Pascal’s Theorem in Real Projective Plane
Coghetto Roland
2017-01-01
In this article we check, with the Mizar system [2], Pascal’s theorem in the real projective plane (in projective geometry Pascal’s theorem is also known as the Hexagrammum Mysticum Theorem)1. Pappus’ theorem is a special case of a degenerate conic of two lines.
Pascal’s Theorem in Real Projective Plane
Directory of Open Access Journals (Sweden)
Coghetto Roland
2017-07-01
Full Text Available In this article we check, with the Mizar system [2], Pascal’s theorem in the real projective plane (in projective geometry Pascal’s theorem is also known as the Hexagrammum Mysticum Theorem1. Pappus’ theorem is a special case of a degenerate conic of two lines.
The generalized back projection theorem for cone beam reconstruction
International Nuclear Information System (INIS)
Peyrin, F.C.
1985-01-01
The use of cone beam scanners raises the problem of three dimensional reconstruction from divergent projections. After a survey on bidimensional analytical reconstruction methods we examine their application to the 3D problem. Finally, it is shown that the back projection theorem can be generalized to cone beam projections. This allows to state a new inversion formula suitable for both the 4 π parallel and divergent geometries. It leads to the generalization of the ''rho-filtered back projection'' algorithm which is outlined
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…
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.
Liouville's theorem and the method of the inverse problem
International Nuclear Information System (INIS)
Its, A.R.
1985-01-01
An approach to the investigation of the Zakharov-Shabat equations is developed. This approach is based on a classical theorem of Liouville and is the synthesis of ''finite-zone'' integration, the matrix Riemann problem method and the theory of isomonodromy deformations of differential equations. The effectiveness of the proposed scheme is demonstrated by developing ''dressing procedures'' for the Bullough-Dodd equation
Negating Four Color Theorem with Neutrosophy and Quadstage Method
Directory of Open Access Journals (Sweden)
Fu Yuhua
2015-03-01
Full Text Available With the help of Neutrosophy and Quad-stage Method, the proof for negation of “the four color theorem” is given. In which the key issue is to consider the color of the boundary, thus “the two color theorem” and “the five color theorem” are derived to replace "the four color theorem".
Limit theorems and inequalities via martingale methods
Directory of Open Access Journals (Sweden)
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 spectral method and ergodic theorems for general Markov chains
International Nuclear Information System (INIS)
Nagaev, S V
2015-01-01
We study the ergodic properties of Markov chains with an arbitrary state space and prove a geometric ergodic theorem. The method of the proof is new: it may be described as an operator method. Our main result is an ergodic theorem for Harris-Markov chains in the case when the return time to some fixed set has finite expectation. Our conditions for the transition function are more general than those used by Athreya-Ney and Nummelin. Unlike them, we impose restrictions not on the original transition function but on the transition function of an embedded Markov chain constructed from the return times to the fixed set mentioned above. The proof uses the spectral theory of linear operators on a Banach space
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)
Central limit theorems for large graphs: Method of quantum decomposition
International Nuclear Information System (INIS)
Hashimoto, Yukihiro; Hora, Akihito; Obata, Nobuaki
2003-01-01
A new method is proposed for investigating spectral distribution of the combinatorial Laplacian (adjacency matrix) of a large regular graph on the basis of quantum decomposition and quantum central limit theorem. General results are proved for Cayley graphs of discrete groups and for distance-regular graphs. The Coxeter groups and the Johnson graphs are discussed in detail by way of illustration. In particular, the limit distributions obtained from the Johnson graphs are characterized by the Meixner polynomials which form a one-parameter deformation of the Laguerre polynomials
DEFF Research Database (Denmark)
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....
Koopmans' theorem in the Hartree-Fock method. General formulation
Plakhutin, Boris N.
2018-03-01
This work presents a general formulation of Koopmans' theorem (KT) in the Hartree-Fock (HF) method which is applicable to molecular and atomic systems with arbitrary orbital occupancies and total electronic spin including orbitally degenerate (OD) systems. The new formulation is based on the full set of variational conditions imposed upon the HF orbitals by the variational principle for the total energy and the conditions imposed by KT on the orbitals of an ionized electronic shell [B. N. Plakhutin and E. R. Davidson, J. Chem. Phys. 140, 014102 (2014)]. Based on these conditions, a general form of the restricted open-shell HF method is developed, whose eigenvalues (orbital energies) obey KT for the whole energy spectrum. Particular attention is paid to the treatment of OD systems, for which the new method gives a number of unexpected results. For example, the present method gives four different orbital energies for the triply degenerate atomic level 2p in the second row atoms B to F. Based on both KT conditions and a parallel treatment of atoms B to F within a limited configuration interaction approach, we prove that these four orbital energies, each of which is triply degenerate, are related via KT to the energies of different spin-dependent ionization and electron attachment processes (2p)N → (2p ) N ±1. A discussion is also presented of specific limitations of the validity of KT in the HF method which arise in OD systems. The practical applicability of the theory is verified by comparing KT estimates of the ionization potentials I2s and I2p for the second row open-shell atoms Li to F with the relevant experimental data.
Projection-slice theorem based 2D-3D registration
Bom, van der M.J.; Pluim, J.P.W.; Homan, R.; Timmer, J.; Bartels, L.W.; Pluim, J.P.W.; Reinhardt, J.M.
2007-01-01
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
The generalized Mayer theorem in the approximating hamiltonian method
International Nuclear Information System (INIS)
Bakulev, A.P.; Bogoliubov, N.N. Jr.; Kurbatov, A.M.
1982-07-01
With the help of the generalized Mayer theorem we obtain the improved inequality for free energies of model and approximating systems, where only ''connected parts'' over the approximating hamiltonian are taken into account. For the concrete system we discuss the problem of convergency of appropriate series of ''connected parts''. (author)
Fixed point theorems in locally convex spacesÃ¢Â€Â”the Schauder mapping method
Directory of Open Access Journals (Sweden)
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.
International Nuclear Information System (INIS)
Ma Zhongqi
2006-01-01
The Levinson theorem is a fundamental theorem in quantum scattering theory, which shows the relation between the number of bound states and the phase shift at zero momentum for the Schroedinger equation. The Levinson theorem was established and developed mainly with the Jost function, with the Green function and with the Sturm-Liouville theorem. In this review, we compare three methods of proof, study the conditions of the potential for the Levinson theorem and generalize it to the Dirac equation. The method with the Sturm-Liouville theorem is explained in some detail. References to development and application of the Levinson theorem are introduced. (topical review)
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.
The spectral method and the central limit theorem for general Markov chains
Nagaev, S. V.
2017-12-01
We consider Markov chains with an arbitrary phase space and develop a modification of the spectral method that enables us to prove the central limit theorem (CLT) for non-uniformly ergodic Markov chains. The conditions imposed on the transition function are more general than those by Athreya-Ney and Nummelin. Our proof of the CLT is purely analytical.
Zhang, Chong; Lü, Qingtian; Yan, Jiayong; Qi, Guang
2018-04-01
Downward continuation can enhance small-scale sources and improve resolution. Nevertheless, the common methods have disadvantages in obtaining optimal results because of divergence and instability. We derive the mean-value theorem for potential fields, which could be the theoretical basis of some data processing and interpretation. Based on numerical solutions of the mean-value theorem, we present the convergent and stable downward continuation methods by using the first-order vertical derivatives and their upward continuation. By applying one of our methods to both the synthetic and real cases, we show that our method is stable, convergent and accurate. Meanwhile, compared with the fast Fourier transform Taylor series method and the integrated second vertical derivative Taylor series method, our process has very little boundary effect and is still stable in noise. We find that the characters of the fading anomalies emerge properly in our downward continuation with respect to the original fields at the lower heights.
Nonlinear realizations, the orbit method and Kohn's theorem
Andrzejewski, K.; Gonera, J.; Kosinski, P.
2012-01-01
The orbit method is used to describe the centre of mass motion of the system of particles with fixed charge to mass ratio moving in homogeneous magnetic field and confined by harmonic potential. The nonlinear action of symmetry group on phase space is identified and compared with the one obtained with the help of Eisenhart lift.
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.
Path integral methods via the use of the central limit theorem and application
International Nuclear Information System (INIS)
Thrapsaniotis, E G
2008-01-01
We consider a path integral in the phase space possibly with an influence functional in it and we use a method based on the use of the central limit theorem on the phase of the path integral representation to extract an equivalent expression which can be used in numerical calculations. Moreover we give conditions under which we can extract closed analytical results. As a specific application we consider a general system of two coupled and forced harmonic oscillators with coupling of the form x 1 x α 2 and we derive the relevant sign solved propagator
International Nuclear Information System (INIS)
Kaneko, K.
1987-01-01
A relationship between the number projection and the shell model methods is investigated in the case of a single-j shell. We can find a one-to-one correspondence between the number projected and the shell model states
Discovering the Theorem of Pythagoras
Lattanzio, Robert (Editor)
1988-01-01
In this 'Project Mathematics! series, sponsored by the California Institute of Technology, Pythagoraus' theorem a(exp 2) + b(exp 2) = c(exp 2) is discussed and the history behind this theorem is explained. hrough live film footage and computer animation, applications in real life are presented and the significance of and uses for this theorem are put into practice.
Projection-iteration methods for solving nonlinear operator equations
International Nuclear Information System (INIS)
Nguyen Minh Chuong; Tran thi Lan Anh; Tran Quoc Binh
1989-09-01
In this paper, the authors investigate a nonlinear operator equation in uniformly convex Banach spaces as in metric spaces by using stationary and nonstationary generalized projection-iteration methods. Convergence theorems in the strong and weak sense were established. (author). 7 refs
Energy Technology Data Exchange (ETDEWEB)
Etim, E; Basili, C [Rome Univ. (Italy). Ist. di Matematica
1978-08-21
The lagrangian in the path integral solution of the master equation of a stationary Markov process is derived by application of the Ehrenfest-type theorem of quantum mechanics and the Cauchy method of finding inverse functions. Applied to the non-linear Fokker-Planck equation the authors reproduce the result obtained by integrating over Fourier series coefficients and by other methods.
Directory of Open Access Journals (Sweden)
Chunyan Han
2015-01-01
Full Text Available Based on the heteroclinic Shil’nikov theorem and switching control, a kind of multipiecewise linear chaotic system is constructed in this paper. Firstly, two fundamental linear systems are constructed via linearization of a chaotic system at its two equilibrium points. Secondly, a two-piecewise linear chaotic system which satisfies the Shil’nikov theorem is generated by constructing heteroclinic loop between equilibrium points of the two fundamental systems by switching control. Finally, another multipiecewise linear chaotic system that also satisfies the Shil’nikov theorem is obtained via alternate translation of the two fundamental linear systems and heteroclinic loop construction of adjacent equilibria for the multipiecewise linear system. Some basic dynamical characteristics, including divergence, Lyapunov exponents, and bifurcation diagrams of the constructed systems, are analyzed. Meanwhile, computer simulation and circuit design are used for the proposed chaotic systems, and they are demonstrated to be effective for the method of chaos anticontrol.
Energy Technology Data Exchange (ETDEWEB)
Miserev, D. S., E-mail: d.miserev@student.unsw.edu.au, E-mail: erazorheader@gmail.com [University of New South Wales, School of Physics (Australia)
2016-06-15
The problem of localized states in 1D systems with a relativistic spectrum, namely, graphene stripes and carbon nanotubes, is studied analytically. The bound state as a superposition of two chiral states is completely described by their relative phase, which is the foundation of the variable phase method (VPM) developed herein. Based on our VPM, we formulate and prove the relativistic Levinson theorem. The problem of bound states can be reduced to the analysis of closed trajectories of some vector field. Remarkably, the Levinson theorem appears as the Poincaré index theorem for these closed trajectories. The VPM equation is also reduced to the nonrelativistic and semiclassical limits. The limit of a small momentum p{sub y} of transverse quantization is applicable to an arbitrary integrable potential. In this case, a single confined mode is predicted.
Tkatchenko, Alexandre; Ambrosetti, Alberto; DiStasio, Robert A.
2013-02-01
Interatomic pairwise methods are currently among the most popular and accurate ways to include dispersion energy in density functional theory calculations. However, when applied to more than two atoms, these methods are still frequently perceived to be based on ad hoc assumptions, rather than a rigorous derivation from quantum mechanics. Starting from the adiabatic connection fluctuation-dissipation (ACFD) theorem, an exact expression for the electronic exchange-correlation energy, we demonstrate that the pairwise interatomic dispersion energy for an arbitrary collection of isotropic polarizable dipoles emerges from the second-order expansion of the ACFD formula upon invoking the random-phase approximation (RPA) or the full-potential approximation. Moreover, for a system of quantum harmonic oscillators coupled through a dipole-dipole potential, we prove the equivalence between the full interaction energy obtained from the Hamiltonian diagonalization and the ACFD-RPA correlation energy. This property makes the Hamiltonian diagonalization an efficient method for the calculation of the many-body dispersion energy. In addition, we show that the switching function used to damp the dispersion interaction at short distances arises from a short-range screened Coulomb potential, whose role is to account for the spatial spread of the individual atomic dipole moments. By using the ACFD formula, we gain a deeper understanding of the approximations made in the interatomic pairwise approaches, providing a powerful formalism for further development of accurate and efficient methods for the calculation of the dispersion energy.
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
International Nuclear Information System (INIS)
Palmer, R.
1994-06-01
Electromagnetic fields can be separated into near and far components. Near fields are extensions of static fields. They do not radiate, and they fall off more rapidly from a source than far fields. Near fields can accelerate particles, but the ratio of acceleration to source fields at a distance R, is always less than R/λ or 1, whichever is smaller. Far fields can be represented as sums of plane parallel, transversely polarized waves that travel at the velocity of light. A single such wave in a vacuum cannot give continuous acceleration, and it is shown that no sums of such waves can give net first order acceleration. This theorem is proven in three different ways; each method showing a different aspect of the situation
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
Virial theorem and hypervirial theorem in a spherical geometry
International Nuclear Information System (INIS)
Li Yan; Chen Jingling; Zhang Fulin
2011-01-01
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)
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...
Debattista, Josephine
2000-01-01
Pythagoras 580 BC was a Greek mathematician who became famous for formulating Pythagoras Theorem but its principles were known earlier. The ancient Egyptians wanted to layout square (90°) corners to their fields. To solve this problem about 2000 BC they discovered the 'magic' of the 3-4-5 triangle.
Energy Technology Data Exchange (ETDEWEB)
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)).
Indian Academy of Sciences (India)
eralizing the method of proof of the well known. Cantor's ... Godel's first incompleteness theorem is proved. ... that the number of elements in any finite set is a natural number. ..... proof also has a Godel number; of course, you have to fix.
Chu, Shih-I.; Telnov, Dmitry A.
2004-02-01
The advancement of high-power and short-pulse laser technology in the past two decades has generated considerable interest in the study of multiphoton and very high-order nonlinear optical processes of atomic and molecular systems in intense and superintense laser fields, leading to the discovery of a host of novel strong-field phenomena which cannot be understood by the conventional perturbation theory. The Floquet theorem and the time-independent Floquet Hamiltonian method are powerful theoretical framework for the study of bound-bound multiphoton transitions driven by periodically time-dependent fields. However, there are a number of significant strong-field processes cannot be directly treated by the conventional Floquet methods. In this review article, we discuss several recent developments of generalized Floquet theorems, formalisms, and quasienergy methods, beyond the conventional Floquet theorem, for accurate nonperturbative treatment of a broad range of strong-field atomic and molecular processes and phenomena of current interests. Topics covered include (a) artificial intelligence (AI)-most-probable-path approach (MPPA) for effective treatment of ultralarge Floquet matrix problem; (b) non-Hermitian Floquet formalisms and complex quasienergy methods for nonperturbative treatment of bound-free and free-free processes such as multiphoton ionization (MPI) and above-threshold ionization (ATI) of atoms and molecules, multiphoton dissociation (MPD) and above-threshold dissociation (ATD) of molecules, chemical bond softening and hardening, charge-resonance enhanced ionization (CREI) of molecular ions, and multiple high-order harmonic generation (HHG), etc.; (c) many-mode Floquet theorem (MMFT) for exact treatment of multiphoton processes in multi-color laser fields with nonperiodic time-dependent Hamiltonian; (d) Floquet-Liouville supermatrix (FLSM) formalism for exact nonperturbative treatment of time-dependent Liouville equation (allowing for relaxations and
International Nuclear Information System (INIS)
Chu, S.-I.; Telnov, D.A.
2004-01-01
The advancement of high-power and short-pulse laser technology in the past two decades has generated considerable interest in the study of multiphoton and very high-order nonlinear optical processes of atomic and molecular systems in intense and superintense laser fields, leading to the discovery of a host of novel strong-field phenomena which cannot be understood by the conventional perturbation theory. The Floquet theorem and the time-independent Floquet Hamiltonian method are powerful theoretical framework for the study of bound-bound multiphoton transitions driven by periodically time-dependent fields. However, there are a number of significant strong-field processes cannot be directly treated by the conventional Floquet methods. In this review article, we discuss several recent developments of generalized Floquet theorems, formalisms, and quasienergy methods, beyond the conventional Floquet theorem, for accurate nonperturbative treatment of a broad range of strong-field atomic and molecular processes and phenomena of current interests. Topics covered include (a) artificial intelligence (AI)-most-probable-path approach (MPPA) for effective treatment of ultralarge Floquet matrix problem; (b) non-Hermitian Floquet formalisms and complex quasienergy methods for nonperturbative treatment of bound-free and free-free processes such as multiphoton ionization (MPI) and above-threshold ionization (ATI) of atoms and molecules, multiphoton dissociation (MPD) and above-threshold dissociation (ATD) of molecules, chemical bond softening and hardening, charge-resonance enhanced ionization (CREI) of molecular ions, and multiple high-order harmonic generation (HHG), etc.; (c) many-mode Floquet theorem (MMFT) for exact treatment of multiphoton processes in multi-color laser fields with nonperiodic time-dependent Hamiltonian; (d) Floquet-Liouville supermatrix (FLSM) formalism for exact nonperturbative treatment of time-dependent Liouville equation (allowing for relaxations and
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.
International Nuclear Information System (INIS)
Veltman, H.
1990-01-01
The equivalence theorem states that, at an energy E much larger than the vector-boson mass M, the leading order of the amplitude with longitudinally polarized vector bosons on mass shell is given by the amplitude in which these vector bosons are replaced by the corresponding Higgs ghosts. We prove the equivalence theorem and show its validity in every order in perturbation theory. We first derive the renormalized Ward identities by using the diagrammatic method. Only the Feynman-- 't Hooft gauge is discussed. The last step of the proof includes the power-counting method evaluated in the large-Higgs-boson-mass limit, needed to estimate the leading energy behavior of the amplitudes involved. We derive expressions for the amplitudes involving longitudinally polarized vector bosons for all orders in perturbation theory. The fermion mass has not been neglected and everything is evaluated in the region m f ∼M much-lt E much-lt m Higgs
Breakthrough Propulsion Physics Project: Project Management Methods
Millis, Marc G.
2004-01-01
To leap past the limitations of existing propulsion, the NASA Breakthrough Propulsion Physics (BPP) Project seeks further advancements in physics from which new propulsion methods can eventually be derived. Three visionary breakthroughs are sought: (1) propulsion that requires no propellant, (2) propulsion that circumvents existing speed limits, and (3) breakthrough methods of energy production to power such devices. Because these propulsion goals are presumably far from fruition, a special emphasis is to identify credible research that will make measurable progress toward these goals in the near-term. The management techniques to address this challenge are presented, with a special emphasis on the process used to review, prioritize, and select research tasks. This selection process includes these key features: (a) research tasks are constrained to only address the immediate unknowns, curious effects or critical issues, (b) reliability of assertions is more important than the implications of the assertions, which includes the practice where the reviewers judge credibility rather than feasibility, and (c) total scores are obtained by multiplying the criteria scores rather than by adding. Lessons learned and revisions planned are discussed.
Uniqueness theorems for variational problems by the method of transformation groups
Reichel, Wolfgang
2004-01-01
A classical problem in the calculus of variations is the investigation of critical points of functionals {\\cal L} on normed spaces V. The present work addresses the question: Under what conditions on the functional {\\cal L} and the underlying space V does {\\cal L} have at most one critical point? A sufficient condition for uniqueness is given: the presence of a "variational sub-symmetry", i.e., a one-parameter group G of transformations of V, which strictly reduces the values of {\\cal L}. The "method of transformation groups" is applied to second-order elliptic boundary value problems on Riemannian manifolds. Further applications include problems of geometric analysis and elasticity.
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.
Generalized Dandelin’s Theorem
Kheyfets, A. L.
2017-11-01
The paper gives a geometric proof of the theorem which states that in case of the plane section of a second-order surface of rotation (quadrics of rotation, QR), such conics as an ellipse, a hyperbola or a parabola (types of conic sections) are formed. The theorem supplements the well-known Dandelin’s theorem which gives the geometric proof only for a circular cone and applies the proof to all QR, namely an ellipsoid, a hyperboloid, a paraboloid and a cylinder. That’s why the considered theorem is known as the generalized Dandelin’s theorem (GDT). The GDT proof is based on a relatively unknown generalized directrix definition (GDD) of conics. The work outlines the GDD proof for all types of conics as their necessary and sufficient condition. Based on the GDD, the author proves the GDT for all QR in case of a random position of the cutting plane. The graphical stereometric structures necessary for the proof are given. The implementation of the structures by 3d computer methods is considered. The article shows the examples of the builds made in the AutoCAD package. The theorem is intended for the training course of theoretical training of elite student groups of architectural and construction specialties.
Fermat's Last Theorem A Theorem at Last!
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 1; Issue 1. Fermat's Last Theorem A Theorem at Last! C S Yogananda. General Article Volume 1 Issue 1 January 1996 pp 71-79. Fulltext. Click here to view fulltext PDF. Permanent link: https://www.ias.ac.in/article/fulltext/reso/001/01/0071-0079 ...
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).
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
Bleiziffer, Patrick; Schmidtel, Daniel; Görling, Andreas
2014-11-28
The occurrence of instabilities, in particular singlet-triplet and singlet-singlet instabilities, in the exact-exchange (EXX) Kohn-Sham method is investigated. Hessian matrices of the EXX electronic energy with respect to the expansion coefficients of the EXX effective Kohn-Sham potential in an auxiliary basis set are derived. The eigenvalues of these Hessian matrices determine whether or not instabilities are present. Similar as in the corresponding Hartree-Fock case instabilities in the EXX method are related to symmetry breaking of the Hamiltonian operator for the EXX orbitals. In the EXX methods symmetry breaking can easily be visualized by displaying the local multiplicative exchange potential. Examples (N2, O2, and the polyyne C10H2) for instabilities and symmetry breaking are discussed. The relation of the stability conditions for EXX methods to approaches calculating the Kohn-Sham correlation energy via the adiabatic-connection fluctuation-dissipation (ACFD) theorem is discussed. The existence or nonexistence of singlet-singlet instabilities in an EXX calculation is shown to indicate whether or not the frequency-integration in the evaluation of the correlation energy is singular in the EXX-ACFD method. This method calculates the Kohn-Sham correlation energy through the ACFD theorem theorem employing besides the Coulomb kernel also the full frequency-dependent exchange kernel and yields highly accurate electronic energies. For the case of singular frequency-integrands in the EXX-ACFD method a regularization is suggested. Finally, we present examples of molecular systems for which the self-consistent field procedure of the EXX as well as the Hartree-Fock method can converge to more than one local minimum depending on the initial conditions.
International Nuclear Information System (INIS)
Bleiziffer, Patrick; Schmidtel, Daniel; Görling, Andreas
2014-01-01
The occurrence of instabilities, in particular singlet-triplet and singlet-singlet instabilities, in the exact-exchange (EXX) Kohn-Sham method is investigated. Hessian matrices of the EXX electronic energy with respect to the expansion coefficients of the EXX effective Kohn-Sham potential in an auxiliary basis set are derived. The eigenvalues of these Hessian matrices determine whether or not instabilities are present. Similar as in the corresponding Hartree-Fock case instabilities in the EXX method are related to symmetry breaking of the Hamiltonian operator for the EXX orbitals. In the EXX methods symmetry breaking can easily be visualized by displaying the local multiplicative exchange potential. Examples (N 2 , O 2 , and the polyyne C 10 H 2 ) for instabilities and symmetry breaking are discussed. The relation of the stability conditions for EXX methods to approaches calculating the Kohn-Sham correlation energy via the adiabatic-connection fluctuation-dissipation (ACFD) theorem is discussed. The existence or nonexistence of singlet-singlet instabilities in an EXX calculation is shown to indicate whether or not the frequency-integration in the evaluation of the correlation energy is singular in the EXX-ACFD method. This method calculates the Kohn-Sham correlation energy through the ACFD theorem theorem employing besides the Coulomb kernel also the full frequency-dependent exchange kernel and yields highly accurate electronic energies. For the case of singular frequency-integrands in the EXX-ACFD method a regularization is suggested. Finally, we present examples of molecular systems for which the self-consistent field procedure of the EXX as well as the Hartree-Fock method can converge to more than one local minimum depending on the initial conditions
Houston, Louis M.
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...
The Patchwork Divergence Theorem
Dray, Tevian; Hellaby, Charles
1994-01-01
The divergence theorem in its usual form applies only to suitably smooth vector fields. For vector fields which are merely piecewise smooth, as is natural at a boundary between regions with different physical properties, one must patch together the divergence theorem applied separately in each region. We give an elegant derivation of the resulting "patchwork divergence theorem" which is independent of the metric signature in either region, and which is thus valid if the signature changes. (PA...
Optical theorem and its history
International Nuclear Information System (INIS)
Newton, R.G.
1978-01-01
A translation is presented of a paper submitted to the symposium ''Concepts and methods in microscopic physics'' held at Washington University in 1974. A detailed description is given of the history of the optical theorem, its various formulations and derivations and its use in the scattering theory. (Z.J.)
International Nuclear Information System (INIS)
Colle, R.; Simonucci, S.
1996-01-01
The theoretical framework of a method that utilizes a projected potential operator to construct scattering wave functions is presented. Theorems and spectral properties of a Hamiltonian with the potential energy operator represented in terms of L'2(R'3)-functions are derived. The computational advantages offered by the method for calculating spectroscopic quantities, like resonance energies, decay probabilities and photoionization cross-sections, are discussed
The Hellmann–Feynman theorem, the comparison theorem, and the envelope theory
Directory of Open Access Journals (Sweden)
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.
Guney, Veli Ugur
In this work we look for novel classes of Bell's inequalities and methods to produce them. We also find their quantum violations including, if possible, the maximum one. The Jordan bases method that we explain in Chapter 2 is about using a pair of certain type of orthonormal bases whose spans are subspaces related to measurement outcomes of incompatible quantities on the same physical system. Jordan vectors are the briefest way of expressing the relative orientation of any two subspaces. This feature helps us to reduce the dimensionality of the parameter space on which we do searches for optimization. The work is published in [24]. In Chapter 3, we attempt to find a connection between group theory and Bell's theorem. We devise a way of generating terms of a Bell's inequality that are related to elements of an algebraic group. The same group generates both the terms of the Bell's inequality and the observables that are used to calculate the quantum value of the Bell expression. Our results are published in [25][26]. In brief, Bell's theorem is the main tool of a research program that was started by Einstein, Podolsky, Rosen [19] and Bohr [8] in the early days of quantum mechanics in their discussions about the core nature of physical systems. These debates were about a novel type of physical states called superposition states, which are introduced by quantum mechanics and manifested in the apparent inevitable randomness in measurement outcomes of identically prepared systems. Bell's huge contribution was to find a means of quantifying the problem and hence of opening the way to experimental verification by rephrasing the questions as limits on certain combinations of correlations between measurement results of spatially separate systems [7]. Thanks to Bell, the fundamental questions related to the nature of quantum mechanical systems became quantifiable [6]. According to Bell's theorem, some correlations between quantum entangled systems that involve incompatible
International Nuclear Information System (INIS)
Li Liang; Chen Zhiqiang; Xing Yuxiang; Zhang Li; Kang Kejun; Wang Ge
2006-01-01
In recent years, image reconstruction methods for cone-beam computed tomography (CT) have been extensively studied. However, few of these studies discussed computing parallel-beam projections from cone-beam projections. In this paper, we focus on the exact synthesis of complete or incomplete parallel-beam projections from cone-beam projections. First, an extended central slice theorem is described to establish a relationship between the Radon space and the Fourier space. Then, data sufficiency conditions are proposed for computing parallel-beam projection data from cone-beam data. Using these results, a general filtered backprojection algorithm is formulated that can exactly synthesize parallel-beam projection data from cone-beam projection data. As an example, we prove that parallel-beam projections can be exactly synthesized in an angular range in the case of circular cone-beam scanning. Interestingly, this angular range is larger than that derived in the Feldkamp reconstruction framework. Numerical experiments are performed in the circular scanning case to verify our method
The relativistic virial theorem
International Nuclear Information System (INIS)
Lucha, W.; Schoeberl, F.F.
1989-11-01
The relativistic generalization of the quantum-mechanical virial theorem is derived and used to clarify the connection between the nonrelativistic and (semi-)relativistic treatment of bound states. 12 refs. (Authors)
Wigner's Symmetry Representation Theorem
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 19; Issue 10. Wigner's Symmetry Representation Theorem: At the Heart of Quantum Field Theory! Aritra Kr Mukhopadhyay. General Article Volume 19 Issue 10 October 2014 pp 900-916 ...
Nonextensive Pythagoras' Theorem
Dukkipati, Ambedkar
2006-01-01
Kullback-Leibler relative-entropy, in cases involving distributions resulting from relative-entropy minimization, has a celebrated property reminiscent of squared Euclidean distance: it satisfies an analogue of the Pythagoras' theorem. And hence, this property is referred to as Pythagoras' theorem of relative-entropy minimization or triangle equality and plays a fundamental role in geometrical approaches of statistical estimation theory like information geometry. Equvalent of Pythagoras' theo...
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
Abstract. The general theme of this note is illustrated by the following theorem: Theorem 1. Suppose K is a compact set in the complex plane and 0 belongs to the boundary ∂K. Let A(K) denote the space of all functions f on K such that f is holo- morphic in a neighborhood of K and f(0) = 0. Also for any given positive integer ...
Application of the electrostatic Thompson–Lampard theorem to resistivity measurements
Czech Academy of Sciences Publication Activity Database
Mareš, Jiří J.; Hubík, Pavel; Krištofik, Jozef
2012-01-01
Roč. 23, č. 4 (2012), s. 1-5 ISSN 0957-0233 R&D Projects: GA ČR GAP204/10/0212 Institutional research plan: CEZ:AV0Z10100521 Keywords : resistivity * Thompson–Lampard theorem * van der Pauw method Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 1.435, year: 2012
Tight closure and vanishing theorems
International Nuclear Information System (INIS)
Smith, K.E.
2001-01-01
Tight closure has become a thriving branch of commutative algebra since it was first introduced by Mel Hochster and Craig Huneke in 1986. Over the past few years, it has become increasingly clear that tight closure has deep connections with complex algebraic geometry as well, especially with those areas of algebraic geometry where vanishing theorems play a starring role. The purpose of these lectures is to introduce tight closure and to explain some of these connections with algebraic geometry. Tight closure is basically a technique for harnessing the power of the Frobenius map. The use of the Frobenius map to prove theorems about complex algebraic varieties is a familiar technique in algebraic geometry, so it should perhaps come as no surprise that tight closure is applicable to algebraic geometry. On the other hand, it seems that so far we are only seeing the tip of a large and very beautiful iceberg in terms of tight closure's interpretation and applications to algebraic geometry. Interestingly, although tight closure is a 'characteristic p' tool, many of the problems where tight closure has proved useful have also yielded to analytic (L2) techniques. Despite some striking parallels, there had been no specific result directly linking tight closure and L∼ techniques. Recently, however, the equivalence of an ideal central to the theory of tight closure was shown to be equivalent to a certain 'multiplier ideal' first defined using L2 methods. Presumably, deeper connections will continue to emerge. There are two main types of problems for which tight closure has been helpful: in identifying nice structure and in establishing uniform behavior. The original algebraic applications of tight closure include, for example, a quick proof of the Hochster-Roberts theorem on the Cohen-Macaulayness of rings of invariants, and also a refined version of the Brianqon-Skoda theorem on the uniform behaviour of integral closures of powers of ideals. More recent, geometric
Qinshan CANDU project open top construction method
International Nuclear Information System (INIS)
Petrunik, K.J.; Wittann, K.; Khan, A.; Ricciuti, R.; Ivanov, A.; Chen, S.
2003-01-01
The significant schedule reductions achieved on the Qinshan CANDU Project were due in large part to the incorporation of advanced construction technologies in project design and delivery. For the Qinshan Project, a number of key advantages were realized through the use of the 'Open Top' construction method. This paper discusses the Qinshan Phase III CANDU Project Open Top implementation method. The Open Top method allowed major equipment to be installed simply, via the use of a Very Heavy Lift (VHL) crane and permitted the use of large-scale modularization. The advantages of Open Top construction, such as simplified access, more flexible project scheduling, improved construction safety and quality, and reduced labours are presented. The large-scale modularization of the Reactor Building Dousing System and the Open Top installation method and advantages relative to traditional CANDU 6 construction practices are also presented. Finally, major improvements for future CANDU plant construction using the Open Top method are discussed. (author)
Stable convergence and stable limit theorems
Häusler, Erich
2015-01-01
The authors present a concise but complete exposition of the mathematical theory of stable convergence and give various applications in different areas of probability theory and mathematical statistics to illustrate the usefulness of this concept. Stable convergence holds in many limit theorems of probability theory and statistics – such as the classical central limit theorem – which are usually formulated in terms of convergence in distribution. Originated by Alfred Rényi, the notion of stable convergence is stronger than the classical weak convergence of probability measures. A variety of methods is described which can be used to establish this stronger stable convergence in many limit theorems which were originally formulated only in terms of weak convergence. Naturally, these stronger limit theorems have new and stronger consequences which should not be missed by neglecting the notion of stable convergence. The presentation will be accessible to researchers and advanced students at the master's level...
On a theorem of Faltings on formal functions
Directory of Open Access Journals (Sweden)
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.
Complex proofs of real theorems
Lax, Peter D
2011-01-01
Complex Proofs of Real Theorems is an extended meditation on Hadamard's famous dictum, "The shortest and best way between two truths of the real domain often passes through the imaginary one." Directed at an audience acquainted with analysis at the first year graduate level, it aims at illustrating how complex variables can be used to provide quick and efficient proofs of a wide variety of important results in such areas of analysis as approximation theory, operator theory, harmonic analysis, and complex dynamics. Topics discussed include weighted approximation on the line, Müntz's theorem, Toeplitz operators, Beurling's theorem on the invariant spaces of the shift operator, prediction theory, the Riesz convexity theorem, the Paley-Wiener theorem, the Titchmarsh convolution theorem, the Gleason-Kahane-Żelazko theorem, and the Fatou-Julia-Baker theorem. The discussion begins with the world's shortest proof of the fundamental theorem of algebra and concludes with Newman's almost effortless proof of the prime ...
DEFF Research Database (Denmark)
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.......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....
Converse Barrier Certificate Theorem
DEFF Research Database (Denmark)
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...
Rationale and methods of the EFCOSUM project
Brussaard, J.H.; Johansson, L.; Kearney, J.
2002-01-01
Objective: To describe the rationale and methods for a European project (EFCOSUM) to develop a method for a European food consumption survey that delivers internationally comparable data on a set of policy-relevant nutritional indicators. Rationale and methods: Currently Member States are collecting
The Fluctuation Theorem and Dissipation Theorem for Poiseuille Flow
International Nuclear Information System (INIS)
Brookes, Sarah J; Reid, James C; Evans, Denis J; Searles, Debra J
2011-01-01
The fluctuation theorem and the dissipation theorem provide relationships to describe nonequilibrium systems arbitrarily far from, or close to equilibrium. They both rely on definition of a central property, the dissipation function. In this manuscript we apply these theorems to examine a boundary thermostatted system undergoing Poiseuille flow. The relationships are verified computationally and show that the dissipation theorem is potentially useful for study of boundary thermostatted systems consisting of complex molecules undergoing flow in the nonlinear regime.
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.…
A Short Proof of Klee's Theorem
Zanazzi, John J.
2013-01-01
In 1959, Klee proved that a convex body $K$ is a polyhedron if and only if all of its projections are polygons. In this paper, a new proof of this theorem is given for convex bodies in $\\mathbb{R}^3$.
Reciprocity theorem in high-temperature superconductors
Czech Academy of Sciences Publication Activity Database
Janeček, I.; Vašek, Petr
2003-01-01
Roč. 390, - (2003), s. 330-340 ISSN 0921-4534 R&D Projects: GA ČR GA202/00/1602; GA AV ČR IAA1010919 Institutional research plan: CEZ:AV0Z1010914 Keywords : transport properties * reciprocity theorem Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 1.192, year: 2003
Dalen, D. van
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
Saikia, Manjil P.
2013-01-01
We give a brief historical overview of the famous Pythagoras' theorem and Pythagoras. We present a simple proof of the result and dicsuss some extensions. We follow \\cite{thales}, \\cite{wiki} and \\cite{wiki2} for the historical comments and sources.
Converse Barrier Certificate Theorems
DEFF Research Database (Denmark)
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...
International Nuclear Information System (INIS)
Cahill, K.
1975-11-01
Local field theory is used to derive formulas that express certain boundary values of the N-point function as sums of products of scattering amplitudes. These formulas constitute a generalization of the optical theorem and facilitate the analysis of multiparticle scattering functions [fr
Telescopic projective methods for parabolic differential equations
Gear, C W
2003-01-01
Projective methods were introduced in an earlier paper [C.W. Gear, I.G. Kevrekidis, Projective Methods for Stiff Differential Equations: problems with gaps in their eigenvalue spectrum, NEC Research Institute Report 2001-029, available from http://www.neci.nj.nec.com/homepages/cwg/projective.pdf Abbreviated version to appear in SISC] as having potential for the efficient integration of problems with a large gap between two clusters in their eigenvalue spectrum, one cluster containing eigenvalues corresponding to components that have already been damped in the numerical solution and one corresponding to components that are still active. In this paper we introduce iterated projective methods that allow for explicit integration of stiff problems that have a large spread of eigenvalues with no gaps in their spectrum as arise in the semi-discretization of PDEs with parabolic components.
Telescopic projective methods for parabolic differential equations
International Nuclear Information System (INIS)
Gear, C.W.; Kevrekidis, Ioannis G.
2003-01-01
Projective methods were introduced in an earlier paper [C.W. Gear, I.G. Kevrekidis, Projective Methods for Stiff Differential Equations: problems with gaps in their eigenvalue spectrum, NEC Research Institute Report 2001-029, available from http://www.neci.nj.nec.com/homepages/cwg/projective.pdf Abbreviated version to appear in SISC] as having potential for the efficient integration of problems with a large gap between two clusters in their eigenvalue spectrum, one cluster containing eigenvalues corresponding to components that have already been damped in the numerical solution and one corresponding to components that are still active. In this paper we introduce iterated projective methods that allow for explicit integration of stiff problems that have a large spread of eigenvalues with no gaps in their spectrum as arise in the semi-discretization of PDEs with parabolic components
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…
Project Oriented Immersion Learning: Method and Results
DEFF Research Database (Denmark)
Icaza, José I.; Heredia, Yolanda; Borch, Ole M.
2005-01-01
A pedagogical approach called “project oriented immersion learning” is presented and tested on a graduate online course. The approach combines the Project Oriented Learning method with immersion learning in a virtual enterprise. Students assumed the role of authors hired by a fictitious publishing...... 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...
A perceptron network theorem prover for the propositional calculus
Drossaers, M.F.J.
In this paper a short introduction to neural networks and a design for a perceptron network theorem prover for the propositional calculus are presented. The theorem prover is a representation of a variant of the semantic tableau method, called the parallel tableau method, by a network of
Fully Quantum Fluctuation Theorems
Åberg, Johan
2018-02-01
Systems that are driven out of thermal equilibrium typically dissipate random quantities of energy on microscopic scales. Crooks fluctuation theorem relates the distribution of these random work costs to the corresponding distribution for the reverse process. By an analysis that explicitly incorporates the energy reservoir that donates the energy and the control system that implements the dynamic, we obtain a quantum generalization of Crooks theorem that not only includes the energy changes in the reservoir but also the full description of its evolution, including coherences. Moreover, this approach opens up the possibility for generalizations of the concept of fluctuation relations. Here, we introduce "conditional" fluctuation relations that are applicable to nonequilibrium systems, as well as approximate fluctuation relations that allow for the analysis of autonomous evolution generated by global time-independent Hamiltonians. We furthermore extend these notions to Markovian master equations, implicitly modeling the influence of the heat bath.
Multivariable Chinese Remainder Theorem
Indian Academy of Sciences (India)
IAS Admin
to sleep. The 3rd thief wakes up and finds the rest of the coins make 7 equal piles excepting a coin which he pockets. If the total number of coins they stole is not more than 200, what is the exact number? With a bit of hit and miss, one can find that 157 is a possible number. The Chinese remainder theorem gives a systematic ...
Projection preconditioning for Lanczos-type methods
Energy Technology Data Exchange (ETDEWEB)
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.
Extended abstract: Partial row projection methods
Energy Technology Data Exchange (ETDEWEB)
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.
Uncertainty Analyses for Back Projection Methods
Zeng, H.; Wei, S.; Wu, W.
2017-12-01
So far few comprehensive error analyses for back projection methods have been conducted, although it is evident that high frequency seismic waves can be easily affected by earthquake depth, focal mechanisms and the Earth's 3D structures. Here we perform 1D and 3D synthetic tests for two back projection methods, MUltiple SIgnal Classification (MUSIC) (Meng et al., 2011) and Compressive Sensing (CS) (Yao et al., 2011). We generate synthetics for both point sources and finite rupture sources with different depths, focal mechanisms, as well as 1D and 3D structures in the source region. The 3D synthetics are generated through a hybrid scheme of Direct Solution Method and Spectral Element Method. Then we back project the synthetic data using MUSIC and CS. The synthetic tests show that the depth phases can be back projected as artificial sources both in space and time. For instance, for a source depth of 10km, back projection gives a strong signal 8km away from the true source. Such bias increases with depth, e.g., the error of horizontal location could be larger than 20km for a depth of 40km. If the array is located around the nodal direction of direct P-waves the teleseismic P-waves are dominated by the depth phases. Therefore, back projections are actually imaging the reflection points of depth phases more than the rupture front. Besides depth phases, the strong and long lasted coda waves due to 3D effects near trench can lead to additional complexities tested here. The strength contrast of different frequency contents in the rupture models also produces some variations to the back projection results. In the synthetic tests, MUSIC and CS derive consistent results. While MUSIC is more computationally efficient, CS works better for sparse arrays. In summary, our analyses indicate that the impact of various factors mentioned above should be taken into consideration when interpreting back projection images, before we can use them to infer the earthquake rupture physics.
A new proof of the positive energy theorem
International Nuclear Information System (INIS)
Witten, E.
1981-01-01
A new proof is given of the positive energy theorem of classical general relativity. Also, a new proof is given that there are no asymptotically Euclidean gravitational instantons. (These theorems have been proved previously, by a different method, by Schoen and Yau). The relevance of these results to the stability of Minkowski space is discussed. (orig.)
International Nuclear Information System (INIS)
Lloyd, Mark Anthony
1999-01-01
We in the nuclear power industry consider ourselves to be at the forefront of civilised progress. Yet, all too often, even we ourselves don't believe our public relations statements about nuclear power. Why is this? Let us approach the question by considering Godel's Theorem. Godel's Theorem is extremely complicated mathematically, but for our purposes can be simplified to the maxim that one cannot validate a system from within that system. Scientists, especially those in the fields of astronomy and nuclear physics, have long realised the implications of Godel's Theorem. The people to whom we must communicate look to us, who officially know everything about our industry, to comfort and reassure them. And we forget that we can only comfort them by addressing their emotional needs, not by demonstrating our chilling o bjectivity . Let us try something completely new in communication. Instead of looking for incremental rules which will help us marginally differentiate the way we communicate about minor or major incidents, let us leapfrog across 'objectivity' to meaning and relevance. If we truly believe that nuclear energy is a good thing, this leap should not be difficult. Finally, if we as communicators are not prepared to be meaningful and relevant - not prepared to leapfrog beyond weasel terms like 'minor incident' - what does that say about the kinds of people we believe the nuclear community to be? Are nuclear people a group apart, divisible from the rest of the human race by their evil? In fact the nuclear community is a living, laughing, normal part of a whole society; and is moreover a good contributor to the technological progress that society demands. When we ourselves recognise this, we will start to communicate nuclear issues in the same language as the rest of society. We will start to speak plainly and convincingly, and our conviction will leapfrog our audience into being able to believe us
Topological interpretation of Luttinger theorem
Seki, Kazuhiro; Yunoki, Seiji
2017-01-01
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 n...
On Callan's proof of the BPHZ theorem
International Nuclear Information System (INIS)
Lesniewski, A.
1984-01-01
The author gives an elementary proof of the BPHZ theorem in the case of the Euclidean lambdaphi 4 theory. The method of proof relies on a detailed analysis of the skeleton structure of graphs and estimates based on the Callan-Symanzik equations. (Auth.)
Czech Academy of Sciences Publication Activity Database
Narins, L.; Tran, Tuan
2017-01-01
Roč. 85, č. 2 (2017), s. 496-524 ISSN 0364-9024 Institutional support: RVO:67985807 Keywords : Turán’s theorem * stability method * multipartite version Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 0.601, year: 2016
Projection operator method for collective tunneling transitions
International Nuclear Information System (INIS)
Kohmura, Toshitake; Ohta, Hirofumi; Hashimoto, Yukio; Maruyama, Masahiro
2002-01-01
Collective tunneling transitions take place in the case that a system has two nearly degenerate ground states with a slight energy splitting, which provides the time scale of the tunneling. The Liouville equation determines the evolution of the density matrix, while the Schroedinger equation determines that of a state. The Liouville equation seems to be more powerful for calculating accurately the energy splitting of two nearly degenerate eigenstates. However, no method to exactly solve the Liouville eigenvalue equation has been established. The usual projection operator method for the Liouville equation is not feasible. We analytically solve the Liouville evolution equation for nuclear collective tunneling from one Hartree minimum to another, proposing a simple and solvable model Hamiltonian for the transition. We derive an analytical expression for the splitting of energy eigenvalues from a spectral function of the Liouville evolution using a half-projected operator method. A full-order analytical expression for the energy splitting is obtained. We define the collective tunneling path of a microscopic Hamiltonian for collective tunneling, projecting the nuclear ground states onto n-particle n-hole state spaces. It is argued that the collective tunneling path sector of a microscopic Hamiltonian can be transformed into the present solvable model Hamiltonian. (author)
Bertrand's theorem and virial theorem in fractional classical mechanics
Yu, Rui-Yan; Wang, Towe
2017-09-01
Fractional classical mechanics is the classical counterpart of fractional quantum mechanics. The central force problem in this theory is investigated. Bertrand's theorem is generalized, and virial theorem is revisited, both in three spatial dimensions. In order to produce stable, closed, non-circular orbits, the inverse-square law and the Hooke's law should be modified in fractional classical mechanics.
Extension and reconstruction theorems for the Urysohn universal metric space
Czech Academy of Sciences Publication Activity Database
Kubiś, Wieslaw; Rubin, M.
2010-01-01
Roč. 60, č. 1 (2010), s. 1-29 ISSN 0011-4642 R&D Projects: GA AV ČR IAA100190901 Institutional research plan: CEZ:AV0Z10190503 Keywords : Urysohn space * bilipschitz homeomorphism * modulus of continuity * reconstruction theorem * extension theorem Subject RIV: BA - General Mathematics Impact factor: 0.265, year: 2010 http://dml.cz/handle/10338.dmlcz/140544
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
Directory of Open Access Journals (Sweden)
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.…
How Agile Methods Conquers General Project Management - The Project Half Double Initiative
DEFF Research Database (Denmark)
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...
A Decomposition Theorem for Finite Automata.
Santa Coloma, Teresa L.; Tucci, Ralph P.
1990-01-01
Described is automata theory which is a branch of theoretical computer science. A decomposition theorem is presented that is easier than the Krohn-Rhodes theorem. Included are the definitions, the theorem, and a proof. (KR)
OTTER, Resolution Style Theorem Prover
International Nuclear Information System (INIS)
McCune, W.W.
2001-01-01
1 - Description of program or function: OTTER (Other Techniques for Theorem-proving and Effective Research) is a resolution-style theorem-proving program for first-order logic with equality. OTTER includes the inference rules binary resolution, hyper-resolution, UR-resolution, and binary para-modulation. These inference rules take as small set of clauses and infer a clause. If the inferred clause is new and useful, it is stored and may become available for subsequent inferences. Other capabilities are conversion from first-order formulas to clauses, forward and back subsumption, factoring, weighting, answer literals, term ordering, forward and back demodulation, and evaluable functions and predicates. 2 - Method of solution: For its inference process OTTER uses the given-clause algorithm, which can be viewed as a simple implementation of the set of support strategy. OTTER maintains three lists of clauses: axioms, sos (set of support), and demodulators. OTTER is not automatic. Even after the user has encoded a problem into first-order logic or into clauses, the user must choose inference rules, set options to control the processing of inferred clauses, and decide which input formulae or clauses are to be in the initial set of support and which, if any, equalities are to be demodulators. If OTTER fails to find a proof, the user may try again different initial conditions. 3 - Restrictions on the complexity of the problem - Maxima of: 5000 characters in an input string, 64 distinct variables in a clause, 51 characters in any symbol. The maxima can be changed by finding the appropriate definition in the header.h file, increasing the limit, and recompiling OTTER. There are a few constraints on the order of commands
A THEOREM ON CENTRAL VELOCITY DISPERSIONS
International Nuclear Information System (INIS)
An, Jin H.; Evans, N. Wyn
2009-01-01
It is shown that, if the tracer population is supported by a spherical dark halo with a core or a cusp diverging more slowly than that of a singular isothermal sphere (SIS), the logarithmic cusp slope γ of the tracers must be given exactly by γ = 2β, where β is their velocity anisotropy parameter at the center unless the same tracers are dynamically cold at the center. If the halo cusp diverges faster than that of the SIS, the velocity dispersion of the tracers must diverge at the center too. In particular, if the logarithmic halo cusp slope is larger than two, the diverging velocity dispersion also traces the behavior of the potential. The implication of our theorem on projected quantities is also discussed. We argue that our theorem should be understood as a warning against interpreting results based on simplifying assumptions such as isotropy and spherical symmetry.
Convergence theorems for quasi-contractive mappings
International Nuclear Information System (INIS)
Chidume, C.E.
1992-01-01
It is proved that each of two well known fixed point iteration methods (the Mann and Ishikawa iteration methods) converges strongly, without any compactness assumption on the domain of the map, to the unique fixed point of a quasi-contractive map in real Banach spacers with property (U, α, m+1, m). These Banach spaces include the L p (or l p ) spaces, p ≥ 2. Our theorems generalize important known results. (author). 29 refs
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...
Strong versions of Bell's theorem
International Nuclear Information System (INIS)
Stapp, H.P.
1994-01-01
Technical aspects of a recently constructed strong version of Bell's theorem are discussed. The theorem assumes neither hidden variables nor factorization, and neither determinism nor counterfactual definiteness. It deals directly with logical connections. Hence its relationship with modal logic needs to be described. It is shown that the proof can be embedded in an orthodox modal logic, and hence its compatibility with modal logic assured, but that this embedding weakens the theorem by introducing as added assumptions the conventionalities of the particular modal logic that is adopted. This weakening is avoided in the recent proof by using directly the set-theoretic conditions entailed by the locality assumption
Green's theorem and Gorenstein sequences
Ahn, Jeaman; Migliore, Juan C.; Shin, Yong-Su
2016-01-01
We study consequences, for a standard graded algebra, of extremal behavior in Green's Hyperplane Restriction Theorem. First, we extend his Theorem 4 from the case of a plane curve to the case of a hypersurface in a linear space. Second, assuming a certain Lefschetz condition, we give a connection to extremal behavior in Macaulay's theorem. We apply these results to show that $(1,19,17,19,1)$ is not a Gorenstein sequence, and as a result we classify the sequences of the form $(1,a,a-2,a,1)$ th...
-Dimensional Fractional Lagrange's Inversion Theorem
Directory of Open Access Journals (Sweden)
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
Project as an education method in teaching of physics
ŽAHOUREK, Martin
2011-01-01
The diploma thesis ?Project as an educational method for teaching physics ?deals with the possibilities of using project-based method for teaching physics at primary schools. Not only does it contain the theoretical background of project-based teaching, but also deals with practical issues in the form of an implementation of a chosen project ?Physics and physical education?. The aim of said project was to evaluate the efficiency of project-based teaching as far as the knowledge of pupils and ...
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...
A primer on Higgs boson low-energy theorems
International Nuclear Information System (INIS)
Dawson, S.; Haber, H.E.; California Univ., Santa Cruz, CA
1989-05-01
We give a pedagogical review of Higgs boson low-energy theorems and their applications in the study of light Higgs boson interactions with mesons and baryons. In particular, it is shown how to combine the chiral Lagrangian method with the Higgs low-energy theorems to obtain predictions for the interaction of Higgs bosons and pseudoscalar mesons. Finally, we discuss the relation between the low-energy theorems and a technique which makes use of the trace of the QCD energy-momentum tensor. 35 refs
Markov's theorem and algorithmically non-recognizable combinatorial manifolds
International Nuclear Information System (INIS)
Shtan'ko, M A
2004-01-01
We prove the theorem of Markov on the existence of an algorithmically non-recognizable combinatorial n-dimensional manifold for every n≥4. We construct for the first time a concrete manifold which is algorithmically non-recognizable. A strengthened form of Markov's theorem is proved using the combinatorial methods of regular neighbourhoods and handle theory. The proofs coincide for all n≥4. We use Borisov's group with insoluble word problem. It has two generators and twelve relations. The use of this group forms the base for proving the strengthened form of Markov's theorem
Method for the Drawing of Newman Projections: Understanding ...
Indian Academy of Sciences (India)
hands-on learning/manipula- tives, Newman projections. Method for the Drawing of Newman Projections: Understanding Newman Projections with the Help of Hands. The interconversion between the perspective formulae and. Newman projections is illustrated here. The method describes how students can look at their ...
The Project Method in Agricultural Education: Then and Now
Roberts, T. Grady; Harlin, Julie F.
2007-01-01
The purpose of this philosophical paper was to synthesize theoretical and historical foundations of the project method and compare them to modern best-practices. A review of historical and contemporary literature related to the project method yielded six themes: 1) purpose of projects; 2) project classification; 3) the process; 4) the context; 5)…
The Levy sections theorem revisited
International Nuclear Information System (INIS)
Figueiredo, Annibal; Gleria, Iram; Matsushita, Raul; Silva, Sergio Da
2007-01-01
This paper revisits the Levy sections theorem. We extend the scope of the theorem to time series and apply it to historical daily returns of selected dollar exchange rates. The elevated kurtosis usually observed in such series is then explained by their volatility patterns. And the duration of exchange rate pegs explains the extra elevated kurtosis in the exchange rates of emerging markets. In the end, our extension of the theorem provides an approach that is simpler than the more common explicit modelling of fat tails and dependence. Our main purpose is to build up a technique based on the sections that allows one to artificially remove the fat tails and dependence present in a data set. By analysing data through the lenses of the Levy sections theorem one can find common patterns in otherwise very different data sets
Ortiz, Guillermo P.; Mochán, W. Luis
2018-02-01
Keller’s theorem relates the components of the macroscopic dielectric response of a binary two-dimensional composite system with those of the reciprocal system obtained by interchanging its components. We present a derivation of the theorem that, unlike previous ones, does not employ the common assumption that the response function relates an irrotational to a solenoidal field and that is valid for dispersive and dissipative anisotropic systems. We show that the usual statement of Keller’s theorem in terms of the conductivity is strictly valid only at zero frequency and we obtain a new generalization for finite frequencies. We develop applications of the theorem to the study of the optical properties of systems such as superlattices, 2D isotropic and anisotropic metamaterials and random media, to test the accuracy of theories and computational schemes, and to increase the accuracy of approximate calculations.
The Levy sections theorem revisited
Figueiredo, Annibal; Gleria, Iram; Matsushita, Raul; Da Silva, Sergio
2007-06-01
This paper revisits the Levy sections theorem. We extend the scope of the theorem to time series and apply it to historical daily returns of selected dollar exchange rates. The elevated kurtosis usually observed in such series is then explained by their volatility patterns. And the duration of exchange rate pegs explains the extra elevated kurtosis in the exchange rates of emerging markets. In the end, our extension of the theorem provides an approach that is simpler than the more common explicit modelling of fat tails and dependence. Our main purpose is to build up a technique based on the sections that allows one to artificially remove the fat tails and dependence present in a data set. By analysing data through the lenses of the Levy sections theorem one can find common patterns in otherwise very different data sets.
Adiabatic theorem and spectral concentration
International Nuclear Information System (INIS)
Nenciu, G.
1981-01-01
The spectral concentration of arbitrary order, for the Stark effect is proved to exist for a large class of Hamiltonians appearing in nonrelativistic and relativistic quantum mechanics. The results are consequences of an abstract theorem about the spectral concentration for self-ad oint operators. A general form of the adiabatic theorem of quantum mechanics, generalizing an earlier result of the author as well as some results of Lenard, is also proved [ru
The Second Noether Theorem on Time Scales
Directory of Open Access Journals (Sweden)
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.
Factor and Remainder Theorems: An Appreciation
Weiss, Michael
2016-01-01
The high school curriculum sometimes seems like a disconnected collection of topics and techniques. Theorems like the factor theorem and the remainder theorem can play an important role as a conceptual "glue" that holds the curriculum together. These two theorems establish the connection between the factors of a polynomial, the solutions…
A remark on three-surface theorem
International Nuclear Information System (INIS)
Lu Zhujia
1991-01-01
The three-surface theorem for uniformly elliptic differential inequalities with nonpositive coefficient of zero-order term in some domain D is included in R n becomes trivial if the maximum of u on two separate boundary surface of D is nonpositive. We give a method in this paper for obtaining a nontrivial estimate of the maximum of u on a family of closed surfaces. (author). 2 refs
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...
A DIDACTIC SURVEY OVER MAIN CHARACTERISTICS OF LAGRANGE'S THEOREM IN MATHEMATICS AND IN ECONOMICS
Xhonneux, Sebastian; Henry, Valérie
2011-01-01
Because of its many uses, the constrained optimization problem is presented in most calculus courses for mathematicians but also for economists. Looking at Lagrange's Theorem we are interested in studying the teaching of this theorem in both branches of study, mathematics and economics. This paper faces a twofold objective: first, we show the methodology of our research project concerning the didactic transposition of Lagrange's Theorem in university mathematics courses. Sec...
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
Restriction Theorem for Principal bundles in Arbitrary Characteristic
DEFF Research Database (Denmark)
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...
Proofs and generalizations of the pythagorean theorem
Directory of Open Access Journals (Sweden)
Lialda B. Cavalcanti
2011-01-01
Full Text Available This article explores a topic developed by a group of researchers of the Science and Technology Teaching School of Instituto Federal de Pernambuco, Brazil (IFPE, in assistance to the development of the Mathematics Practical and Teaching Laboratory of the distance learning Teaching Licensure, financed by the Universidad Abierta de Brasil. In this article, we describe the peculiarities present in the proofs of the Pythagorean theorem with the purpose of illustrating some of these methods. The selection of these peculiarities was founded and based on the comparison of areas by means of the superimposition of geometrical shapes and used several different class resources. Some generalizations of this important theorem in mathematical problem-solving are also shown.
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…
Project Management Methods in Projects Co-financed by EU Funds
Kostalova, Jana; Tetrevova, Libena; Patak, Michal
2017-01-01
This paper deals with the management of projects co-financed by European Union funds (structural funds and the Cohesion Fund) in the Czech Republic (EU projects). The authors aimed to analyze and assess the scope of familiarity with basic project management methods and their application within the implementation of EU projects in the Czech Republic in the Programming Period 2007–2013. Based on a questionnaire survey of EU project organisers, the authors evaluate their attitudes to project man...
Projective Method for Generic Sensor Fusion Problem
International Nuclear Information System (INIS)
Rao, N.S.V.
1999-01-01
In a multiple sensor system, each sensor produces an output which is related to the desired feature according to a certain probability distribution. We propose a fuser that combines the sensor outputs to more accurately predict the desired feature. The fuser utilizes the lower envelope of regression curves of sensors to project the sensor with the least error at each point of the feature space. This fuser is optimal among all projective fusers and also satisfies the isolation property that ensures a performance at least as good as the best sensor. In the case the sensor distributions are not known, we show that a consistent estimator of this fuser can be computed entirely based on a training sample. Compared to linear fusers, the projective fusers provide a complementary performance. We propose two classes of metafusers that utilize both linear and projectives fusers to perform at least as good as the best sensor as well as the best fuser
Theorem Proving In Higher Order Logics
Carreno, Victor A. (Editor); Munoz, Cesar A.; Tahar, Sofiene
2002-01-01
The TPHOLs International Conference serves as a venue for the presentation of work in theorem proving in higher-order logics and related areas in deduction, formal specification, software and hardware verification, and other applications. Fourteen papers were submitted to Track B (Work in Progress), which are included in this volume. Authors of Track B papers gave short introductory talks that were followed by an open poster session. The FCM 2002 Workshop aimed to bring together researchers working on the formalisation of continuous mathematics in theorem proving systems with those needing such libraries for their applications. Many of the major higher order theorem proving systems now have a formalisation of the real numbers and various levels of real analysis support. This work is of interest in a number of application areas, such as formal methods development for hardware and software application and computer supported mathematics. The FCM 2002 consisted of three papers, presented by their authors at the workshop venue, and one invited talk.
Manufacturing Methods and Technology Project Summary Reports
1984-12-01
Powder ME-16 Type Recoil Mechanism Testing Machine (Powder Gymnasticator ) Projects 677, 78 7814 - Synthetic Quenchants for ME-18 Heat Treating Weapon...were deemed most urgent. These two were the prime candidates for the GEPTTA. Figure I is an artist depiction of the General Purpose Transportability...REPORT (RCS DRCMT-302) MMT Project 677 7753 titled "Noise Suppressor for Powder Type Recoil Mecha- nism Testing Machine (Powder Gymnasticator )" was
Preservation theorems on finite structures
International Nuclear Information System (INIS)
Hebert, M.
1994-09-01
This paper concerns classical Preservation results applied to finite structures. We consider binary relations for which a strong form of preservation theorem (called strong interpolation) exists in the usual case. This includes most classical cases: embeddings, extensions, homomorphisms into and onto, sandwiches, etc. We establish necessary and sufficient syntactic conditions for the preservation theorems for sentences and for theories to hold in the restricted context of finite structures. We deduce that for all relations above, the restricted theorem for theories hold provided the language is finite. For the sentences the restricted version fails in most cases; in fact the ''homomorphism into'' case seems to be the only possible one, but the efforts to show that have failed. We hope our results may help to solve this frustrating problem; in the meantime, they are used to put a lower bound on the level of complexity of potential counterexamples. (author). 8 refs
Distributed Research Project Scheduling Based on Multi-Agent Methods
Directory of Open Access Journals (Sweden)
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.
Efficient and effective implementation of alternative project delivery methods.
2017-05-01
Over the past decade, the Maryland Department of Transportation State Highway : Administration (MDOT SHA) has implemented Alternative Project Delivery (APD) methods : in a number of transportation projects. While these innovative practices have produ...
A Borsuk-Ulam type generalization of the Leray-Schauder fixed point theorem
International Nuclear Information System (INIS)
Prykarpatsky, A.K.
2007-05-01
A generalization of the classical Leray-Schauder fixed point theorem, based on the infinite-dimensional Borsuk-Ulam type antipode construction, is proposed. Two completely different proofs based on the projection operator approach and on a weak version of the well known Krein-Milman theorem are presented. (author)
Method ranks competing projects by priorities, risk
International Nuclear Information System (INIS)
Moeckel, D.R.
1993-01-01
A practical, objective guide for ranking projects based on risk-based priorities has been developed by Sun Pipe Line Co. The deliberately simple system guides decisions on how to allocate scarce company resources because all managers employ the same criteria in weighing potential risks to the company versus benefits. Managers at all levels are continuously having to comply with an ever growing amount of legislative and regulatory requirements while at the same time trying to run their businesses effectively. The system primarily is designed for use as a compliance oversight and tracking process to document, categorize, and follow-up on work concerning various issues or projects. That is, the system consists of an electronic database which is updated periodically, and is used by various levels of management to monitor progress of health, safety, environmental and compliance-related projects. Criteria used in determining a risk factor and assigning a priority also have been adapted and found useful for evaluating other types of projects. The process enables management to better define potential risks and/or loss of benefits that are being accepted when a project is rejected from an immediate work plan or budget. In times of financial austerity, it is extremely important that the right decisions are made at the right time
Scale symmetry and virial theorem
International Nuclear Information System (INIS)
Westenholz, C. von
1978-01-01
Scale symmetry (or dilatation invariance) is discussed in terms of Noether's Theorem expressed in terms of a symmetry group action on phase space endowed with a symplectic structure. The conventional conceptual approach expressing invariance of some Hamiltonian under scale transformations is re-expressed in alternate form by infinitesimal automorphisms of the given symplectic structure. That is, the vector field representing scale transformations leaves the symplectic structure invariant. In this model, the conserved quantity or constant of motion related to scale symmetry is the virial. It is shown that the conventional virial theorem can be derived within this framework
Nonperturbative Adler-Bardeen theorem
International Nuclear Information System (INIS)
Mastropietro, Vieri
2007-01-01
The Adler-Bardeen theorem has been proven only as a statement valid at all orders in perturbation theory, without any control on the convergence of the series. In this paper we prove a nonperturbative version of the Adler-Bardeen theorem in d=2 by using recently developed technical tools in the theory of Grassmann integration. The proof is based on the assumption that the boson propagator decays fast enough for large momenta. If the boson propagator does not decay, as for Thirring contact interactions, the anomaly in the WI (Ward Identities) is renormalized by higher order contributions
Combining AHP and DEA Methods for Selecting a Project Manager
Directory of Open Access Journals (Sweden)
Baruch Keren
2014-07-01
Full Text Available A project manager has a major influence on the success or failure of the project. A good project manager can match between the strategy and objectives of the organization and the goals of the project. Therefore, the selection of the appropriate project manager is a key factor for the success of the project. A potential project manager is judged by his or her proven performance and personal qualifications. This paper proposes a method to calculate the weighted scores and the full rank of candidates for managing a project, and to select the best of those candidates. The proposed method combines specific methodologies: the Data Envelopment Analysis (DEA and the Analytical Hierarchical Process (AHP and uses DEA Ranking Methods to enhance selection.
Indian Academy of Sciences (India)
Abstract. Let E be a vector bundle and L be a line bundle over a smooth projective variety X. In this article, we give a condition for the vanishing of Dolbeault cohomology groups of the form H p,q when Sα+β E ⊗ L is ample. This condition is shown to be invariant under the interchange of p and q. The optimality of.
Fermat's last theorem and Catalan's conjecture in weak exponential arithmetics
Czech Academy of Sciences Publication Activity Database
Glivický, Petr; Kala, V.
2017-01-01
Roč. 63, 3-4 (2017), s. 162-174 ISSN 0942-5616 EU Projects: European Commission(XE) 339691 - FEALORA Institutional support: RVO:67985840 Keywords : Fermat's last theorem * Catalan's conjecture Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 0.250, year: 2016 http://onlinelibrary.wiley.com/doi/10.1002/malq.201500069/full
The Semantic Isomorphism Theorem in Abstract Algebraic Logic
Czech Academy of Sciences Publication Activity Database
Moraschini, Tommaso
2016-01-01
Roč. 167, č. 12 (2016), s. 1298-1331 ISSN 0168-0072 R&D Projects: GA ČR GA13-14654S Institutional support: RVO:67985807 Keywords : algebra izable logics * abstract algebra ic logic * structural closure operators * semantic isomorphism theorem * evaluational frames * compositional lattice Subject RIV: BA - General Mathematics Impact factor: 0.647, year: 2016
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.
Kolmogorov-Arnold-Moser Theorem
Indian Academy of Sciences (India)
system (not necessarily the 2-body system). Kolmogorov was the first to provide a solution to the above general problem in a theorem formulated in 1954 (see Suggested. Reading). However, he provided only an outline of the proof. The actual proof (with all the details) turned to be quite difficult and was provided by Arnold ...
Dynamic Newton-Puiseux Theorem
DEFF Research Database (Denmark)
Mannaa, Bassel; Coquand, Thierry
2013-01-01
A constructive version of Newton-Puiseux theorem for computing the Puiseux expansions of algebraic curves is presented. The proof is based on a classical proof by Abhyankar. Algebraic numbers are evaluated dynamically; hence the base field need not be algebraically closed and a factorization...
Opechowski's theorem and commutator groups
International Nuclear Information System (INIS)
Caride, A.O.; Zanette, S.I.
1985-01-01
It is shown that the conditions of application of Opechowski's theorem for double groups of subgroups of O(3) are directly associated to the structure of their commutator groups. Some characteristics of the structure of classes are also discussed. (Author) [pt
Shell theorem for spontaneous emission
DEFF Research Database (Denmark)
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....
KLN theorem and infinite statistics
International Nuclear Information System (INIS)
Grandou, T.
1992-01-01
The possible extension of the Kinoshita-Lee-Nauenberg (KLN) theorem to the case of infinite statistics is examined. It is shown that it appears as a stable structure in a quantum field theory context. The extension is provided by working out the Fock space realization of a 'quantum algebra'. (author) 2 refs
The Geometric Mean Value Theorem
de Camargo, André Pierro
2018-01-01
In a previous article published in the "American Mathematical Monthly," Tucker ("Amer Math Monthly." 1997; 104(3): 231-240) made severe criticism on the Mean Value Theorem and, unfortunately, the majority of calculus textbooks also do not help to improve its reputation. The standard argument for proving it seems to be applying…
Fermion fractionization and index theorem
International Nuclear Information System (INIS)
Hirayama, Minoru; Torii, Tatsuo
1982-01-01
The relation between the fermion fractionization and the Callias-Bott-Seeley index theorem for the Dirac operator in the open space of odd dimension is clarified. Only the case of one spatial dimension is discussed in detail. Sum rules for the expectation values of various quantities in fermion-fractionized configurations are derived. (author)
The Completeness Theorem of Godel
Indian Academy of Sciences (India)
GENERAL I ARTICLE. The Completeness Theorem of Godel. 2. Henkin's Proof for First Order Logic. S M Srivastava is with the. Indian Statistical,. Institute, Calcutta. He received his PhD from the Indian Statistical. Institute in 1980. His research interests are in descriptive set theory. I Part 1. An Introduction to Math- ematical ...
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.)
On the Fourier integral theorem
Koekoek, J.
1987-01-01
Introduction. In traditional proofs of convergence of Fourier series and of the Fourier integraI theorem basic tools are the theory of Dirichlet integraIs and the Riemann-Lebesgue lemma. Recently CHERNOFF [I) and REoIlEFFER (2) gave new proofs of convergenceof Fourier series which make no use of the
Vanishing theorems and effective results in algebraic geometry
International Nuclear Information System (INIS)
Demailly, J.P.; Goettsche, L.; Lazarsfeld, R.
2001-01-01
The School on Vanishing Theorems and Effective Results in Algebraic Geometry took place in ICTP, Trieste from 25 April 2000 to 12 May 2000. It was organized by J. P. Demailly (Universite de Grenoble I) and R. Lazarsfeld (University of Michigan). The main topics considered were vanishing theorems, multiplyer ideal sheaves and effective results in algebraic geometry, tight closure, geometry of higher dimensional projective and Kahler manifolds, hyperbolic algebraic varieties. The school consisted of two weeks of lectures and one week of conference. This volume contains the lecture notes of most of the lectures in the first two weeks
Vanishing theorems and effective results in algebraic geometry
Energy Technology Data Exchange (ETDEWEB)
Demailly, J P [Universite de Grenoble (France); Goettsche, L [Abdus Salam International Centre for Theoretical Physics, Trieste (Italy); Lazarsfeld, R [University of Michigan (United States)
2001-12-15
The School on Vanishing Theorems and Effective Results in Algebraic Geometry took place in ICTP, Trieste from 25 April 2000 to 12 May 2000. It was organized by J. P. Demailly (Universite de Grenoble I) and R. Lazarsfeld (University of Michigan). The main topics considered were vanishing theorems, multiplyer ideal sheaves and effective results in algebraic geometry, tight closure, geometry of higher dimensional projective and Kahler manifolds, hyperbolic algebraic varieties. The school consisted of two weeks of lectures and one week of conference. This volume contains the lecture notes of most of the lectures in the first two weeks.
The Classical Version of Stokes' Theorem Revisited
DEFF Research Database (Denmark)
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...
Budgetary Approach to Project Management by Percentage of Completion Method
Directory of Open Access Journals (Sweden)
Leszek Borowiec
2011-07-01
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.
An extended characterisation theorem for quantum logics
International Nuclear Information System (INIS)
Sharma, C.S.; Mukherjee, M.K.
1977-01-01
Two theorems are proved. In the first properties of an important mapping from an orthocomplemented lattice to itself are studied. In the second the characterisation theorem of Zierler (Pacific J. Math.; 11:1151 (1961)) is extended to obtain a very useful theorem characterising orthomodular lattices. Since quantum logics are merely sigma-complete orthomodular lattices, the principal result is, for application in quantum physics, a characterisation theorem for quantum logics. (author)
Numerical evaluation of methods for computing tomographic projections
International Nuclear Information System (INIS)
Zhuang, W.; Gopal, S.S.; Hebert, T.J.
1994-01-01
Methods for computing forward/back projections of 2-D images can be viewed as numerical integration techniques. The accuracy of any ray-driven projection method can be improved by increasing the number of ray-paths that are traced per projection bin. The accuracy of pixel-driven projection methods can be increased by dividing each pixel into a number of smaller sub-pixels and projecting each sub-pixel. The authors compared four competing methods of computing forward/back projections: bilinear interpolation, ray-tracing, pixel-driven projection based upon sub-pixels, and pixel-driven projection based upon circular, rather than square, pixels. This latter method is equivalent to a fast, bi-nonlinear interpolation. These methods and the choice of the number of ray-paths per projection bin or the number of sub-pixels per pixel present a trade-off between computational speed and accuracy. To solve the problem of assessing backprojection accuracy, the analytical inverse Fourier transform of the ramp filtered forward projection of the Shepp and Logan head phantom is derived
Methods of Choosing an Optimal Portfolio of Projects
Yakovlev, A.; Chernenko, M.
2016-01-01
This paper presents an analysis of existing methods for a portfolio of project optimization. The necessity for their improvement is shown. It is suggested to assess the portfolio of projects on the basis of the amount in the difference between the results and costs during development and implementation of selected projects and the losses caused by non-implementation or delayed implementation of projects that were not included in the portfolio. Consideration of capital and current costs compon...
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.
A definability theorem for first order logic
Butz, C.; Moerdijk, I.
1997-01-01
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
Soft theorems for shift-symmetric cosmologies
Finelli, Bernardo; Goon, Garrett; Pajer, Enrico; Santoni, Luca
2018-03-01
We derive soft theorems for single-clock cosmologies that enjoy a shift symmetry. These so-called consistency conditions arise from a combination of a large diffeomorphism and the internal shift symmetry and fix the squeezed limit of all correlators with a soft scalar mode. As an application, we show that our results reproduce the squeezed bispectrum for ultra-slow-roll inflation, a particular shift-symmetric, nonattractor model which is known to violate Maldacena's consistency relation. Similar results have been previously obtained by Mooij and Palma using background-wave methods. Our results shed new light on the infrared structure of single-clock cosmological spacetimes.
CHARACTERISTICS OF MIRR METHOD IN EVALUATION OF INVESTMENT PROJECTS' EFFECTIVENESS
Directory of Open Access Journals (Sweden)
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.
CHARACTERISTICS OF MIRR METHOD IN EVALUATION OF INVESTMENT PROJECTS' EFFECTIVENESS
P. Kukhta
2014-01-01
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 evalu...
Applying scrum methods to ITS projects.
2017-08-01
The introduction of new technology generally brings new challenges and new methods to help with deployments. Agile methodologies have been introduced in the information technology industry to potentially speed up development. The Federal Highway Admi...
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…
How Agile Methods Inspire Project Management - The Half Double Initiative
DEFF Research Database (Denmark)
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...
The de Finetti theorem for test spaces
International Nuclear Information System (INIS)
Barrett, Jonathan; Leifer, Matthew
2009-01-01
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.
A Randomized Central Limit Theorem
International Nuclear Information System (INIS)
Eliazar, Iddo; Klafter, Joseph
2010-01-01
The Central Limit Theorem (CLT), one of the most elemental pillars of Probability Theory and Statistical Physics, asserts that: the universal probability law of large aggregates of independent and identically distributed random summands with zero mean and finite variance, scaled by the square root of the aggregate-size (√(n)), is Gaussian. The scaling scheme of the CLT is deterministic and uniform - scaling all aggregate-summands by the common and deterministic factor √(n). This Letter considers scaling schemes which are stochastic and non-uniform, and presents a 'Randomized Central Limit Theorem' (RCLT): we establish a class of random scaling schemes which yields universal probability laws of large aggregates of independent and identically distributed random summands. The RCLT universal probability laws, in turn, are the one-sided and the symmetric Levy laws.
Bell's theorem, accountability and nonlocality
International Nuclear Information System (INIS)
Vona, Nicola; Liang, Yeong-Cherng
2014-01-01
Bell's theorem is a fundamental theorem in physics concerning the incompatibility between some correlations predicted by quantum theory and a large class of physical theories. In this paper, we introduce the hypothesis of accountability, which demands that it is possible to explain the correlations of the data collected in many runs of a Bell experiment in terms of what happens in each single run. Under this assumption, and making use of a recent result by Colbeck and Renner (2011 Nature Commun. 2 411), we then show that any nontrivial account of these correlations in the form of an extension of quantum theory must violate parameter independence. Moreover, we analyze the violation of outcome independence of quantum mechanics and show that it is also a manifestation of nonlocality. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘50 years of Bell's theorem’. (paper)
Fluctuation theorems and atypical trajectories
International Nuclear Information System (INIS)
Sahoo, M; Lahiri, S; Jayannavar, A M
2011-01-01
In this work, we have studied simple models that can be solved analytically to illustrate various fluctuation theorems. These fluctuation theorems provide symmetries individually to the distributions of physical quantities such as the classical work (W c ), thermodynamic work (W), total entropy (Δs tot ) and dissipated heat (Q), when the system is driven arbitrarily out of equilibrium. All these quantities can be defined for individual trajectories. We have studied the number of trajectories which exhibit behaviour unexpected at the macroscopic level. As the time of observation increases, the fraction of such atypical trajectories decreases, as expected at the macroscale. The distributions for the thermodynamic work and entropy production in nonlinear models may exhibit a peak (most probable value) in the atypical regime without violating the expected average behaviour. However, dissipated heat and classical work exhibit a peak in the regime of typical behaviour only.
Lectures on Fermat's last theorem
International Nuclear Information System (INIS)
Sury, B.
1993-09-01
The report presents the main ideas involved in the approach towards the so-called Fermat's last theorem (FLT). The discussion leads to the point where recent work of A. Wiles starts and his work is not discussed. After a short history of the FLT and of the present approach, are discussed the elliptic curves and the modular forms with their relations, the Taniyama-Shimura-Well conjecture and the FLT
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.
Manufacturing Methods and Technology Project Summary Reports.
1980-12-01
process using Glidden’s epoxy modified t polyester varnish offered potential economic advantages over the current finish and method of application...fabricate hose and gaskets for fuel service at arctic conditions. Fluorophosphazene polymers with varying concentrations of fluorine content were used to...determine the optimum fluorine content needed to provide the essential fuel resistance and low temperature flexibility. The polymers used in this
Equitable Financial Evaluation Method for Public-Private Partnership Projects
Institute of Scientific and Technical Information of China (English)
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.
International Nuclear Information System (INIS)
Park, Mu-In
2008-01-01
Hawking's area theorem can be understood from a quasi-stationary process in which a black hole accretes positive energy matter, independent of the details of the gravity action. I use this process to study the dynamics of the inner as well as the outer horizons for various black holes which include the recently discovered exotic black holes and three-dimensional black holes in higher derivative gravities as well as the usual BTZ black hole and the Kerr black hole in four dimensions. I find that the area for the inner horizon 'can decrease', rather than increase, with the quasi-stationary process. However, I find that the area for the outer horizon 'never decreases' such that the usual area theorem still works in our examples, though this is quite non-trivial in general. There exists an instability problem of the inner horizons but it seems that the instability is not important in my analysis. I also find a generalized area theorem by combining those of the outer and inner horizons
Constrained variable projection method for blind deconvolution
International Nuclear Information System (INIS)
Cornelio, A; Piccolomini, E Loli; Nagy, J G
2012-01-01
This paper is focused on the solution of the blind deconvolution problem, here modeled as a separable nonlinear least squares problem. The well known ill-posedness, both on recovering the blurring operator and the true image, makes the problem really difficult to handle. We show that, by imposing appropriate constraints on the variables and with well chosen regularization parameters, it is possible to obtain an objective function that is fairly well behaved. Hence, the resulting nonlinear minimization problem can be effectively solved by classical methods, such as the Gauss-Newton algorithm.
Formalization of the Integral Calculus in the PVS Theorem Prover
Directory of Open Access Journals (Sweden)
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.
Formalization of the Integral Calculus in the PVS Theorem Prover
Butler, Ricky W.
2004-01-01
The PVS Theorem prover is a widely used formal verification tool used for the analysis of safety-critical 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.
Educational integrating projects as a method of interactive learning
Directory of Open Access Journals (Sweden)
Иван Николаевич Куринин
2013-12-01
Full Text Available The article describes a method of interactive learning based on educational integrating projects. Some examples of content of such projects for the disciplines related to the study of information and Internet technologies and their application in management are presented.
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…
Projected oriented organizations as development of enterprise management methods
Directory of Open Access Journals (Sweden)
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.
Fourier diffraction theorem for diffusion-based thermal tomography
International Nuclear Information System (INIS)
Baddour, Natalie
2006-01-01
There has been much recent interest in thermal imaging as a method of non-destructive testing and for non-invasive medical imaging. The basic idea of applying heat or cold to an area and observing the resulting temperature change with an infrared camera has led to the development of rapid and relatively inexpensive inspection systems. However, the main drawback to date has been that such an approach provides mainly qualitative results. In order to advance the quantitative results that are possible via thermal imaging, there is interest in applying techniques and algorithms from conventional tomography. Many tomography algorithms are based on the Fourier diffraction theorem, which is inapplicable to thermal imaging without suitable modification to account for the attenuative nature of thermal waves. In this paper, the Fourier diffraction theorem for thermal tomography is derived and discussed. The intent is for this thermal-diffusion based Fourier diffraction theorem to form the basis of tomographic reconstruction algorithms for quantitative thermal imaging
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.
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…
A generalized integral fluctuation theorem for general jump processes
International Nuclear Information System (INIS)
Liu Fei; Ouyang Zhongcan; Luo Yupin; Huang Mingchang
2009-01-01
Using the Feynman-Kac and Cameron-Martin-Girsanov formulae, we obtain a generalized integral fluctuation theorem (GIFT) for discrete jump processes by constructing a time-invariable inner product. The existing discrete IFTs can be derived as its specific cases. A connection between our approach and the conventional time-reversal method is also established. Unlike the latter approach that has been extensively employed in the existing literature, our approach can naturally bring out the definition of a time reversal of a Markovian stochastic system. Additionally, we find that the robust GIFT usually does not result in a detailed fluctuation theorem. (fast track communication)
METHODS OF SELECTING THE EFFECTIVE MODELS OF BUILDINGS REPROFILING PROJECTS
Directory of Open Access Journals (Sweden)
Александр Иванович МЕНЕЙЛЮК
2016-02-01
Full Text Available The article highlights the important task of project management in reprofiling of buildings. It is expedient to pay attention to selecting effective engineering solutions to reduce the duration and cost reduction at the project management in the construction industry. This article presents a methodology for the selection of efficient organizational and technical solutions for the reconstruction of buildings reprofiling. The method is based on a compilation of project variants in the program Microsoft Project and experimental statistical analysis using the program COMPEX. The introduction of this technique in the realigning of buildings allows choosing efficient models of projects, depending on the given constraints. Also, this technique can be used for various construction projects.
Expanding the Interaction Equivalency Theorem
Directory of Open Access Journals (Sweden)
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.
On projection methods, convergence and robust formulations in topology optimization
DEFF Research Database (Denmark)
Wang, Fengwen; Lazarov, Boyan Stefanov; Sigmund, Ole
2011-01-01
alleviated using various projection methods. In this paper we show that simple projection methods do not ensure local mesh-convergence and propose a modified robust topology optimization formulation based on erosion, intermediate and dilation projections that ensures both global and local mesh-convergence.......Mesh convergence and manufacturability of topology optimized designs have previously mainly been assured using density or sensitivity based filtering techniques. The drawback of these techniques has been gray transition regions between solid and void parts, but this problem has recently been...
On Krasnoselskii's Cone Fixed Point Theorem
Directory of Open Access Journals (Sweden)
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.
Confinement, diquarks and goldstone's theorem
International Nuclear Information System (INIS)
Roberts, C.D.
1996-01-01
Determinations of the gluon propagator in the continuum and in lattice simulations are compared. A systematic truncation procedure for the quark Dyson-Schwinger and bound state Bethe-Salpeter equations is described. The procedure ensures the flavor-octet axial- vector Ward identity is satisfied order-by-order, thereby guaranteeing the preservation of Goldstone's theorem; and identifies a mechanism that simultaneously ensures the absence of diquarks in QCD and their presence in QCD N c =2 , where the color singlet diquark is the ''baryon'' of the theory
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
Bernstein Lethargy Theorem and Reflexivity
Aksoy, Asuman Güven; Peng, Qidi
2018-01-01
In this paper, we prove the equivalence of reflexive Banach spaces and those Banach spaces which satisfy the following form of Bernstein's Lethargy Theorem. Let $X$ be an arbitrary infinite-dimensional Banach space, and let the real-valued sequence $\\{d_n\\}_{n\\ge1}$ decrease to $0$. Suppose that $\\{Y_n\\}_{n\\ge1}$ is a system of strictly nested subspaces of $X$ such that $\\overline Y_n \\subset Y_{n+1}$ for all $n\\ge1$ and for each $n\\ge1$, there exists $y_n\\in Y_{n+1}\\backslash Y_n$ such that ...
Cyclic graphs and Apery's theorem
International Nuclear Information System (INIS)
Sorokin, V N
2002-01-01
This is a survey of results about the behaviour of Hermite-Pade approximants for graphs of Markov functions, and a survey of interpolation problems leading to Apery's result about the irrationality of the value ζ(3) of the Riemann zeta function. The first example is given of a cyclic graph for which the Hermite-Pade problem leads to Apery's theorem. Explicit formulae for solutions are obtained, namely, Rodrigues' formulae and integral representations. The asymptotic behaviour of the approximants is studied, and recurrence formulae are found
Abstract decomposition theorem and applications
Grossberg, R; Grossberg, Rami; Lessmann, Olivier
2005-01-01
Let K be an Abstract Elementary Class. Under the asusmptions that K has a nicely behaved forking-like notion, regular types and existence of some prime models we establish a decomposition theorem for such classes. The decomposition implies a main gap result for the class K. The setting is general enough to cover \\aleph_0-stable first-order theories (proved by Shelah in 1982), Excellent Classes of atomic models of a first order tehory (proved Grossberg and Hart 1987) and the class of submodels of a large sequentially homogenuus \\aleph_0-stable model (which is new).
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.
Multiphonon theory: generalized Wick's theorem and recursion formulas
International Nuclear Information System (INIS)
Silvestre-Brac, B.; Piepenbring, R.
1982-04-01
Overlaps and matrix elements of one and two-body operators are calculated in a space spanned by multiphonons of different types taking properly the Pauli principle into account. Two methods are developped: a generalized Wick's theorem dealing with new contractions and recursion formulas well suited for numerical applications
Hamiltonian Noether theorem for gauge systems and two time physics
International Nuclear Information System (INIS)
Villanueva, V M; Nieto, J A; 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
A Neutrosophic Binomial Factorial Theorem with their Refrains
Directory of Open Access Journals (Sweden)
Huda E. Khalid
2016-12-01
Full Text Available 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.
Asset management using an extended Markowitz theorem
Directory of Open Access Journals (Sweden)
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.
Equivalent conserved currents and generalized Noether's theorem
International Nuclear Information System (INIS)
Gordon, T.J.
1984-01-01
A generalized Noether theorem is presented, relating symmetries and equivalence classes of local) conservation laws in classical field theories; this is contrasted with the standard theorem. The concept of a ''Noether'' field theory is introduced, being a theory for which the generalized theorem applies; not only does this include the cases of Lagrangian and Hamiltonian field theories, these structures are ''derived'' from the Noether property in a natural way. The generalized theorem applies to currents and symmetries that contain derivatives of the fields up to an arbitrarily high order
Directory of Open Access Journals (Sweden)
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.
Project Method, as One of the Basic Methods of Environmental Education
Szállassy, Noémi
2008-01-01
Our aim was to present in this paper the one of the most important methods of environmental education, the project method. We present here the steps and phases of project method and we give an example of how to use these elements in planning an activity for celebrating the World Day for Water.
Quantum fluctuation theorems and power measurements
International Nuclear Information System (INIS)
Prasanna Venkatesh, B; Watanabe, Gentaro; Talkner, Peter
2015-01-01
Work in the paradigm of the quantum fluctuation theorems of Crooks and Jarzynski is determined by projective measurements of energy at the beginning and end of the force protocol. In analogy to classical systems, we consider an alternative definition of work given by the integral of the supplied power determined by integrating up the results of repeated measurements of the instantaneous power during the force protocol. We observe that such a definition of work, in spite of taking account of the process dependence, has different possible values and statistics from the work determined by the conventional two energy measurement approach (TEMA). In the limit of many projective measurements of power, the system’s dynamics is frozen in the power measurement basis due to the quantum Zeno effect leading to statistics only trivially dependent on the force protocol. In general the Jarzynski relation is not satisfied except for the case when the instantaneous power operator commutes with the total Hamiltonian at all times. We also consider properties of the joint statistics of power-based definition of work and TEMA work in protocols where both values are determined. This allows us to quantify their correlations. Relaxing the projective measurement condition, weak continuous measurements of power are considered within the stochastic master equation formalism. Even in this scenario the power-based work statistics is in general not able to reproduce qualitative features of the TEMA work statistics. (paper)
Note on Deduction Theorems in contraction-free logics
Czech Academy of Sciences Publication Activity Database
Chvalovský, Karel; Cintula, Petr
2012-01-01
Roč. 58, č. 3 (2012), s. 236-243 ISSN 0942-5616 R&D Projects: GA ČR GAP202/10/1826 Grant - others:Austrian Science Fund (FWF)(AT) START Y544-N23 Institutional research plan: CEZ:AV0Z10300504 Keywords : Local Deduction Theorem * BCI-logic * Substructural logics * Rule of contraction Subject RIV: BA - General Mathematics Impact factor: 0.376, year: 2012
A maximum modulus theorem for the Oseen problem
Czech Academy of Sciences Publication Activity Database
Kračmar, S.; Medková, Dagmar; Nečasová, Šárka; Varnhorn, W.
2013-01-01
Roč. 192, č. 6 (2013), s. 1059-1076 ISSN 0373-3114 R&D Projects: GA ČR(CZ) GAP201/11/1304; GA MŠk LC06052 Institutional research plan: CEZ:AV0Z10190503 Keywords : Oseen problem * maximum modulus theorem * Oseen potentials Subject RIV: BA - General Mathematics Impact factor: 0.909, year: 2013 http://link.springer.com/article/10.1007%2Fs10231-012-0258-x
A p-adic Perron-Frobenius Theorem
Costa, Robert; Dynes, Patrick; Petsche, Clayton
2015-01-01
We prove that if an $n\\times n$ matrix defined over ${\\mathbb Q}_p$ (or more generally an arbitrary complete, discretely-valued, non-Archimedean field) satisfies a certain congruence property, then it has a strictly maximal eigenvalue in ${\\mathbb Q}_p$, and that iteration of the (normalized) matrix converges to a projection operator onto the corresponding eigenspace. This result may be viewed as a $p$-adic analogue of the Perron-Frobenius theorem for positive real matrices.
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…
The rate of convergence in the method of alternating projections
Czech Academy of Sciences Publication Activity Database
Badea, C.; Grivaux, S.; Müller, Vladimír
2012-01-01
Roč. 23, č. 3 (2012), s. 413-434 ISSN 1061-0022 R&D Projects: GA ČR GA201/09/0473; GA AV ČR IAA100190903 Institutional support: RVO:67985840 Keywords : Friedrichs angle * method of alternating projections * arbitrarily slow convergence Subject RIV: BA - General Mathematics Impact factor: 0.460, year: 2012 http://www.ams.org/journals/spmj/2012-23-03/S1061-0022-2012-01202-1/home.html
Extension of moment projection method to the fragmentation process
International Nuclear Information System (INIS)
Wu, Shaohua; Yapp, Edward K.Y.; Akroyd, Jethro; Mosbach, Sebastian; Xu, Rong; Yang, Wenming; Kraft, Markus
2017-01-01
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.
Projection methods for line radiative transfer in spherical media.
Anusha, L. S.; Nagendra, K. N.
An efficient numerical method called the Preconditioned Bi-Conjugate Gradient (Pre-BiCG) method is presented for the solution of radiative transfer equation in spherical geometry. A variant of this method called Stabilized Preconditioned Bi-Conjugate Gradient (Pre-BiCG-STAB) is also presented. These methods are based on projections on the subspaces of the n dimensional Euclidean space mathbb {R}n called Krylov subspaces. The methods are shown to be faster in terms of convergence rate compared to the contemporary iterative methods such as Jacobi, Gauss-Seidel and Successive Over Relaxation (SOR).
Extension of moment projection method to the fragmentation process
Energy Technology Data Exchange (ETDEWEB)
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.
Matching factorization theorems with an inverse-error weighting
Echevarria, Miguel G.; Kasemets, Tomas; Lansberg, Jean-Philippe; Pisano, Cristian; Signori, Andrea
2018-06-01
We propose a new fast method to match factorization theorems applicable in different kinematical regions, such as the transverse-momentum-dependent and the collinear factorization theorems in Quantum Chromodynamics. At variance with well-known approaches relying on their simple addition and subsequent subtraction of double-counted contributions, ours simply builds on their weighting using the theory uncertainties deduced from the factorization theorems themselves. This allows us to estimate the unknown complete matched cross section from an inverse-error-weighted average. The method is simple and provides an evaluation of the theoretical uncertainty of the matched cross section associated with the uncertainties from the power corrections to the factorization theorems (additional uncertainties, such as the nonperturbative ones, should be added for a proper comparison with experimental data). Its usage is illustrated with several basic examples, such as Z boson, W boson, H0 boson and Drell-Yan lepton-pair production in hadronic collisions, and compared to the state-of-the-art Collins-Soper-Sterman subtraction scheme. It is also not limited to the transverse-momentum spectrum, and can straightforwardly be extended to match any (un)polarized cross section differential in other variables, including multi-differential measurements.
Lesion insertion in the projection domain: Methods and initial results
International Nuclear Information System (INIS)
Chen, Baiyu; Leng, Shuai; Yu, Lifeng; Yu, Zhicong; Ma, Chi; McCollough, Cynthia
2015-01-01
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
Lesion insertion in the projection domain: Methods and initial results
Energy Technology Data Exchange (ETDEWEB)
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
SPANDOM - source projection analytic nodal discrete ordinates method
International Nuclear Information System (INIS)
Kim, Tae Hyeong; Cho, Nam Zin
1994-01-01
We describe a new discrete ordinates nodal method for the two-dimensional transport equation. We solve the discrete ordinates equation analytically after the source term is projected and represented in polynomials. The method is applied to two fast reactor benchmark problems and compared with the TWOHEX code. The results indicate that the present method accurately predicts not only multiplication factor but also flux distribution
Waller, Niels
2018-01-01
Kristof's Theorem (Kristof, 1970 ) describes a matrix trace inequality that can be used to solve a wide-class of least-square optimization problems without calculus. Considering its generality, it is surprising that Kristof's Theorem is rarely used in statistics and psychometric applications. The underutilization of this method likely stems, in part, from the mathematical complexity of Kristof's ( 1964 , 1970 ) writings. In this article, I describe the underlying logic of Kristof's Theorem in simple terms by reviewing four key mathematical ideas that are used in the theorem's proof. I then show how Kristof's Theorem can be used to provide novel derivations to two cognate models from statistics and psychometrics. This tutorial includes a glossary of technical terms and an online supplement with R (R Core Team, 2017 ) code to perform the calculations described in the text.
Classification theorem for principal fibre bundles, Berry's phase, and exact cycle evolution
International Nuclear Information System (INIS)
Bohm, A.; Boya, L.J.; Mostafazadeh, A.; Rudolph, G.
1993-03-01
The relation between the two mathematical interpretations of the geometric (Berry) phase is discussed, using either the fibre bundle over parameter space or over projective Hilbert space. It turns out that these two geometric constructions are linked by the classification theorem for vector bundles. The classification theorem provides the means to classify the parameter space bundles for adiabatic evolution and for non-adiabatic cyclic evolution of the statevectors
Stacked spheres and lower bound theorem
Indian Academy of Sciences (India)
BASUDEB DATTA
2011-11-20
Nov 20, 2011 ... Preliminaries. Lower bound theorem. On going work. Definitions. An n-simplex is a convex hull of n + 1 affinely independent points. (called vertices) in some Euclidean space R. N . Stacked spheres and lower bound theorem. Basudeb Datta. Indian Institute of Science. 2 / 27 ...
Howell, Russell W.; Schrohe, Elmar
2017-01-01
Rouché's Theorem is a standard topic in undergraduate complex analysis. It is usually covered near the end of the course with applications relating to pure mathematics only (e.g., using it to produce an alternate proof of the Fundamental Theorem of Algebra). The "winding number" provides a geometric interpretation relating to the…
Other trigonometric proofs of Pythagoras theorem
Luzia, Nuno
2015-01-01
Only very recently a trigonometric proof of the Pythagoras theorem was given by Zimba \\cite{1}, many authors thought this was not possible. In this note we give other trigonometric proofs of Pythagoras theorem by establishing, geometrically, the half-angle formula $\\cos\\theta=1-2\\sin^2 \\frac{\\theta}{2}$.
Borghi, Riccardo
2014-03-01
In the present letter, Newton’s theorem for the gravitational field outside a uniform spherical shell is considered. In particular, a purely geometric proof of proposition LXXI/theorem XXXI of Newton’s Principia, which is suitable for undergraduates and even skilled high-school students, is proposed. Minimal knowledge of elementary calculus and three-dimensional Euclidean geometry are required.
Theorems of low energy in Compton scattering
International Nuclear Information System (INIS)
Chahine, J.
1984-01-01
We have obtained the low energy theorems in Compton scattering to third and fouth order in the frequency of the incident photon. Next we calculated the polarized cross section to third order and the unpolarized to fourth order in terms of partial amplitudes not covered by the low energy theorems, what will permit the experimental determination of these partial amplitudes. (Author) [pt
A density Corradi-Hajnal theorem
Czech Academy of Sciences Publication Activity Database
Allen, P.; Böttcher, J.; Hladký, Jan; Piguet, D.
2015-01-01
Roč. 67, č. 4 (2015), s. 721-758 ISSN 0008-414X Institutional support: RVO:67985840 Keywords : extremal graph theory * Mantel's theorem * Corradi-Hajnal theorem Subject RIV: BA - General Mathematics Impact factor: 0.618, year: 2015 http://cms.math.ca/10.4153/CJM-2014-030-6
Visualizing the Central Limit Theorem through Simulation
Ruggieri, Eric
2016-01-01
The Central Limit Theorem is one of the most important concepts taught in an introductory statistics course, however, it may be the least understood by students. Sure, students can plug numbers into a formula and solve problems, but conceptually, do they really understand what the Central Limit Theorem is saying? This paper describes a simulation…
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 R[superscript 3] follows from an application of Gauss' divergence theorem to a suitable modification of the vector field in a tubular shell around the…
The divergence theorem for unbounded vector fields
De Pauw, Thierry; Pfeffer, Washek F.
2007-01-01
In the context of Lebesgue integration, we derive the divergence theorem for unbounded vector. elds that can have singularities at every point of a compact set whose Minkowski content of codimension greater than two is. nite. The resulting integration by parts theorem is applied to removable sets of holomorphic and harmonic functions.
The Pomeranchuk theorem and its modifications
International Nuclear Information System (INIS)
Fischer, J.; Saly, R.
1980-01-01
A review of the various modifications and improvements of the Pomeranchuk theorem and also of related statements is given. The present status of the Pomeranchuk relation based on dispersion relation is discussed. Numerous problems related to the Pomeranchuk theorem and some answers to these problems are collected in a clear table
Coalgebraic Lindström Theorems
Kurz, A.; Venema, Y.
2010-01-01
We study modal Lindström theorems from a coalgebraic perspective. We provide three different Lindström theorems for coalgebraic logic, one of which is a direct generalisation of de Rijke's result for Kripke models. Both the other two results are based on the properties of bisimulation invariance,
A Metrized Duality Theorem for Markov Processes
DEFF Research Database (Denmark)
Kozen, Dexter; Mardare, Radu Iulian; Panangaden, Prakash
2014-01-01
We extend our previous duality theorem for Markov processes by equipping the processes with a pseudometric and the algebras with a notion of metric diameter. We are able to show that the isomorphisms of our previous duality theorem become isometries in this quantitative setting. This opens the wa...
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 ...
Lesion insertion in the projection domain: Methods and initial results.
Chen, Baiyu; Leng, Shuai; Yu, Lifeng; Yu, Zhicong; Ma, Chi; McCollough, Cynthia
2015-12-01
phantom in terms of Hounsfield unit and high-contrast resolution. For the validation of the lesion realism, lesions of various types were successfully inserted, including well circumscribed and invasive lesions, homogeneous and heterogeneous lesions, high-contrast and low-contrast lesions, isolated and vessel-attached lesions, and small and large lesions. The two experienced radiologists who reviewed the original and inserted lesions could not identify the lesions that were inserted. The same lesion, when inserted into the projection domain and reconstructed with different parameters, demonstrated a parameter-dependent appearance. A framework has been developed for projection-domain insertion of lesions into commercial CT images, which can be potentially expanded to all geometries of CT scanners. Compared to conventional image-domain methods, the authors' method reflected the impact of scan and reconstruction parameters on lesion appearance. Compared to prior projection-domain methods, the authors' method has the potential to achieve higher anatomical complexity by employing clinical patient projections and real patient lesions.
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...
Computational methods for planning and evaluating geothermal energy projects
International Nuclear Information System (INIS)
Goumas, M.G.; Lygerou, V.A.; Papayannakis, L.E.
1999-01-01
In planning, designing and evaluating a geothermal energy project, a number of technical, economic, social and environmental parameters should be considered. The use of computational methods provides a rigorous analysis improving the decision-making process. This article demonstrates the application of decision-making methods developed in operational research for the optimum exploitation of geothermal resources. Two characteristic problems are considered: (1) the economic evaluation of a geothermal energy project under uncertain conditions using a stochastic analysis approach and (2) the evaluation of alternative exploitation schemes for optimum development of a low enthalpy geothermal field using a multicriteria decision-making procedure. (Author)
Riemannian and Lorentzian flow-cut theorems
Headrick, Matthew; Hubeny, Veronika E.
2018-05-01
We prove several geometric theorems using tools from the theory of convex optimization. In the Riemannian setting, we prove the max flow-min cut (MFMC) theorem for boundary regions, applied recently to develop a ‘bit-thread’ interpretation of holographic entanglement entropies. We also prove various properties of the max flow and min cut, including respective nesting properties. In the Lorentzian setting, we prove the analogous MFMC theorem, which states that the volume of a maximal slice equals the flux of a minimal flow, where a flow is defined as a divergenceless timelike vector field with norm at least 1. This theorem includes as a special case a continuum version of Dilworth’s theorem from the theory of partially ordered sets. We include a brief review of the necessary tools from the theory of convex optimization, in particular Lagrangian duality and convex relaxation.
An alternative extragradient projection method for quasi-equilibrium problems.
Chen, Haibin; Wang, Yiju; Xu, Yi
2018-01-01
For the quasi-equilibrium problem where the players' costs and their strategies both depend on the rival's decisions, an alternative extragradient projection method for solving it is designed. Different from the classical extragradient projection method whose generated sequence has the contraction property with respect to the solution set, the newly designed method possesses an expansion property with respect to a given initial point. The global convergence of the method is established under the assumptions of pseudomonotonicity of the equilibrium function and of continuity of the underlying multi-valued mapping. Furthermore, we show that the generated sequence converges to the nearest point in the solution set to the initial point. Numerical experiments show the efficiency of the method.
A Conceptual Grey Analysis Method for Construction Projects
Directory of Open Access Journals (Sweden)
Maria Mikela Chatzimichailidou
2015-05-01
Full Text Available Concerning engineers, project management is a crucial field of research and development. Projects of high uncertainty and scale are characterized by risk, primarily related to their completion time. Thus, safe duration estimations, throughout the planning of a project, are a key objective for project managers. However, traditional linear approaches fail to include and sufficiently serve the dynamic nature of activities duration. On this ground, attention should be paid to designing and implementing methodologies that approximate the duration of the activities during the phase of planning and scheduling too. The grey analysis mathematical modeling seems to gain grounds, since it gradually becomes a well-adapted and up-to-date technique for numerous scientific sectors. This paper examines the contribution of the logic behind the aforementioned analysis, aiming to predict possible future divergences of task durations in big construction projects. Based on time observations of critical instances, a conceptual method is developed for making duration estimations and communicating deviations from the original schedule, in a way that approximations will fit reality better. The whole procedure endeavors to investigate the decrease of uncertainty, regarding project completion time and reduce, up to a scale, a possible inaccurate estimation of a project manager. The utmost effort is about exploiting the gained experience and eliminating the “hedgehog syndrome”. This is attainable by designing a reliable, easily updated, and readable information system. An enlightening example is to be found in the last section.
A method for the efficient prioritization of infrastructure renewal projects
International Nuclear Information System (INIS)
Karydas, D.M.; Gifun, J.F.
2006-01-01
The infrastructure renewal program at MIT consists of a large number of projects with an estimated budget that could approach $1 billion. Infrastructure renewal at the Massachusetts Institute of Technology (MIT) is the process of evaluating and investing in the maintenance of facility systems and basic structure to preserve existing campus buildings. The selection and prioritization of projects must be addressed with a systematic method for the optimal allocation of funds and other resources. This paper presents a case study of a prioritization method utilizing multi-attribute utility theory. This method was developed at MIT's Department of Nuclear Engineering and was deployed by the Department of Facilities after appropriate modifications were implemented to address the idiosyncrasies of infrastructure renewal projects and the competing criteria and constraints that influence the judgment of the decision-makers. Such criteria include minimization of risk, optimization of economic impact, and coordination with academic policies, programs, and operations of the Institute. A brief overview of the method is presented, as well as the results of its application to the prioritization of infrastructure renewal projects. Results of workshops held at MIT with the participation of stakeholders demonstrate the feasibility of the prioritization method and the usefulness of this approach
Integrated project delivery methods for energy renovation of social housing
Directory of Open Access Journals (Sweden)
Tadeo Baldiri Salcedo Rahola
2015-11-01
Full Text Available Optimised project delivery methods forsocial housing energy renovations European 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 Bayesian perspective on Markovian dynamics and the fluctuation theorem
Virgo, Nathaniel
2013-08-01
One of E. T. Jaynes' most important achievements was to derive statistical mechanics from the maximum entropy (MaxEnt) method. I re-examine a relatively new result in statistical mechanics, the Evans-Searles fluctuation theorem, from a MaxEnt perspective. This is done in the belief that interpreting such results in Bayesian terms will lead to new advances in statistical physics. The version of the fluctuation theorem that I will discuss applies to discrete, stochastic systems that begin in a non-equilibrium state and relax toward equilibrium. I will show that for such systems the fluctuation theorem can be seen as a consequence of the fact that the equilibrium distribution must obey the property of detailed balance. Although the principle of detailed balance applies only to equilibrium ensembles, it puts constraints on the form of non-equilibrium trajectories. This will be made clear by taking a novel kind of Bayesian perspective, in which the equilibrium distribution is seen as a prior over the system's set of possible trajectories. Non-equilibrium ensembles are calculated from this prior using Bayes' theorem, with the initial conditions playing the role of the data. I will also comment on the implications of this perspective for the question of how to derive the second law.
Strong converse theorems using Rényi entropies
Energy Technology Data Exchange (ETDEWEB)
Leditzky, Felix; Datta, Nilanjana [Statistical Laboratory, Centre for Mathematical Sciences, University of Cambridge, Cambridge CB3 0WB (United Kingdom); Wilde, Mark M. [Department of Physics and Astronomy, Center for Computation and Technology, Hearne Institute for Theoretical Physics, Louisiana State University, Baton Rouge, Louisiana 70803 (United States)
2016-08-15
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 http://arxiv.org/abs/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.
A generalization of Schauder's theorem and its application to Cauchy-Kovalevskaya problem
Directory of Open Access Journals (Sweden)
Oleg Zubelevich
2003-05-01
Full Text Available We extend the classical majorant functions method to a PDE system which right hand side is a mapping of one functional space to another. This extension is based on some generalization of the Schauder fixed point theorem.
Some Convergence Strategies for the Alternating Generalized Projection Method
Directory of Open Access Journals (Sweden)
Maricarmen Andrade
2013-11-01
Full Text Available In this paper we extend the application of the alternating projection algorithm to solve the problem of finding a point in the intersection of $n$ sets ($n\\geq2$, which are not all of them convex sets. Here we term such method as alternating generalized projection (AGP method. In particular, we are interested in addressing the problem of avoiding the so-called trap points, which may prevent an algorithm to obtain a feasible solution in two or more sets not all convex. Some strategies that allow us to reach the feasible solution are established and conjectured. Finally, we present simple numerical results that illustrate the efficiency of the iterative methods considered.
The classical version of Stokes' Theorem revisited
DEFF Research Database (Denmark)
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...... 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....
Security Theorems via Model Theory
Directory of Open Access Journals (Sweden)
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.
Magnetostatic fields computed using an integral equation derived from Green's theorems
International Nuclear Information System (INIS)
Simkin, J.; Trowbridge, C.W.
1976-04-01
A method of computing magnetostatic fields is described that is based on a numerical solution of the integral equation obtained from Green's Theorems. The magnetic scalar potential and its normal derivative on the surfaces of volumes are found by solving a set of linear equations. These are obtained from Green's Second Theorem and the continuity conditions at interfaces between volumes. Results from a two-dimensional computer program are presented and these show the method to be accurate and efficient. (author)
Energy Technology Data Exchange (ETDEWEB)
Escane, J.M. [Ecole Superieure d' Electricite, 91 - Gif-sur-Yvette (France)
2005-04-01
The first part of this article defines the different elements of an electrical network and the models to represent them. Each model involves the current and the voltage as a function of time. Models involving time functions are simple but their use is not always easy. The Laplace transformation leads to a more convenient form where the variable is no more directly the time. This transformation leads also to the notion of transfer function which is the object of the second part. The third part aims at defining the fundamental operation rules of linear networks, commonly named 'general theorems': linearity principle and superimposition theorem, duality principle, Thevenin theorem, Norton theorem, Millman theorem, triangle-star and star-triangle transformations. These theorems allow to study complex power networks and to simplify the calculations. They are based on hypotheses, the first one is that all networks considered in this article are linear. (J.S.)
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 ...
Theorem on axially symmetric gravitational vacuum configurations
Energy Technology Data Exchange (ETDEWEB)
Papadopoulos, A; Le Denmat, G [Paris-6 Univ., 75 (France). Inst. Henri Poincare
1977-01-24
A theorem is proved which asserts the non-existence of axially symmetric gravitational vacuum configurations with non-stationary rotation only. The eventual consequences in black-hole physics are suggested.
Graph-like continua, augmenting arcs, and Menger's theorem
DEFF Research Database (Denmark)
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......, connected graph. While closed subsets of such a space behave nicely in that they are compact and locally connected (and therefore locally arcwise connected), the general subspaces do not: They may be connected without being arcwise connected. Nevertheless, they satisfy Menger's Theorem......., namely the locally arcwise connected, hereditarily locally connected, metric spaces. Finally, it applies to every space where every point can be separated from every closed set not containing it by a finite set, in particular to every subspace of the Freudenthal compactification of a locally finite...
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...
Electronic-projecting Moire method applying CBR-technology
Kuzyakov, O. N.; Lapteva, U. V.; Andreeva, M. A.
2018-01-01
Electronic-projecting method based on Moire effect for examining surface topology is suggested. Conditions of forming Moire fringes and their parameters’ dependence on reference parameters of object and virtual grids are analyzed. Control system structure and decision-making subsystem are elaborated. Subsystem execution includes CBR-technology, based on applying case base. The approach related to analysing and forming decision for each separate local area with consequent formation of common topology map is applied.
Mathematical foundations of the projection-operator method
International Nuclear Information System (INIS)
Moore, S.M.
1979-01-01
Mathematical foundations are determined for the projection-operator method developed by Zwanzig and Mori and used in the study of cooperative phenomena in non-equilibrium processes. It is shown that the Hilbert space of operators can be taken as the Hilbert-Schmidt class. Comments are made on the possibility of a complete formulation of quantum mechanics in terms of this Hilbert space. (author)
Non-renormalisation theorems in string theory
International Nuclear Information System (INIS)
Vanhove, P.
2007-10-01
In this thesis we describe various non renormalisation theorems for the string effective action. These results are derived in the context of the M theory conjecture allowing to connect the four gravitons string theory S matrix elements with that of eleven dimensional supergravity. These theorems imply that N = 8 supergravity theory has the same UV behaviour as the N = 4 supersymmetric Yang Mills theory at least up to three loops, and could be UV finite in four dimensions. (author)
There is No Quantum Regression Theorem
International Nuclear Information System (INIS)
Ford, G.W.; OConnell, R.F.
1996-01-01
The Onsager regression hypothesis states that the regression of fluctuations is governed by macroscopic equations describing the approach to equilibrium. It is here asserted that this hypothesis fails in the quantum case. This is shown first by explicit calculation for the example of quantum Brownian motion of an oscillator and then in general from the fluctuation-dissipation theorem. It is asserted that the correct generalization of the Onsager hypothesis is the fluctuation-dissipation theorem. copyright 1996 The American Physical Society
Singularity theorems from weakened energy conditions
International Nuclear Information System (INIS)
Fewster, Christopher J; Galloway, Gregory J
2011-01-01
We establish analogues of the Hawking and Penrose singularity theorems based on (a) averaged energy conditions with exponential damping; (b) conditions on local stress-energy averages inspired by the quantum energy inequalities satisfied by a number of quantum field theories. As particular applications, we establish singularity theorems for the Einstein equations coupled to a classical scalar field, which violates the strong energy condition, and the nonminimally coupled scalar field, which also violates the null energy condition.
The matrix Euler-Fermat theorem
International Nuclear Information System (INIS)
Arnol'd, Vladimir I
2004-01-01
We prove many congruences for binomial and multinomial coefficients as well as for the coefficients of the Girard-Newton formula in the theory of symmetric functions. These congruences also imply congruences (modulo powers of primes) for the traces of various powers of matrices with integer elements. We thus have an extension of the matrix Fermat theorem similar to Euler's extension of the numerical little Fermat theorem
Level comparison theorems and supersymmetric quantum mechanics
International Nuclear Information System (INIS)
Baumgartner, B.; Grosse, H.
1986-01-01
The sign of the Laplacian of the spherical symmetric potential determines the order of energy levels with the same principal Coulomb quantum number. This recently derived theorem has been generalized, extended and applied to various situations in particle, nuclear and atomic physics. Besides a comparison theorem the essential step was the use of supersymmetric quantum mechanics. Recently worked out applications of supersymmetric quantum mechanics to index problems of Dirac operators are mentioned. (Author)
Liouville's theorem and phase-space cooling
International Nuclear Information System (INIS)
Mills, R.L.; Sessler, A.M.
1993-01-01
A discussion is presented of Liouville's theorem and its consequences for conservative dynamical systems. A formal proof of Liouville's theorem is given. The Boltzmann equation is derived, and the collisionless Boltzmann equation is shown to be rigorously true for a continuous medium. The Fokker-Planck equation is derived. Discussion is given as to when the various equations are applicable and, in particular, under what circumstances phase space cooling may occur
The Osgood-Schoenflies theorem revisited
International Nuclear Information System (INIS)
Siebenmann, L C
2005-01-01
The very first unknotting theorem of a purely topological character established that every compact subset of the Euclidean plane homeomorphic to a circle can be moved onto a round circle by a globally defined self-homeomorphism of the plane. This difficult hundred-year-old theorem is here celebrated with a partly new elementary proof, and a first but tentative account of its history. Some quite fundamental corollaries of the proof are sketched, and some generalizations are mentioned
Double soft theorem for perturbative gravity
Saha, Arnab
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.
A Converse of Fermat's Little Theorem
Bruckman, P. S.
2007-01-01
As the name of the paper implies, a converse of Fermat's Little Theorem (FLT) is stated and proved. FLT states the following: if p is any prime, and x any integer, then x[superscript p] [equivalent to] x (mod p). There is already a well-known converse of FLT, known as Lehmer's Theorem, which is as follows: if x is an integer coprime with m, such…
The large deviations theorem and ergodicity
International Nuclear Information System (INIS)
Gu Rongbao
2007-01-01
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
The direct Flow parametric Proof of Gauss' Divergence Theorem revisited
DEFF Research Database (Denmark)
Markvorsen, Steen
The standard proof of the divergence theorem in undergraduate calculus courses covers the theorem for static domains between two graph surfaces. We show that within first year undergraduate curriculum, the flow proof of the dynamic version of the divergence theorem - which is usually considered...... we apply the key instrumental concepts and verify the various steps towards this alternative proof of the divergence theorem....
Commentaries on Hilbert's Basis Theorem | Apine | Science World ...
African Journals Online (AJOL)
The famous basis theorem of David Hilbert is an important theorem in commutative algebra. In particular the Hilbert's basis theorem is the most important source of Noetherian rings which are by far the most important class of rings in commutative algebra. In this paper we have used Hilbert's theorem to examine their unique ...
Illustrating the Central Limit Theorem through Microsoft Excel Simulations
Moen, David H.; Powell, John E.
2005-01-01
Using Microsoft Excel, several interactive, computerized learning modules are developed to demonstrate the Central Limit Theorem. These modules are used in the classroom to enhance the comprehension of this theorem. The Central Limit Theorem is a very important theorem in statistics, and yet because it is not intuitively obvious, statistics…
A note on the proof of Bertrand's theorem
Directory of Open Access Journals (Sweden)
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.
Log-Optimal Portfolio Selection Using the Blackwell Approachability Theorem
V'yugin, Vladimir
2014-01-01
We present a method for constructing the log-optimal portfolio using the well-calibrated forecasts of market values. Dawid's notion of calibration and the Blackwell approachability theorem are used for computing well-calibrated forecasts. We select a portfolio using this "artificial" probability distribution of market values. Our portfolio performs asymptotically at least as well as any stationary portfolio that redistributes the investment at each round using a continuous function of side in...
Accelerated Test Method for Corrosion Protective Coatings Project
Falker, John; Zeitlin, Nancy; Calle, Luz
2015-01-01
This project seeks to develop a new accelerated corrosion test method that predicts the long-term corrosion protection performance of spaceport structure coatings as accurately and reliably as current long-term atmospheric exposure tests. This new accelerated test method will shorten the time needed to evaluate the corrosion protection performance of coatings for NASA's critical ground support structures. Lifetime prediction for spaceport structure coatings has a 5-year qualification cycle using atmospheric exposure. Current accelerated corrosion tests often provide false positives and negatives for coating performance, do not correlate to atmospheric corrosion exposure results, and do not correlate with atmospheric exposure timescales for lifetime prediction.
Theorem on magnet fringe field
International Nuclear Information System (INIS)
Wei, Jie; Talman, R.
1995-01-01
Transverse particle motion in particle accelerators is governed almost totally by non-solenoidal magnets for which the body magnetic field can be expressed as a series expansion of the normal (b n ) and skew (a n ) multipoles, B y + iB x = summation(b n + ia n )(x + iy) n , where x, y, and z denote horizontal, vertical, and longitudinal (along the magnet) coordinates. Since the magnet length L is necessarily finite, deflections are actually proportional to ''field integrals'' such as bar BL ≡ ∫ B(x,y,z)dz where the integration range starts well before the magnet and ends well after it. For bar a n , bar b n , bar B x , and bar B y defined this way, the same expansion Eq. 1 is valid and the ''standard'' approximation is to neglect any deflections not described by this expansion, in spite of the fact that Maxwell's equations demand the presence of longitudinal field components at the magnet ends. The purpose of this note is to provide a semi-quantitative estimate of the importance of |Δp ∝ |, the transverse deflection produced by the ion-gitudinal component of the fringe field at one magnet end relative to |Δp 0 |, the total deflection produced by passage through the whole magnet. To emphasize the generality and simplicity of the result it is given in the form of a theorem. The essence of the proof is an evaluation of the contribution of the longitudinal field B x from the vicinity of one magnet end since, along a path parallel to the magnet axis such as path BC
Galerkin projection methods for solving multiple related linear systems
Energy Technology Data Exchange (ETDEWEB)
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.
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.
[Adverse events management. Methods and results of a development project].
Rabøl, Louise Isager; Jensen, Elisabeth Brøgger; Hellebek, Annemarie H; Pedersen, Beth Lilja
2006-11-27
This article describes the methods and results of a project in the Copenhagen Hospital Corporation (H:S) on preventing adverse events. The aim of the project was to raise awareness about patients' safety, test a reporting system for adverse events, develop and test methods of analysis of events and propagate ideas about how to prevent adverse events. H:S developed an action plan and a reporting system for adverse events, founded an organization and developed an educational program on theories and methods of learning from adverse events for both leaders and employees. During the three-year period from 1 January 2002 to 31 December 2004, the H:S staff reported 6011 adverse events. In the same period, the organization completed 92 root cause analyses. More than half of these dealt with events that had been optional to report, the other half events that had been mandatory to report. The number of reports and the front-line staff's attitude towards reporting shows that the H:S succeeded in founding a safety culture. Future work should be centred on developing and testing methods that will prevent adverse events from happening. The objective is to suggest and complete preventive initiatives which will help increase patient safety.
DEFF Research Database (Denmark)
Nest, Ryszard; Tsygan, Boris
2001-01-01
Recently Kontsevich solved the classification problem for deformation quantizations of all Poisson structures on a manifold. In this paper we study those Poisson structures for which the explicit methods of Fedosov can be applied, namely the Poisson structures coming from symplectic Lie algebroids......, as well as holomorphic symplectic structures. For deformations of these structures we prove the classification theorems and a general a general index theorem....
Virial Theorem for Nonrelativistic Quantum Fields in D Spatial Dimensions
International Nuclear Information System (INIS)
Lin, Chris L.; Ordóñez, Carlos R.
2015-01-01
The virial theorem for nonrelativistic complex fields in D spatial dimensions and with arbitrary many-body potential is derived, using path-integral methods and scaling arguments recently developed to analyze quantum anomalies in low-dimensional systems. The potential appearance of a Jacobian J due to a change of variables in the path-integral expression for the partition function of the system is pointed out, although in order to make contact with the literature most of the analysis deals with the J=1 case. The virial theorem is recast into a form that displays the effect of microscopic scales on the thermodynamics of the system. From the point of view of this paper the case usually considered, J=1, is not natural, and the generalization to the case J≠1 is briefly presented
The g-theorem and quantum information theory
Energy Technology Data Exchange (ETDEWEB)
Casini, Horacio; Landea, Ignacio Salazar; Torroba, Gonzalo [Centro Atómico Bariloche and CONICET,S.C. de Bariloche, Río Negro, R8402AGP (Argentina)
2016-10-25
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.
Statistical properties of entropy production derived from fluctuation theorems
International Nuclear Information System (INIS)
Merhav, Neri; Kafri, Yariv
2010-01-01
Several implications of well-known fluctuation theorems, on the statistical properties of entropy production, are studied using various approaches. We begin by deriving a tight lower bound on the variance of the entropy production for a given mean of this random variable. It is shown that the Evans–Searles fluctuation theorem alone imposes a significant lower bound on the variance only when the mean entropy production is very small. It is then nonetheless demonstrated that upon incorporating additional information concerning the entropy production, this lower bound can be significantly improved, so as to capture extensivity properties. Another important aspect of the fluctuation properties of the entropy production is the relationship between the mean and the variance, on the one hand, and the probability of the event where the entropy production is negative, on the other hand. Accordingly, we derive upper and lower bounds on this probability in terms of the mean and the variance. These bounds are tighter than previous bounds that can be found in the literature. Moreover, they are tight in the sense that there exist probability distributions, satisfying the Evans–Searles fluctuation theorem, that achieve them with equality. Finally, we present a general method for generating a wide class of inequalities that must be satisfied by the entropy production. We use this method to derive several new inequalities that go beyond the standard derivation of the second law
Project JADE. Description of the MLH-method
International Nuclear Information System (INIS)
Sandstedt, H.; Munier, R.; Wichmann, C.; Isaksson, Therese
2001-08-01
This report constitutes a part of a series of reports within project JADE, comparison of deposition methods. A comparison of the deposition methods MLH (Medium Long Holes with approximately 25 copper canisters emplaced in a horizontal deposition hole about 200 metres in length bored between central and side tunnels) and KBS-3 (copper canisters are emplaced in vertical deposition holes bored in the floors of horizontal tunnels) has earlier been performed and KBS-3 was judged to be more advantageous than MLH. However, the prerequisites for the comparison have changed with time and an updated evaluation of MLH was therefore required. In this report, the current knowledge of MLH is summarized with focus on geological prerequisites, methods for boring long, horizontal deposition holes, reinforcement and sealing, deposition and cost. Comparisons with KBS-3 are performed sequentially. An MLH-repository is judged to be more sensitive to ingress of water to the deposition holes during the deposition process. This implies that a MLH repository based on today's knowledge is basically recommended for bedrock with fairly low water baring capacity. It has been demonstrated that MLH has considerable economic potential compared to KBS-3. However, the method is judged to be more technically immature than KBS-3. Particularly, methods and equipment for deposition of canisters need to be developed further. Methods and equipment for deposition can be developed, which fulfill the demands on function and safety, in the near future. MLH cannot therefore be rejected as deposition method
Bernstein - Von Mises theorem and its application in survival analysis
Czech Academy of Sciences Publication Activity Database
Timková, Jana
2010-01-01
Roč. 22, č. 3 (2010), s. 115-122 ISSN 1210-8022. [16. letní škola JČMF Robust 2010. Králíky, 30.01.2010-05.02.2010] R&D Projects: GA AV ČR(CZ) IAA101120604 Institutional research plan: CEZ:AV0Z10750506 Keywords : Cox model * bayesian asymptotics * survival function Subject RIV: BB - Applied Statistics, Operational Research http://library.utia.cas.cz/separaty/2010/SI/timkova-bernstein - von mises theorem and its application in survival analysis.pdf
Directory of Open Access Journals (Sweden)
C. A. Shields
2018-06-01
Full Text Available The Atmospheric River Tracking Method Intercomparison Project (ARTMIP is an international collaborative effort to understand and quantify the uncertainties in atmospheric river (AR science based on detection algorithm alone. Currently, there are many AR identification and tracking algorithms in the literature with a wide range of techniques and conclusions. ARTMIP strives to provide the community with information on different methodologies and provide guidance on the most appropriate algorithm for a given science question or region of interest. All ARTMIP participants will implement their detection algorithms on a specified common dataset for a defined period of time. The project is divided into two phases: Tier 1 will utilize the Modern-Era Retrospective analysis for Research and Applications, version 2 (MERRA-2 reanalysis from January 1980 to June 2017 and will be used as a baseline for all subsequent comparisons. Participation in Tier 1 is required. Tier 2 will be optional and include sensitivity studies designed around specific science questions, such as reanalysis uncertainty and climate change. High-resolution reanalysis and/or model output will be used wherever possible. Proposed metrics include AR frequency, duration, intensity, and precipitation attributable to ARs. Here, we present the ARTMIP experimental design, timeline, project requirements, and a brief description of the variety of methodologies in the current literature. We also present results from our 1-month proof-of-concept trial run designed to illustrate the utility and feasibility of the ARTMIP project.
Bayes' theorem and its application to nuclear power plant safety
International Nuclear Information System (INIS)
Matsuoka, Takeshi
2013-01-01
Bayes' theorem has been paid in much attention for its application to Probabilistic Safety Assessment (PSA). In this lecture, the basis for understanding Bayes' theorem is first explained and how to interpret the Bayes' equation with respect to the pair of conjugate distributions between prior distribution and likelihood. Then for the application to PSA, component failure data are evaluated by Bayes' theorem by using the examples of demand probability of the start of diesel generator and failure of pressure sensor. Frequencies of nuclear power plant accidents are also evaluated by Bayes' theorem for the example case of frequency of 'fires in reactor compartment' and 'core melt' frequency with the experience of Fukushima dai-ichi accidents. Lastly, several contrasting arguments are introduced briefly between favorable and critical peoples regarding the Bayes' methods. (author)
Atiyah-Patodi-Singer index theorem for domain-wall fermion Dirac operator
Fukaya, Hidenori; Onogi, Tetsuya; Yamaguchi, Satoshi
2018-03-01
Recently, the Atiyah-Patodi-Singer(APS) index theorem attracts attention for understanding physics on the surface of materials in topological phases. Although it is widely applied to physics, the mathematical set-up in the original APS index theorem is too abstract and general (allowing non-trivial metric and so on) and also the connection between the APS boundary condition and the physical boundary condition on the surface of topological material is unclear. For this reason, in contrast to the Atiyah-Singer index theorem, derivation of the APS index theorem in physics language is still missing. In this talk, we attempt to reformulate the APS index in a "physicist-friendly" way, similar to the Fujikawa method on closed manifolds, for our familiar domain-wall fermion Dirac operator in a flat Euclidean space. We find that the APS index is naturally embedded in the determinant of domain-wall fermions, representing the so-called anomaly descent equations.
Adaptive Fuzzy Robust Control for a Class of Nonlinear Systems via Small Gain Theorem
Directory of Open Access Journals (Sweden)
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.
Quality of the restricted variation after projection method with angular momentum projection
International Nuclear Information System (INIS)
Rodriguez, Tomas R.; Egido, J.L.; Robledo, L.M.; Rodriguez-Guzman, R.
2005-01-01
Recently, the restricted angular momentum variation after projection method, using the quadrupole degree of freedom as a variational coordinate in conjunction with effective interactions of the Skyrme or Gogny type, has been used very successfully to study a variety of phenomena concerning the quadrupole degree of freedom. In this paper, we study the quality of such an approach by considering additional degrees of freedom as variational coordinates: the hexadecapole moment and the fluctuations on the quadrupole moment, particle number, and angular momentum operators. The study has been performed with the Gogny interaction (D1S parametrization) for the nuclei 32 Mg and 34 Mg. The results of the angular momentum projection and the subsequent generator coordinate calculations show that the extra degrees of freedom considered are irrelevant for the description of the lowest lying states for each angular momentum
Thermodynamical and Green function many-body Wick theorems
International Nuclear Information System (INIS)
Westwanski, B.
1987-01-01
The thermodynamical and Green function many-body reduction theorems of Wick type are proved for the arbitrary mixtures of the fermion, boson and spin systems. ''Many-body'' means that the operators used are the products of the arbitrary number of one-body standard basis operators [of the fermion or (and) spin types] with different site (wave vector) indices, but having the same ''time'' (in the interaction representation). The method of proving is based on'' 1) the first-order differential equation of Schwinger type for: 1a) anti T-product of operators; 1b) its average value; 2) KMS boundary conditions for this average. It is shown that the fermion, boson and spin systems can be unified in the many-body formulation (bosonification of the fermion systems). It is impossible in the one-body approach. Both of the many-body versions of the Wick theorem have the recurrent feature: nth order moment diagrams for the free energy or Green functions can be expressed by the (n-1)th order ones. This property corresponds to the automatic realization of: (i) summations over Bose-Einstein or (and) Fermi-Dirac frequencies; (ii) elimination of Bose-Einstein or (and) Fermi-Dirac distributions. The procedures (i) and (ii), being the results of using the Green function one-body reduction theorem, have constituted the significant difficulty up to now in the treatment of quantum systems. (orig.)
An analogue of Wagner's theorem for decompositions of matrix algebras
International Nuclear Information System (INIS)
Ivanov, D N
2004-01-01
Wagner's celebrated theorem states that a finite affine plane whose collineation group is transitive on lines is a translation plane. The notion of an orthogonal decomposition (OD) of a classically semisimple associative algebra introduced by the author allows one to draw an analogy between finite affine planes of order n and ODs of the matrix algebra M n (C) into a sum of subalgebras conjugate to the diagonal subalgebra. These ODs are called WP-decompositions and are equivalent to the well-known ODs of simple Lie algebras of type A n-1 into a sum of Cartan subalgebras. In this paper we give a detailed and improved proof of the analogue of Wagner's theorem for WP-decompositions of the matrix algebra of odd non-square order an outline of which was earlier published in a short note in 'Russian Math. Surveys' in 1994. In addition, in the framework of the theory of ODs of associative algebras, based on the method of idempotent bases, we obtain an elementary proof of the well-known Kostrikin-Tiep theorem on irreducible ODs of Lie algebras of type A n-1 in the case where n is a prime-power.
The Non-Signalling theorem in generalizations of Bell's theorem
International Nuclear Information System (INIS)
Walleczek, J; Grössing, G
2014-01-01
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
Energy Technology Data Exchange (ETDEWEB)
NONE
1997-03-01
This report describes an interim evaluation method and a concrete evaluation method for projects promoted by the Agency of Industrial Science and Technology, and NEDO. As a result of the survey, a method of highly practical interim evaluation, concrete evaluation items, and evaluation criteria have been proposed by assuming that the projects are evaluated by the project evaluation department independent of the project promotion department. Long-term issues for constructing the evaluation system are also described. It is the most essential for the evaluation to fulfill the function of effective promotion of the following projects. It is also indispensable for the evaluation method and issues proposed in this report to communicate closely to project promoters and researchers, and to reassess the projects continuously. Continuous consideration for the feedback of evaluation process and the improvement of evaluation are significant for the long-term construction of system. 21 refs., 9 figs., 23 tabs.
Gleason-Busch theorem for sequential measurements
Flatt, Kieran; Barnett, Stephen M.; Croke, Sarah
2017-12-01
Gleason's theorem is a statement that, given some reasonable assumptions, the Born rule used to calculate probabilities in quantum mechanics is essentially unique [A. M. Gleason, Indiana Univ. Math. J. 6, 885 (1957), 10.1512/iumj.1957.6.56050]. We show that Gleason's theorem contains within it also the structure of sequential measurements, and along with this the state update rule. We give a small set of axioms, which are physically motivated and analogous to those in Busch's proof of Gleason's theorem [P. Busch, Phys. Rev. Lett. 91, 120403 (2003), 10.1103/PhysRevLett.91.120403], from which the familiar Kraus operator form follows. An axiomatic approach has practical relevance as well as fundamental interest, in making clear those assumptions which underlie the security of quantum communication protocols. Interestingly, the two-time formalism is seen to arise naturally in this approach.
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.
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 uniform Tauberian theorem in dynamic games
Khlopin, D. V.
2018-01-01
Antagonistic dynamic games including games represented in normal form are considered. The asymptotic behaviour of value in these games is investigated as the game horizon tends to infinity (Cesàro mean) and as the discounting parameter tends to zero (Abel mean). The corresponding Abelian-Tauberian theorem is established: it is demonstrated that in both families the game value uniformly converges to the same limit, provided that at least one of the limits exists. Analogues of one-sided Tauberian theorems are obtained. An example shows that the requirements are essential even for control problems. Bibliography: 31 titles.
The aftermath of the intermediate value theorem
Directory of Open Access Journals (Sweden)
Morales Claudio H
2004-01-01
Full Text Available The solvability of nonlinear equations has awakened great interest among mathematicians for a number of centuries, perhaps as early as the Babylonian culture (3000300 B.C.E.. However, we intend to bring to our attention that some of the problems studied nowadays appear to be amazingly related to the time of Bolzano's era (17811848. Indeed, this Czech mathematician or perhaps philosopher has rigorously proven what is known today as the intermediate value theorem, a result that is intimately related to various classical theorems that will be discussed throughout this work.
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
Elastic hadron scattering and optical theorem
Lokajicek, Milos V.; Prochazka, Jiri
2014-01-01
In principle all contemporary phenomenological models of elastic hadronic scattering have been based on the assumption of optical theorem validity that has been overtaken from optics. It will be shown that the given theorem which has not been actually proved cannot be applied to short-ranged strong interactions in any case. The actual progress in description of collision processes might then exist only if the initial states are specified on the basis of impact parameter values of colliding particles and probability dependence on this parameter is established.
At math meetings, enormous theorem eclipses fermat.
Cipra, B
1995-02-10
Hardly a word was said about Fermat's Last Theorem at the joint meetings of the American Mathematical Society and the Mathematical Association of America, held this year from 4 to 7 January in San Francisco. For Andrew Wiles's proof, no news is good news: There are no reports of mistakes. But mathematicians found plenty of other topics to discuss. Among them: a computational breakthrough in the study of turbulent diffusion and progress in slimming down the proof of an important result in group theory, whose original size makes checking the proof of Fermat's Last Theorem look like an afternoon's pastime.
A Formula for Fixing Troubled Projects: The Scientific Method Meets Leadership
Wagner, Sandra
2006-01-01
This presentation focuses on project management, specifically addressing project issues using the scientific method of problem-solving. Two sample projects where this methodology has been applied are provided.
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…
Capacity theory with local rationality the strong Fekete-Szegö theorem on curves
Rumely, Robert
2013-01-01
This book is devoted to the proof of a deep theorem in arithmetic geometry, the Fekete-Szegö theorem with local rationality conditions. The prototype for the theorem is Raphael Robinson's theorem on totally real algebraic integers in an interval, which says that if [a,b] is a real interval of length greater than 4, then it contains infinitely many Galois orbits of algebraic integers, while if its length is less than 4, it contains only finitely many. The theorem shows this phenomenon holds on algebraic curves of arbitrary genus over global fields of any characteristic, and is valid for a broad class of sets. The book is a sequel to the author's work Capacity Theory on Algebraic Curves and contains applications to algebraic integers and units, the Mandelbrot set, elliptic curves, Fermat curves, and modular curves. A long chapter is devoted to examples, including methods for computing capacities. Another chapter contains extensions of the theorem, including variants on Berkovich curves. The proof uses both alg...
Study on Top-Down Estimation Method of Software Project Planning
Institute of Scientific and Technical Information of China (English)
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.
Learning Unknown Structure in CRFs via Adaptive Gradient Projection Method
Directory of Open Access Journals (Sweden)
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.
Modelling of Airship Flight Mechanics by the Projection Equivalent Method
Directory of Open Access Journals (Sweden)
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.
Transverse voltage and reciprocity theorem in magnetic fields for high T.sub.c./sub. superconductors
Czech Academy of Sciences Publication Activity Database
Janeček, Ivan; Vašek, Petr
2004-01-01
Roč. 402, - (2004), s. 199-208 ISSN 0921-4534 R&D Projects: GA ČR GA202/00/1602; GA AV ČR IAA1010919 Institutional research plan: CEZ:AV0Z1010914 Keywords : Hall efect * reciprocity theorem Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 1.072, year: 2004
Weak theorems on differential inequalities for two-dimensional functional differential systems
Czech Academy of Sciences Publication Activity Database
Šremr, Jiří
2008-01-01
Roč. 65, č. 2 (2008), s. 157-189 ISSN 0032-5155 R&D Projects: GA ČR(CZ) GA201/06/0254 Institutional research plan: CEZ:AV0Z10190503 Keywords : two-dimensional functional differential system * weak theorem on differential inequalities * Volterra operator Subject RIV: BA - General Mathematics
Deformation quantization and Borel´s theorem in locally convex spaces
Czech Academy of Sciences Publication Activity Database
Engliš, Miroslav; Taskinen, J.
2007-01-01
Roč. 180, č. 1 (2007), s. 77-93 ISSN 0039-3223 R&D Projects: GA ČR GA201/03/0041 Institutional research plan: CEZ:AV0Z10190503 Keywords : Berezin-Toeplitz quantization * Borel theorem * Frechet space Subject RIV: BA - General Mathematics Impact factor: 0.568, year: 2007
Generalized virial theorem for the Liénard-type systems
Indian Academy of Sciences (India)
for second-order differential equations of the Liénard type. The explicit ... Keywords. Virial theorem; Liénard-type equation; Jacobi last multiplier; symplectic form; Banach manifold. ..... 3.1 Application to Gierer–Meinhardt system ..... financial support by the research projects MTMÐ2012/33575 (MINECO, Madrid) and.
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.)
Description of rotational excitations of odd nuclei by the method of projection
International Nuclear Information System (INIS)
Mazepus, V.V.
1981-01-01
We have carried out a projection on the angular-momentum operator eigenspace for deformed nuclei. The space of the trial wave functions is chosen to be broader than in the ordinary projection approach. It is shown that this method of projection leads to the particle + rotor model but not to the cranking model. A comparison is made with the method of approximate projection
A note on the Pfaffian integration theorem
International Nuclear Information System (INIS)
Borodin, Alexei; Kanzieper, Eugene
2007-01-01
Two alternative, fairly compact proofs are presented of the Pfaffian integration theorem that surfaced in the recent studies of spectral properties of Ginibre's Orthogonal Ensemble. The first proof is based on a concept of the Fredholm Pfaffian; the second proof is purely linear algebraic. (fast track communication)
Mean value theorem in topological vector spaces
International Nuclear Information System (INIS)
Khan, L.A.
1994-08-01
The aim of this note is to give shorter proofs of the mean value theorem, the mean value inequality, and the mean value inclusion for the class of Gateaux differentiable functions having values in a topological vector space. (author). 6 refs
1/4-pinched contact sphere theorem
DEFF Research Database (Denmark)
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...
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.
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...
On Noethers theorem in quantum field theory
International Nuclear Information System (INIS)
Buchholz, D.; Doplicher, S.; Longo, R.
1985-03-01
Extending an earlier construction of local generators of symmetries in (S. Doplicher, 1982) to space-time and supersymmetries, we establish a weak form of Noethers theorem in quantum field theory. We also comment on the physical significance of the 'split property', underlying our analysis, and discuss some local aspects of superselection rules following from our results. (orig./HSI)
Green-Tao theorem in function fields
Le, Thai Hoang
2009-01-01
We adapt the proof of the Green-Tao theorem on arithmetic progressions in primes to the setting of polynomials over a finite field, to show that for every $k$, the irreducible polynomials in $\\mathbf{F}_q[t]$ contain configurations of the form $\\{f+ Pg : \\d(P)
Pauli and The Spin-Statistics Theorem
International Nuclear Information System (INIS)
Duck, Ian; Sudarshan, E.C.G.
1998-03-01
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 'everyone knows the spin-statistics theorem, but no one understands it'. This book simplifies and clarifies the formal statements of the theorem, and also corrects the invariably flawed intuitive explanations which are frequently put forward. The book will be of interest to many practising physicists in all fields who have long been frustrated by the impenetrable discussions on the subject which have been available until now.It will also be accessible to students at an advanced undergraduate level as an introduction to modern physics based directly on the classical writings of the founders, including Pauli, Dirac, Heisenberg, Einstein and many others
Central Limit Theorem for Coloured Hard Dimers
Directory of Open Access Journals (Sweden)
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.
Some Generalizations of Jungck's Fixed Point Theorem
Directory of Open Access Journals (Sweden)
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.
Limit theorems for functionals of Gaussian vectors
Institute of Scientific and Technical Information of China (English)
Hongshuai DAI; Guangjun SHEN; Lingtao KONG
2017-01-01
Operator self-similar processes,as an extension of self-similar processes,have been studied extensively.In this work,we study limit theorems for functionals of Gaussian vectors.Under some conditions,we determine that the limit of partial sums of functionals of a stationary Gaussian sequence of random vectors is an operator self-similar process.
Bell's theorem and the nature of reality
International Nuclear Information System (INIS)
Bertlmann, R.A.
1988-01-01
We rediscuss the Einstein-Podolsky-Rosen paradox in Bohm's spin version and oppose to it Bohr's controversial point of view. Then we explain Bell's theorem, Bell inequalities and its consequences. We describe the experiment of Aspect, Dalibard and Roger in detail. Finally we draw attention to the nonlocal structure of the underlying theory. 61 refs., 8 tabs. (Author)
A singularity theorem based on spatial averages
Indian Academy of Sciences (India)
journal of. July 2007 physics pp. 31–47. A singularity theorem based on spatial ... In this paper I would like to present a result which confirms – at least partially – ... A detailed analysis of how the model fits in with the .... Further, the statement that the spatial average ...... Financial support under grants FIS2004-01626 and no.
H-theorems from macroscopic autonomous equations
Czech Academy of Sciences Publication Activity Database
De Roeck, W.; Maes, C.; Netočný, Karel
2006-01-01
Roč. 123, č. 3 (2006), s. 571-583 ISSN 0022-4715 Institutional research plan: CEZ:AV0Z10100520 Keywords : H-theorem, entropy * irreversible equations Subject RIV: BE - Theoretical Physics Impact factor: 1.437, year: 2006
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…
The Embedding Theorems of Whitney and Nash
Indian Academy of Sciences (India)
We begin by briefly motivating the idea of amanifold and then discuss the embedding theorems of Whitney and Nash that allow us toview these objects inside appropriately large Euclidean spaces. Resonance – Journal of Science Education. Current Issue : Vol. 23, Issue 4. Current Issue Volume 23 | Issue 4. April 2018.
Nash-Williams’ cycle-decomposition theorem
DEFF Research Database (Denmark)
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...
General Correlation Theorem for Trinion Fourier Transform
Bahri, Mawardi
2017-01-01
- The trinion Fourier transform is an extension of the Fourier transform in the trinion numbers setting. In this work we derive the correlation theorem for the trinion Fourier transform by using the relation between trinion convolution and correlation definitions in the trinion Fourier transform domains.
Directory of Open Access Journals (Sweden)
SEVER ANGEL POPESCU
2015-03-01
Full Text Available In this note we make some remarks on the classical Laguerre’s theorem and extend it and some other old results of Walsh and Gauss-Lucas to the so called trace series associated with transcendental elements of the completion of the algebraic closure of Q in C, with respect to the spectral norm:
Lagrange’s Four-Square Theorem
Directory of Open Access Journals (Sweden)
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].
Anomalous Levinson theorem and supersymmetric quantum mechanics
International Nuclear Information System (INIS)
Boya, L.J.; Casahorran, J.; Esteve, J.G.
1993-01-01
We analyse the symmetry breaking associated to anomalous realization of supersymmetry in the context of SUSY QM. In this case one of the SUSY partners is singular; that leads to peculiar forms of the Levinson theorem relating phase shifts and bound states. Some examples are exhibited; peculiarities include negative energies, incomplete pairing of states and extra phases in scattering. (Author) 8 refs
Another look at the second incompleteness theorem
Visser, A.
2017-01-01
In this paper we study proofs of some general forms of the Second Incompleteness Theorem. These forms conform to the Feferman format, where the proof predicate is xed and the representation of the axiom set varies. We extend the Feferman framework in one important point: we allow the interpretation
Another look at the second incompleteness theorem
Visser, Albert
2017-01-01
In this paper we study proofs of some general forms of the Second Incompleteness Theorem. These forms conform to the Feferman format, where the proof predicate is fixed and the representation of the axiom set varies. We extend the Feferman framework in one important point: we allow the
Factorization theorems in perturbative quantum field theory
International Nuclear Information System (INIS)
Date, G.D.
1982-01-01
This dissertation deals with factorization properties of Green functions and cross-sections in perturbation theory. It consists of two parts. Part I deals with the factorization theorem for the Drell-Yan cross-section. The new approach developed for this purpose is based upon a renormalization group equation with a generalized anomalous dimension. Using an alternate form of factorization for the Drell-Yan cross-section, derived in perturbation theory, a corresponding generalized anomalous dimension is defined, and explicit Feynman rules for its calculation are given. The resultant renormalization group equation is solved by a formal solution which is exhibited explicitly. Simple, explicit calculations are performed which verify Mueller's conjecture for the recovery of the usual parton model results for the Drell-Yan cross-section. The approach developed in this work offers a general framework to analyze the role played by the group factors in the cancellation of the soft divergences, and study their influence on the asymptotic behavior. Part II deals with factorization properties of the Green functions in position space. In this part, a Landau equation analysis is carried out for the singularities of the position space Green fucntions, in perturbation theory with the theta 4 interaction Lagrangian. A physical picture interpretation is given for the corresponding Landau equations. It is used to suggest a light-cone expansion. Using a power counting method, a formal derivation of the light-cone expansion for the two point function, the three point function and a product of two currents, is given without assuming a short distance expansion. Possible extensions to other theories is also considered
On the Leray-Hirsch Theorem for the Lichnerowicz cohomology
International Nuclear Information System (INIS)
Ait Haddoul, Hassan
2004-03-01
The purpose of this paper is to prove the Leray-Hirsch theorem for the Lichnerowicz; cohomology with respect to basic and vertical closed 1-forms. This is a generalization of the Kfirmeth theorem to fiber bundles. (author)
A Note on a Broken-Cycle Theorem for Hypergraphs
Directory of Open Access Journals (Sweden)
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 STRONG OPTIMIZATION THEOREM IN LOCALLY CONVEX SPACES
Institute of Scientific and Technical Information of China (English)
程立新; 腾岩梅
2003-01-01
This paper presents a geometric characterization of convex sets in locally convex spaces onwhich a strong optimization theorem of the Stegall-type holds, and gives Collier's theorem ofw* Asplund spaces a localized setting.
A projection method for under determined optimal experimental designs
Long, Quan; Scavino, Marco; Tempone, Raul; Wang, Suojin
2014-01-01
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.
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.
Performance assessment plans and methods for the Salt Repository Project
International Nuclear Information System (INIS)
1984-08-01
This document presents the preliminary plans and anticipated methods of the Salt Repository Project (SRP) for assessing the postclosure and radiological aspects of preclosure performance of a nuclear waste repository in salt. This plan is intended to be revised on an annual basis. The emphasis in this preliminary effort is on the method of conceptually dividing the system into three subsystems (the very near field, the near field, and the far field) and applying models to analyze the behavior of each subsystem and its individual components. The next revision will contain more detailed plans being developed as part of Site Characterization Plan (SCP) activities. After a brief system description, this plan presents the performance targets which have been established for nuclear waste repositories by regulatory agencies (Chapter 3). The SRP approach to modeling, including sensitivity and uncertainty techniques is then presented (Chapter 4). This is followed by a discussion of scenario analysis (Chapter 5), a presentation of preliminary data needs as anticipated by the SRP (Chapter 6), and a presentation of the SRP approach to postclosure assessment of the very near field, the near field, and the far field (Chapters 7, 8, and 9, respectively). Preclosure radiological assessment is discussed in Chapter 10. Chapter 11 presents the SRP approach to code verification and validation. Finally, the Appendix lists all computer codes anticipated for use in performance assessments. The list of codes will be updated as plans are revised
Decoupling theorem in supersymmetric theories
Energy Technology Data Exchange (ETDEWEB)
Leon, J; Perez-Mercader, J; Sanchez, M F
1988-07-21
We introduce a superfield extension of Weisberger's method for decoupling calculations in multiscale field theories and generalize our previous method which does not require the computation of any Feynman diagram. We illustrate this for the two-scale Wess-Zumino model, showing explicitly how the decoupling takes place.
Applications of square-related theorems
Srinivasan, V. K.
2014-04-01
The square centre of a given square is the point of intersection of its two diagonals. When two squares of different side lengths share the same square centre, there are in general four diagonals that go through the same square centre. The Two Squares Theorem developed in this paper summarizes some nice theoretical conclusions that can be obtained when two squares of different side lengths share the same square centre. These results provide the theoretical basis for two of the constructions given in the book of H.S. Hall and F.H. Stevens , 'A Shorter School Geometry, Part 1, Metric Edition'. In page 134 of this book, the authors present, in exercise 4, a practical construction which leads to a verification of the Pythagorean theorem. Subsequently in Theorems 29 and 30, the authors present the standard proofs of the Pythagorean theorem and its converse. In page 140, the authors present, in exercise 15, what amounts to a geometric construction, whose verification involves a simple algebraic identity. Both the constructions are of great importance and can be replicated by using the standard equipment provided in a 'geometry toolbox' carried by students in high schools. The author hopes that the results proved in this paper, in conjunction with the two constructions from the above-mentioned book, would provide high school students an appreciation of the celebrated theorem of Pythagoras. The diagrams that accompany this document are based on the free software GeoGebra. The author formally acknowledges his indebtedness to the creators of this free software at the end of this document.
DISCRETE FIXED POINT THEOREMS AND THEIR APPLICATION TO NASH EQUILIBRIUM
Sato, Junichi; Kawasaki, Hidefumi
2007-01-01
Fixed point theorems are powerful tools in not only mathematics but also economic. In some economic problems, we need not real-valued but integer-valued equilibriums. However, classical fixed point theorems guarantee only real-valued equilibria. So we need discrete fixed point theorems in order to get discrete equilibria. In this paper, we first provide discrete fixed point theorems, next apply them to a non-cooperative game and prove the existence of a Nash equilibrium of pure strategies.
A general comparison theorem for backward stochastic differential equations
Cohen, Samuel N.; Elliott, Robert J.; Pearce, Charles E. M.
2010-01-01
A useful result when dealing with backward stochastic differential equations is the comparison theorem of Peng (1992). When the equations are not based on Brownian motion, the comparison theorem no longer holds in general. In this paper we present a condition for a comparison theorem to hold for backward stochastic differential equations based on arbitrary martingales. This theorem applies to both vector and scalar situations. Applications to the theory of nonlinear expectat...
Theorems of Tarski's Undefinability and Godel's Second Incompleteness - Computationally
Salehi, Saeed
2015-01-01
We present a version of Godel's Second Incompleteness Theorem for recursively enumerable consistent extensions of a fixed axiomatizable theory, by incorporating some bi-theoretic version of the derivability conditions (first discussed by M. Detlefsen 2001). We also argue that Tarski's theorem on the Undefinability of Truth is Godel's First Incompleteness Theorem relativized to definable oracles; here a unification of these two theorems is given.
The Interpretability of Inconsistency: Feferman's Theorem and Related Results
Visser, Albert
This paper is an exposition of Feferman's Theorem concerning the interpretability of inconsistency and of further insights directly connected to this result. Feferman's Theorem is a strengthening of the Second Incompleteness Theorem. It says, in metaphorical paraphrase, that it is not just the case
The Interpretability of Inconsistency: Feferman's Theorem and Related Results
Visser, Albert
2014-01-01
This paper is an exposition of Feferman's Theorem concerning the interpretability of inconsistency and of further insights directly connected to this result. Feferman's Theorem is a strengthening of the Second Incompleteness Theorem. It says, in metaphorical paraphrase, that it is not just the case
On Comparison Theorems for Conformable Fractional Differential Equations
Directory of Open Access Journals (Sweden)
Mehmet Zeki Sarikaya
2016-10-01
Full Text Available In this paper the more general comparison theorems for conformable fractional differential equations is proposed and tested. Thus we prove some inequalities for conformable integrals by using the generalization of Sturm's separation and Sturm's comparison theorems. The results presented here would provide generalizations of those given in earlier works. The numerical example is also presented to verify the proposed theorem.
COMPARISON THEOREMS AND APPLICATIONS OF OSCILLATION OF NEUTRAL DIFFERENTIAL EQUATIONS
Institute of Scientific and Technical Information of China (English)
燕居让
1991-01-01
We first establish comparison theorems of the oscillation for a higher-order neutral delaydifferential equation. By these comparison theorems, the criterion of oscillation propertiesof neutral delay differential equation is reduced to that of nonneutral delay differential equa-tion, from which we give a series of oscillation theorems for neutral delay differentialequation.
A generalization of the virial theorem for strongly singular potentials
International Nuclear Information System (INIS)
Gesztesy, F.; Pittner, L.
1978-09-01
Using scale transformations the authors prove a generalization of the virial theorem for the eigenfunctions of non-relativistic Schroedinger Hamiltonians which are defined as the Friedrichs extension of strongly singular differential operators. The theorem also applies to situations where the ground state has divergent kinetic and potential energy and thus the usual version of the virial theorem becomes meaningless. (Auth.)
No-go theorems for the minimization of potentials
International Nuclear Information System (INIS)
Chang, D.; Kumar, A.
1985-01-01
Using a theorem in linear algebra, we prove some no-go theorems in the minimization of potentials related to the problem of symmetry breaking. Some applications in the grand unified model building are mentioned. Another application of the algebraic theorem is also included to demonstrate its usefulness
Search strategy for theorem proving in artificial systems. I
Energy Technology Data Exchange (ETDEWEB)
Lovitskii, V A; Barenboim, M S
1981-01-01
A strategy is contrived, employing the language of finite-order predicate calculus, for finding proofs of theorems. A theorem is formulated, based on 2 known theorems on purity and absorption, and used to determine 5 properties of a set of propositions. 3 references.
Goedel incompleteness theorems and the limits of their applicability. I
International Nuclear Information System (INIS)
Beklemishev, Lev D
2011-01-01
This is a survey of results related to the Goedel incompleteness theorems and the limits of their applicability. The first part of the paper discusses Goedel's own formulations along with modern strengthenings of the first incompleteness theorem. Various forms and proofs of this theorem are compared. Incompleteness results related to algorithmic problems and mathematically natural examples of unprovable statements are discussed. Bibliography: 68 titles.
Directory of Open Access Journals (Sweden)
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.
On a theorem of Cattabriga related to Stokes equations
International Nuclear Information System (INIS)
Georgescu, V.
1978-01-01
We study the ''generalized Stokes boundary value problem'', which is a (generalization of a) linearized version of Navier-Stokes equations and we show the existence and unicity of the weak solution. It is known that these results can be used to prove the existence of weak (local) solutions to the Navier-Stokes equations. However, we are mainly interested in the method of proving it will be seen how easy the result follows from some general theorems about differential forms on a Riemannian manifold. (author)
Extended Hellmann-Feynman theorem for degenerate eigenstates
Zhang, G. P.; George, Thomas F.
2004-04-01
In a previous paper, we reported a failure of the traditional Hellmann-Feynman theorem (HFT) for degenerate eigenstates. This has generated enormous interest among different groups. In four independent papers by Fernandez, by Balawender, Hola, and March, by Vatsya, and by Alon and Cederbaum, an elegant method to solve the problem was devised. The main idea is that one has to construct and diagonalize the force matrix for the degenerate case, and only the eigenforces are well defined. We believe this is an important extension to HFT. Using our previous example for an energy level of fivefold degeneracy, we find that those eigenforces correctly reflect the symmetry of the molecule.
Convergence Theorem for Finite Family of Total Asymptotically Nonexpansive Mappings
Directory of Open Access Journals (Sweden)
E.U. Ofoedu
2015-11-01
Full Text Available In this paper we introduce an explicit iteration process and prove strong convergence of the scheme in a real Hilbert space $H$ to the common fixed point of finite family of total asymptotically nonexpansive mappings which is nearest to the point $u \\in H$. Our results improve previously known ones obtained for the class of asymptotically nonexpansive mappings. As application, iterative method for: approximation of solution of variational Inequality problem, finite family of continuous pseudocontractive mappings, approximation of solutions of classical equilibrium problems and approximation of solutions of convex minimization problems are proposed. Our theorems unify and complement many recently announced results.
Theorems of Leray-Schauder type and applications
Precup, Radu
2002-01-01
This volume presents a systematic and unified treatment of Leray-Schauder continuation theorems in nonlinear analysis. In particular, fixed point theory is established for many classes of maps, such as contractive, non-expansive, accretive, and compact maps, to name but a few. This book also presents coincidence and multiplicity results. Many applications of current interest in the theory of nonlinear differential equations are presented to complement the theory. The text is essentially self-contained, so it may also be used as an introduction to topological methods in nonlinear analysis. This volume will appeal to graduate students and researchers in mathematical analysis and its applications.
Examples of the Zeroth Theorem of the History of Science
Energy Technology Data Exchange (ETDEWEB)
Jackson, J.D.
2007-08-24
The zeroth theorem of the history of science, enunciated byE. P. Fischer, states that a discovery (rule,regularity, insight) namedafter someone (often) did not originate with that person. I present fiveexamples from physics: the Lorentz condition partial muAmu = 0 definingthe Lorentz gauge of the electromagnetic potentials; the Dirac deltafunction, delta(x); the Schumann resonances of the earth-ionospherecavity; the Weizsacker-Williams method of virtual quanta; the BMTequation of spin dynamics. I give illustrated thumbnail sketches of boththe true and reputed discoverers and quote from their "discovery"publications.
An extension of Pohlmeyer's theorem
International Nuclear Information System (INIS)
Rosten, Oliver J
2010-01-01
Applying the exact renormalization group to scalar field theory in Euclidean space of general (not necessarily integer) dimension, it is proven that the only fixed point with vanishing anomalous dimension is the Gaussian one. The proof requires positivity of the two-point connected correlation function together with a technical assumption concerning solutions of the flow equation. The method, in which the representation of the flow equation as a heat equation plays a central role, extends directly to non-gauge theories with arbitrary matter content (though nonlinear sigma models are beyond the scope of the current method).
Information systems project management: methods, tools, and techniques
Mcmanus, John; Wood-Harper, Trevor
2004-01-01
Information Systems Project Management offers a clear and logical exposition of how to plan, organise and monitor projects effectively in order to deliver quality information systems within time, to budget and quality. This new book by John McManus and Trevor Wood-Harper is suitable for upper level undergraduates and postgraduates studying project management and Information Systems. Practising managers will also find it to be a valuable tool in their work. Managing information systems pro...
Participatory Methods and UCA Project: understanding technologies as culture
Directory of Open Access Journals (Sweden)
Magda Pischetola
2015-12-01
Full Text Available Abstract In the complex and changing context of digital culture, the media become an important space of relation, as they have the crucial role of articulating new cultural logics that lead to disruptions in the school environment. To understand this change, new methods of analysis and research have been created, the so-called Participatory Methodologies. They are action research strategies aimed at intervening in a given social situation. In the analysis proposed here, such methodologies will help us to address the challenge of involving digital technologies in school culture, through the participation of different individuals involved. Two qualitative case studies about the project Um Computador por Aluno – the Brazilian One Laptop per Child -, carried out in 2012 in the schools of Santa Catarina and Bahia, are the first of two phases of the research presented. The results concern a "vertical" form of technology insertion in schools, which led to frustration and de-motivation at several levels. Starting from these considerations, the second stage of research proposes a pedagogical intervention in one of four schools in the field. The methodologies of participatory video and photography are chosen as possibilities of action-reflection-action on the sociocultural reality of students through the experience of sharing. The results show the importance of carrying out creative activities, appropriate to a social conception of learning, as well as the centrality of children and youth as agency and a broader need to redefine the relationship between teacher and student, in a more "horizontal" perspective process of teaching and learning. Keywords: Projeto UCA. Participatory Research Method. Innovative teaching-learning.
International Nuclear Information System (INIS)
Zhu Ning; Jiang Yong; Kato, Seizo
2005-01-01
This study uses ultrasound in combination with tomography to obtain three-dimensional temperature measurements using projection data obtained from limited projection angle. The main feature of the new computerized tomography (CT) reconstruction algorithm is to employ extrapolation scheme to make up for the incomplete projection data, it is based on the conventional filtered back projection (FBP) method while on top of that taking into account the correlation between the projection data and Fourier transform-based extrapolation. Computer simulation is conducted to verify the above algorithm. An experimental 3D temperature distribution measurement is also carried out to validate the proposed algorithm. The simulation and experimental results demonstrate that the extrapolated FBP CT algorithm is highly effective in dealing with projection data from limited projection angle
Special relativity theorem and Pythagoras’s magic
Korkmaz, S. D.; Aybek, E. C.; Örücü, M.
2016-03-01
In the modern physics unit included in the course curriculum of grade 10 physics introduced in the 2007-2008 education year, the aim is that students at this grade level are aware of any developments which constitute modern physics and may be considered new, and interpret whether mass, length and time values of the motions at any velocities close to the speed of light vary or not. One of the scientific concepts and subjects among the final ones to be learned in the unit of modern physics with 12 course hours includes the special relativity theorem and its results. The special relativity theorem, the foundation of which was laid by Einstein in 1905, has three significant predictions proven by experiments and observations: time extension, dimensional shortening and mass relativity. At the first stage of this study, a simple and fast solution that uses the Pythagorean relation for problems and must be treated by using the mathematical expressions of the predictions as specified above is given, and this way of solution was taught while the relativity subject was explained to the secondary education students who are fifteen years old from grade 10 in the 2013-2014 education year. At the second stage of the study, a qualitative study is released together with grade 11 students who are sixteen years old in 2014-2015, who learnt to solve any problems in both methods, while the special relativity subject is discussed in the physics course in grade 10. The findings of the study show that the students have a misconception on the relativity theorem and prefer to solve any relativity-related problems by using the Pythagorean method constituting the first stage of this study.
Final Report of the Project "From the finite element method to the virtual element method"
Energy Technology Data Exchange (ETDEWEB)
Manzini, Gianmarco [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Gyrya, Vitaliy [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2017-12-20
The Finite Element Method (FEM) is a powerful numerical tool that is being used in a large number of engineering applications. The FEM is constructed on triangular/tetrahedral and quadrilateral/hexahedral meshes. Extending the FEM to general polygonal/polyhedral meshes in straightforward way turns out to be extremely difficult and leads to very complex and computationally expensive schemes. The reason for this failure is that the construction of the basis functions on elements with a very general shape is a non-trivial and complex task. In this project we developed a new family of numerical methods, dubbed the Virtual Element Method (VEM) for the numerical approximation of partial differential equations (PDE) of elliptic type suitable to polygonal and polyhedral unstructured meshes. We successfully formulated, implemented and tested these methods and studied both theoretically and numerically their stability, robustness and accuracy for diffusion problems, convection-reaction-diffusion problems, the Stokes equations and the biharmonic equations.
Interpreting IDR(s) as a deflation method
Collignon, T.P.; Sleijpen, G.L.G.; Van Gijzen, M.B.
2010-01-01
In this paper the IDR(s) method is interpreted in the context of deflation methods. It is shown that IDR(s) can be seen as a Richardson iteration preconditioned by a variable deflation–type preconditioner. The main result of this paper is the IDR projection theorem, which relates the spectrum of the
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.
Project Management using Critical Path Method (CPM): A Pragmatic ...
African Journals Online (AJOL)
Traditional techniques of decision-making have hindered the technical efficiency of most professionals and executors of the public project in many developing countries such as Nigeria. The use of Gantt chart in project planning has continued to increase as a source of last resort in spite of its severe limitations for ineffective ...
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…
Childhood Obesity Research Demonstration project: Cross-site evaluation method
The Childhood Obesity Research Demonstration (CORD) project links public health and primary care interventions in three projects described in detail in accompanying articles in this issue of Childhood Obesity. This article describes a comprehensive evaluation plan to determine the extent to which th...
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...
Evaluation of Sustainable Practices within Project Management Methods
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Shah Satya
2017-01-01
Full Text Available The purpose of this research study is to investigate some of the sustainable practices within projects with a focus on social projects. The different research methodologies applied through this research consisted both primary and secondary research, including literature review and through case study. The stakeholder’s behavioural needs towards acting and implementing sustainable practices led to the adoption of sustainable practices within projects which are managed across profit and non-profit organisations. Nevertheless, lack of sustainable behaviour was outlined, and henceforth the integration of sustainable development within social projects is crucially important as such projects were identified as the drivers toward educating the society in order to help to produce generations of people who would be more sustainably aware. Currently, sustainable development is very often taken into account when it comes to managing projects. Nevertheless, if the adoption of sustainable practices is well established in some sectors such as construction, literature tends to demonstrate a lack of information regarding other sectors, especially within social projects. This research aims to investigate the adoption of sustainable practices within social projects and therefore to satisfy a literature gap.
A Meinardus Theorem with Multiple Singularities
Granovsky, Boris L.; Stark, Dudley
2012-09-01
Meinardus proved a general theorem about the asymptotics of the number of weighted partitions, when the Dirichlet generating function for weights has a single pole on the positive real axis. Continuing (Granovsky et al., Adv. Appl. Math. 41:307-328, 2008), we derive asymptotics for the numbers of three basic types of decomposable combinatorial structures (or, equivalently, ideal gas models in statistical mechanics) of size n, when their Dirichlet generating functions have multiple simple poles on the positive real axis. Examples to which our theorem applies include ones related to vector partitions and quantum field theory. Our asymptotic formula for the number of weighted partitions disproves the belief accepted in the physics literature that the main term in the asymptotics is determined by the rightmost pole.
Lesovik, G B; Lebedev, A V; Sadovskyy, I A; Suslov, M V; Vinokur, V M
2016-09-12
Remarkable progress of quantum information theory (QIT) allowed to formulate mathematical theorems for conditions that data-transmitting or data-processing occurs with a non-negative entropy gain. However, relation of these results formulated in terms of entropy gain in quantum channels to temporal evolution of real physical systems is not thoroughly understood. Here we build on the mathematical formalism provided by QIT to formulate the quantum H-theorem in terms of physical observables. We discuss the manifestation of the second law of thermodynamics in quantum physics and uncover special situations where the second law can be violated. We further demonstrate that the typical evolution of energy-isolated quantum systems occurs with non-diminishing entropy.
A Geometrical Approach to Bell's Theorem
Rubincam, David Parry
2000-01-01
Bell's theorem can be proved through simple geometrical reasoning, without the need for the Psi function, probability distributions, or calculus. The proof is based on N. David Mermin's explication of the Einstein-Podolsky-Rosen-Bohm experiment, which involves Stern-Gerlach detectors which flash red or green lights when detecting spin-up or spin-down. The statistics of local hidden variable theories for this experiment can be arranged in colored strips from which simple inequalities can be deduced. These inequalities lead to a demonstration of Bell's theorem. Moreover, all local hidden variable theories can be graphed in such a way as to enclose their statistics in a pyramid, with the quantum-mechanical result lying a finite distance beneath the base of the pyramid.
Asymptotic twistor theory and the Kerr theorem
International Nuclear Information System (INIS)
Newman, Ezra T
2006-01-01
We first review asymptotic twistor theory with its real subspace of null asymptotic twistors: a five-dimensional CR manifold. This is followed by a description of the Kerr theorem (the identification of shear-free null congruences, in Minkowski space, with the zeros of holomorphic functions of three variables) and an asymptotic version of the Kerr theorem that produces regular asymptotically shear-free null geodesic congruences in arbitrary asymptotically flat Einstein or Einstein-Maxwell spacetimes. A surprising aspect of this work is the role played by analytic curves in H-space, each curve generating an asymptotically flat null geodesic congruence. Also there is a discussion of the physical space realizations of the two associated five- and three-dimensional CR manifolds
Theorem of comparative sensitivity of fibre sensors
Belovolov, M. I.; Paramonov, V. M.; Belovolov, M. M.
2017-12-01
We report an analysis of sensitivity of fibre sensors of physical quantities based on different types of interferometers. We formulate and prove the following theorem: under the time-dependent external physical perturbations at nonzero frequencies (i.e., except the static and low-frequency ones) on the sensitive arms of an interferometer in the form of multiturn elements (coils), there exist such lengths L of the measuring arms of the fibre interferometers at which the sensitivity of sensors based on the Sagnac fibre interferometers can be comparable with the sensitivity of sensors based on Michelson, Mach - Zehnder, or Fabry - Perot fibre interferometers, as well as exceed it under similar other conditions (similar-type perturbations, similar arm lengths and single-mode fibre types). The consequences that follow from the theorem, important for practical implementation of arrays of fibre sensors for measurement purposes and the devices with stable metrological properties, are discussed.
The self-normalized Donsker theorem revisited
Parczewski, Peter
2016-01-01
We extend the Poincar\\'{e}--Borel lemma to a weak approximation of a Brownian motion via simple functionals of uniform distributions on n-spheres in the Skorokhod space $D([0,1])$. This approach is used to simplify the proof of the self-normalized Donsker theorem in Cs\\"{o}rg\\H{o} et al. (2003). Some notes on spheres with respect to $\\ell_p$-norms are given.
The untyped stack calculus and Bohm's theorem
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Alberto Carraro
2013-03-01
Full Text Available The stack calculus is a functional language in which is in a Curry-Howard correspondence with classical logic. It enjoys confluence but, as well as Parigot's lambda-mu, does not admit the Bohm Theorem, typical of the lambda-calculus. We present a simple extension of stack calculus which is for the stack calculus what Saurin's Lambda-mu is for lambda-mu.
Gauge Invariance and the Goldstone Theorem
Guralnik, Gerald S.
This paper was originally created for and printed in the "Proceedings of seminar on unified theories of elementary particles" held in Feldafing, Germany from July 5 to 16, 1965 under the auspices of the Max-Planck-Institute for Physics and Astrophysics in Munich. It details and expands upon the 1964 Guralnik, Hagen, and Kibble paper demonstrating that the Goldstone theorem does not require physical zero mass particles in gauge theories.
Asynchronous networks: modularization of dynamics theorem
Bick, Christian; Field, Michael
2017-02-01
Building on the first part of this paper, we develop the theory of functional asynchronous networks. We show that a large class of functional asynchronous networks can be (uniquely) represented as feedforward networks connecting events or dynamical modules. For these networks we can give a complete description of the network function in terms of the function of the events comprising the network: the modularization of dynamics theorem. We give examples to illustrate the main results.
Fractional and integer charges from Levinson's theorem
International Nuclear Information System (INIS)
Farhi, E.; Graham, N.; Jaffe, R.L.; Weigel, H.
2001-01-01
We compute fractional and integer fermion quantum numbers of static background field configurations using phase shifts and Levinson's theorem. By extending fermionic scattering theory to arbitrary dimensions, we implement dimensional regularization in a (1+1)-dimensional gauge theory. We demonstrate that this regularization procedure automatically eliminates the anomaly in the vector current that a naive regulator would produce. We also apply these techniques to bag models in one and three dimensions
Theorems for asymptotic safety of gauge theories
Energy Technology Data Exchange (ETDEWEB)
Bond, Andrew D.; Litim, Daniel F. [University of Sussex, Department of Physics and Astronomy, Brighton (United Kingdom)
2017-06-15
We classify the weakly interacting fixed points of general gauge theories coupled to matter and explain how the competition between gauge and matter fluctuations gives rise to a rich spectrum of high- and low-energy fixed points. The pivotal role played by Yukawa couplings is emphasised. Necessary and sufficient conditions for asymptotic safety of gauge theories are also derived, in conjunction with strict no go theorems. Implications for phase diagrams of gauge theories and physics beyond the Standard Model are indicated. (orig.)
Optical theorem, depolarization and vector tomography
International Nuclear Information System (INIS)
Toperverg, B.P.
2003-01-01
A law of the total flux conservation is formulated in the form of the optical theorem. It is employed to explicitly derive equations for the description of the neutron polarization within the range of the direct beam defined by its angular divergence. General considerations are illustrated by calculations using the Born and Eikonal approximations. Results are briefly discussed as applied to Larmor-Fourier tomography
Central limit theorem and deformed exponentials
International Nuclear Information System (INIS)
Vignat, C; Plastino, A
2007-01-01
The central limit theorem (CLT) can be ranked among the most important ones in probability theory and statistics and plays an essential role in several basic and applied disciplines, notably in statistical thermodynamics. We show that there exists a natural extension of the CLT from exponentials to so-called deformed exponentials (also denoted as q-Gaussians). Our proposal applies exactly in the usual conditions in which the classical CLT is used. (fast track communication)
Optical theorem for heavy-ion scattering
International Nuclear Information System (INIS)
Schwarzschild, A.Z.; Auerbach, E.H.; Fuller, R.C.; Kahana, S.
1976-01-01
An heuristic derivation is given of an equivalent of the optical theorem stated in the charged situation with the remainder or nuclear elastic scattering amplitude defined as a difference of elastic and Coulomb amplitudes. To test the detailed behavior of this elastic scattering amplitude and the cross section, calculations were performed for elastic scattering of 18 O + 58 Ni, 136 Xe + 209 Bi, 84 Kr + 208 Pb, and 11 B + 26 Mg at 63.42 to 114 MeV
Applications of Wck's theorem, ch. 17
International Nuclear Information System (INIS)
Brussaard, P.J.; Glaudemans, P.W.M.
1977-01-01
Wick's theorem is introduced and used to write the many-body Hamiltonian in a selfconsistent basis. The terms of a perturbation expansion are evaluated with the use of the second-quantization formalism.The correspondence with Feyman diagrams is demonstrated. For some nuclei a description in terms of particle-hole configurations is quite convenient. The simplest case, i.e. one-particle, one-hole states, is treated
International Nuclear Information System (INIS)
Webb, G M; Dasgupta, B; McKenzie, J F; Hu, Q; Zank, G P
2014-01-01
Conservation laws in ideal gas dynamics and magnetohydrodynamics (MHD) associated with fluid relabeling symmetries are derived using Noether's first and second theorems. Lie dragged invariants are discussed in terms of the MHD Casimirs. A nonlocal conservation law for fluid helicity applicable for a non-barotropic fluid involving Clebsch variables is derived using Noether's theorem, in conjunction with a fluid relabeling symmetry and a gauge transformation. A nonlocal cross helicity conservation law involving Clebsch potentials, and the MHD energy conservation law are derived by the same method. An Euler–Poincaré variational approach is also used to derive conservation laws associated with fluid relabeling symmetries using Noether's second theorem. (paper)
The universality of the Carnot theorem
International Nuclear Information System (INIS)
Gonzalez-Ayala, Julian; Angulo-Brown, F
2013-01-01
It is common in many thermodynamics textbooks to illustrate the Carnot theorem through the use of diverse state equations for gases, paramagnets, and other simple thermodynamic systems. As is well known, the universality of the Carnot efficiency is easily demonstrated in a temperature–entropy diagram, which means that η C is independent of the working substance. In this paper we remark that the universality of the Carnot theorem goes beyond conventional state equations, and is fulfilled by gas state equations that do not correspond to an ideal gas in the dilution limit, namely V → ∞. Some of these unconventional state equations have certain thermodynamic ‘anomalies’ that nonetheless do not forbid them from obeying the Carnot theorem. We discuss how this very general behaviour arises from Maxwell relations, which are connected with a geometrical property expressed through preserving area transformations. A rule is proposed to calculate the Maxwell relations associated with a thermodynamic system by using the preserving area relationships. In this way it is possible to calculate the number of possible preserving area mappings by giving the number of possible Jacobian identities between all pairs of thermodynamic variables included in the corresponding Gibbs equation. This paper is intended for undergraduates and specialists in thermodynamics and related areas. (paper)
Soft theorems from conformal field theory
International Nuclear Information System (INIS)
Lipstein, Arthur E.
2015-01-01
Strominger and collaborators recently proposed that soft theorems for gauge and gravity amplitudes can be interpreted as Ward identities of a 2d CFT at null infinity. In this paper, we will consider a specific realization of this CFT known as ambitwistor string theory, which describes 4d Yang-Mills and gravity with any amount of supersymmetry. Using 4d ambtwistor string theory, we derive soft theorems in the form of an infinite series in the soft momentum which are valid to subleading order in gauge theory and sub-subleading order in gravity. Furthermore, we describe how the algebra of soft limits can be encoded in the braiding of soft vertex operators on the worldsheet and point out a simple relation between soft gluon and soft graviton vertex operators which suggests an interesting connection to color-kinematics duality. Finally, by considering ambitwistor string theory on a genus one worldsheet, we compute the 1-loop correction to the subleading soft graviton theorem due to infrared divergences.
Joint probability distributions and fluctuation theorems
International Nuclear Information System (INIS)
García-García, Reinaldo; Kolton, Alejandro B; Domínguez, Daniel; Lecomte, Vivien
2012-01-01
We derive various exact results for Markovian systems that spontaneously relax to a non-equilibrium steady state by using joint probability distribution symmetries of different entropy production decompositions. The analytical approach is applied to diverse problems such as the description of the fluctuations induced by experimental errors, for unveiling symmetries of correlation functions appearing in fluctuation–dissipation relations recently generalized to non-equilibrium steady states, and also for mapping averages between different trajectory-based dynamical ensembles. Many known fluctuation theorems arise as special instances of our approach for particular twofold decompositions of the total entropy production. As a complement, we also briefly review and synthesize the variety of fluctuation theorems applying to stochastic dynamics of both continuous systems described by a Langevin dynamics and discrete systems obeying a Markov dynamics, emphasizing how these results emerge from distinct symmetries of the dynamical entropy of the trajectory followed by the system. For Langevin dynamics, we embed the 'dual dynamics' with a physical meaning, and for Markov systems we show how the fluctuation theorems translate into symmetries of modified evolution operators
Function Projective Synchronization of Two Identical New Hyperchaotic Systems
International Nuclear Information System (INIS)
Li Xin; Chen Yong
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.
A method multi criterio to evaluate projects of rural electrification
International Nuclear Information System (INIS)
Gonzalez Posse, E.
1994-01-01
In this document about the problem of the evaluation projects methodologies in rural electrification.The low analysis problem is of complex nature, because each project is evaluation object and an economic agent. One of these agents identifies different benefits and cost, and also has a different approaches for value them.In consequence, the form in that it is carried out the evaluation of the one project for each one of this agents that it is usually solved for mechanisms linked to the capacity of incidence or of determination of each one of them, this does not assures a satisfactory results for the general interest
Directory of Open Access Journals (Sweden)
Wang Yajun
2008-12-01
Full Text Available In order to address the complex uncertainties caused by interfacing between the fuzziness and randomness of the safety problem for embankment engineering projects, and to evaluate the safety of embankment engineering projects more scientifically and reasonably, this study presents the fuzzy logic modeling of the stochastic finite element method (SFEM based on the harmonious finite element (HFE technique using a first-order approximation theorem. Fuzzy mathematical models of safety repertories were introduced into the SFEM to analyze the stability of embankments and foundations in order to describe the fuzzy failure procedure for the random safety performance function. The fuzzy models were developed with membership functions with half depressed gamma distribution, half depressed normal distribution, and half depressed echelon distribution. The fuzzy stochastic mathematical algorithm was used to comprehensively study the local failure mechanism of the main embankment section near Jingnan in the Yangtze River in terms of numerical analysis for the probability integration of reliability on the random field affected by three fuzzy factors. The result shows that the middle region of the embankment is the principal zone of concentrated failure due to local fractures. There is also some local shear failure on the embankment crust. This study provides a referential method for solving complex multi-uncertainty problems in engineering safety analysis.
Regularization with higher covariant derivatives, anomalies and the Adler-Bardeen theorem
International Nuclear Information System (INIS)
Day, M.
1983-01-01
Complications arising in the renormalization of a theory regulated by the method of higher covariant derivatives supplemented with a modified Pauli-Villars regularization are discussed. The proof of the Adler-Bardeen theorem using the method of higher covariant derivatives has to be modified. (orig.)
IMPORTANCE OF EARNED VALUE METHOD (EVA IN THE PERFORMANCE ANALYSIS OF PROJECTS
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MARGARITA JANESKA
2016-04-01
Full Text Available The economics of the projects is an important process in the project management. Effective control of projects is based on appropriate methods for monitoring, and the entire project, the timetable, cost, quality and risk. Unlike accounting aspects in project management are looking for information that allow insight into the status and trends of financial progress of the project. Such information provide a method of earned value. It is a key component for assessing the actual performance of the project. The method of earned value is a better indicator of the progress of the project in comparison to the classical method of comparing planned and actual costs. This method shows the profit in relation to actual costs at a specific time point. This method is the basis for calculating the index of the project performance. In this sense, MS Project provides many opportunities for quality control and monitoring of the realization of the projects. In this study will be described the architecture of this method, outlined the benefits of the application of this method, and the basic criteria that should satisfy project management to be able to apply it.
Application fuzzy multi-attribute decision analysis method to prioritize project success criteria
Phong, Nguyen Thanh; Quyen, Nguyen Le Hoang Thuy To
2017-11-01
Project success is a foundation for project owner to manage and control not only for the current project but also for future potential projects in construction companies. However, identifying the key success criteria for evaluating a particular project in real practice is a challenging task. Normally, it depends on a lot of factors, such as the expectation of the project owner and stakeholders, triple constraints of the project (cost, time, quality), and company's mission, vision, and objectives. Traditional decision-making methods for measuring the project success are usually based on subjective opinions of panel experts, resulting in irrational and inappropriate decisions. Therefore, this paper introduces a multi-attribute decision analysis method (MADAM) for weighting project success criteria by using fuzzy Analytical Hierarchy Process approach. It is found that this method is useful when dealing with imprecise and uncertain human judgments in evaluating project success criteria. Moreover, this research also suggests that although cost, time, and quality are three project success criteria projects, the satisfaction of project owner and acceptance of project stakeholders with the completed project criteria is the most important criteria for project success evaluation in Vietnam.
A bi-projection method for Bingham type flows
Chupin , Laurent; Dubois , Thierry
2015-01-01
We propose and study a new numerical scheme to compute the isothermal and unsteady flow of an incompressible viscoplastic Bingham medium.The main difficulty, for both theoretical and numerical approaches, is due to the non-differentiability of the plastic part of stress tensor in regionswhere the rate-of-strain tensor vanishes. This is handled by reformulating the definition of the plastic stress tensor in terms ofa projection.A new time scheme, based on the classical incremental projection m...
Four theorems on the psychometric function.
May, Keith A; Solomon, Joshua A
2013-01-01
In a 2-alternative forced-choice (2AFC) discrimination task, observers choose which of two stimuli has the higher value. The psychometric function for this task gives the probability of a correct response for a given stimulus difference, Δx. This paper proves four theorems about the psychometric function. Assuming the observer applies a transducer and adds noise, Theorem 1 derives a convenient general expression for the psychometric function. Discrimination data are often fitted with a Weibull function. Theorem 2 proves that the Weibull "slope" parameter, β, can be approximated by β(Noise) x β(Transducer), where β(Noise) is the β of the Weibull function that fits best to the cumulative noise distribution, and β(Transducer) depends on the transducer. We derive general expressions for β(Noise) and β(Transducer), from which we derive expressions for specific cases. One case that follows naturally from our general analysis is Pelli's finding that, when d' ∝ (Δx)(b), β ≈ β(Noise) x b. We also consider two limiting cases. Theorem 3 proves that, as sensitivity improves, 2AFC performance will usually approach that for a linear transducer, whatever the actual transducer; we show that this does not apply at signal levels where the transducer gradient is zero, which explains why it does not apply to contrast detection. Theorem 4 proves that, when the exponent of a power-function transducer approaches zero, 2AFC performance approaches that of a logarithmic transducer. We show that the power-function exponents of 0.4-0.5 fitted to suprathreshold contrast discrimination data are close enough to zero for the fitted psychometric function to be practically indistinguishable from that of a log transducer. Finally, Weibull β reflects the shape of the noise distribution, and we used our results to assess the recent claim that internal noise has higher kurtosis than a Gaussian. Our analysis of β for contrast discrimination suggests that, if internal noise is stimulus
Four theorems on the psychometric function.
Directory of Open Access Journals (Sweden)
Keith A May
Full Text Available In a 2-alternative forced-choice (2AFC discrimination task, observers choose which of two stimuli has the higher value. The psychometric function for this task gives the probability of a correct response for a given stimulus difference, Δx. This paper proves four theorems about the psychometric function. Assuming the observer applies a transducer and adds noise, Theorem 1 derives a convenient general expression for the psychometric function. Discrimination data are often fitted with a Weibull function. Theorem 2 proves that the Weibull "slope" parameter, β, can be approximated by β(Noise x β(Transducer, where β(Noise is the β of the Weibull function that fits best to the cumulative noise distribution, and β(Transducer depends on the transducer. We derive general expressions for β(Noise and β(Transducer, from which we derive expressions for specific cases. One case that follows naturally from our general analysis is Pelli's finding that, when d' ∝ (Δx(b, β ≈ β(Noise x b. We also consider two limiting cases. Theorem 3 proves that, as sensitivity improves, 2AFC performance will usually approach that for a linear transducer, whatever the actual transducer; we show that this does not apply at signal levels where the transducer gradient is zero, which explains why it does not apply to contrast detection. Theorem 4 proves that, when the exponent of a power-function transducer approaches zero, 2AFC performance approaches that of a logarithmic transducer. We show that the power-function exponents of 0.4-0.5 fitted to suprathreshold contrast discrimination data are close enough to zero for the fitted psychometric function to be practically indistinguishable from that of a log transducer. Finally, Weibull β reflects the shape of the noise distribution, and we used our results to assess the recent claim that internal noise has higher kurtosis than a Gaussian. Our analysis of β for contrast discrimination suggests that, if internal noise is
Image restoration by the method of convex projections: part 1 theory.
Youla, D C; Webb, H
1982-01-01
A projection operator onto a closed convex set in Hilbert space is one of the few examples of a nonlinear map that can be defined in simple abstract terms. Moreover, it minimizes distance and is nonexpansive, and therefore shares two of the more important properties of ordinary linear orthogonal projections onto closed linear manifolds. In this paper, we exploit the properties of these operators to develop several iterative algorithms for image restoration from partial data which permit any number of nonlinear constraints of a certain type to be subsumed automatically. Their common conceptual basis is as follows. Every known property of an original image f is envisaged as restricting it to lie in a well-defined closed convex set. Thus, m such properties place f in the intersection E(0) = E(i) of the corresponding closed convex sets E(1),E(2),...EE(m). Given only the projection operators PE(i) onto the individual E(i)'s, i = 1 --> m, we restore f by recursive means. Clearly, in this approach, the realization of the P(i)'s in a Hilbert space setting is one of the major synthesis problems. Section I describes the geometrical significance of the three main theorems in considerable detail, and most of the underlying ideas are illustrated with the aid of simple diagrams. Section II presents rules for the numerical implementation of 11 specific projection operators which are found to occur frequently in many signal-processing applications, and the Appendix contains proofs of all the major results.
From statistical proofs of the Kochen-Specker theorem to noise-robust noncontextuality inequalities
Kunjwal, Ravi; Spekkens, Robert W.
2018-05-01
The Kochen-Specker theorem rules out models of quantum theory wherein projective measurements are assigned outcomes deterministically and independently of context. This notion of noncontextuality is not applicable to experimental measurements because these are never free of noise and thus never truly projective. For nonprojective measurements, therefore, one must drop the requirement that an outcome be assigned deterministically in the model and merely require that it be assigned a distribution over outcomes in a manner that is context-independent. By demanding context independence in the representation of preparations as well, one obtains a generalized principle of noncontextuality that also supports a quantum no-go theorem. Several recent works have shown how to derive inequalities on experimental data which, if violated, demonstrate the impossibility of finding a generalized-noncontextual model of this data. That is, these inequalities do not presume quantum theory and, in particular, they make sense without requiring an operational analog of the quantum notion of projectiveness. We here describe a technique for deriving such inequalities starting from arbitrary proofs of the Kochen-Specker theorem. It extends significantly previous techniques that worked only for logical proofs, which are based on sets of projective measurements that fail to admit of any deterministic noncontextual assignment, to the case of statistical proofs, which are based on sets of projective measurements that d o admit of some deterministic noncontextual assignments, but not enough to explain the quantum statistics.
Directory of Open Access Journals (Sweden)
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, ...
Polyanin, A. D.; Sorokin, V. G.
2017-12-01
The paper deals with nonlinear reaction-diffusion equations with one or several delays. We formulate theorems that allow constructing exact solutions for some classes of these equations, which depend on several arbitrary functions. Examples of application of these theorems for obtaining new exact solutions in elementary functions are provided. We state basic principles of construction, selection, and use of test problems for nonlinear partial differential equations with delay. Some test problems which can be suitable for estimating accuracy of approximate analytical and numerical methods of solving reaction-diffusion equations with delay are presented. Some examples of numerical solutions of nonlinear test problems with delay are considered.
How to (properly) strengthen Bell's theorem using counterfactuals
Bigaj, Tomasz
Bell's theorem in its standard version demonstrates that the joint assumptions of the hidden-variable hypothesis and the principle of local causation lead to a conflict with quantum-mechanical predictions. In his latest counterfactual strengthening of Bell's theorem, Stapp attempts to prove that the locality assumption itself contradicts the quantum-mechanical predictions in the Hardy case. His method relies on constructing a complex, non-truth functional formula which consists of statements about measurements and outcomes in some region R, and whose truth value depends on the selection of a measurement setting in a space-like separated location L. Stapp argues that this fact shows that the information about the measurement selection made in L has to be present in R. I give detailed reasons why this conclusion can and should be resisted. Next I correct and formalize an informal argument by Shimony and Stein showing that the locality condition coupled with Einstein's criterion of reality is inconsistent with quantum-mechanical predictions. I discuss the possibility of avoiding the inconsistency by rejecting Einstein's criterion rather than the locality assumption.
A method for the efficient prioritization of infrastructure renewal projects
Karydas, D.M.; Gifun, Joe
2006-01-01
The infrastructure renewal program at MIT consists of a large number of projects with an estimated budget that could approach $1 billion. Infrastructure renewal at the Massachusetts Institute of Technology (MIT) is the process of evaluating and investing in the maintenance of facility systems and
Analysis of Conflict Centers in Projects Procured with Traditional and Integrated Methods in Nigeria
Directory of Open Access Journals (Sweden)
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.
Stochastic thermodynamics, fluctuation theorems and molecular machines
International Nuclear Information System (INIS)
Seifert, Udo
2012-01-01
Stochastic thermodynamics as reviewed here systematically provides a framework for extending the notions of classical thermodynamics such as work, heat and entropy production to the level of individual trajectories of well-defined non-equilibrium ensembles. It applies whenever a non-equilibrium process is still coupled to one (or several) heat bath(s) of constant temperature. Paradigmatic systems are single colloidal particles in time-dependent laser traps, polymers in external flow, enzymes and molecular motors in single molecule assays, small biochemical networks and thermoelectric devices involving single electron transport. For such systems, a first-law like energy balance can be identified along fluctuating trajectories. For a basic Markovian dynamics implemented either on the continuum level with Langevin equations or on a discrete set of states as a master equation, thermodynamic consistency imposes a local-detailed balance constraint on noise and rates, respectively. Various integral and detailed fluctuation theorems, which are derived here in a unifying approach from one master theorem, constrain the probability distributions for work, heat and entropy production depending on the nature of the system and the choice of non-equilibrium conditions. For non-equilibrium steady states, particularly strong results hold like a generalized fluctuation–dissipation theorem involving entropy production. Ramifications and applications of these concepts include optimal driving between specified states in finite time, the role of measurement-based feedback processes and the relation between dissipation and irreversibility. Efficiency and, in particular, efficiency at maximum power can be discussed systematically beyond the linear response regime for two classes of molecular machines, isothermal ones such as molecular motors, and heat engines such as thermoelectric devices, using a common framework based on a cycle decomposition of entropy production. (review article)
The implicit function theorem history, theory, and applications
Krantz, Steven G
2003-01-01
The implicit function theorem is part of the bedrock of mathematics analysis and geometry. Finding its genesis in eighteenth century studies of real analytic functions and mechanics, the implicit and inverse function theorems have now blossomed into powerful tools in the theories of partial differential equations, differential geometry, and geometric analysis. There are many different forms of the implicit function theorem, including (i) the classical formulation for Ck functions, (ii) formulations in other function spaces, (iii) formulations for non-smooth function, (iv) formulations for functions with degenerate Jacobian. Particularly powerful implicit function theorems, such as the Nash-Moser theorem, have been developed for specific applications (e.g., the imbedding of Riemannian manifolds). All of these topics, and many more, are treated in the present volume. The history of the implicit function theorem is a lively and complex store, and intimately bound up with the development of fundamental ideas in a...
Some fixed point theorems in fuzzy reflexive Banach spaces
International Nuclear Information System (INIS)
Sadeqi, I.; Solaty kia, F.
2009-01-01
In this paper, we first show that there are some gaps in the fixed point theorems for fuzzy non-expansive mappings which are proved by Bag and Samanta, in [Bag T, Samanta SK. Fixed point theorems on fuzzy normed linear spaces. Inf Sci 2006;176:2910-31; Bag T, Samanta SK. Some fixed point theorems in fuzzy normed linear spaces. Inform Sci 2007;177(3):3271-89]. By introducing the notion of fuzzy and α- fuzzy reflexive Banach spaces, we obtain some results which help us to establish the correct version of fuzzy fixed point theorems. Second, by applying Theorem 3.3 of Sadeqi and Solati kia [Sadeqi I, Solati kia F. Fuzzy normed linear space and it's topological structure. Chaos, Solitons and Fractals, in press] which says that any fuzzy normed linear space is also a topological vector space, we show that all topological version of fixed point theorems do hold in fuzzy normed linear spaces.
On the inverse of the Pomeranchuk theorem
International Nuclear Information System (INIS)
Nagy, E.
1977-04-01
The Pomeranchuk theorem is valid only for bounded total cross sections at infinite energies, and for arbitrarily rising cross sections one cannot prove the zero asymptotic limit of the difference of the particle and antiparticle total cross sections. In the paper the problem is considered from the inverse point of view. It is proved using dispersion relations that if the total cross sections rise with some power of logarithm and the difference of the particle and antiparticle total cross sections remain finite, then the real to imaginary ratios of both the particle and antiparticle forward scattering amplitudes are bounded. (Sz.N.Z.)
Noncommutative gauge theories and Kontsevich's formality theorem
International Nuclear Information System (INIS)
Jurco, B.; Schupp, P.; Wess, J.
2001-01-01
The equivalence of star products that arise from the background field with and without fluctuations and Kontsevich's formality theorem allow an explicitly construction of a map that relates ordinary gauge theory and noncommutative gauge theory (Seiberg-Witten map.) Using noncommutative extra dimensions the construction is extended to noncommutative nonabelian gauge theory for arbitrary gauge groups; as a byproduct we obtain a 'Mini Seiberg-Witten map' that explicitly relates ordinary abelian and nonabelian gauge fields. All constructions are also valid for non-constant B-field, and even more generally for any Poisson tensor
The Invariance and the General CCT Theorems
Stancu, Alin
2010-01-01
The \\begin{it} Invariance Theorem \\end{it} of M. Gerstenhaber and S. D. Schack states that if $\\mathbb{A}$ is a diagram of algebras then the subdivision functor induces a natural isomorphism between the Yoneda cohomologies of the category $\\mathbb{A}$-$\\mathbf{mod}$ and its subdivided category $\\mathbb{A}'$-$\\mathbf{mod}$. In this paper we generalize this result and show that the subdivision functor is a full and faithful functor between two suitable derived categories of $\\mathbb{A}$-$\\mathb...
No-cloning theorem on quantum logics
International Nuclear Information System (INIS)
Miyadera, Takayuki; Imai, Hideki
2009-01-01
This paper discusses the no-cloning theorem in a logicoalgebraic approach. In this approach, an orthoalgebra is considered as a general structure for propositions in a physical theory. We proved that an orthoalgebra admits cloning operation if and only if it is a Boolean algebra. That is, only classical theory admits the cloning of states. If unsharp propositions are to be included in the theory, then a notion of effect algebra is considered. We proved that an atomic Archimedean effect algebra admitting cloning operation is a Boolean algebra. This paper also presents a partial result, indicating a relation between the cloning on effect algebras and hidden variables.
Paraconsistent Probabilities: Consistency, Contradictions and Bayes’ Theorem
Directory of Open Access Journals (Sweden)
Juliana Bueno-Soler
2016-09-01
Full Text Available This paper represents the first steps towards constructing a paraconsistent theory of probability based on the Logics of Formal Inconsistency (LFIs. We show that LFIs encode very naturally an extension of the notion of probability able to express sophisticated probabilistic reasoning under contradictions employing appropriate notions of conditional probability and paraconsistent updating, via a version of Bayes’ theorem for conditionalization. We argue that the dissimilarity between the notions of inconsistency and contradiction, one of the pillars of LFIs, plays a central role in our extended notion of probability. Some critical historical and conceptual points about probability theory are also reviewed.
Stone's representation theorem in fuzzy topology
Institute of Scientific and Technical Information of China (English)
刘应明; 张德学
2003-01-01
In this paper, a complete solution to the problem of Stone's repesentation theorem in fuzzy topology is given for a class of completely distributive lattices. Precisely, it is proved that if L is a frame such that 0 ∈ L is a prime or 1 ∈ L is a coprime, then the category of distributive lattices is dually equivalent to the category of coherent L-locales and that if L is moreover completely distributive, then the category of distributive lattices is dually equivalent to the category of coherent stratified L-topological spaces.
Central limit theorems under special relativity.
McKeague, Ian W
2015-04-01
Several relativistic extensions of the Maxwell-Boltzmann distribution have been proposed, but they do not explain observed lognormal tail-behavior in the flux distribution of various astrophysical sources. Motivated by this question, extensions of classical central limit theorems are developed under the conditions of special relativity. The results are related to CLTs on locally compact Lie groups developed by Wehn, Stroock and Varadhan, but in this special case the asymptotic distribution has an explicit form that is readily seen to exhibit lognormal tail behavior.
Fixed point theorems in spaces and -trees
Directory of Open Access Journals (Sweden)
Kirk WA
2004-01-01
Full Text Available We show that if is a bounded open set in a complete space , and if is nonexpansive, then always has a fixed point if there exists such that for all . It is also shown that if is a geodesically bounded closed convex subset of a complete -tree with , and if is a continuous mapping for which for some and all , then has a fixed point. It is also noted that a geodesically bounded complete -tree has the fixed point property for continuous mappings. These latter results are used to obtain variants of the classical fixed edge theorem in graph theory.
Logic for computer science foundations of automatic theorem proving
Gallier, Jean H
2015-01-01
This advanced text for undergraduate and graduate students introduces mathematical logic with an emphasis on proof theory and procedures for algorithmic construction of formal proofs. The self-contained treatment is also useful for computer scientists and mathematically inclined readers interested in the formalization of proofs and basics of automatic theorem proving. Topics include propositional logic and its resolution, first-order logic, Gentzen's cut elimination theorem and applications, and Gentzen's sharpened Hauptsatz and Herbrand's theorem. Additional subjects include resolution in fir
On Pythagoras Theorem for Products of Spectral Triples
D'Andrea, Francesco; Martinetti, Pierre
2013-01-01
We discuss a version of Pythagoras theorem in noncommutative geometry. Usual Pythagoras theorem can be formulated in terms of Connes' distance, between pure states, in the product of commutative spectral triples. We investigate the generalization to both non pure states and arbitrary spectral triples. We show that Pythagoras theorem is replaced by some Pythagoras inequalities, that we prove for the product of arbitrary (i.e. non-necessarily commutative) spectral triples, assuming only some un...
A remark on the energy conditions for Hawking's area theorem
Lesourd, Martin
2018-06-01
Hawking's area theorem is a fundamental result in black hole theory that is universally associated with the null energy condition. That this condition can be weakened is illustrated by the formulation of a strengthened version of the theorem based on an energy condition that allows for violations of the null energy condition. With the semi-classical context in mind, some brief remarks pertaining to the suitability of the area theorem and its energy condition are made.
The direct Flow parametric Proof of Gauss' Divergence Theorem revisited
Markvorsen, Steen
2006-01-01
The standard proof of the divergence theorem in undergraduate calculus courses covers the theorem for static domains between two graph surfaces. We show that within first year undergraduate curriculum, the flow proof of the dynamic version of the divergence theorem - which is usually considered only much later in more advanced math courses - is comprehensible with only a little extension of the first year curriculum. Moreover, it is more intuitive than the static proof. We support this intuit...
A Converse to the Cayley-Hamilton Theorem
Indian Academy of Sciences (India)
follows that qj = api, where a is a unit. Thus, we must have that the expansion of I into irreducibles is unique. Hence, K[x] is a UFD. A famous theorem of Gauss implies that K[XI' X2,. ,xn] is also an UFD. Gauss's Theorem: R[x] is a UFD, if and only if R is a UFD. For a proof of Gauss's theorem and a detailed proof of the fact that ...
The Surprise Examination Paradox and the Second Incompleteness Theorem
Kritchman, Shira; Raz, Ran
2010-01-01
We give a new proof for Godel's second incompleteness theorem, based on Kolmogorov complexity, Chaitin's incompleteness theorem, and an argument that resembles the surprise examination paradox. We then go the other way around and suggest that the second incompleteness theorem gives a possible resolution of the surprise examination paradox. Roughly speaking, we argue that the flaw in the derivation of the paradox is that it contains a hidden assumption that one can prove the consistency of the...
Goedel incompleteness theorems and the limits of their applicability. I
Energy Technology Data Exchange (ETDEWEB)
Beklemishev, Lev D [Steklov Mathematical Institute, Russian Academy of Sciences, Moscow (Russian Federation)
2011-01-25
This is a survey of results related to the Goedel incompleteness theorems and the limits of their applicability. The first part of the paper discusses Goedel's own formulations along with modern strengthenings of the first incompleteness theorem. Various forms and proofs of this theorem are compared. Incompleteness results related to algorithmic problems and mathematically natural examples of unprovable statements are discussed. Bibliography: 68 titles.
From Einstein's theorem to Bell's theorem: a history of quantum non-locality
Wiseman, H. M.
2006-04-01
In this Einstein Year of Physics it seems appropriate to look at an important aspect of Einstein's work that is often down-played: his contribution to the debate on the interpretation of quantum mechanics. Contrary to physics ‘folklore’, Bohr had no defence against Einstein's 1935 attack (the EPR paper) on the claimed completeness of orthodox quantum mechanics. I suggest that Einstein's argument, as stated most clearly in 1946, could justly be called Einstein's reality locality completeness theorem, since it proves that one of these three must be false. Einstein's instinct was that completeness of orthodox quantum mechanics was the falsehood, but he failed in his quest to find a more complete theory that respected reality and locality. Einstein's theorem, and possibly Einstein's failure, inspired John Bell in 1964 to prove his reality locality theorem. This strengthened Einstein's theorem (but showed the futility of his quest) by demonstrating that either reality or locality is a falsehood. This revealed the full non-locality of the quantum world for the first time.
Algorithm/Architecture Co-design of the Generalized Sampling Theorem Based De-Interlacer.
Beric, A.; Haan, de G.; Sethuraman, R.; Meerbergen, van J.
2005-01-01
De-interlacing is a major determinant of image quality in a modern display processing chain. The de-interlacing method based on the generalized sampling theorem (GST)applied to motion estimation and motion compensation provides the best de-interlacing results. With HDTV interlaced input material
International Nuclear Information System (INIS)
Fan Hongyi; Hao Ren; Lu Hailiang
2008-01-01
Based on our previous paper (Commun. Theor. Phys. 39 (2003) 417) we derive the convolution theorem of fractional Fourier transformation in the context of quantum mechanics, which seems a convenient and neat way. Generalization of this method to the complex fractional Fourier transformation case is also possible
Penambahan Chinese Reminder Theorem Untuk Mempercepat Proses Enkripsi Dan Dekripsi Pada RSA
Hasibuan, Andi Hazri
2015-01-01
Many methods are used to protect digital data stored or transmitted via electronic media. One way is to use a cryptographic algorithm RSA (Rivest-Shamir-Adleman). Standard RSA uses modular arithmetic to perform the encryption and decryption. In this thesis discussed the addition of Chinese Remainder Theorem to speed up the RSA. 100823021
Korn, Granino A
2000-01-01
A reliable source of definitions, theorems, and formulas, this authoritative handbook provides convenient access to information from every area of mathematics. Coverage includes Fourier transforms, Z transforms, linear and nonlinear programming, calculus of variations, random-process theory, special functions, combinatorial analysis, numerical methods, game theory, and much more.
Perturbative description of the fermionic projector: Normalization, causality, and Furry's theorem
Finster, Felix; Tolksdorf, Jürgen
2014-05-01
The causal perturbation expansion of the fermionic projector is performed with a contour integral method. Different normalization conditions are analyzed. It is shown that the corresponding light-cone expansions are causal in the sense that they only involve bounded line integrals. For the resulting loop diagrams we prove a generalized Furry theorem.
Perturbative description of the fermionic projector: Normalization, causality, and Furry's theorem
Energy Technology Data Exchange (ETDEWEB)
Finster, Felix, E-mail: finster@ur.de [Fakultät für Mathematik, Universität Regensburg, D-93040 Regensburg (Germany); Tolksdorf, Jürgen, E-mail: Juergen.Tolksdorf@mis.mpg.de [Max Planck Institute for Mathematics in the Sciences, Leipzig (Germany)
2014-05-15
The causal perturbation expansion of the fermionic projector is performed with a contour integral method. Different normalization conditions are analyzed. It is shown that the corresponding light-cone expansions are causal in the sense that they only involve bounded line integrals. For the resulting loop diagrams we prove a generalized Furry theorem.
Perturbative description of the fermionic projector: Normalization, causality, and Furry's theorem
International Nuclear Information System (INIS)
Finster, Felix; Tolksdorf, Jürgen
2014-01-01
The causal perturbation expansion of the fermionic projector is performed with a contour integral method. Different normalization conditions are analyzed. It is shown that the corresponding light-cone expansions are causal in the sense that they only involve bounded line integrals. For the resulting loop diagrams we prove a generalized Furry theorem
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,…
Impact of Functional Characteristics on Usage of LSS Methods in IT and Perceived Project Success
Mushi, Francis Jeremiah
2014-01-01
High rates of Information Technology (IT) project failures continues; fail to meet established deadlines, exceeding budget, or not agreed-upon functionality. Failure often results from a fundamental confusion over what is involved in the project. Methods that have provided project success in Service and Manufacturing industries have not been…
THE RISKS’ ASSESSMENT IN INNOVATIVE PROJECTS BY THE METHOD OF VERIFIED EQUIVALENTS
Directory of Open Access Journals (Sweden)
Анатолій Валентинович ШАХОВ
2017-03-01
Full Text Available The article describes the concept of "risk of innovation", identified the causes of the risk and the methods of eliminating of negative manifestations of the risk situations in innovative projects. The advantages and disadvantages of the method of correction of the discount rate and the method of equivalent annuities are considered. The methodical approach in assessing the expected effect of the innovative project based on the concept of probability-interval uncertainty is proposed in the article. It was established that the analyzed approaches can be used for the accounting of the risk of innovative projects. Project manager makes his choice using any method of risk assessment individually, depending on the extent and characteristics of the project, the degree of novelty and scale introduction of innovative products, the number of participants and the level of requirements of the foundation of project efficiency and other factors.
Formalization and Implementation of Algebraic Methods in Geometry
Directory of Open Access Journals (Sweden)
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.
Convergence theorems for strictly hemi-contractive maps
International Nuclear Information System (INIS)
Chidume, C.E.; Osilike, M.O.
1992-04-01
It is proved that each of two well-known fixed point iteration methods (the Mann and the Ishikawa iteration methods) converges strongly to the fixed point of strictly hemi-contractive map in real Banach spaces with property (U, λ, m+1,m), λ is an element of R, m is an element of IN. The class of strictly hemi-contractive maps includes all strictly pseudo-contractive maps with nonempty fixed point sets; and Banach spaces with property (U, λ, m+1, m), λ is an element of R, m is an element of IN include the L p (or l p ) spaces, p≥2. Our theorems generalize important known results. (author). 22 refs
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...
Generalizations of the Nash Equilibrium Theorem in the KKM Theory
Directory of Open Access Journals (Sweden)
Sehie Park
2010-01-01
Full Text Available The partial KKM principle for an abstract convex space is an abstract form of the classical KKM theorem. In this paper, we derive generalized forms of the Ky Fan minimax inequality, the von Neumann-Sion minimax theorem, the von Neumann-Fan intersection theorem, the Fan-type analytic alternative, and the Nash equilibrium theorem for abstract convex spaces satisfying the partial KKM principle. These results are compared with previously known cases for G-convex spaces. Consequently, our results unify and generalize most of previously known particular cases of the same nature. Finally, we add some detailed historical remarks on related topics.
Samáková, Jana; Babčanová, Dagmar; Hrablikchovanová, Henrieta; Mesárošová, Jana; Šujanová, Jana
2017-09-01
Effective communication is the most significant ability for project manager and successful project. However, during the management of projects communication, it is very often forgotten, often overlooked or taken for granted. In the management of projects, it is principally necessary to deal with communication during all project lifecycle. Within the project communication, it is very important to define the main methods, tools, support of communication and frequency of communication; these belong to the most important elements of the communication channel which is very often forgotten. Therefore, the main aim of the paper is to analyse the utilisation of the communication channel: communication methods, communication tools, communication frequency and to support project communication in industrial manufacturing enterprises in Slovakia. Based on the research, we can conclude that communication channel is not adequately elaborated in international methodologies and standards of project management as well as in industrial manufacturing enterprises. These facts are very negative, conclusion and it is therefore necessary to deal with the problem.
A Projected Conjugate Gradient Method for Sparse Minimax Problems
DEFF Research Database (Denmark)
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...... with the method are presented. In fact, we find that the number of iterations required is comparable to that of state-of-the-art quasi-Newton codes....
Empirical projection-based basis-component decomposition method
Brendel, Bernhard; Roessl, Ewald; Schlomka, Jens-Peter; Proksa, Roland
2009-02-01
Advances in the development of semiconductor based, photon-counting x-ray detectors stimulate research in the domain of energy-resolving pre-clinical and clinical computed tomography (CT). For counting detectors acquiring x-ray attenuation in at least three different energy windows, an extended basis component decomposition can be performed in which in addition to the conventional approach of Alvarez and Macovski a third basis component is introduced, e.g., a gadolinium based CT contrast material. After the decomposition of the measured projection data into the basis component projections, conventional filtered-backprojection reconstruction is performed to obtain the basis-component images. In recent work, this basis component decomposition was obtained by maximizing the likelihood-function of the measurements. This procedure is time consuming and often unstable for excessively noisy data or low intrinsic energy resolution of the detector. Therefore, alternative procedures are of interest. Here, we introduce a generalization of the idea of empirical dual-energy processing published by Stenner et al. to multi-energy, photon-counting CT raw data. Instead of working in the image-domain, we use prior spectral knowledge about the acquisition system (tube spectra, bin sensitivities) to parameterize the line-integrals of the basis component decomposition directly in the projection domain. We compare this empirical approach with the maximum-likelihood (ML) approach considering image noise and image bias (artifacts) and see that only moderate noise increase is to be expected for small bias in the empirical approach. Given the drastic reduction of pre-processing time, the empirical approach is considered a viable alternative to the ML approach.
Randomized central limit theorems: A unified theory.
Eliazar, Iddo; Klafter, Joseph
2010-08-01
The central limit theorems (CLTs) characterize the macroscopic statistical behavior of large ensembles of independent and identically distributed random variables. The CLTs assert that the universal probability laws governing ensembles' aggregate statistics are either Gaussian or Lévy, and that the universal probability laws governing ensembles' extreme statistics are Fréchet, Weibull, or Gumbel. The scaling schemes underlying the CLTs are deterministic-scaling all ensemble components by a common deterministic scale. However, there are "random environment" settings in which the underlying scaling schemes are stochastic-scaling the ensemble components by different random scales. Examples of such settings include Holtsmark's law for gravitational fields and the Stretched Exponential law for relaxation times. In this paper we establish a unified theory of randomized central limit theorems (RCLTs)-in which the deterministic CLT scaling schemes are replaced with stochastic scaling schemes-and present "randomized counterparts" to the classic CLTs. The RCLT scaling schemes are shown to be governed by Poisson processes with power-law statistics, and the RCLTs are shown to universally yield the Lévy, Fréchet, and Weibull probability laws.
Birth of a theorem a mathematical adventure
Villani, Cédric
2015-01-01
This man could plainly do for mathematics what Brian Cox has done for physics" (Sunday Times). What goes on inside the mind of a rock-star mathematician? Where does inspiration come from? With a storyteller's gift, Cedric Villani takes us on a mesmerising journey as he wrestles with a new theorem that will win him the most coveted prize in mathematics. Along the way he encounters obstacles and setbacks, losses of faith and even brushes with madness. His story is one of courage and partnership, doubt and anxiety, elation and despair. We discover how it feels to be obsessed by a theorem during your child's cello practise and throughout your dreams, why appreciating maths is a bit like watching an episode of Columbo, and how sometimes inspiration only comes from locking yourself away in a dark room to think. Blending science with history, biography with myth, Villani conjures up an inimitable cast of characters including the omnipresent Einstein, mad genius Kurt Godel, and Villani's personal hero, John Nash. Bir...
Risk Evaluation on UHV Power Transmission Construction Project Based on AHP and FCE Method
Huiru Zhao; Sen Guo
2014-01-01
Ultra high voltage (UHV) power transmission construction project is a high-tech power grid construction project which faces many risks and uncertainty. Identifying the risk of UHV power transmission construction project can help mitigate the risk loss and promote the smooth construction. The risk evaluation on “Zhejiang-Fuzhou” UHV power transmission construction project was performed based on analytic hierarchy process (AHP) and fuzzy comprehensive evaluation (FCE) method in this paper. Afte...
A note on Robinson-Ursescu and Lyusternik-Graves theorem
Czech Academy of Sciences Publication Activity Database
Cibulka, R.; Fabian, Marián
2013-01-01
Roč. 139, 1-2 (2013), s. 89- 101 ISSN 0025-5610 R&D Projects: GA ČR(CZ) GAP201/11/0345 Institutional research plan: CEZ:AV0Z10190503 Keywords : open mapping * restrictive metricregularity * graves theorem Subject RIV: BA - General Mathematics Impact factor: 1.984, year: 2013 http://link.springer.com/article/10.1007%2Fs10107-013-0662-z
Comparison theorems and strong oscillation in the half-linear discrete oscillation theory
Czech Academy of Sciences Publication Activity Database
Řehák, Pavel
2003-01-01
Roč. 33, č. 1 (2003), s. 333-352 ISSN 0035-7596 R&D Projects: GA ČR GA201/98/0677; GA ČR GA201/99/0295 Institutional research plan: CEZ:AV0Z1019905; CEZ:AV0Z1019905 Keywords : half-linear difference equation * comparison theorems * strong oscillation Subject RIV: BA - General Mathematics Impact factor: 0.187, year: 2003
On the Chern-Gauss-Bonnet theorem for the noncommutative 4-sphere
Arnlind, Joakim; Wilson, Mitsuru
2017-01-01
We construct a differential calculus over the noncommutative 4-sphere in the framework of pseudo-Riemannian calculi, and show that for every metric in a conformal class of perturbations of the round metric, there exists a unique metric and torsion-free connection. Furthermore, we find a localization of the projective module corresponding to the space of vector fields, which allows us to formulate a Chern-Gauss-Bonnet type theorem for the noncommutative 4-sphere.
International Nuclear Information System (INIS)
Guedouar, R.; Zarrad, B.
2010-01-01
For algebraic reconstruction techniques both forward and back projection operators are needed. The ability to perform accurate reconstruction relies fundamentally on the forward projection and back projection methods which are usually, the transpose of each other. Even though the mis-matched pairs may introduce additional errors during the iterative process, the usefulness of mis-matched projector/back projector pairs has been proved in image reconstruction. This work investigates the performance of matched and mis-matched reconstruction pairs using popular forward projectors and their transposes when used in reconstruction tasks with additive simultaneous iterative reconstruction techniques (ASIRT) in a parallel beam approach. Simulated noiseless phantoms are used to compare the performance of the investigated pairs in terms of the root mean squared errors (RMSE) which are calculated between reconstructed slices and the reference in different regions. Results show that mis-matched projection/back projection pairs can promise more accuracy of reconstructed images than matched ones. The forward projection operator performance seems independent of the choice of the back projection operator and vice versa.
Energy Technology Data Exchange (ETDEWEB)
Guedouar, R., E-mail: raja_guedouar@yahoo.f [Higher School of Health Sciences and Techniques of Monastir, Av. Avicenne, 5060 Monastir, B.P. 128 (Tunisia); Zarrad, B., E-mail: boubakerzarrad@yahoo.f [Higher School of Health Sciences and Techniques of Monastir, Av. Avicenne, 5060 Monastir, B.P. 128 (Tunisia)
2010-07-21
For algebraic reconstruction techniques both forward and back projection operators are needed. The ability to perform accurate reconstruction relies fundamentally on the forward projection and back projection methods which are usually, the transpose of each other. Even though the mis-matched pairs may introduce additional errors during the iterative process, the usefulness of mis-matched projector/back projector pairs has been proved in image reconstruction. This work investigates the performance of matched and mis-matched reconstruction pairs using popular forward projectors and their transposes when used in reconstruction tasks with additive simultaneous iterative reconstruction techniques (ASIRT) in a parallel beam approach. Simulated noiseless phantoms are used to compare the performance of the investigated pairs in terms of the root mean squared errors (RMSE) which are calculated between reconstructed slices and the reference in different regions. Results show that mis-matched projection/back projection pairs can promise more accuracy of reconstructed images than matched ones. The forward projection operator performance seems independent of the choice of the back projection operator and vice versa.
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 ...
METHOD FOR SELECTION OF PROJECT MANAGEMENT APPROACH BASED ON FUZZY CONCEPTS
Directory of Open Access Journals (Sweden)
Igor V. KONONENKO
2017-03-01
Full Text Available Literature analysis of works that devoted to research of the selection a project management approach and development of effective methods for this problem solution is given. Mathematical model and method for selection of project management approach with fuzzy concepts of applicability of existing approaches are proposed. The selection is made of such approaches as the PMBOK Guide, the ISO21500 standard, the PRINCE2 methodology, the SWEBOK Guide, agile methodologies Scrum, XP, and Kanban. The number of project parameters which have a great impact on the result of the selection and measure of their impact is determined. Project parameters relate to information about the project, team, communication, critical project risks. They include the number of people involved in the project, the customer's experience with this project team, the project team's experience in this field, the project team's understanding of requirements, adapting ability, initiative, and others. The suggested method is considered on the example of its application for selection a project management approach to software development project.
Project scheduling method with time using MRP system – A case study: Construction project in Libya
Directory of Open Access Journals (Sweden)
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.
Sparse Pseudo Spectral Projection Methods with Directional Adaptation for Uncertainty Quantification
Winokur, J.; Kim, D.; Bisetti, Fabrizio; Le Maî tre, O. P.; Knio, Omar
2015-01-01
We investigate two methods to build a polynomial approximation of a model output depending on some parameters. The two approaches are based on pseudo-spectral projection (PSP) methods on adaptively constructed sparse grids, and aim at providing a
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
Variational, projection methods and Pade approximants in scattering theory
International Nuclear Information System (INIS)
Turchetti, G.
1980-12-01
Several aspects on the scattering theory are discussed in a perturbative scheme. The Pade approximant method plays an important role in such a scheme. Solitons solutions are also discussed in this same scheme. (L.C.) [pt
Neutron method for NDA in the Sapphire Project
International Nuclear Information System (INIS)
Lewis, K.D.
1995-01-01
The implementation of Project Sapphire, the top-secret mission to the Republic of Kazakhstan to recover weapons-grade nuclear materials, consisted of four major elements: (1) repacking of fissile material from Kazakh containers into suitable U.S. containers; (2) nondestructive analyses (NDA) to quantify the 235 U content of each container for nuclear criticality safety and compliance purposes; (3) packaging of the fissile material containers into 6M/2R drums, which are internationally approved for shipping fissile material; and (4) shipping or transport of the recovered fissile material to the United States. This paper discusses the development and application of a passive neutron counting technique used in the NDA phase of the Sapphire operations to analyze uranium/beryllium (U/Be) alloys and compounds for 235 U content
A neutron method for NDA analysis in the SAPPHIRE Project
International Nuclear Information System (INIS)
Lewis, K.D.
1995-01-01
The implementation of Project SAPPHIRE, the top secret mission to the Republic of Kazakhstan to recover weapons grade nuclear materials, consisted of four major elements: (1) the re-packing of fissile material from Kazakh containers into suitable US containers; (2) nondestructive analyses (NDA) to quantify the U-235 content of each container for Nuclear Criticality Safety and compliance purposes; (3) the packaging of the fissile material containers into 6M/2R drums, which are internationally approved for shipping fissile material; and (4) the shipping or transport of the recovered fissile material to the United States. This paper discusses the development and application of a passive neutron counting technique used in the NDA phase of SAPPHIRE operations to analyze uranium/beryllium (U/Be) alloys and compounds for U-235 content
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…
Projected Gauss-Seidel subspace minimization method for interactive rigid body dynamics
DEFF Research Database (Denmark)
Silcowitz-Hansen, Morten; Abel, Sarah Maria Niebe; Erleben, Kenny
2010-01-01
artifacts such as viscous or damped contact response. In this paper, we present a new approach to contact force determination. We formulate the contact force problem as a nonlinear complementarity problem, and discretize the problem to derive the Projected Gauss–Seidel method. We combine the Projected Gauss......–Seidel method with a subspace minimization method. Our new method shows improved qualities and superior convergence properties for specific configurations....
Dose fractionation theorem in 3-D reconstruction (tomography)
International Nuclear Information System (INIS)
Glaeser, R.M.
1997-01-01
It is commonly assumed that the large number of projections for single-axis tomography precludes its application to most beam-labile specimens. However, Hegerl and Hoppe have pointed out that the total dose required to achieve statistical significance for each voxel of a computed 3-D reconstruction is the same as that required to obtain a single 2-D image of that isolated voxel, at the same level of statistical significance. Thus a statistically significant 3-D image can be computed from statistically insignificant projections, as along as the total dosage that is distributed among these projections is high enough that it would have resulted in a statistically significant projection, if applied to only one image. We have tested this critical theorem by simulating the tomographic reconstruction of a realistic 3-D model created from an electron micrograph. The simulations verify the basic conclusions of high absorption, signal-dependent noise, varying specimen contrast and missing angular range. Furthermore, the simulations demonstrate that individual projections in the series of fractionated-dose images can be aligned by cross-correlation because they contain significant information derived from the summation of features from different depths in the structure. This latter information is generally not useful for structural interpretation prior to 3-D reconstruction, owing to the complexity of most specimens investigated by single-axis tomography. These results, in combination with dose estimates for imaging single voxels and measurements of radiation damage in the electron microscope, demonstrate that it is feasible to use single-axis tomography with soft X-ray microscopy of frozen-hydrated specimens
Dose fractionation theorem in 3-D reconstruction (tomography)
Energy Technology Data Exchange (ETDEWEB)
Glaeser, R.M. [Lawrence Berkeley National Lab., CA (United States)
1997-02-01
It is commonly assumed that the large number of projections for single-axis tomography precludes its application to most beam-labile specimens. However, Hegerl and Hoppe have pointed out that the total dose required to achieve statistical significance for each voxel of a computed 3-D reconstruction is the same as that required to obtain a single 2-D image of that isolated voxel, at the same level of statistical significance. Thus a statistically significant 3-D image can be computed from statistically insignificant projections, as along as the total dosage that is distributed among these projections is high enough that it would have resulted in a statistically significant projection, if applied to only one image. We have tested this critical theorem by simulating the tomographic reconstruction of a realistic 3-D model created from an electron micrograph. The simulations verify the basic conclusions of high absorption, signal-dependent noise, varying specimen contrast and missing angular range. Furthermore, the simulations demonstrate that individual projections in the series of fractionated-dose images can be aligned by cross-correlation because they contain significant information derived from the summation of features from different depths in the structure. This latter information is generally not useful for structural interpretation prior to 3-D reconstruction, owing to the complexity of most specimens investigated by single-axis tomography. These results, in combination with dose estimates for imaging single voxels and measurements of radiation damage in the electron microscope, demonstrate that it is feasible to use single-axis tomography with soft X-ray microscopy of frozen-hydrated specimens.
Work fluctuation theorems and free energy from kinetic theory
Brey, J. Javier; Ruiz-Montero, M. J.; Domínguez, Álvaro
2018-01-01
The formulation of the first and second principles of thermodynamics for a particle in contact with a heat bath and submitted to an external force is analyzed, by means of the Boltzmann-Lorentz kinetic equation. The possible definitions of the thermodynamic quantities are discussed in the light of the H theorem verified by the distribution of the particle. The work fluctuation relations formulated by Bochkov and Kuzovlev, and by Jarzynski, respectively, are derived from the kinetic equation. In addition, particle simulations using both the direct simulation Monte Carlo method and molecular dynamics, are used to investigate the practical accuracy of the results. Work distributions are also measured, and they turn out to be rather complex. On the other hand, they seem to depend very little, if any, on the interaction potential between the intruder and the bath.
Formal Analysis of Soft Errors using Theorem Proving
Directory of Open Access Journals (Sweden)
Sofiène Tahar
2013-07-01
Full Text Available Modeling and analysis of soft errors in electronic circuits has traditionally been done using computer simulations. Computer simulations cannot guarantee correctness of analysis because they utilize approximate real number representations and pseudo random numbers in the analysis and thus are not well suited for analyzing safety-critical applications. In this paper, we present a higher-order logic theorem proving based method for modeling and analysis of soft errors in electronic circuits. Our developed infrastructure includes formalized continuous random variable pairs, their Cumulative Distribution Function (CDF properties and independent standard uniform and Gaussian random variables. We illustrate the usefulness of our approach by modeling and analyzing soft errors in commonly used dynamic random access memory sense amplifier circuits.
Gleason-kahane-Żelazko theorem for spectrally bounded algebra
Directory of Open Access Journals (Sweden)
S. H. Kulkarni
2005-01-01
Full Text Available We prove by elementary methods the following generalization of a theorem due to Gleason, Kahane, and Żelazko. Let A be a real algebra with unit 1 such that the spectrum of every element in A is bounded and let φ:A→ℂ be a linear map such that φ(1=1 and (φ(a2+(φ(b2≠0 for all a, b in A satisfying ab=ba and a2+b2 is invertible. Then φ(ab=φ(aφ(b for all a, b in A. Similar results are proved for real and complex algebras using Ransford's concept of generalized spectrum. With these ideas, a sufficient condition for a linear transformation to be multiplicative is established in terms of generalized spectrum.
A method for weighted projections to the positive definite cone
Valkonen, Tuomo
2014-01-01
© 2014 Taylor & Francis. We study the numerical solution of the problem (Formula presented.) , where (Formula presented.) is a symmetric square matrix, and (Formula presented.) is a linear operator, such that (Formula presented.) is invertible. With (Formula presented.) the desired fractional duality gap, and (Formula presented.) the condition number of (Formula presented.) , we prove (Formula presented.) iteration complexity for a simple primal-dual interior point method directly based on those for linear programs with semi-definite constraints. We do not, however, require the numerically expensive scalings inherent in these methods to force fast convergence. For low-dimensional problems (Formula presented.), our numerical experiments indicate excellent performance and only a very slowly growing dependence of the convergence rate on (Formula presented.). While our algorithm requires somewhat more iterations than existing interior point methods, the iterations are cheaper. This gives better computational times.
A method for weighted projections to the positive definite cone
Valkonen, Tuomo
2014-06-24
© 2014 Taylor & Francis. We study the numerical solution of the problem (Formula presented.) , where (Formula presented.) is a symmetric square matrix, and (Formula presented.) is a linear operator, such that (Formula presented.) is invertible. With (Formula presented.) the desired fractional duality gap, and (Formula presented.) the condition number of (Formula presented.) , we prove (Formula presented.) iteration complexity for a simple primal-dual interior point method directly based on those for linear programs with semi-definite constraints. We do not, however, require the numerically expensive scalings inherent in these methods to force fast convergence. For low-dimensional problems (Formula presented.), our numerical experiments indicate excellent performance and only a very slowly growing dependence of the convergence rate on (Formula presented.). While our algorithm requires somewhat more iterations than existing interior point methods, the iterations are cheaper. This gives better computational times.
The Bolmen tunnel project - evaluation of geophysical site investigation methods
International Nuclear Information System (INIS)
Stanfors, R.
1987-12-01
The report presents geophysical measurements along and adjacent to the tunnel and an evaluation of the ability of the various methods to permit prediction of rock mass parameters of significance to stability and water bearing ability. The evaluation shows that, using airborne electro-magnetic surveys, it was possible to indicate about 80% of alla the zones of weakness more than 50 m wide in the tunnel. Airborne magnetic surveys located about 90% of all dolerite dykes more than 10 m wide. Ground-level VLF and Slingram methods of electro-magnetic measurement indicated 75% and 85% respectively of all zones of weakness more than 50 m wide. Resistivity methods were successfully used to locate clay filled and water-bearing fracture zones. About 75% of the length of tunnel over which resistivity values below 500 ohm m were measured required shotcrete support and pre-grouting. (orig./DG)
Tangent stiffness matrices for projection methods in elasto-plasticity
International Nuclear Information System (INIS)
Gruttmann, F.; Stein, E.
1988-01-01
In classical elastoplasticity with v. Mises yield condition and associate flow rule it is necessary to integrate the plastic strain rate. The radial return integration algorithm is employed to calculate elastoplastic stresses. In the context of the finite element method, the formulation and numerical solution of nonlinear problems in continuum mechanics is based on the weak form of the momentum balance equation (principle of virtual work). The solution of the nonlinear equations is achieved by the Newton-Raphson method in which a sequence of linear problems is solved. If the linear problem is obtained by consistent linearization one gets a quadratic rate of convergence. (orig.) [de
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.
Leaning on Socrates to Derive the Pythagorean Theorem
Percy, Andrew; Carr, Alistair
2010-01-01
The one theorem just about every student remembers from school is the theorem about the side lengths of a right angled triangle which Euclid attributed to Pythagoras when writing Proposition 47 of "The Elements". Usually first met in middle school, the student will be continually exposed throughout their mathematical education to the…
COMPARISON THEOREM OF BACKWARD DOUBLY STOCHASTIC DIFFERENTIAL EQUATIONS
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
This paper is devoted to deriving a comparison theorem of solutions to backward doubly stochastic differential equations driven by Brownian motion and backward It-Kunita integral. By the application of this theorem, we give an existence result of the solutions to these equations with continuous coefficients.
The Boundary Crossing Theorem and the Maximal Stability Interval
Directory of Open Access Journals (Sweden)
Jorge-Antonio López-Renteria
2011-01-01
useful tools in the study of the stability of family of polynomials. Although both of these theorem seem intuitively obvious, they can be used for proving important results. In this paper, we give generalizations of these two theorems and we apply such generalizations for finding the maximal stability interval.
K S Krishnan's 1948 Perception of the Sampling Theorem
Indian Academy of Sciences (India)
K S Krishnan's 1948 Perception of the. Sampling Theorem. Raiiah Simon is a. Professor at the Institute of Mathematical. Sciences, Chennai. His primary interests are in classical and quantum optics, geometric phases, group theoretical techniques and quantum information science. Keywords. Sompling theorem, K S ...
On Frobenius, Mazur, and Gelfand-Mazur theorems on division ...
African Journals Online (AJOL)
... R of real numbers, the field C of complex numbers, or the non-commutative algebra Q of quaternions. Gelfand [15] proved that every normed division algebra over the field C is isomorphic to C. He named this theorem, which is fundamental for the development of the theory of Banach Algebras, the Gelfand-Mazur theorem.
An extension of Brosowski-Meinardus theorem on invariant approximation
International Nuclear Information System (INIS)
Liaqat Ali Khan; Abdul Rahim Khan.
1991-07-01
We obtain a generalization of a fixed point theorem of Dotson for non-expansive mappings on star-shaped sets and then use it to prove a unified Brosowski-Meinardus theorem on invariant approximation in the setting of p-normed linear spaces. (author). 13 refs
A general conservative extension theorem in process algebras with inequalities
d' Argenio, P.R.; Verhoef, Chris
1997-01-01
We prove a general conservative extension theorem for transition system based process theories with easy-to-check and reasonable conditions. The core of this result is another general theorem which gives sufficient conditions for a system of operational rules and an extension of it in order to
A power counting theorem for Feynman integrals on the lattice
International Nuclear Information System (INIS)
Reisz, T.
1988-01-01
A convergence theorem is proved, which states sufficient conditions for the existence of the continuum limit for a wide class of Feynman integrals on a space-time lattice. A new kind of a UV-divergence degree is introduced, which allows the formulation of the theorem in terms of power counting conditions. (orig.)
A Hohenberg-Kohn theorem for non-local potentials
International Nuclear Information System (INIS)
Meron, E.; Katriel, J.
1977-01-01
It is shown that within any class of commuting one-body potentials a Hohenberg-Kohn type theorem is satisfied with respect to an appropriately defined density. The Hohenberg-Kohn theorem for local potentials follows as a special case. (Auth.)
A note on the homomorphism theorem for hemirings
Directory of Open Access Journals (Sweden)
D. M. Olson
1978-01-01
Full Text Available The fundamental homomorphism theorem for rings is not generally applicable in hemiring theory. In this paper, we show that for the class of N-homomorphism of hemirings the fundamental theorem is valid. In addition, the concept of N-homomorphism is used to prove that every hereditarily semisubtractive hemiring is of type (K.
On the Riesz representation theorem and integral operators ...
African Journals Online (AJOL)
We present a Riesz representation theorem in the setting of extended integration theory as introduced in [6]. The result is used to obtain boundedness theorems for integral operators in the more general setting of spaces of vector valued extended integrable functions. Keywords: Vector integral, integral operators, operator ...
Automated Theorem Proving in High-Quality Software Design
Schumann, Johann; Swanson, Keith (Technical Monitor)
2001-01-01
The amount and complexity of software developed during the last few years has increased tremendously. In particular, programs are being used more and more in embedded systems (from car-brakes to plant-control). Many of these applications are safety-relevant, i.e. a malfunction of hardware or software can cause severe damage or loss. Tremendous risks are typically present in the area of aviation, (nuclear) power plants or (chemical) plant control. Here, even small problems can lead to thousands of casualties and huge financial losses. Large financial risks also exist when computer systems are used in the area of telecommunication (telephone, electronic commerce) or space exploration. Computer applications in this area are not only subject to safety considerations, but also security issues are important. All these systems must be designed and developed to guarantee high quality with respect to safety and security. Even in an industrial setting which is (or at least should be) aware of the high requirements in Software Engineering, many incidents occur. For example, the Warshaw Airbus crash, was caused by an incomplete requirements specification. Uncontrolled reuse of an Ariane 4 software module was the reason for the Ariane 5 disaster. Some recent incidents in the telecommunication area, like illegal "cloning" of smart-cards of D2GSM handies, or the extraction of (secret) passwords from German T-online users show that also in this area serious flaws can happen. Due to the inherent complexity of computer systems, most authors claim that only a rigorous application of formal methods in all stages of the software life cycle can ensure high quality of the software and lead to real safe and secure systems. In this paper, we will have a look, in how far automated theorem proving can contribute to a more widespread application of formal methods and their tools, and what automated theorem provers (ATPs) must provide in order to be useful.
Application of FMEA method in railway signalling projects
Directory of Open Access Journals (Sweden)
Szmel Dariusz
2017-06-01
Full Text Available The article presents the FMEA method application, which is relevant in verification of design of two separated railway signalling systems. The efficiency of the method at the stage of the design was discussed. The method was identified as an important element of safety management process and as safety analysis method, which is included in the Safety Case and is applied for the sake of safety arguments and its assessment. Safety process management comprises several phases and appropriate actions, linked with each other in the way to create safety life cycle consistent with system life cycle. The safety case is a set of documents demonstrating that the product is compliant with defined safety requirements including analysis that indicates the correctness of the design and the correct reaction of the system to the failures, with appropriate and requested fail-safe reaction. It is necessary that railway signalling system should fulfil SIL4 requirement and remain safe in case of occurrence any kind of single failure of the equipment considered as possible.
A New Group-Formation Method for Student Projects
Borges, Jose; Dias, Teresa Galvao; Cunha, Joao Falcao E.
2009-01-01
In BSc/MSc engineering programmes at Faculty of Engineering of the University of Porto (FEUP), the need to provide students with teamwork experiences close to a real world environment was identified as an important issue. A new group-formation method that aims to provide an enriching teamwork experience is proposed. Students are asked to answer a…
Calculation Method for the Projection of Future Spent Nuclear Fuel Discharges
International Nuclear Information System (INIS)
B. McLeod
2002-01-01
This report describes the calculation method developed for the projection of future utility spent nuclear fuel (SNF) discharges in regard to their timing, quantity, burnup, and initial enrichment. This projection method complements the utility-supplied RW-859 data on historic discharges and short-term projections of SNF discharges by providing long-term projections that complete the total life cycle of discharges for each of the current U.S. nuclear power reactors. The method was initially developed in mid-1999 to update the SNF discharge projection associated with the 1995 RW-859 utility survey (CRWMS M and O 1996). and was further developed as described in Rev. 00 of this report (CRWMS M and O 2001a). Primary input to the projection of SNF discharges is the utility projection of the next five discharges from each nuclear unit, which is provided via the revised final version of the Energy Information Administration (EIA) 1998 RW-859 utility survey (EIA 2000a). The projection calculation method is implemented via a set of Excel 97 spreadsheets. These calculations provide the interface between receipt of the utility five-discharge projections that are provided in the RW-859 survey, and the delivery of projected life-cycle SNF discharge quantities and characteristics in the format requisite for performing logistics analysis to support design of the Civilian Radioactive Waste Management System (CRWMS). Calculation method improvements described in this report include the addition of a reactor-specific maximum enrichment-based discharge burnup limit. This limit is the consequence of the enrichment limit, currently 5 percent. which is imposed as a Nuclear Regulatory Commission (NRC) license condition on nuclear fuel fabrication plants. In addition, the calculation method now includes the capability for projecting future nuclear plant power upratings, consistent with many such recent plant uprates and the prospect of additional future uprates. Finally. this report
Discounted Cash Flow and Modern Asset Pricing Methods - Project Selection and Policy Implications
Energy Technology Data Exchange (ETDEWEB)
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
International Nuclear Information System (INIS)
Emhjellen, Magne; Alaouze, Chris M.
2002-01-01
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
Energy Technology Data Exchange (ETDEWEB)
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)
Study on operation I and C DCS test method of EPR project
International Nuclear Information System (INIS)
Meng Ying; Lv Zhihong; Huang Xinnian; Fan Haiying; Li Zhuojia; Xiao Shushu
2014-01-01
Through summarization and optimization of the method for operation I and C DCS test of the European pressurized reactor project, the conclusions play a guiding role on the operation I and C DCS test of the domestic advanced nuclear power plant. The study of the method focuses on the test platform, the test process and the optimization of method of operation I and C DCS test with the practical experience. The reasonable and reliable test method for operation I and C DCS test of the European pressurized reactor project is worthy of the reference and the development in the project of the domestic advanced nuclear power plant. (authors)
International Nuclear Information System (INIS)
Emhjellen, Magne; Alaouze, Chris M.
2003-01-01
We examine the differences in the net present values (NPVs) of North Sea oil projects obtained using the weighted average cost of capital and a modern asset pricing (MAP) method which involves the separate discounting of project cashflow components. NPV differences of more than $10 million were found for some oil projects. Thus, the choice of valuation method will affect the development decisions of oil companies and could influence tax policy. 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
Bell's "Theorem": loopholes vs. conceptual flaws
Kracklauer, A. F.
2017-12-01
An historical overview and detailed explication of a critical analysis of what has become known as Bell's Theorem to the effect that, it should be impossible to extend Quantum Theory with the addition of local, real variables so as to obtain a version free of the ambiguous and preternatural features of the currently accepted interpretations is presented. The central point on which this critical analysis, due originally to Edwin Jaynes, is that Bell incorrectly applied probabilistic formulas involving conditional probabilities. In addition, mathematical technicalities that have complicated the understanding of the logical or mathematical setting in which current theory and experimentation are embedded, are discussed. Finally, some historical speculations on the sociological environment, in particular misleading aspects, in which recent generations of physicists lived and worked are mentioned.
A Theorem on Grid Access Control
Institute of Scientific and Technical Information of China (English)
XU ZhiWei(徐志伟); BU GuanYing(卜冠英)
2003-01-01
The current grid security research is mainly focused on the authentication of grid systems. A problem to be solved by grid systems is to ensure consistent access control. This problem is complicated because the hosts in a grid computing environment usually span multiple autonomous administrative domains. This paper presents a grid access control model, based on asynchronous automata theory and the classic Bell-LaPadula model. This model is useful to formally study the confidentiality and integrity problems in a grid computing environment. A theorem is proved, which gives the necessary and sufficient conditions to a grid to maintain confidentiality.These conditions are the formalized descriptions of local (node) relations or relationship between grid subjects and node subjects.
Theorem Proving in Intel Hardware Design
O'Leary, John
2009-01-01
For the past decade, a framework combining model checking (symbolic trajectory evaluation) and higher-order logic theorem proving has been in production use at Intel. Our tools and methodology have been used to formally verify execution cluster functionality (including floating-point operations) for a number of Intel products, including the Pentium(Registered TradeMark)4 and Core(TradeMark)i7 processors. Hardware verification in 2009 is much more challenging than it was in 1999 - today s CPU chip designs contain many processor cores and significant firmware content. This talk will attempt to distill the lessons learned over the past ten years, discuss how they apply to today s problems, outline some future directions.
Virial Theorem in Nonlocal Newtonian Gravity
Directory of Open Access Journals (Sweden)
Bahram Mashhoon
2016-05-01
Full Text Available Nonlocal gravity is the recent classical nonlocal generalization of Einstein’s theory of gravitation in which the past history of the gravitational field is taken into account. In this theory, nonlocality appears to simulate dark matter. The virial theorem for the Newtonian regime of nonlocal gravity theory is derived and its consequences for “isolated” astronomical systems in virial equilibrium at the present epoch are investigated. In particular, for a sufficiently isolated nearby galaxy in virial equilibrium, the galaxy’s baryonic diameter D 0 —namely, the diameter of the smallest sphere that completely surrounds the baryonic system at the present time—is predicted to be larger than the effective dark matter fraction f D M times a universal length that is the basic nonlocality length scale λ 0 ≈ 3 ± 2 kpc.
On a curvature-statistics theorem
International Nuclear Information System (INIS)
Calixto, M; Aldaya, V
2008-01-01
The spin-statistics theorem in quantum field theory relates the spin of a particle to the statistics obeyed by that particle. Here we investigate an interesting correspondence or connection between curvature (κ = ±1) and quantum statistics (Fermi-Dirac and Bose-Einstein, respectively). The interrelation between both concepts is established through vacuum coherent configurations of zero modes in quantum field theory on the compact O(3) and noncompact O(2; 1) (spatial) isometry subgroups of de Sitter and Anti de Sitter spaces, respectively. The high frequency limit, is retrieved as a (zero curvature) group contraction to the Newton-Hooke (harmonic oscillator) group. We also make some comments on the physical significance of the vacuum energy density and the cosmological constant problem.
On a curvature-statistics theorem
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Calixto, M [Departamento de Matematica Aplicada y Estadistica, Universidad Politecnica de Cartagena, Paseo Alfonso XIII 56, 30203 Cartagena (Spain); Aldaya, V [Instituto de Astrofisica de Andalucia, Apartado Postal 3004, 18080 Granada (Spain)], E-mail: Manuel.Calixto@upct.es
2008-08-15
The spin-statistics theorem in quantum field theory relates the spin of a particle to the statistics obeyed by that particle. Here we investigate an interesting correspondence or connection between curvature ({kappa} = {+-}1) and quantum statistics (Fermi-Dirac and Bose-Einstein, respectively). The interrelation between both concepts is established through vacuum coherent configurations of zero modes in quantum field theory on the compact O(3) and noncompact O(2; 1) (spatial) isometry subgroups of de Sitter and Anti de Sitter spaces, respectively. The high frequency limit, is retrieved as a (zero curvature) group contraction to the Newton-Hooke (harmonic oscillator) group. We also make some comments on the physical significance of the vacuum energy density and the cosmological constant problem.