Three-dimensional numerical modeling of thermohaline and wind-driven circulations in the Persian Gulf

The Persian Gulf circulation is investigated with respect to the relevant forcing mechanism including wind stress and thermohaline surface fluxes by using a three-dimensional numerical hydrodynamic model. The model results show a correlation between the strength of the bottom layer outflow of the Persian Gulf and that of the Indian Ocean Surface Water (IOSW) inflow into the Gulf. The inflow of IOSW into the Gulf attain maximum values in May–June in conjunction with peak bottom outflow through the Hormuz Strait. The results of sensitivity experiment indicate that circulation is dominated by thermohaline flows at almost all parts of the Gulf. The heat fluxes play an essential role on the general circulation of the Persian Gulf. In spring and summer, the wind stress generates southeast-flowing surface currents of magnitude about 5 cm/s along the Saudi Arabia and Iranian coasts on the northern Gulf. In winter and autumn, due to weak static stability, the wind produces mesoscale eddies in most parts of the Gulf. In winter and spring the wind stress acts to reinforce the thermohaline circulation of deep outflow. Conversely, in summer and autumn the wind forcing acts in opposition to the thermohaline forcing and causes a bottom inflow from Oman Sea into the Gulf.     

Numerical modeling of hydrodynamic and hydrothermal characteristics in subtropical alpine lake

A three-dimensional, time-dependent hydrodynamic and hydrothermal model was performed and applied to the subtropical alpine Yuan-Yang Lake (YYL) in northeastern region of Taiwan. The model was driven with discharge inflow, heat, and wind stress to simulate the hydrodynamic and hydrothermal in the lake. The model was validated with measured water surface elevation, current, and temperature in 2008. The overall model simulation results are in quantitative agreement with the available field data. The validated model was then used to investigate wind-driven current, mean circulation, and residence time in the YYL. The modeling results reveal that the velocity field along the wind axis present the variations over depth with return current where the velocity at the surface layer is along the wind direction while it is opposite near 1 m below water surface. The simulated mean current indicates that the surface currents flow towards the southwest direction and form a clock-wise rotation. The calculated residence time is strongly dependent on the inflows and wind effects. Regression analysis of model results reveals that an exponential regression equation can be employed to correlate the residence time to change of discharge input. The residence time without wind stress is higher than that with wind effect, indicating that wind plays an important role in lake mixing. The calculated residence time is approximately 2-2.5 days under low inflow with wind effect.     

On asymptotic behavior of solutions of <Emphasis Type="Italic">n</Emphasis>-TH order Emden-Fowler differential equations with advanced argument

We study oscillatory properties of solutions of the Emden-Fowler type differential equation

Discrete Approximation of Finite-Horizon American-Style Options

We discuss the convergence of prices of standard American-style options in a complete market setting. We consider the continuous Black-Merton-Scholes model and discrete Cox-Ross-Rubinstein model and establish results for both customer and purchaser options. In the optimal stopping problem, we consider both cases and . __________ Translated from Lietuvos Matematikos Rinkinys, Vol. 45, No. 4, pp. 525–536, October–December, 2005.     

The Cauchy-Dirichlet problem for the heat equation in Besov spaces

The solvability in anisotropic spaces , σ ∈ ℝ₊, p, q ∈ (1, ∞), of the heat equation u_t − Δu = f in Ω^T ≡ (0, T) × Ω is studied under the boundary and initial conditions u = g on S^T, u|_t=0 = u₀ in Ω, where S is the boundary of a bounded domain Ω ⊂ ℝⁿ. The existence of a unique solution of the above problem is proved under the assumptions that and under some additional conditions on the data. The existence is proved by the technique of regularizers. For this purpose the local-in-space solvability near the boundary and near an interior point of Ω is needed. To show the local-in-space existence, the definition of Besov spaces by the dyadic decomposition of a partition of unity is used. This enables us to get an appropriate estimate in a new and promising way without applying either the potential technique or the resolvent estimates or the interpolation. Bibliography: 26 titles. Published in Zapiski Nauchnykh Seminarov POMI, Vol. 348, 2007, pp. 40–97.     

浅水中污染物扩散的自适应有限元分析法

介绍浅水中污染物扩散分析中的有限元法.分析包括两个部分:1)流场速度、水面高度的计算;2)根据扩散模型计算污染物浓度场.联合使用了自适应网格技术以期提高解的精度,同时减少计算时间和计算机内存的消耗.通过几个有已知解的实例验证了有限元公式和计算机程序.最后,使用这种联合方法分析泰国Chao Phraya河附近海湾中的污染物扩散.     

Some properties of the absolute galois group of a hilbertian field

LetK be a hilbertian field,G(K) its absolute Galois group. IfK is countable, then for a.a. inG(K) ^e , and there is no intermediate field with . Let ∈G(K) ^e . Then for a.a. in .     

Synthesis of invariantly stable discrete uncertain systems

A control of an nth-order discrete system under an external perturbation is considered. The elements of the matrix of the system are functionals of any nature. The observation matrix is constant and has arbitrary size m × n. A control ensuring the independence of the output σ _k on the external perturbation ψ _k is synthesized; moreover,

Improvement of source and wind field input of atmospheric dispersion model by assimilation of concentration measurements: Method and applications in idealized settings

The problem of correcting the pollutant source emission rate and the wind velocity field inputs in a puff atmospheric dispersion model by data assimilation of concentration measurements has been considered. Variational approach to data assimilation has been used, in which the specified cost function is minimized with respect to source strength and/or wind field. The analyzed wind field satisfied the constraints derived from the conditions of mass conservation and linearized flow equations for perturbations from the first guess wind field. ‘Identical twin’ numerical experiments have been performed for the validation of the method. The first guess estimation errors of source emission rate and wind field were set to a factor of up to 10 and up to 6 m/s respectively. The calculations results showed that in most studied cases an improvement of vector wind difference (VWD) error by about 0.7–1 m/s could be achieved. The resulting normalized mean square error (NMSE) of concentration field was also reduced significantly.     

On estimation and detection of a function of infinitely many variables

We observe an unknown function of infinitely many variables f = f(t), t = (t₁, ..., t_n, ... ) ∈, [0, 1]^∞, in the Gaussian white noise of level ε > 0. We suppose that in each variable there exists a 1-periodical σ-smooth extension of the function f(t) to IR ^∞. Taking a quantity σ > 0 and a positive sequence a = {a_k}, we consider the set that consists of functions f such that . We consider the cases a_k = k^α and a_k = exp(λk), α > 0, λ > 0. We would like to estimate a function f ∈ or to test the null hypothesis H₀: f = 0 against the alternatives f ∈ , where the set consists of functions f ∈ such that ∥f∥₂ ≥ r. In the estimation problem, we obtain the asymptotics (as ε → 0) of the minimax quadratic risk. In the detection problem, we study the sharp asymptotics of minimax separation rates f _ɛ ^* that provide distiguishability in the problems. Bibliography: 12 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 328, 2005, pp. 91–113.     

Parameter Estimates in Random Intercept Mixed Effects Model for Repeated Measures

In this article the following random intercept mixed effects model will be considered： yij = vi =v^τijβ＋ εij,i=1,…,m;j=1,2,…,ni, where {vi} are i.i.d, random effects with mean α 2. 2 and finite variance σ^2 v, {εij} are i.i.d, random errors with finite variance ε^2 ε. Here we will estimate α,σ^2 v,σ^2 ε,β and study their large sample properties, such as strong consistency, strong convergence rates and asymptotic normality.     

Degree of approximation by superpositions of a sigmoidal function

In this paper we study the degree of approximation by superpositions of a sigmoidal function. We mainly consider the univariate case. If f is a continuous function, we prove that for any bounded sigmoidal function σ, . For the Heaviside function H(x), we prove that . If f is a continuous function of bounded variation, we prove that and . For he Heaviside function, the coefficient 1 and the approximation orders are the best possible. We compare these results with the classical Jackson and Bernstein theorems, and make some conjectures for further study.     

A minimax regret estimator of a normal mean after preliminary test

Summary This paper considers the problem of estimating a normal mean from the point of view of the estimation after preliminary test of significance. But our point of view is different from the usual one. The difference is interpretation about a null hypothesis. Let denote the sample mean based on a sample of sizen from a normal population with unknown mean μ and known varianceσ ². We consider the estimator that assumes the value when and the value when where ω is a real number such that 0≤ω≤1 andC is some positive constant. We prove the existence of ω, satisfying the minimax regret criterion and make a numerical comparison among estimators by using the mean square error as a criterion of goodness of estimators.     

On best localized bandlimited functions

Let, for σ > 0, be the set of complex functions f ∈ L ¹ (ℝ) with the Fourier transforms vanishing outside the interval [−σ; σ]. In this paper, we study the problem of the best approximation of the Dirac function δ (which has the Fourier transform with widest support supp ) by functions . More precisely, we consider the quantity inf and its extremal functions . __________ Translated from Lietuvos Matematikos Rinkinys, Vol. 46, No. 4, pp. 548–564, October–December, 2006.     

Oscillation of second-order quasilinear neutral delay difference equations

By using the Riccati transformation and mathematical analytic methods,some sufficient conditions are obtained for oscillation of the second-order quasilinear neutral delay difference equations Δ[r n |Δz n | α-1 Δ z n ] + q n f (x n-σ)=0,where z n=x n + p n x n τ and ∞ Σ n=0 1 /r n 1/α < ∞.     

Graph homology of the moduli space of pointed real curves of genus zero

The moduli space parameterizes the isomorphism classes of S-pointed stable real curves of genus zero which are invariant under relabeling by the involution σ. This moduli space is stratified according to the degeneration types of σ-invariant curves. The degeneration types of σ-invariant curves are encoded by their dual trees with additional decorations. We construct a combinatorial graph complex generated by the fundamental classes of strata of . We show that the homology of is isomorphic to the homology of our graph complex. We also give a presentation of the fundamental group of .      

Invertibility of linear f-order preservers

In this paper, we prove that monotonic linear transformations with respect to partial orders and are invertible. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 9, No. 3, pp. 3–11, 2003.     

Approximation properties of certain interpolation operators of entire exponential type inL p (−∞,+∞) spaces

In this paper, we consider the convergence and saturation problems of the following discrete type interpolation operators:

A Chebotarev Theorem for finite homogeneous extensions of shifts

We derive a Chebotarev Theorem for finite homogeneous extensions of shifts of finite type. These extensions are of the form :X×G/H→X×G/H where (x,gH)=(σx, α(x)gH), for some finite groupG and subgroupH. Given a σ-closed orbit τ, the periods of the -closed orbits covering τ define a partition of the integer |G/H|. The theorem then gives us an asymptotic formula for the number of closed orbits with respect to the various partitions of the integer |G/H|. We apply our theorem to the case of a finite extension and of an automorphism extension of shifts of finite type. We also give a further application to ‘automorphism extensions’ of hyperbolic toral automorphisms. Financially supported by Universiti Kebangsaan Malaysia     

How big are the increments of lp-valued Gaussian processes?

Let be a sequence of independent Gaussian processes with (h) Put . The large increments forY(·) with bounded σ(p, h) are investigated. As an example the large increments of infinite-dimensional fractional Ornstein-Uhlenbeck process in I^P are given. The method can also be applied to certain processes with stationary increments. Project supported by the National Natural Science Foundation of China and the Natural Science Foundation of Zhejiang Province.