Set Of Basic Functions Research Articles

Theory of the dielectric susceptibility of nonpolar biaxial liquid crystals

A statistical theory of the dielectric susceptibility of nonpolar liquid crystals, whose constituent molecules are biaxial, is proposed. The ordering is described by means of the mean field theory, in which a set of basic functions is introduced. The dielectric susceptibilities are derived using a generalized Clausius-Mossotti approach. The theory was used to calculate the temperature and the density dependence of the order parameters and of the susceptibilities. On increasing the density, an ordering reversal of the corresponding susceptibilities is obtained.

CONTROL SYNTHESIS FOR RECONFIGURABLE DISTRIBUTED SYSTEMS WITH APPLICATIONS IN MANUFACTURING

We present a framework for control synthesis of reconfigurable distributed agent systems, where each agent includes its own set of basic functions and local rules. There are also global rules, which govern the interaction and communication between these agents. Agents are logically defined by a control synthesizer, communicator, and executer. The control synthesis is capable of detecting and avoiding single level deadlocks at execution level. We illustrate the concept through an example.

Mathematical Structure of Anomalous Dimensions and QCD Wilson Coefficients in Higher Order

The alternating and non-alternating harmonic sums and other algebraic objects of the same equivalence class are connected by algebraic relations which are induced by the product of these quantities and which depend on their index class rather than on their value. We show how to find a basis of the associated algebra. The length of the basis $l$ is found to be $\leq 1/d$, where $d$ is the depth of the sums considered and is given by the 2nd {\sc Witt} formula. It can be also determined counting the {\sc Lyndon} words of the respective index set. There are two further classes of relations: structural relations between {\sc Nielsen}--type integrals and relations due to the specific structure of {\sc Feynman} diagrams which lead to a considerable reduction of the set of basic functions. The relations derived can be used to simplify results of higher order calculations in QED and QCD. We also report on results calculating the 16th non--singlet moment of unpolarized structure functions at 3--loop order in the $\bar{\rm MS}$ scheme.

Comments on "An innovative fast powerful method for tackling electromagnetic eigenvalue problems for multistrip transmission lines" [with reply

For original paper see A. Casanueva and J.L. Garcia, ibid., vol.50, no.1, p.36-40 (2002). The original authors applied a technique developed by the commenter to calculate dispersion characteristics of multistrip transmission lines. The novelty of the work lay in the technique for solving the resulting eigenvalue problem. Casanueva and Garcia treated the problem as a system of homogeneous equations and advocate solving it by using singular value decomposition (SVD) combined with the search of minimum on the complex /spl beta/ plane. The commenter clarifies an apparent misunderstanding as to the numerical treatment of the eigenvalue problem. In reply, Casanueva and Garcia agree with the general outline and accept that the numerical technique suggested by Mrozowski is more orthodox than the one they used. They conclude by stressing that Mrozowski's proposed algorithms are valid for planar transmission lines when both the spectral-domain approach and the singular-value-decomposition technique have been implemented to obtain an accurate set of basic functions.

A relational database for physical data from TJ-II discharges

A relational database (RDB) has been developed for classifying TJ-II experimental data according to physical criteria. Two objectives have been achieved: the design and the implementation of the database and the software tools for data access depending on a single software driver. TJ-II data were arranged in several tables with a flexible design, speedy performance, efficient search capacity and adaptability to meet present and future, requirements. The software has been developed to allow the access to the TJ-II RDB from a variety of computer platforms ( alpha axp/True64 unix, cray/ unicos, Intel Linux, Sparc/Solaris and Intel/Windows 95/98/NT) and programming languages ( fortran and c/ c++). The database resides in a Windows NT Server computer and is managed by Microsoft SQL Server. The access software is based on open network computing remote procedure call and follows client/server model. A server program running in the Windows NT computer controls data access. Operations on the database (through a local ODBC connection) are performed according to predefined permission protocols. A client library providing a set of basic functions for data integration and retrieval has been built in both static and dynamic link versions. The dynamic version is essential in accessing RDB data from 4GL environments (IDL and PV-WAVE among others).

From Fourier Expansions to Arithmetic-Haar Expressions on Quaternion Groups

Arithmetic expressions for switching functions are introduced through the replacement of Boolean operations with arithmetic equivalents. In this setting, they can be regarded as the integer counterpart of Reed-Muller expressions for switching functions. However, arithmetic expressions can be interpreted as series expansions in the space of complex valued functions on finite dyadic groups in terms of a particular set of basic functions. In this case, arithmetic expressions can be derived from the Walsh series expansions, which are the Fourier expansions on finite dyadic groups. In this paper, we extend the arithmetic expressions to non-Abelian groups by the example of quaternion groups. Similar to the case of finite dyadic groups, the arithmetic expressions on quaternion groups are derived from the Fourier expansions. Attempts are done to get the related transform matrices with a struc- ture similar to that of the Haar transform matrices, which ensures efficiency of computation of arithmetic coefficients.

Harmonic sums and Mellin transforms up to two-loop order

A systematic study is performed on the finite harmonic sums up to level four. These sums form the general basis for the Mellin transforms of all individual functions ${f}_{i}(x)$ of the momentum fraction x emerging in the quantities of massless QED and QCD up to two-loop order, as the unpolarized and polarized splitting functions, coefficient functions, and hard scattering cross sections for space and timelike momentum transfer. The finite harmonic sums are calculated explicitly in the linear representation. Algebraic relations connecting these sums are derived to obtain representations based on a reduced set of basic functions. The Mellin transforms of all the corresponding Nielsen functions are calculated.

Wavelet transform in electrocardiography—data compression

An application of the wavelet transform to electrocardiography is described in the paper. The transform is used as a first stage of a lossy compression algorithm for efficient coding of rest ECG signals. The proposed technique is based on the decomposition of the ECG signal into a set of basic functions covering the time-frequency domain. Thus, non-stationary character of ECG data is considered. Some of the time-frequency signal components are removed because of their low influence to signal characteristics. Resulting components are efficiently coded by quantization, composition into a sequence of coefficients and compression by a run-length coder and a entropie Huffman coder. The proposed wavelet-based compression algorithm can compress data to average code length about 1 bit/sample. The algorithm can be also implemented to a real-time processing system when wavelet transform is computed by fast linear filters described in the paper. © 1997 Elsevier Science Ireland Ltd.

The use of bubble functions for the stability of plates with different end conditions

A modified semi-analytical finite strip method of buckling analysis in which the usual restriction of two, opposite, simply supported ends is removed by assuming appropriate longitudinal functions is described. Two sets of basic functions (denoted I and II) are used in the buckling study and the accuracy of these basic functions is evaluated. It is shown that the use of so-called bubble functions significantly improves the convergence of the finite strip method for local buckling problems. The analytical procedure is used to investigate the local buckling behaviour of isotropic plates with different boundary conditions along all edges under both uniaxial and biaxial compression, and the buckling of stiffened plates under compression. The bubble formulation provides a powerful tool for the efficient analysis of a variety of local buckling problems.

Rigidly rotating modes of the solar magnetic field

Discrete rigidly rotating components (modes) of the large-scale solar magnetic field have been investigated. We have used a specially calculated basic set of functions to resolve the observed magnetic field into discrete components. This adaptive set of functions, as well as the expansion coefficients, have been found by processing a series of digitized synoptic maps of the background magnetic field over a 20-year period. As a result, dependences have been obtained which describe the spatial structure and the temporal evolution of the 27-day and 28-day rigidly rotating modes of the Sun's magnetic field. The spatial structure of the modes has been compared with simulations based on the known flux-transport equation. In the simulations, the rigidly rotating modes were regarded as stationary states of the magnetic field whose rigid rotation and stability were maintained by a balance between the emergence of magnetic flux from stationary sources located at low latitudes and the horizontal transport of flux by turbulent diffusion and poleward directed meridional flow. Under these assumptions, the structure of the modes is determined solely by the horizontal velocity field of the plasma, except for the low-latitude zone where sources of magnetic flux concentrate. We have found a detailed agreement between the simulations and the results of the data analysis, provided that the amplitude of the meridional flow velocity and the diffusion constant are equal to 9.5 m s−1 and 600 km2 s−1, respectively. The analysis of the expansion coefficients has shown that the rigidly rotating modes undergo rapid step-like variations which occur quasi-periodically with a period of about two years. These variations are caused by separate surges of magnetic flux in the photosphere, so that each new surge gives rise to a rapid replacement of old large-scale magnetic structures by newly arisen ones.

Intermittency and multifractality of medium-energy particles in proton-nucleus interactions at 800 GeV.

We investigate the intermittent and multifractal behaviors of the multiplicity fluctuations of medium energy particles in 800 GeV proton interactions with emulsion nuclei. For our analysis, we have used ordinary scaled factorial moments (SFM) denoted as ${\mathit{F}}_{\mathit{q}}$, modified SFM, (${\mathit{F}}_{\mathit{q}}^{\ensuremath{'}}$) and modified multifractal moments, (${\mathit{G}}_{\mathit{q}}^{\ensuremath{'}}$) with suppressed statistical contributions. For a close comparison between the ${\mathit{F}}_{\mathit{q}}^{\ensuremath{'}}$ and ${\mathit{G}}_{\mathit{q}}^{\ensuremath{'}}$ moments, they have both been expanded in a set of basic functions each of which has a characteristic fractal behavior as a function of the resolution in phase space. The experimental values of anomalous fractal dimensions ${\mathit{d}}_{\mathit{q}}$ and Renyi dimensions ${\mathit{D}}_{\mathit{q}}$ are determined for q=2-5. The latter are corrected for statistical contamination in the multiplicity fluctuations. The observed variation of ${\mathit{d}}_{\mathit{q}}$ and ${\mathit{D}}_{\mathit{q}}^{\mathrm{dyn}}$ with q supports a self-similar random cascading mechanism for the particle production process. It is found that ${\mathit{D}}_{\mathit{q}}^{\mathrm{dyn}}$+${\mathit{d}}_{\mathit{q}}$=1.

SUPER: Visual Interfaces for Object + Relationship Data Models

SUPER is an exploratory project into the next generation of user-DBMS interfaces. Its main objective is to demonstrate that a visual paradigm can lead to powerful and user-friendly interfaces supporting all phases of the database life cycle (i.e. creation, manipulation and evolution). Visual interaction in SUPER is based on direct manipulation of objects and functions, with a special focus on providing users with maximum flexibility and independence from database technicalities. The set of tools offers facilities to meet the varied demands from categories of users with different levels of skill. Diagrammatic representations and a basic set of functions are better suited for novice and occasional users, while menus and dialog boxes speed up the dialog for expert users. At the same times a consistent interaction style over the various functions and tools has been emphasized. SUPER has been designed as a front end to a relational or an object-oriented DBMS, i.e. the persistence of data, consistency and concurrency problems are delegated to an off-the-shelf database management system. The current prototype supports schema definition, query formulation and browsing using a powerful data model based on objects and relationships.

Modeling of Multibody Systems Connected by Standard Engineering Joints

This paper demonstrates that, when modeling multibody systems connected by standard engineering joints, the resulting mathematical model can be cast in a singularly perturbed formulation. The modeling method described here may be used to model mechanical joints that admit microscopic deformation that can be numerically evaluated on widely available 64-bit computers. As opposed to classical multibody modeling methods, the singularly perturbed formulation produces the dynamic equations in an explicit state-space form that is well-suited for parallel processing. Furthermore, the main advantage of singularly perturbed formulation is the ease with which it can be implemented. This paper first gives a theorem which demonstrates that standard, non-abstracted, kinematic joints can be modeled in a singularly perturbed formulation. Furthermore, the perturbation parameters are shown to be capable of modeling joint clearance and stiffness. Power conservation principles are then used to provide a set of basic functions that can be grouped to obtain a differential equation description of various kinematic joints. Finally, a general form of the aggregate dynamic equation of multibody systems modeled in singularly perturbed formulation is constructed. This form, which is cast in state space, demonstrates the explicit nature of the singularly perturbed formulation of multibody systems.

Fractal behavior of multiplicity fluctuations in high-energy collisions

It is shown that the multiplicity fluctuations of the particles produced in high-energy hadron collisions can be systematically quantified by the $G$ moments, which can be defined to suppress the statistical contributions. Expansion in terms of a set of basic functions ${B}_{q,k}(M)$ provides simple fractal interpretation for the asymptotic power-law behavior of $〈{G}_{q}〉$. The connection with the scaled factorial moments is investigated. An extension to nonintegral values of $q$ is considered. The generalized fractal dimension ${D}_{q}$ is determined. Calculations of all quantities involving multiplicity fluctuations are done using a Monte Carlo code (ECCO) based on the geometrical branching model, which has previously been shown to yield the correct degree of intermittency as determined by the NA22 experiment on hadronic collisions.

Quantum topology and quantisation on the lattice of topologies

The concept of 'quantum topology' is studied via a quantisation of the set tau (X) of all topologies on a given set X. A natural lattice structure exists on this set induced by the idea of one topology having more, or less, open sets than other. This is used to provide a basic set of functions on tau (X) which generate a commutative algebra (the v operation on the lattice) whose spectral theory forms the basis for a general quantisation. It is shown that the analogue of a 'distributional' topology is an ideal in the lattice tau (X) and the spectral theory is used to place a natural topology on the set of all such ideals. The next step is to discuss the existence of variables conjugate to the basic functions on tau (X).

Generalized moment method analysis of planar reactively loaded rectangular waveguide arrays

A combined modal expansion and moment method is applied for analyzing finite planar arrays of rectangular waveguides in an infinite ground plane including reactively loaded waveguide elements. The analysis, which is based on the moment method for solving the aperture problem, in combination with the modal analysis for the reactively loaded waveguide cavities or feeding waveguides, extends the network formulation of single apertures to multiple waveguide arrays including reactively loaded elements. Two orthogonally polarized sets of basic functions are utilized to model the expansion into the complete set of eigenmodes is used to formulate the waveguide cavity problem. The theory is applied to a finite planar array of arbitrarily spaced rectangular waveguides, where reactive loads are realized by placing sliding electrical conductors at specified distances in each of the unfed waveguides. Numerical design examples show that beamforming, beamsteering, and the improvement of the crosspolarization behavior is possible by a suitable choice of the geometrical parameters. The theory is verified by results available from the literature as well as newly performed experimental measurements. >

Stage model of stress-strain relationship for concrete under short-term load Part 3. Descending branch

While the distinctive feature of the ascending branch in the stress-strain diagram (SSD) of concrete is the atrophying effect, the descending branch (DB) is distinguished by progressive macrodestruction. It is shown that the DB model should consist of two macro-components: the central function, adopted through introduction of macrorigidity, and the internal friction potential. The macrorigidity function is seen to be a combination of the latter with the Gaussian of macrodestruction. It is also established that the specific energy of the destruction process decreases linearly with strength, and that the absolute term of the function represents the internal friction potential - which is intensively manifested with the onset of macrocracking and subsequently “consumed” by the energy released in the process. The DB model predicts adequately the course of the descending branch, including the friction “plateau”; it is thus essential for stress analysis of elements in bending and eccentric compression. It consists of a set of basic functions, each of them representing an aspect of the actual physical process taking place under load beyond the strength limit.

MKS: Machining Kernel Software for CAM-System

A Machining Kernel Software (MKS) which provides a set of basic functions for the CAM system was developed. The main aim of introducing MKS for the CAM system is to allow application programmers to easily form a direct link between CAD and the machining system while interactively processing the machining information. In order to form the direct link between CAD and CAM, a rational parametric representation of a geometric model which is supported by IGES and CCM (Cell-Constructed-geometric-Model) which is proposed by the authors are employed for the interface. MKS is featured by a hierarchical module processing structure, which consists of Data Handling Module, Interactive Machining Information Processing Module and Machine Handling Module, based on CCM. In this paper, the concept of MKS, the relationship between CAD system and MKS/CAM, the basic functions of MKS and some examples of the data processing are described.

Hierarchies of primitive recursive wordsequence functions: Comparisons and decision problems

In this paper we consider wordsequence functions, i.e., functions of the type ƒ: Σ ∗′ → Σ ∗‵ where Σ is a finite alphabet and r ⩾ 0, s > 0. By starting with finite sets of basic functions and by taking the closure with respect to composition, cylindrification and iteration, we give some characterizations of primitive recursive wordsequence functions. We define some hierarchies of length ω 2 of these functions by bounding the number of successive compositions and the depth of the nested iterations in the definitions of the functions. In such a manner we obtain refinements of the Axt, Grzegorczyk and Meyer and Ritchie generalized hierarchies of length ω of primitive recursive wordfunctions defined by Von Henke, Indermark and Weihrauch (1972). We consider Loop programs on words (see Ausiello and Moscarini (1976)) by allowing more than one output register, and we prove that the class of functions computed by these programs coincides with the class of primitive recursive wordsequence functions. The hierarchies of functions induce some hierarchies of programs. For the case of functions ƒ: Σ ∗′ → Σ ∗ , our hierarchies are compared with the Axt et al. generalized hierarchies. We also compare our hierarchies with storage hierarchies, and we analyze the power of the Loop programs as acceptors. Finally, we state some decidability results for the considered classes.

Abbreviated representation of measuring information for the construction of compression systems

1. The ever-rising demands made upon the metrological and technical-economic characteristics of present-day measuring and calculating complexes necessitates the development of methods of reducing the volume of the measuring signal, while retaining all the required amount of information in the latter. 2. An effective method of compressing the measuring signal (for a specified reliability of obtaining information) is that of expressing it in discrete form in a space delineated by an optimally-selected set of basic functions making up the whole signal. 3. On using a uniform approximation criterion, the greatest compression is obtained for the class of continuous signals by expanding the signal into a system of Haar functions, constituting a family of rectangular oscillations, in contrast to the family of sine or cosine oscillations corresponding to the trigonometrical Fourier transformation. 4. The results may be used for constructing a measuring-information compression system.