Let $f$ and $g$ be two different newforms without complex multiplication
having the same coefficient field. The main result of the present article
proves that a congruence between the Galois ...representations attached to $f$ and
to $g$ for a large prime $p$ implies an isomorphism between the endomorphism
algebras of the abelian varieties $A_f$ and $A_g$ attached to $f$ and $g$ by
the Eichler-Shimura construction. This implies important relations between
their building blocks. A non-trivial application of our result is that for all
prime numbers $d$ congruent to $3$ modulo $8$ satisfying that the class number
of $\mathbb{Q}(\sqrt{-d})$ is prime to $3$, the equation $x^4+dy^2 =z^p$ has no
non-trivial primitive solutions when $p$ is large enough. We prove a similar
result for the equation $x^2+dy^6=z^p$.
We describe a general method to compute weight-
modular
forms "associated" with a given weight-2 modular form ƒ of
level N, and relate its Fourier coefficients to central values of
quadratic twists ...(real and imaginary) of L(ƒ, s). We will focus
on examples for levels N = 27, N = 15, and N = 75.
Let $E$ be a rational elliptic curve and let $p$ be an odd prime of additive
reduction. Let $K$ be an imaginary quadratic field and fix a positive integer
$c$ prime to the conductor of $E$. The main ...goal of the present article is to
define an anticyclotomic $p$-adic $L$-function $\L$ attached to $E/K$ when
$E/\QQ_p$ attains semistable reduction over an abelian extension. We prove that
$\L$ satisfies the expected interpolation properties; namely, we show that if
$\chi$ is an anticyclotomic character of conductor $cp^n$ then $\chi(\L)$ is
equal (up to explicit constants) to $L(E,\chi,1)$ or $L'(E,\chi,1)$.
The pathophysiology of sensitive skin is largely unknown and no univocal data on the role of the epidermal barrier impairment have been identified. The aim of this study was to assess whether ...subjects with or without sensitive skin differ for some biophysical skin parameters, which reflect skin barrier integrity or skin hyperactivity.
This observational, cross-sectional study included adult volunteers not affected with chronic inflammatory skin diseases who attended the Unit of Dermatology and the Center of Cosmetology of the University of Ferrara, Ferrara, Italy, between March 2021 and November 2022. All subjects, subdivided into those with or without sensitive skin, based on either Lactic Acid Stinging Test (LAST) result or a questionnaire-based skin sensitivity score ≥4, were tested for transepidermal water loss (TEWL), skin elasticity and hydrations and dermographism.
One hundred and eighty-seven subjects were included. No significant differences in terms of TEWL, elasticity and hydration levels were recorded between subjects with sensitive skin and those without, subdivided according to both the LAST result and the questionnaire score. Dermographism was elicited more in subjects with sensitive skin than in the others, although without statistical significance.
The study failed to find significant biophysical differences between sensitive and non-sensitive skin. Therefore, the role of skin barrier impairment does not appear to be a necessary condition in determining an abnormal skin sensitivity to potentially unpleasant and irritating stimuli. These findings indirectly support the relevance of a peripheral sensory neural hyperactivity in the pathophysiology of sensitive skin.
Phys. Rev. C 103, 035203 (2021) The data on the proton form factors in the time-like region from the BaBar,
BESIII and CMD-3 Collaborations are examined to have coherent pieces of
information on the ...proton structure. Oscillations in the annihilation cross
section, previously observed, are determined with better precision. The moduli
of the individual form factors, determined for the first time, their ratio and
the angular asymmetry of the annihilation reaction $e^+e^-\to\bar p p$ are
discussed. Fiits of the available data on the cross section, the effective form
factor, and the form factor ratio, allow to propose a description of the
electric and magnetic time-like form factors from the threshold up to the
highest momenta.
Nausea and vomiting have a negative influence on the quality of life of patients receiving chemotherapy. The Consensus Conference held in 1997 outlined the therapeutic procedure to prevent delayed ...emesis that might otherwise be induced by chemotherapy. So far, no study has evaluated the correct management of delayed emesis in clinical practice. This study was performed in an attempt to verify the conformity of the delayed emesis therapy administered in some oncological centres with the Consensus Conference guidelines. A total of 149 patients were observed for a minimum of one up to a maximum of four chemotherapy cycles; analysis of the data took account of whether the chemotherapy had a high (HEC), moderate (MEC) or low (LEC) emetogenic potential. Among 42 patients who received HEC, 18 (43%) received antiemetic prophylaxis conforming to standards; 23 (54.7%) of these 42 had delayed emesis, only 8 (34.7%) of whom were treated with adequate antiemetic protection. MEC was administered to 72 patients, 46 (64%) of whom received adequate prophylaxis; delayed emesis was observed in 31 (43%) of the 72 patients, 20 (64.5%) of whom received antiemetic prophylaxis according to established guidelines. Of 35 patients treated with LEC, 22.8% manifested delayed emesis; a high percentage of these patients, 68.5%, received prophylaxis, even though it was unnecessary. Of all patients observed, only 50.3% received correct antiemetic protection. We deduce from the study that antiemetic treatment for delayed emesis in clinical practice needs more attention. Correct prophylaxis is necessary when HEC is given, and antiemetic protection for patients receiving MEC must be improved; among patients treated with LEC those at high risk must be identified so that overtreatment can be avoided.
A very general class of axially-symmetric metrics in general relativity (GR) that includes rotations is used to discuss the dynamics of rotationally-supported galaxies. The exact vacuum solutions of ...the Einstein equations for this extended Weyl class of metrics allow us to deduce rigorously the following: (i) GR rotational velocity always exceeds the Newtonian velocity (thanks to Lenz's law in GR); (ii) A non-vanishing intrinsic angular momentum (\(J\)) for a galaxy demands the asymptotic constancy of the Weyl (vectorial) length parameter (\(a\)) -a behavior identical to that found for the Kerr metric; (iii) Asymptotic constancy of the same parameter \(a\) also demands a plateau in the rotational velocity. Unlike the Kerr metric, the extended Weyl metric can and has been continued within the galaxy and it has been shown under what conditions Gau\ss\ \&\ Ampére laws emerge along with Ludwig's extended GEM theory with its attendant non-linear rate equations for the velocity field. Better estimates (than that from the Newtonian theory) for the escape velocity of the Sun and a reasonable rotation curve \&\ \(J\) for our own galaxy has been presented.
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