Auxiliary Coefficients Research Articles

Использование компьютерной программы «ПРОЕКТ ВПУ» для проведения технологического расчета и анализа технологий обессоливания воды на ТЭС и АЭС

There are many viable options of desalination schemes that allow us to obtain purified water of the required quality. To conduct process design of a water treatment plant, thermal power plants and nuclear power plants use special software provided by manufacturers of ion exchangers and membrane elements. However, these software programs consider individual water treatment technologies and are attached to filter and membrane materials of a specific manufacturer. They do not provide the ability to calculate complete water desalination schemes, as well as determine the performance indicators of the water treatment plant. It is relevant to develop a software program that allows us to conduct process design of complete water treatment schemes, which include various water treatment technologies, and to determine technological, environmental, and technical-economic indicators. Multivariate calculations with different initial data will allow us to identify the advantages and disadvantages of scheme solutions and determine areas of their rational use. The method of mathematical modeling of chemical and technological processes of water treatment at thermal power plants and nuclear power plants has been used. An application software program “PROJECT WTP” has been developed. It is designed for process design of various water treatment schemes, which are visually assembled from individual elements, and allows one to determine the technological, environmental, and performance indicators of the operation of water treatment plant. Computation data on the auxiliary need coefficient has been obtained for the main water desalination schemes and under condition of different mineralization of the source water. The developed software program can be used for process design of various water treatment schemes and assessment of the degree of improvement of water desalination technology.

Features of the Use of Capitalization Ratios to Assess the Economic Efficiency of Investments in Real Estate

The article discusses some ways to assess the economic efficiency of investments in real estate. The initial premise of the study was the property of real estate, which consists in the variety of motives for its acquisition, which can lead to a change in the value of the same property, depending on the nature of its use. Currently, real estate is becoming a popular investment tool for many investors, including those who do not have deep economic knowledge. For this reason, such methods of assessing the economic efficiency of investments that require a minimum of initial data and require simplicity and accessibility of calculations become especially relevant. As such methods for real estate, it is advisable to use the calculation of capitalization ratios, as well as auxiliary ratios: operating expenses ratio and debt coverage ratio. The article analyzes the features of the calculation of income and expenses associated with the operation of real estate. The specificity of the use of various sources of information depending on the goals of investment analysis is revealed. The features of the calculation of capitalization coefficients, auxiliary coefficients are considered, as well as various options for interpreting the results of calculating these coefficients, depending on the tasks being solved. The advantages and disadvantages of using the mentioned indicators, their areas of application are revealed.

Pattern-Reconfigurable Sparse Linear Array Synthesis Under Minimum Element Spacing Control by Alternating Sequential Quadratic Programming

A new method called alternating sequential quadratic programming (ASQP) is proposed to synthesize pattern-reconfigurable sparse linear arrays with minimum element spacing control. The method can find the common element positions and multiple sets of excitations for generating multiple reconfigurable patterns which accurately meet their given upper and lower pattern bounds. In addition, by introducing auxiliary weighting coefficients and collective excitation coefficient vectors and choosing them as optimization variables alternately, the proposed method can appropriately incorporate the minimum element spacing constraint into the pattern synthesis. Synthesized results show that the proposed method can give satisfactory reconfigurable pattern performance but save much more elements compared with some existing methods.

Example of Calculation of Auxiliary Coefficient of Three-dimensional Contact Pressure

Example of Calculation of Auxiliary Coefficient of Three-dimensional Contact Pressure

Stochastic daily hydrothermal scheduling based on decomposition and parallelization

This paper studies the stochastic short term hydrothermal scheduling of systems that have a significant contribution from controllable reservoirs, focusing on the reservoirs’ operation policy when non-linearity and deployment of supplementary reserves at the real operation stage are modeled. Wind power and forced outages of power plants and transmission lines are treated as stochastic variables, and the total reserve is an endogenous variable to the model. The problem includes cascaded hydro systems with head-sensitive plants, a DC power flow representation with nonlinear transmission losses, and four types of operating reserves; and it aims at pre-positioning generation and reserves schedules in the light of the expected deployment of operating reserves throughout the day. To solve the optimization problem, a hybrid scheme elaborated from outer approximation and Benders decomposition is applied. The proposed solution method is tested in a real-size system, where its effectiveness, in terms of computational speed and accuracy, is demonstrated.The main nomenclature used is presented next. Other auxiliary variables, coefficients, dual variables and scalars are detailed within the section they are mentioned.

A game-theoretic approach to optimize the Time-of-Use pricing considering customer behaviors

Time-of-Use (TOU) pricing is an electricity demand response program with great potential to shave the peak demand and eliminate the need for extra power plants. It is necessary to distinguish which TOU program will lead to profitable results to the utility and customers when the customer behaviors and real work shifts are considered. In this paper, a game-theoretic approach is introduced to formulate the problem using a two-layer mathematical programming model, which is solved by the backward induction to gain the Nash-equilibrium. The case study results show that the equilibrium can create a win-win situation for the utility and customers, i.e. the utility increases its profit and the customer reduces its cost. Among different customers, the utility can focus on the customer with a small penalty factor and a large auxiliary coefficient, who prefers to join the TOU program. Even only a small portion of customers joins the TOU program, large improvements in utility's profit can be made.

Example-based learning using heuristic orthogonal matching pursuit teaching mechanism with auxiliary coefficient representation for the problem of de-fencing and its affiliated applications

Orthogonal Matching Pursuit (OMP) is a good candidate for solving energy function optimization problems. In this paper, we propose a novel auxiliary coefficient representation for the problem of image de-fencing. To improve the optimization efficiency of the OMP algorithm, we propose a heuristic form of the OMP (named h-OMP) approximation based on auxiliary coefficient representation. A frequency-domain optimization approach is derived by selecting an over-complete example set for the image signal, the h-OMP algorithm is used to simultaneously remove the fences on the image matrix and find the auxiliary coefficient basis to form the image segment. Experiments show that the proposed h-OMP algorithm generates better output image, whose performance is superior in terms of both subjective and objective evaluation criteria.

Efficient numerical solution of acoustic scattering from doubly-periodic arrays of axisymmetric objects

We present a high-order accurate boundary-based solver for three-dimensional (3D) frequency-domain scattering from a doubly-periodic grating of smooth axisymmetric sound-hard or transmission obstacles. We build the one-obstacle solution operator using separation into P azimuthal modes via the FFT, the method of fundamental solutions (with N proxy points lying on a curve), and dense direct least-squares solves; the effort is O(N3P) with a small constant. Periodizing then combines fast multipole summation of nearest neighbors with an auxiliary global Helmholtz basis expansion to represent the distant contributions, and enforcing quasiperiodicity and radiation conditions on the unit cell walls. Eliminating the auxiliary coefficients, and preconditioning with the one-obstacle solution operator, leaves a well-conditioned square linear system that is solved iteratively. The solution time per incident wave is then O(NP) at fixed frequency. Our scheme avoids singular quadratures, periodic Green's functions, and lattice sums, and its convergence rate is unaffected by resonances within obstacles. We include numerical examples such as scattering from a grating of period 13λ×13λ comprising highly-resonant sound-hard “cups” each needing NP=64800 surface unknowns, to 10-digit accuracy, in half an hour on a desktop.

Supercuspidal ramification of modular endomorphism algebras

The endomorphism algebra X f X_f attached to a non-CM primitive cusp form f f of weight at least two is a 2-torsion element in the Brauer group of a number field F F . We give formulas for the ramification of X f X_f locally at primes lying above the odd supercuspidal primes of f f . We show that the local Brauer class is determined by the underlying local Galois representation together with an auxiliary Fourier coefficient.

An Optical Mode-Matching Method With Improved Accuracy and Efficiency

Two fundamental principles of the mode-matching method-mode orthogonality and tangential field continuity conditions have been revisited in depth. With a finite number of modes employed in the conventional method, the tangential field continuity condition at the waveguide-discontinuity interface fails leading to a field mismatch error. We propose an alternate, superior mode-matching method implemented by reconstruction of the auxiliary coefficient matrix, rather than by applying the abovementioned continuity and orthogonality. Detailed transfer-matrix equations have been derived for the finite-mode-number case. We showed that the improved mode-matching method yields a smaller field mismatch error under equal computational effort. Examples of bent and faceted waveguide structure have been investigated and the numerical simulation results demonstrated that the newly proposed method has the merits of simple implementation, high accuracy, and high computational efficiency for application in high-index-contrast photonic integrated circuits.

A Multigrid Method for Adaptive Sparse Grids

Sparse grids have become an important tool to reduce the number of degrees of freedom of discretizations of moderately high-dimensional partial differential equations; however, the reduction in degrees of freedom comes at the cost of an almost dense and unconventionally structured system of linear equations. To guarantee overall efficiency of the sparse grid approach, special linear solvers are required. We present a multigrid method that exploits the sparse grid structure to achieve an optimal runtime that scales linearly with the number of sparse grid points. Our approach is based on a novel decomposition of the right-hand sides of the coarse grid equations that leads to a reformulation in so-called auxiliary coefficients. With these auxiliary coefficients, the right-hand sides can be represented in a nodal point basis on low-dimensional full grids. Our proposed multigrid method directly operates in this auxiliary coefficient representation, circumventing most of the computationally cumbersome sparse gr...

Improvement in Estimating the Population Median in Simple Random Sampling and Stratified Random Sampling Using Auxiliary Information

This paper deals with estimation of population median in simple and stratified random samplings by using auxiliary information. Auxiliary information is rarely used in estimating population median, although there have been many studies to estimate population mean using auxiliary information. In this study, we suggest some estimators using auxiliary information such as mode and range of an auxiliary variable and correlation coefficient. We also expand these estimators to stratified random sampling for combined and separate estimators. We obtain mean square error equations for all proposed estimators and find theoretical conditions. These conditions are also supported by using numerical examples.

Radiation force exerted on a sphere by focused Laguerre-Gaussian beams.

The generalized Lorenz-Mie theory is employed to calculate the force exerted on a sphere by focused Laguerre-Gaussian beams. The key parameters of the theory, namely, the multipole coefficients of the beams, are exactly derived from the beams' angular spectra in terms of some auxiliary coefficients. Several recurrence formulas, which can improve the calculation of the auxiliary coefficients and accordingly the force, are also derived. According to the calculated force, the trapping performances of the beams are investigated in the Mie regime. It is found that low(high)-azimuthal-order beams usually have advantages in the radial trapping of the high(low)-refractive-index sphere and the axial trapping of the low(high)-refractive-index sphere. The influences of the parameters of the beams, lens, and sphere on the trapping performance are also investigated.

DETERMINATION OF VARIABLE PSEUDO-VISCOSITY COEFFICIENTS FOR OILS WITH THE RIVLIN-ERICKSEN PROPERTIES

Modern oils, that lubricate the sliding friction pairs, contain more and more additives. These additives change the oil properties to the non-Newtonian. Furthermore, the friction and wear products and also the products of combustion in internal combustion engines, result in a change of the oil properties, from Newtonian to the non-Newtonian. Frequently, researchers suggest to use so-called „smart fluids”, for example, the ferro-oils as lubricants of sliding friction pairs exposed to strong magnetic fields or the absence of gravity. The ferro-oils are also characterized by the non-Newtonian properties. The viscosity characteristics of these oils are described rather well by the Rivlin-Ericksen constitutive equation. The Rivlin-Ericksen constitutive equation contains the coefficients, which are difficult to estimate or determine experimentally. One of the possibilities to determine these coefficients is the method proposed by Prof. K. Wierzcholski [12]. This method requires the experimental results of dynamic viscosity changes as a function of shear rate. The measurements of dynamic viscosity should be conducted for the widest possible range of shear rates. Then, using the viscosity curves and nonlinear system of equations, the auxiliary coefficients are determined. These coefficients generate the equations that describe the variable pseudo-viscosity coefficients. Not all oils have an intensive exponential character of viscosity changes in dependence on shear rate. In these cases it is possible to determine the constant coefficients of pseudo-viscosity [1, 3, 7, 8]. This paper presents the examples of determination of the variable pseudo-viscosity coefficients for the selected lubricating oils and ferro-oils.

Recovery of sparse translation-invariant signals with continuous basis pursuit.

We consider the problem of decomposing a signal into a linear combination of features, each a continuously translated version of one of a small set of elementary features. Although these constituents are drawn from a continuous family, most current signal decomposition methods rely on a finite dictionary of discrete examples selected from this family (e.g., shifted copies of a set of basic waveforms), and apply sparse optimization methods to select and solve for the relevant coefficients. Here, we generate a dictionary that includes auxiliary interpolation functions that approximate translates of features via adjustment of their coefficients. We formulate a constrained convex optimization problem, in which the full set of dictionary coefficients represents a linear approximation of the signal, the auxiliary coefficients are constrained so as to only represent translated features, and sparsity is imposed on the primary coefficients using an L1 penalty. The basis pursuit denoising (BP) method may be seen as a special case, in which the auxiliary interpolation functions are omitted, and we thus refer to our methodology as continuous basis pursuit (CBP). We develop two implementations of CBP for a one-dimensional translation-invariant source, one using a first-order Taylor approximation, and another using a form of trigonometric spline. We examine the tradeoff between sparsity and signal reconstruction accuracy in these methods, demonstrating empirically that trigonometric CBP substantially outperforms Taylor CBP, which in turn offers substantial gains over ordinary BP. In addition, the CBP bases can generally achieve equally good or better approximations with much coarser sampling than BP, leading to a reduction in dictionary dimensionality.

Improved Estimation of the Population Mean Using Known Parameters of an Auxiliary Variable

An improved ratio-cum-product type estimator of the finite population mean is proposed using known information on the coefficient of variation of an auxiliary variate and correlation coefficient between a study variate and an auxiliary variate. Realistic conditions are obtained under which the proposed estimator is more efficient than the simple mean estimator, usual ratio and product estimators and estimators proposed by Singh and Diwivedi (1981), Pandey and Dubey (1988), Upadhaya and Singh (1999), and Singh, et al., (2004). An empirical study supports theoretical findings.

Implementation of Collocated Surface Impedance Boundary Conditions in FDTD

Surface impedance boundary conditions (SIBCs) for finite-difference time-domain (FDTD) are implemented with collocated H and E components in which first-order spatial finite difference have been used for the spatial derivatives. Transient error analysis is done for the reflected field for the whole possible range of modeled material conductivity. Magnitude and phase error analysis of the calculated reflection coefficients for wideband pulses is presented as well. The resulting numerical errors are compared with the errors of traditional SIBCs implementation when the tangential magnetic fields on the boundary are approximated with the neighboring FDTD magnetic field component located at half-cell size distance in space and half time step behind in time. It is shown that the collocated fields approach is considerably more accurate for both constant real resistive and dispersive complex lossy dielectric SIBCs, in both magnitude and especially phase. Unlike the traditional approach, it is stable for all values of modeled material conductivity. The collocated fields approach is also applied to SIBCs with coating, and the transient and reflection coefficient errors are studied. It is shown that in contrast to the traditional implementation, it is stable for arbitrarily thin coating and for any substrate conductivity, and requires storage only half of the auxiliary coefficients when computing the convolution integrals.

Involutions and representations for reduced quantum algebras

In the context of deformation quantization, there exist various procedures to deal with the quantization of a reduced space M red . We shall be concerned here mainly with the classical Marsden–Weinstein reduction, assuming that we have a proper action of a Lie group G on a Poisson manifold M, with a moment map J for which zero is a regular value. For the quantization, we follow Bordemann et al. (2000) [6] (with a simplified approach) and build a star product ⋆ red on M red from a strongly invariant star product ⋆ on M. The new questions which are addressed in this paper concern the existence of natural ∗-involutions on the reduced quantum algebra and the representation theory for such a reduced ∗-algebra. We assume that ⋆ is Hermitian and we show that the choice of a formal series of smooth densities on the embedded coisotropic submanifold C = J − 1 ( 0 ) , with some equivariance property, defines a ∗-involution for ⋆ red on the reduced space. Looking into the question whether the corresponding ∗-involution is the complex conjugation (which is a ∗-involution in the Marsden–Weinstein context) yields a new notion of quantized modular class. We introduce a left ( C ∞ ( M ) 〚 λ 〛 , ⋆ ) -submodule and a right ( C ∞ ( M red ) 〚 λ 〛 , ⋆ red ) -submodule C cf ∞ ( C ) 〚 λ 〛 of C ∞ ( C ) 〚 λ 〛 ; we define on it a C ∞ ( M red ) 〚 λ 〛 -valued inner product and we establish that this gives a strong Morita equivalence bimodule between C ∞ ( M red ) 〚 λ 〛 and the finite rank operators on C cf ∞ ( C ) 〚 λ 〛 . The crucial point is here to show the complete positivity of the inner product. We obtain a Rieffel induction functor from the strongly non-degenerate ∗-representations of ( C ∞ ( M red ) 〚 λ 〛 , ⋆ red ) on pre-Hilbert right D -modules to those of ( C ∞ ( M ) 〚 λ 〛 , ⋆ ) , for any auxiliary coefficient ∗-algebra D over C 〚 λ 〛 .

An Efficient Hybrid Estimator

This paper presents an efficient state estimation algorithm for hybrid systems based on a least-squares Interacting Multiple-Model setup. Under some conditions, the proposed algorithm is shown to perform similarly and even better than the Kalman filter. However, due to the possibility of incorrect estimation of the discrete mode, performance deterioration may occur. The computational efficiency of the proposed algorithm is obtained by discarding as many discrete mode sequences as possible while performing the least computations possible. This is done by rapidly computing good estimates, separating the constrained and unconstrained estimates and using some auxiliary coefficients computed off-line. A numerical example shows the characteristics of the proposed algorithm and compares it with the Kalman filter.

A compact equation for the prediction of eddy-induced slip in centrifugal impellers

The single relative eddy (SRE) method for the prediction of relative-eddy-induced slip in centrifugal impellers proposes the existence of only one slip-inducing eddy in a rotating impeller, compared with the commonly assumed multiple eddies, with one eddy per blade passage. In the SRE method, the eddy-induced slip factor depends on the blade solidity, weighted by an auxiliary coefficient F that is a function of blade angle and blade number. The paper presents a series of increasingly accurate new expressions for F. The best fit leads to a compact equation for slip factor, giving very good agreement (within 0.003) with the numerically calculated slip factors of Busemann for impellers with four or more blades and reasonable agreement (within 0.02) for single-bladed impellers for any blade angle from 0° to 90°.