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This paper consists of several new results about Length property of the module M. F-length of any Module comes from several concepts like Neotherian module and Artinian modules (Neo and Art) with comp- sition series. We proved that any Neo-module has submodule T and Neo-module is F-length. This implies that T also has F-length Property. Finally, some remarks, examples and definitions have been presented in this paper. [ABSTRACT FROM AUTHOR]

The problem of unsteady rotational motion of electrically conducting viscous incompressible fluid, contained within two asxially concentric cylinders of finite length in the presence of an axial symmetric magnetic field of constant strength, has been solved exactly using finite Hankel transform in combination with a technique presented in this paper. This paper presents a complete of the problem under consideration, which has been of interest for many years; moreover the Pneuman-Lykoudis solution in Magnetohydrodynamics and Childyat solution in hydrodynamics appears as a special case of this study. The analysis shows that the disturbance in the fluid disappears by increasing the magnetic field. [ABSTRACT FROM AUTHOR]

In cylindrical roller bearings, the drag effect may be induced by the rolling element translating in a fluid environment of the bearing cavity. In this article, the computational fluid dynamics method and experimental tests are employed to analyse its flow characteristics and pressure distribution. The results indicate that the pressure difference between the windward side and the leeward side of the cylinder is raised in view of it blocking the flow field. Four whirl vortexes are formed in four outlets of two wedge-shaped areas between the front part of the cylindrical surface and adjacent walls for the cylinder of L / D = 1.5 at Re = 4.5 × 103. Vortex shedding is found in the direction of cylinder axis at Re = 4.5 × 104. The relationship between drag coefficient and Reynolds number is illustrated, obviously higher than that of the two-dimensional cylinder in open space. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Harbin Institute of Technology. Social Sciences Edition / Haerbin Gongye Daxue Xuebao. Shehui Kexue Ban is the property of Harbin Institute of Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

One of the most problems that affects the performance of the journal bearing is the shaft misalignment. Misalignment may result due to installation error, shaft deformation, manufacturing error, bearing wear, etc. This paper presents a solution for the misaligned journal bearing problem under hydrodynamic regime. The Reynolds equation has been solved numerically for a finite length bearing based on the finite difference method. The solution demonstrates a new model for the representation of the 3D misalignment geometry and also a detailed procedure for the implementation of the boundary condition in the numerical solution is explained. Furthermore, the convergence of the solution to the required load is investigated. The results reveal a severe thinning in the levels of film thickness and significant rising of the maximum pressure value when the misalignment is taken into consideration.

[Objectives]In this paper, in order to study the flow characteristics and mechanism of three-dimensional flow around a circular cylinder of finite length,[Methods] a numerical simulation using a Large Eddy Simulation (LES) and vortex structural classification technology is carried out, and the accuracy of the simulation is proven.[Results] When analyzing the flow field, it is found that the length of the recirculation zone is smaller for a circular cylinder of finite length. In addition, the downstream from the free end can suppress the common phenomenon of Karman-Vortex-Street which leads to a loss of drag-coefficient. Compared with the fixed wall at the bottom, the free end surface has a higher influence on the onstream-wise velocity. The ‘mushroom’ vortex appears in pairs and two original points exist on the free end. The circular cylinder of finite length appears to be strongly three-dimensional with a lower drag-coefficient. Moreover, there is a tip vortex behind the free end and a horseshoe vortex in the cylinder-wall junction.[Conclusions] The results of this paper give a relatively comprehensive description of the flow characteristics of a circular cylinder of finite length, and can provide useful references for relevant research。

The stress–strain state of an inhomogeneous hollow cylinder with clamped edges is studied using the three-dimensional elasticity theory. The problem is solved with the spline-approximation and finite-element methods. To reduce the system of partial differential equations to a system of ordinary high-order differential equations, two-dimensional splines are applied. The one-dimensional problem is solved with the method of discrete orthgonalization. The results obtained with the spline-approximation and finite-element methods for an open inhomogeneous cylinder with a radially varying elastic modulus are compared. [ABSTRACT FROM AUTHOR]

Various signals of finite length are often analysed by the Wigner‐Ville distribution (WVD). Thus, this article deals with the implementation of their discrete WVDs on field‐programmable gate arrays (FPGAs). For the discrete WVD, its calculation procedures are composed of the autocorrelation function and Fourier transform. Since the autocorrelation procedure is the most time‐consuming step in the entire computation process, the authors analyse the calculation procedure of autocorrelation function in detail. Here the proposed efficient method just calculates partial non‐zero elements of the autocorrelation matrices in order to reduce the computation complexity. The FFT (built‐in FPGAs) is then utilised to acquire the discrete WVD. In addition, the idea of the fully‐pipelined and parallelism is borrowed to reduce the running time but at the cost of recourses. Finally, the authors provide implementations of both authors proposed method and two other algorithms on different FPGAs. The experimental results show that the Intel Arria‐10 FPGA families are the better choice in the floating point arithmetic and that authors method has the best performance. [ABSTRACT FROM AUTHOR]

Abstract A generalized correspondence functor is a functor from the category of finite sets and T -generalized correspondences to the category of all k -modules, where T is a finite distributive lattice and k a commutative ring. We parametrize simple generalized correspondence functors using the notions of T -module and presheaf of posets. As an application, we prove finiteness and stabilization results. In particular, when k is a field, any finitely generated correspondence functor has finite length, and when k is noetherian, any subfunctor of a finitely generated functor is finitely generated. [ABSTRACT FROM AUTHOR]

Abstract In this paper we study the effect of absorption peak correlation in finite length carbon nanotubes and graphene nanoribbons. It is shown, in the orthogonal π-orbital tight-binding model with the nearest neighbor approximation, that if the ribbon width is a half of the tube circumference the effect takes place for all achiral ribbons (zigzag, armchair and bearded), and corresponding tubes, starting from lengths of about 30 nm. This correlation should be useful in designing nanoribbon-based optoelectronics devices fully integrated into a single layer of graphene. [ABSTRACT FROM AUTHOR]

Abstract: The error exponent of the regular graph-based binary low-density parity-check (LDPC) codes under the maximum likelihood (ML) decoding algorithm in the binary symmetric channel (BSC) is analyzed. Unlike most other papers where error exponents are considered for the case when the length of LDPC codes tends to infinity (asymptotic analysis), the finite length case (finite length analysis) is considered. In this paper, a method of deriving the lower bound on the error exponent for a regular graph-based LDPC code with finite length under ML decoding is described. Also we analyze Dependences of the error exponent on various LDPC code parameters are also analyzed. The numerical results obtained for the considered lower bound are represented and analyzed at the end of the paper. [ABSTRACT FROM AUTHOR]

When dealing with 50–60 Hz inductive electromagnetic interference from power lines on pipelines, the key parameter is represented by the per unit length mutual impedance between the power line conductor‐Earth and pipe‐Earth circuits. Different philosophies can be followed concerning the evaluation of this parameter, i.e.: modelling the power line conductors by wires of finite length or by wires of infinite length. What is missing in the literature is a comparison of the interference results (i.e. overvoltage and overcurrent induced on the pipeline) that are obtained by following these different approaches. Thus, this study is devoted to investigate this neglected point relevant to the 50–60 Hz interference issue. To this aim, the authors[AQ ID=Q2] also present and compare some results of interference calculated in real cases and, on the basis of them, they draw some conclusions concerning which, in their opinion, is the best approach. [ABSTRACT FROM AUTHOR]

In this paper, a semi-analytical solution is presented for the problem of modal acoustic radiation efficiency of a finite-length rotating cylinder. The cylinder is immersed in an irrotational inviscid compressible fluid. Assuming the cylinder to vibrate sinusoidally in transverse direction and rotate at constant angular velocity, the scalar equation of sound propagation is decomposed into a coupled set of time independent equations. Using Galerkin method and employing spherical eigen-functions as a complete set of solution, modal acoustic pressure and acoustic radiation efficiency of the cylinder are calculated. Numerical solutions are presented to discuss modal radiation efficiency corresponding to forward and backward circumferential waves. [ABSTRACT FROM AUTHOR]

One of the most problems that affects the performance of the journal bearing is the shaft misalignment. Misalignment may result due to installation error, shaft deformation, manufacturing error, bearing wear, etc. This paper presents a solution for the misaligned journal bearing problem under hydrodynamic regime. The Reynolds equation has been solved numerically for a finite length bearing based on the finite difference method. The solution demonstrates a new model for the representation of the 3D misalignment geometry and also a detailed procedure for the implementation of the boundary condition in the numerical solution is explained. Furthermore, the convergence of the solution to the required load is investigated. The results reveal a severe thinning in the levels of film thickness and significant rising of the maximum pressure value when the misalignment is taken into consideration. [ABSTRACT FROM AUTHOR]

We investigate the representation theory of finite sets. The correspondence functors are the functors from the category of finite sets and correspondences to the category of k -modules, where k is a commutative ring. They have various specific properties which do not hold for other types of functors. In particular, if k is a field and if F is a correspondence functor, then F is finitely generated if and only if the dimension of F ( X ) grows exponentially in terms of the cardinality of the finite set X . Moreover, in such a case, F has actually finite length. Also, if k is noetherian, then any subfunctor of a finitely generated functor is finitely generated. [ABSTRACT FROM AUTHOR]

A circular coil equipped with magnetic core of finite length and constant permeability is difficult to analyse by traditional analytical methods in consequence of the complicated boundary conditions. The difficulties can be overcome by using the truncated region eigenfunction expansion method, and with the aid of a special source function K(z) introduced in the work, this method can be simplified remarkably and concise expressions of the inductance of coils with magnetic cores are obtained. In addition, the calculations can be extended readily to a pair of coaxial coils with magnetic cores of finite length and different permeability. The eigenvalues and inversions of matrices are implemented numerically in the solving process, while most of calculations are accomplished by analytic integrations and matrix algebra, by which the deduced expressions are quite suitable for numerical evaluations. The proposed method is verified by the numerical results compared with those of finite‐element method simulations, from which it is confirmed that the proposed method is much faster and more memory efficient. [ABSTRACT FROM AUTHOR]

This paper considers the analytical free time domain response and energy in an axially translating and laterally vibrating string. The domain of the string is either a constant or variable length, dependent upon the general initial conditions. The translating tensioned strings possess either fixed-fixed or fixed-free boundaries. An alternative analytical solution using a reflected wave superposition method is presented for a finite translating string. Firstly, the cycles of vibration for both constant and variable length strings are provided, which for the latter are dependent upon the variable string length. Each cycle is divided into three time intervals according to the magnitude and the direction of the translating string velocity. Applying d’Alembert's method combined with the reflection properties, expressions for the reflected waves at the two boundaries are obtained. Subsequently, superposition of all of the incident and reflected waves provides results for the free vibration of the string over the three time intervals. The variation in the total mechanical energy of the string system is also shown. The accuracy and efficiency of the proposed method are confirmed numerically by comparison to simulations produced using a Newmark-Beta method solution and an existing state space function representation of the string dynamics. [ABSTRACT FROM AUTHOR]

Theoretical characteristics of the flow in scrolls of hydraulic turbines whose cross-sectional dimensions and shapes are determined using the equations of the potential flow induced by a vortex sink cylinder of finite length located on an impermeable cylinder of infinite length in an ideal fluid are calculated. The theoretical distributions of the components of the velocity and the directions of its horizontal and vertical projections (vertical turbine) are determined and plotted. They are favorable for hydraulic turbines and are in good agreement with the values set at the stator inlet, which confirms the effectiveness of the new approach to studying potential flows whose velocity potential cannot be expressed analytically. [ABSTRACT FROM AUTHOR]

For a Cohen-Macaulay ring R, we exhibit the equivalence of the bounded derived categories of certain resolving subcategories, which, amongst other results, yields an equivalence of the bounded derived category of finite length and finite projective dimension modules with the bounded derived category of projective modules with finite length homologies. This yields isomorphisms of K-theory and Witt groups (amongst other invariants) and improves on terms of associated spectral sequences and Gersten complexes. [ABSTRACT FROM AUTHOR]

Ductborne noise within HVAC and exhaust systems may transfer into the surrounding environment through the walls of the duct. This breakout noise normally needs to be lowered in order to meet health and safety guidelines. This means that the ability of the duct walls to lower breakout noise needs to be predicted during the design stage of the duct systems. Significant work has been conducted into the prediction of breakout noise for infinite length ducts, however there is little to be found on finite length ducts. In particular there are very few studies on the difference between finite and infinite length duct breakout, especially where the noise source lies within the internal fluid. The aim of this work is therefore to investigate the difference in breakout noise between finite length and equivalent infinite length ducts when excited by an internal noise source. This is performed through numerical experiments using the semi analytical finite element method which enables the equations of elasticity for the duct wall, as well as a surrounding fluid, to be accommodated. Axial continuity equations at each end of a finite length elastic duct are then enforced through the point collocation method. It is observed that high sound power levels are emitted at axial resonances of the finite length duct. In the low frequency region these resonances have a narrow bandwidth and are expected to be of little practical significance. However, above the critical frequency the resonance bandwidth increases and this is observed to significantly lower the transverse transmission loss of the duct wall when compared to an infinite length duct. This phenomenon is observed for both clamped and simply supported ducts, as well as for two different internal sound sources. It is concluded that breakout noise from axial resonances in finite length ducts should be examined in design calculations in order to avoid excessive breakout noise. [Display omitted] • Break out noise from infinite and finite length cylindrical ducts is compared. • The semi analytical finite element method is used to predict transmission loss. • An internal acoustic source is observed to excite axial resonances in the duct wall. • The effect of these resonances on transmission loss is discussed. [ABSTRACT FROM AUTHOR]

The matrix elements of electron-photon interaction were investigated in a one-dimensional model of a finite length crystal lattice. Its electronic stationary states belong both to quasi-discrete and to continuous energy band spectra. We analyze formation and degree of applicability for the law of 'momentum' conservation and for the vertical transitions approximation as the lattice length increases. The values of matrix elements and their dependence on lattice length are different for the cases when the final state is lying under the vacuum level and when the final state is lying above this level. In the latter case, the resonant penetration of electrons in the lattice may increase the matrix elements by many orders of magnitude. The results are different in the middle and near the thresholds of the energy bands, for the cases of tight and weak binding of electrons in the lattice cell. The selection rules of the 'momentum' conservation and the approximation of vertical transitions disappear at extremely weak binding. [ABSTRACT FROM AUTHOR]

Potential flow is considered in a cylindrical coordinate system ( r, z, θ), caused by a vortex filament located on the z-axis and a finite length vortex inflow-cylinder of uniform intensity distribution located on an infinite impermeable cylinder, the centerline of which coincides with the z axis, in infinite space filled with an ideal liquid. Equipotential surface (line) equations and flow surfaces (lines) are given, along with relations for determining velocity components. It is shown that the flow lines caused by a vortex inflow-cylinder lie on the flow surfaces created generated by the inflow-cylinder. Equations are given that allow lines of total flow to be projected onto planes normal to the z axis using the finite difference method. It is noted that the shape of the flow lines on the respective flow surfaces depend only on the ratio of the vortex filament intensity to inflow-cylinder flow rate. [ABSTRACT FROM AUTHOR]

The stress-strain state of an inhomogeneous hollow cylinder with different boundary conditions at the ends is analyzed using the three-dimensional theory of elasticity. Spline collocation is used to reduce the two-dimensional boundary-value problem to a boundary-value problem for a system of ordinary differential equations of high order with respect to the radial coordinate, which is solved with the stable discrete-orthogonalization method. The results obtained using the spline-collocation, Fourier-series, and finite-element methods are compared [ABSTRACT FROM AUTHOR]