Бидний тухай
Багш ажилтан
Objectives Hepatitis delta virus (HDV) is the smallest human virus that causes the most severe form of viral hepatitis. However, the virus's biological features, transmission routes and causes of endemicity in particular populations are not yet fully understood. HDV shares the hepatitis B virus (HBV) parenteral mode of transmission with HBV; therefore, sexual transmissions are also possible. However, data on sexual transmission of HDV are limited. Methods This study included 60 patients with chronic HBV/HDV coinfection. The median age (IQR) of patients was 35 (23-47) years, and all were Mongolian. HDV-RNA, HBV-DNA and hepatitis B surface antigens were tested in serum, seminal plasma and cervical swab samples collected at the Liver Centre, Mongolia. Binary logistic regression analysis was used to create a model that predicts the possibility of HDV detection in seminal plasma and cervical swab samples based on HDV-RNA levels in serum samples. Results HDV-RNA was detected in cervical swab samples from 24 of 30 patients (80%) and in seminal plasma from 15 of 30 patients (50%) (Fisher's exact test, p=0.03). Patients with detectable HDV-RNA in either seminal or cervical fluid samples showed higher levels of HDV-RNA in serum ((females: 6.44 vs 4.21 log IU/mL (p<0.0001); males: 6.69 vs 5.65 log IU/mL (p<0.0001)). A correlation between HDV-RNA levels in the serum was identified in females (r=0.56, p=0.004; 95% CI 0.206 to 0.788) but not in males (r=0.38, p=0.15, 95% CI -0.15 to 0.75). The regression model identified threshold points of serum HDV-RNA levels that can be used to predict HDV-RNA detection in seminal plasma and cervical swabs. Conclusions HDV-RNA can be detected in cervical swabs and seminal plasma of patients with HBV/HDV coinfection, and the detection was more common in females than in males. The probability of HDV-RNA detection in male seminal plasma and female cervical swab samples can be predicted based on the HDV viral load in serum.
We prove that the wave operators of the scattering theory for the fourth order Schrödinger operator Δ2+V(x) on R4 are bounded in Lp (R4) for the set of p’s of (1,∞) depending on the kind of spectral singularities of H at zero which can be described by the space of bounded solutions of (Δ 2+V(x))u(x)=0.
Жил бүр зохион байгуулагддаг Аж Үйлдвэртэй Хамтарсан Математик Хэрэглээ Семинарын үйл ажиллагаанаас хийсэн дүгнэлт, сургамжийг талаар илтгэж, их сургуулийн инноваци хэрэглээний судалгааны хандлагын талаар дүгнэлээ.
We prove that the wave operators for the fourth order Schrödinger operator R^4 are bounded in L^p for the set of p's of (1,∞) depending on the kind of spectral singularities of H at zero.
We prove that the wave operators for the fourth order Schr¨odinger operator in R4 are bounded in L^p for the set of p>1, depending on the kind of spectral singularities of H at zero
Энэ ажилд R4 огторгуйд Δ2 + V операторын долгионы опера- тор нь |x| → ∞ үед V (x) = O(|x|−d), d > 1 байх дурын потенциа- лын хувьд бүх p ∈ (4,∞)-ийн утганд Lp → Lp зааглагддаг байх боломжгүй гэж баталсан.
The scattering theory of higher-order Schrödinger operator H, with sufficiently small potentials, has been extensively studied in specific dimensions. One interesting problem related to the wave operators of higher-order Schrödinger operators is the L^p-L^p boundedness problem. This property allows us to derive properties of f(H)P_{ac} for any Borel function f on the real line, leveraging the interwining properties of wave operators. Another fascinating problem is the time decay estimation of higher-order Schrödinger operators, which provides L^p-L^q estimates with 1/p + 1/q = 1 for the one-parameter unitary group associated with the operator H. Under certain conditions on the potentials, both of these problems can be reduced to estimating the spectral integral on the half line. A common strategy to tackle this problem is to decompose the integral into the sum of two integrals, known as the low-energy and high-energy parts. In this study, our focus is on the wave operators of two-dimensional second-order Schrödinger operators with sufficiently small potentials. With some spectral properties for this operator obtained by A.Soffer and others in study of time decay estimation, we consider some problems related to the wave operators.
Шредингерийн операторын хувьд V (x) бодит потенциал нь ⟨x⟩^{12}V (x) ∈ L^2(R^4) ∩ L^1(R^4) нөхцлийг хангадаг байг. Тэгвэл уг оператор L^2(R^4)-д өөртөө хосмог бөгөөд түүний хувийн утгууд дискрет, зааглагдсан байх ба спектр нь [0,+∞] завсарт абсолют тасралтгүй байдаг. Чөлөөт Шредингерийн операторыг H_0 гэж тэмдэглэвэл W± долгионы оператор нь L^2(R^4) дээрх хүчтэй нийлэлтийн утгаар W± = lim_{t→±∞} e^{itH}e{−itH_0} гэж тодорхойлогддог. Энэ ажлаар W± нь 4 < p < +∞ үед L^p(R^4) дээр үл зааглагдах оператор болохыг харуулсан.
Савласан зэсийн баяжмалыг гадаад орчинд ил байрлуулах тохиолдолд исэлдэх, агуулгад өөрчлөлт орох процесс явагддаг бөгөөд энэ нь агаарын температур, чийгшил, баяжмалын шүлтлэгийн хэмжээ зэргээс хамаарсан химийн олон урвалууд явагдсаны үр дүн байдаг. Энэхүү исэлдэх процессыг хянах, баяжмалын агуулгад орох өөрчлөлтийг урьдчилан таамаглах зэрэг нь баяжмалын үйлдвэрийн үйл ажиллагаа, менежментийн чухал хэсэг бөгөөд баяжмалын дээжид агуулга тодорхойлох химийн анализ олон дахин хийхэд ихээхэн зардалтай байдаг. Иймээс исэлдэх процессыг тайлбарлах, агуулгын өөрчлөлтийн хэмжээг тодорхойлох математик загварыг боловсруулах шаардлага үүсдэг бөгөөд практикт энэ төрлийн комплекс процессыг загварчлахдаа тэдгээр урвалуудын кинетик хурдыг тодорхойлж, тохирох ердийн дифференциал тэгшитгэлийг байгуулах нь нийтлэг байдаг. Энэ судалгааны хүрээнд бид тодорхой хугацааны интервалтайгаар авсан баяжмалын дээжний шинжилгээний үр дүнгүүдийг ашиглан исэлдэх урвалын кинетик хурдыг тодорхойлох арга боловсруулах оролдлогыг хийж, үүнтэй зэрэгцэн баяжмалын агуулгын өөрчлөлтийг хянах экспоненциал хэлбэрийн дөхөлтийн функцийг байгуулах ажлуудыг хийж гүйцэтгэлээ.
We consider the Pauli–Fierz model, which describes a particle (an electron) coupled to the quantized electromagnetic field and limit the number of photons to less than 2. By computing the resolvent explicitly, we located the spectrum of the Hamiltonian mass. Our results do not depend on the coupling constant e nor on the infrared cutoff parameter R.
Let L ≥ 0 and 0 < ɛ ≪ 1. Consider the following time-dependent family of 1D Schrödinger equations with scaled harmonic oscillator potentials iε∂tuε=−12∂2xuε+V(t,x)uε, uɛ(−L − 1, x) = π−1/4 exp(−x2/2), where V(t, x) = (t + L)2x2/2, t < − L, V(t, x) = 0, − L ≤ t ≤ L, and V(t, x) = (t − L)2x2/2, t > L. The initial value problem is explicitly solvable in terms of Bessel functions. Using the explicit solutions, we show that the adiabatic theorem breaks down as ɛ → 0. For the case L = 0, complete results are obtained. The survival probability of the ground state π−1/4 exp(−x2/2) at microscopic time t = 1/ɛ is 1/2‾√+O(ε). For L > 0, the framework for further computations and preliminary results are given.
We prove that the wave operators for Schr\"odinger operators with multi-center local point interactions are the scaling limits of the ones for Schr\"odinger operators with regular potentials. We simultaneously present a proof of the corresponding well known result for the resolvent which substantially simplifies the one by Albeverio et al.
We prove that the wave operators for Schr\"odinger operators with multi-center local point interactions are the scaling limits of the ones for Schr\"odinger operators with regular potentials. We simultaneously present a proof of the corresponding well known result for the resolvent which substantially simplifies the one by Albeverio et al.
We prove that the wave operators for Schrodinger operators with multi-center local point interactions are the scaling limits of the ones for Schrodinger operators with regular potentials. We simultaneously present a proof of the corresponding well known result for the resolvent which substantially simplifies the one by Albeverio et al.
