scholarly journals Mathematical framework for detection and quantification of nonclassical correlation

2011 ◽  
Vol 11 (1&2) ◽  
pp. 167-180
Author(s):  
Akira SaiToh ◽  
Robabeh Rahimi ◽  
Mikio Nakahara
Keyword(s):  
Computational Cost ◽  
Mathematical Framework ◽  
Completely Positive ◽  
New Class ◽  
Linear And Nonlinear ◽  
Detection And Quantification

Existing measures of bipartite nonclassical correlation that is typically characterized by nonvanishing nonlocalizable information under the zero-way CLOCC protocol are expensive in computational cost. We define and evaluate economical measures on the basis of a new class of maps, eigenvalue-preserving-but-not-completely-eigenvalue-preserving (EnCE) maps. The class is in analogy to the class of positive-but-not-completely-positive (PnCP) maps that have been commonly used in the entanglement theories. Linear and nonlinear EnCE maps are investigated. We also prove subadditivity of the measures in the form of logarithmic fidelity.

scholarly journals The Independent Variable Interpolation Technique for Nonuniformly Sampled Shallow-Angle Lidar Data

2011 ◽  
Vol 28 (12) ◽  
pp. 1672-1678 ◽  
Author(s):  
M. R. Belmont ◽  
P. Ashwin
Keyword(s):  
Computational Cost ◽  
Lidar Data ◽  
Distributed Data ◽  
Sampled Data ◽  
Sea Waves ◽  
Energy Capture ◽  
New Class ◽  
Lidar Measurements ◽  
Practical Engineering ◽  
Independent Variable

Abstract Shallow-angle lidar offers an attractive approach to acquiring spatial profiles of sea waves, which are of value in both oceanographic research and practical engineering applications, such as in the control of wave energy capture devices and for a variety of vessel operations. However, the wave elevation values produced by shallow-angle lidar are inevitably nonuniformly distributed in space and, given that most processing algorithms require uniformly sampled data, an equivalent set of uniformly distributed data must be derived from the lidar measurements. A new class of algorithm is introduced to achieve this goal and applied to experimental shallow-angle lidar data. Compared to traditional methods the new approach has advantages in terms of both computational cost and the degree of nonuniformity that can be accommodated.

scholarly journals The nonlinear structure of linkage disequilibrium

2019 ◽  
Author(s):  
Reginald D. Smith
Keyword(s):  
Linkage Disequilibrium ◽  
Frequency Dependence ◽  
Allele Frequency ◽  
Allele Frequencies ◽  
Nonlinear Dependence ◽  
Mathematical Framework ◽  
Linkage Disequilibrium Structure ◽  
Nonlinear Structure ◽  
Linear And Nonlinear ◽  
Fundamental Shift

AbstractThe allele frequency dependence of the ranges of all measures of linkage disequilibrium is well-known. The maximum values of commonly used parameters such as r2 and D vary depending on the allele frequencies at each locus. However, though this phenomenon is recognized and accounted for in many studies, the comprehensive mathematical framework underlying the limits of linkage disequilibrium measures at various frequency combinations is often heuristic or empirical. Here, it is demonstrated that underlying this behavior is the fundamental shift between linear and nonlinear dependence in the linkage disequilibrium structure between loci. The proportion of linear and nonlinear dependence can be estimated and it demonstrates how even the same values of r2 can have different implications for the nature of the overall dependence. One result of this is the value of D′, when defined as only a positive number, has a minimum value of |r|. Understanding this dependence is crucial to making correct inferences about the relationships between two loci in linkage disequilibrium.

scholarly journals Rosenbrock Type Methods for Solving Non-Linear Second-Order in Time Problems

Mathematics ◽  
2021 ◽  
Vol 9 (18) ◽  
pp. 2225
Author(s):  
Maria Jesus Moreta
Keyword(s):  
Computational Cost ◽  
Intermediate Stage ◽  
Second Order ◽  
First Order ◽  
New Class ◽  
Nyström Methods ◽  
Non Linear ◽  
Second Order In Time ◽  
Linear Problems ◽  
Runge Kutta

In this work, we develop a new class of methods which have been created in order to numerically solve non-linear second-order in time problems in an efficient way. These methods are of the Rosenbrock type, and they can be seen as a generalization of these methods when they are applied to second-order in time problems which have been previously transformed into first-order in time problems. As they also follow the ideas of Runge–Kutta–Nyström methods when solving second-order in time problems, we have called them Rosenbrock–Nyström methods. When solving non-linear problems, Rosenbrock–Nyström methods present less computational cost than implicit Runge–Kutta–Nyström ones, as the non-linear systems which arise at every intermediate stage when Runge–Kutta–Nyström methods are used are replaced with sequences of linear ones.

scholarly journals Modeling of Abradable Coating Removal in Aircraft Engines Through Delay Differential Equations

2013 ◽  
Vol 135 (10) ◽  
Author(s):  
Nicolas Salvat ◽  
Alain Batailly ◽  
Mathias Legrand
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Computational Cost ◽  
Mathematical Framework ◽  
Machining Processes ◽  
Abradable Coating ◽  
Excited Vibration ◽  
Time Marching ◽  
Coating Removal ◽  
Delay Differential

In modern turbomachinery, abradable materials are implemented on casings to reduce operating tip clearances and mitigate direct unilateral contact occurrences between rotating and stationary components. However, both experimental and numerical investigations revealed that blade/abradable interactions may lead to blade failures. In order to comprehend the underlying mechanism, an accurate modeling of the abradable removal process is required. Time-marching strategies where the abradable removal is modeled through plasticity are available but another angle of attack is proposed in this work. It is assumed that the removal of abradable liners shares similarities with machine tool chatter encountered in manufacturing. Chatter is a self-excited vibration caused by the interaction between the machine and the workpiece through the cutting forces and the corresponding dynamics are efficiently captured by delay differential equations. These equations differ from ordinary differential equations in the sense that previous states of the system are involved in the formulation. This mathematical framework is employed here for the exploration of the blade stability during abradable removal. The proposed tool advantageously features a reduced computational cost and consistency with existing time-marching solution methods. Potentially dangerous interaction regimes are accurately predicted and instability lobes match both the flexural and torsional modal responses. Essentially, the regenerative nature of chatter in machining processes can also be attributed to abradable coating removal in turbomachinery.

Properties of Materials

2004 ◽  
Author(s):  
Robert E. Newnham
Keyword(s):  
Chemical Properties ◽  
Mathematical Framework ◽  
Structure Property ◽  
Magnetic Structures ◽  
Wide Range ◽  
Basic Physics ◽  
Piezoelectricity And Electrostriction ◽  
Linear And Nonlinear ◽  
Textured Materials ◽  
Physical And Chemical

Crystals are sometimes called 'Flowers of the Mineral Kingdom'. In addition to their great beauty, crystals and other textured materials are enormously useful in electronics, optics, acoustics and many other engineering applications. This richly illustrated text describes the underlying principles of crystal physics and chemistry, covering a wide range of topics and illustrating numerous applications in many fields of engineering using the most important materials today. Tensors, matrices, symmetry and structure-property relationships form the main subjects of the book. While tensors and matrices provide the mathematical framework for understanding anisotropy, on which the physical and chemical properties of crystals and textured materials often depend, atomistic arguments are also needed to quantify the property coefficients in various directions. The atomistic arguments are partly based on symmetry and partly on the basic physics and chemistry of materials. After introducing the point groups appropriate for single crystals, textured materials and ordered magnetic structures, the directional properties of many different materials are described: linear and nonlinear elasticity, piezoelectricity and electrostriction, magnetic phenomena, diffusion and other transport properties, and both primary and secondary ferroic behavior. With crystal optics (its roots in classical mineralogy) having become an important component of the information age, nonlinear optics is described along with the piexo-optics, magneto-optics, and analogous linear and nonlinear acoustic wave phenomena. Enantiomorphism, optical activity, and chemical anisotropy are discussed in the final chapters of the book.

A fixed point theorem for JS-contraction type mappings with applications to polynomial approximations

Filomat ◽  
2017 ◽  
Vol 31 (15) ◽  
pp. 4969-4978 ◽  
Author(s):  
Ishak Altun ◽  
Arifi Al ◽  
Mohamed Jleli ◽  
Aref Lashine ◽  
Bessem Samet
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Stancu Operators ◽  
Polynomial Approximations ◽  
New Class ◽  
Contraction Type ◽  
Linear And Nonlinear

A fixed point theorem is established for a new class of JS-contraction type mappings. As applications, some Kelisky-Rivlin type results are obtained for linear and nonlinear q-Bernstein-Stancu operators.

scholarly journals Beyond Newton: A New Root-Finding Fixed-Point Iteration for Nonlinear Equations

Algorithms ◽  
2020 ◽  
Vol 13 (4) ◽  
pp. 78
Author(s):  
Ankush Aggarwal ◽  
Sanjay Pant
Keyword(s):  
Newton’S Method ◽  
Newton's Method ◽  
Short Note ◽  
Basin Of Attraction ◽  
Computational Cost ◽  
Initial Guess ◽  
Mathematical Functions ◽  
New Class ◽  
Root Finding ◽  
Roots Of Equations

Finding roots of equations is at the heart of most computational science. A well-known and widely used iterative algorithm is Newton’s method. However, its convergence depends heavily on the initial guess, with poor choices often leading to slow convergence or even divergence. In this short note, we seek to enlarge the basin of attraction of the classical Newton’s method. The key idea is to develop a relatively simple multiplicative transform of the original equations, which leads to a reduction in nonlinearity, thereby alleviating the limitation of Newton’s method. Based on this idea, we derive a new class of iterative methods and rediscover Halley’s method as the limit case. We present the application of these methods to several mathematical functions (real, complex, and vector equations). Across all examples, our numerical experiments suggest that the new methods converge for a significantly wider range of initial guesses. For scalar equations, the increase in computational cost per iteration is minimal. For vector functions, more extensive analysis is needed to compare the increase in cost per iteration and the improvement in convergence of specific problems.

scholarly journals Design criteria of X-wave launchers for millimeter-wave applications

2019 ◽  
Vol 11 (9) ◽  
pp. 939-947
Author(s):  
Walter Fuscaldo ◽  
Santi C. Pavone ◽  
Davide Comite ◽  
Guido Valerio ◽  
Matteo Albani ◽  
...  
Keyword(s):  
Millimeter Wave ◽  
Millimeter Waves ◽  
Bessel Beam ◽  
Operating Conditions ◽  
Mathematical Framework ◽  
Specific Interest ◽  
Small Aperture ◽  
New Class ◽  
Practical Design ◽  
Definition Of

AbstractBessel-beam launchers are promising and established technologies for focusing applications at microwaves. Their use in time-domain leads to the definition of a new class of devices, namely, the X-wave launchers. In this work, we discuss the focusing features of such devices with a specific interest at millimeter waves. The spatial resolutions of such systems are described under a rigorous mathematical framework to derive novel operating conditions for designing X-wave launchers. These criteria might be particularly appealing for specific millimeter-wave applications. In particular, it is shown that an electrically large aperture is not strictly required, as it seemed from previous works. However, the use of an electrically small aperture would demand a considerably wideband capability. The various discussions presented here provide useful information for the design of X-wave launchers. This aspect is finally shown with reference to the practical design of two different X-wave launchers.

scholarly journals Orthonormalized basic of fractal stepped multiwavelets – a new multiwavelet technology for signal and image processing

2021 ◽  
pp. 91-95
Author(s):  
Lev Hnativ
Keyword(s):  
Image Processing ◽  
Computational Complexity ◽  
Classical Method ◽  
Multiplicative Complexity ◽  
New Class ◽  
Step Functions ◽  
Multiwavelet Transform ◽  
Additive Complexity ◽  
Linear And Nonlinear ◽  
Discrete Multiwavelet Transform

A new class of fractal step functions with linear and nonlinear changes in values is described, and on their basis a recurrent method for constructing functions of a new class of fractal step multiwavelets (FSMW) of various shapes with linear and nonlinear changes in values is developed. A method and an algorithm for constructing a whole family of basic FSMW systems have been developed. An algorithm for calculating the coefficients of a discrete multiwavelet transform based on a multiwavelet packet without performing convolution and decimated sampling operations, in contrast to the classical method, is presented. A method and algorithm for fast multiwavelet transform of low computational complexity has been developed, which, in comparison with the well-known classical Mall's algorithm, is 70 times less in multiplicative complexity, and 20 times less in additive complexity.

scholarly journals A Pathfinding Problem for Fork-Join Directed Acyclic Graphs with Unknown Edge Length

Algorithms ◽  
2021 ◽  
Vol 14 (12) ◽  
pp. 367
Author(s):  
Kunihiko Hiraishi
Keyword(s):  
Nonnegative Integer ◽  
General Class ◽  
Optimality Criterion ◽  
Computational Cost ◽  
Edge Length ◽  
Directed Acyclic Graphs ◽  
New Class ◽  
Acyclic Graphs

In a previous paper by the author, a pathfinding problem for directed trees is studied under the following situation: each edge has a nonnegative integer length, but the length is unknown in advance and should be found by a procedure whose computational cost becomes exponentially larger as the length increases. In this paper, the same problem is studied for a more general class of graphs called fork-join directed acyclic graphs. The problem for the new class of graphs contains the previous one. In addition, the optimality criterion used in this paper is stronger than that in the previous paper and is more appropriate for real applications.

Sign in / Sign up

Export Citation Format

Share Document