Representations of twisted Yangians associated with skew Young diagrams

Let $G_M$ be either the orthogonal group $O_M$ or the symplectic group $Sp_M$ over the complex field; in the latter case the non-negative integer $M$ has to be even. Classically, the irreducible polynomial representations of the group $G_M$ are labeled by partitions $\mu=(\mu_{1},\mu_{2},\,\ldots)$ such that $\mu^{\prime}_1+\mu^{\prime}_2\le M$ in the case $G_M=O_M$, or $2\mu^{\prime}_1\le M$ in the case $G_M=Sp_M$. Here $\mu^{\prime}=(\mu^{\prime}_{1},\mu^{\prime}_{2},\,\ldots)$ is the partition conjugate to $\mu$. Let $W_\mu$ be the irreducible polynomial representation of the group $G_M$ corresponding to $\mu$. Regard $G_N\times G_M$ as a subgroup of $G_{N+M}$. Then take any irreducible polynomial representation $W_\lambda$ of the group $G_{N+M}$. The vector space $W_{\lambda}(\mu)={\rm Hom}_{\,G_M}( W_\mu, W_\lambda)$ comes with a natural action of the group $G_N$. Put $n=\lambda_1-\mu_1+\lambda_2-\mu_2+\ldots\,$. In this article, for any standard Young tableau $\varOmega$ of skew shape $\lm$ we give a realization of $W_{\lambda}(\mu)$ as a subspace in the $n$-fold tensor product $(\mathbb{C}^N)^{\bigotimes n}$, compatible with the action of the group $G_N$. This subspace is determined as the image of a certain linear operator $F_\varOmega (M)$ on $(\mathbb{C}^N)^{\bigotimes n}$, given by an explicit formula. When $M=0$ and $W_{\lambda}(\mu)=W_\lambda$ is an irreducible representation of the group $G_N$, we recover the classical realization of $W_\lambda$ as a subspace in the space of all traceless tensors in $(\mathbb{C}^N)^{\bigotimes n}$. Then the operator $F_\varOmega\(0)$ may be regarded as the analogue for $G_N$ of the Young symmetrizer, corresponding to the standard tableau $\varOmega$ of shape $\lambda$. This symmetrizer is a certain linear operator on $\CNn$$(\mathbb{C}^N)^{\bigotimes n} $ with the image equivalent to the irreducible polynomial representation of the complex general linear group $GL_N$, corresponding to the partition $\lambda$. Even in the case $M=0$, our formula for the operator $F_\varOmega(M)$ is new. Our results are applications of the representation theory of the twisted Yangian, corresponding to the subgroup $G_N$ of $GL_N$. This twisted Yangian is a certain one-sided coideal subalgebra of the Yangian corresponding to $GL_N$. In particular, $F_\varOmega(M)$ is an intertwining operator between certain representations of the twisted Yangian in $(\mathbb{C}^N)^{\bigotimes n}$.     

High-dimensional model representations generated from low order terms--lp-RS-HDMR

High-dimensional model representation (HDMR) is a general set of quantitative model assessment and analysis tools for improving the efficiency of deducing high dimensional input-output system behavior. RS-HDMR is a particular form of HDMR based on random sampling (RS) of the input variables. The component functions in an HDMR expansion are optimal choices tailored to the n-variate function f(x) being represented over the desired domain of the n-dimensional vector x. The high-order terms (usually larger than second order, or equivalently beyond cooperativity between pairs of variables) in the expansion are often negligible. When it is necessary to go beyond the first and the second order RS-HDMR, this article introduces a modified low-order term product (lp)-RS-HDMR method to approximately represent the high-order RS-HDMR component functions as products of low-order functions. Using this method the high-order truncated RS-HDMR expansions may be constructed without directly computing the original high-order terms. The mathematical foundations of lp-RS-HDMR are presented along with an illustration of its utility in an atmospheric chemical kinetics model.     

First observation of the sigma(*+)(c) baryon and a new measurement of the sigma(*+)(c) mass

Using data recorded with the CLEO II and CLEO II.V detector configurations at the Cornell Electron Storage Rings, we report the first observation and mass measurement of the Sigma(*+)(c) charmed baryon, and an updated measurement of the mass of the Sigma(+)(c) baryon. We find M(Sigma(*+)(c))-M(Lambda(+)(c)) = (231.0+/-1.1+/-2.0) MeV, and M(Sigma(+)(c))-M(Lambda(+)(c)) = (166.4+/-0.2+/-0.3) MeV, where the errors are statistical and systematic, respectively.     

Investigation of heat transfer from a lead heat carrier to a tube streamlined longitudinally

Results of experimental studies on the local characteristics of heat transfer from a lead heat carrier to the surface of a cooled tube in an annular gap are shown at control and alteration of oxygen admixture content under the conditions of power circuits with heavy liquid-metal heat-transfer agent. This work is aimed at obtaining the grounded formulas for engineering calculations of heat transfer surfaces. Investigations were carried out at the lead temperature of 400–500 °C, the average velocity of heat-transfer agent of 0.1–1.5 m/s, the range of Prandtl number of 0.0123–0.0211 and Peclet numbers of 500–7000. The heat flux changed within 50–160 kW/m². Controllable changing content of oxygen admixture changed from the value of thermodynamic activity of oxygen from 10⁻⁵-10⁰ to saturation and higher with deposition of lead oxides near the heat-transferring surface.     

Investigation of BiFeO3 Multiferroic thin films prepared by metalloorganic chemical vapor deposition

BiFeO₃ thin oriented films are grown on SrTiO₃(001) and ZrO₂(Y₂O₃)(001) substrates by metalloorganic chemical vapor deposition (MOCVD) in the temperature range T= 500–800°C. Iron dipivaloylmethanate Fe(thd)₃ and triphenylbismuth Bi(C₆H₅)₃ are used as volatile precursors. It is shown that the high thermal stability of Bi(C₆H₅)₃ leads to significant deviations of the Bi: Fe ratio in the film from their ratio in the precursor flow. An increase in the residence time of the precursor flow in the reactor makes this ratio close to unity. The film-substrate epitaxial relations are determined. It is found that the film orientation on the ZrO₂(Y₂O₃)(001) substrate changes with increasing temperature. Optical second harmonic generation (SHG) measurements show the presence of ferroelectric ordering in the films. A significant decrease in the Curie temperature due to epitaxial stress is found. At the same time, the magnetization noticeably increases as compared to a BiFeO₃ single crystal.     

New phosphonium salts based on 3-(diphenylphosphino)propanoic and ω-haloalkanoic acids

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