pinecone/core-2020-05-10-deduplication huggingface dataset:
Algebraic and abelian solutions to the projective translation equation

Let $\mathbf{x}=(x,y)$. A projective 2-dimensional flow is a solution to a
2-dimensional projective translation equation (PrTE)
$(1-z)\phi(\mathbf{x})=\phi(\phi(\mathbf{x}z)(1-z)/z)$,
$\phi:\mathbb{C}^{2}\mapsto\mathbb{C}^{2}$. Previously we have found all
solutions of the PrTE which are rational functions. The rational flow gives
rise to a vector field $\varpi(x,y)\bullet\varrho(x,y)$ which is a pair of
2-homogenic rational functions. On the other hand, only very special pairs of
2-homogenic rational functions, as vector fields, give rise to rational flows.
The main ingredient in the proof of the classifying theorem is a reduction
algorithm for a pair of 2-homogenic rational functions. This reduction method
in fact allows to derive more results.
  Namely, in this work we find all projective flows with rational vector fields
whose orbits are algebraic curves. We call these flows abelian projective
flows, since either these flows are parametrized by abelian functions and with
the help of 1-homogenic birational plane transformations (1-BIR) the orbits of
these flows can be transformed into algebraic curves
$x^{A}(x-y)^{B}y^{C}\equiv\mathrm{const.}$ (abelian flows of type I), or there
exists a 1-BIR which transforms the orbits into the lines
$y\equiv\mathrm{const.}$ (abelian flows of type II), and generally the latter
flows are described in terms of non-arithmetic functions.
  Our second result classifies all abelian flows which are given by two
variable algebraic functions. We call these flows algebraic projective flows,
and these are abelian flows of type I. We also provide many examples of
algebraic, abelian and non-abelian flows.Comment: 31 pages, 5 figure
On permutable meromorphic functions

We study the class $\mathcal{M}$ of functions meromorphic outside a countable
closed set of essential singularities. We show that if a function in
$\mathcal{M}$, with at least one essential singularity, permutes with a
non-constant rational map $g$, then $g$ is a M\"{o}bius map that is not
conjugate to an irrational rotation. For a given function $ f \in\mathcal{M}$
which is not a M\"{o}bius map, we show that the set of functions in
$\mathcal{M}$ that permute with $ f $ is countably infinite. Finally, we show
that there exist transcendental meromorphic functions $f: \mathbb{C} \to
\mathbb{C}$ such that, among functions meromorphic in the plane, $f$ permutes
only with itself and with the identity map
Realizations of abstract regular polytopes from a representation
  theoretic view

Peter McMullen has developed a theory of realizations of abstract regular
polytopes, and has shown that the realizations up to congruence form a pointed
convex cone which is the direct product of certain irreducible subcones. We
show that each of these subcones is isomorphic to a set of positive
semi-definite hermitian matrices of dimension $m$ over either the real numbers,
the complex numbers or the quaternions. In particular, we correct an erroneous
computation of the dimension of these subcones by McMullen and Monson. We show
that the automorphism group of an abstract regular polytope can have an
irreducible character $\chi$ with $\chi\neq \overline{\chi}$ and with
arbitrarily large essential Wythoff dimension. This gives counterexamples to a
result of Herman and Monson, which was derived from the erroneous computation
mentioned before.
  We also discuss a relation between cosine vectors of certain pure
realizations and the spherical functions appearing in the theory of Gelfand
pairs.Comment: 22 pages, PDFLaTex + biblatex. v2: corrected a few typos. Content
  identical to final publication. in Aequationes Math. (2016
On regularity for de Rham's functional equations

We consider regularity for solutions of a class of de Rham's functional
equations. Under some smoothness conditions of functions consisting the
equation, we improve some results in Hata (Japan J. Appl. Math. 1985). Our
results are applicable to some cases that the functions consisting the equation
are non-linear functions on an interval, specifically, polynomials and linear
fractional transformations. Our results imply singularity of some well-known
singular functions, in particular, Minkowski's question-mark function, and,
some small perturbed functions of the singular functions.Comment: 14 pages, 3 figure
On the generalized associativity equation

The so-called generalized associativity functional equation G(J(x,y),z) =
H(x,K(y,z)) has been investigated under various assumptions, for instance when
the unknown functions G, H, J, and K are real, continuous, and strictly
monotonic in each variable. In this note we investigate the following related
problem: given the functions J and K, find every function F that can be written
in the form F(x,y,z) = G(J(x,y),z) = H(x,K(y,z)) for some functions G and H. We
show how this problem can be solved when any of the inner functions J and K has
the same range as one of its sections
Reducible means and reducible inequalities

It is well-known that if a real valued function acting on a convex set
satisfies the $n$-variable Jensen inequality, for some natural number $n\geq
2$, then, for all $k\in\{1,\dots, n\}$, it fulfills the $k$-variable Jensen
inequality as well. In other words, the arithmetic mean and the Jensen
inequality (as a convexity property) are both reducible. Motivated by this
phenomenon, we investigate this property concerning more general means and
convexity notions. We introduce a wide class of means which generalize the
well-known means for arbitrary linear spaces and enjoy a so-called reducibility
property. Finally, we give a sufficient condition for the reducibility of the
$(M,N)$-convexity property of functions and also for H\"older--Minkowski type
inequalities
On $n$-norm preservers and the Aleksandrov conservative $n$-distance
  problem

The goal of this paper is to point out that the results obtained in the
recent papers [7,8,10,11] can be seriously strengthened in the sense that we
can significantly relax the assumptions of the main results so that we still
get the same conclusions. In order to do this first, we prove that for $n \geq
3$ any transformation which preserves the $n$-norm of any $n$ vectors is
automatically plus-minus linear. This will give a re-proof of the well-known
Mazur--Ulam-type result that every $n$-isometry is automatically affine ($n
\geq 2$) which was proven in several papers, e.g. in [9]. Second, following the
work of Rassias and \v{S}emrl [23], we provide the solution of a natural
Aleksandrov-type problem in $n$-normed spaces, namely, we show that every
surjective transformation which preserves the unit $n$-distance in both
directions ($n\geq 2$) is automatically an $n$-isometry
Category-measure duality: convexity, mid-point convexity and Berz sublinearity

Category-measure duality concerns applications of Baire-category methods that have measure-theoretic analogues. The set-theoretic axiom needed in connection with the Baire category theorem is the Axiom of Dependent Choice, DC rather than the Axiom of Choice, AC. Berz used the Hahn–Banach theorem over Q to prove that the graph of a measurable sublinear function that is  Q+ -homogeneous consists of two half-lines through the origin. We give a category form of the Berz theorem. Our proof is simpler than that of the classical measure-theoretic Berz theorem, our result contains Berz’s theorem rather than simply being an analogue of it, and we use only DC rather than AC. Furthermore, the category form easily generalizes: the graph of a Baire sublinear function defined on a Banach space is a cone. The results are seen to be of automatic-continuity type. We use Christensen Haar null sets to extend the category approach beyond the locally compact setting where Haar measure exists. We extend Berz’s result from Euclidean to Banach spaces, and beyond. Passing from sublinearity to convexity, we extend the Bernstein–Doetsch theorem and related continuity results, allowing our conditions to be ‘local’—holding off some exceptional set
Around Jensen's inequality for strongly convex functions

In this paper we use basic properties of strongly convex functions to obtain
new inequalities including Jensen's type and Jensen-Mercer type inequalities.
Applications for special means are pointed out as well. We also give a Jensen's
operator inequality for strongly convex functions. As a corollary, we improve
H\"older-McCarthy inequality under suitable conditions. More precisely we show
that if $Sp\left( A \right)\subset I\subseteq \left( 1,\infty \right)$, then
\[{{\left\langle Ax,x \right\rangle }^{r}}\le \left\langle {{A}^{r}}x,x
\right\rangle -\frac{{{r}^{2}}-r}{2}\left( \left\langle {{A}^{2}}x,x
\right\rangle -{{\left\langle Ax,x \right\rangle }^{2}} \right),\quad r\ge 2\]
and if $Sp\left( A \right)\subset I\subseteq \left( 0,1 \right)$, then
\[\left\langle {{A}^{r}}x,x \right\rangle \le {{\left\langle Ax,x \right\rangle
}^{r}}+\frac{r-{{r}^{2}}}{2}\left( {{\left\langle Ax,x \right\rangle
}^{2}}-\left\langle {{A}^{2}}x,x \right\rangle \right),\quad 0<r<1\] for each
positive operator $A$ and $x\in \mathcal{H}$ with $\left\| x \right\|=1$.Comment: arXiv admin note: text overlap with arXiv:1611.01084, to appear in
  Aequationes Mat
The projective translation equation and rational plane flows. II.
  Corrections and additions

In this second part of the work, we correct the flaw which was left in the
proof of the main Theorem in the first part. This affects only a small part of
the text in this first part and two consecutive papers. Yet, some additional
arguments and additions are needed to claim the validity of the classification
results.
  With these new results in a disposition, algebraic and rational flows can be
much more easily and transparently classified. It also turns out that the
notion of an algebraic projective flow is a very natural one. For example, we
give an inductive (on dimension) method to build algebraic projective flows
with rational vector fields, and ask whether these account for all such flows.
  Further, we expand on results concerning rational flows in dimension $2$.
Previously we found such flows symmetric with respect to a linear involution
$i(x,y)=(y,x)$. Here we find all rational flows symmetric with respect to a
non-linear $1$-homogeneous involution $i(x,y)=(\frac{y^2}{x},y)$. We also find
all solenoidal rational flows. Up to linear conjugation, there appears to be
exactly two non-trivial examples.Comment: 32 pages, 1 figur
Lower estimation of the difference among quasi-arithmetic means

Quasi-arithmetic means are defined for every continuous, strictly monotone
function $f \colon U \rightarrow \mathbb{R}$, ($U$ -- an interval). For an
$n$-tuple $a \in U^n$ with corresponding vector of weights $w=(w_1,\dots,w_n)$
($w_i>0$, $\sum w_i=1$) it equals $f^{-1}\left( \sum_{i=1}^{n} w_i
f(a_i)\right)$. In 1960s Cargo and Shisha defined a metric in a family of
quasi-arithmetic means defined on a common interval as the maximal possible
difference between these means taken over all admissible vectors with
corresponding weights. During the years 2013--16 we proved that, having two
quasi-arithmetic means, we can majorized distance between them in terms of
Arrow-Pratt index $f''/f'$. In this paper we are going to proof that this
operator can be also used to establish certain lower boundaries of this
distance.Comment: 14 page
A characterization of affinely regular polygons

In 1970, Coxeter gave a short and elegant geometric proof showing that if
$p_1, p_2, \ldots, p_n$ are vertices of an $n$-gon $P$ in cyclic order, then
$P$ is affinely regular if, and only if there is some $\lambda \geq 0$ such
that $p_{j+2}-p_{j-1} = \lambda (p_{j+1}-p_j)$ for $j=1,2,\ldots, n$. The aim
of this paper is to examine the properties of polygons whose vertices
$p_1,p_2,\ldots,p_n \in \mathbb{C}$ satisfy the property that
$p_{j+m_1}-p_{j+m_2} = w (p_{j+k}-p_j)$ for some $w \in \mathbb{C}$ and
$m_1,m_2,k \in \mathbb{Z}$. In particular, we show that in `most' cases this
implies that the polygon is affinely regular, but in some special cases there
are polygons which satisfy this property but are not affinely regular. The
proofs are based on the use of linear algebraic and number theoretic tools. In
addition, we apply our method to characterize polytopes with certain symmetry
groups.Comment: 11 pages, 1 figur
Role of nitric oxide in the local and systemic pathophysiological effects induced by Bothrops asper snake venom in mice

Objective

To assess the role of nitric oxide in the most relevant local and systemic manifestations in mice injected with the venom of the snake Bothrops asper. Mice were pretreated with nitric oxide synthase inhibitors, and the modifications of the pathological effects induced by the venom were tested.
Results

Inhibition of NO synthesis did not affect acute local myonecrosis and hemorrhage in muscle tissue upon intramuscular injection of venom. Local footpad edema was reduced in mice pretreated with the NO synthase inhibitor L-NAME, and a reduction in the extent of inflammatory infiltrate in muscle tissue was observed after envenomation in mice pretreated with L-NAME and aminoguanidine. The most pronounced effect of NOS inhibition by L-NAME was an increment in the lethal activity of the venom, when injected by the intraperitoneal route.
Conclusion

Nitric oxide does not seem to play a significant role in the local acute pathological alterations (hemorrhage and myonecrosis) induced by B. asper venom in mice, although it contributes to edema and inflammatory infiltrate. Nitric oxide exerts a protective role in the systemic pathophysiological manifestations leading to lethality.Universidad de Costa Rica/[2075-06-01]/UCR/Costa RicaUCR::Investigación::Unidades de Investigación::Ciencias de la Salud::Instituto Clodomiro Picado (ICP
Imaging biomarkers of inflammation in situ with functionalized quantum dots in the dextran sodium sulfate (DSS) model of mouse colitis

Inflammation Research, 56(12): pp. 502-510.Objective and Design: Myeloperoxidase (MPO) and proinflammatory cytokines play an important role in the development of inflammation. These markers are generally measured using tedious ELISA procedures. In this study, a novel technique utilizing antibody conjugated quantum dot nanoparticles was developed to detect myeloperoxidase, IL-1 α and TNF-α in vivo in the dextran sodium sulfate (DSS) model of experimental colitis. Materials and Methods: Colitis was induced in animals (n=8 animals/ group) by feeding 4% DSS solution ad libitum for seven to eight days. Quantum Dots exhibiting fluorescence at various wavelengths were conjugated to MPO, IL-1 α and TNF-α polyclonal antibodies and tested in vivo at various stages of colitis. Tissue sections obtained were imaged with confocal microscope. The image intensity obtained from the tissue specimen was correlated with clinical activity measured as Disease Activity Index (DAI).
Results: Myeloperoxidase, IL-1α and TNF-α were visualized with quantum dots on various days of disease. The intensity of quantum dots increased with increase in inflammation. The increase in intensity showed an excellent correlation with the DAI based on the clinical parameters.
Conclusion: The study demonstrated that multiple biomarkers can be detected simultaneously and their quantitative expression correlated well with clinical disease severity. This novel technology should facilitate design of a novel optical platform for imaging various biomarkers of inflammation, early detection of acute and chronic disease markers and inflammation-mediated cancer markers. This detection may also facilitate determination of therapeutic success
Characterisation of nicotine receptors on human peripheral blood mononuclear cells (PBMC)

???The original publication is available at www.springerlink.com???. Copyright Springer. DOI: 10.1007/s00011-008-8171-xAim and objective: The aim of the work was to characterise the nAChRs on human PBMC. Method: PBMC were isolated from human blood buffy coats provided by the blood transfusion service and were used for radioligand binding studies with [3H]-nicotine. RT-PCR experiments were used to determine nAChR subunit expression while immunoblotting experiments were used to confirm that nAChR subunits identified by RT-PCR were translated into protein. Results: Binding studies suggested the presence of one binding site for (-)- nicotine on human peripheral blood lymphocytes. Competition studies showed that only (-)- nicotine, epibatidine and ??-bungarotoxin, displaced radiolabelled nicotine from cells. RT-PCR studies demonstrated mRNA for ??4, ??5, ??7, ??1 and ??2 nAChRs subunits in PBMC. Expression of mRNA for the a5 subunit of nAChR was observed in all lymphocyte samples tested. In contrast, the expression pattern of mRNAs for ??4, ??7, ??1, and ??2 mRNAs subunits of nAChRs, varied between samples. Western blot analysis showed that protein for ??4, ??5, and ??7 and ??2 nAChR subunits was expressed in most, but not all of the PBMC samples tested but some of the bands obtained were faint. Conclusion: The results obtained suggest that human PBMC contain nAChRs containing ??4??2, ??4??2??5, and/or ??7 subunits
Evidence that 13???14 di-hydro, 15-keto prostaglandin D2-induced airway eosinophilia in guinea-pigs is independent of interleukin-5

???The original publication is available at www.springerlink.com???. Copyright Springer. DOI: 10.1007/s00011-009-8112-3Objective and design: Prostaglandin D2 (PGD2) has been shown to cause eosinophil, basophil and Th2 cell chemotaxis in vitro and in vivo through an action on the prostaglandin CRTH2 receptor. In the present study, the dependence of PGD2-induced eosinophil accumulation in vivo on interleukin-5 (IL-5) blood eosinophilia was investigated. Materials: Guinea-pigs were exposed to aerosols of 13,14dihydro 15-keto PGD2 (DK-PGD2) or platelet activating factor (PAF) and the eosinophil content of the bronchoalveolar lavage fluid or blood determined. In some experiments, DK-PGD2 was administered systemically and eosinophilia measured. Results: Aerosols of DK-PGD2 caused eosinophil accumulation in the lungs 24h after exposure. DK-PGD2 (10 ??g.ml-1) -induced airway eosinophilia was inhibited when animals were treated with the CRTH2 receptor antagonist ramatroban. 1???4h after exposure to DK-PGD2 a significant decrease in blood eosinophil count was measured. The anti-IL-5 antibody TRFK-5 had no inhibitory effect of DK-PGD2-induced airway eosinophilia, but abolished airway eosinophilia induced by exposure of guinea-pigs to aerosols of PAF. Intracardiac injection of DK-PGD2 induced a dose-related increase in blood eosinophil numbers. Conclusions: It is concluded that, in the guinea-pig, DKPGD2-induced airway eosinophilia is mediated by an action on prostaglandin CRTH2 receptors and that this response appears to be independent of IL-5
The selective COX-2 inhibitor etoricoxib reduces acute inflammatory markers in a model of neurogenic laryngitis but loses its efficacy with prolonged treatment

The selective COX-2 inhibitor Etoricoxib reduces acute inflammatory markers in a model of neurogenic laryngitis but loses its efficacy with prolonged treatment.OBJECTIVE:
A randomised experimental study was used to evaluate the therapeutic effect of a selective cyclooxygenase-2 (COX-2) inhibitor in neurogenic laryngitis.
MATERIALS AND METHODS:
Male Wistar Han rats were subjected to the nasogastric intubation model (NGI) of laryngitis for 1 and 2 weeks. The NGI animals were divided into three groups: (1) treated with COX-2 inhibitor Etoricoxib, (2) vehicle and (3) non-intubated animals. A fourth group of animals was submitted to NGI only. Laryngeal sections were immunostained for substance P (SP) and calcitonin gene-related peptide (CGRP) fibre-immunoreactivity (IR) and quantification of COX-2 positive cells through stereological analysis. The expression of COX-2, interleukins IL-1beta, IL-6, IL-10 and tumour necrosis factor-alpha (TNF-alpha) was determined by quantitative real time QRT-PCR.
TREATMENT:
Etoricoxib (6 mg/kg/day) was prepared in 0.9% sterile saline with 5% glucose (vehicle) and administered daily during 1 or 2 weeks.
RESULTS:
Treatment for 1 week with Etoricoxib attenuated the CGRP-IR fibre depletion, the COX-2-IR increased cell number and the TNF-alpha and COX-2 mRNA increased levels induced by NGI. Two weeks of treatment had no beneficial effect.
CONCLUSIONS:
Etoricoxib is effective in neurogenic laryngitis for limited periods of administration, indicating that selective COX-2 inhibitors should be evaluated in the future.This study was supported by Fundacao Calouste Gulbenkian Project No 74551 and Fundacao Grunenthal (Portugal)
Comparison of acid-induced inflammatory responses in the rat lung during high frequency oscillatory and conventional mechanical ventilation

The present study was performed to compare the effects of high frequency oscillatory ventilation (HFOV) with conventional mechanical ventilation (CMV) on pulmonary inflammatory responses in a rat acid-induced lung injury model. Anesthetized rats were instilled intratracheally with HCl (0.1 N, 2 mL/kg) and then randomly divided into three mechanical ventilation settings: HFOV (an oscillatory frequency of 15 Hz, mean airway pressure (MAP) of 9 cmH(2)O), CMV at tidal volume of 12 and 6 mL/kg for 5 h. After HCl instillation, HFOV significantly attenuated the increases in neutrophil infiltration and TNF-alpha concentration in bronchoalveolar lavage fluid compared with the CMV groups. During HFOV, there was an inhibition of an increase in TNF-alpha mRNA expression and a decrease in SP-A mRNA expression induced by acid instillation. This animal study demonstrates that HFOV is a suitable form of mechanical ventilation to prevent inflammatory responses in acid-induced lung injury
Scavenger Receptors and \(\beta\)-Glucan Receptors Participate in the Recognition of Yeasts by Murine Macrophages

Objectives: Numerous receptors have been implicated in recognition of pathogenic fungi by macrophages, including the \(\beta\)-glucan receptor dectin-1. The role of scavenger receptors (SRs) in anti-fungal immunity is not well characterized. Methods: We studied uptake of unopsonized Saccharomycetes cerevisiae (zymosan) and live Candida albicans yeasts as well as zymosan-stimulated \(H_2O_2\) production in J774 macrophage-like cells and peritoneal exudate macrophages (PEMs). The role of different receptors was assessed with the use of competitive ligands, transfected cells and receptor-deficient macrophages. Results: The uptake of zymosan by untreated J774 cells was mediated approximately half by SRs and half by a \(\beta\)-glucan receptor which was distinct from dectin-1 and not linked to stimulation of \(H_2O_2\) production. Ligands of \(\beta\)-glucan receptors and of SRs also inhibited uptake of C. albicans by macrophages (J774 cells and PEMs). In macrophages pretreated with a CpG motif-containing oligodeoxynucleotide (CpG-ODN) the relative contribution of SRs to yeast uptake increased and that of \(\beta\)-glucan receptors decreased. Whereas the class A SR MARCO participated in the uptake of both zymosan and C. albicans by CpG-ODN-pretreated, but not untreated macrophages, the related receptor SR-A/CD204 was involved in the uptake of zymosan, but not of C. albicans. The reduction of zymosan-stimulated \(H_2O_2\) production observed in DS-pretreated J774 cells and in class A SRs-deficient PEMs suggest that class A SRs mediate part of this process. Conclusions: Our results revealed that SRs belong to a redundant system of receptors for yeasts. Binding of yeasts to different receptors in resting versus CpG-ODN-pre-exposed macrophages may differentially affect polarization of adaptive immune responses