Relevant bibliographies by topics / Functions of one, two or three variables

Contents

  1. Journal articles

Academic literature on the topic 'Functions of one, two or three variables'

Author: Grafiati
Published: 4 June 2021
Last updated: 13 February 2022

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the lists of relevant articles, books, theses, conference reports, and other scholarly sources on the topic 'Functions of one, two or three variables.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Journal articles on the topic "Functions of one, two or three variables"

1

Ostaszewski, Krzysztof. "The space of Henstock integrable functions of two variables." International Journal of Mathematics and Mathematical Sciences 11, no. 1 (1988): 15–21. http://dx.doi.org/10.1155/s0161171288000043.

Full text
Abstract:
We consider the space of Henstock integrable functions of two variables. Equipped with the Alexiewicz norm the space is proved to be barrelled. We give a partial description of its dual. We show by an example that the dual can't be described in a manner analogous to the one-dimensional case, since in two variables there exist functions whose distributional partials are measures and which are not multipliers for Henstock integrable functions.
APA, Harvard, Vancouver, ISO, and other styles
2

Revenko, Victor. "Representation of the stress state of some orthotropic materials by three harmonic functions of three variables." Scientific journal of the Ternopil national technical university 100, no. 4 (2020): 20–28. http://dx.doi.org/10.33108/visnyk_tntu2020.04.020.

Full text
Abstract:
The model of an orthotropic deformable body based on the representation of stresses in terms of displacements is considered. The method of integration of three equations of the elastic equilibrium is used, based on the elimination of separate displacements. Problems related to the elimination of unnecessary functions from the representation of the general solution of the equations of the theory of elasticity are considered. Criteria are found that determine such a class of orthotropic materials that their stress-strain state can be expressed in terms of two functions. One function satisfies the equation of the second order in partial derivatives, and the other of the fourth order. It is established that the equation of the fourth order, in the general case, is not decomposed into two operator factors. Criteria were found for the expansion of a fourth-order equation into the product of two second-order equations. An equation has been written that must be satisfied by the elastic constants of an orthotropic material. The expression of deformations and stresses by introduced harmonic functions was written down.
APA, Harvard, Vancouver, ISO, and other styles
3

Vu, Hung Q., and Delwyn G. Fredlund. "The prediction of one-, two-, and three-dimensional heave in expansive soils." Canadian Geotechnical Journal 41, no. 4 (2004): 713–37. http://dx.doi.org/10.1139/t04-023.

Full text
Abstract:
The prediction of heave in unsaturated, expansive soils has historically been studied primarily as a one-dimensional type analysis. This paper proposes a methodology that can be used for the prediction of one-, two-, or three-dimensional heave. It is suggested that negative pore-water pressures (i.e., soil suctions) can be estimated through a saturated–unsaturated seepage analysis. The results of the seepage analysis are then used as input for the prediction of displacements in a stress–deformation analysis. The formulation of the governing partial differential equations for both seepage and stress–deformation is based on the general theory of unsaturated soils using two independent stress state variables. The elasticity parameter functions required for a stress–deformation analysis can be calculated from various tests, including conventional one-dimensional oedometer tests. The proposed method is studied and tested against data collected on a case history involving a slab-on-ground floor on Regina clay. The predicted results from the two-dimensional analysis agree well with the measured data in terms of both total vertical displacements and final water contents in the soil. The results of a parametric study are also presented to show the effect of measured soil parameters (i.e., swelling index and initial void ratio) and assumed parameters (i.e., Poisson's ratio and coefficient of earth pressure at rest) on the predicted displacements.Key words: heave prediction, unsaturated soil, expansive soil, seepage analysis, stress analysis.
APA, Harvard, Vancouver, ISO, and other styles
4

Goodman, T. N. T., and S. L. Lee. "Homogeneous polynomial splines." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 117, no. 1-2 (1991): 89–102. http://dx.doi.org/10.1017/s0308210500027621.

Full text
Abstract:
SynopsisWe construct functions which are piecewise homogeneous polynomials in the positive octant in three dimensions. These give a rich and elegant theory which combines properties of polynomial box splines see [6] and the references therein) with the explicit representation of simple exponential box splines [11], while enjoying complete symmetry in the three variables. By a linear transformation followed by a projection on suitable planes, one obtains piecewise polynomial functions of two variables on a mesh formed by three pencils of lines. The vertices of these pencils may be finite or one or two may be infinite, i.e. the corresponding pencils may comprise parallel lines. As a limiting case, all three vertices become infinite and one recovers polynomial box splines on a three-direction mesh.
APA, Harvard, Vancouver, ISO, and other styles
5

Mitrofanov, Sergey, Nikolay Novikov, Vasily Nikitin, and Sergey Belykh. "Mathematical models and soil fertility management software." E3S Web of Conferences 210 (2020): 04008. http://dx.doi.org/10.1051/e3sconf/202021004008.

Full text
Abstract:
The article presents the results of studies on parametric approximation in spaces R2 (functions of one variable), R3 (functions of two variables) and Rn(n>3) (functions of three or more variables). Various classes of functions satisfying a priori conditions were studied: f(0, 0, 0)=0, $\mathop {\lim 1}\limits_{{x_i} \to + \infty } \,\,({x_1},\, \ldots ,\,{x_n}) = {c_i}$, ci = cont. Working algorithms and C/C++ software functioning in Microsoft Visual Studio 2019 system in Microsoft Windows 10 environment were developed. The main studies of the authors were aimed at developing effective computational algorithms for constructing approximating functions of two variables from various given classes of three-dimensional data samples (three-dimensional interconnected time series). The article provides a detailed description of the problem statement, introduces classes of approximating functions, provides algorithms for estimating the parameters of approximating functions and a description of the software. The estimation algorithm considered in the article is constructed according to the scheme of the coordinate descent method with optimization of the step length (Gauss-Seidel method).
APA, Harvard, Vancouver, ISO, and other styles
6

Vitanov, Nikolay K., Zlatinka I. Dimitrova, and Kaloyan N. Vitanov. "On the Use of Composite Functions in the Simple Equations Method to Obtain Exact Solutions of Nonlinear Differential Equations." Computation 9, no. 10 (2021): 104. http://dx.doi.org/10.3390/computation9100104.

Full text
Abstract:
We discuss the Simple Equations Method (SEsM) for obtaining exact solutions of a class of nonlinear differential equations containing polynomial nonlinearities. We present an amended version of the methodology, which is based on the use of composite functions. The number of steps of the SEsM was reduced from seven to four in the amended version of the methodology. For the case of nonlinear differential equations with polynomial nonlinearities, SEsM can reduce the solved equations to a system of nonlinear algebraic equations. Each nontrivial solution of this algebraic system leads to an exact solution of the solved nonlinear differential equations. We prove the theorems and present examples for the use of composite functions in the methodology of the SEsM for the following three kinds of composite functions: (i) a composite function of one function of one independent variable; (ii) a composite function of two functions of two independent variables; (iii) a composite function of three functions of two independent variables.
APA, Harvard, Vancouver, ISO, and other styles
7

Suzuki, Alfredo Takashi. "Correspondence between the one-loop three-point vertex and the Y and Δ electric resistor networks". Canadian Journal of Physics 92, № 2 (2014): 131–35. http://dx.doi.org/10.1139/cjp-2012-0403.

Full text
Abstract:
Different mathematical methods have been applied to obtain the analytic result for the massless triangle Feynman diagram yielding a sum of four linearly independent (LI) hypergeometric functions of two variables F4. This result is not physically acceptable when it is embedded in higher loops, because all four hypergeometric functions in the triangle result have the same region of convergence and further integration means going outside those regions of convergence. We could go outside those regions by using the well-known analytic continuation formulas obeyed by the F4, but there are at least two ways we can do this. Which is the correct one? Whichever continuation one uses, it reduces a number of F4 from four to three. This reduction in the number of hypergeometric functions can be understood by taking into account the fundamental physical constraint imposed by the conservation of momenta flowing along the three legs of the diagram. With this, the number of overall LI functions that enter the most general solution must reduce accordingly. It remains to determine which set of three LI solutions needs to be taken. To determine the exact structure and content of the analytic solution for the three-point function that can be embedded in higher loops, we use the analogy that exists between Feynman diagrams and electric circuit networks, in which the electric current flowing in the network plays the role of the momentum flowing in the lines of a Feynman diagram. This analogy is employed to define exactly which three out of the four hypergeometric functions are relevant to the analytic solution for the Feynman diagram. The analogy is built based on the equivalence between electric resistance circuit networks of types Y and Δ in which flows a conserved current. The equivalence is established via the theorem of minimum energy dissipation within circuits having these structures.
APA, Harvard, Vancouver, ISO, and other styles
8

BANERJEE, SANTO, and A. ROY CHOWDHURY. "FUNCTIONAL SYNCHRONIZATION AND ITS APPLICATION TO SECURE COMMUNICATIONS." International Journal of Modern Physics B 23, no. 09 (2009): 2285–95. http://dx.doi.org/10.1142/s0217979209052157.

Full text
Abstract:
A new kind of synchronization in which some well-defined functions of dynamical variables tend to each other as time evolves is shown to take place in two distinct three-dimensional nonlinear systems. This new kind of functional synchronization is analyzed using the partial Lyapunov functions which help one to construct the functions of the nonlinear variables which synchronize. In the next phase we show how one can develop a set of keys to encode and decode a signal which is to be transmitted. Since the key construction is very much dependent on the chosen function, the whole system is highly secure.
APA, Harvard, Vancouver, ISO, and other styles
9

TONTI, ENZO. "A DIRECT DISCRETE FORMULATION FOR THE WAVE EQUATION." Journal of Computational Acoustics 09, no. 04 (2001): 1355–82. http://dx.doi.org/10.1142/s0218396x01001455.

Full text
Abstract:
The paper shows how to give a direct discrete formulation of the wave equation starting directly from physical laws, i.e. without passing through differential formulation. Using global variables instead of scalar and vector field functions, a close link between global variables and spatial and temporal elements immediately appears. A preliminary classification of physical variables into three classes: configuration, source and energy variables and the use of two cell complexes, one dual of the other, gives an unambiguous association of global variables to the spatial and temporal elements of the two complexes. Thus, one arrives at a discrete formulation of d'Alembert equation on an unstructured mesh.
APA, Harvard, Vancouver, ISO, and other styles
10

Chen, W. Q., and H. J. Ding. "A State-Space-Based Stress Analysis of a Multilayered Spherical Shell With Spherical Isotropy." Journal of Applied Mechanics 68, no. 1 (2000): 109–14. http://dx.doi.org/10.1115/1.1343913.

Full text
Abstract:
This paper presents an exact static stress analysis of a multilayered elastic spherical shell (hollow sphere) completely based on three-dimensional elasticity for spherical isotropy. Two independent state equations are derived after introducing three displacement functions and two stress functions. In particular, a variable substitution technique is used to derive the state equations with constant coefficients. Matrix theory is then employed to obtain the relationships between the state variables at the upper and lower surfaces of each lamina. By virtue of the continuity conditions between two adjacent layers, a second-order linear algebraic equation and a fourth-order one about the boundary variables at the inner and outer surfaces of a multilayered spherical shell are obtained. Numerical examples are presented to show the effectiveness of the present method.
APA, Harvard, Vancouver, ISO, and other styles
More sources
You might also be interested in the extended bibliographies on the topic 'Functions of one, two or three variables' for particular source types:
Journal articles
We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!

To the bibliography