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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.
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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.
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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.
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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.
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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.
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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 saturatedunsaturated seepage analysis. The results of the seepage analysis are then used as input for the prediction of displacements in a stressdeformation analysis. The formulation of the governing partial differential equations for both seepage and stressdeformation is based on the general theory of unsaturated soils using two independent stress state variables. The elasticity parameter functions required for a stressdeformation 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.
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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.
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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.
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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.
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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).
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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Kim Karlsson, Hyunjoo, Yushu Li, and Ghazi Shukur. "The Causal Nexus between Oil Prices, Interest Rates, and Unemployment in Norway Using Wavelet Methods." Sustainability 10, no. 8 (2018): 2792. http://dx.doi.org/10.3390/su10082792.
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This paper applies wavelet multi-resolution analysis (MRA), combined with two types of causality tests, to investigate causal relationships between three variables: real oil price, real interest rate, and unemployment in Norway. Impulse response functions were also utilised to examine effects of innovation in one variable on the other variables. We found that causal relations between the variables tend to be stronger as the wavelet time scale increases; specifically, there were no causal relationships between the variables at the lowest time scales of one to three months. A causal relationship between unemployment rate and interest rate was observed during the period of two quarters to two years, during which time a feedback mechanism was also detected between unemployment and interest rate. Causal relationships between oil price and both interest rate and unemployment were observed at the longest time scale of eight quarters. In conjunction with Granger causality analysis, impulse response functions showed that unemployment rates in Norway respond negatively to oil price shocks around two years after the shocks occur. As an oil exporting country, increases (or decreases) in oil prices reduce (or increase) unemployment in Norway under a time horizon of about two years; previous studies focused on oil importing economies have generally found the inverse to be true. Unlike most studies in this field, we decomposed the implicit aggregation for all time scales by applying MRA with a focus on the Norwegian economy. Thus, one main contribution of this paper is that we unveil and systematically distinguish the nature of the time-scale dependent relationship between real oil price, real interest rate, and unemployment using wavelet decomposition.
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Ortigosa, Nuria, Marcos Orellana-Panchame, Juan Carlos Castro-Palacio, Pedro Fernández de Córdoba, and J. M. Isidro. "Monte Carlo Simulation of a Modified Chi Distribution Considering Asymmetry in the Generating Functions: Application to the Study of Health-Related Variables." Symmetry 13, no. 6 (2021): 924. http://dx.doi.org/10.3390/sym13060924.
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Random variables in biology, social and health sciences commonly follow skewed distributions. Many of these variables can be represented by exGaussian functions; however, in practice, they are sometimes considered as Gaussian functions when statistical analysis is carried out. The asymmetry can play a fundamental role which can not be captured by central tendency estimators such as the mean. By means of Monte Carlo simulations, the effect of a small asymmetry in the generating functions of the chi distribution is studied. To this end, the k generating functions are taken as exGaussian functions. The limits of this approximation are tested numerically for the practical case of three health-related variables: one physical (body mass index) and two cognitive (verbal fluency and short-term memory). This work is in line with our previous works on a physics-inspired mathematical model to represent the reaction times of a group of individuals.
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Gustafson, Sven-Åke. "Investigating semi-infinite programs using penalty functions and Lagrangian methods." Journal of the Australian Mathematical Society. Series B. Applied Mathematics 28, no. 2 (1986): 158–69. http://dx.doi.org/10.1017/s0334270000005270.
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AbstractIn this paper the relations between semi-infinite programs and optimisation problems with finitely many variables and constraints are reviewed. Two classes of convex semi-infinite programs are defined, one based on the fact that a convex set may be represented as the intersection of closed halfspaces, while the other class is defined using the representation of the elements of a convex set as convex combinations of points and directions. Extension to nonconvex problems is given. A common technique of solving a semi-infinite program computationally is to derive necessary conditions for optimality in the form of a nonlinear system of equations with finitely many equations and unknowns. In the three-phase algorithm, this system is constructed from the optimal solution of a discretised version of the given semi-infinite program. i.e. a problem with finitely many variables and constraints. The system is solved numerically, often by means of some linearisation method. One option is to use a direct analog of the familiar SOLVER method.
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Greb, Fabian, Wolff Schlotz, and Jochen Steffens. "Personal and situational influences on the functions of music listening." Psychology of Music 46, no. 6 (2017): 763–94. http://dx.doi.org/10.1177/0305735617724883.
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On the one hand, the majority of research on the functions of music listening focuses on individual differences; on the other hand, a growing amount of research investigates situational influences. However, the question of how much of our daily engagement with music is attributable to individual characteristics and how much it depends on the situation is still under-researched. To answer this question and to reveal the most important predictors of the two domains, participants ( n = 587) of an online study reported on questions regarding the situation, the music, and the functions of music listening for three self-selected situations. Additionally, multiple person-related variables were measured. Results revealed that the influence of individual and situational variables on the functions of music listening varied across functions. The influence of situational variables on the functions of music listening outweighed the influence of individual characteristics. On the situational level, main activity while listening to music showed the greatest impact, while on the individual level, intensity of music preference was most influential. Our findings suggest that research on music in everyday life should incorporate both – individual and situational – variables determining the complex behavior of people interacting with music in a certain situation.
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Chaturvedi, Aparna, and Prakriti Rai. "Some Properties of Extended Hypergeometric Function and Its Transformations." Journal of the Indian Mathematical Society 85, no. 3-4 (2018): 305. http://dx.doi.org/10.18311/jims/2018/20979.
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There emerges different extended versions of Beta function and hypergeometric functions containing extra parameters. We obtain some properties of certain functions like extended Generalized Gauss hypergeometric functions, extended Confluent hypergeometric functions including transformation formulas, Mellin transformation for the generalized extended Gauss hypergeometric function in one, two and more variables.
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PAPAKONSTANTINOU, GEORGE. "A PARALLEL ALGORITHM FOR MINIMIZING ESOP EXPRESSIONS." Journal of Circuits, Systems and Computers 23, no. 01 (2014): 1450015. http://dx.doi.org/10.1142/s0218126614500157.
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Two parallel algorithms are proposed in this paper for solving the problem of finding exact exclusive-or sum of products (ESOP) expressions for an arbitrary Boolean function. This minimization problem is a very difficult one and solutions have been proposed only for up to seven variables. The processing time for some symmetric functions of seven variables is of the order of weeks. The proposed algorithm is a hybrid one (OpenMP, MPI) and a speed-up of more than nine could be achieved, for a cluster of three nodes with four cores each.
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Yulianto, Yulianto, Namira Robihaningrum, and Bella Dhea Elinda. "Management Multivariate Analysis Methods for Variables Measurement in Scientific Papers." Aptisi Transactions on Management (ATM) 3, no. 1 (2019): 65–72. http://dx.doi.org/10.33050/atm.v3i1.826.
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The management of writing a scientific papers we already know has important chapters in the writing. And have a way of choosing in a variety of methods. There are problems in this study, namely the absence of the use of research methods in scientific-rich management. Then one of them is needed by multivariate data analysis management to become one of the methods in writing scientific papers. Multivariate data is data collected from two or more observations by measuring these observations with several characteristics. There are 2 (two) methods in multivariate data, namely dependency and interdependence methods. Dependency analysis functions to explain or predict dependent variables by using two or more independent variables. Focused on the dependency method there are 9 (nine) classifications. It is expected that the multivariate data analysis management can help writers to use scientific research methods well and be able to analyze the influence of several variables on other variables at the same time
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Karimov, K. T. "Keldysh problem for a three-dimensional equation of mixed type with three singular coefficients in a semi-infinite parallelepiped." Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki 30, no. 1 (2020): 31–48. http://dx.doi.org/10.35634/vm200103.
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This article studies the Keldysh problem for a three-dimensional equation of mixed type with three singular coefficients in a semi-infinite parallelepiped. Based on the completeness property of eigenfunction systems of two one-dimensional spectral problems, the uniqueness theorem is proved. To prove the existence of a solution to the problem, the Fourier spectral method based on the separation of variables is used. The solution to this problem is constructed in the form of a sum of a double Fourier-Bessel series. In substantiating the uniform convergence of the constructed series, we used asymptotic estimates of the Bessel functions of the real and imaginary argument. Based on them, estimates were obtained for each member of the series, which made it possible to prove the convergence of the series and its derivatives to the second order inclusive, as well as the existence theorem in the class of regular solutions.
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Khan, Muhammad Altaf, Saeed Islam, Sher Afzal Khan, Ilyas Khan, Sharidan Shafie, and Taza Gul. "Prevention of Leptospirosis Infected Vector and Human Population by Multiple Control Variables." Abstract and Applied Analysis 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/619035.
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Leptospirosis is an infectious disease that damages the liver and kidneys, found mainly in dogs and farm animals and caused by bacteria. In this paper, we present the optimal control problem applied to a dynamical leptospirosis infected vector and human population by using multiple control variables. First, we show the existence of the control problem and then use analytical and numerical techniques to investigate the existence cost effective control efforts for prevention of indirect and direct transmission of this disease. In order to do this, we consider three control functions two for human and one for vector population. We completely characterize the optimal control problem and compute the numerical solution of the optimality system using an iterative method.
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Popkov, Kirill Andreevich. "On self-correcting logic circuits of unreliable gates." Keldysh Institute Preprints, no. 49 (2021): 1–18. http://dx.doi.org/10.20948/prepr-2021-49.
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The following statements are proved: 1) for any integer m ≥ 3 there is a basis consisting of Boolean functions of no more than m variables, in which any Boolean function can be implemented by a logic circuit of unreliable gates that self-corrects relative to certain faults in an arbitrary number of gates; 2) for any positive integer k there are bases consisting of Boolean functions of no more than two variables, in each of which any Boolean function can be implemented by a logic circuit of unreliable gates that self-correct relative to certain faults in no more than k gates; 3) there is a functionally complete basis consisting of Boolean functions of no more than two variables, in which almost no Boolean function can be implemented by a logic circuit of unreliable gates that self-correct relative to at least some faults in no more than one gate.
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Lizzi, Fedele, Manolo Rivera, and Patrizia Vitale. "Green’s functions for translation invariant star products." Modern Physics Letters A 30, no. 36 (2015): 1550194. http://dx.doi.org/10.1142/s0217732315501941.
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We calculate the Green’s functions for a scalar field theory with quartic interactions for which the fields are multiplied with a generic translation invariant star product. Our analysis involves both non-commutative products, for which there is the canonical commutation relation among coordinates, and nonlocal commutative products. We give explicit expressions for the one-loop corrections to the two- and four-point functions. We find that the phenomenon of ultraviolet/infrared mixing is always a consequence of the presence of non-commuting variables. The commutative part of the product does not have the mixing.
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Dou, Xinyuan, Guangbin Ren, Irene Sabadini, and Ting Yang. "Weak Slice Regular Functions on the n-Dimensional Quadratic Cone of Octonions." Journal of Geometric Analysis 31, no. 11 (2021): 11312–37. http://dx.doi.org/10.1007/s12220-021-00682-5.
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AbstractIn the literature on slice analysis in the hypercomplex setting, there are two main approaches to define slice regular functions in one variable: one consists in requiring that the restriction to any complex plane is holomorphic (with the same complex structure of the complex plane), the second one makes use of stem and slice functions. So far, in the setting of several hypercomplex variables, only the second approach has been considered, i.e. the one based on stem functions. In this paper, we use instead the first definition on the so-called n-dimensional quadratic cone of octonions. These two approaches yield the same class of slice regular functions on axially symmetric slice-domains, however, they are different on other types of domains. We call this new class of functions weak slice regular. We show that there exist weak slice regular functions which are not slice regular in the second approach. Moreover, we study various properties of these functions, including a Taylor expansion.
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Liu, Na, and Huazhong Tang. "A High-Order Accurate Gas-Kinetic Scheme for One- and Two-Dimensional Flow Simulation." Communications in Computational Physics 15, no. 4 (2014): 911–43. http://dx.doi.org/10.4208/cicp.130313.210613s.
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AbstractThis paper develops a high-order accurate gas-kinetic scheme in the framework of the finite volume method for the one- and two-dimensional flow simulations, which is an extension of the third-order accurate gas-kinetic scheme [Q.B. Li, K. Xu, and S. Fu, J. Comput. Phys., 229(2010), 6715-6731] and the second-order accurate gas-kinetic scheme [K. Xu, J. Comput. Phys., 171(2001), 289-335]. It is formed by two parts: quartic polynomial reconstruction of the macroscopic variables and fourth-order accurate flux evolution. The first part reconstructs a piecewise cell-center based quartic polynomial and a cell-vertex based quartic polynomial according to the “initial” cell average approximation of macroscopic variables to recover locally the non-equilibrium and equilibrium single particle velocity distribution functions around the cell interface. It is in view of the fact that all macroscopic variables become moments of a single particle velocity distribution function in the gas-kinetic theory. The generalized moment limiter is employed there to suppress the possible numerical oscillation. In the second part, the macroscopic flux at the cell interface is evolved in fourth-order accuracy by means of the simple particle transport mechanism in the microscopic level, i.e. free transport and the Bhatnagar-Gross-Krook (BGK) collisions. In other words, the fourth-order flux evolution is based on the solution (i.e. the particle velocity distribution function) of the BGK model for the Boltzmann equation. Several 1D and 2D test problems are numerically solved by using the proposed high-order accurate gas-kinetic scheme. By comparing with the exact solutions or the numerical solutions obtained the second-order or third-order accurate gas-kinetic scheme, the computations demonstrate that our scheme is effective and accurate for simulating invisid and viscous fluid flows, and the accuracy of the high-order GKS depends on the choice of the (numerical) collision time.
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Abdul – Razaq, T. S., and H. M. Motair. ""On the Two Machine Permutation Flowshop Scheduling Problems Using Variable Neighborhood Search Algorithms "." Muthanna Journal of Pure Science 5, no. 1 (2018): 36–47. http://dx.doi.org/10.52113/2/05.01.2018/36-47.
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"This paper considers the two machine permutation flow shop scheduling problem PFSSP. We study some special cases of the problem 2||( , Σ , , Σ ) (P). In the first one, the special cases to find the exact non dominated solutions for problem () are based on the relation between processing times , and the due dates on machine A and machine B, ( = 1,2, … , ). In the second one, the special cases are based on the lexicographical order minimization to solve three problems, in each one the primary objective function is maximum completion time ( ), while the secondary objective function is one of the objective functions: total completion times (Σ ), maximum tardiness ( ) and total tardiness (Σ ), the resulting problems are (P1), (P2), (P3). We propose three algorithms: Variable neighborhood simulated annealing(VNSA), Variable neighborhood descent method(VNDM) and Variable neighborhood with modefied NEH algorithm(VNMNEH). The comparison results show the efficiency of the proposed algorithms. All algorithmes were coded in Matlab programe."
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Panarelli, EA, AM Güntzel, and CN Borges. "How does the Taquari River influence in the cladoceran assemblages in three oxbow lakes?" Brazilian Journal of Biology 73, no. 4 (2013): 717–25. http://dx.doi.org/10.1590/s1519-69842013000400006.
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This study examined the cladoceran assemblages in three oxbow lakes of the Taquari River floodplain, near the transition between the plateau and the plain. We sought to answer the following questions: does the Taquari River function as a geographical barrier or dispersal corridor for Cladocera? Can different degrees of connection induce different structures in the assemblages in each lake? Cladocerans and limnological variables were sampled every other month for one year. Forty-one species were recorded, four of which were common to all the lakes. Our results indicated that the different degrees of connection between the river and the oxbow lakes favoured environmental heterogeneity and diversification in the cladoceran assemblages. The greatest dissimilarity between the two lakes connected with the river indicates that in this case the river functions better as a barrier than a dispersal corridor.
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Marsee, Monica A., Paul J. Frick, Christopher T. Barry, Eva R. Kimonis, Luna C. Muñoz Centifanti, and Katherine J. Aucoin. "Profiles of the forms and functions of self-reported aggression in three adolescent samples." Development and Psychopathology 26, no. 3 (2014): 705–20. http://dx.doi.org/10.1017/s0954579414000339.
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AbstractIn the current study, we addressed several issues related to the forms (physical and relational) and functions (reactive and proactive) of aggression in community (n = 307), voluntary residential (n = 1,917), and involuntarily detained (n = 659) adolescents (ages 11–19 years). Across samples, boys self-reported more physical aggression and girls reported more relational aggression, with the exception of higher levels of both forms of aggression in detained girls. Further, few boys showed high rates of relational aggression without also showing high rates of physical aggression. In contrast, it was not uncommon for girls to show high rates of relational aggression alone, and these girls tended to also have high levels of problem behavior (e.g., delinquency) and mental health problems (e.g., emotional dysregulation and callous–unemotional traits). Finally, for physical aggression in both boys and girls, and for relational aggression in girls, there was a clear pattern of aggressive behavior that emerged from cluster analyses across samples. Two aggression clusters emerged, with one group showing moderately high reactive aggression and a second group showing both high reactive and high proactive aggression (combined group). On measures of severity (e.g., self-reported delinquency and arrests) and etiologically important variables (e.g., emotional regulation and callous–unemotional traits), the reactive aggression group was more severe than a nonaggressive cluster but less severe than the combined aggressive cluster.
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VACARU, SERGIU I. "PARAMETRIC NONHOLONOMIC FRAME TRANSFORMS AND EXACT SOLUTIONS IN GRAVITY." International Journal of Geometric Methods in Modern Physics 04, no. 08 (2007): 1285–334. http://dx.doi.org/10.1142/s0219887807002570.
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A generalized geometric method is developed for constructing exact solutions of gravitational field equations in Einstein theory and generalizations. First, we apply the formalism of nonholonomic frame deformations (formally considered for nonholonomic manifolds and Finsler spaces) when the gravitational field equations transform into systems of nonlinear partial differential equations which can be integrated in general form. The new classes of solutions are defined by generic off-diagonal metrics depending on integration functions on one, two and three (or three and four) variables if we consider four (or five) dimensional spacetimes. Second, we use a general scheme when one (two) parameter families of exact solutions are defined by any source-free solutions of Einstein's equations with one (two) Killing vector field(s). A successive iteration procedure results in new classes of solutions characterized by an infinite number of parameters for a non-Abelian group involving arbitrary functions on one variable. Five classes of exact off-diagonal solutions are constructed in vacuum Einstein and in string gravity describing solitonic pp-wave interactions. We explore possible physical consequences of such solutions derived from primary Schwarzschild or pp-wave metrics.
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Zeitsch, Peter. "On the Riemann Function." Mathematics 6, no. 12 (2018): 316. http://dx.doi.org/10.3390/math6120316.
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Riemann’s method is one of the definitive ways of solving Cauchy’s problem for a second order linear hyperbolic partial differential equation in two variables. The first review of Riemann’s method was published by E.T. Copson in 1958. This study extends that work. Firstly, three solution methods were overlooked in Copson’s original paper. Secondly, several new approaches for finding Riemann functions have been developed since 1958. Those techniques are included here and placed in the context of Copson’s original study. There are also numerous equivalences between Riemann functions that have not previously been identified in the literature. Those links are clarified here by showing that many known Riemann functions are often equivalent due to the governing equation admitting a symmetry algebra isomorphic to S L ( 2 , R ) . Alternatively, the equation admits a Lie-Bäcklund symmetry algebra. Combining the results from several methods, a new class of Riemann functions is then derived which admits no symmetries whatsoever.
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Savoia, M., and J. N. Reddy. "A Variational Approach to Three-Dimensional Elasticity Solutions of Laminated Composite Plates." Journal of Applied Mechanics 59, no. 2S (1992): S166—S175. http://dx.doi.org/10.1115/1.2899483.
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The displacements in a laminated composite are represented as products of two sets of unknown functions, one of which is only a function of the thickness coordinate and the other is a function of the in-plane coordinates (i.e., separation of variables approach), and the minimization of the total potential energy is reduced to a sequence of iterative linear problems. Analytical solutions are developed for cross-ply and angle-ply laminated composite rectangular plates. The solution for simply-supported cross-ply plates under sinusoidal transverse load reduces to that of Pagano. Numerical results for stresses and displacements for antisymmetric angle-ply laminates are presented. The three-dimensional elasticity solutions developed are important because they can be used to study the behavior of composite laminates, in addition to serving as reference for approximate solutions by numerical methods and twodimensional theories.
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Podkopayev, A. O., and M. A. Stepanov. "SYNTHESIS OF TWO-POINT PARTIALLY COHERENT MODEL, PROVIDING SPECIFIED CORRELATION CHARACTERISTICS OF ANGULAR NOISE, BASED ON ITS EQUIVALENCE OF THREE-POINT NON-COHERENT MODEL WITH SEPARABILITY OF SPATIAL AND TEMPORAL COORDINATES." Issues of radio electronics, no. 4 (May 10, 2019): 16–21. http://dx.doi.org/10.21778/2218-5453-2019-4-16-21.
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The paper considers approaches developed for the synthesis of a two-point geometric model that emits correlated signals and forms angular noise with given spectral-correlation properties, based on its equivalence of a three-point model that emits noncorrelated signals. Analytical relationships have been obtained that allow us to determine the spectral correlation characteristics of the signals supplied to the emitters of the two-point partially coherent model. The basis for the synthesis of a two-point model, emitting correlated signals, is a three-point model, emitting non-correlated signals. The considered models can replace a one-dimensional object that has the property of separating the spatial and temporal variables in functions that determine the distribution of the density of the auto- and cross-correlation quadrature components of the echo signal over the object. In this case, all points of the object being replaced reflect echoes with the same spectral and correlation properties. The obtained theoretical results are confirmed by digital modeling. The obtained probability density distributions of the angular noise and their correlation functions coincide for the two considered models.
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Zacks, Shelemyahu. "Two-stage and sequential sampling for estimation and testing with prescribed precision." Encyclopedia with Semantic Computing and Robotic Intelligence 01, no. 01 (2017): 1650004. http://dx.doi.org/10.1142/s2425038416500048.
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Statistical data analysis includes several phases. First, there is the phase of data collection. Second, there is the phase of analysis and inference. The two phases are interconnected. There are two types of data analysis. One type is called parametric and the other type is nonparametric. In the present paper, we discuss parametric inference. In parametric inference, we model the results of a given experiment as realization of random variables having a particular distribution, which is specified by its parameters. A random sample is a sequence of independent and identically distributed (i.i.d.) random variables. Statistics are functions of the data in the sample, which do not involve unknown parameters. A statistical inference is based on statistics of a given sample. We discuss two kinds of parametric inference. Estimating the values of parameters, or testing hypotheses concerning the parameters in either kind of inference, we are concerned with the accuracy and precision of the results. In estimation of parameters, the results are precise if, with high probability, they belong to a specified neighborhoods of the parameters. In testing hypotheses, one has to decide which one of two or several hypotheses should be accepted. Hypotheses which are not accepted are rejected. We distinguish between two types of errors. Type I error is the one committed by rejecting a correct hypothesis. Type II is that of accepting a wrong hypothesis. It is desired that both types of errors will occur simultaneously with small probabilities. Both precision in estimation or small error probabilities in testing depend on the statistics used (estimators or test functions) and on the sample size. In this paper, we present sampling procedures that attain the desired objectives. In Sec. 2, we discuss estimation of the parameters of a binomial distribution. In Sec. 3, more general results about estimation of expected values are presented. In Sec. 4, we discuss the Wald Sequential Probability Ratio Test (SPRT), which has optimal properties for testing two simple hypotheses.
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Somaratna, Nihal, and T. C. T. Ting. "Three-Dimensional Stress Singularities at Conical Notches and Inclusions in Transversely Isotropic Materials." Journal of Applied Mechanics 53, no. 1 (1986): 89–96. http://dx.doi.org/10.1115/1.3171744.
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This study examines analytically the possible existence of stress singularities of the form σ = ρδf(θ,φ) at the apex of axisymmetric conical boundaries in transversely isotropic materials. (ρ, θ, φ) refer to spherical coordinates with the origin at the apex. The problems of one conical boundary and of two conical boundaries with a common apex are considered. The boundaries are either rigidly clamped or traction free. Separation of variables enables the general solution to be expressed in terms of Legendre functions of the first and second kind. Imposition of boundary conditions leads to an eigenequation that would determine possible values of δ. The degenerate case that arises when the eigenvalues of the elasiticity constants are identical is also discussed. Isotropic materials constitute only a particular case in this class of degenerate materials and previously reported eigenequations corresponding to isotropic materials are shown to be recoverable from the present results. Numerical results corresponding to a few selected cases are also presented to illustrate the solution procedure.
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Cooper, M. C., and S. Zivny. "Tractable Triangles and Cross-Free Convexity in Discrete Optimisation." Journal of Artificial Intelligence Research 44 (July 27, 2012): 455–90. http://dx.doi.org/10.1613/jair.3598.
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The minimisation problem of a sum of unary and pairwise functions of discrete variables is a general NP-hard problem with wide applications such as computing MAP configurations in Markov Random Fields (MRF), minimising Gibbs energy, or solving binary Valued Constraint Satisfaction Problems (VCSPs). We study the computational complexity of classes of discrete optimisation problems given by allowing only certain types of costs in every triangle of variable-value assignments to three distinct variables. We show that for several computational problems, the only non- trivial tractable classes are the well known maximum matching problem and the recently discovered joint-winner property. Our results, apart from giving complete classifications in the studied cases, provide guidance in the search for hybrid tractable classes; that is, classes of problems that are not captured by restrictions on the functions (such as submodularity) or the structure of the problem graph (such as bounded treewidth). Furthermore, we introduce a class of problems with convex cardinality functions on cross-free sets of assignments. We prove that while imposing only one of the two conditions renders the problem NP-hard, the conjunction of the two gives rise to a novel tractable class satisfying the cross-free convexity property, which generalises the joint-winner property to problems of unbounded arity.
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Tafreshi, A. "Shape optimization of two-dimensional anisotropic structures using the boundary element method." Journal of Strain Analysis for Engineering Design 38, no. 3 (2003): 219–32. http://dx.doi.org/10.1243/030932403765310554.
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A shape optimization procedure is developed, using the boundary element method, for two-dimensional anisotropic structures to minimize weight while satisfying certain constraints upon stresses and geometry. A directly differentiated form of boundary integral equation with respect to geometric design variables is used to calculate shape design sensitivities of anisotropic materials. The boundary element method is very suitable for shape optimization and in comparison with the finite element method needs much fewer data, related only to the boundary of the structure being considered. Because a directly differentiated form of the boundary integral equation can be used to determine the derivatives of the objective and constraint functions, the accuracy of computation is very high. Because of the non-linear nature of weight and stresses, the numerical optimization method used in the program is the feasible direction approach, together with the golden section method for the one-dimensional search. Three example problems with anisotropic material properties are presented to demonstrate the applications of this general-purpose program.
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Xu, Younan, and Fengfeng Xi. "A Real-Time Method for Solving the Forward Kinematics of a Tripod With Fixed-Length Legs." Journal of Manufacturing Science and Engineering 128, no. 1 (2005): 204–12. http://dx.doi.org/10.1115/1.2114928.
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This paper presents a real-time method for solving the forward kinematics of a tripod with fixed-length legs. The basic idea is to model the problem at hand based on a spatial four-bar linkage through which three sliding legs can be interrelated by choosing one link as a driving variable and other two links as driven variables. As a result, the original multivariable nonlinear problem with three variables can be reduced to one variable problem. A complete approach is provided to solve the unitary nonlinear programing problem. This includes a method for solving the implicit functions in terms of the driving and driven variables, and an approximation method for selecting an initial value leading to a fast solution. The simulation results show that (i) the method is effective, (ii) can reach very accurate results within five iterations for an error bound of 10−10, and (iii) numerically very stable. The experiment results show that the proposed forward kinematic method is fast enough to be implemented in real time to provide an accurate prediction of the tool pose from the joint encoder measurement.
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Duran, Ignacio, and Stephane Moreau. "Solution of the quasi-one-dimensional linearized Euler equations using flow invariants and the Magnus expansion." Journal of Fluid Mechanics 723 (April 16, 2013): 190–231. http://dx.doi.org/10.1017/jfm.2013.118.
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AbstractThe acoustic and entropy transfer functions of quasi-one-dimensional nozzles are studied analytically for both subsonic and choked flows with and without shock waves. The present analytical study extends both the compact nozzle solution obtained by Marble & Candel (J. Sound Vib., vol. 55, 1977, pp. 225–243) and the effective nozzle length proposed by Stow, Dowling & Hynes (J. Fluid Mech., vol. 467, 2002, pp. 215–239) and by Goh & Morgans (J. Sound Vib., vol. 330, 2011, pp. 5184–5198) to non-zero frequencies for both modulus and phase through an asymptotic expansion of the linearized Euler equations. It also extends the piecewise-linear approximation of the velocity profile in the nozzle proposed by Moase, Brear & Manzie (J. Fluid Mech., vol. 585, 2007, pp. 281–304) to any arbitrary profile or equivalently any nozzle geometry. The equations are written as a function of three variables, namely the dimensionless mass, total temperature and entropy fluctuations, yielding a first-order linear system of differential equations with varying coefficients, which is solved using the Magnus expansion. The solution shows that both the modulus and the phase of the transfer functions of the nozzle have a strong dependence on the frequency. This holds for both choked flows and subsonic converging–diverging nozzles. The method is used to compare two different nozzle geometries with the same inlet and outlet Mach numbers, showing that, even if the compact solution predicts no differences between the transfer functions of the two nozzles, significant differences are found at non-zero frequencies. A parametric study is finally performed to calculate the indirect to direct noise ratio for a model combustor, showing that this ratio decreases at higher frequencies.
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SATO, HARU-TADA, and HISAO SUZUKI. "ON BOGOLIUBOV TRANSFORMATION OF SCALAR WAVE FUNCTIONS IN DE SITTER SPACE." Modern Physics Letters A 09, no. 39 (1994): 3673–84. http://dx.doi.org/10.1142/s0217732394003518.
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We discuss the Bogoliubov transformation of the scalar wave functions caused by the change of coordinates in four-dimensional de Sitter space. It is shown that the exact Bogoliubov coefficients can be obtained from the global coordinates to the static coordinates where there exists manifest horizon. We consider two types of global coordinates. In one global coordinates, it is shown that the Bogoliubov transformation to the static coordinates can be expressed by the discontinuous integral of Weber and Schafheitlin. The positive and negative energy states in the global coordinates degenerate in the static coordinates. In the other global coordinates, we obtain the Bogoliubov coefficients by using the analytic continuation of the hypergeometric functions in two variables. We also discuss the relation between two types of global coordinates and find an integral relation between the mode functions.
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Subani, Norazlina, Muhammad Aniq Qayyum Mohamad Sukry, Muhammad Arif Hannan, Faizzuddin Jamaluddin, and Ahmad Danial Hidayatullah Badrolhisam. "Analysis of Different Boundary Conditions on Homogeneous One-Dimensional Heat Equation." Malaysian Journal of Science Health & Technology 7, no. 1 (2021): 15–21. http://dx.doi.org/10.33102/mjosht.v7i1.153.
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Partial differential equations involve results of unknown functions when there are multiple independent variables. There is a need for analytical solutions to ensure partial differential equations could be solved accurately. Thus, these partial differential equations could be solved using the right initial and boundaries conditions. In this light, boundary conditions depend on the general solution; the partial differential equations should present particular solutions when paired with varied boundary conditions. This study analysed the use of variable separation to provide an analytical solution of the homogeneous, one-dimensional heat equation. This study is applied to varied boundary conditions to examine the flow attributes of the heat equation. The solution is verified through different boundary conditions: Dirichlet, Neumann, and mixed-insulated boundary conditions. the initial value was kept constant despite the varied boundary conditions. There are two significant findings in this study. First, the temperature profile changes are influenced by the boundary conditions, and that the boundary conditions are dependent on the heat equation’s flow attributes.
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Pedroli, Elisa, Filippo La Paglia, Pietro Cipresso, Caterina La Cascia, Giuseppe Riva, and Daniele La Barbera. "A Computational Approach for the Assessment of Executive Functions in Patients with Obsessive–Compulsive Disorder." Journal of Clinical Medicine 8, no. 11 (2019): 1975. http://dx.doi.org/10.3390/jcm8111975.
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Previous studies on obsessive–compulsive disorder (OCD) showed impairments in executive domains, particularly in cognitive inhibition. In this perspective, the use of virtual reality showed huge potential in the assessment of executive functions; however, unfortunately, to date, no study on the assessment of these patients took advantage of the use of virtual environments. One of the main problems faced within assessment protocols is the use of a limited number of variables and tools when tailoring a personalized program. The main aim of this study was to provide a heuristic decision tree for the future development of tailored assessment protocols. To this purpose, we conducted a study that involved 58 participants (29 OCD patients and 29 controls) to collect both classic neuropsychological data and precise data based on a validated protocol in virtual reality for the assessment of executive functions, namely, the VMET (virtual multiple errands test). In order to provide clear indications for working on executive functions with these patients, we carried out a cross-validation based on three learning algorithms and computationally defined two decision trees. We found that, by using three neuropsychological tests and two VMET scores, it was possible to discriminate OCD patients from controls, opening a novel scenario for future assessment protocols based on virtual reality and computational techniques.
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NAVASCUÉS, M. A., and M. V. SEBASTIÁN. "FITTING FRACTAL SURFACES ON NON-RECTANGULAR GRIDS." Fractals 16, no. 02 (2008): 151–58. http://dx.doi.org/10.1142/s0218348x08003910.
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In a complex society, the visualization and interpretation of large amounts of data acquires an increasing importance. This can be done at once by means of two- or three-dimensional maps. To approach this problem, we undertake the construction of several variable fractal functions. In the first place, we introduce real fractal functions defined as perturbations of the classical ones. These basic mappings allow us to compute multidimensional approximations of experimental variables by means of linear combinations of products of fractal functions of Legendre type. The paper proposes a method of non-smooth representation for a large number of three-dimensional data on non-uniform grids. The procedures described are applied in the last part of the paper to the implementation of fitting maps for brain electrical activity.
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LEISSA, A. W., C. S. HUANG, and M. J. CHANG. "ACCURATE FREQUENCIES AND MODE SHAPES FOR MODERATELY THICK, CANTILEVERED, SKEW PLATES." International Journal of Structural Stability and Dynamics 07, no. 03 (2007): 425–40. http://dx.doi.org/10.1142/s0219455407002356.
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Accurate free vibration frequencies and mode shapes are presented for complete sets of moderately thick, cantilevered skew plates of triangular, trapezoidal and parallelogram shape. These accurate results are obtained by using the Ritz method applied to the Mindlin plate theory. Two sets of functions are employed simultaneously for each of the three dependent variables: transverse displacement (w) and bending rotations (ϕx and ϕy). One set is the widely used algebraic polynomials. The other is the set of corner functions which provide the proper stress singularities in the reentrant clamped-free corner, and accelerates the convergence of the solutions. The extensive frequencies presented are exact to the four digits shown. Corresponding mode shapes are also shown, by means of nodal patterns, most of which are novel in the published literature.
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Oosten, Jaap Van. "Two remarks on the Lifschitz realizability topos." Journal of Symbolic Logic 61, no. 1 (1996): 70–79. http://dx.doi.org/10.2307/2275598.
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The purpose of this note is to clarify two points about the topos Lif, introduced in [13] as a generalization of Lifschitz' realizability ([9, 12]). Lif is a subtopos of Hyland's Effective topos ([1]). The points I want to make are:Remark 1. Lif is the largest subtopos of satisfying the axiom (O):where denotes partial recursive application, and “∈ Tot” means that e and f range over codes for total recursive functions. One may read (O) as the statement “The union of two -sets is again a -set”. That is, let be a subtopos of . Then (O) is true in for the standard interpretation (the variables range over the natural numbers object of , etc.) if and only if the inclusion ↣ factors through the inclusion Lif ↣ .Remark 2. Like , Lif contains at least two weakly complete internal full subcategories, thus providing us with more models of polymorphism and other impredicative type theories.The principle (O) has some standing in the history of constructive mathematics:- H. Friedman has proved that (O) is equivalent to a formulation of intuitionistic completeness of the intuitionistic predicate calculus for Tarskian semantics; see [8]. This is not to imply that this result is of immediate relevance to Lif: Friedman works in a system of analysis, a theory of lawless sequences with an axiom of “open data” for arithmetical formulas, which at least for the domain of all functions from N to N fails in Lif. However, there might exist a “nonstandard model” of arithmetic and a corresponding system of analysis, in which we may be able to carry out his proof.- Moreover, Remark 2 entails that Lif should provide us with models of synthetic domain theory (for an exposition, see [3]), and one with the nice property that the dual of one of the axioms (axiom 7 in [3]) comes for free, by (O).
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Beckwith, Joan B. "PSYCHOLOGICAL FUNCTIONS OF EATING, DRINKING, AND SMOKING IN ADULT WOMEN." Social Behavior and Personality: an international journal 15, no. 2 (1987): 185–206. http://dx.doi.org/10.2224/sbp.1987.15.2.185.
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The psychological functions of eating, drinking, and smoking were analyzed in relation to the self-reported behaviors of 20 to 30 year old women. Participants were recruited from a range of sources, and the 766 volunteers generated two quasi-representative samples of 265 subjects each which matched each other and census data on a range of demographic variables. Eight scales of psychological functions were developed. In each domain, one scale reflected behavior aimed at relief of negative effect, and one scale reflected positively motivated behavior. In the eating domain, a third scale represented eating in response to external cues, and in the drinking domain there was a scale of socially motivated drinking. Psychometric properties of each scale were investigated. Multiple correlations between the scales and their criteria ranged from R = .63 to R = .75 reflecting the importance of the predictors studied. Functions were compared within and between behavioral domains and the role of habit was also compared across domains.
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Gupta, V. K., and O. J. Mesa. "Horton laws for hydraulic–geometric variables and their scaling exponents in self-similar Tokunaga river networks." Nonlinear Processes in Geophysics 21, no. 5 (2014): 1007–25. http://dx.doi.org/10.5194/npg-21-1007-2014.
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Abstract. An analytical theory is developed that obtains Horton laws for six hydraulic–geometric (H–G) variables (stream discharge Q, width W, depth D, velocity U, slope S, and friction n') in self-similar Tokunaga networks in the limit of a large network order. The theory uses several disjoint theoretical concepts like Horton laws of stream numbers and areas as asymptotic relations in Tokunaga networks, dimensional analysis, the Buckingham Pi theorem, asymptotic self-similarity of the first kind, or SS-1, and asymptotic self-similarity of the second kind, or SS-2. A self-contained review of these concepts, with examples, is given as "methods". The H–G data sets in channel networks from three published studies and one unpublished study are summarized to test theoretical predictions. The theory builds on six independent dimensionless river-basin numbers. A mass conservation equation in terms of Horton bifurcation and discharge ratios in Tokunaga networks is derived. Assuming that the H–G variables are homogeneous and self-similar functions of stream discharge, it is shown that the functions are of a power law form. SS-1 is applied to predict the Horton laws for width, depth and velocity as asymptotic relationships. Exponents of width and the Reynolds number are predicted and tested against three field data sets. One basin shows deviations from theoretical predictions. Tentatively assuming that SS-1 is valid for slope, depth and velocity, corresponding Horton laws and the H–G exponents are derived. Our predictions of the exponents are the same as those previously predicted for the optimal channel network (OCN) model. In direct contrast to our work, the OCN model does not consider Horton laws for the H–G variables, and uses optimality assumptions. The predicted exponents deviate substantially from the values obtained from three field studies, which suggests that H–G in networks does not obey SS-1. It fails because slope, a dimensionless river-basin number, goes to 0 as network order increases, but, it cannot be eliminated from the asymptotic limit. Therefore, a generalization of SS-1, based on SS-2, is considered. It introduces two anomalous scaling exponents as free parameters, which enables us to show the existence of Horton laws for channel depth, velocity, slope and Manning friction. These two exponents are not predicted here. Instead, we used the observed exponents of depth and slope to predict the Manning friction exponent and to test it against field exponents from three studies. The same basin mentioned above shows some deviation from the theoretical prediction. A physical reason for this deviation is given, which identifies an important topic for research. Finally, we briefly sketch how the two anomalous scaling exponents could be estimated from the transport of suspended sediment load and the bed load. Statistical variability in the Horton laws for the H–G variables is also discussed. Both are important open problems for future research.
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Cheng, Heng, Miaojuan Peng, and Yumin Cheng. "A Fast Complex Variable Element-Free Galerkin Method for Three-Dimensional Wave Propagation Problems." International Journal of Applied Mechanics 09, no. 06 (2017): 1750090. http://dx.doi.org/10.1142/s1758825117500909.
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In this paper, combining the dimension splitting method with the improved complex variable element-free Galerkin (ICVEFG) method, we present a fast ICVEFG method for three-dimensional wave propagation problems. Using the dimension splitting method, the equations of three-dimensional wave propagation problems are translated into a series of two-dimensional ones in another one-dimensional direction. The new Galerkin weak form of the dimension splitting method for three-dimensional wave propagation problems is obtained. The improved complex variable moving least-square (ICVMLS) approximation is used to obtain the shape functions, and the penalty method is used to apply the essential boundary conditions, finite difference method is used in the one-dimensional direction, then the formulae of the ICVEFG method for three-dimensional wave propagation problems are obtained. The convergence and the corresponding parameters in the ICVEFG method are discussed. Some numerical examples are given to show that the new method has higher computational precision, and can improve the computational efficiency of the conventional meshless methods for three-dimensional problems greatly.
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Senjanović, Ivo, Marko Tomić, Nikola Vladimir, and Dae Seung Cho. "Analytical Solution for Free Vibrations of a Moderately Thick Rectangular Plate." Mathematical Problems in Engineering 2013 (2013): 1–13. http://dx.doi.org/10.1155/2013/207460.
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In the present thick plate vibration theory, governing equations of force-displacement relations and equilibrium of forces are reduced to the system of three partial differential equations of motion with total deflection, which consists of bending and shear contribution, and angles of rotation as the basic unknown functions. The system is starting one for the application of any analytical or numerical method. Most of the analytical methods deal with those three equations, some of them with two (total and bending deflection), and recently a solution based on one equation related to total deflection has been proposed. In this paper, a system of three equations is reduced to one equation with bending deflection acting as a potential function. Method of separation of variables is applied and analytical solution of differential equation is obtained in closed form. Any combination of boundary conditions can be considered. However, the exact solution of boundary value problem is achieved for a plate with two opposite simply supported edges, while for mixed boundary conditions, an approximate solution is derived. Numerical results of illustrative examples are compared with those known in the literature, and very good agreement is achieved.
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Chernykh, Nikolai I. "INTERPOLATING WAVELETS ON THE SPHERE." Ural Mathematical Journal 5, no. 2 (2019): 3. http://dx.doi.org/10.15826/umj.2019.2.001.
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There are several works where bases of wavelets on the sphere (mainly orthogonal and wavelet-like bases) were constructed. In all such constructions, the authors seek to preserve the most important properties of classical wavelets including constructions on the basis of the lifting-scheme. In the present paper, we propose one more construction of wavelets on the sphere. Although two of three systems of wavelets constructed in this paper are orthogonal, we are more interested in their interpolation properties. Our main idea consists in a special double expansion of the unit sphere in \(\mathbb{R}^3\) such that any continuous function on this sphere defined in spherical coordinates is easily mapped into a \(2\pi\)-periodic function on the plane. After that everything becomes simple, since the classical scheme of the tensor product of one-dimensional bases of functional spaces works to construct bases of spaces of functions of several variables.
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Burmasheva, N. V., and E. Yu Prosviryakov. "Isothermal layered flows of a viscous incompressible fluid with spatial acceleration in the case of three Coriolis parameters." Diagnostics, Resource and Mechanics of materials and structures, no. 3 (May 2020): 29–46. http://dx.doi.org/10.17804/2410-9908.2020.3.029-046.
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We study the solvability of the overdetermined system of Navier–Stokes equations, supple-mented by the incompressibility equation, which is used to describe isothermal large-scale shear flows of a rotating viscous incompressible fluid. Large–scale flows are studied in a thin-layer ap-proximation (the vertical velocity of the fluid is assumed to be zero). The rotation of a continuous fluid medium is described by three Coriolis parameters. The solution of the reduced system of Na-vier–Stokes equations is constructed in the Lin–Sidorov–Aristov class. In this case, both nonzero components of the velocity vector, the pressure and temperature fields are assumed to be full linear forms of two Cartesian coordinates, and the dependence on the third Cartesian coordinate has an arbitrary form (including non-polynomial). It is shown that the nonlinear overdetermined system of Navier–Stokes equations and of the incompressibility equation in the framework of the Lin–Sidorov–Aristov class reduces to the equivalent nonlinear overdetermined system of ordinary dif-ferential equations, in which the components of the hydrodynamic fields act as unknown functions. The compatibility condition for the equations of the resulting system is derived. It is shown that, if this compatibility condition is fulfilled, the system has a unique solution, and the spatial accelera-tions in both variables (the linearity with respect to them was postulated when choosing the solution class) prove to be constant functions. These results are a generalization of similar results obtained earlier in the study of solvability in the cases of one and two Coriolis parameters.
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Samart, Detchat. "Mahler Measures as Linear Combinations of L–values of Multiple Modular Forms." Canadian Journal of Mathematics 67, no. 2 (2015): 424–49. http://dx.doi.org/10.4153/cjm-2014-012-8.
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AbstractWe study the Mahler measures of certain families of Laurent polynomials in two and three variables. Each of the known Mahler measure formulas for these families involves L–values of at most one newform and/or at most one quadratic character. In this paper we show, either rigorously or numerically, that the Mahler measures of some polynomials are related to L–values of multiple newforms and quadratic characters simultaneously. The results suggest that the number of modular L–values appearing in the formulas significantly depends on the shape of the algebraic value of the parameter chosen for each polynomial. As a consequence, we also obtain new formulas relating special values of hypergeometric series evaluated at algebraic numbers to special values of L–functions.
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Su, Hai-Jun, and J. Michael McCarthy. "Synthesis of Bistable Compliant Four-Bar Mechanisms Using Polynomial Homotopy." Journal of Mechanical Design 129, no. 10 (2006): 1094–98. http://dx.doi.org/10.1115/1.2757192.
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In this paper we formulate and solve the synthesis equations for a compliant four-bar linkage with three specified equilibrium configurations in the plane. The kinematic synthesis equations as for rigid-body mechanisms are combined with equilibrium constraints at the flexure pivots to form design equations. These equations are simplified by modeling the joint angle variables in the equilibrium equations using sine and cosine functions. Polynomial homotopy continuation is applied to compute all of the design candidates that satisfy these design equations, which are refined using a Newton-Raphson technique. A numerical example demonstrates design methodology in which the homotopy solver obtained eight real solutions. Two of them provide two stable and one unstable equilibrium, and hence, can be used as the prototype of bistable compliant mechanisms.