It is well-known that the Lipschitz stability originated from the paper 32 of J. Tabor. In this work, we establish the general solution of the new class of generalized multi-quadratic functional ...equationf(x1,…,xi−1,xi+kyi,xi+1,...,xn)+f(x1,…,xi−1,xi−kyi,xi+1,…,xn)=f(x1,…,xi−1,xi+ℓyi,xi+1,…,xn)+f(x1,…,xi−1,xi−ℓyi,xi+1,…,xn)+2(k2−ℓ2)f(x1,...,xi−1,yi,xi+1,...,xn),xi,yi∈G,i∈{1,...,n} where k,ℓ are two fixed integers with k≠±ℓ and G is an Abelian group. Under some natural conditions, we prove the stability of the above equation in Lipschitz spaces. Moreover, some results concerning the stability of the generalized multi-quadratic type functional equation in the Lipschitz norms are presented. Our main results improve and generalize results obtained in 5,10–12,25–27.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
The proton is one of the main building blocks of all visible matter in the Universe
. Among its intrinsic properties are its electric charge, mass and spin
. These properties emerge from the complex ...dynamics of its fundamental constituents-quarks and gluons-described by the theory of quantum chromodynamics
. The electric charge and spin of protons, which are shared among the quarks, have been investigated previously using electron scattering
. An example is the highly precise measurement of the electric charge radius of the proton
. By contrast, little is known about the inner mass density of the proton, which is dominated by the energy carried by gluons. Gluons are hard to access using electron scattering because they do not carry an electromagnetic charge. Here we investigated the gravitational density of gluons using a small colour dipole, through the threshold photoproduction of the J/ψ particle. We determined the gluonic gravitational form factors of the proton
from our measurement. We used a variety of models
and determined, in all cases, a mass radius that is notably smaller than the electric charge radius. In some, but not all cases, depending on the model, the determined radius agrees well with first-principle predictions from lattice quantum chromodynamics
. This work paves the way for a deeper understanding of the salient role of gluons in providing gravitational mass to visible matter.
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GEOZS, IJS, IMTLJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBMB, UL, UM, UPUK, ZAGLJ
The fundamental building blocks of the proton-quarks and gluons-have been known for decades. However, we still have an incomplete theoretical and experimental understanding of how these particles and ...their dynamics give rise to the quantum bound state of the proton and its physical properties, such as its spin
. The two up quarks and the single down quark that comprise the proton in the simplest picture account only for a few per cent of the proton mass, the bulk of which is in the form of quark kinetic and potential energy and gluon energy from the strong force
. An essential feature of this force, as described by quantum chromodynamics, is its ability to create matter-antimatter quark pairs inside the proton that exist only for a very short time. Their fleeting existence makes the antimatter quarks within protons difficult to study, but their existence is discernible in reactions in which a matter-antimatter quark pair annihilates. In this picture of quark-antiquark creation by the strong force, the probability distributions as a function of momentum for the presence of up and down antimatter quarks should be nearly identical, given that their masses are very similar and small compared to the mass of the proton
. Here we provide evidence from muon pair production measurements that these distributions are considerably different, with more abundant down antimatter quarks than up antimatter quarks over a wide range of momenta. These results are expected to revive interest in several proposed mechanisms for the origin of this antimatter asymmetry in the proton that had been disfavoured by previous results
, and point to future measurements that can distinguish between these mechanisms.
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GEOZS, IJS, IMTLJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBMB, UL, UM, UPUK, ZAGLJ
The atomic nucleus is composed of two different kinds of fermions: protons and neutrons. If the protons and neutrons did not interact, the Pauli exclusion principle would force the majority of ...fermions (usually neutrons) to have a higher average momentum. Our high-energy electron-scattering measurements using 12C, 27Al, 56Fe, and 208Pb targets show that even in heavy, neutron-rich nuclei, short-range interactions between the fermions form correlated high-momentum neutron-proton pairs. Thus, in neutron-rich nuclei, protons have a greater probability than neutrons to have momentum greater than the Fermi momentum. This finding has implications ranging from nuclear few-body systems to neutron stars and may also be observable experimentally in two-spin–state, ultracold atomic gas systems.
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BFBNIB, NMLJ, NUK, PNG, SAZU, UL, UM, UPUK
The aim of this paper is first to reformulate the fixed point theorem 4, Theorem 1 in 2-Banach spaces, after it, we introduce and solve the radical quartic functional equationf(x4+y44)=f(x)+f(y). We ...also show that the fixed point methods allow to investigate Ulam's type stability of radical quartic functional equation in 2-Banach spaces.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
Etudier les corrélations entre la dysfonction sexuelle et le profil clinicobiologique de l’insuffisant rénal chronique en hémodialyse (HD) au CHU Hassan II de Fès, Maroc
Nous avons réalisé une étude ...transversale descriptive et analytique à propos de 73 patients incluant les malades des deux sexes âgés de plus de 18ans et suivis pour insuffisance rénale chronique (IRC) en stade d’HD. Une recherche de dysfonction sexuelle ainsi que l’étude de paramètres cliniques: âge, comorbidités, durée d’HD, néphropathie initiale et biologiques: taux d’hémoglobine, ferritine, LH, FSH, prolactine, œstradiol et testostérone ont été réalisés.
L’âge moyen de nos malades était de 45,5+/-1,5ans avec une médiane de 45ans. Environ 56% des malades étaient de sexe masculin. La néphropathie diabétique (11 cas, 15%) et la néphroangiosclérose (14 cas, 19,2%) étaient les néphropathies initiales les plus fréquentes. La durée moyenne de dialyse était 101,9+/-6,17mois. La fréquence de la dysfonction sexuelle était de 78% tous grades confondus. Les patients présentant une dysfonction sexuelle avaient un âge plus avancé, un début de dialyse plus ancien et des troubles hormonaux significativement plus marqués que les patients sans dysfonction sexuelle. La téstostéronémie était basse chez 32 patients et a été significativement plus bas chez les hommes présentant des troubles sexuels (p=0,020). Les concentrations de l’estradiol n’étaient pas liées à la dysfonction sexuelle chez les femmes (p=0,345).
Certains facteurs cliniques et perturbations biologiques peuvent aider à la compréhension de l’étiopathogénie de ces troubles. Une approche globale peut être proposée basée sur une optimisation des facteurs intervenants. Notre étude souligne l’intérêt d’une surveillance clinique, biologique et hormonale de ces patients.
To determine the correlation between sexual dysfunction and the clinical and biological profiles of chronic renal failure patients on hemodialysis (HD) at the Hassan II university teaching hospital, Fez, Morocco
We conducted a descriptive and analytical crosssectional study that included male and female patients over 18 years of age diagnosed with end stage renal disease requiring hemodialysis. All patients answered a personal questionnaire on their sexuel activity. We studied clinical parameters such as age, comorbidities, hemodialysis duration, initial nephropathy and biological parameters such as hemoglobin, ferritin, LH, FSH, prolactin, estradiol and testosterone.
The present study was conducted on 73 patients. The mean age of our patients was 45,5+/-1,5. Diabetic nephropathy (11 patients, 15%) and nephrosclerosis (14 patients, 19.2%) were the most frequent initial nephropathies. The mean duration of dialysis was 101.9+/-6.17 months. The prevalence of sexual dysfunction was 78%. Ageing, years of hemodialysis and hormonal abnormalities correlated significantly with the appearance of sexual dysfunctions. Testosterone level was low in 32 patients and was significantly lower in men with erectile dysfunction (p=0,020). There was no significant correlation between estradiol levels and sexual dysfunction in women (p=0,345).
Some clinical factors and biological disorders may help to understand the pathogenesis of sexual dysfunction. A global approach can be proposed based on the correct management of these intervening factors and the optimization of biological and hormonal surveillance and management of intervening factors.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
The goal of this paper is to study the general solution of the following general radical quintic functional equationf(ax5+by55)=rf(x)+sf(y) for f a mapping from the field of real numbers into a ...vector space, where a,b,r,s are fixed nonzero reals. Also, we prove the generalized hyperstability results for the general radical quintic functional equation by using the fixed point theorem (cf. Dung and Hang (2018) 15, Theorem 2.1) in quasi-β-Banach spaces. Namely, we show, under some weak natural assumptions, functions satisfying the above equation approximately (in some sense) must be actually solutions to it.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
Let R be the set of real numbers. In this paper, we first introduce the notions of non-Archimedean (2,β)-normed spaces (X,‖⋅,⋅‖⁎,β) and we will reformulate the fixed point theorem 10, Theorem 1 in ...this space, after it, we introduce and solve the radical quintic functional equationf(x5+y55)=f(x)+f(y),x,y∈R. Also, under some weak natural assumptions on the function γ:R×R×X→0,∞), we show that this theorem is a very efficient and convenient tool for proving the hyperstability results when f:R→X satisfy the following radical quintic inequality‖f(x5+y55)−f(x)−f(y),z‖⁎,β≤γ(x,y,z),x,y∈R∖{0},z∈X, with x≠−y.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
The aim of this paper is to obtain some characterizations (or representations) of set-valued solutions defined on an Abelian monoid with values in a Hausdorff topological vector space of a new class ...of functional equations.
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DOBA, EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, IZUM, KILJ, KISLJ, MFDPS, NLZOH, NUK, OILJ, PILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UILJ, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
Background: The electromagnetic form factors of the proton measured by unpolarized and polarized electron scattering experiments show a significant disagreement that grows with the squared four ...momentum transfer (Q2). Calculations have shown that the two measurements can be largely reconciled by accounting for the contributions of two-photon exchange (TPE). TPE effects are not typically included in the standard set of radiative corrections since theoretical calculations of the TPE effects are highly model dependent, and, until recently, no direct evidence of significant TPE effects has been observed. Purpose: We measured the ratio of positron-proton to electron-proton elastic-scattering cross sections in order to determine the TPE contribution to elastic electron-proton scattering and thereby resolve the proton electric form factor discrepancy. Methods: We produced a mixed simultaneous electron-positron beam in Jefferson Lab's Hall B by passing the 5.6 GeV primary electron beam through a radiator to produce a bremsstrahlung photon beam and then passing the photon beam through a convertor to produce electron/positron pairs. The mixed electron-positron (lepton) beam with useful energies from approximately 0.85 to 3.5 GeV then struck a 30-cm long liquid hydrogen (LH2) target located within the CEBAF Large Acceptance Spectrometer (CLAS). By detecting both the scattered leptons and the recoiling protons we identified and reconstructed elastic scattering events and determined the incident lepton energy. A detailed description of the experiment is presented. Results: We present previously unpublished results for the quantity R2γ, the TPE correction to the elastic- scattering cross section, at Q2 ≈ 0:85 and 1.45 GeV2 over a large range of virtual photon polarization ε. Conclusions: Our results, along with recently published results from VEPP-3, demonstrate a non-zero contribution from TPE effects and are in excellent agreement with the calculations that include TPE effects and largely reconcile the form-factor discrepancy up to Q2 ≈ 2 GeV2. These data are consistent with an increase in R2γ with decreasing " at Q2 ≈ 0:85 and 1.45 GeV2. There are indications of a slight increase in R2γ with Q2.
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CMK, CTK, FMFMET, IJS, NUK, PNG, UM
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