Affine and Projective Tree Metric Theorems
Harel, Matan; Pachter, Lior
2011-01-01
The tree metric theorem provides a combinatorial four point condition that characterizes dissimilarity maps derived from pairwise compatible split systems. A similar (but weaker) four point condition characterizes dissimilarity maps derived from circular split systems (Kalmanson metrics). The tree metric theorem was first discovered in the context of phylogenetics and forms the basis of many tree reconstruction algorithms, whereas Kalmanson metrics were first considered by computer scientists, and are notable in that they are a non-trivial class of metrics for which the traveling salesman problem is tractable. We present a unifying framework for these theorems based on combinatorial structures that are used for graph planarity testing. These are (projective) PC-trees, and their affine analogs, PQ-trees. In the projective case, we generalize a number of concepts from clustering theory, including hierarchies, pyramids, ultrametrics and Robinsonian matrices, and the theorems that relate them. As with tree metric...
Kim Jong
2011-01-01
Full Text Available Abstract We consider a hybrid projection method for finding a common element in the fixed point set of an asymptotically quasi-ϕ-nonexpansive mapping and in the solution set of an equilibrium problem. Strong convergence theorems of common elements are established in a uniformly smooth and strictly convex Banach space which has the Kadec-Klee property. 2000 Mathematics subject classification: 47H05, 47H09, 47H10, 47J25
Projection-slice theorem based 2D-3D registration
van der Bom, M. J.; Pluim, J. P. W.; Homan, R.; Timmer, J.; Bartels, L. W.
2007-03-01
In X-ray guided procedures, the surgeon or interventionalist is dependent on his or her knowledge of the patient's specific anatomy and the projection images acquired during the procedure by a rotational X-ray source. Unfortunately, these X-ray projections fail to give information on the patient's anatomy in the dimension along the projection axis. It would be very profitable to provide the surgeon or interventionalist with a 3D insight of the patient's anatomy that is directly linked to the X-ray images acquired during the procedure. In this paper we present a new robust 2D-3D registration method based on the Projection-Slice Theorem. This theorem gives us a relation between the pre-operative 3D data set and the interventional projection images. Registration is performed by minimizing a translation invariant similarity measure that is applied to the Fourier transforms of the images. The method was tested by performing multiple exhaustive searches on phantom data of the Circle of Willis and on a post-mortem human skull. Validation was performed visually by comparing the test projections to the ones that corresponded to the minimal value of the similarity measure. The Projection-Slice Theorem Based method was shown to be very effective and robust, and provides capture ranges up to 62 degrees. Experiments have shown that the method is capable of retrieving similar results when translations are applied to the projection images.
Student Research Project: Goursat's Other Theorem
Petrillo, Joseph
2009-01-01
In an elementary undergraduate abstract algebra or group theory course, a student is introduced to a variety of methods for constructing and deconstructing groups. What seems to be missing from contemporary texts and syllabi is a theorem, first proved by Edouard Jean-Baptiste Goursat (1858-1936) in 1889, which completely describes the subgroups of…
A generalization of Marstrand's theorem for projections of cartesian products
López, Jorge Erick
2011-01-01
We prove the following variant of Marstrand's theorem about projections of cartesian products of sets: Let $K_1,...,K_n$ Borel subsets of $\\mathbb R^{m_1},... ,\\mathbb R^{m_n}$ respectively, and $\\pi:\\mathbb R^{m_1}\\times...\\times\\mathbb R^{m_n}\\to\\mathbb R^k$ be a surjective linear map. We set $$\\mathfrak{m}:=\\min\\{\\sum_{i\\in I}\\dim_H(K_i) + \\dim\\pi(\\bigoplus_{i\\in I^c}\\mathbb R^{m_i}), I\\subset\\{1,...,n\\}, I\
The Orthogonal Projection and the Riesz Representation Theorem
Narita Keiko
2015-09-01
Full Text Available In this article, the orthogonal projection and the Riesz representation theorem are mainly formalized. In the first section, we defined the norm of elements on real Hilbert spaces, and defined Mizar functor RUSp2RNSp, real normed spaces as real Hilbert spaces. By this definition, we regarded sequences of real Hilbert spaces as sequences of real normed spaces, and proved some properties of real Hilbert spaces. Furthermore, we defined the continuity and the Lipschitz the continuity of functionals on real Hilbert spaces.
A variant of Marstrand's theorem for projections of cartesian products
Velázquez, Jorge Erick López
2011-01-01
We prove the following variant of Marstrand's theorem about projections of cartesian products of sets: Consider the space $\\Lambda_m=\\set{(t,O), t\\in\\R, O\\in SO(m)}$ with the natural measure and set $\\Lambda=\\Lambda_{m_1}\\times\\ppp\\times\\Lambda_{m_n}$. For every $\\la=(t_1,O_1,\\ppp,t_n,O_n)\\in\\Lambda$ and every $x=(x^1,\\ppp,x^n)\\in\\R^{m_1}\\times\\ppp\\times\\R^{m_n}$ we define $\\pi_\\la(x)=\\pi(t_1O_1x^1,\\ppp,t_nO_nx^n)$. Suppose that $\\pi$ is surjective and set $$\\mathfrak{m}:=\\min\\set{\\sum_{i\\in I}\\dim_H(K_i) + \\dim\\pi(\\bigoplus_{i\\in I^c}\\R^{m_i}), I\\subset\\set{1,\\ppp,n}, I\
A General Theorem Characterizing some Absolute Summability Methods
W T Sulaiman
2002-11-01
A general theorem is given which gives the necessary and sufficient conditions satisfied by a sequence $(_n)$ in order to have the series $\\sum a_n_n$ summable to || whenever $\\sum a_n$ is summable to || for some summability method .
CONVERGENCE THEOREMS FOR THE AOR METHOD
黄廷祝; 王广彬
2002-01-01
Practical sufficient conditions for the convergence of the AOR method and a practical sufficient condition for H-matrices are studied. The obtained convergence conditions suited to matrices which need not to be diagonally dominant.
Limit theorems and inequalities via martingale methods
Chazottes Jean-René
2014-01-01
Full Text Available In these notes, we first give a brief overwiew of martingales methods, from Paul Lévy (1935 untill now, to explain why these methods have become a central tool in probability, statistics and ergodic theory. Next, we present some recent results for/or based on martingales: exponential bounds for super-martingales, concentration inequalities for Lipschitz functionals of dynamical systems, oracle inequalities for the Cox model in a high dimensional setting, and invariance principles for stationary sequences.
The Variation Theorem Applied to H-2+: A Simple Quantum Chemistry Computer Project
Robiette, Alan G.
1975-01-01
Describes a student project which requires limited knowledge of Fortran and only minimal computing resources. The results illustrate such important principles of quantum mechanics as the variation theorem and the virial theorem. Presents sample calculations and the subprogram for energy calculations. (GS)
Wigner's theorem - revisited. A simple proof using projective geometry
Keller, Kai Johannes [II. Institut fuer Theoretische Physik der Universitaet Hamburg (Germany); Institut fuer Physik der Universitaet Mainz (Germany); Papadopoulos, Nikolaos A. [Institut fuer Physik der Universitaet Mainz (Germany); Reyes Lega, Andres Fernando [Universidad de los Andes, Bogota (Colombia)
2008-07-01
This talk presents a a simple, geometric proof of Wigner's theorem on the realization of symmetries in quantum mechanics, that clarifies its relation to projective geometry. Although there exist several proofs, it seems that the relevance of Wigner's theorem is not fully appreciated in general. It is Wigner's theorem, which allows the use of linear realizations of symmetries and therefore guarantees that, in the end, quantum theory stays a linear theory. The proof presented here takes a strictly geometrical point of view. It becomes apparent, that Wigner's theorem is nothing else but a corollary of the fundamental theorem of projective geometry. In this sense the proof is simple, transparent and therefore accessible even to elementary treatments in quantum mechanics.
Wagner, Falko Jens; Poulsen, Mikael Zebbelin
1999-01-01
When trying to solve a DAE problem of high index with more traditional methods, it often causes instability in some of the variables, and finally leads to breakdown of convergence and integration of the solution. This is nicely shown in [ESF98, p. 152 ff.].This chapter will introduce projection...... methods as a way of handling these special problems. It is assumed that we have methods for solving normal ODE systems and index-1 systems....
Fixed point theorems in locally convex spaces—the Schauder mapping method
2006-01-01
Full Text Available In the appendix to the book by F. F. Bonsal, Lectures on Some Fixed Point Theorems of Functional Analysis (Tata Institute, Bombay, 1962 a proof by Singbal of the Schauder-Tychonoff fixed point theorem, based on a locally convex variant of Schauder mapping method, is included. The aim of this note is to show that this method can be adapted to yield a proof of Kakutani fixed point theorem in the locally convex case. For the sake of completeness we include also the proof of Schauder-Tychonoff theorem based on this method. As applications, one proves a theorem of von Neumann and a minimax result in game theory.
The splitting method and Poincare's theorem: (I - the geometric part
Maurice Margenstern
2002-11-01
Full Text Available In this paper we revisit Poincare's theorem in the light of the splitting method which was introduced by the author in [3]. This led to the definition of combinatoric tilings. We show that all tessellations which are constructed on a triangle with interior angles $\\displaystyle{\\pi\\over p}$, $\\displaystyle{\\pi\\over q}$ and $\\displaystyle{\\pi\\over p}$ with $\\displaystyle{{1\\over p} + {1\\over q} + {1\\over r} = 5. However, all the tessellations which are constructed on an equilateral triangle with interior angle $\\displaystyle{{2\\pi}\\over p}$ are combinatoric tilings.
Optical applications of von Neumann's alternating-projection theorem.
Montgomery, W D
1982-01-01
The previous work of Gerchberg [Opt. Acta 21, 709 (1974)], Papoulis [IEEE Trans. Circuits Syst. CAS-22, 735 (1975)], Youla [IEEE Trans. Circuits Syst. CAS-25, 694 (1978)], and Stark et al. [J. Opt. Soc. Am. 71, 735 (1981)] on image restoration is presented in a generalized setting. New examples using three projections are given. The method is used to solve the general problem of diffraction by a perfectly conducting plane screen of arbitrary configuration.
Szatmári, Daniel
2015-12-01
Disadvantages of the currently used Křovák's map projection in the Slovak Republic, such as large scale distortion, became evident after the division of Czechoslovakia. The aim of this paper is to show the results of the optimization of cartographic projections using Chebyshev's theorem for conformal projections and its application to the territory of the Slovak Republic. The calculus used, the scale distortions achieved and their comparison with the scale distortions of currently used map projections will be demonstrated.
De Zela, F.
2016-10-01
Born's quantum probability rule is traditionally included among the quantum postulates as being given by the squared amplitude projection of a measured state over a prepared state, or else as a trace formula for density operators. Both Gleason's theorem and Busch's theorem derive the quantum probability rule starting from very general assumptions about probability measures. Remarkably, Gleason's theorem holds only under the physically unsound restriction that the dimension of the underlying Hilbert space {H} must be larger than two. Busch's theorem lifted this restriction, thereby including qubits in its domain of validity. However, while Gleason assumed that observables are given by complete sets of orthogonal projectors, Busch made the mathematically stronger assumption that observables are given by positive operator-valued measures. The theorem we present here applies, similarly to the quantum postulate, without restricting the dimension of {H} and for observables given by complete sets of orthogonal projectors. We also show that the Born rule applies beyond the quantum domain, thereby exhibiting the common root shared by some quantum and classical phenomena.
Comparison theorem with modified Gauss-Seidel and modified Jacobi methods by M-matrix
Tofigh Allahviranloo
2012-12-01
Full Text Available In the current work, the comparison theorem with modified Gauss-Seidel method and modified Jacobi method, are proved in detail and superiority of MGS method is illustrated by solving some numerical examples.
Michael E. Goerndt; W. Keith Moser; Patrick D. Miles; Dave Wear; Ryan D. DeSantis; Robert J. Huggett; Stephen R. Shifley; Francisco X. Aguilar; Kenneth E. Skog
2016-01-01
One purpose of the Northern Forest Futures Project is to predict change in future forest attributes across the 20 States in the U.S. North for the period that extends from 2010 to 2060. The forest attributes of primary interest are the 54 indicators of forest sustainability identified in the Montreal Process Criteria and Indicators (Montreal Process Working Group, n.d...
EXTENSION OF THE PROJECTION THEOREM ON HILBERT SPACE TO FUZZY HILBERT SPACE OVER FUZZY NUMBER SPACE
K. P. DEEPA; Dr.S.Chenthur Pandian
2012-01-01
In this paper, we extend the projection theorem on Hilbert space to its fuzzy version over fuzzy number space embedded with fuzzy number mapping. To prove this we discuss the concepts of fuzzy Hilbert space over fuzzy number space with fuzzy number mapping. The fuzzy orthogonality, fuzzy orthonormality, fuzzy complemented subset property etc. of fuzzy Hilbert space over fuzzy number space using fuzzy number mapping also been discussed.
2008-01-01
In this paper, we generalize the method of mechanical theorem proving in curves to prove theorems about surfaces in differential geometry with a mechanical procedure. We improve the classical result on Wronskian determinant, which can be used to decide whether the elements in a partial differential field are linearly dependent over its constant field. Based on Wronskian determinant, we can describe the geometry statements in the surfaces by an algebraic language and then prove them by the characteristic set method.
Fixed point theorems in locally convex spacesÃ¢Â€Â”the Schauder mapping method
S. Cobzaş
2006-03-01
Full Text Available In the appendix to the book by F. F. Bonsal, Lectures on Some Fixed Point Theorems of Functional Analysis (Tata Institute, Bombay, 1962 a proof by Singbal of the Schauder-Tychonoff fixed point theorem, based on a locally convex variant of Schauder mapping method, is included. The aim of this note is to show that this method can be adapted to yield a proof of Kakutani fixed point theorem in the locally convex case. For the sake of completeness we include also the proof of Schauder-Tychonoff theorem based on this method. As applications, one proves a theorem of von Neumann and a minimax result in game theory.
ON A GENERALIZED TAYLOR THEOREM: A RATIONAL PROOF OF THE VALIDITY OF THE HOMOTOPY ANALYSIS METHOD
廖世俊
2003-01-01
A generalized Taylor series of a complex function was derived and some relatedtheorems about its convergence region were given. The generalized Taylor theorem can beapplied to greatly enlarge convergence regions of approximation series given by othertraditional techniques. The rigorous proof of the generalized Taylor theorem also provides uswith a rational base of the validity of a new kind of powerful analytic technique for nonlinearproblems, namely the homotopy analysis method.
FENG RuYong; YU JianPing
2008-01-01
In this paper,we generalize the method of mechanical theorem proving in curves to prove theorems about surfaces in differential geometry with a mechanical procedure.We improve the classical result on Wronskian determinant,which can be used to decide whether the elements in a partial differential field are linearly dependent over its constant field.Based on Wronskian determinant,we can describe the geometry statements in the surfaces by an algebraic language and then prove them by the characteristic set method.
METHODS OF EXPERIMENTAL VERIFICATION OF STEINER THEOREM IN PHYSICAL PRACTICUM AND LABORATORY WORK
Zharilkasin Iskakov
2014-07-01
Full Text Available In this paper, the technique of laboratory work on experimental verification of Steiner’s Theorem in laboratory conditions is developed. To do this, specially designed experimental device was used. The main part of such device is a simple physical pendulum, swinging freely about the axis of suspension, consisting of a cylindrical disc set on a thin rod. To determine the moment of inertia of cylindrical body about the axis of vibrations, property of a physical quantity additivity was used. When processing experimental results, functional approximation by a least squares method was applied; as a result, the empirical expression of Steiner’s Theorem was achieved. Results of experimental studies were very close to the results of theoretical calculations. Laboratory work can be easily repeated for a body of arbitrary shape. The methodology used can be recommended for physical practicum in universities as an effective and easy way of experimental verification of Steiner’s theorem.
A comparison theorem for the SOR iterative method
Sun, Li-Ying
2005-09-01
In 1997, Kohno et al. have reported numerically that the improving modified Gauss-Seidel method, which was referred to as the IMGS method, is superior to the SOR iterative method. In this paper, we prove that the spectral radius of the IMGS method is smaller than that of the SOR method and Gauss-Seidel method, if the relaxation parameter [omega][set membership, variant](0,1]. As a result, we prove theoretically that this method is succeeded in improving the convergence of some classical iterative methods. Some recent results are improved.
Shakedown Analysis of 3-D Structures Using the Boundary Element Method Based on the Static Theorem
张晓峰; 刘应华; 岑章志
2003-01-01
The static shakedown theorem was reformulated for the boundary element method (BEM) rather than the finite element method with Melan's theorem, then used to develop a numerical solution procedure for shakedown analysis. The self-equilibrium stress field was constructed by a linear combination of several basis self-equilibrium stress fields with undetermined parameters. These basis self-equilibrium stress fields were expressed as elastic responses of the body to imposed permanent strains obtained using a 3-D BEM elastic-plastic incremental analysis. The lower bound for the shakedown load was obtained from a series of nonlinear mathematical programming problems solved using the Complex method. Numerical examples verified the precision of the present method.
Kaehler, G; Wagner, A J
2013-06-01
Current implementations of fluctuating ideal-gas descriptions with the lattice Boltzmann methods are based on a fluctuation dissipation theorem, which, while greatly simplifying the implementation, strictly holds only for zero mean velocity and small fluctuations. We show how to derive the fluctuation dissipation theorem for all k, which was done only for k=0 in previous derivations. The consistent derivation requires, in principle, locally velocity-dependent multirelaxation time transforms. Such an implementation is computationally prohibitively expensive but, with a small computational trick, it is feasible to reproduce the correct FDT without overhead in computation time. It is then shown that the previous standard implementations perform poorly for non vanishing mean velocity as indicated by violations of Galilean invariance of measured structure factors. Results obtained with the method introduced here show a significant reduction of the Galilean invariance violations.
Limit theorems in the imitative monomer-dimer mean-field model via Stein's method
Chen, Wei-Kuo
2016-08-01
We consider the imitative monomer-dimer model on the complete graph introduced in the work of Alberici et al. [J. Math. Phys. 55, 063301-1-063301-27 (2014)]. It was shown that this model is described by the monomer density and has a phase transition along certain coexistence curve, where the monomer and dimer phases coexist. More recently, it was understood [D. Alberici et al., Commun. Math. Phys. (published online, 2016)] that the monomer density exhibits the central limit theorem away from the coexistence curve and enjoys a non-normal limit theorem at criticality with normalized exponent 3/4. By reverting the model to a weighted Curie-Weiss model with hard core interaction, we establish the complete description of the fluctuation properties of the monomer density on the full parameter space via Stein's method of exchangeable pairs. Our approach recovers what were established in the work of Alberici et al. [Commun. Math. Phys. (published online, 2016)] and furthermore allows to obtain the conditional central limit theorems along the coexistence curve. In all these results, the Berry-Esseen inequalities for the Kolmogorov-Smirnov distance are given.
John C Pfeiffer
2004-01-01
In the design/build (D/B) method of implementing plant construction projects, the owner contracts with the engineer/contractor or contractor/engineer company or team-depending upon who takes the lead in the project to develop...
A comparison theorem for the iterative method with the preconditioner (I+Smax)
Kotakemori, Hisashi; Harada, Kyouji; Morimoto, Munenori; Niki, Hiroshi
2002-08-01
In 1991, Gunawardena et al. (Linear Algebra Appl. 154-156 (1991) 123) have reported the modified Gauss-Seidel method with a preconditioner (I+S). In this article, we propose to use a preconditioner (I+Smax) instead of (I+S). Here, Smax is constructed by only the largest element at each row of the upper triangular part of A. By using the lemma established Neumann and Plemmons (Linear Algebra Appl. 88/89 (1987) 559), we get the comparison theorem for the proposed method. Simple numerical examples are also given.
Vorticity, Stokes' Theorem and the Gauss's Theorem
Narayanan, M.
2004-12-01
Vorticity is a property of the flow of any fluid and moving fluids acquire properties that allow an engineer to describe that particular flow in greater detail. It is important to recognize that mere motion alone does not guarantee that the air or any fluid has vorticity. Vorticity is one of four important quantities that define the kinematic properties of any fluid flow. The Navier-Stokes equations are the foundation of fluid mechanics, and Stokes' theorem is used in nearly every branch of mechanics as well as electromagnetics. Stokes' Theorem also plays a vital role in many secondary theorems such as those pertaining to vorticity and circulation. However, the divergence theorem is a mathematical statement of the physical fact that, in the absence of the creation or destruction of matter, the density within a region of space can change only by having it flow into, or away from the region through its boundary. This is also known as Gauss's Theorem. It should also be noted that there are many useful extensions of Gauss's Theorem, including the extension to include surfaces of discontinuity in V. Mathematically expressed, Stokes' theorem can be expressed by considering a surface S having a bounding curve C. Here, V is any sufficiently smooth vector field defined on the surface and its bounding curve C. Integral (Surface) [(DEL X V)] . dS = Integral (Contour) [V . dx] In this paper, the author outlines and stresses the importance of studying and teaching these mathematical techniques while developing a course in Hydrology and Fluid Mechanics. References Arfken, G. "Gauss's Theorem." 1.11 in Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 57-61, 1985. Morse, P. M. and Feshbach, H. "Gauss's Theorem." In Methods of Theoretical Physics, Part I. New York: McGraw-Hill, pp. 37-38, 1953. Eric W. Weisstein. "Divergence Theorem." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/DivergenceTheorem.html
Algorithmic complexity for psychology: a user-friendly implementation of the coding theorem method.
Gauvrit, Nicolas; Singmann, Henrik; Soler-Toscano, Fernando; Zenil, Hector
2016-03-01
Kolmogorov-Chaitin complexity has long been believed to be impossible to approximate when it comes to short sequences (e.g. of length 5-50). However, with the newly developed coding theorem method the complexity of strings of length 2-11 can now be numerically estimated. We present the theoretical basis of algorithmic complexity for short strings (ACSS) and describe an R-package providing functions based on ACSS that will cover psychologists' needs and improve upon previous methods in three ways: (1) ACSS is now available not only for binary strings, but for strings based on up to 9 different symbols, (2) ACSS no longer requires time-consuming computing, and (3) a new approach based on ACSS gives access to an estimation of the complexity of strings of any length. Finally, three illustrative examples show how these tools can be applied to psychology.
Vempala, Santosh S
2005-01-01
Random projection is a simple geometric technique for reducing the dimensionality of a set of points in Euclidean space while preserving pairwise distances approximately. The technique plays a key role in several breakthrough developments in the field of algorithms. In other cases, it provides elegant alternative proofs. The book begins with an elementary description of the technique and its basic properties. Then it develops the method in the context of applications, which are divided into three groups. The first group consists of combinatorial optimization problems such as maxcut, graph coloring, minimum multicut, graph bandwidth and VLSI layout. Presented in this context is the theory of Euclidean embeddings of graphs. The next group is machine learning problems, specifically, learning intersections of halfspaces and learning large margin hypotheses. The projection method is further refined for the latter application. The last set consists of problems inspired by information retrieval, namely, nearest neig...
Ring-tool profiling - graphical method in CATIA based on Generating trajectories theorem
Frumuşanu, G.; Teodor, V.; Oancea, N.
2016-11-01
Machining of threads having high dimensions and multiple starts by turning is a challenging problem. An alternative possibility is to machine them by milling. The most productive milling solution is when using tools with inner active surface, namely ring tools. In the case of threads with multiple starts, the reciprocal enwrapped profile of the ring tool is considerably different to the shape of the thread axial (normal) section. In this paper, we suggest a methodology to profile the generator ring tool, based on a complementary theorem from enwrapped surfaces field. At the same time, a graphical algorithm aiming to find the ring tool profile, developed in CATIA graphical environment has been applied in the concrete case of a trapezoidal thread. The graphical profiling solution is presented in comparison to an analytical solution, in order to test the results precision. The graphical profiling method proves to be rigorous, easy to apply and highly intuitive.
Another Method for Deriving two Results Contiguous to Kummer's Second Theorem
Deepa Ainkooran
2013-10-01
Full Text Available The aim of this research paper is to derive two results closely related to the well known classical and useful Kummer's second theorem obtained earlier by Kim et al. [Comput. Math. & Math. Phys., 50 (3 (2010, 387 - 402] by employing classical Gauss's summation theorem for the series $_{2}F_{1}$.
Deepthi, Dasika Ratna
2009-01-01
In this paper, we prove a crucial theorem called Mirroring Theorem which affirms that given a collection of samples with enough information in it such that it can be classified into classes and subclasses then (i) There exists a mapping which classifies and subclassifies these samples (ii) There exists a hierarchical classifier which can be constructed by using Mirroring Neural Networks (MNNs) in combination with a clustering algorithm that can approximate this mapping. Thus, the proof of the Mirroring theorem provides a theoretical basis for the existence and a practical feasibility of constructing hierarchical classifiers, given the maps. Our proposed Mirroring Theorem can also be considered as an extension to Kolmogrovs theorem in providing a realistic solution for unsupervised classification. The techniques we develop, are general in nature and have led to the construction of learning machines which are (i) tree like in structure, (ii) modular (iii) with each module running on a common algorithm (tandem a...
Testing the no-hair theorem with the continuum-fitting and the iron line methods: a short review
Bambi, Cosimo; Steiner, James F
2015-01-01
The continuum-fitting and the iron line methods are leading techniques capable of probing the spacetime geometry around astrophysical black hole candidates and testing the no-hair theorem. In the present paper, we review the two approaches, from the astrophysical models and their assumptions, to the constraining power with present and future facilities.
Gain and offset analysis of comparator using the bisection theorem and a balanced method
Nessir Zghoul, Fadi; Ay, Suat U.; Ababneh, Ahmad
2016-12-01
Gain and offset represent two important measures to determine the accuracy of a comparator. Thus, analysis on these parameters is very important as they offer designers better understanding of the circuit and allow exploring trade-offs during design. In this paper, two methods were presented to derive a set of design equations that describe the gain, sensitivity, offset, and systematic mismatches observed in typical comparator circuits. A three-stage, fast complementary metal-oxide semiconductor (CMOS) comparator structure is analysed and simulated in order to validate the proposed methods. A 0.13 μm CMOS technology is used for simulations with 1.5 V supply voltage. Bisection theorem was used for gain and sensitivity analysis. Simulation results show that high gain improvement can be possible by using the design equations. The input offset voltage, due to mismatch in the width of the metal oxide semiconductor field-effect transistors (MOSFET) (W) and mismatches in the threshold voltages of the N and P type MOSFETs (VTHN, VTHP), is analysed using a proposed balanced method. The same comparator structure is used for the input offset voltage analysis. Simulations show that an offset improvement can be achieved following the design equations found through the proposed method.
Flatto, Leopold
2009-01-01
Poncelet's theorem is a famous result in algebraic geometry, dating to the early part of the nineteenth century. It concerns closed polygons inscribed in one conic and circumscribed about another. The theorem is of great depth in that it relates to a large and diverse body of mathematics. There are several proofs of the theorem, none of which is elementary. A particularly attractive feature of the theorem, which is easily understood but difficult to prove, is that it serves as a prism through which one can learn and appreciate a lot of beautiful mathematics. This book stresses the modern appro
Automated Discovery of Inductive Theorems
McCasland, Roy; Bundy, Alan; Serge, Autexier
2007-01-01
Inductive mathematical theorems have, as a rule, historically been quite difficult to prove – both for mathematics students and for auto- mated theorem provers. That said, there has been considerable progress over the past several years, within the automated reasoning community, towards proving some of these theorems. However, little work has been done thus far towards automatically discovering them. In this paper we present our methods of discovering (as well as proving) inductive theorems, ...
Wouters, Sebastian; Nakatani, Naoki; Van Neck, Dimitri; Chan, Garnet Kin-Lic
2013-08-01
The similarities between Hartree-Fock (HF) theory and the density matrix renormalization group (DMRG) are explored. Both methods can be formulated as the variational optimization of a wave-function Ansatz. Linearization of the time-dependent variational principle near a variational minimum allows to derive the random phase approximation (RPA). We show that the nonredundant parameterization of the matrix product state (MPS) tangent space [J. Haegeman, J. I. Cirac, T. J. Osborne, I. Pižorn, H. Verschelde, and F. Verstraete, Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.107.070601 107, 070601 (2011)] leads to the Thouless theorem for MPS, i.e., an explicit nonredundant parameterization of the entire MPS manifold, starting from a specific MPS reference. Excitation operators are identified, which extends the analogy between HF and DMRG to the Tamm-Dancoff approximation (TDA), the configuration interaction (CI) expansion, and coupled cluster theory. For a small one-dimensional Hubbard chain, we use a CI-MPS Ansatz with single and double excitations to improve on the ground state and to calculate low-lying excitation energies. For a symmetry-broken ground state of this model, we show that RPA-MPS allows to retrieve the Goldstone mode. We also discuss calculations of the RPA-MPS correlation energy. With the long-range quantum chemical Pariser-Parr-Pople Hamiltonian, low-lying TDA-MPS and RPA-MPS excitation energies for polyenes are obtained.
Evaluation methods for hospital projects.
Buelow, Janet R; Zuckweiler, Kathryn M; Rosacker, Kirsten M
2010-01-01
The authors report the findings of a survey of hospital managers on the utilization of various project selection and evaluation methodologies. The focus of the analysis was the empirical relationship between a portfolio of project evaluation(1) methods actually utilized for a given project and several measures of perceived project success. The analysis revealed that cost-benefit analysis and top management support were the two project evaluation methods used most often by the hospital managers. The authors' empirical assessment provides evidence that top management support is associated with overall project success.
Virial theorem and hypervirial theorem in a spherical geometry
Li Yan; Chen Jingling [Theoretical Physics Division, Chern Institute of Mathematics, Nankai University, Tianjin 300071 (China); Zhang Fulin, E-mail: flzhang@tju.edu.cn, E-mail: chenjl@nankai.edu.cn [Physics Department, School of Science, Tianjin University, Tianjin 300072 (China)
2011-09-09
The virial theorem in the one- and two-dimensional spherical geometry are presented in both classical and quantum mechanics. Choosing a special class of hypervirial operators, the quantum hypervirial relations in the spherical spaces are obtained. With the aid of the Hellmann-Feynman theorem, these relations can be used to formulate a perturbation theorem without wavefunctions, corresponding to the hypervirial-Hellmann-Feynman theorem perturbation theorem of Euclidean geometry. The one-dimensional harmonic oscillator and two-dimensional Coulomb system in the spherical spaces are given as two sample examples to illustrate the perturbation method. (paper)
Dasika Ratna Deepthi
2009-10-01
Full Text Available In this paper, we prove a crucial theorem called “Mirroring Theorem” which affirms that given a collection of samples with enough information in it such that it can be classified into classes and sub-classes then (i There exists a mapping which classifies and subclassifies these samples (ii There exists a hierarchical classifier which can be constructed by using Mirroring Neural Networks (MNNs in combination with a clustering algorithm that can approximate this mapping. Thus, the proof of the Mirroring theorem provides a theoretical basis for the existence and a practical feasibility of constructing hierarchical classifiers, given the maps. Our proposed Mirroring Theorem can also be considered as an extension to Kolmogrov’s theorem in providing a realistic solution for unsupervised classification. The techniques we develop, are general in nature and have led to the construction of learning machines which are (i tree like in structure, (ii modular (iii with each module running on a common algorithm (tandem algorithm and (iv self-supervised. We have actually built the architecture, developed the tandem algorithm of such a hierarchical classifier and demonstrated it on an example problem.
A Class of Strong Limit Theorems and Moment Generating Function Method
Wen Han LI; Gao Rong LI; Nan Bin CAO
2012-01-01
In virtue of the notion of likelihood ratio and moment generating function,the limit properties of the sequences of absolutely continuous random variables are studied,and a class of strong limit theorems represented by inequalities with random bounds are obtained.
Heck, Richard G
2011-01-01
Frege's Theorem collects eleven essays by Richard G Heck, Jr, one of the world's leading authorities on Frege's philosophy. The Theorem is the central contribution of Gottlob Frege's formal work on arithmetic. It tells us that the axioms of arithmetic can be derived, purely logically, from a single principle: the number of these things is the same as the number of those things just in case these can be matched up one-to-one with those. But that principle seems so utterlyfundamental to thought about number that it might almost count as a definition of number. If so, Frege's Theorem shows that a
Du Wei-Shih
2011-01-01
Full Text Available Abstract In this paper, we introduce a new approach method to find a common element in the intersection of the set of the solutions of a finite family of equilibrium problems and the set of fixed points of a nonexpansive mapping in a real Hilbert space. Under appropriate conditions, some strong convergence theorems are established. The results obtained in this paper are new, and a few examples illustrating these results are given. Finally, we point out that some 'so-called' mixed equilibrium problems and generalized equilibrium problems in the literature are still usual equilibrium problems. 2010 Mathematics Subject Classification: 47H09; 47H10, 47J25.
Extended Eckart Theorem and New Variation Method for Excited States of Atoms
Xiong, Zhuang; Bacalis, N C; Zhou, Qin
2016-01-01
We extend the Eckart theorem, from the ground state to excited statew, which introduces an energy augmentation to the variation criterion for excited states. It is shown that the energy of a very good excited state trial function can be slightly lower than the exact eigenvalue. Further, the energy calculated by the trial excited state wave function, which is the closest to the exact eigenstate through Gram-Schmidt orthonormalization to a ground state approximant, is lower than the exact eigenvalue as well. In order to avoid the variation restrictions inherent in the upper bound variation theory based on Hylleraas, Undheim, and McDonald [HUM] and Eckart Theorem, we have proposed a new variation functional Omega-n and proved that it has a local minimum at the eigenstates, which allows approaching the eigenstate unlimitedly by variation of the trial wave function. As an example, we calculated the energy and the radial expectation values of Triplet-S(even) Helium atom by the new variation functional, and by HUM a...
Toh, K.C.; Trefethen, L.N. [Cornell Univ., Ithaca, NY (United States)
1994-12-31
What properties of a nonsymmetric matrix A determine the convergence rate of iterations such as GMRES, QMR, and Arnoldi? If A is far from normal, should one replace the usual Ritz values {r_arrow} eigenvalues notion of convergence of Arnoldi by alternative notions such as Arnoldi lemniscates {r_arrow} pseudospectra? Since Krylov subspace iterations can be interpreted as minimization processes involving polynomials of matrices, the answers to questions such as these depend upon mathematical problems of the following kind. Given a polynomial p(z), how can one bound the norm of p(A) in terms of (1) the size of p(z) on various sets in the complex plane, and (2) the locations of the spectrum and pseudospectra of A? This talk reports some progress towards solving these problems. In particular, the authors present theorems that generalize the Kreiss matrix theorem from the unit disk (for the monomial A{sup n}) to a class of general complex domains (for polynomials p(A)).
TANG Yi; FANG Yong-li; YANG Luo; SUN Yu-xin; YU Zheng-hua
2012-01-01
A new accurate calculation method of electric power harmonic parameters was presented.Based on the delay time theorem of Fourier transform,the frequency of the electric power was calculated,and then,suing interpolation in the frequency domain of the windows,the parameters (amplitude and phase) of each harmonic frequency signals were calculated accurately.In the paper,the effect of the delay time and the windows on the electric power harmonic calculation accuracy was analysed.The digital simulation and the physical measurement tests show that the proposed method is effective and has more advantages than other methods which are based on multipoint interpolation especially in calculation time cost; therefore,it is very suitable to be used in the single chip DSP micro-processor.
Ordering in mechanical geometry theorem proving
李洪波￥
1997-01-01
Ordering in mechanical geometry theorem proving is studied from geometric viewpoint and some new ideas are proposed. For Thebault’s theorem which is the most difficult theorem that has ever been proved by Wu’ s method, a very simple proof using Wu’s method under a linear order is discovered.
Jose Ernie C. Lope
2013-12-01
Full Text Available In their 2012 work, Lope, Roque, and Tahara considered singular nonlinear partial differential equations of the form tut = F(t; x; u; ux, where the function F is assumed to be continuous in t and holomorphic in the other variables. They have shown that under some growth conditions on the coefficients of the partial Taylor expansion of F as t 0, the equation has a unique solution u(t; x with the same growth order as that of F(t; x; 0; 0. Koike considered systems of partial differential equations using the Banach fixed point theorem and the iterative method of Nishida and Nirenberg. In this paper, we prove the result obtained by Lope and others using the method of Koike, thereby avoiding the repetitive step of differentiating a recursive equation with respect to x as was done by the aforementioned authors.
DUAN Shi-Mei; SHOU Wen-De; HE Pei-Zhong; QIAN De-Chu; XIA Rong-Min
2005-01-01
@@ A novel method to measure acoustic power of focusing transducer based on the self-reciprocity theorem of con vergent spherical acoustic wave is proposed. The performance of this reciprocity method is compared with that of the radiation force balance (RFB) method and the admittance circle method. The average deviations of the reciprocity method from RFB in measurements of the acoustic power and the radiation conductance for a focusing transducer of 1.525 MHz are 7.5% and 3.6% respectively, and for another focusing transducer of 5.27MHz,they are 1.7% and 1.1%. The measured radiation conductance deviation by the reciprocity method from the admittance circle method for the focusing transducer of 1.525 MHz is 7.9%. It presents encouraging results even in measuring low acoustic power level. The overall uncertainty of acoustic power measurement using the method is evaluated below 10%, and it has many advantages such as high signal-to-noise ratio, good stability and less interference of bubbles and environment.
P Dutt; Akhlaq Husain; A S Vasudeva Murthy; C S Upadhyay
2015-08-01
This is the second of a series of papers devoted to the study of ℎ- spectral element methods for three dimensional elliptic problems on non-smooth domains. The present paper addresses the proof of the main stability theorem.We assume that the differential operator is a strongly elliptic operator which satisfies Lax–Milgram conditions. The spectral element functions are non-conforming. The stability estimate theorem of this paper will be used to design a numerical scheme which give exponentially accurate solutions to three dimensional elliptic problems on non-smooth domains and can be easily implemented on parallel computers.
The quantitative Morse theorem
Loi, Ta Le; Phien, Phan
2013-01-01
In this paper, we give a proof of the quantitative Morse theorem stated by {Y. Yomdin} in \\cite{Y1}. The proof is based on the quantitative Sard theorem, the quantitative inverse function theorem and the quantitative Morse lemma.
Noether's theorem and one-step corrections method for holonomic system
Shang Mei; Chen Xiang-Wei
2006-01-01
In this paper, a new computational method for improving the accuracy of numerically computed solutions is introduced. The computational method is based on the one-step method and conserved quantities of holonomic systems are considered as kinematical constraints in this method.
Fan beam image reconstruction with generalized Fourier slice theorem.
Zhao, Shuangren; Yang, Kang; Yang, Kevin
2014-01-01
For parallel beam geometry the Fourier reconstruction works via the Fourier slice theorem (or central slice theorem, projection slice theorem). For fan beam situation, Fourier slice can be extended to a generalized Fourier slice theorem (GFST) for fan-beam image reconstruction. We have briefly introduced this method in a conference. This paper reintroduces the GFST method for fan beam geometry in details. The GFST method can be described as following: the Fourier plane is filled by adding up the contributions from all fanbeam projections individually; thereby the values in the Fourier plane are directly calculated for Cartesian coordinates such avoiding the interpolation from polar to Cartesian coordinates in the Fourier domain; inverse fast Fourier transform is applied to the image in Fourier plane and leads to a reconstructed image in spacial domain. The reconstructed image is compared between the result of the GFST method and the result from the filtered backprojection (FBP) method. The major differences of the GFST and the FBP methods are: (1) The interpolation process are at different data sets. The interpolation of the GFST method is at projection data. The interpolation of the FBP method is at filtered projection data. (2) The filtering process are done in different places. The filtering process of the GFST is at Fourier domain. The filtering process of the FBP method is the ramp filter which is done at projections. The resolution of ramp filter is variable with different location but the filter in the Fourier domain lead to resolution invariable with location. One advantage of the GFST method over the FBP method is in short scan situation, an exact solution can be obtained with the GFST method, but it can not be obtained with the FBP method. The calculation of both the GFST and the FBP methods are at O(N^3), where N is the number of pixel in one dimension.
[SENTIERI Project: materials and methods].
Conti, Susanna; Crocetti, Emanuele; Buzzoni, Carlotta; Comba, Pietro; Fazzo, Lucia; Iavarone, Ivano; Manno, Valerio; Minelli, Giada; Pasetto, Roberto; Pirastu, Roberta; Ricci, Paolo; Zona, Amerigo; Fusco, Mario
2014-01-01
The Report considers three health outcomes - mortality, cancer incidence and hospital discharges - studied using homogenous methods and using data from official sources, namely the National Institute of Statistics (Istat), Italian Network of Cancer Registries (AIRTUM) and the Health Ministry. The timeframes of observation are: 2003-2010 for mortality, 1996-2005 for cancer incidence and 2005-2010 for hospital discharges. The causes of death are those examined by the SENTIERI Project. Hospital discharges are analysed with reference to the main diagnosis. The study of cancer incidence applies to the sites selected by AIRTUM. Statistical parameters (SMR, Standardized Mortality Ratio; SIR, Standardized Incidence Ratio; SHR, Standardized Hospitalization Ratio) were computed with a 90% confidence interval; the estimators were adjusted for age and socioeconomic status.
The truncated Second Main Theorem and uniqueness theorems
无
2010-01-01
In this paper, we first establish a truncated Second Main Theorem for algebraically nondegenerate holomorphic mappings from the complex plane into a complex projective variety V intersecting hypersurfaces. We then prove some uniqueness results for meromorphic mappings. The result of Demailly about a partial solution to the Fujita’s conjecture is used.
Duan Peichao
2010-01-01
Full Text Available Let be strict pseudo-contractions defined on a closed and convex subset of a real Hilbert space . We consider the problem of finding a common element of fixed point set of these mappings and the solution set of a system of equilibrium problems by parallel and cyclic algorithms. In this paper, new iterative schemes are proposed for solving this problem. Furthermore, we prove that these schemes converge strongly by hybrid methods. The results presented in this paper improve and extend some well-known results in the literature.
Generalized Fourier slice theorem for cone-beam image reconstruction.
Zhao, Shuang-Ren; Jiang, Dazong; Yang, Kevin; Yang, Kang
2015-01-01
The cone-beam reconstruction theory has been proposed by Kirillov in 1961, Tuy in 1983, Feldkamp in 1984, Smith in 1985, Pierre Grangeat in 1990. The Fourier slice theorem is proposed by Bracewell 1956, which leads to the Fourier image reconstruction method for parallel-beam geometry. The Fourier slice theorem is extended to fan-beam geometry by Zhao in 1993 and 1995. By combining the above mentioned cone-beam image reconstruction theory and the above mentioned Fourier slice theory of fan-beam geometry, the Fourier slice theorem in cone-beam geometry is proposed by Zhao 1995 in short conference publication. This article offers the details of the derivation and implementation of this Fourier slice theorem for cone-beam geometry. Especially the problem of the reconstruction from Fourier domain has been overcome, which is that the value of in the origin of Fourier space is 0/0. The 0/0 type of limit is proper handled. As examples, the implementation results for the single circle and two perpendicular circle source orbits are shown. In the cone-beam reconstruction if a interpolation process is considered, the number of the calculations for the generalized Fourier slice theorem algorithm is O(N^4), which is close to the filtered back-projection method, here N is the image size of 1-dimension. However the interpolation process can be avoid, in that case the number of the calculations is O(N5).
Manufacturing Methods and Technology Project Summary Reports.
1980-12-01
as high speed machining. Except for the abrasive aluminum alloys like A356 which must be machined with carbide, either carbide or high speed steel...Shear Forging Processes for Missile 82 Primary Structure Project 376 3230 - Manufacturing Methods for High Speed Machining of 85 Aluminum Project 376 3231...Production Methods for Squeeze Castings 88 Projects 471 4312 and 472 4312 - Hard Face Coating to Aluminum Com- 91 ponents Project 576 6759
Towards the Carpenter's Theorem
Argerami, Martin
2008-01-01
Let M be a II_1 factor, A a masa in M and E the unique conditional expectation on A. Under some technical assumptions on the inclusion of A in M, which hold true for any semiregular masa of a separable factor, we show that for every discrete a in the positive part of the unit ball of A it is possible to find a projection p in M such that E(p)=a$. We also show an example of a diffuse operator x in A such that there exists a projection q in M with E(q)=x. These results show a new family of instances of a conjecture by Kadison, the so-called ``Carpenter's Theorem''.
Lagrange Theorem for polygroups
alireza sedighi
2014-12-01
Full Text Available So far?, ?isomorphism theorems in hyperstructure were proved for different structures of polygroups?, ?hyperrings and etc?. ?In this paper?, ?the polygroups properties is studied with the introduction of a suitable equivalence relation?. ?We show that the above relation is strongly regular?. ?Our main purpose in the paper is investigating Lagrang theorem and other expressing of isomorphism theorems for polygroups?.
Wang Yun-Hua; Zhang Yan-Min; He Ming-Xia; Guo Li-Xin
2008-01-01
This paper proposes a hybrid method based on the forward-backward method(FBM)and the reciprocity theorem(RT)for evaluating the scattering field from dielectric rough surface with a 2D target above it.Here,the equivalent electric/magnetic current densities on the rough surface as well as the scattering field from it are numerically calculated by FBM,and the scattered field from the isolated target is obtained utilizing the method of moments(MOM).Meanwhile,the rescattered coupling interactions between the target and the surface are evaluated employing the combination of FBM and RT.Our hybrid method is first validated by available MOM results.Then,the functional dependences of bistatic and monostatic scattering from the target above rough surface upon the target altitude,incident and scattering angles are numerically simulated and discussed.This study presents a numerical description for the scattering mechanism associated with rescattered coupling interactions between a target and an underlying randomly rough surface.
Levinson, N
1940-01-01
A typical gap theorem of the type discussed in the book deals with a set of exponential functions { \\{e^{{{i\\lambda}_n} x}\\} } on an interval of the real line and explores the conditions under which this set generates the entire L_2 space on this interval. A typical gap theorem deals with functions f on the real line such that many Fourier coefficients of f vanish. The main goal of this book is to investigate relations between density and gap theorems and to study various cases where these theorems hold. The author also shows that density- and gap-type theorems are related to various propertie
Lp-inverse theorem for modified beta operators
V. K. Jain
2003-04-01
Full Text Available We obtain a converse theorem for the linear combinations of modified beta operators whose weight function is the Baskakov operators. To prove our inverse theorem, we use the technique of linear approximating method, namely, Steklov mean.
Methods for Project Tracking in Creative Environment
Eva Šviráková
2017-06-01
Full Text Available The objective of this paper is to design new alternative methods for project tracking in creative industry environment. One of the research method is system dynamics modelling. A dynamics model accepts problems which were identified based on qualitative research and assessed using the system thinking method. A system dynamics model contains a project reference mode which correctly and provably expresses the planned and actual project development in terms of scope and budget. Reference mode of the project was discovered on the basis of Earned Value Management method modification. System dynamics modelling suitability is demonstrated on a case study of a creative project called “Water for Everyone”. If the project is behind schedule, the simulation explains why it happened and forecasts further project development. Managers can use the modelling process to evaluate the impact of their decisions on the next stages of the project life cycle and adopt new management practices using scenarios. The published research is valuable for key stakeholders as it is practically focused on ascertaining essential information about the project progress.
Yan Tang
2013-01-01
Full Text Available Suppose that C is a nonempty closed convex subset of a real reflexive Banach space E which has a uniformly Gateaux differentiable norm. A viscosity iterative process is constructed in this paper. A strong convergence theorem is proved for a common element of the set of fixed points of a finite family of pseudocontractive mappings and the set of solutions of a finite family of monotone mappings. And the common element is the unique solution of certain variational inequality. The results presented in this paper extend most of the results that have been proposed for this class of nonlinear mappings.
Project Management Concepts, Methods, and Techniques
Maley, Claude H
2011-01-01
In order to succeed in today's increasingly competitive environment, corporations, companies, governments, and nonprofit organizations must be conversant with modern project management techniques. This is especially true for individuals looking to remain professionally competitive. Illustrating the why, what, and how of project management, Project Management Concepts, Methods, and Techniques will help readers develop and refine the skills needed to achieve strategic objectives. It presents a balanced blend of detailed explanatory texts and more than 200 illustrations to supply readers with act
Louis M. Houston
2012-01-01
Sign data are the signs of signal added to noise. It is well known that a constant signal can be recovered from sign data. In this paper, we show that an integral over variant signal can be recovered from an integral over sign data based on the variant signal. We refer to this as a generalized sign data average. We use this result to derive a Green's theorem for sign data. Green's theorem is important to various seismic processing methods, including seismic migration. Results in this paper ge...
Lu, Bin
2012-12-01
In this paper, a effective method for searching infinite sequence periodic and solitary wave solutions to nonlinear partial differential equations (NLPDEs) is proposed. A simple transformation technique and division theorem are used to reduce some class of NLPDEs to the Riccati equation, and then the infinite sequence periodic and solitary wave solutions of some class of NLPDEs are constructed by using Bäcklund transformation of Riccati equation and nonlinear superposition principle. As illustrative examples, we obtain the infinite sequence travelling-wave solutions of the three special equations, respectively.
Numerical Methods through Open-Ended Projects
Cline, Kelly S.
2005-01-01
We present a design for a junior level numerical methods course that focuses on a series of five open-ended projects in applied mathematics. These projects were deliberately designed to present many of the ambiguities and complexities that appear any time we use mathematics in the real world, and so they offered the students a variety of possible…
LUROTH'S THEOREM IN DIFFERENTIAL FIELDS
GAO Xiaoshan; XU Tao
2002-01-01
In this paper, we present a constructive proof of Liroth's theorem in differentialcase. We also give a method to find the inversion maps for general differential rationalparametric equations. As a consequence, we prove that a differential rational curve alwayshas a set of proper parametric equations.
The asymmetric sandwich theorem
Simons, Stephen
2011-01-01
We discuss the asymmetric sandwich theorem, a generalization of the Hahn-Banach theorem. As applications, we derive various results on the existence of linear functionals that include bivariate, trivariate and quadrivariate generalizations of the Fenchel duality theorem. Most of the results are about affine functions defined on convex subsets of vector spaces, rather than linear functions defined on vector spaces. We consider both results that use a simple boundedness hypothesis (as in Rockafellar's version of the Fenchel duality theorem) and also results that use Baire's theorem (as in the Robinson-Attouch-Brezis version of the Fenchel duality theorem). This paper also contains some new results about metrizable topological vector spaces that are not necessarily locally convex.
2011-01-01
Arvanitakis established recently a theorem which is a common generalization of Michael's convex selection theorem and Dugundji's extension theorem. In this note we provide a short proof of a more general version of Arvanitakis' result.
Using Replication Projects in Teaching Research Methods
Standing, Lionel G.; Grenier, Manuel; Lane, Erica A.; Roberts, Meigan S.; Sykes, Sarah J.
2014-01-01
It is suggested that replication projects may be valuable in teaching research methods, and also address the current need in psychology for more independent verification of published studies. Their use in an undergraduate methods course is described, involving student teams who performed direct replications of four well-known experiments, yielding…
Multiple Methods: Research Methods in Education Projects at NSF
Suter, Larry E.
2005-01-01
Projects on science and mathematics education research supported by the National Science Foundation (US government) rarely employ a single method of study. Studies of educational practices that use experimental design are very rare. The most common research method is the case study method and the second most common is some form of experimental…
The Hellmann–Feynman theorem, the comparison theorem, and the envelope theory
Claude Semay
2015-01-01
Full Text Available The envelope theory is a convenient method to compute approximate solutions for bound state equations in quantum mechanics. It is shown that these approximate solutions obey a kind of Hellmann–Feynman theorem, and that the comparison theorem can be applied to these approximate solutions for two ordered Hamiltonians.
Projection preconditioning for Lanczos-type methods
Bielawski, S.S.; Mulyarchik, S.G.; Popov, A.V. [Belarusian State Univ., Minsk (Belarus)
1996-12-31
We show how auxiliary subspaces and related projectors may be used for preconditioning nonsymmetric system of linear equations. It is shown that preconditioned in such a way (or projected) system is better conditioned than original system (at least if the coefficient matrix of the system to be solved is symmetrizable). Two approaches for solving projected system are outlined. The first one implies straightforward computation of the projected matrix and consequent using some direct or iterative method. The second approach is the projection preconditioning of conjugate gradient-type solver. The latter approach is developed here in context with biconjugate gradient iteration and some related Lanczos-type algorithms. Some possible particular choices of auxiliary subspaces are discussed. It is shown that one of them is equivalent to using colorings. Some results of numerical experiments are reported.
Existence theorems for ordinary differential equations
Murray, Francis J
2007-01-01
Theorems stating the existence of an object-such as the solution to a problem or equation-are known as existence theorems. This text examines fundamental and general existence theorems, along with the Picard iterants, and applies them to properties of solutions and linear differential equations.The authors assume a basic knowledge of real function theory, and for certain specialized results, of elementary functions of a complex variable. They do not consider the elementary methods for solving certain special differential equations, nor advanced specialized topics; within these restrictions, th
On a theorem of Faltings on formal functions
Paola Bonacini
2007-12-01
Full Text Available In 1980, Faltings proved, by deep local algebra methods, a local resultregarding formal functions which has the following global geometric factas a consequence. Theorem. − Let k be an algebraically closed field (ofany characteristic. Let Y be a closed subvariety of a projective irreduciblevariety X defined over k. Assume that X ⊂ P^n , dim(X = d > 2 and Yis the intersection of X with r hyperplanes of P^n , with r ≤ d − 1. Then,every formal rational function on X along Y can be (uniquely extended toa rational function on X . Due to its importance, the aim of this paper is toprovide two elementary global geometric proofs of this theorem.
Extended abstract: Partial row projection methods
Bramley, R.; Lee, Y. [Indiana Univ., Bloomington, IN (United States)
1996-12-31
Accelerated row projection (RP) algorithms for solving linear systems Ax = b are a class of iterative methods which in theory converge for any nonsingular matrix. RP methods are by definition ones that require finding the orthogonal projection of vectors onto the null space of block rows of the matrix. The Kaczmarz form, considered here because it has a better spectrum for iterative methods, has an iteration matrix that is the product of such projectors. Because straightforward Kaczmarz method converges slowly for practical problems, typically an outer CG acceleration is applied. Definiteness, symmetry, or localization of the eigenvalues, of the coefficient matrix is not required. In spite of this robustness, work has generally been limited to structured systems such as block tridiagonal matrices because unlike many iterative solvers, RP methods cannot be implemented by simply supplying a matrix-vector multiplication routine. Finding the orthogonal projection of vectors onto the null space of block rows of the matrix in practice requires accessing the actual entries in the matrix. This report introduces a new partial RP algorithm which retains advantages of the RP methods.
On the Equivalence of Weyl Theorem and Generalized Weyl Theorem
M. BERKANI
2007-01-01
We know that an operator T acting on a Banach space satisfying generalized Weyl's theorem also satisfies Weyl's theo rem. Conversely we show that if all isolated eigenvalues of T are poles of its resolvent and if T satisfies Weyl's theorem, then it also satisfies generalized Weyl's theorem. We give also a similar result for the equivalence of a-Weyl's theorem and generalized a-Weyl's theorem. Using these results, we study the case of polaroid operators, and in particular paranormal operators.
To string together six theorems of physics by Pythagoras theorem
Cui, H Y
2002-01-01
In this paper, we point out that there are at lest six theorems in physics sharing common virtue of Pythagoras theorem, so that it is possible to string these theorems together with the Pythagoras theorem for physics teaching, the six theorems are Newton's three laws of motion, universal gravitational force, Coulomb's law, and the formula of relativistic dynamics. Knowing the internal relationships between them, which have never been clearly revealed by other author, will benefit the logic of physics teaching.
Trigonometry, Including Snell's Theorem.
Kent, David
1980-01-01
Aspects of the instruction of trigonometry in secondary school mathematics are reviewed. Portions of this document cover basic introductions, a student-developed theorem, the cosine rule, inverse functions, and a sample outdoor activity. (MP)
Trigonometry, Including Snell's Theorem.
Kent, David
1980-01-01
Aspects of the instruction of trigonometry in secondary school mathematics are reviewed. Portions of this document cover basic introductions, a student-developed theorem, the cosine rule, inverse functions, and a sample outdoor activity. (MP)
关于Newton-like-iterative方法新的收敛性定理%New convergence theorems for Newton-like-iterative methods
武敏
2010-01-01
用迭代法求解Newton-like法中的方程,T.J. Ypma提出Newton-like-iterative方法.在其早期的文章中,不精确牛顿法理论用来研究Newton-like-iterative方法的收敛性.与以往方法不同,今提出用不精确Newton-like法做相关的收敛性分析,所得定理更加简单,同时具有仿射不变性.%Newton-like-iterative methods proposed by T.J. Ypma are obtained by using an iterative method to solve Newton-like equations. In the early paper of Ypma, the theory of inexact Newton methods was applied to study the convergence of Newton-like-iterative methods. Unlike earlier results, new local convergence theorems for Newton-like-iterative methods by applying the theory of inexact Newton-like methods is proposed in this paper, which is seemed simpler and clearer. Moreover, the analysis is carried out in affine invariant terms.
Teaching Method for Two Theorems in Functional Analysis and Their Applications%《泛函分析》中两个定理的教学与应用
刘迎东
2001-01-01
In this paper we discuss the teaching method for Schauder theorem and Arzela-Ascoli theorem in functional analysis and use them in a cooperation model to get a sufficient condition ensuring the coexistence of two species.%本文讨论《泛函分析》中Schauder不动点定理和Arzela-Ascoli定理的教学方法并把它们用于互助生态模型得到两物种共存的一个充分条件.
Coincidence Point Theorems, Intersection Theorems and Saddle Point Theorems on FC-spaces
PIAO YONG-JIE; YIN ZHE
2009-01-01
In this paper, we first give the definitions of finitely continuous topological space and FC-subspace generated by some set, and obtain coincidence point theorem, whole intersection theorems and Ky Fan type matching theorems, and finally discuss the existence of saddle point as an application of coincidence point theorem.
Second derivatives for approximate spin projection methods.
Thompson, Lee M; Hratchian, Hrant P
2015-02-07
The use of broken-symmetry electronic structure methods is required in order to obtain correct behavior of electronically strained open-shell systems, such as transition states, biradicals, and transition metals. This approach often has issues with spin contamination, which can lead to significant errors in predicted energies, geometries, and properties. Approximate projection schemes are able to correct for spin contamination and can often yield improved results. To fully make use of these methods and to carry out exploration of the potential energy surface, it is desirable to develop an efficient second energy derivative theory. In this paper, we formulate the analytical second derivatives for the Yamaguchi approximate projection scheme, building on recent work that has yielded an efficient implementation of the analytical first derivatives.
李黎明; 关永; 吴敏华; 张杰; 施智平
2012-01-01
SpaceWire bus is applied in Space Solar Telescope (SST) project. Testing and simulation are the main methods for verification of SpaceWire bus, but these verifications are incomplete. This study focused on verifying whether the DS encoder circuit developed for SST had faithfully implemented the specification in SpaceWire standard. With the aid of HOL4 tool, this equivalence checking was carried out in a formal verification method, theorem proving. It overcame the limitation of testing and simulation.%我国空间太阳望远镜(SST)项目采用了StaceWire作为传输总线,目前针对Spacewire总线的验证主要采用测试和模拟等传统的方法,这类验证方法是不完备的.本文旨在对SST项目中SpaceWire总线的DS编码电路是否如实地实现标准中的规范要求进行验证,运用定理证明的形式化方法,在HOL4工具上对该电路的设计实现与规范要求的一致性进行验证,克服了传统验证方法的局限性.
Navier Stokes Theorem in Hydrology
Narayanan, M.
2005-12-01
In a paper presented at the 2004 AGU International Conference, the author outlined and stressed the importance of studying and teaching certain important mathematical techniques while developing a course in Hydrology and Fluid Mechanics. The Navier-Stokes equations are the foundation of fluid mechanics, and Stokes' theorem is used in nearly every branch of mechanics as well as electromagnetics. Stokes' Theorem also plays a vital role in many secondary theorems such as those pertaining to vorticity and circulation. Mathematically expressed, Stokes' theorem can be expressed by considering a surface S having a bounding curve C. Here, V is any sufficiently smooth vector field defined on the surface and its bounding curve C. In an article entitled "Corrections to Fluid Dynamics" R. F. Streater, (Open Systems and Information Dynamics, 10, 3-30, 2003.) proposes a kinetic model of a fluid in which five macroscopic fields, the mass, energy, and three components of momentum, are conserved. The dynamics is constructed using the methods of statistical dynamics, and results in a non-linear discrete-time Markov chain for random fields on a lattice. In the continuum limit he obtains a non-linear coupled parabolic system of field equations, showing a correction to the Navier-Stokes equations. In 2001, David Hoff published an article in Journees Equations aux derivees partielles. (Art. No. 7, 9 p.). His paper is entitled : Dynamics of Singularity Surfaces for Compressible Navier-Stokes Flows in Two Space Dimensions. In his paper, David Hoff proves the global existence of solutions of the Navier-Stokes equations of compressible, barotropic flow in two space dimensions with piecewise smooth initial data. These solutions remain piecewise smooth for all time, retaining simple jump discontinuities in the density and in the divergence of the velocity across a smooth curve, which is convected with the flow. The strengths of these discontinuities are shown to decay exponentially in time
Methods for the Drug Effectiveness Review Project
McDonagh Marian S
2012-09-01
Full Text Available Abstract The Drug Effectiveness Review Project was initiated in 2003 in response to dramatic increases in the cost of pharmaceuticals, which lessened the purchasing power of state Medicaid budgets. A collaborative group of state Medicaid agencies and other organizations formed to commission high-quality comparative effectiveness reviews to inform evidence-based decisions about drugs that would be available to Medicaid recipients. The Project is coordinated by the Center for Evidence-based Policy (CEbP at Oregon Health & Science University (OHSU, and the systematic reviews are undertaken by the Evidence-based Practice Centers (EPCs at OHSU and at the University of North Carolina. The reviews adhere to high standards for comparative effectiveness reviews. Because the investigators have direct, regular communication with policy-makers, the reports have direct impact on policy and decision-making, unlike many systematic reviews. The Project was an innovator of methods to involve stakeholders and continues to develop its methods in conducting reviews that are highly relevant to policy-makers. The methods used for selecting topics, developing key questions, searching, determining eligibility of studies, assessing study quality, conducting qualitative and quantitative syntheses, rating the strength of evidence, and summarizing findings are described. In addition, our on-going interactions with the policy-makers that use the reports are described.
Answering Junior Ant's "Why" for Pythagoras' Theorem
Pask, Colin
2002-01-01
A seemingly simple question in a cartoon about Pythagoras' Theorem is shown to lead to questions about the nature of mathematical proof and the profound relationship between mathematics and science. It is suggested that an analysis of the issues involved could provide a good vehicle for classroom discussions or projects for senior students.…
ANDRAGOGY OF DEVELOPMENT: BASIC THEOREMS
A. G. Teslinov
2016-01-01
Full Text Available The article presents criticism of the state of scientific knowledge about adult education and provides the reasons for the choice of directions of its development.Methods. The approach to the substantiation of directions of development of andragogy includes aspectual analysis of scientific rhetoric of adult education; summarizing the symptoms and causes of the problems of educational practice examples of education managers; the analysis of the status of andragogy as a scientific paradigm; a conceptual analysis of the key theses of the modern synthesis of andragogy and the provisions for developmental adult education.Results and scientific novelty. Four theorems are formulated that specify the complete set of propositions about a developmental approach to adult education. These theorems are presented as a scientific hypothesis about the features of the approach. The theorems are proved, and the substantiation of the conditions of emergence of the adult education of educational properties is described. The idea of adult education as a developing culture is in the centre of reasoning. It is shown that the assertions of theorems form the conceptual core of the scientific branches in adult education – andragogy of development. The effect of the practical interpretation of its provisions is disclosed.Practical significance. Disclosed meanings and recommendations may be oriented to developers of educational systems and media for adults while creating the developmental components. These references will help to overcome the evident trend information of adult education to the "pulling" them up to continually outdated standards, and to give it the look of a truly developing technology.
Vallès, Jean
2012-01-01
Our aim is to prove a Poncelet type theorem for a line configuration on the complex projective. More precisely, we say that a polygon with 2n sides joining 2n vertices A1, A2,..., A2n is well inscribed in a configuration Ln of n lines if each line of the configuration contains exactly two points among A1, A2, ..., A2n. Then we prove : "Let Ln be a configuration of n lines and D a smooth conic in the complex projective plane. If it exists one polygon with 2n sides well inscribed in Ln and circumscribed around D then there are infinitely many such polygons. In particular a general point in Ln is a vertex of such a polygon." We propose an elementary proof based on Fr\\'egier's involution. We begin by recalling some facts about these involutions. Then we explore the following question : When does the product of involutions correspond to an involution? It leads to Pascal theorem, to its dual version proved by Brianchon, and to its generalization proved by M\\"obius.
Simple Weighting Methods to Combine Multimodel Projections
Lorenz, R.; Sedlacek, J.; Knutti, R.
2016-12-01
Multimodel ensembles of global climate models are very heterogeneous and some models perform better than others for a certain purpose. Nevertheless, weighting of models is rarely performed and there is a debate about whether and how to weight model projections when combining simulations. We argue that the growing number of models with different characteristics and considerable interdependence, at least for cases where relevant metrics of model performance are clear, requires to make use of model constraints to decrease uncertainties in model projections. Steps towards this should involve a) showing unweighted results along with weighted ones, b) testing the robustness of the results towards different metrics or constraints to maximize transparency and comparability across studies, c) an explicit discussion of the choice of metrics, including the physical reasoning why those quantities matter, d) an assessment of the uncertainties in observations, e) testing the sensitivity towards different datasets, time periods, seasonal vs. annual mean values, grid point vs. spatially aggregated data, etc., and f) exploring whether the choice of metric may lead to overconfident results. Several prerequisites need to be met for such approaches to work. For instance, we need available observations, a certain degree of model skill as well as observable relationships that relate to the projections in question. Here we explore projections of summer temperature over central North America. Many CMIP5 models show a pronounced bias of summer temperature over central North America in present climate. We investigate possible causes for this bias and possibilities to constrain the CMIP5 ensemble. We will show if and how uncertainties of projections change depending on weighting method, observational dataset and constraint used.
Theorem on six vertices of a plane curve via the Sturm theory
Guieu, L; Ovsienko, V Yu
1995-01-01
We discuss the theorem on the existence of six points on a convex closed plane curve in which the curve has a contact of order six with the osculating conic. (This is the ``projective version'' of the well known four vertices theorem for a curve in the Euclidean plane.) We obtain this classical fact as a corollary of some general Sturm-type theorems.
ON RANGE DECOMPOSITION THEOREMS
吴利生
1990-01-01
We prove the following theorems.Theorem 1.Suppose f:X→Y is a closed map.X is a ωγ and β space,then Y=Y0∪(∪n=1∞Yn),where f-1(y) is countably compact for each y ∈Y0 and Yn is closed discrete in Y for each n≥1,Theorem 2-3:Suppose f:X→Y is a closed map,X is stratifable space,then Y=Y0 ∪(∪n=1∞Yn),where f-1(y) is compact for each y∈Y0 and Yn is closed discrete in Y for each n≥1.
D'Agostini, G
2005-01-01
It is curious to learn that Enrico Fermi knew how to base probabilistic inference on Bayes theorem, and that some influential notes on statistics for physicists stem from what the author calls elsewhere, but never in these notes, {\\it the Bayes Theorem of Fermi}. The fact is curious because the large majority of living physicists, educated in the second half of last century -- a kind of middle age in the statistical reasoning -- never heard of Bayes theorem during their studies, though they have been constantly using an intuitive reasoning quite Bayesian in spirit. This paper is based on recollections and notes by Jay Orear and on Gauss' ``Theoria motus corporum coelestium'', being the {\\it Princeps mathematicorum} remembered by Orear as source of Fermi's Bayesian reasoning.
P Dutt; Akhlaq Husain; A S Vasudeva Murthy; C S Upadhyay
2015-05-01
This is the first of a series of papers devoted to the study of ℎ- spectral element methods for solving three dimensional elliptic boundary value problems on non-smooth domains using parallel computers. In three dimensions there are three different types of singularities namely; the vertex, the edge and the vertex-edge singularities. In addition, the solution is anisotropic in the neighbourhoods of the edges and vertex-edges. To overcome the singularities which arise in the neighbourhoods of vertices, vertex-edges and edges, we use local systems of coordinates. These local coordinates are modified versions of spherical and cylindrical coordinate systems in their respective neighbourhoods. Away from these neighbourhoods standard Cartesian coordinates are used. In each of these neighbourhoods we use a geometrical mesh which becomes finer near the corners and edges. The geometrical mesh becomes a quasi-uniform mesh in the new system of coordinates. We then derive differentiability estimates in these new set of variables and state our main stability estimate theorem using a non-conforming ℎ- spectral element method whose proof is given in a separate paper.
Converse Barrier Certificate Theorem
Wisniewski, Rafael; Sloth, Christoffer
2013-01-01
This paper presents a converse barrier certificate theorem for a generic dynamical system.We show that a barrier certificate exists for any safe dynamical system defined on a compact manifold. Other authors have developed a related result, by assuming that the dynamical system has no singular...... points in the considered subset of the state space. In this paper, we redefine the standard notion of safety to comply with generic dynamical systems with multiple singularities. Afterwards, we prove the converse barrier certificate theorem and illustrate the differences between ours and previous work...
Kartavtsev, Alexander
2014-01-01
According to the Goldstone theorem a scalar theory with a spontaneously broken global symmetry contains strictly massless states. In this letter we identify a loophole in the current-algebra proof of the theorem. Therefore, the question whether in models with Mexican hat potential the tangential excitations are strictly massless or are just almost massless as compared to the radial ones remains open. We also argue that mass of the tangential excitations approaches zero even if the symmetry is not spontaneously broken but a combination of the field components invariant under the symmetry transformations acquires a large vacuum expectation value.
Pérez-Espigares, Carlos; Redig, Frank; Giardinà, Cristian
2015-08-01
For non-equilibrium systems of interacting particles and for interacting diffusions in d-dimensions, a novel fluctuation relation is derived. The theorem establishes a quantitative relation between the probabilities of observing two current values in different spatial directions. The result is a consequence of spatial symmetries of the microscopic dynamics, generalizing in this way the Gallavotti-Cohen fluctuation theorem related to the time-reversal symmetry. This new perspective opens up the possibility of direct experimental measurements of fluctuation relations of vectorial observables.
Zhang, Dengfeng; Nakaya, Naoshi; Koui, Yuuji; Yoshida, Hitoaki
Recently, the appearance frequency of computer virus variants has increased. Updates to virus information using the normal pattern matching method are increasingly unable to keep up with the speed at which viruses occur, since it takes time to extract the characteristic patterns for each virus. Therefore, a rapid, automatic virus detection algorithm using static code analysis is necessary. However, recent computer viruses are almost always compressed and obfuscated. It is difficult to determine the characteristics of the binary code from the obfuscated computer viruses. Therefore, this paper proposes a method that unpacks compressed computer viruses automatically independent of the compression format. The proposed method unpacks the common compression formats accurately 80% of the time, while unknown compression formats can also be unpacked. The proposed method is effective against unknown viruses by combining it with the existing known virus detection system like Paul Graham's Bayesian Virus Filter etc.
Numerical cubature from Archimedes' hat-box theorem
Kuperberg, Greg
2004-01-01
Archimedes' hat-box theorem states that uniform measure on a sphere projects to uniform measure on an interval. This fact can be used to derive Simpson's rule. We present various constructions of, and lower bounds for, numerical cubature formulas using moment maps as a generalization of Archimedes' theorem. We realize some well-known cubature formulas on simplices as projections of spherical designs. We combine cubature formulas on simplices and tori to make new formulas on spheres. In partic...
Virial Theorem and Scale Transformations.
Kleban, Peter
1979-01-01
Discussed is the virial theorem, which is useful in classical, quantum, and statistical mechanics. Two types of derivations of this theorem are presented and the relationship between the two is explored. (BT)
Certified Kruskal's Tree Theorem
Christian Sternagel
2014-07-01
Full Text Available This article presents the first formalization of Kurskal's tree theorem in aproof assistant. The Isabelle/HOL development is along the lines of Nash-Williams' original minimal bad sequence argument for proving the treetheorem. Along the way, proofs of Dickson's lemma and Higman's lemma, as well as some technical details of the formalization are discussed.
Thomassen, Carsten
2004-01-01
We present a short proof of the theorem of Tutte that every planar 3-connected graph has a drawing in the plane such that every vertex which is not on the outer cycle is the barycenter of its neighbors. Moreover, this holds for any prescribed representation of the outer cycle. (C) 2004 Wiley Peri...
Törnquist, Asger Dag; Weiss, W.
2009-01-01
We prove the following descriptive set-theoretic analogue of a theorem of R. 0. Davies: Every σ function f:ℝ × ℝ → ℝ can be represented as a sum of rectangular Σ functions if and only if all reals are constructible. © Instytut Matematyczny PAN, 2009....
Rediscovering Schreinemakers' Theorem.
Bathurst, Bruce
1983-01-01
Schreinemakers' theorem (arrangement of curves around an invariant point), derived from La Chatelier's principle, can be rediscovered by students asked to use the principle when solving a natural problem such as "How does diluting a mineral/fluid alter shape of a pressure/temperature diagram?" Background information and instructional…
Teleman, Nicolae
2011-01-01
$Local^{3}$ Index Theorem means $Local(Local(Local \\;Index \\; Theorem)))$. $Local \\; Index \\; Theorem$ is the Connes-Moscovici local index theorem \\cite{Connes-Moscovici1}, \\cite{Connes-Moscovici2}. The second "Local" refers to the cyclic homology localised to a certain separable subring of the ground algebra, while the last one refers to Alexander-Spanier type cyclic homology. The Connes-Moscovici work is based on the operator $R(A) = \\mathbf{P} - \\mathbf{e}$ associated to the elliptic pseudo-differential operator $A$ on the smooth manifold $M$, where $\\mathbf{P}$, $\\mathbf{e}$ are idempotents, see \\cite{Connes-Moscovici1}, Pg. 353. The operator $R(A)$ has two main merits: it is a smoothing operator and its distributional kernel is situated in an arbitrarily small neighbourhood of the diagonal in $M \\times M$. The operator $R(A)$ has also two setbacks: -i) it is not an idempotent (and therefore it does not have a genuine Connes-Chern character); -ii) even if it were an idempotent, its Connes-Chern character ...
Multivariate irregular sampling theorem
无
2009-01-01
In this paper,we prove a Marcinkiewicz-Zygmund type inequality for multivariate entire functions of exponential type with non-equidistant spaced sampling points. And from this result,we establish a multivariate irregular Whittaker-Kotelnikov-Shannon type sampling theorem.
Multivariate irregular sampling theorem
CHEN GuangGui; FANG GenSun
2009-01-01
In this paper, we prove a Marcinkiewicz-Zygmund type inequality for multivariate entire functions of exponential type with non-equidistant spaced sampling points. And from this result, we establish a multivariate irregular Whittaker-Kotelnikov-Shannon type sampling theorem.
Dalen, D. van
2008-01-01
The following pages make form a new chapter for the book Logic and Structure. This chapter deals with the incompleteness theorem, and contains enough basic material for the treatment of the required notions of computability, representability and the like. This chapter will appear in the next edition
Converse Barrier Certificate Theorems
Wisniewski, Rafael; Sloth, Christoffer
2016-01-01
This paper shows that a barrier certificate exists for any safe dynamical system. Specifically, we prove converse barrier certificate theorems for a class of structurally stable dynamical systems. Other authors have developed a related result by assuming that the dynamical system has neither sing...
Ferromagnetism beyond Lieb's theorem
Costa, Natanael C.; Mendes-Santos, Tiago; Paiva, Thereza; Santos, Raimundo R. dos; Scalettar, Richard T.
2016-10-01
The noninteracting electronic structures of tight-binding models on bipartite lattices with unequal numbers of sites in the two sublattices have a number of unique features, including the presence of spatially localized eigenstates and flat bands. When a uniform on-site Hubbard interaction U is turned on, Lieb proved rigorously that at half-filling (ρ =1 ) the ground state has a nonzero spin. In this paper we consider a "CuO2 lattice" (also known as "Lieb lattice," or as a decorated square lattice), in which "d orbitals" occupy the vertices of the squares, while "p orbitals" lie halfway between two d orbitals; both d and p orbitals can accommodate only up to two electrons. We use exact determinant quantum Monte Carlo (DQMC) simulations to quantify the nature of magnetic order through the behavior of correlation functions and sublattice magnetizations in the different orbitals as a function of U and temperature; we have also calculated the projected density of states, and the compressibility. We study both the homogeneous (H) case, Ud=Up , originally considered by Lieb, and the inhomogeneous (IH) case, Ud≠Up . For the H case at half-filling, we found that the global magnetization rises sharply at weak coupling, and then stabilizes towards the strong-coupling (Heisenberg) value, as a result of the interplay between the ferromagnetism of like sites and the antiferromagnetism between unlike sites; we verified that the system is an insulator for all U . For the IH system at half-filling, we argue that the case Up≠Ud falls under Lieb's theorem, provided they are positive definite, so we used DQMC to probe the cases Up=0 ,Ud=U and Up=U ,Ud=0 . We found that the different environments of d and p sites lead to a ferromagnetic insulator when Ud=0 ; by contrast, Up=0 leads to to a metal without any magnetic ordering. In addition, we have also established that at density ρ =1 /3 , strong antiferromagnetic correlations set in, caused by the presence of one fermion on each
The Second Noether Theorem on Time Scales
Malinowska, Agnieszka B.; Natália Martins
2013-01-01
We extend the second Noether theorem to variational problems on time scales. As corollaries we obtain the classical second Noether theorem, the second Noether theorem for the $h$ -calculus and the second Noether theorem for the $q$ -calculus.
An Extension of Sobolev's Theorem
无
2000-01-01
Sobolev's Theorem is the most fundamental theorem in the theory of Invariant Cubature Formulas (ICFs). In this paper, a quantitative structure is established for the classical ICFs. Enlightened by this structure, the author generalizes the concept of ICFs and extends the Sobolev's Theorem to the case of generalized ICFs. Several illustrative examples are given.
Russell, Alan R.
2004-01-01
Pick's theorem can be used in various ways just like a lemon. This theorem generally finds its way in the syllabus approximately at the middle school level and in fact at times students have even calculated the area of a state considering its outline with the help of the above theorem.
Generalized no-broadcasting theorem.
Barnum, Howard; Barrett, Jonathan; Leifer, Matthew; Wilce, Alexander
2007-12-14
We prove a generalized version of the no-broadcasting theorem, applicable to essentially any nonclassical finite-dimensional probabilistic model satisfying a no-signaling criterion, including ones with "superquantum" correlations. A strengthened version of the quantum no-broadcasting theorem follows, and its proof is significantly simpler than existing proofs of the no-broadcasting theorem.
Applying a life cycle approach to project management methods
Biggins, David; Trollsund, F.; Høiby, A.L.
2016-01-01
Project management is increasingly important to organisations because projects are the method\\ud by which organisations respond to their environment. A key element within project management\\ud is the standards and methods that are used to control and conduct projects, collectively known as\\ud project management methods (PMMs) and exemplified by PRINCE2, the Project Management\\ud Institute’s and the Association for Project Management’s Bodies of Knowledge (PMBOK and\\ud APMBOK. The purpose of t...
Commutative algebra constructive methods finite projective modules
Lombardi, Henri
2015-01-01
Translated from the popular French edition, this book offers a detailed introduction to various basic concepts, methods, principles, and results of commutative algebra. It takes a constructive viewpoint in commutative algebra and studies algorithmic approaches alongside several abstract classical theories. Indeed, it revisits these traditional topics with a new and simplifying manner, making the subject both accessible and innovative. The algorithmic aspects of such naturally abstract topics as Galois theory, Dedekind rings, Prüfer rings, finitely generated projective modules, dimension theory of commutative rings, and others in the current treatise, are all analysed in the spirit of the great developers of constructive algebra in the nineteenth century. This updated and revised edition contains over 350 well-arranged exercises, together with their helpful hints for solution. A basic knowledge of linear algebra, group theory, elementary number theory as well as the fundamentals of ring and module theory is r...
An Alternative Method to Project Wind Patterns
Fadillioglu, Cagla; Kiyisuren, I. Cagatay; Collu, Kamil; Turp, M. Tufan; Kurnaz, M. Levent; Ozturk, Tugba
2016-04-01
Wind energy is one of the major clean and sustainable energy sources. Beside its various advantages, wind energy has a downside that its performance cannot be projected very accurately in the long-term. In this study, we offer an alternative method which can be used to determine the best location to install a wind turbine in a large area aiming maximum energy performance in the long run. For this purpose, a regional climate model (i.e. RegCM4.4) is combined with a software called Winds on Critical Streamline Surfaces (WOCSS) in order to identify wind patterns for any domains even in a changing climate. As a special case, Çanakkale region is examined due to the terrain profile having both coastal and mountainous features. WOCSS program was run twice for each month in the sample years in a double nested fashion, using the provisional RegCM4.4 wind data between years 2020 and 2040. Modified version of WOCSS provides terrain following flow surfaces and by processing those data, it makes a wind profile output for certain heights specified by the user. The computational time of WOCSS is also in reasonable range. Considering the lack of alternative methods for long-term wind performance projection, the model used in this study is a very good way for obtaining quick indications for wind performance taking the impact of the terrain effects into account. This research has been supported by Boǧaziçi University Research Fund Grant Number 10421.
Wiyada Kumam
2010-01-01
Full Text Available The purpose of this paper is to consider a shrinking projection method for finding a common element of the set of solutions of generalized mixed equilibrium problems, the set of fixed points of a finite family of quasi-nonexpansive mappings, and the set of solutions of variational inclusion problems. Then, we prove a strong convergence theorem of the iterative sequence generated by the shrinking projection method under some suitable conditions in a real Hilbert space. Our results improve and extend recent results announced by Peng et al. (2008, Takahashi et al. (2008, S.Takahashi and W. Takahashi (2008, and many others.
Taylor, Marika
2016-01-01
The F theorem states that, for a unitary three dimensional quantum field theory, the F quantity defined in terms of the partition function on a three sphere is positive, stationary at fixed point and decreases monotonically along a renormalization group flow. We construct holographic renormalization group flows corresponding to relevant deformations of three-dimensional conformal field theories on spheres, working to quadratic order in the source. For these renormalization group flows, the F quantity at the IR fixed point is always less than F at the UV fixed point, but F increases along the RG flow for deformations by operators of dimension $3/2 < \\Delta < 5/2$. Therefore the strongest version of the F theorem is in general violated.
N V Rao
2003-02-01
The general theme of this note is illustrated by the following theorem: Theorem 1. Suppose is a compact set in the complex plane and 0 belongs to the boundary . Let $\\mathcal{A}(K)$ denote the space of all functions on such that is holomorphic in a neighborhood of and (0) = 0. Also for any given positive integer , let $\\mathcal{A}(m, K)$ denote the space of all such that is holomorphic in a neighborhood of and $f(0) = f'(0) = \\cdots = f^{(m)}(0) = 0$. Then $\\mathcal{A}(m, K)$ is dense in $\\mathcal{A}(K)$ under the supremum norm on provided that there exists a sector $W = \\{re^{i}; 0 ≤ r ≤ , ≤ ≤ \\}$ such that $W \\cap K = \\{0\\}$. (This is the well-known Poincare's external cone condition).} We present various generalizations of this result in the context of higher dimensions replacing holomorphic with harmonic.
1987-03-20
with standard expressions of spherical trigonometry is sinr)0 = cos0 sini//0 (4.37) which is consistent with the results obtained previously with...theorems for discrete transforms. However, sampling questions inlroduce difficult obstacles in the develop- ment of a discrete theory. First, sampling...additional obstacle to discrete represen- tations of the CT. An example of qualitative predication of the shape of silhouettes with the Silhouette-Slice
Gouin, Henri
2015-01-01
Comments on Archimedes' theorem about sphere and cylinder; In his treatise addressed to Dositheus of Pelusium, Archimedes of Syracuse obtained the result of which he was the most proud: a sphere has two-thirds the volume of its circumscribing cylinder. At his request a sculpted sphere and cylinder were placed on his tomb near Syracuse. Usually, it is admitted that to find this formula, Archimedes used a half polygon inscribed in a semicircle; then he performed rotations of these two figures t...
Sandwich classification theorem
Alexey Stepanov
2015-09-01
Full Text Available The present note arises from the author's talk at the conference ``Ischia Group Theory 2014''. For subgroups FleN of a group G denote by Lat(F,N the set of all subgroups of N , containing F . Let D be a subgroup of G . In this note we study the lattice LL=Lat(D,G and the lattice LL ′ of subgroups of G , normalized by D . We say that LL satisfies sandwich classification theorem if LL splits into a disjoint union of sandwiches Lat(F,N G (F over all subgroups F such that the normal closure of D in F coincides with F . Here N G (F denotes the normalizer of F in G . A similar notion of sandwich classification is introduced for the lattice LL ′ . If D is perfect, i.,e. coincides with its commutator subgroup, then it turns out that sandwich classification theorem for LL and LL ′ are equivalent. We also show how to find basic subroup F of sandwiches for LL ′ and review sandwich classification theorems in algebraic groups over rings.
FIXED POINTS THEOREMS IN MULTI-METRIC SPACES
Laurentiu I. Calmutchi
2011-07-01
Full Text Available The aim of the present article is to give some general methods inthe fixed point theory for mappings of general topological spaces. Using the notions of the multi-metric space and of the E-metric space, we proved the analogous of several classical theorems: Banach fixed point principle, Theorems of Edelstein, Meyers, Janos etc.
Multi-Role Project (MRP): A New Project-Based Learning Method for STEM
Warin, Bruno; Talbi, Omar; Kolski, Christophe; Hoogstoel, Frédéric
2016-01-01
This paper presents the "Multi-Role Project" method (MRP), a broadly applicable project-based learning method, and describes its implementation and evaluation in the context of a Science, Technology, Engineering, and Mathematics (STEM) course. The MRP method is designed around a meta-principle that considers the project learning activity…
Kamonrat Nammanee
2012-01-01
Full Text Available We introduce hybrid-iterative schemes for solving a system of the zero-finding problems of maximal monotone operators, the equilibrium problem, and the fixed point problem of weak relatively nonexpansive mappings. We then prove, in a uniformly smooth and uniformly convex Banach space, strong convergence theorems by using a shrinking projection method. We finally apply the obtained results to a system of convex minimization problems.
Geometry Theorem Proving by Decomposing Polynomial System into Strong Regular Sets
Yong-Bin Li; Wu Liu; Xiao-Lin Xiang
2004-01-01
This paper presents a complete method to prove geometric theorem by decomposing the corresponding polynomial system into strong regular sets, by which one can compute some components for which the geometry theorem is true and exclude other components for which the geometry theorem is false. Two examples are given to show that the geometry theorems are conditionally true for some components which are excluded by other methods.
How Agile Methods Conquers General Project Management - The Project Half Double Initiative
Tordrup Heeager, Lise; Svejvig, Per; Schlichter, Bjarne Rerup
2016-01-01
Increased complexity in projects has forced new project management initiatives. In software development several agile methods have emerged and methods such as Scrum are today highly implemented in practice. General project management practice has been inspired by agile software development....... But in order to fully understand and to provide suggestions for future practice on how agility can be incorporated in general project management, this paper addresses how agile methods have inspired general project management practices. To answer the research question, the paper provides an analysis which...... compares ten characteristics of agile software development (identified in theory) and the general project management method developed by the Danish Project Half Double (PHD) initiative. The method consists of 10 leading stars for rethinking project management the impact, flow and leadership (ILF) method...
Projective geometry and projective metrics
Busemann, Herbert
2005-01-01
The basic results and methods of projective and non-Euclidean geometry are indispensable for the geometer, and this book--different in content, methods, and point of view from traditional texts--attempts to emphasize that fact. Results of special theorems are discussed in detail only when they are needed to develop a feeling for the subject or when they illustrate a general method. On the other hand, an unusual amount of space is devoted to the discussion of the fundamental concepts of distance, motion, area, and perpendicularity.Topics include the projective plane, polarities and conic sectio
Bezout's theorem and Cohen-Macaulay modules
1999-01-01
We define very proper intersections of modules and projective subschemes. It turns out that equidimensional locally Cohen-Macaulay modules intersect very properly if and only if they intersect properly. We prove a Bezout theorem for modules which meet very properly. Furthermore, we show for equidimensional subschemes $X$ and $Y$: If they intersect properly in an arithmetically Cohen-Macaulay subscheme of positive dimension then $X$ and $Y$ are arithmetically Cohen-Macaulay. The module version...
Distributed Research Project Scheduling Based on Multi-Agent Methods
Constanta Nicoleta Bodea
2011-01-01
Full Text Available Different project planning and scheduling approaches have been developed. The Operational Research (OR provides two major planning techniques: CPM (Critical Path Method and PERT (Program Evaluation and Review Technique. Due to projects complexity and difficulty to use classical methods, new approaches were developed. Artificial Intelligence (AI initially promoted the automatic planner concept, but model-based planning and scheduling methods emerged later on. The paper adresses the project scheduling optimization problem, when projects are seen as Complex Adaptive Systems (CAS. Taken into consideration two different approaches for project scheduling optimization: TCPSP (Time- Constrained Project Scheduling and RCPSP (Resource-Constrained Project Scheduling, the paper focuses on a multiagent implementation in MATLAB for TCSP. Using the research project as a case study, the paper includes a comparison between two multi-agent methods: Genetic Algorithm (GA and Ant Colony Algorithm (ACO.
Developing New Testing Methods for Nanosatellites Project
National Aeronautics and Space Administration — Thermal modeling and Test plan to be carried out and developed by Goddard Space Flight Center. This project will be done in collaboration with partners at MIT and...
Manufacturing Methods and Technology Project Summary Reports
1982-06-01
variation. The goal of this FY78 project was to solve these problems, develop pilot line production of 200 ferrites , and test them. SWITCHING ...WIRES FERRITE HIGH &. DIELECTRIC ^ mm i ii ’&Z2ZL f M Figure 1 - Non-Reciprocal Latching Phase Shifter - Side Loaded Geometry 39 i SUMMARY...Control Manufacturing Modernization Plan 18 ELECTRONICS Project 273 9638 - Integrated Hybrid Transistor Switch for Solid 21 State Converter
Transfinite Approximation of Hindman's Theorem
Beiglböck, Mathias
2010-01-01
Hindman's Theorem states that in any finite coloring of the integers, there is an infinite set all of whose finite sums belong to the same color. This is much stronger than the corresponding finite form, stating that in any finite coloring of the integers there are arbitrarily long finite sets with the same property. We extend the finite form of Hindman's Theorem to a "transfinite" version for each countable ordinal, and show that Hindman's Theorem is equivalent to the appropriate transfinite approximation holding for every countable ordinal. We then give a proof of Hindman's Theorem by directly proving these transfinite approximations.
The Action-Project Method in Counseling Psychology
Young, Richard A.; Valach, Ladislav; Domene, Jose F.
2005-01-01
The qualitative action-project method is described as an appropriate and heuristic qualitative research method for use in counseling psychology. Action theory, which addresses human intentional, goal-directed action, project, and career, provides the conceptual framework for the method. Data gathering and analysis involve multiple procedures to…
A Projection-Programming Method of Combination Weighting
ZeshuiXu; LiLi
2004-01-01
This paper proposes a projection programming method of combination weighting. The method combines subjective weights and objective weights, and derives the weights of attributes by solving a projection-programming model. The method is simple, practical and easy to implement on computer. A numerical example is also given.
The Action-Project Method in Counseling Psychology
Young, Richard A.; Valach, Ladislav; Domene, Jose F.
2005-01-01
The qualitative action-project method is described as an appropriate and heuristic qualitative research method for use in counseling psychology. Action theory, which addresses human intentional, goal-directed action, project, and career, provides the conceptual framework for the method. Data gathering and analysis involve multiple procedures to…
Budgetary Approach to Project Management by Percentage of Completion Method
Leszek Borowiec
2010-06-01
Full Text Available Efficient and effective project management process is made possible by the use of methods and techniques of project management. The aim of this paper is to present the problems of project management by using Percentage of Completion method. The research material was gathered based on the experience in implementing this method by the Johnson Controls International Company. The article attempts to demonstrate the validity of the thesis that the POC project management method, allows for effective implementation and monitoring of the project and thus is an effective tool in the managing of companies which exploit the budgetary approach. The study presents planning process of basic parameters affecting the effectiveness of the project (such as costs, revenue, margin and characterized how the primary measurements used to evaluate it. The present theme is illustrating by numerous examples for showing the essence of the raised problems and the results are presenting by using descriptive methods, graphical and tabular.
Reciprocity Theorems for Ab Initio Force Calculations
Wei, C; Mele, E J; Rappe, A M; Lewis, Steven P.; Rappe, Andrew M.
1996-01-01
We present a method for calculating ab initio interatomic forces which scales quadratically with the size of the system and provides a physically transparent representation of the force in terms of the spatial variation of the electronic charge density. The method is based on a reciprocity theorem for evaluating an effective potential acting on a charged ion in the core of each atom. We illustrate the method with calculations for diatomic molecules.
Manufacturing Methods and Technology Project Summary Reports
1982-12-01
MORE INFORMATION 1 Additional information can be obtained from the project officer, Mr. Nathaniel Scott, ARRADCOM, AV 880-6945 or Commercial (201...QAM6, Mr. S. R. Caswell Cdr, Hawthorne AAP, Attn: SARHW-CO Cdr, Holston AAP, Attn: SARHO-CO Cdr, Indiana AAP, Attn: SARIN-CO AII-3 DRXIB-MT
Project Oriented Immersion Learning: Method and Results
Icaza, José I.; Heredia, Yolanda; Borch, Ole M.
2005-01-01
house that develops digital products including e-books, tutorials, web sites and so on. The students defined the problem that their product was to solve; choose the type of product and the content; and built the product following a strict project methodology. A wiki server was used as a platform to hold...
The Non-Signalling theorem in generalizations of Bell's theorem
Walleczek, J.; Grössing, G.
2014-04-01
Does "epistemic non-signalling" ensure the peaceful coexistence of special relativity and quantum nonlocality? The possibility of an affirmative answer is of great importance to deterministic approaches to quantum mechanics given recent developments towards generalizations of Bell's theorem. By generalizations of Bell's theorem we here mean efforts that seek to demonstrate the impossibility of any deterministic theories to obey the predictions of Bell's theorem, including not only local hidden-variables theories (LHVTs) but, critically, of nonlocal hidden-variables theories (NHVTs) also, such as de Broglie-Bohm theory. Naturally, in light of the well-established experimental findings from quantum physics, whether or not a deterministic approach to quantum mechanics, including an emergent quantum mechanics, is logically possible, depends on compatibility with the predictions of Bell's theorem. With respect to deterministic NHVTs, recent attempts to generalize Bell's theorem have claimed the impossibility of any such approaches to quantum mechanics. The present work offers arguments showing why such efforts towards generalization may fall short of their stated goal. In particular, we challenge the validity of the use of the non-signalling theorem as a conclusive argument in favor of the existence of free randomness, and therefore reject the use of the non-signalling theorem as an argument against the logical possibility of deterministic approaches. We here offer two distinct counter-arguments in support of the possibility of deterministic NHVTs: one argument exposes the circularity of the reasoning which is employed in recent claims, and a second argument is based on the inconclusive metaphysical status of the non-signalling theorem itself. We proceed by presenting an entirely informal treatment of key physical and metaphysical assumptions, and of their interrelationship, in attempts seeking to generalize Bell's theorem on the basis of an ontic, foundational
A Time scales Noether's theorem
Anerot, Baptiste; Cresson, Jacky; Pierret, Frédéric
2016-01-01
We prove a time scales version of the Noether's theorem relating group of symmetries and conservation laws. Our result extends the continuous version of the Noether's theorem as well as the discrete one and corrects a previous statement of Bartosiewicz and Torres in \\cite{BT}.
Abelian theorems for Whittaker transforms
Richard D. Carmichael
1987-01-01
Full Text Available Initial and final value Abelian theorems for the Whittaker transform of functions and of distributions are obtained. The Abelian theorems are obtained as the complex variable of the transform approaches 0 or ∞ in absolute value inside a wedge region in the right half plane.
Lopez-Real, Francis
2008-01-01
While the author was searching the web, he came across an article by Michael Keyton of IMSA (Illinois Mathematics and Science Academy) called "Theorems of mystery". The phrase is Keyton's own, and he defines such a theorem as "a result that has considerable structure with minimal hypotheses." The simplest of his 10 examples is one that many…
Coghetto Roland
2015-06-01
Full Text Available Morley’s trisector theorem states that “The points of intersection of the adjacent trisectors of the angles of any triangle are the vertices of an equilateral triangle” [10]. There are many proofs of Morley’s trisector theorem [12, 16, 9, 13, 8, 20, 3, 18]. We follow the proof given by A. Letac in [15].
Geometry of the Adiabatic Theorem
Lobo, Augusto Cesar; Ribeiro, Rafael Antunes; Ribeiro, Clyffe de Assis; Dieguez, Pedro Ruas
2012-01-01
We present a simple and pedagogical derivation of the quantum adiabatic theorem for two-level systems (a single qubit) based on geometrical structures of quantum mechanics developed by Anandan and Aharonov, among others. We have chosen to use only the minimum geometric structure needed for the understanding of the adiabatic theorem for this case.…
Some Theorems on Generalized Basic Hypergeometric Series
A. D. Wadhwa
1972-07-01
Full Text Available In an earlier paper the author has established two theorems on generalized hypergeometric functions. In each theorem a numerator differs from a denominator by a positive integer. These theorems were further used to prove some theorems on the sums of Kampe de Feriet functions. Here, we have established the theorems which are the basic analogues of the theorems proved in the earlier paper.
Overlap Removal Methods for Data Projection Algorithms
Spicker, Marc
2011-01-01
Projection algorithms map high dimensional data points to lower dimensions. However, when adding arbitrary shaped objects as representatives for these data points, they may intersect. The positions of these representatives have to be modi ed in order to remove existing overlaps. There are multiple algorithms designed to deal with this layout adjustment problem, which lead to very di erent results. These adjustment strategies are evaluated according to di erent measures for comparison: euclide...
Combinatorial Reciprocity Theorems
Beck, Matthias
2012-01-01
A common theme of enumerative combinatorics is formed by counting functions that are polynomials evaluated at positive integers. In this expository paper, we focus on four families of such counting functions connected to hyperplane arrangements, lattice points in polyhedra, proper colorings of graphs, and $P$-partitions. We will see that in each instance we get interesting information out of a counting function when we evaluate it at a \\emph{negative} integer (and so, a priori the counting function does not make sense at this number). Our goals are to convey some of the charm these "alternative" evaluations of counting functions exhibit, and to weave a unifying thread through various combinatorial reciprocity theorems by looking at them through the lens of geometry, which will include some scenic detours through other combinatorial concepts.
CHARACTERISTICS OF MIRR METHOD IN EVALUATION OF INVESTMENT PROJECTS' EFFECTIVENESS
P. Kukhta
2014-09-01
Full Text Available There were analyzed characteristics of the Modified Internal Rate of Return method in the evaluation of investment projects, restrictions connected with its application, advantages and disadvantages compared with indicators of the original Internal Rate of Return and Net Present Value for projects with certain baseline characteristics. It was determined opportunities to adapt the method of Modified Internal Rate of Return to alternative computational approaches of the project cash flows evaluation.
A novel background field removal method for MRI using projection onto dipole fields (PDF).
Liu, Tian; Khalidov, Ildar; de Rochefort, Ludovic; Spincemaille, Pascal; Liu, Jing; Tsiouris, A John; Wang, Yi
2011-11-01
For optimal image quality in susceptibility-weighted imaging and accurate quantification of susceptibility, it is necessary to isolate the local field generated by local magnetic sources (such as iron) from the background field that arises from imperfect shimming and variations in magnetic susceptibility of surrounding tissues (including air). Previous background removal techniques have limited effectiveness depending on the accuracy of model assumptions or information input. In this article, we report an observation that the magnetic field for a dipole outside a given region of interest (ROI) is approximately orthogonal to the magnetic field of a dipole inside the ROI. Accordingly, we propose a nonparametric background field removal technique based on projection onto dipole fields (PDF). In this PDF technique, the background field inside an ROI is decomposed into a field originating from dipoles outside the ROI using the projection theorem in Hilbert space. This novel PDF background removal technique was validated on a numerical simulation and a phantom experiment and was applied in human brain imaging, demonstrating substantial improvement in background field removal compared with the commonly used high-pass filtering method. Copyright © 2011 John Wiley & Sons, Ltd.
How Agile Methods Inspire Project Management - The Half Double Initiative
Heeager, Lise Tordrup; Svejvig, Per; Schlichter, Bjarne Rerup
Increased complexity in projects has forced new project management initiatives. In software development several agile methods have emerged and are today highly implemented in practice. Observations of general project management practice show how it has been inspired by agile software development......, but very little research addresses the issue of agile project management. In order to understand and to provide suggestions for future practice on how agility can be incorporated in general project management, this paper provides an analysis which compares ten characteristics of agile software development...... (identified in theory) and the Half Double Methodology developed by the Danish Project Half Double initiative; a Methodology developed with practitioners and tested in seven Danish case companies. The analysis shows how the general project management to a great extent has been inspired by agile methods...
An Analytical Method for Measuring Competence in Project Management
González-Marcos, Ana; Alba-Elías, Fernando; Ordieres-Meré, Joaquín
2016-01-01
The goal of this paper is to present a competence assessment method in project management that is based on participants' performance and value creation. It seeks to close an existing gap in competence assessment in higher education. The proposed method relies on information and communication technology (ICT) tools and combines Project Management…
Fuzzy Assessment Method and Its Application to Selecting Project Managers
无
2006-01-01
Open competition is a new form of the assessment of candidates and selection of project managers. This has many merits compared to the traditional administrative method of appointment. This article introduces a method of fuzzy assessment of project manager candidates. Fuzzy assessment unifies objective qualitative and quantitative appraisal and can be used for improving decision-making in the selection process.
An update on projection methods for transient incompressible viscous flow
Gresho, P.M.; Chan, S.T.
1995-07-01
Introduced in 1990 was the biharmonic equation (for the pressure) and the concomitant biharmonic miracle when transient incompressible viscous flow is solved approximately by a projection method. Herein is introduced the biharmonic catastrophe that sometimes occurs with these same projection methods.
An Analytical Method for Measuring Competence in Project Management
González-Marcos, Ana; Alba-Elías, Fernando; Ordieres-Meré, Joaquín
2016-01-01
The goal of this paper is to present a competence assessment method in project management that is based on participants' performance and value creation. It seeks to close an existing gap in competence assessment in higher education. The proposed method relies on information and communication technology (ICT) tools and combines Project Management…
Hybrid Prediction Method for Aircraft Interior Noise Project
National Aeronautics and Space Administration — The goal of the project is research and development of methods for application of the Hybrid FE-SEA method to aircraft vibro-acoustic problems. This proposal...
The RISKMED project: philosophy, methods and products
Bartzokas, A.; Azzopardi, J.; Bertotti, L.; Buzzi, A.; Cavaleri, L.; Conte, D.; Davolio, S.; Dietrich, S.; Drago, A.; Drofa, O.; Gkikas, A.; Kotroni, V.; Lagouvardos, K.; Lolis, C. J.; Michaelides, S.; Miglietta, M.; Mugnai, A.; Music, S.; Nikolaides, K.; Porcù, F.; Savvidou, K.; Tsirogianni, M. I.
2010-07-01
This paper presents RISKMED, a project targeted to create an Early Warning System (EWS) in case of severe or extreme weather events in the central and eastern Mediterranean and specifically in southern Italy, northwestern Greece, Malta and Cyprus. As severe or extreme weather events are considered, cases when the values of some meteorological parameters (temperature, wind, precipitation) exceed certain thresholds, and/or a severe weather phenomenon (thunderstorm, snowfall) occurs. For an accurate weather forecast, selected meteorological models have been operated daily, based on a nesting strategy using two or three domains, providing detailed forecasts over the above mentioned areas. The forecast results are further exploited for the evaluation and prediction of human discomfort and fire weather indices. Finally, sea wave models have also been operating daily over the central and eastern Mediterranean Sea. In case a severe or extreme weather event is forecasted within the next 48 or 72 h for selected target areas (sub-regions defined by their morphological and population characteristics), the local authorities and the public are informed via a user-friendly graphic system, the so-called RISK MAP. On the web page of the Project ( http://www.riskmed.net ), additional information is provided about the real-time values of some meteorological parameters, the latest satellite picture and the time and space distribution of lightning during the last 24 h. The RISKMED project was financed by the EU and th Ministries of National Economy of Greece, Italy, Malta and Cyprus, in the frame of INTERREG IIIB/ARCHIMED programme.
Smorynski, Craig
2017-01-01
This book is about the rise and supposed fall of the mean value theorem. It discusses the evolution of the theorem and the concepts behind it, how the theorem relates to other fundamental results in calculus, and modern re-evaluations of its role in the standard calculus course. The mean value theorem is one of the central results of calculus. It was called “the fundamental theorem of the differential calculus” because of its power to provide simple and rigorous proofs of basic results encountered in a first-year course in calculus. In mathematical terms, the book is a thorough treatment of this theorem and some related results in the field; in historical terms, it is not a history of calculus or mathematics, but a case study in both. MVT: A Most Valuable Theorem is aimed at those who teach calculus, especially those setting out to do so for the first time. It is also accessible to anyone who has finished the first semester of the standard course in the subject and will be of interest to undergraduate mat...
Equitable Financial Evaluation Method for Public-Private Partnership Projects
KE Yongjian; LIU Xinping; WANG Shouqing
2008-01-01
The feasibility study of a public-private partnership (PPP) project is regarded as one of the critical factors for successful implementation,but unfortunately the common financial evaluation methods currently used only represent the benefits of the private sector.There is,therefore,an urgent need to develop an equitable financial evaluation method for PPP projects.This paper presents a comprehensive literature review that examines international practices.An equitable financial evaluation method was then developed taking into account the inherent characteristics of PPP projects using six separate indicators and Monte Carlo simulations.The result for a bridge project in Romania shows that the method combines the viewpoints of all the relevant stakeholders to achieve an equitable financial evaluation of PPP projects.
Noncommutative topology and the world's simplest index theorem.
van Erp, Erik
2010-05-11
In this article we outline an approach to index theory on the basis of methods of noncommutative topology. We start with an explicit index theorem for second-order differential operators on 3-manifolds that are Fredholm but not elliptic. This low-brow index formula is expressed in terms of winding numbers. We then proceed to show how it is derived as a special case of an index theorem for hypoelliptic operators on contact manifolds. Finally, we discuss the noncommutative topology that is employed in the proof of this theorem. The article is intended to illustrate that noncommutative topology can be a powerful tool for proving results in classical analysis and geometry.
Restriction Theorem for Principal bundles in Arbitrary Characteristic
Gurjar, Sudarshan
2015-01-01
The aim of this paper is to prove two basic restriction theorem for principal bundles on smooth projective varieties in arbitrary characteristic generalizing the analogues theorems of Mehta-Ramanathan for vector bundles. More precisely, let G be a reductive algebraic group over an algebraically...... closed field k and let X be a smooth, projective variety over k together with a very ample line bundle O(1). The main result of the paper is that if E is a semistable (resp. stable) principal G-bundle on X w.r.t O(1), then the restriction of E to a general, high multi-degree, complete-intersection curve...
-Dimensional Fractional Lagrange's Inversion Theorem
F. A. Abd El-Salam
2013-01-01
Full Text Available Using Riemann-Liouville fractional differential operator, a fractional extension of the Lagrange inversion theorem and related formulas are developed. The required basic definitions, lemmas, and theorems in the fractional calculus are presented. A fractional form of Lagrange's expansion for one implicitly defined independent variable is obtained. Then, a fractional version of Lagrange's expansion in more than one unknown function is generalized. For extending the treatment in higher dimensions, some relevant vectors and tensors definitions and notations are presented. A fractional Taylor expansion of a function of -dimensional polyadics is derived. A fractional -dimensional Lagrange inversion theorem is proved.
Complex integration and Cauchy's theorem
Watson, GN
2012-01-01
This brief monograph by one of the great mathematicians of the early twentieth century offers a single-volume compilation of propositions employed in proofs of Cauchy's theorem. Developing an arithmetical basis that avoids geometrical intuitions, Watson also provides a brief account of the various applications of the theorem to the evaluation of definite integrals.Author G. N. Watson begins by reviewing various propositions of Poincaré's Analysis Situs, upon which proof of the theorem's most general form depends. Subsequent chapters examine the calculus of residues, calculus optimization, the
Fluctuation theorem: A critical review
Malek Mansour, M.; Baras, F.
2017-10-01
Fluctuation theorem for entropy production is revisited in the framework of stochastic processes. The applicability of the fluctuation theorem to physico-chemical systems and the resulting stochastic thermodynamics were analyzed. Some unexpected limitations are highlighted in the context of jump Markov processes. We have shown that these limitations handicap the ability of the resulting stochastic thermodynamics to correctly describe the state of non-equilibrium systems in terms of the thermodynamic properties of individual processes therein. Finally, we considered the case of diffusion processes and proved that the fluctuation theorem for entropy production becomes irrelevant at the stationary state in the case of one variable systems.
Limit theorem and uniqueness theorem of backward stochastic differential equations
JIANG; Long
2006-01-01
This paper establishes a limit theorem for solutions of backward stochastic differential equations (BSDEs). By this limit theorem, this paper proves that, under the standard assumption g(t,y,0)≡0, the generator g of a BSDE can be uniquely determined by the corresponding g-expectation εg; this paper also proves that if a filtration consistent expectation ε can be represented as a g-expectation εg, then the corresponding generator g must be unique.
Higher-Order Semi-Implicit Projection Methods
Minion, M L
2001-09-06
A semi-implicit form of the method of spectral deferred corrections is applied to the solution of the incompressible Navier-Stokes equations. A methodology for constructing semi-implicit projection methods with arbitrarily high order of temporal accuracy in both the velocity and pressure is presented. Three variations of projection methods are discussed which differ in the manner in which the auxiliary velocity and the pressure are calculated. The presentation will make clear that project methods in general need not be viewed as fractional step methods as is often the practice. Two simple numerical examples re used to demonstrate fourth-order accuracy in time for an implementation of each variation of projection method.
Lattice Regenerative Cooling Methods (LRCM) Project
National Aeronautics and Space Administration — ORBITEC proposes to develop and demonstrate a novel cooling concept called Lattice Regenerative Cooling Methods (LRCM) for future high thrust in-space propulsion...
Mechanical theorem proving in differential geometry——Local theory of surfaces
李洪波
1997-01-01
An automated reasoning method, based on Wu’s method and calculus of differential forms, is proposed for mechanical theorem proving in local theory of space surfaces in differential geometry. The method has been used to simplify one of Chern’s theorems: "The non-trivial families of isometric surfaces having the same principal curvatures are W-surfaces." Some other theorems are also tested by this method. The proofs are generally simpler than those in differential geometry textbooks.
Projected oriented organizations as development of enterprise management methods
S.I. Pavlova
2016-12-01
Full Text Available Dynamic external environment, significant shortage of product life cycle, increase of product technological difficulty, extension of innovative knowledge motivates managers to look for and use in their activities keys that will provide constant, stable development of organizational structures. The methodology of project enterprise management meets the requirements of «preservation through development». The articles researches the integration of methods and procedures of project management into the enterprise management system. Project management philosophy is the efficient way of existence in the competitive environment and the means for internal development of a company. The author conducts an analysis, determines the essence and peculiarities of a project-oriented enterprise, performs comparing characteristics of functional and project management, describes the stages of gradual transformation of an enterprise organizational structure into a project-oriented one. It is defined that a project-oriented enterprise is that one which functions on the base of innovative development and are scientific, creative and widely use the project activity as the means of a steady development. The article describes internal and external instruments of project management, base knowledge systems on project management and possibilities of enterprises on audit of state of system project management in an enterprise according to the IPMA certification program on the territory of Ukraine.
An adaptive projection method for the incompressible Euler equations
Almgren, Ann S.; Bell, John B.; Colella, Phillip; Howell, Louis H.
A new adaptive projection method has been developed for time-dependent incompressible variable density flow. The levels in the adaptive mesh hierarchy are refined in both space and time. The advection step takes place on individual grids in an approach similar to that of the single grid method. The projection at each level is similar to the uniform grid projection but must now incorporate multiple grids per level. A sync projection is introduced which is needed to synchronize the solution at each level l with the data at the levels above it at the end of each level l time step. This adaptive projection method is second-order accurate and provides an accurate and efficient tool for modeling variable density flows.
Cardioids and Morley's Trisector Theorem
J. Brinkhuis (Jan); van de Craats, J.
2017-01-01
textabstractA self-contained account of Morley's own proof of his celebrated trisector theorem is given. This makes this elegant and almost forgotten fragment of analytic Euclidean geometry more accessible to modern readers
Statistics, Causality and Bell's theorem
Gill, Richard D
2012-01-01
Bell's (1964) theorem is popularly supposed to establish the non-locality of quantum physics as a mathematical-physical theory. Building from this, observed violation of Bell's inequality in experiments such as that of Aspect and coworkers (1982) is popularly supposed to provide empirical proof of non-locality in the real world. This paper reviews recent work on Bell's theorem, linking it to issues in causality as understood by statisticians. The paper starts with a new proof of a strong (finite sample) version of Bell's theorem which relies only on elementary arithmetic and (counting) probability. This proof underscores the fact that Bell's theorem tells us that quantum theory is incompatible with the conjunction of three cherished and formerly uncontroversial physical principles, nicknamed here locality, realism, and freedom. The first, locality, is obviously connected to causality: causal influences need time to propagate spatially. Less obviously, the other two principles, realism and freedom, are also fo...
Effective Teaching Methods--Project-based Learning in Physics
Holubova, Renata
2008-01-01
The paper presents results of the research of new effective teaching methods in physics and science. It is found out that it is necessary to educate pre-service teachers in approaches stressing the importance of the own activity of students, in competences how to create an interdisciplinary project. Project-based physics teaching and learning…
The Kolmogorov-Riesz compactness theorem
Hanche-Olsen, Harald
2009-01-01
We show that the Arzela-Ascoli theorem and Kolmogorov compactness theorem both are consequences of a simple lemma on compactness in metric spaces. Their relation to Helly's theorem is discussed. The paper contains a detailed discussion on the historical background of the Kolmogorov compactness theorem.
The Second Noether Theorem on Time Scales
Agnieszka B. Malinowska
2013-01-01
Full Text Available We extend the second Noether theorem to variational problems on time scales. As corollaries we obtain the classical second Noether theorem, the second Noether theorem for the h-calculus and the second Noether theorem for the q-calculus.
The second Noether theorem on time scale
Malinowska, Agnieszka B.; Martins, Natália
2014-01-01
We extend the second Noether theorem to variational problems on time scales. Our result provides as corollaries the classical second Noether theorem, the second Noether theorem for the $h$-calculus and the second Noether theorem for the $q$-calculus.
Local virial and tensor theorems.
Cohen, Leon
2011-11-17
We show that for any wave function and potential the local virial theorem can always be satisfied 2K(r) = r·ΔV by choosing a particular expression for the local kinetic energy. In addition, we show that for each choice of local kinetic energy there are an infinite number of quasi-probability distributions which will generate the same expression. We also consider the local tensor virial theorem.
Integrating factors and conservation theorems of constrained Birkhoffian systems
Qiao Yong-Fen; Zhao Shu-Hong; Li Ren-Jie
2006-01-01
In this paper the conservation theorems of the constrained Birkhoffian systems are studied by using the method of integrating factors. The differential equations of motion of the system are written. The definition of integrating factors is given for the system. The necessary conditions for the existence of the conserved quantity for the system are studied.The conservation theorem and its inverse for the system are established. Finally, an example is given to illustrate the application of the results.
Generalization of the hypervirial and Feynman-Hellman theorems
Nadareishvili, Teimuraz
2013-01-01
Using well-known methods we generalize (hyper)virial theorems to case of singular potential. Discussion is carried on for most general second order differential equation, which involves all physically interesting cases, such as Schr\\"odinger and two-body Klein-Gordon equations with singular potentials. Some physical consequences are discussed. The connection with Feynman-Hellmann like theorems are also considered and some relevant differences are underlined.
Advanced Bayesian Methods for Lunar Surface Navigation Project
National Aeronautics and Space Administration — The key innovation of this project is the application of advanced Bayesian methods to integrate real-time dense stereo vision and high-speed optical flow with an...
Advanced Bayesian Methods for Lunar Surface Navigation Project
National Aeronautics and Space Administration — The key innovation of this project will be the application of advanced Bayesian methods to integrate real-time dense stereo vision and high-speed optical flow with...
Fixed-point-like theorems on subspaces
Bernard Cornet
2004-08-01
Full Text Available We prove a fixed-point-like theorem for multivalued mappings defined on the finite Cartesian product of Grassmannian manifolds and convex sets. Our result generalizes two different kinds of theorems: the fixed-point-like theorem by Hirsch et al. (1990 or Husseini et al. (1990 and the fixed-point theorem by Gale and Mas-Colell (1975 (which generalizes Kakutani's theorem (1941.
On the accuracy of low-order projection methods
Paul Pichler
2007-01-01
We use low-order projection methods to compute numerical solutions of the basic neoclassical stochastic growth model. We assess the quality of the obtained solutions, and compare them to numerical approximations derived with first and second-order perturbation techniques. We show that projection methods perform surprisingly poor when the degree of approximation is very low, and we provide some intuition behind this finding.
Multideviations: The hidden structure of Bell's theorems
Fogel, Brandon
2015-01-01
Specification of the strongest possible Bell inequalities for arbitrarily complicated physical scenarios -- any number of observers choosing between any number of observables with any number of possible outcomes -- is currently an open problem. Here I provide a new set of tools, which I refer to as "multideviations", for finding and analyzing these inequalities for the fully general case. In Part I, I introduce the multideviation framework and then use it to prove an important theorem: the Bell distributions can be generated from the set of joint distributions over all observables by deeming specific degrees of freedom unobservable. In Part II, I show how the theorem provides a new method for finding tight Bell inequalities. I then specify a set of new tight Bell inequalities for arbitrary event spaces -- the "even/odd" inequalities -- which have a straightforward interpretation when expressed in terms of multideviations. The even/odd inequalities concern degrees of freedom that are independent of those invol...
Thermodynamics of biochemical networks and duality theorems.
De Martino, Daniele
2013-05-01
One interesting yet difficult computational issue has recently been posed in biophysics in regard to the implementation of thermodynamic constraints to complex networks. Biochemical networks of enzymes inside cells are among the most efficient, robust, differentiated, and flexible free-energy transducers in nature. How is the second law of thermodynamics encoded for these complex networks? In this article it is demonstrated that for chemical reaction networks in the steady state the exclusion (presence) of closed reaction cycles makes possible (impossible) the definition of a chemical potential vector. Interestingly, this statement is encoded in one of the key results in combinatorial optimization, i.e., the Gordan theorem of the alternatives. From a computational viewpoint, the theorem reveals that calculating a reaction's free energy and identifying infeasible loops in flux states are dual problems whose solutions are mutually exclusive, and this opens the way for efficient and scalable methods to perform the energy balance analysis of large-scale biochemical networks.
宋岱才; 敬长红; 陈德艳
2011-01-01
针对线性方程组的系数矩阵为α-链严格对角占优矩阵和双严格对角占优矩阵的情况,讨论了线性方程组求解时常用的SOR迭代方法的收敛性,给出了迭代法收敛性定理,解决了以往估计迭代矩阵谱半径的问题.结果不仅适用于这两类矩阵,还适用于广义严格对角占优矩阵类,最后举例说明了所给结果的优越性.%In this paper Convergence theorem of SOR iteration method for solving linear system is studied, when coefficient matrix is a-chain diagonal strictly dominance or doubly diagonal strictly dominance, and some convergence theorems are given,which solves the problem of spectral radius of iterative matrices. Results obtained are applicable for a- chain diagonal strictly dominance matrix or doubly diagonal strictly dominance matrix, and improve the known results and are applicable for generalized diagonal strictly dominance matrices.Finally, a numerical example is given for illustrating advantage of the results in this paper.
Insurance ratemaking method for risk of construction diversion project
Chen Zhiding; Hu Zhigen
2012-01-01
Based on analyzing risk factors of diversion project, synthetic risk rate and engineering insurance period, the frequency and distribution law of loss are researched on the grounds that foundation pit is submerged after diversion project ceases to be effective. And then, the standpoint that these total loss is subject to non-homogeneous compound Poisson processes is put forward. Furthermore, the collective risk model of the total loss about engineering insurance is established on the basis of construction diversion project risk. Ultimately, insurance ratemaking method for construction engineering risk and its mathematical expression are presented, which provides theoretical method for the insurance ratemaking of hydropower engineering to some extent.
A PROJECTION-TYPE METHOD FOR SOLVING VARIOUS WEBER PROBLEMS
Jian-lin Jiang; Bo Chen
2006-01-01
This paper investigates various Weber problems including unconstrained Weber problems and constrained Weber problems under l1,l2 and l∞-norms. First with a transformation technique various Weber problems are turned into a class of monotone linear variational inequalities. By exploiting the favorable structure of these variational inequalities, we present a new projection-type method for them. Compared with some other projection-type methods which can solve monotone linear variational inequality, this new projection-type method is simple in numerical implementations and more efficient for solving this class of problems; Compared with some popular methods for solving unconstrained Weber problem and constrained Weber problem, a singularity would not happen in this new method and it is more reliable by using this new method to solve various Weber problems.
A Modified Projection Method for Linear Feasibility Problems
Yi-Ju Wang; Hong-Yu Zhang
2009-01-01
In this paper, we present a modified projection method for the linear feasibility problems (LFP). Compared with the existing methods, the new method adopts a surrogate technique to obtain new iteration instead of the line search procedure with fixed stepsize. For the new method, we first show its global convergence under the condition that the solution set is nonempty, and then establish its linear convergence rate. Preliminary numerical experiments show that this method has good performance.
Generalized Chung-Feller Theorems for Lattice Paths (Thesis)
Huq, Aminul
2009-01-01
In this thesis we develop generalized versions of the Chung-Feller theorem for lattice paths constrained in the half plane. The beautiful cycle method which was developed by Devoretzky and Motzkin as a means to prove the ballot problem is modified and applied to generalize the classical Chung-Feller theorem. We use Lagrange inversion to derive the generalized formulas. For the generating function proof we study various ways of decomposing lattice paths. We also show some results related to equidistribution properties in terms of Narayana and Catalan generating functions. We then develop generalized Chung-Feller theorems for Motzkin and Schroeder paths. Finally we study generalized paths and the analogue of the Chung-Feller theorem for them.
Noncommutative topology and the world's simplest index theorem
van Erp, Erik
2010-01-01
This is an expository article. It discusses an approach to hypoelliptic Fredholm index theory based on noncommutative methods (groupoids, C*-algebras, K-theory). The paper starts with an explicit index theorem for scalar second order differential operators on 3-manifolds that are Fredholm but not elliptic. This low-brow index formula is expressed in terms of winding numbers. We then proceed to show how this theorem is a special case of a much more general index theorem for subelliptic operators on contact manifolds. Finally we discuss the noncommutative topology that is employed in the proof of this theorem. We present these results as an instance in which noncommutative topology is fruitful in proving a very explicit (analytic/geometric) classical result.
Formalization and Implementation of Algebraic Methods in Geometry
Marić, Filip; Petrović, Danijela; Janičić, Predrag; 10.4204/EPTCS.79.4
2012-01-01
We describe our ongoing project of formalization of algebraic methods for geometry theorem proving (Wu's method and the Groebner bases method), their implementation and integration in educational tools. The project includes formal verification of the algebraic methods within Isabelle/HOL proof assistant and development of a new, open-source Java implementation of the algebraic methods. The project should fill-in some gaps still existing in this area (e.g., the lack of formal links between algebraic methods and synthetic geometry and the lack of self-contained implementations of algebraic methods suitable for integration with dynamic geometry tools) and should enable new applications of theorem proving in education.
Expanding the Action Project Method to Encompass Comparative Analyses
José F. Domene PhD
2008-03-01
Full Text Available This article is an exploration of the possibility and pragmatics of conducting between-groups comparative analysis in action theory and the action project method of qualitative research. After establishing the need for such a procedure and describing the compatibility of these analyses with the paradigm assumptions of action theory, the authors describe a specific set of procedures for conducting qualitative comparisons within the action project method. They also discuss limitations of the procedure and future directions for continuing the expansion of methods of comparison in qualitative research. Finally, they present a case illustration of the use of this comparative analysis method.
Project-Method Fit: Exploring Factors That Influence Agile Method Use
Young, Diana K.
2013-01-01
While the productivity and quality implications of agile software development methods (SDMs) have been demonstrated, research concerning the project contexts where their use is most appropriate has yielded less definitive results. Most experts agree that agile SDMs are not suited for all project contexts. Several project and team factors have been…
On some Frobenius Restriction Theorems for Semistable Sheaves
V B Mehta; V Trivedi
2009-02-01
We prove a version of an effective Frobenius restriction theorem for semistable bundles in characteristic . The main novelty is in restricting the bundle to the -fold thickening of a hypersurface section. The base variety is /, an abelian variety or a smooth projective toric variety.
Altürk, Ahmet
2016-01-01
Mean value theorems for both derivatives and integrals are very useful tools in mathematics. They can be used to obtain very important inequalities and to prove basic theorems of mathematical analysis. In this article, a semi-analytical method that is based on weighted mean-value theorem for obtaining solutions for a wide class of Fredholm integral equations of the second kind is introduced. Illustrative examples are provided to show the significant advantage of the proposed method over some ...
Projection methods for the numerical solution of Markov chain models
Saad, Youcef
1989-01-01
Projection methods for computing stationary probability distributions for Markov chain models are presented. A general projection method is a method which seeks an approximation from a subspace of small dimension to the original problem. Thus, the original matrix problem of size N is approximated by one of dimension m, typically much smaller than N. A particularly successful class of methods based on this principle is that of Krylov subspace methods which utilize subspaces of the form span(v,av,...,A(exp m-1)v). These methods are effective in solving linear systems and eigenvalue problems (Lanczos, Arnoldi,...) as well as nonlinear equations. They can be combined with more traditional iterative methods such as successive overrelaxation, symmetric successive overrelaxation, or with incomplete factorization methods to enhance convergence.
Nambu-Goldstone theorem and spin-statistics theorem
Fujikawa, Kazuo
2016-05-01
On December 19-21 in 2001, we organized a yearly workshop at Yukawa Institute for Theoretical Physics in Kyoto on the subject of “Fundamental Problems in Field Theory and their Implications”. Prof. Yoichiro Nambu attended this workshop and explained a necessary modification of the Nambu-Goldstone theorem when applied to non-relativistic systems. At the same workshop, I talked on a path integral formulation of the spin-statistics theorem. The present essay is on this memorable workshop, where I really enjoyed the discussions with Nambu, together with a short comment on the color freedom of quarks.
Composite orthogonal projection methods for large matrix eigenproblems
贾仲孝
1999-01-01
For classical orthogonal projection methods for large matrix eigenproblems, it may be much more difficult for a Ritz vector to converge than for its corresponding Ritz value when the matrix in question is non-Hermitian. To this end, a class of new refined orthogonal projection methods has been proposed. It is proved that in some sense each refined method is a composite of two classical orthogonal projections, in which each refined approximate eigenvector is obtained by realizing a new one of some Hermitian semipositive definite matrix onto the same subspace. A priori error bounds on the refined approximate eigenvector are established in terms of the sine of acute angle of the normalized eigenvector and the subspace involved. It is shown that the sufficient conditions for convergence of the refined vector and that of the Ritz value are the same, so that the refined methods may be much more efficient than the classical ones.
PRECONDITIONED SPECTRAL PROJECTED GRADIENT METHOD ON CONVEX SETS
Lenys Bello; Marcos Raydan
2005-01-01
The spectral gradient method has proved to be effective for solving large-scale unconstrained optimization problems. It has been recently extended and combined with the projected gradient method for solving optimization problems on convex sets. This combination includes the use of nonmonotone line search techniques to preserve the fast local convergence. In this work we further extend the spectral choice of steplength to accept preconditioned directions when a good preconditioner is available. We present an algorithm that combines the spectral projected gradient method with preconditioning strategies to increase the local speed of convergence while keeping the global properties. We discuss implementation details for solving large-scale problems.
Selection of renewable energy project using Multicriteria Method
DADDA Afaf1 , OUHBI Brahim1
2015-10-01
Full Text Available Nowadays, many investors are interesting on implementing new renewable energy project around the world. The success of the decision making process regarding the selection of this projects, depends a lot on the effectiveness of the feasibility stage. During last decades, it is observed that many researches had used the Multicriteria Decision Making Methods to assist decision makers. Therefore, this paper proposes a comparative study of a three decision making process, applied in different countries. This study compares the related process in different levels. A new process is also proposed to validate a local renewable energy project
Training two-layered feedforward networks with variable projection method.
Kim, C T; Lee, J J
2008-02-01
The variable projection (VP) method for separable nonlinear least squares (SNLLS) is presented and incorporated into the Levenberg-Marquardt optimization algorithm for training two-layered feedforward neural networks. It is shown that the Jacobian of variable projected networks can be computed by simple modification of the backpropagation algorithm. The suggested algorithm is efficient compared to conventional techniques such as conventional Levenberg-Marquardt algorithm (LMA), hybrid gradient algorithm (HGA), and extreme learning machine (ELM).
Application of Participatory Method to Selection of Project Demonstration Area
无
2011-01-01
The Sino-Japan cooperation project of "Vegetation Rehabilitation Demonstration and Planning in Sandstorm Jeopardized Area around Beijing" introduced participatory method to select the project area. Through investigating the socioeconomic indicators of 9 villages in Beijing and Hebei Province as well as the farmers’ willingness to participate in forestry operation activities, the vegetation restoration demonstration areas were selected, including Hantai Village, Baicaowa Village and Xiabachi Village, respect...
Fluctuation theorems for quantum processes
Albash, Tameem; Marvian, Milad; Zanardi, Paolo
2013-01-01
We present fluctuation theorems and moment generating function equalities for generalized thermodynamic observables and quantum dynamics described by completely positive trace preserving (CPTP) maps, with and without feedback control. Our results include the quantum Jarzynski equality and Crooks fluctuation theorem, and clarify the special role played by the thermodynamic work and thermal equilibrium states in previous studies. We show that unitality replaces micro-reversibility as the condition for the physicality of the reverse process in our fluctuation theorems. We present an experimental application of our theory to the problem of extracting the system-bath coupling magnitude, which we do for a system of pairs of coupled superconducting flux qubits undergoing quantum annealing.
Lesion insertion in the projection domain: Methods and initial results
Chen, Baiyu; Leng, Shuai; Yu, Lifeng; Yu, Zhicong; Ma, Chi; McCollough, Cynthia, E-mail: mccollough.cynthia@mayo.edu [Department of Radiology, Mayo Clinic, Rochester, Minnesota 55905 (United States)
2015-12-15
Purpose: To perform task-based image quality assessment in CT, it is desirable to have a large number of realistic patient images with known diagnostic truth. One effective way of achieving this objective is to create hybrid images that combine patient images with inserted lesions. Because conventional hybrid images generated in the image domain fails to reflect the impact of scan and reconstruction parameters on lesion appearance, this study explored a projection-domain approach. Methods: Lesions were segmented from patient images and forward projected to acquire lesion projections. The forward-projection geometry was designed according to a commercial CT scanner and accommodated both axial and helical modes with various focal spot movement patterns. The energy employed by the commercial CT scanner for beam hardening correction was measured and used for the forward projection. The lesion projections were inserted into patient projections decoded from commercial CT projection data. The combined projections were formatted to match those of commercial CT raw data, loaded onto a commercial CT scanner, and reconstructed to create the hybrid images. Two validations were performed. First, to validate the accuracy of the forward-projection geometry, images were reconstructed from the forward projections of a virtual ACR phantom and compared to physically acquired ACR phantom images in terms of CT number accuracy and high-contrast resolution. Second, to validate the realism of the lesion in hybrid images, liver lesions were segmented from patient images and inserted back into the same patients, each at a new location specified by a radiologist. The inserted lesions were compared to the original lesions and visually assessed for realism by two experienced radiologists in a blinded fashion. Results: For the validation of the forward-projection geometry, the images reconstructed from the forward projections of the virtual ACR phantom were consistent with the images physically
Improvement of Hartman's linearization theorem
SHI; Jinlin(史金麟)
2003-01-01
Hartman's linearization theorem tells us that if matrix A has no zero real part and f(x) isbounded and satisfies Lipchitz condition with small Lipchitzian constant, then there exists a homeomorphismof Rn sending the solutions of nonlinear system x' = Ax + f(x) onto the solutions of linear system x' = Ax.In this paper, some components of the nonlinear item f(x) are permitted to be unbounded and we provethe result of global topological linearization without any special limitation and adding any condition. Thus,Hartman's linearization theorem is improved essentially.
Poutiainen, H. (Hayley)
2015-01-01
Group theory is a mathematical domain where groups and their properties are studied. The evolution of group theory as an area of study is said to be the result of the parallel development of a variety of different studies in mathematics. Sylow’s Theorems were a set of theorems proved around the same time the concept of group theory was being established, in the 1870s. Sylow used permutation groups in his proofs which were then later generalized and shown to hold true for all finite groups. Th...
Noether theorems and higher derivatives
Townsend, Paul K
2016-01-01
A simple proof of Noether's first theorem involves the promotion of a constant symmetry parameter $\\epsilon$ to an arbitrary function of time; the Noether charge $Q$ is then the coefficient of $\\dot\\epsilon$ in the variation of the action. Here we examine the validity of this proof for Lagrangian mechanics with arbitrarily-high time derivatives, in which context "higher-level" analogs of Noether's theorem can be similarly proved, and "Noetherian charges" read off from, e.g. the coefficient of $\\ddot \\epsilon$ in the variation of the action. While $Q=0$ implies a restricted gauge invariance, an unrestricted gauge invariance requires zero Noetherian charges too. Some illustrative examples are considered.
Pasicki, Lech
2011-01-01
Many versions of the Stokes theorem are known. More advanced of them require complicated mathematical machinery to be formulated which discourages the users. Our theorem is sufficiently simple to suit the handbooks and yet it is pretty general, as we assume the differential form to be continuous on a compact set F(A) and C1 "inside" while F(A) is built of "bricks" and its inner part is a C1 manifold. There is no problem of orientability and the integrals under consideration are convergent. The proof is based on integration by parts and inner approximation.
Extension of moment projection method to the fragmentation process
Wu, Shaohua; Yapp, Edward K. Y.; Akroyd, Jethro; Mosbach, Sebastian; Xu, Rong; Yang, Wenming; Kraft, Markus
2017-04-01
The method of moments is a simple but efficient method of solving the population balance equation which describes particle dynamics. Recently, the moment projection method (MPM) was proposed and validated for particle inception, coagulation, growth and, more importantly, shrinkage; here the method is extended to include the fragmentation process. The performance of MPM is tested for 13 different test cases for different fragmentation kernels, fragment distribution functions and initial conditions. Comparisons are made with the quadrature method of moments (QMOM), hybrid method of moments (HMOM) and a high-precision stochastic solution calculated using the established direct simulation algorithm (DSA) and advantages of MPM are drawn.
Extension of moment projection method to the fragmentation process
Wu, Shaohua [Department of Mechanical Engineering, National University of Singapore, Engineering Block EA, Engineering Drive 1, 117576 (Singapore); Yapp, Edward K.Y.; Akroyd, Jethro; Mosbach, Sebastian [Department of Chemical Engineering and Biotechnology, University of Cambridge, New Museums Site, Pembroke Street, Cambridge, CB2 3RA (United Kingdom); Xu, Rong [School of Chemical and Biomedical Engineering, Nanyang Technological University, 62 Nanyang Drive, 637459 (Singapore); Yang, Wenming [Department of Mechanical Engineering, National University of Singapore, Engineering Block EA, Engineering Drive 1, 117576 (Singapore); Kraft, Markus, E-mail: mk306@cam.ac.uk [Department of Chemical Engineering and Biotechnology, University of Cambridge, New Museums Site, Pembroke Street, Cambridge, CB2 3RA (United Kingdom); School of Chemical and Biomedical Engineering, Nanyang Technological University, 62 Nanyang Drive, 637459 (Singapore)
2017-04-15
The method of moments is a simple but efficient method of solving the population balance equation which describes particle dynamics. Recently, the moment projection method (MPM) was proposed and validated for particle inception, coagulation, growth and, more importantly, shrinkage; here the method is extended to include the fragmentation process. The performance of MPM is tested for 13 different test cases for different fragmentation kernels, fragment distribution functions and initial conditions. Comparisons are made with the quadrature method of moments (QMOM), hybrid method of moments (HMOM) and a high-precision stochastic solution calculated using the established direct simulation algorithm (DSA) and advantages of MPM are drawn.
Reconstruction of CT images by the Bayes- back projection method
Haruyama, M; Takase, M; Tobita, H
2002-01-01
In the course of research on quantitative assay of non-destructive measurement of radioactive waste, the have developed a unique program based on the Bayesian theory for reconstruction of transmission computed tomography (TCT) image. The reconstruction of cross-section images in the CT technology usually employs the Filtered Back Projection method. The new imaging reconstruction program reported here is based on the Bayesian Back Projection method, and it has a function of iterative improvement images by every step of measurement. Namely, this method has the capability of prompt display of a cross-section image corresponding to each angled projection data from every measurement. Hence, it is possible to observe an improved cross-section view by reflecting each projection data in almost real time. From the basic theory of Baysian Back Projection method, it can be not only applied to CT types of 1st, 2nd, and 3rd generation. This reported deals with a reconstruction program of cross-section images in the CT of ...
On local-hidden-variable no-go theorems
Methot, A. A.
2006-06-01
The strongest attack against quantum mechanics came in 1935 in the form of a paper by Einstein, Podolsky, and Rosen. It was argued that the theory of quantum mechanics could not be called a complete theory of Nature, for every element of reality is not represented in the formalism as such. The authors then put forth a proposition: we must search for a theory where, upon knowing everything about the system, including possible hidden variables, one could make precise predictions concerning elements of reality. This project was ultimately doomed in 1964 with the work of Bell, who showed that the most general local hidden variable theory could not reproduce correlations that arise in quantum mechanics. There exist mainly three forms of no-go theorems for local hidden variable theories. Although almost every physicist knows the consequences of these no-go theorems, not every physicist is aware of the distinctions between the three or even their exact definitions. Thus, we will discuss here the three principal forms of no-go theorems for local hidden variable theories of Nature. We will define Bell theorems, Bell theorems without inequalities, and pseudo-telepathy. A discussion of the similarities and differences will follow.
Robustness Proof on A United Watermarking Based on CRT Theorem
LIU Li-gang; CHEN Xiao-su; XIAO Dao-ju; HU Lei
2005-01-01
A new method of embedding and detecting a joint watermarking is proposed. It applies the asmuth-bloom secret sharing scheme, which is based on CRT (Chinese remainder theorem) theorem, to the digital watermarking technology. On the base of describing the watermarking embedding proceeding and analyzing the watermarking detection proceeding, a series of experiments is done. The experiments emphasize on the method's robust proving and security analysis. And the experiments show that the method can resist the attacks of JPEG compress, geometry, noise and gray adjusting. The results of the experiments show that the method has a nice recognition of copyright for joint ownership.
Stochastic number projection method in the pairing-force problem
Capote, R; Capote, Roberto; Gonzalez, Augusto
1999-01-01
A new stochastic number projection method is proposed. The component of the BCS wave function corresponding to the right number of particles is obtained by means of a Metropolis algorithm in which the weight functions are constructed from the single-particle occupation probability. Either standard BCS or Lipkin-Nogami probability distributions can be used, thus the method is applicable for any pairing strength. The accuracy of the method is tested in the computation of pairing energies of model and real systems.
F Laytimi; W Nahm
2013-11-01
Let be a vector bundle and be a line bundle over a smooth projective variety . In this article, we give a condition for the vanishing of Dolbeault cohomology groups of the form $H^{p,q}(X, S^ E \\otimes {\\wedge}^ E \\otimes L)$ when $S^{+} E \\otimes L$ is ample. This condition is shown to be invariant under the interchange of and . The optimality of this condition is discussed for some parameter values.
Hu Jian-Bing; Zhao Ling-Dong; Xie Zheng-Guang
2013-01-01
In this paper,an intermittent synchronizing delayed fractional nonlinear system is studied.We propose a novel intermittent stable theorem for the delayed fractional system and derive a new synchronization criterion for delayed fractional systems by means of fractional stable theorem and the differential inequality method.Intermittent synchronizing fractional delayed Newton-Leipnik system is taken as an illustrative example and numerical simulation of this example is presented to show the feasibility and effectiveness of the proposed theorem.
Integrated project delivery methods for energy renovation of social housing
Tadeo Baldiri Salcedo Rahola
2015-11-01
Full Text Available Optimised project delivery methods forsocial housing energy renovationsEuropean Social Housing Organisations (SHOs are currently facing challenging times. The ageing of their housing stock and the economic crisis, which has affected both their finances and the finances of their tenants, are testing their capacity to stick to their aim of providing decent and affordable housing. Housing renovation projects offer the possibility of upgrading the health and comfort levels of their old housing stock to current standards and improve energy efficiency, and this solution also addresses the fuel poverty problems suffered by some tenants. Unfortunately, the limited financial capacity of SHOs is hampering the scale of housing renovation projects and the energy savings achieved. At the same time, the renovation of the existing housing stock is seen as one of the most promising alternative routes to achieving the ambitious CO2 emissions reduction targets set by European authorities – namely, to reduce EU CO2 emissions to 20% below their 1990 levels by 2020. The synergy between European targets and the aims of SHOs has been addressed by the energy policies of the member states, which focus on the potential energy savings achievable by renovating social housing. In fact, the European initiatives have prioritised energy savings in social housing renovations to such an extent that these are referred to as ‘energy renovations’. Energy renovation is therefore a renovation project with higher energy savings target than a regular renovation project.In total, European SHOs own 21.5 million dwellings representing around 9.4% of the total housing stock. Each SHO owns a large number of dwellings, which means there are fewer people to convince of the need to make energy savings through building renovations, maximising the potentially high impact of decisions. Moreover, SHOs are responsible for maintaining and upgrading their properties in order to continue
A normal form theorem around symplectic leaves
Crainic, M.N.; Marcut, I.T.
2012-01-01
We prove the Poisson geometric version of the Local Reeb Stability (from foliation theory) and of the Slice Theorem (from equivariant geometry), which is also a generalization of Conn’s linearization theorem.
Von Laue's theorem and its applications
Wang, Changbiao
2012-01-01
Von Laue's theorem is strictly proved in detail to clarify confusions in textbook and literature. This theorem is used to analyze the classical electron and the static electric field confined in a finite region of space.
The Classical Version of Stokes' Theorem Revisited
Markvorsen, Steen
2005-01-01
Using only fairly simple and elementary considerations - essentially from first year undergraduate mathematics - we prove that the classical Stokes' theorem for any given surface and vector field in $\\mathbb{R}^{3}$ follows from an application of Gauss' divergence theorem to a suitable modification...... of the vector field in a tubular shell around the given surface. The intuitive appeal of the divergence theorem is thus applied to bootstrap a corresponding intuition for Stokes' theorem. The two stated classical theorems are (like the fundamental theorem of calculus) nothing but shadows of the general version...... to above. Our proof that Stokes' theorem follows from Gauss' divergence theorem goes via a well known and often used exercise, which simply relates the concepts of divergence and curl on the local differential level. The rest of the paper uses only integration in $1$, $2$, and $3$ variables together...
THEORETICAL AND NUMERICAL COMPARISON ON DOUBLE-PROJECTION METHODS FOR VARIATIONAL INEQUALITIES
WANG Yiju; SUN Wenyu
2003-01-01
Recently, double projection methods for solving variational inequalities have received much attention due to their fewer projection times at each iteration. In this paper, we unify these double projection methods within two unified frameworks, which contain the existing double projection methods as special cases. On the basis of this unification, theoretical and numerical comparison between these double projection methods is presented.
Shell theorem for spontaneous emission
Kristensen, Philip Trøst; Mortensen, Jakob Egeberg; Lodahl, Peter;
2013-01-01
and therefore is given exactly by the dipole approximation theory. This surprising result is a spontaneous emission counterpart to the shell theorems of classical mechanics and electrostatics and provides insights into the physics of mesoscopic emitters as well as great simplifications in practical calculations....
JACKSON'S THEOREM FOR COMPACT GROUPS
H. Vaezi; S. F. Rzaev
2002-01-01
In this article we consider the generalized shift operator defined by(Sh.f)(g) = ∫Gf (tut-1g)dton compact group G and by help of this operator we define "Spherical" modulus of continuity. So we proveStechkin and Jackson type theorems.
Angle Defect and Descartes' Theorem
Scott, Paul
2006-01-01
Rene Descartes lived from 1596 to 1650. His contributions to geometry are still remembered today in the terminology "Descartes' plane". This paper discusses a simple theorem of Descartes, which enables students to easily determine the number of vertices of almost every polyhedron. (Contains 1 table and 2 figures.)
GENERALIZED RECIPROCAL THEOREMS AND THEIR APPLICATIONS
付宝连
2002-01-01
Generalized reciprocal theorems of non-coupled and coupled systems , which are valid for two deformed bodies with different constitutive relations are established by generalizing the idea of Betti ' s reciprocal theorem. When the constitutive relations of the two deformed bodies are all alike and linear elastic, the generalized reciprocal theorem of non-coupled systems just becomes Betti' s . Meanwhile, the generalized reciprocal theorems are applied to simulate calculations in elasticity.
A vector bundle proof of Poncelet theorem
Vallès, Jean
2012-01-01
In the town of Saratov where he was prisonner, Poncelet, continuing the work of Euler and Steiner on polygons simultaneously inscribed in a circle and circumscribed around an other circle, proved the following generalization : "Let C and D be two smooth conics in the projective complex plane. If D passes through the n(n-1)/2 vertices of a complete polygon with n sides tangent to C then D passes through the vertices of infinitely many such polygons." According to Marcel Berger this theorem is the nicest result about the geometry of conics. Even if it is, there are few proofs of it. To my knowledge there are only three. The first proof, published in 1822 and based on infinitesimal deformations, is due to Poncelet. Later, Jacobi proposed a new proof based on finite order points on elliptic curves; his proof, certainly the most famous, is explained in a modern way and in detail by Griffiths and Harris. In 1870 Weyr proved a Poncelet theorem in space (more precisely for two quadrics) that implies the one above whe...
A definability theorem for first order logic
Butz, C.; Moerdijk, I.
2001-01-01
In this paper we will present a definability theorem for first order logic This theorem is very easy to state and its proof only uses elementary tools To explain the theorem let us first observe that if M is a model of a theory T in a language L then clearly any definable subset S M ie a subset S
A note on generalized Weyl's theorem
Zguitti, H.
2006-04-01
We prove that if either T or T* has the single-valued extension property, then the spectral mapping theorem holds for B-Weyl spectrum. If, moreover T is isoloid, and generalized Weyl's theorem holds for T, then generalized Weyl's theorem holds for f(T) for every . An application is given for algebraically paranormal operators.
On Brayton and Moser's missing stability theorem
Jeltsema, D.; Scherpen, J. M. A.
2005-01-01
In the early 1960s, Brayton and Moser proved three theorems concerning the stability of nonlinear electrical circuits. The applicability of each theorem depends on three different conditions on the type of admissible nonlinearities in circuit. Roughly speaking, this means that the theorems apply to
Fiolhais, Miguel C N; Providencia, C; Nordmark, Arne B
2010-01-01
We prove a theorem on the magnetic energy minimum in a system of perfect, or ideal, conductors. It is analogous to Thomson's theorem on the equilibrium electric field and charge distribution in a system of conductors. We first prove Thomson's theorem using a variational principle. Our new theorem is then derived by similar methods. We find that magnetic energy is minimized when the current distribution is a surface current density with zero interior magnetic field; perfect conductors are perfectly diamagnetic. The results agree with currents in superconductors being confined near the surface. The theorem implies a generalized force that expels current and magnetic field from the interior of a conductor that loses its resistivity. Examples of solutions that obey the theorem are presented.
A fast alternating projection method for complex frequency estimation
Andersson, Fredrik; Ivert, Per-Anders
2011-01-01
The problem of approximating a sampled function using sums of a fixed number of complex exponentials is considered. We use alternating projections between fixed rank matrices and Hankel matrices to obtain such an approximation. Convergence, convergence rates and error estimates for this technique are proven, and fast algorithms are developed. We compare the numerical results obtain with the MUSIC and ESPRIT methods.
Implementation of Relevant Methods in Assessing Traffic-Technological Projects
Danijela Barić
2007-09-01
Full Text Available The assessment of investment traffic-technological projectsmeans a set of activities whose basic aim is to determine the justificationand feasibility of the projects. The decision-makingprocess, including the decision-making on investments is an extremelycomplex process, and the decision-maker has to have avision of the future and make decisions accordingly in a modemand flexible manner. Therefore, the decisions need to be theresult of a planning and research process based on relevant scientificmethods. The work includes the selected, analysed andpresented methods of cost-benefit analysis, methods of multi-criteria decision-making and SWOT (Strengths, Weaknesses,Opportunities, and Threats analysis methods. Regarding thebasic characteristics, the mentioned methods have been compared,the order of their implementation has been determined,and then they have been implemented in assessing the traffic-technological projects of reconstmction with the aim of selectingthe optimal variant solution.
Researching on quantitative project management plan and implementation method
Wang, Xin; Ren, Aihua; Liu, Xiangshang
2017-08-01
With the practice of high maturity process improvement, more and more attention has been paid to CMMI and other process improvement frameworks. The key to improve the process of high maturity is to quantify the process. At present, the method of improving the software process of high maturity is lack of specific introduction to the corresponding improvement link or process implementation. In this paper, based on the current improvement in the quantitative management of the framework and statistical analysis technical of the high maturity recommended for the enterprise to improve the process of planning and implementation methods. These methods provide quantitative process management for the enterprise, as well as quantitative management of the project to provide a systematic process, and finally evaluate the effectiveness of quantitative management projects. Finally, this method is used to verify the effectiveness of the framework in guiding the enterprise to improve the process of high maturity.
Study on Method of Comprehensive Evaluating for Information System Projects
无
2000-01-01
In this paper, a new method of evaluation for information system project is propoeed on the basis of the meta-synthesis methodology from qualitative analysis to quantitative analysis. DHGF is an integrated method of improved Delphi, analytic hierarchy process, grey interconnect degree and fuzzy comprehensive evaluating. It gives full play to their advantages and controls theirs disadvantages. The feasibility and effectiveness of DHGF are shown in the practical example.
A General, Mass-Preserving Navier-Stokes Projection Method
Salac, David
2015-01-01
The conservation of mass is common issue with multiphase fluid simulations. In this work a novel projection method is presented which conserves mass both locally and globally. The fluid pressure is augmented with a time-varying component which accounts for any global mass change. The resulting system of equations is solved using an efficient Schur-complement method. Using the proposed method four numerical examples are performed: the evolution of a static bubble, the rise of a bubble, the breakup of a thin fluid thread, and the extension of a droplet in shear flow. The method is capable of conserving the mass even in situations with morphological changes such as droplet breakup.
A decoupled monolithic projection method for natural convection problems
Pan, Xiaomin; Kim, Kyoungyoun; Lee, Changhoon; Choi, Jung-Il
2016-06-01
We propose an efficient monolithic numerical procedure based on a projection method for solving natural convection problems. In the present monolithic method, the buoyancy, linear diffusion, and nonlinear convection terms are implicitly advanced by applying the Crank-Nicolson scheme in time. To avoid an otherwise inevitable iterative procedure in solving the monolithic discretized system, we use a linearization of the nonlinear convection terms and approximate block lower-upper (LU) decompositions along with approximate factorization. Numerical simulations demonstrate that the proposed method is more stable and computationally efficient than other semi-implicit methods, preserving temporal second-order accuracy.
On the inversion of Fueter's theorem
Dong, Baohua; Kou, Kit Ian; Qian, Tao; Sabadini, Irene
2016-10-01
The well known Fueter theorem allows to construct quaternionic regular functions or monogenic functions with values in a Clifford algebra defined on open sets of Euclidean space R n + 1, starting from a holomorphic function in one complex variable or, more in general, from a slice hyperholomorphic function. Recently, the inversion of this theorem has been obtained for odd values of the dimension n. The present work extends the result to all dimensions n by using the Fourier multiplier method. More precisely, we show that for any axially monogenic function f defined in a suitable open set in R n + 1, where n is a positive integer, we can find a slice hyperholomorphic function f → such that f =Δ (n - 1) / 2 f →. Both the even and the odd dimensions are treated with the same, viz., the Fourier multiplier, method. For the odd dimensional cases the result obtained by the Fourier multiplier method coincides with the existing result obtained through the pointwise differential method.
Risk Management Method in IT Project: A Review
Ikhtiar Faahakhododo
2016-09-01
can produce a useful product and make a profit. This article clarified some of the methods of risk management exist. There was two techniques to determine the risks used in this study, those were Metrics of Process Structure and Referential Model or could be referred as the Comparison to the Referential Model technique. That technique will produce Software Process Meta Model, Model of Risk Management, and Manage Risks in Project models. Those models were used to help managers in mapping the risks of the project.
A multilevel adaptive projection method for unsteady incompressible flow
Howell, Louis H.
1993-11-01
There are two main requirements for practical simulation of unsteady flow at high Reynolds number: the algorithm must accurately propagate discontinuous flow fields without excessive artificial viscosity, and it must have some adaptive capability to concentrate computational effort where it is most needed. We satisfy the first of these requirements with a second-order Godunov method similar to those used for high-speed flows with shocks, and the second with a grid-based refinement scheme which avoids some of the drawbacks associated with unstructured meshes. These two features of our algorithm place certain constraints on the projection method used to enforce incompressibility. Velocities are cell-based, leading to a Laplacian stencil for the projection which decouples adjacent grid points. We discuss features of the multigrid and multilevel iteration schemes required for solution of the resulting decoupled problem. Variable-density flows require use of a modified projection operator--we have found a multigrid method for this modified projection that successfully handles density jumps of thousands to one. Numerical results are shown for the 2D adaptive and 3D variable-density algorithms.
A projection method for LES of incompressible turbulent combustion
LIU Yi; GUO Yincheng
2004-01-01
In this paper, the "incompressible" property of a turbulent combustion with Ma<<1 is analyzed, and a projection method for simulation of low Ma number turbulent combustions is discussed. The density is calculated explicitly,and the projection is only applied to the momentum equations and thus greatly saves the calculation cost. Large eddy simulation of methane-air turbulent planar jet combustion is performed using this projection method. A reduced four-step chemical kinetic mechanism is applied for the simulation of methane-air combustion. A dynamic eddy viscosity model is utilized for the sub-grid scales turbulence modulation. The SGS model for the filtered reaction rate is a dynamic similarity model. Simulation results depict the detailed coherent structures in the jet flame along with the vortex-flame interactions in the flow field. Besides, it is found that the chemical reaction has the effect of "energy rearrangement" in the flow field, which may greatly reduce the turbulence. Simulation results show the satisfactory performance of this projection method in simulating turbulent combustion under the condition of Ma<<1.
The de Finetti theorem for test spaces
Barrett, Jonathan; Leifer, Matthew
2009-03-01
We prove a de Finetti theorem for exchangeable sequences of states on test spaces, where a test space is a generalization of the sample space of classical probability theory and the Hilbert space of quantum theory. The standard classical and quantum de Finetti theorems are obtained as special cases. By working in a test space framework, the common features that are responsible for the existence of these theorems are elucidated. In addition, the test space framework is general enough to imply a de Finetti theorem for classical processes. We conclude by discussing the ways in which our assumptions may fail, leading to probabilistic models that do not have a de Finetti theorem.
The de Finetti theorem for test spaces
Barrett, Jonathan [H H Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL (United Kingdom); Leifer, Matthew [Institute for Quantum Computing, University of Waterloo, 200 University Avenue West, Waterloo, Ontario N2L 3G1 (Canada)], E-mail: j.barrett@bristol.ac.uk, E-mail: matt@mattleifer.info
2009-03-15
We prove a de Finetti theorem for exchangeable sequences of states on test spaces, where a test space is a generalization of the sample space of classical probability theory and the Hilbert space of quantum theory. The standard classical and quantum de Finetti theorems are obtained as special cases. By working in a test space framework, the common features that are responsible for the existence of these theorems are elucidated. In addition, the test space framework is general enough to imply a de Finetti theorem for classical processes. We conclude by discussing the ways in which our assumptions may fail, leading to probabilistic models that do not have a de Finetti theorem.
Fast alternating projection methods for constrained tomographic reconstruction.
Liu, Li; Han, Yongxin; Jin, Mingwu
2017-01-01
The alternating projection algorithms are easy to implement and effective for large-scale complex optimization problems, such as constrained reconstruction of X-ray computed tomography (CT). A typical method is to use projection onto convex sets (POCS) for data fidelity, nonnegative constraints combined with total variation (TV) minimization (so called TV-POCS) for sparse-view CT reconstruction. However, this type of method relies on empirically selected parameters for satisfactory reconstruction and is generally slow and lack of convergence analysis. In this work, we use a convex feasibility set approach to address the problems associated with TV-POCS and propose a framework using full sequential alternating projections or POCS (FS-POCS) to find the solution in the intersection of convex constraints of bounded TV function, bounded data fidelity error and non-negativity. The rationale behind FS-POCS is that the mathematically optimal solution of the constrained objective function may not be the physically optimal solution. The breakdown of constrained reconstruction into an intersection of several feasible sets can lead to faster convergence and better quantification of reconstruction parameters in a physical meaningful way than that in an empirical way of trial-and-error. In addition, for large-scale optimization problems, first order methods are usually used. Not only is the condition for convergence of gradient-based methods derived, but also a primal-dual hybrid gradient (PDHG) method is used for fast convergence of bounded TV. The newly proposed FS-POCS is evaluated and compared with TV-POCS and another convex feasibility projection method (CPTV) using both digital phantom and pseudo-real CT data to show its superior performance on reconstruction speed, image quality and quantification.
Steinitz theorems for simple orthogonal polyhedra
David Eppstein
2014-09-01
Full Text Available We define a simple orthogonal polyhedron to be a three-dimensional polyhedron with the topology of a sphere in which three mutually-perpendicular edges meet at each vertex.By analogy to Steinitz's theorem characterizing the graphs of convex polyhedra, we find graph-theoretic characterizations of three classes of simple orthogonal polyhedra: corner polyhedra, which can be drawn by isometric projection in the plane with only one hidden vertex, xyz polyhedra, in which each axis-parallel line through a vertex contains exactly one other vertex, and arbitrary simple orthogonal polyhedra. In particular, the graphs of xyz polyhedra are exactly the bipartite cubic polyhedral graphs, and every bipartite cubic polyhedral graph with a 4-connected dual graph is the graph of a corner polyhedron. Based on our characterizations we find efficient algorithms for constructing orthogonal polyhedra from their graphs.
Multiwavelet sampling theorem in Sobolev spaces
无
2010-01-01
This paper is to establish the multiwavelet sampling theorem in Sobolev spaces. Sampling theorem plays a very important role in digital signal communication. The most classical sampling theorem is Shannon sampling theorem, which works for bandlimited signals. Recently, sampling theorems in wavelets or multiwavelets subspaces are extensively studied in the literature. In this paper, we firstly propose the concept of dual multiwavelet frames in dual Sobolev spaces (H s (R) , H-s (R)). Then we construct a special class of dual multiwavelet frames, from which the multiwavelet sampling theorem in Sobolev spaces is obtained. That is, for any f ∈ H s (R) with s > 1/2, it can be exactly recovered by its samples. Especially, the sampling theorem works for continuous signals in L 2 (R), whose Sobolev exponents are greater than 1 /2.
The relativistic virial theorem and scale invariance
Gaite, Jose
2013-01-01
The virial theorem is related to the dilatation properties of bound states. This is realized, in particular, by the Landau-Lifshitz formulation of the relativistic virial theorem, in terms of the trace of the energy-momentum tensor. We construct a Hamiltonian formulation of dilatations in which the relativistic virial theorem naturally arises as the condition of stability against dilatations. A bound state becomes scale invariant in the ultrarelativistic limit, in which its energy vanishes. However, for very relativistic bound states, scale invariance is broken by quantum effects and the virial theorem must include the energy-momentum tensor trace anomaly. This quantum field theory virial theorem is directly related to the Callan-Symanzik equations. The virial theorem is applied to QED and then to QCD, focusing on the bag model of hadrons. In massless QCD, according to the virial theorem, 3/4 of a hadron mass corresponds to quarks and gluons and 1/4 to the trace anomaly.
Projected discrete ordinates methods for numerical transport problems
Larsen, E.W.
1985-01-01
A class of Projected Discrete-Ordinates (PDO) methods is described for obtaining iterative solutions of discrete-ordinates problems with convergence rates comparable to those observed using Diffusion Synthetic Acceleration (DSA). The spatially discretized PDO solutions are generally not equal to the DSA solutions, but unlike DSA, which requires great care in the use of spatial discretizations to preserve stability, the PDO solutions remain stable and rapidly convergent with essentially arbitrary spatial discretizations. Numerical results are presented which illustrate the rapid convergence and the accuracy of solutions obtained using PDO methods with commonplace differencing methods.
A New Proof of a TheoremAbout Wave Equation
朱佑彬
2005-01-01
@@ 1 Introduction and Main Results In book [1], Professor C. D. Sogge proved the Theorem 2.2 (page 15) by the method presented by F. John. But I think we can also prove it by another method which is simpler and more direct than the original approach.
On Feynman's Triangle Problem and the Routh Theorem
Man, Yiu-Kwong
2009-01-01
In this article, we give a brief history of the Feynman's Triangle problem and describe a simple method to solve a general version of this problem, which is called the Routh Theorem. This method could be found useful to school teachers, instructors or lecturers who are involved in teaching geometry.
Automated Theorem Proving in Temporal Logic：T—Resolution
招兆铿; 戴军; 等
1994-01-01
This paper presentes a novel resolution method,T-resolution,based on the first order temporal logic.The primary claim of this method is its soundness and completeness.For this purpose,we construct the corresponding semantic trees and extend Herbrand's Theorem.
Graph-like continua, augmenting arcs, and Menger's theorem
Thomassen, Carsten; Vella, Antoine
2008-01-01
We show that an adaptation of the augmenting path method for graphs proves Menger's Theorem for wide classes of topological spaces. For example, it holds for locally compact, locally connected, metric spaces, as already known. The method lends itself particularly well to another class of spaces...
Expectation Value in Bell's Theorem
Wang, Zheng-Chuan
2006-01-01
We will demonstrate in this paper that Bell's theorem (Bell's inequality) does not really conflict with quantum mechanics, the controversy between them originates from the different definitions for the expectation value using the probability distribution in Bell's inequality and the expectation value in quantum mechanics. We can not use quantum mechanical expectation value measured in experiments to show the violation of Bell's inequality and then further deny the local hidden-variables theor...
An improvement of Papadakis' theorem
ZHANG Zhihua; MU Lehua; ZHANG Peixuan
2004-01-01
There exist many orthonormal wavelets which cannot be derived by multiresolution analysis (MRA) with a single scaling function.In 2000,Papadakis announced that any orthonormal wavelet is derived by a generalized MRA with countable scaling functions at most.We improve Papadakis' theorem and find that for any othonormal wavelet,the least number of the corresponding scaling functions is just the essential supremum of the dimension function of the orthonormal wavelet.Moreover,we construct directly the fewest scaling functions.
Pythagoras Theorem and Relativistic Kinematics
Mulaj, Zenun; Dhoqina, Polikron
2010-01-01
In two inertial frames that move in a particular direction, may be registered a light signal that propagates in an angle with this direction. Applying Pythagoras theorem and principles of STR in both systems, we can derive all relativistic kinematics relations like the relativity of simultaneity of events, of the time interval, of the length of objects, of the velocity of the material point, Lorentz transformations, Doppler effect and stellar aberration.
Compactness theorems of fuzzy semantics
无
2000-01-01
The relationship among diverse fuzzy semantics vs. the corresponding logic consequence operators has been analyzed systematically. The results that compactness and logical compactness of fuzzy semantics are equivalent to compactness and continuity of the logic consequence operator induced by the semantics respectively have been proved under certain conditions. A general compactness theorem of fuzzy semantics have been established which says that every fuzzy semantics defined on a free algebra with members corresponding to continuous functions is compact.
Formalization of the Integral Calculus in the PVS Theorem Prover
Ricky Wayne Butler
2009-04-01
Full Text Available The PVS Theorem prover is a widely used formal verification tool used for the analysis of safetycritical systems. The PVS prover, though fully equipped to support deduction in a very general logic framework, namely higher-order logic, it must nevertheless, be augmented with the definitions and associated theorems for every branch of mathematics and Computer Science that is used in a verification. This is a formidable task, ultimately requiring the contributions of researchers and developers all over the world. This paper reports on the formalization of the integral calculus in the PVS theorem prover. All of the basic definitions and theorems covered in a first course on integral calculus have been completed.The theory and proofs were based on Rosenlicht’s classic text on real analysis and follow the traditional epsilon-delta method. The goal of this work was to provide a practical set of PVS theories that could be used for verification of hybrid systems that arise in air traffic management systems and other aerospace applications. All of the basic linearity, integrability, boundedness, and continuity properties of the integral calculus were proved. The work culminated in the proof of the Fundamental Theorem Of Calculus. There is a brief discussion about why mechanically checked proofs are so much longer than standard mathematics textbook proofs.
Software Reliability through Theorem Proving
S.G.K. Murthy
2009-05-01
Full Text Available Improving software reliability of mission-critical systems is widely recognised as one of the major challenges. Early detection of errors in software requirements, designs and implementation, need rigorous verification and validation techniques. Several techniques comprising static and dynamic testing approaches are used to improve reliability of mission critical software; however it is hard to balance development time and budget with software reliability. Particularly using dynamic testing techniques, it is hard to ensure software reliability, as exhaustive testing is not possible. On the other hand, formal verification techniques utilise mathematical logic to prove correctness of the software based on given specifications, which in turn improves the reliability of the software. Theorem proving is a powerful formal verification technique that enhances the software reliability for missioncritical aerospace applications. This paper discusses the issues related to software reliability and theorem proving used to enhance software reliability through formal verification technique, based on the experiences with STeP tool, using the conventional and internationally accepted methodologies, models, theorem proving techniques available in the tool without proposing a new model.Defence Science Journal, 2009, 59(3, pp.314-317, DOI:http://dx.doi.org/10.14429/dsj.59.1527
Scrum Method Implementation in a Software Development Project Management
Putu Adi Guna Permana
2015-09-01
Full Text Available To maximize the performance, companies conduct a variety of ways to increase the business profit. The work management between one company and the other company is different, so the differences in the management may cause the software to have a different business process. Software development can be defined as creating a new software or fixing the existing one. Technology developments led to increasing demand for software, Industrial Technology (IT Companies should be able to project well maintenance. The methodology in software development is used in accordance with the company's needs based on the SDLC (Software Development Life Cycle. Scrum method is a part of the Agile method that is expected to increase the speed and flexibility in software development project management.
Modelling of Airship Flight Mechanics by the Projection Equivalent Method
Frantisek Jelenciak; Michael Gerke; Ulrich Borgolte
2015-01-01
This article describes the projection equivalent method (PEM) as a specific and relatively simple approach for the modelling of aircraft dynamics. By the PEM it is possible to obtain a mathematic al model of the aerodynamic forces and momentums acting on different kinds of aircraft during flight. For the PEM, it is a characteristic of it that - in principle - it provides an acceptable regression model of aerodynamic forces and momentums which exhibits reasonable and plausible behaviour from a...
Manufacturing Methods & Technology Project Execution Report. Second Half CY 1980
1981-03-01
U.S. ARMY MATER-IEL DEVELOP AND READINESS COMMAND Lu ti MAANUFACTURING METHODS & 0 ~ ECHNOLOGY ELECTE, hAY 4 19 81 PROJECT EXECUTION REPORTautw w...Armament Materiel Readiness Command (Ammunition) . ... 83 Armament R&D Cormtand Armament Materiel Readiness Command (Weapons) .. . . . 105 Mobility ... MOBILIZATION PRODUCTION RATES ARE ESTIMATED TO BE S1t6 6000 PER YEAR. 5 78 4288 EXPLOSIVE SAFE SEPARATION AND SENSITIVITY CRITERIA ZERO PALLET SPACING
La Salle定理的推广%GENERALIZATION OF LA SALLE'S THEOREM
甘作新; 韩京清; 王培光
2001-01-01
In this paper, by using the method of Lyapunov function we generalize the theorem of La Salle from Lurie control system to general Lurie control system. Our result is concise and is easy to be tested. Hence, we improve the proof and extend the applied range of La Salle's Theorem.
A Note on the Uniqueness of Koebe-Andreev-Thurston Theorem
Xiao Jun HUANG; Zi Peng WANG
2012-01-01
In this paper,we present a new proof of the uniqueness of Koebe-Andreev-Thurston theorem.Our method is based on the argument principle in complex analysis and reviews the connection between the circle packing theorem and complex analysis.
The fixed point theorems of 1-set-contractive operators in Banach space
Wang Shuang
2011-01-01
Full Text Available Abstract In this paper, we obtain some new fixed point theorems and existence theorems of solutions for the equation Ax = μx using properties of strictly convex (concave function and theories of topological degree. Our results and methods are different from the corresponding ones announced by many others. MSC: 47H09, 47H10
Lusternik-Schnirelmann 定理的推广%Generalized Lusternik-Schnirelmann Theorem
刘宇红; 付军
2002-01-01
本文根据Brouwer 映射度的理论和微分拓扑的基本方法推广了Lusternik-Schnirelmann 定理.%This paper generilized Lusternik-Schnirelmann theorem by the Brouwer degree of mapping theorem and the elementary methods of differential topology.
Bayes' Theorem: An Old Tool Applicable to Today's Classroom Measurement Needs. ERIC/AE Digest.
Rudner, Lawrence M.
This digest introduces ways of responding to the call for criterion-referenced information using Bayes' Theorem, a method that was coupled with criterion-referenced testing in the early 1970s (see R. Hambleton and M. Novick, 1973). To illustrate Bayes' Theorem, an example is given in which the goal is to classify an examinee as being a master or…
Approximate Fixed Point Theorems in Banach Spaces with Applications in Game Theory
Brânzei, R.; Morgan, J.; Scalzo, V.; Tijs, S.H.
2002-01-01
In this paper some new approximate fixed point theorems for multifunctions in Banach spaces are presented and a method is developed indicating how to use approximate fixed point theorems in proving the existence of approximate Nash equilibria for non-cooperative games.
A Strong Limit Theorem on Generalized Random Selection for m-valued Random Sequences
WANGZhong-zhi; XUFu-xia
2003-01-01
In this paper, a strong limit theorem on gambling strategy for binary Bernoulli sequence, i.e.irregularity theorem, is extended to random selection for dependent m-valued random variables, via using a new method-differentiability on net. Furthermore, by allowing the selection function to take value in finite interval [-M, M], the conception of random selection is generalized.
Convolution theorems for the linear canonical transform and their applications
DENG Bing; TAO Ran; WANG Yue
2006-01-01
As generalization of the fractional Fourier transform (FRFT), the linear canonical transform (LCT) has been used in several areas, including optics and signal processing. Many properties for this transform are already known, but the convolution theorems, similar to the version of the Fourier transform, are still to be determined. In this paper, the authors derive the convolution theorems for the LCT, and explore the sampling theorem and multiplicative filter for the band limited signal in the linear canonical domain. Finally, the sampling and reconstruction formulas are deduced, together with the construction methodology for the above mentioned multiplicative filter in the time domain based on fast Fourier transform (FFT), which has much lower computational load than the construction method in the linear canonical domain.
Deviations from Wick's theorem in the canonical ensemble
Schönhammer, K.
2017-07-01
Wick's theorem for the expectation values of products of field operators for a system of noninteracting fermions or bosons plays an important role in the perturbative approach to the quantum many-body problem. A finite-temperature version holds in the framework of the grand canonical ensemble, but not for the canonical ensemble appropriate for systems with fixed particle number such as ultracold quantum gases in optical lattices. Here we present formulas for expectation values of products of field operators in the canonical ensemble using a method in the spirit of Gaudin's proof of Wick's theorem for the grand canonical case. The deviations from Wick's theorem are examined quantitatively for two simple models of noninteracting fermions.
A New Method To Convert the Fischer Projection of a Monosaccharide to the Haworth Projection
Zhang, Qing-Zhi; Zhang, Shen-Song
1999-06-01
This method is based upon the R,S-configuration designation of each asymmetric carbon of a monosaccharide. According to the rule of configurational retention of each original asymmetric carbon, the Fischer projection of a monosaccharide can be converted into different views of the Haworth projection (the carbon-numbering orientation of the Haworth ring can be in either a clockwise or a counterclockwise direction, and the oxygen atom can be written at any corner of the ring). The D,L-configuration of a sugar in Haworth projection can be directly determined by designating the R,S-configuration of the highest-numbered asymmetric carbon; that is, the most distant carbon from the anomeric carbon. The R-configuration at this carbon corresponds to the D-family, and S- to the L-family. By comparing the stereochemistry of the anomeric carbon with that of the highest-numbered asymmetric carbon, the a, b-anomer of a Haworth projection is directly notated. If these two carbons have the same configuration (R,R or S,S), the anomer is b; if different (R,S or S,R), the anomer is a. This method proves to be general and widely applicable.
Successive projection method for solving the unbalanced Procrustes problem
ZHANG Zhenyue; DU Keqin
2006-01-01
We present a successive projection method for solving the unbalanced Procrustes problem: given matrix A ∈ Rn×n and B ∈ Rn×κ, n ＞κ, minimize the residual ‖AQ - B‖F with the orthonormal constraint QTQ = Iκ on the variant Q ∈ Rn×κ. The presented algorithm consists of solving k least squares problems with quadratic constraints and an expanded balance problem at each sweep. We give a detailed convergence analysis. Numerical experiments reported in this paper show that our new algorithm is superior to other existing methods.
Methods for cost estimation in software project management
Briciu, C. V.; Filip, I.; Indries, I. I.
2016-02-01
The speed in which the processes used in software development field have changed makes it very difficult the task of forecasting the overall costs for a software project. By many researchers, this task has been considered unachievable, but there is a group of scientist for which this task can be solved using the already known mathematical methods (e.g. multiple linear regressions) and the new techniques as genetic programming and neural networks. The paper presents a solution for building a model for the cost estimation models in the software project management using genetic algorithms starting from the PROMISE datasets related COCOMO 81 model. In the first part of the paper, a summary of the major achievements in the research area of finding a model for estimating the overall project costs is presented together with the description of the existing software development process models. In the last part, a basic proposal of a mathematical model of a genetic programming is proposed including here the description of the chosen fitness function and chromosome representation. The perspective of model described it linked with the current reality of the software development considering as basis the software product life cycle and the current challenges and innovations in the software development area. Based on the author's experiences and the analysis of the existing models and product lifecycle it was concluded that estimation models should be adapted with the new technologies and emerging systems and they depend largely by the chosen software development method.
Galerkin projection methods for solving multiple related linear systems
Chan, T.F.; Ng, M.; Wan, W.L.
1996-12-31
We consider using Galerkin projection methods for solving multiple related linear systems A{sup (i)}x{sup (i)} = b{sup (i)} for 1 {le} i {le} s, where A{sup (i)} and b{sup (i)} are different in general. We start with the special case where A{sup (i)} = A and A is symmetric positive definite. The method generates a Krylov subspace from a set of direction vectors obtained by solving one of the systems, called the seed system, by the CG method and then projects the residuals of other systems orthogonally onto the generated Krylov subspace to get the approximate solutions. The whole process is repeated with another unsolved system as a seed until all the systems are solved. We observe in practice a super-convergence behaviour of the CG process of the seed system when compared with the usual CG process. We also observe that only a small number of restarts is required to solve all the systems if the right-hand sides are close to each other. These two features together make the method particularly effective. In this talk, we give theoretical proof to justify these observations. Furthermore, we combine the advantages of this method and the block CG method and propose a block extension of this single seed method. The above procedure can actually be modified for solving multiple linear systems A{sup (i)}x{sup (i)} = b{sup (i)}, where A{sup (i)} are now different. We can also extend the previous analytical results to this more general case. Applications of this method to multiple related linear systems arising from image restoration and recursive least squares computations are considered as examples.
Variable operator technique and the min-max theorem
Sambhu Nath Datta
2000-09-01
We investigate a variation method where the trial function is generated from the application of a variable operator on a reference function. Two conditions are identiﬁed, one for obtaining a maximum and another for a minimum. Although the conditions are easy to understand, the overall formulation is somewhat unusual as each condition gives rise to a two-step variation process. As an example, projection operators are used to form the variable operator, and by this tactics one obtains the new interpretation that the pseudopotential formalism is in fact equivalent to a minimax procedure. The two-step variational process is nevertheless more ﬂexible than the pseudopotential formalism, for it can also be used when the variable operator isnot manifestly expressed in terms of projectors. This is illustrated by a comparison of the two-step method with the variational solution of Dirac’s relativistic electron equation. The same comparison leads to an alternative proof that the process of maximizing energy by varying the – coupling operator eliminates all negative-energy contributions from a trial spinor. The latter observation is crucial for the derivation of the min-max theorem in relativistic quantum mechanics.
Bishop-Runge approximations and inversion of a Riemann-Klein theorem
Henkin, G. M.; Michel, V.
2015-02-01
In this paper we give results about projective embeddings of Riemann surfaces, smooth or nodal, which we apply to the inverse Dirichlet-to-Neumann problem and to the inversion of a Riemann-Klein theorem. To produce useful embeddings, we adapt a technique of Bishop in the open bordered case and use a Runge-type harmonic approximation theorem in the compact case. Bibliography: 37 titles.
Mechanical Geometry Theorem Proving Based on Groebner Bases
吴尽昭
1997-01-01
A new method for the mechanical elementary geometry theorem proving is presented by using Groebner bases of polynomial ideals.It has two main advantages over the approach proposed in literature:(i)It is complete and not a refutational procdure;(ii) The subcases of the geometry statements which are not generally true can be differentiated clearly.
Decomposition Theorems for Various Kinds of Languages Parallel in Nature
Skyum, Sven
1976-01-01
In this paper we give a method for decomposing subclasses of different families of languages, parallel in nature, into other families. These decomposition theorems can be used to produce languages not it a family by using examples of languages not belonging to some “smaller” family....
Hamiltonian Noether theorem for gauge systems and two time physics
Villanueva, V M; Ruiz, L; Silvas, J
2005-01-01
The Noether theorem for Hamiltonian constrained systems is revisited. In particular, our review presents a novel method to show that the gauge transformations are generated by the conserved quantities associated with the first class constraints. We apply our results to the relativistic point particle, to the Friedberg et al. model and, with special emphasis, to two time physics.
Razumikhin Stability Theorem for Fractional Systems with Delay
D. Baleanu
2010-01-01
Full Text Available Fractional calculus techniques and methods started to be applied successfully during the last decades in several fields of science and engineering. In this paper we studied the stability of fractional-order nonlinear time-delay systems for Riemann-Liouville and Caputo derivatives and we extended Razumikhin theorem for the fractional nonlinear time-delay systems.
-Statistical Extension of the Korovkin Type Approximation Theorem
Esra Erkus; Oktay Duman
2005-11-01
In this paper, using the concept of -statistical convergence which is a regular (non-matrix) summability method, we obtain a general Korovkin type approximation theorem which concerns the problem of approximating a function by means of a sequence $\\{L_nf\\}$ of positive linear operators.
Integral formulas and the Ohsawa-Takegoshi extension theorem
Bo Berndtsson
2005-01-01
We construct a semiexplicit integral representation of the canonical solution to the (-δ)-equation with respect to a plurisubharmonic weight function in a pseudoconvex domain. The construction is based on a construction related to the Ohsawa-Takegoshi extension theorem combined with a method to construct weighted integral representations due to M. Andersson.
A Neutrosophic Binomial Factorial Theorem with their Refrains
Khalid, Huda; Smarandache, Florentin; Essa, Ahmed
2016-01-01
The Neutrosophic Precalculus and the Neutrosophic Calculus can be developed in many ways, depending on the types of indeterminacy one has and on the method used to deal with such indeterminacy. This article is innovative since the form of neutrosophic binomial factorial theorem was constructed in addition to its refrains.
Quantum optical ABCD theorem in two-mode case
Fan Hong-Yi; Hu Li-Yun
2008-01-01
By introducing the entangled Fresnel operator (EFO) this paper demonstrates that there exists ABCD theorem for two-mode entangled case in quantum optics.The canonical operator method as mapping of ray-transfer ABCD matrix is explicitly shown by EFO's normally ordered expansion through the coherent state representation and the technique of integration within an ordered product of operators.
The classical version of Stokes' Theorem revisited
Markvorsen, Steen
2008-01-01
Using only fairly simple and elementary considerations - essentially from first year undergraduate mathematics - we show how the classical Stokes' theorem for any given surface and vector field in $\\mathbb{R}^{3}$ follows from an application of Gauss' divergence theorem to a suitable modification...... of the vector field in a tubular shell around the given surface. The two stated classical theorems are (like the fundamental theorem of calculus) nothing but shadows of the general version of Stokes' theorem for differential forms on manifolds. The main points in the present paper, however, is firstly...... exercise, which simply relates the concepts of divergence and curl on the local differential level. The rest of the paper uses only integration in $1$, $2$, and $3$ variables together with a 'fattening' technique for surfaces and the inverse function theorem....
On Krasnoselskii's Cone Fixed Point Theorem
Man Kam Kwong
2008-04-01
Full Text Available In recent years, the Krasnoselskii fixed point theorem for cone maps and its many generalizations have been successfully applied to establish the existence of multiple solutions in the study of boundary value problems of various types. In the first part of this paper, we revisit the Krasnoselskii theorem, in a more topological perspective, and show that it can be deduced in an elementary way from the classical Brouwer-Schauder theorem. This viewpoint also leads to a topology-theoretic generalization of the theorem. In the second part of the paper, we extend the cone theorem in a different direction using the notion of retraction and show that a stronger form of the often cited Leggett-Williams theorem is a special case of this extension.
The Helmholtz theorem and retarded fields
Heras, Ricardo
2016-11-01
Textbooks frequently use the Helmholtz theorem to derive expressions for electrostatic and magnetostatic fields but they do not usually apply this theorem to derive expressions for time-dependent electric and magnetic fields, even when there is no formal objection to doing so because the proof of the theorem does not involve time derivatives but only spatial derivatives. Here we address the question as to whether the Helmholtz theorem is useful in deriving expressions for the fields of Maxwell’s equations. We show that when this theorem is applied to Maxwell’s equations we obtain instantaneous expressions of the electric and magnetic fields, which are formally correct but of little practical usefulness. We then discuss two generalizations of the theorem which are shown to be useful in deriving the retarded fields.
The Helmholtz theorem and retarded fields
Heras, Ricardo
2016-01-01
Textbooks frequently use the Helmholtz theorem to derive expressions for the electrostatic and magnetostatic fields but they do not usually apply this theorem to derive expressions for the time-dependent electric and magnetic fields, even when there is no formal objection to doing so because the proof of the theorem does not involve time derivatives but only spatial derivatives. Here we address the question as to whether the Helmholtz theorem is useful to derive expressions for the fields of Maxwell's equations. We show that when this theorem is applied to Maxwell's equations we obtain instantaneous expressions of the electric and magnetic fields, which are formally correct but of little practical usefulness. We then discuss two generalizations of the theorem which are shown to be useful to derive the retarded fields.
Symbolic logic and mechanical theorem proving
Chang, Chin-Liang
1969-01-01
This book contains an introduction to symbolic logic and a thorough discussion of mechanical theorem proving and its applications. The book consists of three major parts. Chapters 2 and 3 constitute an introduction to symbolic logic. Chapters 4-9 introduce several techniques in mechanical theorem proving, and Chapters 10 an 11 show how theorem proving can be applied to various areas such as question answering, problem solving, program analysis, and program synthesis.
Expanding the Interaction Equivalency Theorem
Brenda Cecilia Padilla Rodriguez
2015-06-01
Full Text Available Although interaction is recognised as a key element for learning, its incorporation in online courses can be challenging. The interaction equivalency theorem provides guidelines: Meaningful learning can be supported as long as one of three types of interactions (learner-content, learner-teacher and learner-learner is present at a high level. This study sought to apply this theorem to the corporate sector, and to expand it to include other indicators of course effectiveness: satisfaction, knowledge transfer, business results and return on expectations. A large Mexican organisation participated in this research, with 146 learners, 30 teachers and 3 academic assistants. Three versions of an online course were designed, each emphasising a different type of interaction. Data were collected through surveys, exams, observations, activity logs, think aloud protocols and sales records. All course versions yielded high levels of effectiveness, in terms of satisfaction, learning and return on expectations. Yet, course design did not dictate the types of interactions in which students engaged within the courses. Findings suggest that the interaction equivalency theorem can be reformulated as follows: In corporate settings, an online course can be effective in terms of satisfaction, learning, knowledge transfer, business results and return on expectations, as long as (a at least one of three types of interaction (learner-content, learner-teacher or learner-learner features prominently in the design of the course, and (b course delivery is consistent with the chosen type of interaction. Focusing on only one type of interaction carries a high risk of confusion, disengagement or missed learning opportunities, which can be managed by incorporating other forms of interactions.
Image processing methods to obtain symmetrical distribution from projection image.
Asano, H; Takenaka, N; Fujii, T; Nakamatsu, E; Tagami, Y; Takeshima, K
2004-10-01
Flow visualization and measurement of cross-sectional liquid distribution is very effective to clarify the effects of obstacles in a conduit on heat transfer and flow characteristics of gas-liquid two-phase flow. In this study, two methods to obtain cross-sectional distribution of void fraction are applied to vertical upward air-water two-phase flow. These methods need projection image only from one direction. Radial distributions of void fraction in a circular tube and a circular-tube annuli with a spacer were calculated by Abel transform based on the assumption of axial symmetry. On the other hand, cross-sectional distributions of void fraction in a circular tube with a wire coil whose conduit configuration rotates about the tube central axis periodically were measured by CT method based on the assumption that the relative distributions of liquid phase against the wire were kept along the flow direction.
Inverting the central limit theorem
Navascues, Miguel; Villanueva, Ignacio
2011-01-01
The central limit theorem states that the sum of N independently distributed n-tuples of real variables (subject to appropriate normalization) tends to a multivariate gaussian distribution for large N. Here we propose to invert this argument: given a set of n correlated gaussian variables, we try to infer information about the structure of the discrete microscopic probability distributions whose convolution generated such a macroscopic behavior. The techniques developed along the article are applied to prove that the classical description of certain macroscopic optical experiments is infinitely more complex than the quantum one.
Comparison theorems in Riemannian geometry
Cheeger, Jeff
2008-01-01
The central theme of this book is the interaction between the curvature of a complete Riemannian manifold and its topology and global geometry. The first five chapters are preparatory in nature. They begin with a very concise introduction to Riemannian geometry, followed by an exposition of Toponogov's theorem-the first such treatment in a book in English. Next comes a detailed presentation of homogeneous spaces in which the main goal is to find formulas for their curvature. A quick chapter of Morse theory is followed by one on the injectivity radius. Chapters 6-9 deal with many of the most re
Asset management using an extended Markowitz theorem
Paria Karimi
2014-06-01
Full Text Available Markowitz theorem is one of the most popular techniques for asset management. The method has been widely used to solve many applications, successfully. In this paper, we present a multi objective Markowitz model to determine asset allocation by considering cardinality constraints. The resulted model is an NP-Hard problem and the proposed study uses two metaheuristics, namely genetic algorithm (GA and particle swarm optimization (PSO to find efficient solutions. The proposed study has been applied on some data collected from Tehran Stock Exchange over the period 2009-2011. The study considers four objectives including cash return, 12-month return, 36-month return and Lower Partial Moment (LPM. The results indicate that there was no statistical difference between the implementation of PSO and GA methods.
Phylogenetic and functional assessment of orthologs inference projects and methods.
Adrian M Altenhoff
2009-01-01
Full Text Available Accurate genome-wide identification of orthologs is a central problem in comparative genomics, a fact reflected by the numerous orthology identification projects developed in recent years. However, only a few reports have compared their accuracy, and indeed, several recent efforts have not yet been systematically evaluated. Furthermore, orthology is typically only assessed in terms of function conservation, despite the phylogeny-based original definition of Fitch. We collected and mapped the results of nine leading orthology projects and methods (COG, KOG, Inparanoid, OrthoMCL, Ensembl Compara, Homologene, RoundUp, EggNOG, and OMA and two standard methods (bidirectional best-hit and reciprocal smallest distance. We systematically compared their predictions with respect to both phylogeny and function, using six different tests. This required the mapping of millions of sequences, the handling of hundreds of millions of predicted pairs of orthologs, and the computation of tens of thousands of trees. In phylogenetic analysis or in functional analysis where high specificity is required, we find that OMA and Homologene perform best. At lower functional specificity but higher coverage level, OrthoMCL outperforms Ensembl Compara, and to a lesser extent Inparanoid. Lastly, the large coverage of the recent EggNOG can be of interest to build broad functional grouping, but the method is not specific enough for phylogenetic or detailed function analyses. In terms of general methodology, we observe that the more sophisticated tree reconstruction/reconciliation approach of Ensembl Compara was at times outperformed by pairwise comparison approaches, even in phylogenetic tests. Furthermore, we show that standard bidirectional best-hit often outperforms projects with more complex algorithms. First, the present study provides guidance for the broad community of orthology data users as to which database best suits their needs. Second, it introduces new methodology
A parametrization of the abstract Ramsey theorem
Mijares, Jose G
2010-01-01
We give a parametrization with perfect subsets of $2^{\\infty}$ of the abstract Ramsey theorem (see \\cite{todo}) Our main tool is an extension of the parametrized version of the combinatorial forcing developed in \\cite{nash} and \\cite{todo}, used in \\cite{mij} to the obtain a parametrization of the abstract Ellentuck theorem. As one of the consequences, we obtain a parametrized version of the Hales-Jewett theorem. Finally, we conclude that the family of perfectly ${\\cal S}$-Ramsey subsets of $2^{\\infty}\\times {\\cal R}$ is closed under the Souslin operation. {\\bf Key words and phrases}: Ramsey theorem, Ramsey space, parametrization.
A generalised Sylvester-Gallai Theorem
L. M. Pretorius
2007-09-01
Full Text Available We give an algorithmic proof for the contrapositive of the following theorem that has recently been proved by the authors:Let S be a ﬁnite set of points in the plane, with each point coloured red, blue or with both colours. Suppose that for any two distinct points A and B in S sharing a colour k, there is a third point in S which has (inter alia the colour different from k and is collinear with A and B. Then all the points in S are collinear.This theorem is a generalization of both the Sylvester-Gallai Theorem and the Motzkin-Rabin Theorem.
A History of the Central Limit Theorem
Fischer, Hans
2011-01-01
This study discusses the history of the central limit theorem and related probabilistic limit theorems from about 1810 through 1950. In this context the book also describes the historical development of analytical probability theory and its tools, such as characteristic functions or moments. The central limit theorem was originally deduced by Laplace as a statement about approximations for the distributions of sums of independent random variables within the framework of classical probability, which focused upon specific problems and applications. Making this theorem an autonomous mathematical
A generalized preimage theorem in global analysis
MA; Jipu
2001-01-01
［1］Ma Jipu, (1.2) inverses of operators between Banach spaces and conjugacy theorem, Chinese Annals of Math., B, 1999, 20(1): 57.［2］Ma Jipu, Rank theorem of operators between Banach spaces, Science in China, Ser. A, 2000, 43(1): 1.［3］Ma Jipu, Local conjugacy theorem, rank theorems in advenced calculus and a generalized principle constructing Banach manifolds, Science in China, Ser. A, 2000, 43(12): 1233.［4］Zeidler, A. E., Nonlinear Function Analysis and Its Applications, IV: Applications to Mathematical Physics, New York: Springer-Verlag, 1988.
Sol Swords
2011-10-01
Full Text Available Interactive theorem proving requires a lot of human guidance. Proving a property involves (1 figuring out why it holds, then (2 coaxing the theorem prover into believing it. Both steps can take a long time. We explain how to use GL, a framework for proving finite ACL2 theorems with BDD- or SAT-based reasoning. This approach makes it unnecessary to deeply understand why a property is true, and automates the process of admitting it as a theorem. We use GL at Centaur Technology to verify execution units for x86 integer, MMX, SSE, and floating-point arithmetic.
Risk assessment method of major unsafe hydroelectric project
2008-01-01
Based on the characteristics of major unsafe hydroelectric projects and the data from field detection, in situ monitoring, and regular safety inspection, the funda-mental principles of operation risk assessment are proposed in this paper. Mean-while, a three layer hierarchical system is constructed, and an improved analytical hierarchical process combining genetic algorithm and analytical hierarchical process is established, with corresponding program. The operation risk of some unsafe dam was assessed with the principles, method and program presented in this paper and the major factors which would affect the operation of the dam were pointed out.
Theory of secondary vocational English project teaching method
张梅
2016-01-01
Under the impetus of the rapid development of science and technology and economy,Social productivity level and greatly enhance people's quality of life,education level also got further development.Under the influence of the globalization development trend,English gradually become the most widely used foreign language of people daily life. Secondary vocational English is a public basic course of secondary vocational school students, as an important part of secondary vocational students training plan, has received the widespread attention.In this study, secondary vocational English project teaching method is briefly discussed.
Risk assessment method of major unsafe hydroelectric project
WU ZhongRu; SU HuaiZhi; GUO HaiQing
2008-01-01
Based on the characteristics of major unsafe hydroelectric projects and the data from field detection, in situ monitoring, and regular safety inspection, the funda- menial principles of operation risk assessment are proposed in this paper. Mean- while, a three layer hierarchical system is constructed, and an improved analytical hierarchical process combining genetic algorithm and analytical hierarchical process is established, with corresponding program. The operation risk of some unsafe dam was assessed with the principles, method and program presented in this paper and the major factors which would affect the operation of the dam were pointed out.
The matching theorems and coincidence theorems for generalized R-KKM mapping in topological spaces
Huang, Jianhua
2005-12-01
In this paper we present some new matching theorems with open cover and closed cover by using the generalized R-KKM theorems [L. Deng, X. Xia, Generalized R-KKM theorem in topological space and their applications, J. Math. Anal. Appl. 285 (2003) 679-690] in the topological spaces with property (H). As applications, some coincidence theorems are established in topological spaces. Our results extend and generalize some known results.
Sutinen, Ari
2013-01-01
The project method became a famous teaching method when William Heard Kilpatrick published his article "Project Method" in 1918. The key idea in Kilpatrick's project method is to try to explain how pupils learn things when they work in projects toward different common objects. The same idea of pupils learning by work or action in an…
An elementary derivation of the quantum virial theorem from Hellmann-Feynman theorem
İpekoğlu, Y.; Turgut, S.
2016-07-01
A simple proof of the quantum virial theorem that can be used in undergraduate courses is given. The proof proceeds by first showing that the energy eigenvalues of a Hamiltonian remain invariant under a scale transformation. Then invoking the Hellmann-Feynman theorem produces the final statement of the virial theorem.
Study on Top-Down Estimation Method of Software Project Planning
ZHANG Jun-guang; L(U) Ting-jie; ZHAO Yu-mei
2006-01-01
This paper studies a new software project planning method under some actual project data in order to make software project plans more effective. From the perspective of system theory, our new method regards a software project plan as an associative unit for study. During a top-down estimation of a software project, Program Evaluation and Review Technique (PERT) method and analogy method are combined to estimate its size, then effort estimation and specific schedules are obtained according to distributions of the phase effort. This allows a set of practical and feasible planning methods to be constructed. Actual data indicate that this set of methods can lead to effective software project planning.
One-and-a-half quantum de Finetti theorems
Christandl, M; Mitchison, G; Renner, R; Christandl, Matthias; Koenig, Robert; Mitchison, Graeme; Renner, Renato
2006-01-01
We prove a new kind of quantum de Finetti theorem for representations of the unitary group U(d). Consider a pure state that lies in the irreducible representation U_{mu+nu} for Young diagrams mu and nu. U_{mu+nu} is contained in the tensor product of U_mu and U_nu; let xi be the state obtained by tracing out U_nu. We show that xi is close to a convex combination of states Uv, where U is in U(d) and v is the highest weight vector in U_mu. When U_{mu+nu} is the symmetric representation, this yields the conventional quantum de Finetti theorem for symmetric states, and our method of proof gives near-optimal bounds for the approximation of xi by a convex combination of product states. For the class of symmetric Werner states, we give a second de Finetti-style theorem (our 'half' theorem); the de Finetti-approximation in this case takes a particularly simple form, involving only product states with a fixed spectrum. Our proof uses purely group theoretic methods, and makes a link with the shifted Schur functions. It...
A method to study the management of urban development projects
Heurkens, E.
2011-01-01
The management of urban development projects in the Netherlands has changed significantly in recent years. These projects have become mainly ‘led’ by developers as they manage the entire life cycle of development projects, while public actors mainly facilitate development projects. This changes the
A method to study the management of urban development projects
Heurkens, E.
2011-01-01
The management of urban development projects in the Netherlands has changed significantly in recent years. These projects have become mainly ‘led’ by developers as they manage the entire life cycle of development projects, while public actors mainly facilitate development projects. This changes the
The Schur-Horn theorem for operators with finite spectrum
Bhat, B V Rajarama
2011-01-01
The carpenter problem in the context of $II_1$ factors, formulated by Kadison asks: Let $\\mathcal{A} \\subset \\mathcal{M}$ be a masa in a type $II_1$ factor and let $E$ be the normal conditional expectation from $\\mathcal{M}$ onto $\\mathcal{A}$. Then, is it true that for every positive contraction $A$ in $\\mathcal{A}$, there is a projection $P$ in $\\mathcal{M}$ such that $E(P) = A$? In this note, we show that this is true if $A$ has finite spectrum. We will then use this result to prove an exact Schur-Horn theorem for (positive)operators with finite spectrum and an approximate Schur-Horn theorem for general (positive)operators.
Narin Petrot
2009-01-01
Full Text Available We prove some strong convergence theorems for fixed points of modified Ishikawa and Halpern iterative processes for a countable family of hemi-relatively nonexpansive mappings in a uniformly convex and uniformly smooth Banach space by using the hybrid projection methods. Moreover, we also apply our results to a class of relatively nonexpansive mappings, and hence, we immediately obtain the results announced by Qin and Su's result (2007, Nilsrakoo and Saejung's result (2008, Su et al.'s result (2008, and some known corresponding results in the literatures.
THE EXISTENCE THEOREM OF OPTIMAL GROWTH MODEL
Gong Liutang; Peng Xianze
2005-01-01
This paper proves a general existence theorem of optimal growth theory. This theorem is neither restricted to the case of a constant technology progress, nor stated in terms of mathematical conditions which have no direct economic interpretation and moreover, are difficult to apply.
Euler and the Fundamental Theorem of Algebra.
Duham, William
1991-01-01
The complexity of the proof of the Fundamental Theorem of Algebra makes it inaccessible to lower level students. Described are more understandable attempts of proving the theorem and a historical account of Euler's efforts that relates the progression of the mathematical process used and indicates some of the pitfalls encountered. (MDH)
A note on the tolerated Tverberg theorem
2016-01-01
In this paper we give an asymptotically tight bound for the tolerated Tverberg Theorem when the dimension and the size of the partition are fixed. To achieve this we study certain partitions of order-type homogeneous sets and use a generalization of the Erd\\H{o}s-Szekeres theorem.
A New Fixed Point Theorem and Applications
Min Fang
2013-01-01
Full Text Available A new fixed point theorem is established under the setting of a generalized finitely continuous topological space (GFC-space without the convexity structure. As applications, a weak KKM theorem and a minimax inequalities of Ky Fan type are also obtained under suitable conditions. Our results are different from known results in the literature.
Double soft theorem for perturbative gravity
Saha, Arnab Priya
2016-09-01
Following up on the recent work of Cachazo, He and Yuan [1], we derive the double soft graviton theorem in perturbative gravity. We show that the double soft theorem derived using CHY formula precisely matches with the perturbative computation involving Feynman diagrams. In particular, we find how certain delicate limits of Feynman diagrams play an important role in obtaining this equivalence.
On the Hausdorff-Young theorem
Nasserddine, W
2005-01-01
Let $G_{mn}=ax + b$ be the matricial group of a local field. The Hausdorff-Young theorem for $G_{11}$ was proved by Eymard-Terp in 1978. We will establish here the Hausdorff-Young theorem for $G_{nn}$ for all $n \\in \\mathbb{N}$.
Abel's theorem in the noncommutative case
Leitenberger, Frank
2004-03-01
We define noncommutative binary forms. Using the typical representation of Hermite we prove the fundamental theorem of algebra and we derive a noncommutative Cardano formula for cubic forms. We define quantized elliptic and hyperelliptic differentials of the first kind. Following Abel we prove Abel's theorem.
A New Type of Singularity Theorem
Senovilla, José M M
2007-01-01
A new type of singularity theorem, based on spatial averages of physical quantities, is presented and discussed. Alternatively, the results inform us of when a spacetime can be singularity-free. This theorem provides a decisive observational difference between singular and non-singular, globally hyperbolic, open cosmological models.
Interpolation theorems on weighted Lorentz martingale spaces
2007-01-01
In this paper several interpolation theorems on martingale Lorentz spaces are given.The proofs are based on the atomic decompositions of martingale Hardy spaces over weighted measure spaces.Applying the interpolation theorems,we obtain some inequalities on martingale transform operator.
The Euler Line and Nine-Point-Circle Theorems.
Eccles, Frank M.
1999-01-01
Introduces the Euler line theorem and the nine-point-circle theorem which emphasize transformations and the power of functions in a geometric concept. Presents definitions and proofs of theorems. (ASK)
Pointwise ergodic theorems beyond amenable groups
Bowen, Lewis
2011-01-01
We prove pointwise and maximal ergodic theorems for probability measure preserving actions of any countable group, provided it admits an essentially free, weakly mixing amenable action of stable type III_r for some r >0. Our approach is based on the following two principles. First, it is possible to generalize the ergodic theory of measure-preserving actions of amenable groups to include probability-measure-preserving amenable equivalence relations. Second, it is possible to reduce the proof of ergodic theorems for actions of a general group to the proof of ergodic theorems in an associated measure-preserving amenable equivalence relation, provided the group admits an amenable action with the properties stated above. The general ergodic theorems established here are used in a sequel paper to prove mean and pointwise ergodic theorems for arbitrary Gromov-hyperbolic groups.
Generalized fluctuation theorems for classical systems
Agarwal, G S
2015-01-01
Fluctuation theorems have a very special place in the study of non equilibrium dynamics of physical systems. The form in which it is used most extensively is the Gallavoti-Cohen Fluctuation Theorem which is in terms of the distribution of the work $p(W)/p(-W)=\\exp(\\alpha W)$. We derive the general form of the fluctuation theorems for an arbitrary Gaussian Markov process and find conditions when the parameter $\\alpha$ becomes a universal parameter $1/kT$. As an application we consider fluctuation theorems for classical cyclotron motion of an electron in a parabolic potential. The motion of the electron is described by four coupled Langevin equations and thus is non-trivial. The generalized theorems are equally valid for non-equilibrium steady states.
Reflections on the PBR Theorem: Reality Criteria & Preparation Independence
Shane Mansfield
2014-12-01
Full Text Available This paper contains initial work on attempting to bring recent developments in the foundations of quantum mechanics concerning the nature of the wavefunction within the scope of more logical and structural methods. A first step involves dualising a criterion for the reality of the wavefunction proposed by Harrigan & Spekkens, which was central to the Pusey-Barrett-Rudolph theorem. The resulting criterion has several advantages, including the avoidance of certain technical difficulties relating to sets of measure zero. By considering the 'reality' not of the wavefunction but of the observable properties of any ontological physical theory a new characterisation of non-locality and contextuality is found. Secondly, a careful analysis of preparation independence, one of the key assumptions of the PBR theorem, leads to a precise analogy with the kind of locality prohibited by Bell's theorem. Motivated by this, we propose a weakening of the assumption to something analogous to no-signalling. This amounts to allowing global or non-local correlations in the joint ontic state, which nevertheless do not allow for superluminal signalling. This is, at least, consistent with the Bell and Kochen-Specker theorems. We find a counter-example to the PBR argument, which violates preparation independence, but does satisfy this physically motivated assumption. The question of whether the PBR result can be strengthened to hold under the relaxed assumption is therefore posed.
Uniqueness theorems in linear elasticity
Knops, Robin John
1971-01-01
The classical result for uniqueness in elasticity theory is due to Kirchhoff. It states that the standard mixed boundary value problem for a homogeneous isotropic linear elastic material in equilibrium and occupying a bounded three-dimensional region of space possesses at most one solution in the classical sense, provided the Lame and shear moduli, A and J1 respectively, obey the inequalities (3 A + 2 J1) > 0 and J1>O. In linear elastodynamics the analogous result, due to Neumann, is that the initial-mixed boundary value problem possesses at most one solution provided the elastic moduli satisfy the same set of inequalities as in Kirchhoffs theorem. Most standard textbooks on the linear theory of elasticity mention only these two classical criteria for uniqueness and neglect altogether the abundant literature which has appeared since the original publications of Kirchhoff. To remedy this deficiency it seems appropriate to attempt a coherent description ofthe various contributions made to the study of uniquenes...
Strong converse theorems using Rényi entropies
Leditzky, Felix; Wilde, Mark M.; Datta, Nilanjana
2016-08-01
We use a Rényi entropy method to prove strong converse theorems for certain information-theoretic tasks which involve local operations and quantum (or classical) communication between two parties. These include state redistribution, coherent state merging, quantum state splitting, measurement compression with quantum side information, randomness extraction against quantum side information, and data compression with quantum side information. The method we employ in proving these results extends ideas developed by Sharma [preprint arXiv:1404.5940 [quant-ph] (2014)], which he used to give a new proof of the strong converse theorem for state merging. For state redistribution, we prove the strong converse property for the boundary of the entire achievable rate region in the (e, q)-plane, where e and q denote the entanglement cost and quantum communication cost, respectively. In the case of measurement compression with quantum side information, we prove a strong converse theorem for the classical communication cost, which is a new result extending the previously known weak converse. For the remaining tasks, we provide new proofs for strong converse theorems previously established using smooth entropies. For each task, we obtain the strong converse theorem from explicit bounds on the figure of merit of the task in terms of a Rényi generalization of the optimal rate. Hence, we identify candidates for the strong converse exponents for each task discussed in this paper. To prove our results, we establish various new entropic inequalities, which might be of independent interest. These involve conditional entropies and mutual information derived from the sandwiched Rényi divergence. In particular, we obtain novel bounds relating these quantities, as well as the Rényi conditional mutual information, to the fidelity of two quantum states.
Learning Unknown Structure in CRFs via Adaptive Gradient Projection Method
Wei Xue
2016-08-01
Full Text Available We study the problem of fitting probabilistic graphical models to the given data when the structure is not known. More specifically, we focus on learning unknown structure in conditional random fields, especially learning both the structure and parameters of a conditional random field model simultaneously. To do this, we first formulate the learning problem as a convex minimization problem by adding an l_2-regularization to the node parameters and a group l_1-regularization to the edge parameters, and then a gradient-based projection method is proposed to solve it which combines an adaptive stepsize selection strategy with a nonmonotone line search. Extensive simulation experiments are presented to show the performance of our approach in solving unknown structure learning problems.
Various Tunnel Excavation Methods used on the LHC Project
Fielder, R
2000-01-01
Civil Engineering construction work for the LHC Project began in April 1998 and is now well underway. A major part of this work is the construction of the new tunnels, caverns and cavern enlargements for the LHC experiments and machine. Currently, this underground work is being carried out for the two injection tunnels, TI2 and TI8, and at Point 1 for the Atlas Experiment. There are three contractors involved in these tunnelling works and each contactor is using a different technique. This paper will outline the different methods used for excavation and the reasons for these differences. It will also examine the other operations involved in the construction of major underground structures such as supply of materials to the tunnel face, evacuation of excavated material and ventilation.
Singlet and triplet instability theorems
Yamada, Tomonori; Hirata, So
2015-09-01
A useful definition of orbital degeneracy—form-degeneracy—is introduced, which is distinct from the usual energy-degeneracy: Two canonical spatial orbitals are form-degenerate when the energy expectation value in the restricted Hartree-Fock (RHF) wave function is unaltered upon a two-electron excitation from one of these orbitals to the other. Form-degenerate orbitals tend to have isomorphic electron densities and occur in the highest-occupied and lowest-unoccupied molecular orbitals (HOMOs and LUMOs) of strongly correlated systems. Here, we present a mathematical proof of the existence of a triplet instability in a real or complex RHF wave function of a finite system in the space of real or complex unrestricted Hartree-Fock wave functions when HOMO and LUMO are energy- or form-degenerate. We also show that a singlet instability always exists in a real RHF wave function of a finite system in the space of complex RHF wave functions, when HOMO and LUMO are form-degenerate, but have nonidentical electron densities, or are energy-degenerate. These theorems provide Hartree-Fock-theory-based explanations of Hund's rule, a singlet instability in Jahn-Teller systems, biradicaloid electronic structures, and a triplet instability during some covalent bond breaking. They also suggest (but not guarantee) the spontaneous formation of a spin density wave (SDW) in a metallic solid. The stability theory underlying these theorems extended to a continuous orbital-energy spectrum proves the existence of an oscillating (nonspiral) SDW instability in one- and three-dimensional homogeneous electron gases, but only at low densities or for strong interactions.
Xiang Ding
2014-01-01
Full Text Available Project delivery planning is a key stage used by the project owner (or project investor for organizing design, construction, and other operations in a construction project. The main task in this stage is to select an appropriate project delivery method. In order to analyze different factors affecting the PDM selection, this paper establishes a multiagent model mainly to show how project complexity, governance strength, and market environment affect the project owner’s decision on PDM. Experiment results show that project owner usually choose Design-Build method when the project is very complex within a certain range. Besides, this paper points out that Design-Build method will be the prior choice when the potential contractors develop quickly. This paper provides the owners with methods and suggestions in terms of showing how the factors affect PDM selection, and it may improve the project performance.
Posterior Probability and Fluctuation Theorem in Stochastic Processes
Ohkubo, Jun
2009-12-01
A generalization of fluctuation theorems in stochastic processes is proposed. The new theorem is written in terms of posterior probabilities, which are introduced via Bayes’ theorem. In conventional fluctuation theorems, a forward path and its time reversal play an important role, so that a microscopically reversible condition is essential. In contrast, the microscopically reversible condition is not necessary in the new theorem. It is shown that the new theorem recovers various theorems and relations previously known, such as the Gallavotti-Cohen-type fluctuation theorem, the Jarzynski equality, and the Hatano-Sasa relation, when suitable assumptions are employed.
Investment Lending as a Method Of Investment Projects Financing
Svitlana Urvantseva
2014-01-01
The article deals with the genesis consideration of "investment loan" definition. The author provides comparative characteristics of the main forms of investment projects financing involving credit institution. A generalized definition of the project financing and investment lending essence are suggested.
Investment Lending as a Method Of Investment Projects Financing
Svitlana Urvantseva
2014-01-01
The article deals with the genesis consideration of "investment loan" definition. The author provides comparative characteristics of the main forms of investment projects financing involving credit institution. A generalized definition of the project financing and investment lending essence are suggested.
Modelling of Airship Flight Mechanics by the Projection Equivalent Method
Frantisek Jelenciak
2015-12-01
Full Text Available This article describes the projection equivalent method (PEM as a specific and relatively simple approach for the modelling of aircraft dynamics. By the PEM it is possible to obtain a mathematic al model of the aerodynamic forces and momentums acting on different kinds of aircraft during flight. For the PEM, it is a characteristic of it that - in principle - it provides an acceptable regression model of aerodynamic forces and momentums which exhibits reasonable and plausible behaviour from a dynamics viewpoint. The principle of this method is based on applying Newton's mechanics, which are then combined with a specific form of the finite element method to cover additional effects. The main advantage of the PEM is that it is not necessary to carry out measurements in a wind tunnel for the identification of the model’s parameters. The plausible dynamical behaviour of the model can be achieved by specific correction parameters, which can be determined on the basis of experimental data obtained during the flight of the aircraft. In this article, we present the PEM as applied to an airship as well as a comparison of the data calculated by the PEM and experimental flight data.
Modelling of Airship Flight Mechanics by the Projection Equivalent Method
Frantisek Jelenciak
2015-12-01
Full Text Available This article describes the projection equivalent method (PEM as a specific and relatively simple approach for the modelling of aircraft dynamics. By the PEM it is possible to obtain a mathematic al model of the aerodynamic forces and momentums acting on different kinds of aircraft during flight. For the PEM, it is a characteristic of it that -in principle - it provides an acceptable regression model of aerodynamic forces and momentums which exhibits reasonable and plausible behaviour from a dynamics viewpoint. The principle of this method is based on applying Newton's mechanics, which are then combined with a specific form of the finite element method to cover additional effects. The main advantage of the PEM is that it is not necessary to carry out measurements in a wind tunnel for the identification of the model's parameters. The plausible dynamical behaviour of the model can be achieved by specific correction parameters, which can be determined on the basis of experimental data obtained during the flight of the aircraft. In this article, we present the PEM as applied to an airship as well as a comparison of the data calculated by the PEM and experimental flight data.
Implementing Kernel Methods Incrementally by Incremental Nonlinear Projection Trick.
Kwak, Nojun
2016-05-20
Recently, the nonlinear projection trick (NPT) was introduced enabling direct computation of coordinates of samples in a reproducing kernel Hilbert space. With NPT, any machine learning algorithm can be extended to a kernel version without relying on the so called kernel trick. However, NPT is inherently difficult to be implemented incrementally because an ever increasing kernel matrix should be treated as additional training samples are introduced. In this paper, an incremental version of the NPT (INPT) is proposed based on the observation that the centerization step in NPT is unnecessary. Because the proposed INPT does not change the coordinates of the old data, the coordinates obtained by INPT can directly be used in any incremental methods to implement a kernel version of the incremental methods. The effectiveness of the INPT is shown by applying it to implement incremental versions of kernel methods such as, kernel singular value decomposition, kernel principal component analysis, and kernel discriminant analysis which are utilized for problems of kernel matrix reconstruction, letter classification, and face image retrieval, respectively.
YANG Min; JIN Xu-Ling; LI Bao-Lei
2010-01-01
In order to determine the projected coordinate origin in the cone-beam CT scanning system with respect to the Feldkamp-Davis-Kress(FDK)algorithm,we propose a simple yet feasible method to accurately measure the projected coordinate origin.This method was established on the basis of the theory that the projection of a spherical object in the cone-beam field is an ellipse.We first utilized image processing and the least square estimation method to get each major axis of the elliptical Digital Radiography(DR)projections of a group of spherical objects.Then we determined the intersection point of the group of major axis by solving an over-determined equation set that was composed by the major axis equations of all the elliptical projections.Based on the experimental results,this new method was proved to be easy to implement in practical scanning systems with high accuracy and anti-noise capability.
The pointwise Hellmann-Feynman theorem
David Carfì
2010-02-01
Full Text Available In this paper we study from a topological point of view the Hellmann-Feynman theorem of Quantum Mechanics. The goal of the paper is twofold: On one hand we emphasize the role of the strong topology in the classic version of the theorem in Hilbert spaces, for what concerns the kind of convergence required on the space of continuous linear endomorphisms, which contains the space of (continuous observables.On the other hand we state and prove a new pointwise version of the classic Hellmann-Feynman theorem. This new version is not yet present in the literature and follows the idea of A. Bohm concerning the topology which is desiderable to use in Quantum Mechanics. It is indeed out of question that this non-trivial new version of the Hellmann-Feynman theorem is the ideal one - for what concerns the continuous observables on Hilbert spaces, both from a theoretical point of view, since it is the strongest version obtainable in this context - we recall that the pointwise topology is the coarsest one compatible with the linear structure of the space of continuous observables -, and from a practical point of view, because the pointwise topology is the easiest to use among topologies: it brings back the problems to the Hilbert space topology. Moreover, we desire to remark that this basic theorem of Quantum Mechanics, in his most desiderable form, is deeply interlaced with two cornerstones of Functional Analysis: the Banach-Steinhaus theorem and the Baire theorem.
A projection method for under determined optimal experimental designs
Long, Quan
2014-01-09
A new implementation, based on the Laplace approximation, was developed in (Long, Scavino, Tempone, & Wang 2013) to accelerate the estimation of the post–experimental expected information gains in the model parameters and predictive quantities of interest. A closed–form approximation of the inner integral and the order of the corresponding dominant error term were obtained in the cases where the parameters are determined by the experiment. In this work, we extend that method to the general cases where the model parameters could not be determined completely by the data from the proposed experiments. We carry out the Laplace approximations in the directions orthogonal to the null space of the corresponding Jacobian matrix, so that the information gain (Kullback–Leibler divergence) can be reduced to an integration against the marginal density of the transformed parameters which are not determined by the experiments. Furthermore, the expected information gain can be approximated by an integration over the prior, where the integrand is a function of the projected posterior covariance matrix. To deal with the issue of dimensionality in a complex problem, we use Monte Carlo sampling or sparse quadratures for the integration over the prior probability density function, depending on the regularity of the integrand function. We demonstrate the accuracy, efficiency and robustness of the proposed method via several nonlinear under determined numerical examples.
New rates for exponential approximation and the theorems of R\\'enyi and Yaglom
Peköz, Erol
2009-01-01
We introduce two abstract theorems that reduce a variety of complex exponential distributional approximation problems to the construction of couplings. These are applied to obtain rates of convergence with respect to the Wasserstein and Kolmogorov metrics for the theorem of R\\'enyi on random sums and generalizations of it, hitting times for Markov chains, and to obtain a new rate for the classical theorem of Yaglom on the exponential asymptotic behavior of a critical Galton-Watson process conditioned on non-extinction. The primary tools are an adaptation of Stein's method, Stein couplings, as well as the equilibrium distributional transformation from renewal theory.
A rigorous proof of the scallop theorem and a finite mass effect of a microswimmer
Ishimoto, Kenta
2011-01-01
We reconsider fluid dynamics for a self-propulsive swimmer in Stokes flow. With an exact definition of deformation of a swimmer, a proof is given to Purcell's scallop theorem including the body rotation. The breakdown of the theorem due to a finite Stokes number is discussed by using a perturbation expansion method and it is found that the breakdown generally occurs at the first order of the Stokes number. In addition, employing the Purcell's "scallop" model, we show that the theorem holds up to a higher order if the strokes of the swimmer has some symmetry.
Haag's theorem in renormalised quantum field theories
Klaczynski, Lutz
2016-01-01
We review a package of no-go results in axiomatic quantum field theory with Haag's theorem at its centre. Since the concept of operator-valued distributions in this framework comes very close to what we believe canonical quantum fields are about, these results are of consequence to quantum field theory: they suggest the seeming absurdity that this highly victorious theory is incapable of describing interactions. We single out unitarity of the interaction picture's intertwiner as the most salient provision of Haag's theorem and critique canonical perturbation theory to argue that renormalisation bypasses Haag's theorem by violating this very assumption.
Effective randomness, strong reductions and Demuth's theorem
Bienvenu, Laurent
2011-01-01
We study generalizations of Demuth's Theorem, which states that the image of a Martin-L\\"of random real under a tt-reduction is either computable or Turing equivalent to a Martin-L\\"of random real. We show that Demuth's Theorem holds for Schnorr randomness and computable randomness (answering a question of Franklin), but that it cannot be strengthened by replacing the Turing equivalence in the statement of the theorem with wtt-equivalence. We also provide some additional results about the Turing and tt-degrees of reals that are random with respect to some computable measure.
Smagin, V. V.
1997-04-01
We consider a weakly solvable parabolic problem in a separable Hilbert space. We seek approximations to the exact solution by projective and projective-difference methods. In this connection the discretization of the problem with respect to the spatial variables is carried out by the semidiscrete method of Galerkin, and with respect to time by the implicit method of Euler. In this paper we establish a coercive mean-square error estimate for the approximate solutions. We illustrate the effectiveness of these estimates with parabolic equations of second order with Dirichlet or Neumann boundary conditions in projective subspaces of finite element type.
A hybrid incremental projection method for thermal-hydraulics applications
Christon, Mark A.; Bakosi, Jozsef; Nadiga, Balasubramanya T.; Berndt, Markus; Francois, Marianne M.; Stagg, Alan K.; Xia, Yidong; Luo, Hong
2016-07-01
A new second-order accurate, hybrid, incremental projection method for time-dependent incompressible viscous flow is introduced in this paper. The hybrid finite-element/finite-volume discretization circumvents the well-known Ladyzhenskaya-Babuška-Brezzi conditions for stability, and does not require special treatment to filter pressure modes by either Rhie-Chow interpolation or by using a Petrov-Galerkin finite element formulation. The use of a co-velocity with a high-resolution advection method and a linearly consistent edge-based treatment of viscous/diffusive terms yields a robust algorithm for a broad spectrum of incompressible flows. The high-resolution advection method is shown to deliver second-order spatial convergence on mixed element topology meshes, and the implicit advective treatment significantly increases the stable time-step size. The algorithm is robust and extensible, permitting the incorporation of features such as porous media flow, RANS and LES turbulence models, and semi-/fully-implicit time stepping. A series of verification and validation problems are used to illustrate the convergence properties of the algorithm. The temporal stability properties are demonstrated on a range of problems with 2 ≤ CFL ≤ 100. The new flow solver is built using the Hydra multiphysics toolkit. The Hydra toolkit is written in C++ and provides a rich suite of extensible and fully-parallel components that permit rapid application development, supports multiple discretization techniques, provides I/O interfaces, dynamic run-time load balancing and data migration, and interfaces to scalable popular linear solvers, e.g., in open-source packages such as HYPRE, PETSc, and Trilinos.
刘原华; 牛新亮; 张美玲
2014-01-01
为增大QC-LDPC码围长的同时减少码中包含的短环，提高其纠错性能，提出了一种基于中国剩余定理( CRT)的QC-LDPC码改进联合构造方法。该方法将设计围长为g的长码长的QC-LD-PC码的问题简化为设计一个围长为g的短分量码的问题，然后通过对其余分量码校验矩阵的列块进行适当置换，使得构造出的QC-LDPC码具有更少的短环和更优的性能，更适于可靠性要求较高的通信系统。仿真结果表明，与已有的CRT联合构造方法设计的QC-LDPC码相比，新方法构造的QC-LDPC码具有更少的短环，在误码率为10-6时获得了1.2 dB的编码增益。%An improved combining method for designing quasi-cyclic low-density parity-check ( QC-LD-PC) codes based on Chinese Remainder Theorem( CRT) is proposed to improve the error-correcting per-formance by increasing the girth and decreasing the number of short cycles. With the CRT combining method,the difficult problem of designing QC-LDPC codes with girth g is translated into a task of desig-ning one component code with girth g. By properly permuting the column blocks of parity-check matrices of other component codes,a lot of QC-LDPC codes with much shorter cycles and better performance can be designed,which are more suitable for communication systems with request of high reliability. Simulations show that compared with existing CRT-based QC-LDPC codes,the proposed QC-LDPC codes have much shorter cycles and obtain 1. 2 dB coding gain at bit error rate(BER) of 10-6.
Security Theorems via Model Theory
Joshua Guttman
2009-11-01
Full Text Available A model-theoretic approach can establish security theorems for cryptographic protocols. Formulas expressing authentication and non-disclosure properties of protocols have a special form. They are quantified implications for all xs . (phi implies for some ys . psi. Models (interpretations for these formulas are *skeletons*, partially ordered structures consisting of a number of local protocol behaviors. *Realized* skeletons contain enough local sessions to explain all the behavior, when combined with some possible adversary behaviors. We show two results. (1 If phi is the antecedent of a security goal, then there is a skeleton A_phi such that, for every skeleton B, phi is satisfied in B iff there is a homomorphism from A_phi to B. (2 A protocol enforces for all xs . (phi implies for some ys . psi iff every realized homomorphic image of A_phi satisfies psi. Hence, to verify a security goal, one can use the Cryptographic Protocol Shapes Analyzer CPSA (TACAS, 2007 to identify minimal realized skeletons, or "shapes," that are homomorphic images of A_phi. If psi holds in each of these shapes, then the goal holds.
Index theorems for quantum graphs
Fulling, S A; Wilson, J H
2007-01-01
In geometric analysis, an index theorem relates the difference of the numbers of solutions of two differential equations to the topological structure of the manifold or bundle concerned, sometimes using the heat kernels of two higher-order differential operators as an intermediary. In this paper, the case of quantum graphs is addressed. A quantum graph is a graph considered as a (singular) one-dimensional variety and equipped with a second-order differential Hamiltonian H (a "Laplacian") with suitable conditions at vertices. For the case of scale-invariant vertex conditions (i.e., conditions that do not mix the values of functions and of their derivatives), the constant term of the heat-kernel expansion is shown to be proportional to the trace of the internal scattering matrix of the graph. This observation is placed into the index-theory context by factoring the Laplacian into two first-order operators, H =A*A, and relating the constant term to the index of A. An independent consideration provides an index f...
Applications of the ergodic iteration theorem
Zapletal, J.
2010-01-01
I prove several natural preservation theorems for the countable support iteration. This solves a question of Roslanowski regarding the preservation of localization properties and greatly simplifies the proofs in the area.
The virial theorem for nonlinear problems
Amore, Paolo [Facultad de Ciencias, Universidad de Colima, Bernal DIaz del Castillo 340, Colima (Mexico); Fernandez, Francisco M [INIFTA (UNLP, CCT La Plata-CONICET), Division Quimica Teorica, Blvd 113 S/N, Sucursal 4, Casilla de Correo 16, 1900 La Plata (Argentina)], E-mail: paolo.amore@gmail.com, E-mail: fernande@quimica.unlp.edu.ar
2009-09-15
We show that the virial theorem provides a useful simple tool for approximating nonlinear problems. In particular, we consider conservative nonlinear oscillators and obtain the same main result derived earlier from the expansion in Chebyshev polynomials. (letters and comments)
Transformation groups and the virial theorem
Kampen, N.G. van
1972-01-01
A generalization of Noether's result for classical mechanics is given, which shows that the virial theorem is related to an invariance property of the Lagrange function. Two examples are discussed in detail.
Dimensional analysis beyond the Pi theorem
Zohuri, Bahman
2017-01-01
Dimensional Analysis and Physical Similarity are well understood subjects, and the general concepts of dynamical similarity are explained in this book. Our exposition is essentially different from those available in the literature, although it follows the general ideas known as Pi Theorem. There are many excellent books that one can refer to; however, dimensional analysis goes beyond Pi theorem, which is also known as Buckingham’s Pi Theorem. Many techniques via self-similar solutions can bound solutions to problems that seem intractable. A time-developing phenomenon is called self-similar if the spatial distributions of its properties at different points in time can be obtained from one another by a similarity transformation, and identifying one of the independent variables as time. However, this is where Dimensional Analysis goes beyond Pi Theorem into self-similarity, which has represented progress for researchers. In recent years there has been a surge of interest in self-similar solutions of the First ...
Two No-Go Theorems on Superconductivity
Tada, Yasuhiro
2016-01-01
We study lattice superconductors such as attractive Hubbard models. As is well known, Bloch's theorem asserts absence of persistent current in ground states and equilibrium states for general fermion systems. While the statement of the theorem is true, we can show that the theorem cannot exclude possibility of a surface persistent current. Such a current can be stabilized by boundary magnetic fields which do not penetrate into the bulk region of a superconductor, provided emergence of massive photons, i.e., Meissner effect. Therefore, we can expect that a surface persistent current is realized for a ground/equilibrium state in the sense of stability against local perturbations. We also apply Elitzur's theorem to superconductors at finite temperatures. As a result, we prove absence of symmetry breaking of the global U(1) phase of electrons for almost all gauge fixings. These observations suggest that the nature of superconductivity is the emergence of massive photons rather than the symmetry breaking of the U(...
Rank theorems of operators between Banach spaces
2000-01-01
Let E and F be Banach spaces, and B( E, F) all of bounded linear operators on E into F. Let T0 ∈ B( E, F) with an outer inverse T0# ∈ B( F, E). Then a characteristic condition of S= (I + T0# ( T- T0))-1 T0# with T∈ B( E, F) and || T0# ( T- T0) || < 1, being a generalized inverse of T, is presented, and hence, a rank theorem of operators on E into F is established (which generalizes the rank theorem of matrices to Banach spaces). Consequently, an improved finite rank theorem and a new rank theorem are deduced. These results will be very useful to nonlinear functional analysis.
Rank theorems of operators between Banach spaces
无
2000-01-01
Let E and F be Banach spaces, and B(E,F) all of bounded linear operators on E into F. Let T0∈B(E,F) with an outer inverse T#0∈B(F,E). Then a characteristic condition of S=(I+T#0(T-T0))-1T#0 with T∈B(E,F) and ‖T#0(T-T0)‖<1, being a generalized inverse of T, is presented, and hence, a rank theorem of operators on E into F is established (which generalizes the rank theorem of matrices to Banach spaces). Consequently, an improved finite rank theorem and a new rank theorem are deduced. These results will be very useful to nonlinear functional analysis.
A generalized preimage theorem in global analysis
无
2001-01-01
The concept of locally fine point and generalized regular valueof a C1 map between Banach spaces were carried over C1 map between Banach manifolds. Hence the preimage theorem, a principle constructing Banach manifolds in global analysis, is generalized.
Utilizing the Project Method for Teaching Culture and Intercultural Competence
Euler, Sasha S.
2017-01-01
This article presents a detailed methodological outline for teaching culture through project work. It is argued that because project work makes it possible to gain transferrable and applicable knowledge and insight, it is the ideal tool for teaching culture with the aim of achieving real intercultural communicative competence (ICC). Preceding the…
Social Science Methods Used in the RESTORE Project
Lynne M. Westphal; Cristy Watkins; Paul H. Gobster; Liam Heneghan; Kristen Ross; Laurel Ross; Madeleine Tudor; Alaka Wali; David H. Wise; Joanne Vining; Moira. Zellner
2014-01-01
The RESTORE (Rethinking Ecological and Social Theories of Restoration Ecology) project is an interdisciplinary, multi-institutional research endeavor funded by the National Science Foundation's Dynamics of Coupled Natural Human Systems program. The goal of the project is to understand the links between organizational type, decision making processes, and...
A note on the proof of Bertrand's theorem
Jovanović Vladimir
2015-01-01
Full Text Available In this paper we fill a common gap in the proof of Bertrand' theorem present both the in Bertrand's original paper Théorème relatif au movement d'un point attiré vers un centre fixe and in the Arnold's book Mathematical methods of classical mechanics, by providing missing details which pertain to the problem of how to single out elastic and gravitational potentials among the power law ones.
A note on the proof of Bertrand's theorem
Jovanović Vladimir
2015-01-01
In this paper we fill a common gap in the proof of Bertrand' theorem present both the in Bertrand's original paper Théorème relatif au movement d'un point attiré vers un centre fixe and in the Arnold's book Mathematical methods of classical mechanics, by providing missing details which pertain to the problem of how to single out elastic and gravitational potentials among the power law ones.
Noether theorem for Birkhoffian systems on time scales
Song, Chuan-Jing; Zhang, Yi
2015-10-01
Birkhoff equations on time scales and Noether theorem for Birkhoffian system on time scales are studied. First, some necessary knowledge of calculus on time scales are reviewed. Second, Birkhoff equations on time scales are obtained. Third, the conditions for invariance of Pfaff action and conserved quantities are presented under the special infinitesimal transformations and general infinitesimal transformations, respectively. Fourth, some special cases are given. And finally, an example is given to illustrate the method and results.
Adaptive Fuzzy Robust Control for a Class of Nonlinear Systems via Small Gain Theorem
Xingjian Wang
2013-01-01
Full Text Available Practical nonlinear systems can usually be represented by partly linearizable models with unknown nonlinearities and external disturbances. Based on this consideration, we propose a novel adaptive fuzzy robust control (AFRC algorithm for such systems. The AFRC effectively combines techniques of adaptive control and fuzzy control, and it improves the performance by retaining the advantages of both methods. The linearizable part will be linearly parameterized with unknown but constant parameters, and the discontinuous-projection-based adaptive control law is used to compensate these parts. The Takagi-Sugeno fuzzy logic systems are used to approximate unknown nonlinearities. Robust control law ensures the robustness of closed-loop control system. A systematic design procedure of the AFRC algorithm by combining the backstepping technique and small-gain approach is presented. Then the closed-loop stability is studied by using small gain theorem, and the result indicates that the closed-loop system is semiglobally uniformly ultimately bounded.
Sahoo- and Wayment-Type Integral Mean Value Theorems
Tiryaki, Aydin; Cakmak, Devrim
2010-01-01
In this article, by using Rolle's theorem, we establish some results related to the mean value theorem for integrals. Our results are different from the set of integral mean value theorems which are given by Wayment ["An integral mean value theorem", Math. Gazette 54 (1970), pp. 300-301] and Sahoo ["Some results related to the integral mean value…
A New GLKKM Theorem and Its Application to Abstract Economies
WEN Kai-ting
2012-01-01
In this paper,a new GLKKM theorem in L-convex spaces is established.As applications,a new fixed point theorem and a maximal element theorem are obtained in Lconvex spaces.Finally,equilibrium existence theorems for abstract economies and qualitative games in L-convex spaces are yielded.
Sahoo- and Wayment-Type Integral Mean Value Theorems
Tiryaki, Aydin; Cakmak, Devrim
2010-01-01
In this article, by using Rolle's theorem, we establish some results related to the mean value theorem for integrals. Our results are different from the set of integral mean value theorems which are given by Wayment ["An integral mean value theorem", Math. Gazette 54 (1970), pp. 300-301] and Sahoo ["Some results related to the integral mean value…
EQUIVALENCE OF REFINED THEORY AND DECOMPOSED THEOREM OF AN ELASTIC PLATE
ZHAO Bao-sheng; WANG Min-zhong
2005-01-01
A connection between Cheng's refined theory and Gregory's decomposed theorem is analyzed. The equivalence of the refined theory and the decomposed theorem is given. Using operator matrix determinant of partial differential equation, Cheng gained one equation, and he substituted the sum of the general integrals of three differential equations for the solution of the equation. But he did not prove the rationality of substitute. There, a whole proof for the refined theory from Papkovich-Neuber solution was given. At first expressions were obtained for all the displacements and stress components in term of the midplane displacement and its derivatives. Using Lur'e method and the theorem of appendix,the refined theory was given. At last, using basic mathematic method, the equivalence between Cheng's refined theory and Gregory's decomposed theorem was proved, i.e.,Cheng' s bi-harmonic equation, shear equation and transcendental equation are equivalent to Gregory's interior state, shear state and Papkovich-Fadle state, respectively.
Double Soft Theorem for Perturbative Gravity
Saha, Arnab Priya
2016-01-01
Following up on the recent work of Cachazo, He and Yuan \\cite{arXiv:1503.04816 [hep-th]}, we derive the double soft graviton theorem in perturbative gravity. We show that the double soft theorem derived using CHY formula precisely matches with the perturbative computation involving Feynman diagrams. In particular, we find how certain delicate limits of Feynman diagrams play an important role in obtaining this equivalence.
Transversality theorems for the weak topology
2011-01-01
In his 1979 paper Trotman proves, using the techniques of the Thom transversality theorem, that under some conditions on the dimensions of the manifolds under consideration, openness of the set of maps transverse to a stratification in the strong (Whitney) topology implies that the stratification is $(a)$-regular. Here we first discuss the Thom transversality theorem for the weak topology and then give a similiar kind of result for the weak topology, under very weak hypotheses. Recently sever...
Optical theorem for Aharonov-Bohm scattering
Sitenko, Yu A
2011-01-01
Quantum-mechanical scattering off an impermeable magnetic vortex is considered and the optical theorem is derived. The nonvanishing transverse size of the vortex is taken into account, and the Robin boundary condition is imposed on the particle wave function at the edge of the vortex. The persistence of the Fraunhofer diffraction in the short-wavelength limit is shown to be crucial for maintaining the optical theorem in the quasiclassical limit.
The large deviations theorem and ergodicity
Gu Rongbao [School of Finance, Nanjing University of Finance and Economics, Nanjing 210046 (China)
2007-12-15
In this paper, some relationships between stochastic and topological properties of dynamical systems are studied. For a continuous map f from a compact metric space X into itself, we show that if f satisfies the large deviations theorem then it is topologically ergodic. Moreover, we introduce the topologically strong ergodicity, and prove that if f is a topologically strongly ergodic map satisfying the large deviations theorem then it is sensitively dependent on initial conditions.
Herbrand's theorem and non-Euclidean geometry
Beeson, Michael; Boutry, Pierre; Narboux, Julien
2014-01-01
International audience; We use Herbrand's theorem to give a new proof that Eu- clid's parallel axiom is not derivable from the other axioms of first-order Euclidean geometry. Previous proofs involve constructing models of non- Euclidean geometry. This proof uses a very old and basic theorem of logic together with some simple properties of ruler-and-compass constructions to give a short, simple, and intuitively appealing proof.
Ruixiang XING
2009-01-01
In this paper,we derive an upper bound estimate of the blow-up rate for positive solutions of indefinite parabolic equations from Liouville type theorems. We also use moving plane method to prove the related Liouville type theorems for semilinear parabolic problems.
Mental Constructions for The Group Isomorphism Theorem
Arturo Mena-Lorca
2016-03-01
Full Text Available The group isomorphism theorem is an important subject in any abstract algebra undergraduate course; nevertheless, research shows that it is seldom understood by students. We use APOS theory and propose a genetic decomposition that separates it into two statements: the first one for sets and the second with added structure. We administered a questionnaire to students from top Chilean universities and selected some of these students for interviews to gather information about the viability of our genetic decomposition. The students interviewed were divided in two groups based on their familiarity with equivalence relations and partitions. Students who were able to draw on their intuition of partitions were able to reconstruct the group theorem from the set theorem, while those who stayed on the purely algebraic side could not. Since our approach to learning this theorem was successful, it may be worthwhile to gather data while teaching it the way we propose here in order to check how much the learning of the group isomorphism theorem is improved. This approach could be expanded to other group homomorphism theorems provided further analysis is conducted: going from the general (e.g., sets to the particular (e.g., groups might not always the best strategy, but in some cases we may just be turning to more familiar settings.
A novel sampling theorem on the sphere
McEwen, J D
2011-01-01
We develop a novel sampling theorem on the sphere and corresponding fast algorithms by associating the sphere with the torus through a periodic extension. The fundamental property of any sampling theorem is the number of samples required to represent a band-limited signal. To represent exactly a signal on the sphere band-limited at L, all sampling theorems on the sphere require O(L^2) samples. However, our sampling theorem requires less than half the number of samples of other equiangular sampling theorems on the sphere and an asymptotically identical, but smaller, number of samples than the Gauss-Legendre sampling theorem. The complexity of our algorithms scale as O(L^3), however, the continual use of fast Fourier transforms reduces the constant prefactor associated with the asymptotic scaling considerably, resulting in algorithms that are fast. Furthermore, we do not require any precomputation and our algorithms apply to both scalar and spin functions on the sphere without any change in computational comple...
Khare, A; Paranjape, M B; Khare, Avinash; MacKenzie, R; Paranjape, M B
1994-01-01
The Coleman-Hill theorem prohibits the appearance of radiative corrections to the topological mass (more precisely, to the parity-odd part of the vacuum polarization tensor at zero momentum) in a wide class of abelian gauge theories in 2+1 dimensions. We re-express the theorem in terms of the effective action rather than in terms of the vacuum polarization tensor. The theorem so restated becomes somewhat stronger: a known exception to the theorem, spontaneously broken scalar Chern-Simons electrodynamics, obeys the new non-renormalization theorem. Whereas the vacuum polarization {\\sl does} receive a one-loop, parity-odd correction, this does not translate to a radiative contribution to the Chern-Simons term in the effective action. We also point out a new situation, involving scalar fields and parity-odd couplings, which was overlooked in the original analysis, where the conditions of the theorem are satisfied and where the topological mass does, in fact, get a radiative correction.
The modified Poynting theorem and the concept of mutual energy
Zhao, Shuang-ren; Yang, Kang; Yang, Xingang; Yang, Xintie
2015-01-01
The Poynting theorem is generalized to the modified Poynting theorem. In the modified Poynting theorem the electromagnetic field is superimposition of different electromagnetic fields including the field of retarded potential and advanced potential. The media epsilon (permittivity) and mu (permeability) can also be different in the different fields. The concept of mutual energy is introduced which is the difference between the total energy and self-energy. Using the modified Poynting theorem with the concept of the mutual energy the modified mutual energy theorem is derived. Applying time-offset transform and time integral to the modified mutual energy theorem, the time-correlation modified mutual energy theorem is obtained. Assume there are only two fields which are retarded potential, and there is only one media, the modified time-correlation energy theorem becomes the time-correlation energy theorem, which is also referred as the time-correlation reciprocity theorem. Assume there are two electromagnetic fi...
Poincaré recurrence theorem for non-smooth vector fields
Euzébio, Rodrigo D.; Gouveia, Márcio R. A.
2017-04-01
In this paper, some ergodic aspects of non-smooth vector fields are studied. More specifically, the concepts of recurrence and invariance of a measure by a flow are discussed, and two versions of the classical Poincaré Recurrence Theorem are presented. The results allow us to soften the hypothesis of the classical Poincaré Recurrence Theorem by admitting non-smooth multivalued flows. The methods used in order to prove the results involve elements from both measure theory and topology.
QIAO Yong-Fen; ZHAO Shu-Hong
2006-01-01
The conservation theorems of the generalized Lagrangian equations for nonconservative mechanical system are studied by using method of integrating factors. Firstly, the differential equations of motion of system are given, and the definition of integrating factors is given. Next, the necessary conditions for the existence of the conserved quantity are studied in detail. Finally, the conservation theorem and its inverse for the system are established, and an example is given to illustrate the application of the result.
Noise-Resistant Quantum Teleportation, Ansibles, and the No-Projector Theorem
Hedemann, Samuel R
2016-01-01
A method is presented for achieving entanglement-free teleportation of a quantum state subject to any quantum noise. We apply this as a light-speed noise-resistant communicator, but also treat the possibility of a quantum ansible, a device for effectively superluminal communication and quantum broadcasting. The results suggest a "no-projector theorem" analogous to the no-cloning theorem. We then show how to build a pseudo-ansible for connection-free light-speed communication.
Lei DENG; Ming Ge YANG
2006-01-01
Some new coincidence theorems involving admissible set-valued mappings are proved in general noncompact topological spaces. As applications, some new minimax inequalities, section theorem, best approximation theorem, existence theorems of weighted Nash equilibria and Pareto equilibria for multiobjective games are given in general topological spaces.
Limit Theorems For Closed Queuing Networks With Excess Of Servers
Tsitsiashvili, G.
2013-01-01
In this paper limit theorems for closed queuing networks with excess of servers are formulated and proved. First theorem is a variant of the central limit theorem and is proved using classical results of V.I. Romanovskiy for discrete Markov chains. Second theorem considers a convergence to chi square distribution. These theorems are mainly based on an assumption of servers excess in queuing nodes.
On multigrid methods for image reconstruction from projections
Henson, V.E.; Robinson, B.T. [Naval Postgraduate School, Monterey, CA (United States); Limber, M. [Simon Fraser Univ., Burnaby, British Columbia (Canada)
1994-12-31
The sampled Radon transform of a 2D function can be represented as a continuous linear map R : L{sup 1} {yields} R{sup N}. The image reconstruction problem is: given a vector b {element_of} R{sup N}, find an image (or density function) u(x, y) such that Ru = b. Since in general there are infinitely many solutions, the authors pick the solution with minimal 2-norm. Numerous proposals have been made regarding how best to discretize this problem. One can, for example, select a set of functions {phi}{sub j} that span a particular subspace {Omega} {contained_in} L{sup 1}, and model R : {Omega} {yields} R{sup N}. The subspace {Omega} may be chosen as a member of a sequence of subspaces whose limit is dense in L{sup 1}. One approach to the choice of {Omega} gives rise to a natural pixel discretization of the image space. Two possible choices of the set {phi}{sub j} are the set of characteristic functions of finite-width `strips` representing energy transmission paths and the set of intersections of such strips. The authors have studied the eigenstructure of the matrices B resulting from these choices and the effect of applying a Gauss-Seidel iteration to the problem Bw = b. There exists a near null space into which the error vectors migrate with iteration, after which Gauss-Seidel iteration stalls. The authors attempt to accelerate convergence via a multilevel scheme, based on the principles of McCormick`s Multilevel Projection Method (PML). Coarsening is achieved by thickening the rays which results in a much smaller discretization of an optimal grid, and a halving of the number of variables. This approach satisfies all the requirements of the PML scheme. They have observed that a multilevel approach based on this idea accelerates convergence at least to the point where noise in the data dominates.
Function Projective Synchronization of Two Identical New Hyperchaotic Systems
无
2007-01-01
A function projective synchronization of two identical hyperchaotic systems is defined and the theorem of sufficient condition is given. Based on the active control method and symbolic computation Maple, the scheme of function projective synchronization is developed to synchronize the two identical new hyperchaotic systems constructed by Yan up to a scaling function matrix with different initial values. Numerical simulations are used to verify the effectiveness of the scheme.
Inverse Finite Element Method Investigation for Adaptive Structures Project
National Aeronautics and Space Administration — This research project is evaluating an innovative technique that uses fiber optic strain sensors to measure structural deformations and full field strains. An...
Low Cost Method of Manufacturing Space Optics Project
National Aeronautics and Space Administration — The Phase I project successfully demonstrated the feasibility of developing a technology that will reduce cost and manufacturing time, broaden design options, and...
About Shape Identification Methods of Objects Invariant to Projective Transformations
Gostev Ivan M.
2016-01-01
Full Text Available Diffculties concerning the choice of the invariants of the projective transformation groups used for the identification of the shapes of planar objects are illustrated and solutions allowing the derivation of robust identification criteria are discussed.
The g-theorem and quantum information theory
Casini, Horacio; Torroba, Gonzalo
2016-01-01
We study boundary renormalization group flows between boundary conformal field theories in $1+1$ dimensions using methods of quantum information theory. We define an entropic $g$-function for theories with impurities in terms of the relative entanglement entropy, and we prove that this $g$-function decreases along boundary renormalization group flows. This entropic $g$-theorem is valid at zero temperature, and is independent from the $g$-theorem based on the thermal partition function. We also discuss the mutual information in boundary RG flows, and how it encodes the correlations between the impurity and bulk degrees of freedom. Our results provide a quantum-information understanding of (boundary) RG flow as increase of distinguishability between vacuum states.
The g-theorem and quantum information theory
Casini, Horacio; Landea, Ignacio Salazar; Torroba, Gonzalo
2016-10-01
We study boundary renormalization group flows between boundary conformal field theories in 1 + 1 dimensions using methods of quantum information theory. We define an entropic g-function for theories with impurities in terms of the relative entanglement entropy, and we prove that this g-function decreases along boundary renormalization group flows. This entropic g-theorem is valid at zero temperature, and is independent from the g-theorem based on the thermal partition function. We also discuss the mutual information in boundary RG flows, and how it encodes the correlations between the impurity and bulk degrees of freedom. Our results provide a quantum-information understanding of (boundary) RG flow as increase of distinguishability between the UV fixed point and the theory along the RG flow.
Gleason's Theorem for Rectangular JBW-Triples
Edwards, C. Martin; Rüttimann, Gottfried T.
A JBW*-triple B is said to be rectangular if there exists a W*-algebra A and a pair (p,q) of centrally equivalent elements of the complete orthomodular lattice of projections in A such that B is isomorphic to the JBW*-triple pAq. Any weak*-closed injective operator space provides an example of a rectangular JBW*-triple. The principal order ideal of the complete *-lattice of centrally equivalent pairs of projections in a W*-algebra A, generated by (p,q), forms a complete lattice that is order isomorphic to the complete lattice of weak*-closed inner ideals in B and to the complete lattice of structural projections on B. Although not itself, in general, orthomodular, possesses a complementation that allows for definitions of orthogonality, centre, and central orthogonality to be given. A less familiar notion in lattice theory, that is well-known in the theory of Jordan algebras and Jordan triple systems, is that of rigid collinearity of a pair (e2,f2) and (e2,f2) of elements of . This is defined and characterized in terms of properties of . A W*-algebra A is sometimes thought of as providing a model for a statistical physical system. In this case B, or, equivalently, pAq, may be thought of as providing a model for a fixed sub-system of that represented by A. Therefore, may be considered to represent the set consisting of a particular kind of sub-system of that represented by pAq. Central orthogonality and rigid collinearity of pairs of elements of may be regarded as representing two different types of disjointness, the former, classical disjointness, and the latter, decoherence, of the two sub-systems. It is therefore natural to consider bounded measures m on that are additive on centrally orthogonal and rigidly collinear pairs of elements. Using results of J.D.M. Wright, it is shown that, provided that neither of the two hereditary sub-W*-algebras pAp and qAq of A has a weak*-closed ideal of Type I2, such measures are precisely those that are the restrictions of
Analysis of Conflict Centers in Projects Procured with Traditional and Integrated Methods in Nigeria
Martin O. Dada
2012-07-01
Full Text Available Conflicts in any organization can either be functional or dysfunctional and can contribute to or detract from the achievement of organizational or project objectives. This study investigated the frequency and intensity of conflicts, using five conflict centers, on projects executed with either the integrated or traditional method in Nigeria. Questionnaires were administered through purposive and snowballing techniques on 274 projects located in twelve states of Nigeria and Abuja. 94 usable responses were obtained. The collected data were subjected to both descriptive and inferential statistical analysis. In projects procured with traditional methods, conflicts relating to resources for project execution had the greatest frequency, while conflicts around project/client goals had the least frequency. For projects executed with integrated methods, conflicts due to administrative procedures were ranked highest while conflicts due to project/client goals were ranked least. Regarding seriousness of conflict, conflicts due to administrative procedures and resources for project execution were ranked highest respectively for projects procured with traditional and integrated methods. Additionally, in terms of seriousness, personality issues and project/client goals were the least sources of conflict in projects executed with traditional and integrated methods. There were no significant differences in the incidence of conflicts, using the selected conflict centers, between the traditional and integrated procurement methods. There was however significant difference in the intensity or seriousness of conflicts between projects executed with the traditional method and those executed with integrated methods in the following areas: technical issues, administrative matters and personality issues. The study recommends that conscious efforts should be made at teambuilding on projects executed with integrated methods.
"Voici ce que j'ai trouve": Sophie Germain's grand plan to prove Fermat's Last Theorem
Laubenbacher, Reinhard
2008-01-01
A study of Sophie Germain's extensive manuscripts on Fermat's Last Theorem calls for a reassessment of her work in number theory. There is much in these manuscripts beyond the single theorem for Case 1 for which she is known from a published footnote by Legendre. Germain had a fully-fledged, highly developed, sophisticated plan of attack on Fermat's Last Theorem. The supporting algorithms she invented for this plan are based on theoretical concepts, ideas and results discovered independently only much later by others, and her methods are quite different from any of Legendre's. In addition to her program for proving Fermat's Last Theorem in its entirety, Germain also made major efforts at proofs for particular families of exponents. The isolation Germain worked in, due in substantial part to her difficult position as a woman, was perhaps sufficient that much of this extensive and impressive work may never have been studied and understood by anyone.
Multi-channel sampling theorems for band-limited signals with fractional Fourier transform
2008-01-01
Multi-channel sampling for band-limited signals is fundamental in the theory of multi-channel parallel A/D environment and multiplexing wireless communication environment. As the fractional Fourier transform has been found wide applications in signal processing fields, it is necessary to consider the multi-channel sampling theorem based on the fractional Fourier transform. In this paper, the multi-channel sampling theorem for the fractional band-limited signal is firstly proposed, which is the generalization of the well-known sampling theorem for the fractional Fourier transform. Since the periodic nonuniformly sampled signal in the fractional Fourier domain has valuable applications, the reconstruction expression for the periodic nonuniformly sampled signal has been then obtained by using the derived multi-channel sampling theorem and the specific space-shifting and phase-shifting properties of the fractional Fourier transform. Moreover, by designing different fractional Fourier filters, we can obtain reconstruction methods for other sampling strategies.
Aleksius Madu
2016-10-01
Full Text Available The purpose of this study is to predict the number of traffic accident victims who died in Timor Tengah Regency with Trend Projection method and Backpropagation method, and compare the two methods based on the degree of guilt and predict the number traffic accident victims in the Timor Tengah Regency for the coming year. This research was conducted in Timor Tengah Regency where data used in this study was obtained from Police Unit in Timor Tengah Regency. The data is on the number of traffic accidents in Timor Tengah Regency from 2000 – 2013, which is obtained by a quantitative analysis with Trend Projection and Backpropagation method. The results of the data analysis predicting the number of traffic accidents victims using Trend Projection method obtained the best model which is the quadratic trend model with equation Yk = 39.786 + (3.297 X + (0.13 X2. Whereas by using back propagation method, it is obtained the optimum network that consists of 2 inputs, 3 hidden screens, and 1 output. Based on the error rates obtained, Back propagation method is better than the Trend Projection method which means that the predicting accuracy with Back propagation method is the best method to predict the number of traffic accidents victims in Timor Tengah Regency. Thus obtained predicting the numbers of traffic accident victims for the next 5 years (Years 2014-2018 respectively - are 106 person, 115 person, 115 person, 119 person and 120 person. Keywords: Trend Projection, Back propagation, Predicting.
Arnault, Denise Saint; Fetters, Michael D.
2011-01-01
Mixed methods research has made significant in-roads in the effort to examine complex health related phenomenon. However, little has been published on the funding of mixed methods research projects. This paper addresses that gap by presenting an example of an NIMH funded project using a mixed methods QUAL-QUAN triangulation design entitled “The Mixed-Method Analysis of Japanese Depression.” We present the Cultural Determinants of Health Seeking model that framed the study, the specific aims, ...
Generalization of Cramer's rule and its application to the projection of Hartree-Fock wave function
Hage-Hassan, Mehdi
2009-01-01
We generalize the Cramer's rule of linear algebra. We apply it to calculate the spectra of nucleus by applying Hill-Wheeler projection operator to Hartree-Fock wave function, and to derive L\\"owdin formula and Thouless theorem. We derive by an elementary method the infinitesimal or L\\"owdin projection operators and its integral representation to be useful for the projection of Slater determinant.
Freek Wiedijk
2009-02-01
A small project in which I encoded a proof of Arrow’s theorem—probably the most famous results in the economics ﬁeld of social choice theory—in the computer using the Mizar system is presented here. The details of this speciﬁc project, as well as the process of formalization (encoding proofs in the computer) in general are discussed.
Some Representation Theorems for Recovering Contraction Relations
Ping Hou
2005-01-01
One of the important topics in the study of contraction inference relations is to establish the representation theorems for them. Various methods have been employed for giving representation of a broad class of contraction operations.However, there was not any canonical approach to dealing with the representation results for the contraction relations in the literature. Recently, in order to obtain the representation result for recovering contraction inference relations satisfying the condition weak conjunctive inclusion (wci), a notion of an image structure associated with the canonical epistemic state has been introduced. Based on the image structure, this paper establishes three representation results for recovering contraction inference relations which satisfy the conditions CL, CR1 and DR* respectively by the standard epistemic AGM states. A unique technique and uniform proofs to represent these contraction relations are adopted, which could overcome the core objection in previous description of contraction relations. The paper shows as well that the image structure and canonical epistemic states can be used not only to get the representation result for wci-recovering contraction relation, but also to provide semantic characterizations for a wide range of recovering contraction relations.
Jayaweera, T.; Haeri, H.
2013-04-01
Under the Uniform Methods Project, DOE is developing a framework and a set of protocols for determining the energy savings from specific energy efficiency measures and programs. The protocols provide a straightforward method for evaluating gross energy savings for common residential and commercial measures offered in ratepayer-funded initiatives in the United States. They represent a refinement of the body of knowledge supporting energy efficiency evaluation, measurement, and verification (EM&V) activities. This document deals with savings from the following measures: commercial and industrial lighting, commercial and industrial lighting controls, small commercial and residential unitary and split system HVAC cooling equipment, residential furnaces and boilers, residential lighting, refrigerator recycling, whole-building retrofit using billing analysis, metering, peak demand and time-differentiated energy savings, sample design, survey design and implementation, and assessing persistence and other evaluation issues.
Methods and Management of the Healthy Brain Study: A Large Multisite Qualitative Research Project
Laditka, Sarah B.; Corwin, Sara J.; Laditka, James N.; Liu, Rui; Friedman, Daniela B.; Mathews, Anna E.; Wilcox, Sara
2009-01-01
Purpose of the study: To describe processes used in the Healthy Brain project to manage data collection, coding, and data distribution in a large qualitative project, conducted by researchers at 9 universities in 9 states. Design and Methods: Project management protocols included: (a) managing audiotapes and surveys to ensure data confidentiality,…
Methods and Management of the Healthy Brain Study: A Large Multisite Qualitative Research Project
Laditka, Sarah B.; Corwin, Sara J.; Laditka, James N.; Liu, Rui; Friedman, Daniela B.; Mathews, Anna E.; Wilcox, Sara
2009-01-01
Purpose of the study: To describe processes used in the Healthy Brain project to manage data collection, coding, and data distribution in a large qualitative project, conducted by researchers at 9 universities in 9 states. Design and Methods: Project management protocols included: (a) managing audiotapes and surveys to ensure data confidentiality,…
A very Simple Proof of Pascal's Hexagon Theorem and some Applications
Nedeljko Stefanović; Miloš Milošević
2010-11-01
In this article we present a simple and elegant algebraic proof of Pascal’s hexagon theorem which requires only knowledge of basics on conic sections without theory of projective transformations. Also, we provide an efficient algorithm for finding an equation of the conic containing five given points and a criterion for verification whether a set of points is a subset of the conic.
Simultaneous Generalizations of the Theorems of Ceva and Menelaus for Field Planes
Houston, Kelly B.; Powers, Robert C.
2009-01-01
In 1992, Klamkin and Liu proved a very general result in the Extended Euclidean Plane that contains the theorems of Ceva and Menelaus as special cases. In this article, we extend the Klamkin and Liu result to projective planes "PG"(2, F) where F is a field. (Contains 2 figures.)
An Extension of the Cartan-Nochka Second Main Theorem for Hypersurfaces
Dethloff, Gerd; Thai, Do Duc
2009-01-01
In 1983, Nochka proved a conjecture of Cartan on defects of holomorphic curves in CP^n relative to a possibly degenerate set of hyperplanes. In this paper, we generalize the Nochka's theorem to the case of curves in a complex projective variety intersecting hypersurfaces in subgeneral position.
Social Network Processes in the Isabelle and Coq Theorem Proving Communities
Fleuriot, Jacques; Scott, Phil
2016-01-01
We identify the main actors in the Isabelle and Coq communities and describe how they affect and influence their peers. This work explores selected foundations of social networking analysis that we expect to be useful in the context of the ProofPeer project, which is developing a new model for interactive theorem proving based on collaboration and social interactions.
无
2000-01-01
Applications of locally fine property for operators are further developed. Let E and F be Banach spaces and f: be C1 nonlinear map, where U (x0) is an open set containing point x0∈E. With the locally fine property for Frechet derivatives f′(x) and generalized rank theorem for f′(x), a local conjugacy theorem, i.e. a characteristic condition for f being conjugate to f′(x0) near x0,is proved. This theorem gives a complete answer to the local conjugacy problem. Consequently, several rank theorems in advanced calculus are established, including a theorem for C1 Fredholm map which has been so far unknown. Also with this property the concept of regular value is extended, which gives rise to a generalized principle for constructing Banach submanifolds.
马吉溥
2000-01-01
Applications of locally fine property for operators are further developed. Let E and F be Banach spaces and f: U( x0) E—→F be C1 nonlinear map, where U (x0) is an open set containing point x0∈ E. With the locally fine property for Frechet derivatives f’ (x) and generalized rank theorem for f ’( x), a local conjugacy theorem, i. e. a characteristic condition for f being conjugate to f (x0) near x0,is proved. This theorem gives a complete answer to the local conjugacy problem. Consequently, several rank theorems in advanced calculus are established, including a theorem for C1 Fredholm map which has been so far unknown. Also with this property the concept of regular value is extended, which gives rise to a generalized principle for constructing Banach submanifolds.
Topological interpretation of the Luttinger theorem
Seki, Kazuhiro; Yunoki, Seiji
2017-08-01
Based solely on the analytical properties of the single-particle Green's function of fermions at finite temperatures, we show that the generalized Luttinger theorem inherently possesses topological aspects. The topological interpretation of the generalized Luttinger theorem can be introduced because (i) the Luttinger volume is represented as the winding number of the single-particle Green's function and, thus, (ii) the deviation of the theorem, expressed with a ratio between the interacting and noninteracting single-particle Green's functions, is also represented as the winding number of this ratio. The formulation based on the winding number naturally leads to two types of the generalized Luttinger theorem. Exploring two examples of single-band translationally invariant interacting electrons, i.e., simple metal and Mott insulator, we show that the first type falls into the original statement for Fermi liquids given by Luttinger, where poles of the single-particle Green's function appear at the chemical potential, while the second type corresponds to the extended one for nonmetallic cases with no Fermi surface such as insulators and superconductors generalized by Dzyaloshinskii, where zeros of the single-particle Green's function appear at the chemical potential. This formulation also allows us to derive a sufficient condition for the validity of the Luttinger theorem of the first type by applying the Rouche's theorem in complex analysis as an inequality. Moreover, we can rigorously prove in a nonperturbative manner, without assuming any detail of a microscopic Hamiltonian, that the generalized Luttinger theorem of both types is valid for generic interacting fermions as long as the particle-hole symmetry is preserved. Finally, we show that the winding number of the single-particle Green's function can also be associated with the distribution function of quasiparticles, and therefore the number of quasiparticles is equal to the Luttinger volume. This implies that
A Novel Method for Assessing and Optimizing Software Project Process Based Risk Control
无
2006-01-01
A new approach for assessing and optimizing software project process based on software risk control pre-sented, which evaluates and optimizes software project process from the view of controlling the software project risks. A model for optimizing software risk control is given, a discrete optimization algorithm based on dynamic programming is proposed and an example of using above method to solve a problem is also included in this paper. By improving the old passive post-project control into an active effective pre-action, this new method can greatly promote the possibility of success of software projects.
WEYL'S TYPE THEOREMS AND HYPERCYCLIC OPERATORS
M.H. M. Rashid
2012-01-01
For a bounded operator T acting on an infinite dimensional separable Hilbert space H,we prove the following assertions: (i) If T or T* ∈ SC,then generalized aBrowder's theorem holds for f(T) for every f ∈ Hol(σ(T)).(ii) If T or T* ∈ HC has topological uniform descent at all λ ∈ iso(σ(T)),then generalized Weyl's theorem holds for f(T) for every f ∈ Hol(σ(T)).(iii) If T ∈ HC has topological uniform descent at all λ ∈ E(T),then T satisfies generalized Weyl's theorem.(iv) Let T ∈ HC.If T satisfies the growth condition Gd(d ≥ 1),then generalized Weyl's theorem holds for f(T) for every f ∈ Hol(σ(T)).(v) If T ∈ SC,then,f(σSBF-+ (T)) =σSBF-+ (f(T)) for all f ∈ Hol(σ(T)).(vi) Let T be a-isoloid such that T* ∈ HC.If T - λI has finite ascent at every λ ∈ Ea(T)and if F is of finite rank on H such that TF =FT,then T + F obeys generalized a-Weyl's theorem.
Anti-Bell - Refutation of Bell's theorem
Barukčić, Ilija
2012-12-01
In general, Albert Einstein as one of "the founding fathers of quantum mechanics" had some problems to accept especially the Copenhagen dominated interpretation of quantum mechanics. Einstein's dissatisfaction with Copenhagen's interpretation of quantum mechanics, the absence of locality and causality within the Copenhagen dominated quantum mechanics lead to the well known Einstein, Podolsky and Rosen thought experiment. According to Einstein et al., the Copenhagen dominated quantum mechanics cannot be regarded as a complete physical theory. The Einstein, Podolsky and Rosen thought experiment was the origin of J. S. Bell's publication in 1964; known as Bell's theorem. Meanwhile, some dramatic violations of Bell's inequality (by so called Bell test experiments) have been reported which is taken as an empirical evidence against local realism and causality at quantum level and as positive evidence in favor of the Copenhagen dominated quantum mechanics. Thus far, Quantum mechanics is still regarded as a "strictly" non-local theory. The purpose of this publication is to refute Bell's original theorem. Thus far, if we accept Bell's theorem as correct, we must accept that +0> = +1. We can derive a logical contradiction out of Bell's theorem, Bell's theorem is refuted.
Generalized fluctuation theorems for classical systems
Agarwal, G. S.; Dattagupta, Sushanta
2015-11-01
The fluctuation theorem has a very special place in the study of nonequilibrium dynamics of physical systems. The form in which it is used most extensively is the Gallavoti-Cohen fluctuation theorem which is in terms of the distribution of the work p (W )/p (-W )=exp(α W ) . We derive the general form of the fluctuation theorems for an arbitrary multidimensional Gaussian Markov process. Interestingly, the parameter α is by no means universal, hitherto taken for granted in the case of linear Gaussian processes. As a matter of fact, conditions under which α does become a universal parameter 1 /K T are found to be rather restrictive. As an application we consider fluctuation theorems for classical cyclotron motion of an electron in a parabolic potential. The motion of the electron is described by four coupled Langevin equations and thus is nontrivial. The generalized theorems are equally valid for nonequilibrium steady states and could be especially important in the presence of anisotropic diffusion.
Ergodic theorem, ergodic theory, and statistical mechanics.
Moore, Calvin C
2015-02-17
This perspective highlights the mean ergodic theorem established by John von Neumann and the pointwise ergodic theorem established by George Birkhoff, proofs of which were published nearly simultaneously in PNAS in 1931 and 1932. These theorems were of great significance both in mathematics and in statistical mechanics. In statistical mechanics they provided a key insight into a 60-y-old fundamental problem of the subject--namely, the rationale for the hypothesis that time averages can be set equal to phase averages. The evolution of this problem is traced from the origins of statistical mechanics and Boltzman's ergodic hypothesis to the Ehrenfests' quasi-ergodic hypothesis, and then to the ergodic theorems. We discuss communications between von Neumann and Birkhoff in the Fall of 1931 leading up to the publication of these papers and related issues of priority. These ergodic theorems initiated a new field of mathematical-research called ergodic theory that has thrived ever since, and we discuss some of recent developments in ergodic theory that are relevant for statistical mechanics.
Harmonizing and Optimizing Fish Testing Methods: The OECD Framework Project
The Organisation for Economic Cooperation and Development (OECD) serves a key role in the international harmonization of testing of a wide variety of chemicals. An integrated fish testing framework project was initiated in mid-2009 through the OECD with the US as the lead country...
MINRES Seed Projection Methods for Solving Symmetric Linear Systems with Multiple Right-Hand Sides
Xin Li
2014-01-01
Full Text Available We consider the MINRES seed projection method for solving multiple right-hand side linear systems AX=B, where A∈Rn×n is a nonsingular symmetric matrix, B∈Rn×p. In general, GMRES seed projection method is one of the effective methods for solving multiple right-hand side linear systems. However, when the coefficient matrix is symmetric, the efficiency of this method would be weak. MINRES seed projection method for solving symmetric systems with multiple right-hand sides is proposed in this paper, and the residual estimation is analyzed. The numerical examples show the efficiency of this method.
$(k,s)$-positivity and vanishing theorems for compact Kahler manifolds
Yang, Qi-Lin
2010-01-01
We study the $(k,s)$-positivity for holomorphic vector bundles on compact complex manifolds. $(0,s)$-positivity is exactly the Demailly $s$-positivity and a $(k,1)$-positive line bundle is just a $k$-positive line bundle in the sense of Sommese. In this way we get a unified theory for all kinds of positivities used for semipositive vector bundles. Several new vanishing theorems for $(k,s)$-positive vector bundles are proved and the vanishing theorems for $k$-ample vector bundles on projective algebraic manifolds are generalized to $k$-positive vector bundles on compact K\\"ahler manifolds.
Vinayaka : A Semi-Supervised Projected Clustering Method Using Differential Evolution
Satish Gajawada; Durga Toshniwal
2012-01-01
Differential Evolution (DE) is an algorithm for evolutionary optimization. Clustering problems have beensolved by using DE based clustering methods but these methods may fail to find clusters hidden insubspaces of high dimensional datasets. Subspace and projected clustering methods have been proposed inliterature to find subspace clusters that are present in subspaces of dataset. In this paper we proposeVINAYAKA, a semi-supervised projected clustering method based on DE. In this method DE opt...
Lin Zhenghua
2005-01-01
In this paper, we discuss the relationship between the sparse symmetric Broyden (SPSB) method [1, 2] and m-time secant-like multi-projection (SMP) method [3] and prove that when m goes to infinity, the SMP method is corresponding to the SPSB method.
Adiabatic Theorem for Quantum Spin Systems
Bachmann, S.; De Roeck, W.; Fraas, M.
2017-08-01
The first proof of the quantum adiabatic theorem was given as early as 1928. Today, this theorem is increasingly applied in a many-body context, e.g., in quantum annealing and in studies of topological properties of matter. In this setup, the rate of variation ɛ of local terms is indeed small compared to the gap, but the rate of variation of the total, extensive Hamiltonian, is not. Therefore, applications to many-body systems are not covered by the proofs and arguments in the literature. In this Letter, we prove a version of the adiabatic theorem for gapped ground states of interacting quantum spin systems, under assumptions that remain valid in the thermodynamic limit. As an application, we give a mathematical proof of Kubo's linear response formula for a broad class of gapped interacting systems. We predict that the density of nonadiabatic excitations is exponentially small in the driving rate and the scaling of the exponent depends on the dimension.
Bayes' theorem: scientific assessment of experience
Lex Rutten
2010-10-01
Full Text Available Homeopathy is based on experience and this is a scientific procedure if we follow Bayes' theorem. Unfortunately this is not the case at the moment. Symptoms are added to our materia medica based on absolute occurrence, while Bayes theorem tells us that this should be based on relative occurrence. Bayes theorem can be applied on prospective research, but also on retrospective research and consensus based on a large number of cases. Confirmation bias is an important source of false data in experience based systems like homeopathy. Homeopathic doctors should become more aware of this and longer follow-up of cases could remedy this. The existing system of adding symptoms to our materia medica is obsolete.
Some Limit Theorems in Geometric Processes
Yeh Lam; Yao-hui Zheng; Yuan-lin Zhang
2003-01-01
Geometric process (GP) was introduced by Lam[4,5], it is defined as a stochastic process {Xn, n =1, 2,...} for which there exists a real number a > 0, such that {an-1Xn, n = 1, 2,...} forms a renewal process (RP). In this paper, we study some limit theorems in GP. We first derive the Wald equation for GP and then obtain the limit theorems of the age, residual life and the total life at t for a GP. A general limit theorem for Sn with a > 1 is also studied. Furthermore, we make a comparison between GP and RP, including the comparison of their limit distributions of the age, residual life and the total life at t.
Causality, Bell's theorem, and Ontic Definiteness
Henson, Joe
2011-01-01
Bell's theorem shows that the reasonable relativistic causal principle known as "local causality" is not compatible with the predictions of quantum mechanics. It is not possible maintain a satisfying causal principle of this type while dropping any of the better-known assumptions of Bell's theorem. However, another assumption of Bell's theorem is the use of classical logic. One part of this assumption is the principle of "ontic definiteness", that is, that it must in principle be possible to assign definite truth values to all propositions treated in the theory. Once the logical setting is clarified somewhat, it can be seen that rejecting this principle does not in any way undermine the type of causal principle used by Bell. Without ontic definiteness, the deterministic causal condition known as Einstein Locality succeeds in banning superluminal influence (including signalling) whilst allowing correlations that violate Bell's inequalities. Objections to altering logic, and the consequences for operational and...
Proposed Project Selection Method for Human Support Research and Technology Development (HSR&TD)
Jones, Harry
2005-01-01
The purpose of HSR&TD is to deliver human support technologies to the Exploration Systems Mission Directorate (ESMD) that will be selected for future missions. This requires identifying promising candidate technologies and advancing them in technology readiness until they are acceptable. HSR&TD must select an may of technology development projects, guide them, and either terminate or continue them, so as to maximize the resulting number of usable advanced human support technologies. This paper proposes an effective project scoring methodology to support managing the HSR&TD project portfolio. Researchers strongly disagree as to what are the best technology project selection methods, or even if there are any proven ones. Technology development is risky and outstanding achievements are rare and unpredictable. There is no simple formula for success. Organizations that are satisfied with their project selection approach typically use a mix of financial, strategic, and scoring methods in an open, established, explicit, formal process. This approach helps to build consensus and develop management insight. It encourages better project proposals by clarifying the desired project attributes. We propose a project scoring technique based on a method previously used in a federal laboratory and supported by recent research. Projects are ranked by their perceived relevance, risk, and return - a new 3 R's. Relevance is the degree to which the project objective supports the HSR&TD goal of developing usable advanced human support technologies. Risk is the estimated probability that the project will achieve its specific objective. Return is the reduction in mission life cycle cost obtained if the project is successful. If the project objective technology performs a new function with no current cost, its return is the estimated cash value of performing the new function. The proposed project selection scoring method includes definitions of the criteria, a project evaluation
Project Management Optimistic (GPO): A Method that Integra Pert / CPM to CCPM
Novais, Igor Fontes; Jorge, Eduardo Manoel de Freitas; Junior, Carlos Pereira Costa; Souza, Daniele Tavares
2011-01-01
The time factor for project managers is one of the most worrisome because of difficulties in keeping projects on time, making interesting use of traditional techniques such as PERT/CPM. Another interesting technique that supports the management of time is the Critical Chain (CCPM) based on the Theory of Constraints (TOC). This article presents the method Optimistic Project Management (GPO) that is based on PERT/CPM and CCPM. The method GPO brings as differential a new way of assembling a sche...
Spectral mapping theorems a bluffer's guide
Harte, Robin
2014-01-01
Written by an author who was at the forefront of developments in multi-variable spectral theory during the seventies and the eighties, this guide sets out to describe in detail the spectral mapping theorem in one, several and many variables. The basic algebraic systems – semigroups, rings and linear algebras – are summarised, and then topological-algebraic systems, including Banach algebras, to set up the basic language of algebra and analysis. Spectral Mapping Theorems is written in an easy-to-read and engaging manner and will be useful for both the beginner and expert. It will be of great importance to researchers and postgraduates studying spectral theory.
Jarzynski's theorem for lattice gauge theory
Caselle, Michele; Nada, Alessandro; Panero, Marco; Toniato, Arianna
2016-01-01
Jarzynski's theorem is a well-known equality in statistical mechanics, which relates fluctuations in the work performed during a non-equilibrium transformation of a system, to the free-energy difference between two equilibrium states. In this article, we extend Jarzynski's theorem to lattice gauge theory, and present examples of applications for two challenging computational problems, namely the calculation of interface free energies and the determination of the equation of state. We conclude with a discussion of further applications of interest in QCD and in other strongly coupled gauge theories, in particular for the Schroedinger functional and for simulations at finite density using reweighting techniques.
Central Limit Theorem for Nonlinear Hawkes Processes
Zhu, Lingjiong
2012-01-01
Hawkes process is a self-exciting point process with clustering effect whose jump rate depends on its entire past history. It has wide applications in neuroscience, finance and many other fields. Linear Hawkes process has an immigration-birth representation and can be computed more or less explicitly. It has been extensively studied in the past and the limit theorems are well understood. On the contrary, nonlinear Hawkes process lacks the immigration-birth representation and is much harder to analyze. In this paper, we obtain a functional central limit theorem for nonlinear Hawkes process.
Limit theorems for fragmentation processes with immigration
Knobloch, Robert
2012-01-01
In this paper we extend two limit theorems which were recently obtained for fragmentation processes to such processes with immigration. More precisely, in the setting with immigration we consider a limit theorem for the process counted with a random characteristic as well as the asymptotic behaviour of an empirical measure associated with the stopping line corresponding to the first blocks, in their respective line of descent, that are smaller than a given size. In addition, we determine the asymptotic decay rate of the size of the largest block in a homogeneous fragmentation process with immigration. The techniques used to proves these results are based on submartingale arguments.
A Noether Theorem for Markov Processes
Baez, John C
2012-01-01
Noether's theorem links the symmetries of a quantum system with its conserved quantities, and is a cornerstone of quantum mechanics. Here we prove a version of Noether's theorem for Markov processes. In quantum mechanics, an observable commutes with the Hamiltonian if and only if its expected value remains constant in time for every state. For Markov processes that no longer holds, but an observable commutes with the Hamiltonian if and only if both its expected value and standard deviation are constant in time for every state.
General Common Fixed Point Theorems and Applications
Shyam Lal Singh
2012-01-01
Full Text Available The main result is a common fixed point theorem for a pair of multivalued maps on a complete metric space extending a recent result of Đorić and Lazović (2011 for a multivalued map on a metric space satisfying Ćirić-Suzuki-type-generalized contraction. Further, as a special case, we obtain a generalization of an important common fixed point theorem of Ćirić (1974. Existence of a common solution for a class of functional equations arising in dynamic programming is also discussed.
Pauli and the spin-statistics theorem
Duck, Ian M
1997-01-01
This book makes broadly accessible an understandable proof of the infamous spin-statistics theorem. This widely known but little-understood theorem is intended to explain the fact that electrons obey the Pauli exclusion principle. This fact, in turn, explains the periodic table of the elements and their chemical properties. Therefore, this one simply stated fact is responsible for many of the principal features of our universe, from chemistry to solid state physics to nuclear physics to the life cycle of stars.In spite of its fundamental importance, it is only a slight exaggeration to say that
Generalizations of the Abstract Boundary singularity theorem
Whale, Ben E; Scott, Susan M
2015-01-01
The Abstract Boundary singularity theorem was first proven by Ashley and Scott. It links the existence of incomplete causal geodesics in strongly causal, maximally extended spacetimes to the existence of Abstract Boundary essential singularities, i.e., non-removable singular boundary points. We give two generalizations of this theorem: the first to continuous causal curves and the distinguishing condition, the second to locally Lipschitz curves in manifolds such that no inextendible locally Lipschitz curve is totally imprisoned. To do this we extend generalized affine parameters from $C^1$ curves to locally Lipschitz curves.
Risk Determination in Projects. The Advantages and Disadvantages of Stochastic Methods
Leonard Lepadatu
2009-10-01
Full Text Available This paper is a comparative study about the principal stochastic methods that is used in Project Management. Risk determination is a mustfor every Project Manager worldwide, but the methods have, of course, advantages and disadvantages. Further, many Project Managers work withdeterministic methods, but they see only the advantages or disadvantages of those methods. In Subject of this paper it is Risk determination inprojects. The advantages and disadvantages of stochastic methods. Choosing the theme of this paper is not randomly, it continues a series of articlespublished for strengthen of scientific research in the Doctorate studies that I followed since 2005.
Monotone projected gradient methods for large-scale box-constrained quadratic programming
ZHOU Bin; GAO Li; DAI Yuhong
2006-01-01
Inspired by the success of the projected Barzilai-Borwein (PBB) method for largescale box-constrained quadratic programming, we propose and analyze the monotone projected gradient methods in this paper. We show by experiments and analyses that for the new methods,it is generally a bad option to compute steplengths based on the negative gradients. Thus in our algorithms, some continuous or discontinuous projected gradients are used instead to compute the steplengths. Numerical experiments on a wide variety of test problems are presented, indicating that the new methods usually outperform the PBB method.
Ossai, Peter Agbadobi Uloku
2016-01-01
This study examined the relationship between students' scores on Research Methods and statistics, and undergraduate project at the final year. The purpose was to find out whether students matched knowledge of research with project-writing skill. The study adopted an expost facto correlational design. Scores on Research Methods and Statistics for…
Linear algebra and projective geometry
Baer, Reinhold
2005-01-01
Geared toward upper-level undergraduates and graduate students, this text establishes that projective geometry and linear algebra are essentially identical. The supporting evidence consists of theorems offering an algebraic demonstration of certain geometric concepts. These focus on the representation of projective geometries by linear manifolds, of projectivities by semilinear transformations, of collineations by linear transformations, and of dualities by semilinear forms. These theorems lead to a reconstruction of the geometry that constituted the discussion's starting point, within algebra
Raphael, B.; Fikes, R.; Waldinger, R.
1973-01-01
The results are summarised of a project aimed at the design and implementation of computer languages to aid in expressing problem solving procedures in several areas of artificial intelligence including automatic programming, theorem proving, and robot planning. The principal results of the project were the design and implementation of two complete systems, QA4 and QLISP, and their preliminary experimental use. The various applications of both QA4 and QLISP are given.
Full Poncelet Theorem in Minkowski dS and AdS Spaces
WANG Yao-Xiong; FAN Heng; SHI Kang-Jie; WANG Chun; ZHANG Kai; ZENG Yu
2009-01-01
We study the reflection of a straight line or a billiard on a plane in an n-dimensional Minkowski space. It is found that the reflection law coincides with that defined with respect to confocal quadratic surfaces in projective geometry. We then establish the full Poncelet theorem which holds in projective geometry in n-dimensional Minkowski space and in their quadratic surfaces including de Sitter and AdS spaces.
Formalization and Implementation of Algebraic Methods in Geometry
Filip Marić
2012-02-01
Full Text Available We describe our ongoing project of formalization of algebraic methods for geometry theorem proving (Wu's method and the Groebner bases method, their implementation and integration in educational tools. The project includes formal verification of the algebraic methods within Isabelle/HOL proof assistant and development of a new, open-source Java implementation of the algebraic methods. The project should fill-in some gaps still existing in this area (e.g., the lack of formal links between algebraic methods and synthetic geometry and the lack of self-contained implementations of algebraic methods suitable for integration with dynamic geometry tools and should enable new applications of theorem proving in education.
Prioritizing sewer rehabilitation projects using AHP-PROMETHEE II ranking method.
Kessili, Abdelhak; Benmamar, Saadia
2016-01-01
The aim of this paper is to develop a methodology for the prioritization of sewer rehabilitation projects for Algiers (Algeria) sewer networks to support the National Sanitation Office in its challenge to make decisions on prioritization of sewer rehabilitation projects. The methodology applies multiple-criteria decision making. The study includes 47 projects (collectors) and 12 criteria to evaluate them. These criteria represent the different issues considered in the prioritization of the projects, which are structural, hydraulic, environmental, financial, social and technical. The analytic hierarchy process (AHP) is used to determine weights of the criteria and the Preference Ranking Organization Method for Enrichment Evaluations (PROMETHEE II) method is used to obtain the final ranking of the projects. The model was verified using the sewer data of Algiers. The results have shown that the method can be used for prioritizing sewer rehabilitation projects.
Height projection methods and sensitivity study. Technical report
Mikhail, A. S.; Justus, C. G.
1979-06-01
A brief description is given of the different techniques for height projection of wind speed that have been developed at Georgia Tech. One of these techniques, the similarity model, is based on Monin-Obukhov similarity theory. Other models examined are the empirical velocity-dependent power law model (power law model) and the semi-empirical modified velocity-dependent power law model (modified power law model). A detailed description of the methodologies is given and example applications are illustrated, with all the necessary input parameters to the models.
A Projected Conjugate Gradient Method for Sparse Minimax Problems
Madsen, Kaj; Jonasson, Kristjan
1993-01-01
A new method for nonlinear minimax problems is presented. The method is of the trust region type and based on sequential linear programming. It is a first order method that only uses first derivatives and does not approximate Hessians. The new method is well suited for large sparse problems...... as it only requires that software for sparse linear programming and a sparse symmetric positive definite equation solver are available. On each iteration a special linear/quadratic model of the function is minimized, but contrary to the usual practice in trust region methods the quadratic model is only...
Risk management for engineering projects procedures, methods and tools
Munier, Nolberto
2014-01-01
Many people see risk in engineering projects as an imprecise and nebulous problem - something that exists, is feared and is impossible to deal with. Nothing could be further from the truth. While risk is certainly ubiquitous, sometimes difficult to detect, and cannot always be completely avoided, it can generally be mitigated, reduced or prevented through timely analysis and action. This book covers the entire process of risk management by providing methodologies for determining the sources of project risk, and once threats have been identified, managing them through: · identification and assessment (probability, relative importance, variables, risk breakdown structure, etc.) · implementation of measures for their prevention, reduction or mitigation · evaluation of impacts and quantification of risks · establishment of control measures It also considers sensitivity analysis to determine the influence of uncertain parameters values ...
Projection and quasi-compressibility methods for solving the incompressible Navier-Stokes equations
Prohl, Andreas
1997-01-01
Projection methods had been introduced in the late sixties by A. Chorin and R. Teman to decouple the computation of velocity and pressure within the time-stepping for solving the nonstationary Navier-Stokes equations. Despite the good performance of projection methods in practical computations, their success remained somewhat mysterious as the operator splitting implicitly introduces a nonphysical boundary condition for the pressure. The objectives of this monograph are twofold. First, a rigorous error analysis is presented for existing projection methods by means of relating them to so-called quasi-compressibility methods (e.g. penalty method, pressure stabilzation method, etc.). This approach highlights the intrinsic error mechanisms of these schemes and explains the reasons for their limitations. Then, in the second part, more sophisticated new schemes are constructed and analyzed which are exempted from most of the deficiencies of the classical projection and quasi-compressibility methods. "... this book ...
Project scheduling method with time using MRP system – A case study: Construction project in Libya
Abdallah Ali Imetieg
2015-04-01
Full Text Available Materials Requirements and Planning (MRP is a system of production planning and inventory control, which is used to manage manufacturing processes. Most MRP systems are software-based and are used to ensure that the materials are available for production, that the products are available for delivery to customers, that the lowest possible material and product level is maintained in store, as well as to plan delivery schedules and purchasing activities. Upon completion of scheduling, begins the process of follow-up, which includes the achievement of the project goals in terms of quantity, quality and costs in accordance with deadlines. MRP system was applied to project of 5000 housing units in Solug area, which is close to Benghazi city, Libya, with the aim to provide necessary cash flow to pay dues on time without delay to all involved project sub-contractors and material suppliers, to ensure the smooth flow of operations, as well as to diminish costs by reduction of temporary storages and rented areas. There is a correlation between time and cost of each activity. If the required time is shorter than the scheduled time of the certain activity, it would demand more resources, which further leads to the increase in direct costs of the given activity. Therefore, the output of MRP is important since commands are issued through planning in order to launch the suggested orders with the required quantities and within the limited time period.
A Dual of the Compression-Expansion Fixed Point Theorems
Henderson Johnny
2007-01-01
Full Text Available This paper presents a dual of the fixed point theorems of compression and expansion of functional type as well as the original Leggett-Williams fixed point theorem. The multi-valued situation is also discussed.
A Note on a Broken-Cycle Theorem for Hypergraphs
Trinks Martin
2014-08-01
Full Text Available Whitney’s Broken-cycle Theorem states the chromatic polynomial of a graph as a sum over special edge subsets. We give a definition of cycles in hypergraphs that preserves the statement of the theorem there
A duality theorem of crossed coproduct for Hopf algebras
王栓宏
1995-01-01
A duality theorem for Hopf crossed coproduct is proved. This theorem plays a role similar to that appearing in the work of Koppinen (which generalized the corresponding results of group grraded ring).
Adiabatic limits,vanishing theorems and the noncommutative residue
无
2009-01-01
In this paper,we compute the adiabatic limit of the scalar curvature and prove several vanishing theorems by taking adiabatic limits.As an application,we give a Kastler-Kalau-Walze type theorem for foliations.
Application of the residue theorem to bilateral hypergeometric series
Wenchang Chu
2007-12-01
Full Text Available The application of the residue theorem to bilateral hypergeometric series identities is systematically reviewed by exemplifying three classes of summation theorems due to Dougall (1907, Jackson (1949, 1952 and Slater-Lakin (1953.
An existence theorem for Volterra integrodifferential equations with infinite delay
Ferenc Izsak
2003-01-01
Full Text Available Using Schauder's fixed point theorem, we prove an existence theorem for Volterra integrodifferential equations with infinite delay. As an appplication, we consider an $n$ species Lotka-Volterra competitive system.
Advanced Aqueous Phase Catalyst Development using Combinatorial Methods Project
National Aeronautics and Space Administration — Combinatorial methods are proposed to develop advanced Aqueous Oxidation Catalysts (AOCs) with the capability to mineralize organic contaminants present in effluents...
HOMES - Holographic Optical Method for Exoplanet Spectroscopy Project
National Aeronautics and Space Administration — HOMES (Holographic Optical Method for Exoplanet Spectroscopy) is a space telescope designed for exoplanet discovery. Its double dispersion architecture employs a...
Discounted Cash Flow and Modern Asset Pricing Methods - Project Selection and Policy Implications
Emhjellen, Magne; Alaouze, Chris M.
2002-07-01
We examine the differences in the net present values (NPV's) of North Sea oil projects obtained using the Weighted Average Cost of Capital (WACC) and a Modern Asset Pricing (MAP) method which involves the separate discounting of project cash flow components. NPV differences of more than $1 Om were found for some oil projects. Thus, the choice of valuation method will affect the development decisions of oil companies. The results of the MAP method are very sensitive to the choice of parameter values for the stochastic process used to model oil prices. Further research is recommended before the MAP method is used as the sole valuation model. (author)
Discounted Cash Flow and Modern Asset Pricing Methods - Project Selection and Policy Implications
Emhjellen, Magne; Alaouze, Chris M.
2002-07-01
We examine the differences in the net present values (NPV's) of North Sea oil projects obtained using the Weighted Average Cost of Capital (WACC) and a Modern Asset Pricing (MAP) method which involves the separate discounting of project cash flow components. NPV differences of more than $1 Om were found for some oil projects. Thus, the choice of valuation method will affect the development decisions of oil companies. The results of the MAP method are very sensitive to the choice of parameter values for the stochastic process used to model oil prices. Further research is recommended before the MAP method is used as the sole valuation model. (author)
Central Limit Theorem for Coloured Hard Dimers
Maria Simonetta Bernabei
2010-01-01
Full Text Available We study the central limit theorem for a class of coloured graphs. This means that we investigate the limit behavior of certain random variables whose values are combinatorial parameters associated to these graphs. The techniques used at arriving this result comprise combinatorics, generating functions, and conditional expectations.
Generalization of the Hellmann-Feynman theorem
Esteve, J.G., E-mail: esteve@unizar.e [Departamento de Fisica Teorica, Facultad de Ciencias, Universidad de Zaragoza, 50009 Zaragoza (Spain); Instituto de Biocomputacion y Fisica de Sistemas complejos (BIFI), Universidad de Zaragoza, 50009 Zaragoza (Spain); Falceto, Fernando [Departamento de Fisica Teorica, Facultad de Ciencias, Universidad de Zaragoza, 50009 Zaragoza (Spain); Instituto de Biocomputacion y Fisica de Sistemas complejos (BIFI), Universidad de Zaragoza, 50009 Zaragoza (Spain); Garcia Canal, C. [Laboratorio de Fisica Teorica, Departamento de Fisica, Facultad de Ciencias Exactas, Universidad Nacional de La Plata and IFLP-CONICET (Argentina)
2010-01-25
The well-known Hellmann-Feynman theorem of quantum mechanics connected with the derivative of the eigenvalues with respect to a parameter upon which the Hamiltonian depends, is generalized to include cases in which the domain of definition of the Hamiltonian of the system also depends on that parameter.
A simpler derivation of the coding theorem
Lomnitz, Yuval
2012-01-01
A simple proof for the Shannon coding theorem, using only the Markov inequality, is presented. The technique is useful for didactic purposes, since it does not require many preliminaries and the information density and mutual information follow naturally in the proof. It may also be applicable to situations where typicality is not natural.
Generalizations of Brandl's theorem on Engel length
Quek, S. G.; Wong, K. B.; Wong, P. C.
2013-04-01
Let n Engel cycle generated by g and h. The length of the Engel cycle is m-n. A group G is said to have Engel length r, if all the length of the Engel cycles in G divides r. In this paper we discuss the Brandl's theorem on Engel length and give some of its generalizations.
Ptolemy's Theorem and Familiar Trigonometric Identities.
Bidwell, James K.
1993-01-01
Integrates the sum, difference, and multiple angle identities into an examination of Ptolemy's Theorem, which states that the sum of the products of the lengths of the opposite sides of a quadrilateral inscribed in a circle is equal to the product of the lengths of the diagonals. (MDH)
The central limit theorem and chaos
NIU Ying-xuan
2009-01-01
Let X be a compact metric space and f : X → X be a continuous map. This paper studies some relationships between stochastic and topological properties of dynamical systems.It is shown that if f satisfies the central limit theorem, then f is topologically ergodic and f is sensitively dependent on initial conditions if and only if f is neither minimal nor equicontinuous.
JACKSON‘S THEOREM FOR COMPACT GROUPS
H.Vaezi; S.F.Rzaev
2002-01-01
In this article we consider the generalized shift operator defined by (Shuf)(g)=∫Gf(tut-1g)dt on compact group G and by help of this operator we define “Spherical” modulus of continuity.So we prove Stechkin and Jackson type theorems.
A cosmological no-hair theorem
Chambers, C M; Chris M Chambers; Ian G Moss
1994-01-01
A generalisation of Price's theorem is given for application to Inflationary Cosmologies. Namely, we show that on a Schwarzschild--de Sitter background there are no static solutions to the wave or gravitational perturbation equations for modes with angular momentum greater than their intrinsic spin.
Multiplier theorems for special Hermite expansions on
张震球; 郑维行
2000-01-01
The weak type (1,1) estimate for special Hermite expansions on Cn is proved by using the Calderon-Zygmund decomposition. Then the multiplier theorem in Lp(1 < p < ω ) is obtained. The special Hermite expansions in twisted Hardy space are also considered. As an application, the multipli-ers for a certain kind of Laguerre expansions are given in Lp space.
Lagrange’s Four-Square Theorem
Watase Yasushige
2015-02-01
Full Text Available This article provides a formalized proof of the so-called “the four-square theorem”, namely any natural number can be expressed by a sum of four squares, which was proved by Lagrange in 1770. An informal proof of the theorem can be found in the number theory literature, e.g. in [14], [1] or [23].
SOME REFINEMENTS OF ENESTROM-KAKEYA THEOREM
A.Aziz; B.A.Zargar
2007-01-01
In this paper we present certain interesting refinements of a well-known Enestrom-Kakeya theorem in the theory of distribution of zeros of polynomials which among other things also improve upon some results of Aziz and Mohammad, Govil and Rehman and others.
The Viner-Wong Envelope Theorem.
Silberberg, Eugene
1999-01-01
Observes that the envelope theorem, a fundamental tool in duality analysis, is still a puzzle to many people. Argues that the essence of a solution proposed by Paul Samuelson (1947) is also unclear to many people, but can be communicated with a simple cost diagram. Presents and explains the proposed diagram. (DSK)
Some Generalizations of Jungck's Fixed Point Theorem
J. R. Morales
2012-01-01
Full Text Available We are going to generalize the Jungck's fixed point theorem for commuting mappings by mean of the concepts of altering distance functions and compatible pair of mappings, as well as, by using contractive inequalities of integral type and contractive inequalities depending on another function.
A non-differentiable Noether's theorem
Cresson, Jacky; Greff, Isabelle
2011-02-01
In the framework of the nondifferentiable embedding of Lagrangian systems, defined by Cresson and Greff [non-dierentiable embedding of lagrangian systems and partial dierential equations. Preprint Max-Plank-Institut für Mathematik in den Naturwissenschaften, Leipzig 16, 26 (2010)], we prove a Noether's theorem based on the lifting of one-parameter groups of diffeomorphisms.
Fixed Point Theorems for Asymptotically Contractive Multimappings
M. Djedidi
2012-01-01
Full Text Available We present fixed point theorems for a nonexpansive set-valued mapping from a closed convex subset of a reflexive Banach space into itself under some asymptotic contraction assumptions. Some existence results of coincidence points and eigenvalues for multimappings are given.
Agreement Theorems in Dynamic-Epistemic Logic
Degremont, Cedric; Roy, Oliver
2012-01-01
This paper introduces Agreement Theorems to dynamic-epistemic logic. We show first that common belief of posteriors is sufficient for agreement in epistemic-plausibility models, under common and well-founded priors. We do not restrict ourselves to the finite case, showing that in countable structure
An extension theorem for conformal gauge singularities
Tod, Paul
2007-01-01
We analyse conformal gauge, or isotropic, singularities in cosmological models in general relativity. Using the calculus of tractors, we find conditions in terms of tractor curvature for a local extension of the conformal structure through a cosmological singularity and prove a local extension theorem.
A Generalized Krein-Rutman Theorem
Zhang, Lei
2016-01-01
A generalized Krein-Rutman theorem for a strongly positive bounded linear operator whose spectral radius is larger than essential spectral radius is established: the spectral radius of the operator is an algebraically simple eigenvalue with strongly positive eigenvector and other eigenvalues are less than the spectral radius.
Stokes' theorem, volume growth and parabolicity
Valtorta, Daniele
2010-01-01
We present some new Stokes'type theorems on complete non-compact manifolds that extend, in different directions, previous work by Gaffney and Karp and also the so called Kelvin-Nevanlinna-Royden criterion for (p-)parabolicity. Applications to comparison and uniqueness results involving the p-Laplacian are deduced.
Generalized Friedland's theorem for C0-semigroups
Cichon, Dariusz; Jung, Il Bong; Stochel, Jan
2008-07-01
Friedland's characterization of bounded normal operators is shown to hold for infinitesimal generators of C0-semigroups. New criteria for normality of bounded operators are furnished in terms of Hamburger moment problem. All this is achieved with the help of the celebrated Ando's theorem on paranormal operators.
The Fundamental Theorems of Interval Analysis
van Emden, M. H.; Moa, B.
2007-01-01
Expressions are not functions. Confusing the two concepts or failing to define the function that is computed by an expression weakens the rigour of interval arithmetic. We give such a definition and continue with the required re-statements and proofs of the fundamental theorems of interval arithmetic and interval analysis. Revision Feb. 10, 2009: added reference to and acknowledgement of P. Taylor.
Automated theorem proving theory and practice
Newborn, Monty
2001-01-01
As the 21st century begins, the power of our magical new tool and partner, the computer, is increasing at an astonishing rate. Computers that perform billions of operations per second are now commonplace. Multiprocessors with thousands of little computers - relatively little! -can now carry out parallel computations and solve problems in seconds that only a few years ago took days or months. Chess-playing programs are on an even footing with the world's best players. IBM's Deep Blue defeated world champion Garry Kasparov in a match several years ago. Increasingly computers are expected to be more intelligent, to reason, to be able to draw conclusions from given facts, or abstractly, to prove theorems-the subject of this book. Specifically, this book is about two theorem-proving programs, THEO and HERBY. The first four chapters contain introductory material about automated theorem proving and the two programs. This includes material on the language used to express theorems, predicate calculus, and the rules of...
Nash-Williams’ cycle-decomposition theorem
Thomassen, Carsten
2016-01-01
We give an elementary proof of the theorem of Nash-Williams that a graph has an edge-decomposition into cycles if and only if it does not contain an odd cut. We also prove that every bridgeless graph has a collection of cycles covering each edge at least once and at most 7 times. The two results...
Tennis Rackets and the Parallel Axis Theorem
Christie, Derek
2014-01-01
This simple experiment uses an unusual graph straightening exercise to confirm the parallel axis theorem for an irregular object. Along the way, it estimates experimental values for g and the moment of inertia of a tennis racket. We use Excel to find a 95% confidence interval for the true values.
Average sampling theorems for shift invariant subspaces
无
2000-01-01
The sampling theorem is one of the most powerful results in signal analysis. In this paper, we study the average sampling on shift invariant subspaces, e.g. wavelet subspaces. We show that if a subspace satisfies certain conditions, then every function in the subspace is uniquely determined and can be reconstructed by its local averages near certain sampling points. Examples are given.
On the Hardy-Littlewood maximal theorem
Shinji Yamashita
1982-01-01
Full Text Available The Hardy-Littlewood maximal theorem is extended to functions of class PL in the sense of E. F. Beckenbach and T. Radó, with a more precise expression of the absolute constant in the inequality. As applications we deduce some results on hyperbolic Hardy classes in terms of the non-Euclidean hyperbolic distance in the unit disk.
Crum's Theorem for `Discrete' Quantum Mechanics
Odake, Satoru; Sasaki, Ryu
2009-01-01
In one-dimensional quantum mechanics, or the Sturm-Liouville theory, Crum's theorem describes the relationship between the original and the associated Hamiltonian systems, which are iso-spectral except for the lowest energy state. Its counterpart in `discrete' quantum mechanics is formulated algebraically, elucidating the basic structure of the discrete quantum mechanics, whose Schr\\"odinger equation is a difference equation.
1/4-pinched contact sphere theorem
Ge, Jian; Huang, Yang
2016-01-01
Given a closed contact 3-manifold with a compatible Riemannian metric, we show that if the sectional curvature is 1/4-pinched, then the contact structure is universally tight. This result improves the Contact Sphere Theorem in [EKM12], where a 4/9-pinching constant was imposed. Some tightness res...
Green's Theorem for Generalized Fractional Derivatives
Odzijewicz, Tatiana; Torres, Delfim F M
2012-01-01
We study three types of generalized partial fractional operators. An extension of Green's theorem, by considering partial fractional derivatives with more general kernels, is proved. New results are obtained, even in the particular case when the generalized operators are reduced to the standard partial fractional derivatives and fractional integrals in the sense of Riemann-Liouville or Caputo.
On Viviani's Theorem and Its Extensions
Abboud, Elias
2010-01-01
Viviani's theorem states that the sum of distances from any point inside an equilateral triangle to its sides is constant. Here, in an extension of this result, we show, using linear programming, that any convex polygon can be divided into parallel line segments on which the sum of the distances to the sides of the polygon is constant. Let us say…
A non-archimedean Montel's theorem
Favre, Charles; Trucco, Eugenio
2011-01-01
We prove a version of Montel's theorem for analytic functions over a non-archimedean complete valued field. We propose a definition of normal family in this context, and give applications of our results to the dynamics of non-archimedean entire functions.
Norton's theorem for batch routing queueing networks
Bause, Falko; Boucherie, Richard J.; Buchholz, Peter
2001-01-01
This paper shows that the aggregation and decomposition result known as Norton’s theorem for queueing networks can be extended to a general class of batch routing queueing networks with product-form solution that allows for multiple components to simultaneously release and receive (batches of) custo
ORBAN Magdalena
2015-06-01
Full Text Available The paper presents a comparative graphical and analytical study concerning the possibility of applying methods of transforming the projection – rotation and change of projection planes - for determination of spatial image of some machine parts whose edges or plane faces form imposed angles with the projection planes. An analysis of the existing relation between the two methods respectively with the axonometric representation realized by the coordinate’s method is also performed, highlighting the advantages presented by each of the considered methods. In both cases, the double rotation, respectively the double change of projection planes will be applied, equivalent to an intuitive axonometric representation which will meet, at the same time, some concrete requirements of a project.