singular minimal laminations
Authors: Meeks III William H. , Pérez Joaquín , Ros Antonio 
Published: January 2019

Abstract
We apply the local removable singularity theorem for
minimal laminations [W. H. Meeks III, J. Pérez and A. Ros,
Local removable singularity theorems for minimal laminations,
J. Differential Geom. 103 (2016), no. 2, 319–362] and the local picture theorem on
the scale of topology [W. H. Meeks III, J. Pérez and A. Ros,
The local picture theorem on the scale of topology,
J. Differential Geom. 109 (2018), no. 3, 509–565] to obtain two descriptive results
for certain possibly singular minimal laminations of

ℝ
3

{\mathbb{R}^{3}}

.
These two global structure theorems will be applied
in [W. H. Meeks III, J. Pérez and A. Ros,
Bounds on the topology and index of classical minimal surfaces,
preprint 2016] to obtain bounds on the index
and the number of ends of complete, embedded minimal surfaces of
fixed genus and finite topology in

ℝ
3

{\mathbb{R}^{3}}

, and in [W. H. Meeks III, J. Pérez and A. Ros,
The embedded Calabi–Yau conjectures for finite genus,
preprint 2018] to prove that a complete, embedded
minimal surface in

ℝ
3

{\mathbb{R}^{3}}

with finite genus and a countable number
of ends is proper.
Linear extension operators between spaces of Lipschitz maps and optimal transport
Authors: Ambrosio Luigi , Puglisi Daniele 
Published: January 2019

Abstract
Motivated by the notion of

K

{K\hskip-0.284528pt}

-gentle partition of unity introduced in [J. R. Lee and A. Naor,
Extending Lipschitz functions via random metric partitions,
Invent. Math. 160 (2005), no. 1, 59–95] and the notion of

K

{K\kern-0.284528pt}

-Lipschitz retract studied in [S. I. Ohta,
Extending Lipschitz and Hölder maps between metric spaces,
Positivity 13 (2009), no. 2, 407–425], we study a weaker notion related to
the Kantorovich–Rubinstein transport distance that we call

K

{K\kern-0.284528pt}

-random projection. We
show that

K

{K\kern-0.284528pt}

-random projections can still be used to provide linear extension operators for Lipschitz maps. We also prove that the existence of these
random projections is necessary and sufficient for the existence of weak

*

{{}^{*}}

continuous operators. Finally, we use this notion to characterize
the metric spaces

(
X
,
d
)

{(X,d)}

such that the free space

ℱ
⁢

(
X
)

{\mathcal{F}(X)}

has the bounded approximation propriety.
Hessenberg varieties and hyperplane arrangements
Authors: Abe Takuro , Horiguchi Tatsuya , Masuda Mikiya , Murai Satoshi , Sato Takashi 
Published: January 2019

Abstract
Given a semisimple complex linear algebraic group

G

{{G}}

and a lower ideal I in positive roots of G, three objects arise:
the ideal arrangement

𝒜
I

{\mathcal{A}_{I}}

, the regular nilpotent Hessenberg variety

Hess
⁡

(
N
,
I
)

{\operatorname{Hess}(N,I)}

, and the regular semisimple Hessenberg variety

Hess
⁡

(
S
,
I
)

{\operatorname{Hess}(S,I)}

.
We show that
a certain graded ring derived from the logarithmic derivation module of

𝒜
I

{\mathcal{A}_{I}}

is isomorphic to

H
*

⁢

(

Hess
⁡

(
N
,
I
)

)

{H^{*}(\operatorname{Hess}(N,I))}

and

H
*

⁢

(

Hess
⁡

(
S
,
I
)

)

W

{H^{*}(\operatorname{Hess}(S,I))^{W}}

,
the invariants in

H
*

⁢

(

Hess
⁡

(
S
,
I
)

)

{H^{*}(\operatorname{Hess}(S,I))}

under an action of the Weyl group W of G.
This isomorphism is shown
for general Lie type,
and generalizes Borel’s celebrated theorem showing that the coinvariant algebra of W is isomorphic to the cohomology ring of the flag variety

G
/
B

{G/B}

.
This surprising connection between Hessenberg varieties and hyperplane
arrangements enables us to produce a number of interesting
consequences. For instance, the surjectivity of the restriction map

H
*

⁢

(

G
/
B

)

→

H
*

⁢

(

Hess
⁡

(
N
,
I
)

)

{H^{*}(G/B)\to H^{*}(\operatorname{Hess}(N,I))}

announced by Dale
Peterson
and an affirmative answer to
a conjecture of Sommers and Tymoczko are immediate consequences. We also
give an explicit ring presentation of

H
*

⁢

(

Hess
⁡

(
N
,
I
)

)

{H^{*}(\operatorname{Hess}(N,I))}

in
types B, C, and G. Such a presentation was already known in type
A and when

Hess
⁡

(
N
,
I
)

{\operatorname{Hess}(N,I)}

is the Peterson variety. Moreover, we find
the volume polynomial of

Hess
⁡

(
N
,
I
)

{\operatorname{Hess}(N,I)}

and see that the hard
Lefschetz property and the Hodge–Riemann relations hold for

Hess
⁡

(
N
,
I
)

{\operatorname{Hess}(N,I)}

, despite the fact that it is a singular variety in general.
Kähler geometry of horosymmetric varieties, and application to Mabuchi’s K-energy functional
Authors: Delcroix Thibaut 
Published: January 2019

Abstract
We introduce a class of almost homogeneous varieties contained in the class of spherical
varieties and containing horospherical varieties as well as complete symmetric
varieties. We develop Kähler geometry on these varieties, with applications to
canonical metrics in mind, as a generalization of the Guillemin–Abreu–Donaldson
geometry of toric varieties. Namely we associate convex functions with Hermitian
metrics on line bundles, and express the curvature form in terms of this function,
as well as the corresponding Monge–Ampère volume form and scalar curvature.
We provide an expression for the Mabuchi functional and derive as an
application a combinatorial sufficient condition of properness similar to
one obtained by Li, Zhou and Zhu on
group compactifications. This finally translates to a sufficient criterion of
existence of constant scalar curvature Kähler metrics thanks to the recent work of
Chen and Cheng. It yields infinitely many new examples of explicit Kähler classes
admitting cscK metrics.
Dehn functions and Hölder extensions in asymptotic cones
Authors: Lytchak Alexander , Wenger Stefan , Young Robert 
Published: January 2019

AbstractThe Dehn function measures the area of minimal discs that fill closed curves in a space; it is an important invariant in analysis, geometry, and geometric group theory. There are several equivalent ways to define the Dehn function, varying according to the type of disc used. In this paper, we introduce a new definition of the Dehn function and use it to prove several theorems. First, we generalize the quasi-isometry invariance of the Dehn function to a broad class of spaces. Second, we prove Hölder extension properties for spaces with quadratic Dehn function and their asymptotic cones. Finally, we show that ultralimits and asymptotic cones of spaces with quadratic Dehn function also have quadratic Dehn function. The proofs of our results rely on recent existence and regularity results for area-minimizing Sobolev mappings in metric spaces.
Rational torsion of generalized Jacobians of modular and Drinfeld modular curves
Authors: Wei Fu-Tsun , Yamazaki Takao 
Published: January 2019

AbstractWe consider the generalized JacobianJ~{\widetilde{J}}of the modular curveX0⁢(N){X_{0}(N)}of levelNwith respect to a reduced divisor consisting of all cusps. SupposingNis square free, we explicitly determine the structure of theℚ{\mathbb{Q}}-rational torsion points onJ~{\widetilde{J}}up to 6-primary torsion. The result depicts a fuller picture than [18] where the case of prime power level was studied. We also obtain an analogous result for Drinfeld modular curves. Our proof relies on similar results for classical Jacobians due to Ohta, Papikian and the first author. We also discuss the Hecke action onJ~{\widetilde{J}}and its Eisenstein property.
Neuroprotective Effects of the Anthocleista Schweinfurthii Gilg. (Loganiaceae) Stem Bark Extract in Postmenopause-Like Model of Ovariectomized Wistar Rats
Authors: Chantal Ngoungoure Madeleine , Paul Désiré Dzeufiet Djomeni , Caude Bilanda Danielle , Yolande Sandrine Mengue Ngandena , Lohik Mbolang Nguegang , Francine Mballa Marguerite , Larissa Dzekui Tchuo , Mireille Kameni Poumeni , Pierre Kamtchouing 
Published: January 2019

Abstract

Background
Estrogen deficiency in postmenopausal period causes severe neuroendocrine changes in brain which influences memory and other nervous functions. Anthocleista schweinfurthii is used traditionally to treat female infertility and menopause related symptoms. This study was performed to investigate the potential neuroprotective effects of aqueous extract of Anthocleista schweinfurthii on brain in a postmenopause-like model of ovariectomized Wistar rats.

Methods
Thirty animals were sham-operated or ovariectomized (Ovx) 84 days after surgery, six groups of five rats each were daily treated orally during 28 days with: distilled water for groups 1 (sham-operated) and 2 (Ovx), estradiol valerate (group 3) and the three doses of extracts {groups 4, 5 and 6 (Ovx)}. Biochemical and histological evaluations focused on brain.

Results
Compared to sham-operated control, ovariectomy decreased total protein levels in brain (p<0.01) which was increased by plant extract at the dose of 300 mg/kg (p<0.05), underlying its anabolic properties. Ovariectomy significantly decreased magnesium levels in brain (p<0.001). Anthocleista schweinfurthii increased significantly magnesium levels (p<0.01), showing its capacity to act on synaptic conduction. Ovariectomy induced oxidative stress by increasing malondialdehyde levels (p<0.05) and decreasing reduced glutathione levels (p<0.05) in brain. The plant extract exhibited antioxidative activity by reducing malondialdehyde levels and increasing glutathione levels in brain. Damage in brain structure which was caused by ovariectomy disappeared following the treatment.

Conclusions
Results suggest that Anthocleista schweinfurthii may have neuroprotective effects in Ovx Wistar rats by increasing total protein, magnesium levels and reducing oxidative stress in brain.
Use of natural remedies to treat oral diseases among female patients in Al Madinah, western Saudi Arabia
Authors: Dar-Odeh Najla S. , Gasim Rafal A. , Binsaad Sara M , Abu-Hammad Shaden , Abu-Hammad Osama A 
Published: January 2019

Abstract

Background
The study aimed to investigate natural remedies use (NRU) for oral diseases among female patients.

Methods
Dental patients attending the female section of Taibah University Dental Hospital were invited to complete an online questionnaire which explored demographic data, and pattern of NRU for oral diseases.

Results
A total of 540 patients participated in the survey. A total of 232 patients (43%) used natural remedies to treat oral diseases. The most commonly cited reasons for NRU were financial reasons (n=79, 34.1%). The practice had a statistically significant association with older participants (p=0.003), and those working as employees (p=0.031). Most of the natural remedies used (n=17) were herbal, with cloves (71.1%) and miswak (26.7%) being the most frequently reported. Acute dental pain (n=157, 67.7%) and halitosis (n= 51, 22%) were the most frequently cited oral conditions associated with NRU. A percentage of 87.1% of patients using natural remedies (n=202) perceived improvement of symptoms upon use of natural remedies, however, 2.2% (n=5) reported complications.

Conclusions
Substantial proportion of patients use natural remedies to treat their oral disease. Patients were mostly satisfied with natural remedies in terms of effectiveness and lack of complications.
Phytochemical analysis, cytotoxic and antioxidant activities of Myrtus communis essential oil from Morocco
Authors: Harassi Younes , Tilaoui Mounir , Idir Abderrazak , Frédéric Jullien , Baudino Sylvie , Ajouaoi Sana , Mouse Hassan Ait , Zyad Abdelmajid 
Published: January 2019

Abstract

Background

Myrtus communis L. is an aromatic evergreen plant common in Morocco. In addition to its culinary uses, it has been used medicinally as a disinfectant, an antiseptic or as a hypoglycemic agent. However, its cytotoxic activity has not been well investigated so far. The current study describes the chemical composition, cytotoxic and antioxidant activities of Myrtus communis L essential oil obtained from different regions of Morocco.

Methods

Myrtus communis essential oils were obtained by hydrodistillation, and analyzed by gas chromatography coupled with mass spectrometry. Cytotoxic activity was evaluated in murine mastocytoma P815 and MCF-7 breast cancer cells, using the MTT assay. In addition, DNA fragmentation was assessed by gel electrophoresis. The antioxidant effect was determined by measuring bleaching of β-carotene with the linoleic acid and the DPPH radical scavenging methods.

Results
GC-MS analysis showed high amounts of methyl eugenol (18.7%), α-terpineol (15.5%) and geranyl acetate (11.64%) in essential oil from the Benslimane region. In contrast, essential oil from Ouazzane was particularly rich in 1,8-cineole (36.3%). The cytotoxicity results showed that MCF-7 cells were more sensitive than P815 cells to the essential oils from Ouazzane and Benslimane regions with IC50 values of 4 and 6.25 µg/mL, respectively. Moreover, this cytotoxicity was partly associated with DNA fragmentation, which is one of the characteristics of apoptosis. The tested essential oils did not show strong antioxidant activity.

Conclusions

Myrtus communis L. essential oil exhibits a weak antioxidant effect, but induced remarkable cytotoxic activity by a mechanism related to apoptosis, suggesting a possible application of the bioactive compounds as natural anticancer compounds.
Evaluating the effect of lifestyle education based on peer model on anxiety in patients with acute myocardial infarction
Authors: Mohammadpourhodki Reza , Bagheri Hosein , Basirinezhad Mohammad Hasan , Ramzani Hosein , Keramati Maryam 
Published: January 2019

Abstract

Background
Anxiety in patients with myocardial infarction (MI) which has a very negative effect on the prognosis of their disease and their physical and mental health. We performed this study in order to find the impact of a peer based education (PE) on anxiety in patients with MI.

Methods
This was a randomized clinical trial study. The study participants included 60 patient with MI, who were randomly divided into two groups. The first group received routine education and the other one received PE. We assessed anxiety before and 30 days after the intervention through a valid questionnaires. Data were analyzed by independent sample t-test, two-way ANOVA and the Bonferroni test.

Results
The majority of samples were male, married, self-employer, and living in city. After 30 days intervention the anxiety score was significantly lower in the PE group compare to the control group.

Conclusion
Our findings indicated that the implication of PE as an educational element in decreasing anxiety score and can be considered as a method for continuing of care, and could as well as be a good approach for other patients.
Effects of dietary supplementations and herbs on migraine – a systematic review
Authors: Rehman Tayyeba , Ahmad Saeed , Fatima Qindeel 
Published: January 2019

Abstract

Background
Migraine is a disabling disease and conventional treatment has many side effects. Dietary supplements and various herbs have reported valuable effects on migraine.

Aim
The present study systematically review the effects of these dietary supplements and herbs on migraine.

Methods
The literature search was done on electronic databases PubMed, Google Scholar and Science direct (2005–2015). The quality of articles was assessed through a criteria list of methodological quality assessment of randomized controlled trials (RCTs). The papers got C50 points considered to be of good quality methodology. The maximum score was 100.

Results
Fourteen RCTs on migraine were included in this review. The range of quality score varied from 37 to 65 points.

Conclusion
Various RCTs suggested that dietary and vitamin supplementation and different herbs might be effective in treatment of migraine. Evaluated RCTs have various methodological shortcomings. So, a firm conclusion can’t be made for the efficacy of dietary supplementation and herbs in the treatment of migraine.
On a theorem of Avez
Authors: Elder Murray , Rogers Cameron 
Published: January 2019

AbstractFor each symmetric, aperiodic probability measure μ on a finitely generated groupG, we define a subsetAμ{A_{\mu}}consisting of group elementsgfor which the limit of the ratioμ∗n⁢(g)/μ∗n⁢(e){{\mu^{\ast n}(g)}/{\mu^{\ast n}(e)}}tends to 1. We prove thatAμ{A_{\mu}}is a subgroup, is amenable, contains every finite normal subgroup, andG=Aμ{G=A_{\mu}}if and only ifGis amenable. For non-amenable groups we show thatAμ{A_{\mu}}is not always a normal subgroup and can depend on the measure. We formulate some conjectures relatingAμ{A_{\mu}}to the amenable radical.
Groups whose Chermak–Delgado lattice is a quasi-antichain
Authors: An Lijian 
Published: January 2019

Abstract
A quasi-antichain is a lattice consisting of a maximum, a minimum, and the atoms of the lattice.
The width of a quasi-antichain is the number of atoms.
For a positive integer

w
≥
3

{w\geq 3}

, a quasi-antichain of width w is denoted by

ℳ
w

{\mathcal{M}_{w}}

.
In [B. Brewster, P. Hauck and E. Wilcox,
Quasi-antichain Chermak–Delgado lattice of finite groups,
Arch. Math. 103 2014, 4, 301–311],
it is proved that

ℳ
w

{\mathcal{M}_{w}}

can be the Chermak–Delgado lattice of a finite group if and only if

w
=

1
+

p
a

{w=1+p^{a}}

for some positive integer a and some prime p.
Let t be the number of abelian atoms in

𝒞
⁢
𝒟
⁢

(
G
)

{\mathcal{CD}(G)}

.
In this paper, we completely answer the following question: which values of t are possible in quasi-antichain Chermak–Delgado lattices?
(3, 𝑞, 𝑟)-generations of Fischer's sporadic group Fi′24
Authors: Ali Faryad , Ibrahim Mohammed Ali Faya , Woldar Andrew 
Published: January 2019

Abstract
A group G is said to be

(
l
,
m
,
n
)

{(l,m,n)}

-generated if it can be generated by two suitable elements x and y such that

o
⁢

(
x
)

=
l

{o(x)=l}

,

o
⁢

(
y
)

=
m

{o(y)=m}

and

o
⁢

(

x
⁢
y

)

=
n

{o(xy)=n}

.
In [J. Moori,

(
p
,
q
,
r
)

{(p,q,r)}

-generations for the Janko groups

J
1

{J_{1}}

and

J
2

{J_{2}}

,
Nova J. Algebra Geom. 2 1993, 3, 277–285],
J. Moori posed the problem of finding all triples of distinct primes

(
p
,
q
,
r
)

{(p,q,r)}

for which a finite non-abelian simple group is

(
p
,
q
,
r
)

{(p,q,r)}

-generated.
In the present article, we partially answer this question for Fischer’s largest sporadic simple group

Fi
24
′

{\mathrm{Fi}_{24}^{\prime}}

by determining all

(
3
,
q
,
r
)

{(3,q,r)}

-generations, where q and r are prime divisors of

|

Fi
24
′

|

{\lvert\mathrm{Fi}_{24}^{\prime}\rvert}

with

3
<
q
<
r

{3<q<r}

.
The Schur multiplier of groups of order 𝑝5
Authors: Hatui Sumana , Kakkar Vipul , Yadav Manoj K. 
Published: January 2019

Abstract
In this article, we compute the Schur multiplier, non-abelian tensor square and exterior square of non-abelian p-groups of order

p
5

{p^{5}}

. As an application, we determine the capability of groups of order

p
5

{p^{5}}

.
On the lifting of the Dade group
Authors: Lassueur Caroline , Thévenaz Jacques 
Published: January 2019

Abstract
For the group of endo-permutation modules of a finite p-group, there is a surjective reduction homomorphism from a complete discrete valuation ring of characteristic 0 to its residue field of characteristic p.
We prove that this reduction map always has a section which is a group homomorphism.
On a conjecture by Haipeng Qu
Authors: Tărnăuceanu Marius 
Published: January 2019

Abstract
In this note, we prove that

D
8

×

C
2

n
-
3

{D_{8}\times C_{2}^{n-3}}

is the non-elementary abelian 2-group of order

2
n

{2^{n}}

,

n
≥
3

{n\geq 3}

,
whose number of subgroups of possible orders is maximal. This solves a conjecture by Haipeng Qu. A formula
for counting the subgroups of an (almost) extraspecial 2-group is also presented.
Inverse problem for one-dimensional wave equation with matrix potential
Authors: Khanfer Ammar , Bukhgeim Alexander 
Published: January 2019

Abstract
We prove a global uniqueness theorem of reconstruction of a matrix-potential

a
⁢

(
x
,
t
)

{a(x,t)}

of one-dimensional wave equation

□
⁢
u

+

a
⁢
u

=
0

{\square u+au=0}

,

x
>
0

,

t
>
0

{x>0,t>0}

,

□
=

∂
t
2

-

∂
x
2

{\square=\partial_{t}^{2}-\partial_{x}^{2}}

with
zero Cauchy data for

t
=
0

{t=0}

and given Cauchy data for

x
=
0

{x=0}

,

u
⁢

(
0
,
t
)

=
0

{u(0,t)=0}

,

u
x

⁢

(
0
,
t
)

=

g
⁢

(
t
)

{u_{x}(0,t)=g(t)}

. Here

u
,
a
,
f

{u,a,f}

, and g are

n
×
n

{n\times n}

smooth real matrices,

det
⁡

(

f
⁢

(
0
)

)

≠
0

{\det(f(0))\neq 0}

, and the matrix

∂
t

⁡
a

{\partial_{t}a}

is known.
A note on prime divisors of polynomials P(Tk
); k ≥ 1
Authors: Legrand François 
Published: January 2019

Abstract
Let F be a number field, OF
the integral closure of ℤ in F, and P(T) ∈ OF
[T] a monic separable polynomial such that P(0) ≠ 0 and P(1) ≠ 0. We give precise sufficient conditions on a given positive integer k for the following condition to hold: there exist infinitely many non-zero prime ideals 𝓟 of OF
such that the reduction modulo 𝓟 of P(T) has a root in the residue field OF
/𝓟, but the reduction modulo 𝓟 of P(Tk
) has no root in OF
/𝓟. This makes a result from a previous paper (motivated by a problem in field arithmetic) asserting that there exist (infinitely many) such integers k more precise.