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Sifting for small primes from an arithmetic progression

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Science China mathematics 2023年第12期66卷 2715-2730页

作者： John B.friedlander Henryk Iwaniec Department of mathematics University of TorontoTorontoON M5S 2E4Canada Department of mathematics Rutgers UniversityPiscatawayNJ 08903USA

In this work and its sister paper(friedlander and Iwaniec(2023)),we give a new proof of the famous Linnik theorem bounding the least prime in an arithmetic *** sieve machinery in both papers,we are able to dispensh with the log-free zero density bounds and the repulsion property of exceptional zeros,two deep innovations begun by Linnik and relied on in earlier proofs.

关键词： sieve small primes Linnik theorem

The sexually dimorphic expression of glutamate transporters and their implication in pain after spinal cord injury

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Neural Regeneration Research 2025年第11期20卷 3317-3329页

作者： Jennifer m.Colón-mercado Aranza I.Torrado-Tapias Iris K.Salgado Jose m.Santiago Samuel e.Ocasio Rivera Dina P.Bracho-Rincon Luis H.Pagan Rivera Jorge D.miranda Department of Physiology University of Puerto RicoMedical Sciences CampusSan JuanPRUSA National Institutes of Health National Human Genome Research InstituteBethesdaMDUSA Universidad Central del Caribe School of MedicineBayamónPRUSA University of Puerto Rico Carolina CampusCarolinaPRUSA Institute of Neurobiology San JuanPRUSA

In addition to the loss of motor function,~60% of patients develop pain after spinal cord *** cellular-molecular mechanisms are not well understood,but the data suggests that plasticity within the rostral,epicenter,and caudal penumbra of the injury site initiates a cellularmolecular interplay that acts as a rewiring mechanism leading to central neuropathic *** can lead to the formation of new connections triggering abnormal sensory *** excitatory glutamate transporters are responsible for the reuptake of extracellular glutamate which makes them a critical target to prevent neuronal hyperexcitability and *** previous studies showed a sexually dimorphic therapeutic window for spinal cord injury after treatment with the selective estrogen receptor modulator *** this study,we investigated the anti-allodynic effects of tamoxifen in male and female rats with spinal cord *** hypothesized that tamoxifen exerts anti-allodynic effects by increasing the expression of glutamate transporters,leading to reduced hyperexcitability of the secondary neuron or by decreasing aberrant *** and female rats received a moderate contusion to the thoracic spinal cord followed by subcutaneous slow-release treatment of tamoxifen or matrix pellets as a control(placebo).We used von Frey monofilaments and the“up-down method”to evaluate mechanical *** treatment decreased allodynia only in female rats with spinal cord injury revealing a sexdependent *** expression profile of glutamatergic transporters(excitatory amino acid transporter 1/glutamate aspartate transporter and excitatory amino acid transporter 2/glutamate transporter-1)revealed a sexual dimorphism in the rostral,epicenter,and caudal areas of the spinal cord with a pattern of expression primarily on *** rodents showed a significantly higher level of excitatory amino acid transporter-1 expression while male rodents showed increased

关键词： allodynia central neuropathic pain eAAT-1/GLAST eAAT-2/GLT-1 glutamate transporters selective estrogen receptor modulator sexual dimorphism spinal cord injury trauma

Impact of Zika virus non-structural protein mutations on hippocampal damage

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Neural Regeneration Research 2025年第8期20卷 2307-2308页

作者： Larissa m.G.Cassiano Roney S.Coimbra Neurogenômica/Imunopatologia Instituto RenéRachouFiocruzBelo HorizonteBrazil Departamento de Bioquímica e Imunologia Instituto de Ciências BiológicasUniversidade Federal de Minas GeraisBelo HorizonteBrazil

The Zika virus(ZIKV),a member of the Flaviviridae family,attracted worldwide attention for its connection to severe neurological effects,notably microcephaly in newborns,first reported during the 2015 epidemic in ***,its impact goes beyond fetal and neonatal abnormalities,also affecting the central nervous system(CNS)in both children and adults,leading to enduring cognitive and behavioral impairments.

关键词： damage fetal neonatal

environmental chemical study on the marsh of Fatimid cemetery at Aswan City, egypt

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Journal of environmental Sciences 2002年第4期14卷 464-473页

作者： m.e.Soltan Chemistry Department Faculty of Science

environmental chemical study were carried out on the Fatimid cemetery marsh at Aswan City(24°1'N and 32°9'e), egypt. marsh contents(warter, soil, sediment, metal and nonmetal bearing salts, and emergent weed) were analysed to known the source of marsh water, speciation of the different elements between the marsh contents, and the toleration of emergent weed (Phargmites australies) for different metals and their bioaccumulation coefficients. Thus, metals(Ca, mg, Na, K, Ni, Fe, mn, Cu, Zn, Cd and Pb) and nonmetals(CO 2- 3, HCO - 3, Cl -, SO 2- 4, PO 3- 4, NO - 3, SiO 2, organic matter and pH value) were determined in the samples. According to the chemical analysis, and applying the base exchange equation(water type) and calculate the hydrochemical parameters for marsh water samples, we can indicate that the marsh water is ground water with Na SO 4 type and deep meteoric genesis. Topsoil of marsh dry land characterized by CaCl as dominant salt,while NaCl is a dominant salt in subsoil. The elevated pH values of marsh contents minimized the metal solubilities in different samples. Phragmites australies showed a strong ability to accumulate mn and Fe in the aerial part in opposite to Co, Ni and Cd.

关键词： marsh water soil sediment emergent weed egypt

INVeRSe PROBLemS FOR A GeNeRAL mULTI-CONNeCTeD BOUNDeD DRUm WITH APPLICATIONS IN PHYSICS

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Acta mathematica Scientia 2003年第1期23卷 104-116页

作者： e.m.e.Zayed mathematics Department Faculty of Science Zagazig University Zagazig Egypt

This paper studies the influence of a finite container on an ideal *** trace of the heat kernel (t) =exp, where are the eigenvalues of the negative Laplacian -in Rn(n = 2 or 3), is studied for a general multi-connected bounded drum ft which is surrounded by simply connected bounded domains Ωi with smooth boundaries Ωi(i = 1,… ,m) where the Dirichlet, Neumann and Robin boundary conditions on Ωi(i = 1,…,m) are considered. Some geometrical properties of Ω are determined. The thermodynamic quantities for an ideal gas enclosed in Ω are examined by using the asymptotic expansions of (t) for short-time t. It is shown that the ideal gas can not feel the shape of its container Ω, although it can feel some geometrical properties of it.

关键词： Inverse problem heat kernel eigenvalues an ideal gas multi-connected bounded domain

The Asymptotics of the Two-Dimensional Wave equation for a General multi-Connected Vibrating membrane with Piecewise Smooth Robin Boundary Conditions

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Acta mathematica Sinica,english Series 2004年第2期20卷 209-222页

作者： e.m.e.ZAYeD Department of mathematics Faculty of ScienceZagazig UniversityZagazigEgypt

The asymptotic expansion for small |t| of the trace of the wave kernel , where and are the eigenvalues of the negative Laplacian in the (x 2,x 2)-plane, is studied for a multi-connected vibrating membrane ? in R 2 surrounded by simply connected bounded domains ? j with smooth boundaries ?? j (j = 1, ..., n), where a finite number of piecewise smooth Robin boundary conditions on the piecewise smooth components Γ i (i = 1+k j?1, ..., k j ) of the boundaries ?? j are considered, such that and k 0 = 0. The basic problem is to extract information on the geometry of ? using the wave equation approach. Some geometric quantities of ? (e. g. the area of ?, the total lengths of its boundary, the curvature of its boundary, the number of the holes of ?, etc.) are determined from the asymptotic expansion of the trace of the wave kernel for small |t|.

关键词： Inverse problem Wave kernel eigenvalues Robin boundary conditions Vibrating membrane Hearing the shape of a drum

The 3D Inverse Problem of the Wave equation for a General multi-connected Vibrating membrane with a Finite Number of Piecewise Smooth Boundary Conditions

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Acta mathematica Sinica,english Series 2005年第4期21卷 733-752页

作者： e.m.e.ZAYeD mathematics Department Faculty of ScienceZagazig UniversityZagazig.Egypt

The trace of the wave kernel μ（t） =∑ω=1^∞ exp（-iteω^1/2）, where {eω}ω^∞=1 are the eigenvalues of the negative Laplacian -△↓2 = -∑k^3=1 （δ/δxk）^2 in the （x^1, x^2, x^3）-space, is studied for a variety of bounded domains, where -∞ 〈 t 〈 ∞ and i= √-1. The dependence of μ （t） on the connectivity of bounded domains and the Dirichlet, Neumann and Robin boundary conditions are analyzed. Particular attention is given for a multi-connected vibrating membrane Ω in Ra surrounded by simply connected bounded domains Ω j with smooth bounding surfaces S j （j = 1,……, n）, where a finite number of piecewise smooth Dirichlet, Neumann and Robin boundary conditions on the piecewise smooth components Si^＊（i = 1 ＋ kj-1,……, kj） of the bounding surfaces S j are considered, such that S j = Ui-1＋kj-1^kj Si^＊, where k0=0. The basic problem is to extract information on the geometry Ω by using the wave equation approach from a complete knowledge of its eigenvalues. Some geometrical quantities of Ω （e.g. the volume, the surface area, the mean curvuture and the Gaussian curvature） are determined from the asymptotic expansion ofexpansion of μ（t） for small │t│.

关键词： Inverse problem Wave kernal eigenvalues Greens function multi-connected vibrating membrane Negative Laplacian Heat kernel

Asymptotic expansions of the Heat Kernel of the Laplacian for General Annular Bounded Domains with Robin Boundary Conditions：Further Results

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Acta mathematica Sinica,english Series 2003年第4期19卷 679-694页

作者： e.m.e.ZAYeD Departmentofmathematics FacultyofScienceZagazigUniversityZagazigEgypt

The asymptotic expansions of the trace of the heat kernel Θ(t) = Σ_(v =1)~∞exp(-tλ_v) for small positive t, where {λ_v} are the eigenvalues of the negative Laplacian-△_n = -Σ_(i = 1)~n(partial deriv/(partial deriv)x^i)~2 in R^n (n = 2 or 3), are studied for ageneral annular bounded domain Ω with a smooth inner boundary (partial deriv)Ω_1 and a smoothouter boundary (partial deriv)Ω_2, where a finite number of piecewise smooth Robin boundaryconditions (partial deriv/(partial deriv)n_j + γ_j)φ = 0 on the components Γ_j(j = 1, …, k) of(partial deriv)Ω_1 and on the components Γ_j(j = k + 1, …, m) of (partial deriv)Ω_2 areconsidered such that (partial deriv)Ω_1 = ∪_(j = 1)~kΓ_j and (partial deriv)Ω_2 = ∪_(j = k +1)~mΓ_j and where the coefficients γ_j(j = 1, …, m) are piecewise smooth positive functions. Someapplications of Θ(t) for an ideal gas enclosed in the general annular bounded domain Ω are *** results are also obtained.

关键词： inverse problem heat kernel eigenvalues Robin boundary conditions classical ideal gas

Influence of the Choice of NN Potential model on γd→τ~0d Observables near η-Threshold

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Chinese Physics Letters 2016年第4期33卷 14-18页

作者： e.m.Darwish Physics Department Faculty of ScienceTaibah University Physics Department Faculty of ScienceSohag University

Influence of the choice of the NN potential model governing the deuteron wave function on the observables for coherent π0-photoproduction on the deuteron near η-threshom is investigated by using a three-body model for the intermediate ηN N system with separable two-body interactions. Results for unpolarized differential cross section and polarization observables are predicted. It is revealed that the choice of the NN potential model has a visible effect on the differential cross section and most of the polarization observables, especially in the photon energy range of 600-800 meV and extreme backward pion angles. We find that the deviation among results obtained by using different deuteron wave functions is quite large. The use of the CD-Bonn NN potential for deuteron wave function doubles the differential cross section in this kinematic region. Compared with the experimental data from CLAS collaboration for differential cross section, sizeable discrepancies are found.

关键词： of in Observables near Threshold NN that for on CLAS