The Quadratic Graver Cone, Quadratic Integer Minimization, and Extensions
Lee, Jon; Romanchuk, Lyubov; Weismantel, Robert
2010-01-01
We consider the nonlinear integer programming problem of minimizing a quadratic function over the integer points in variable dimension satisfying a system of linear inequalities. We show that when the Graver basis of the matrix defining the system is given, and the quadratic function lies in a suitable {\\em dual Graver cone}, the problem can be solved in polynomial time. We discuss the relation between this cone and the cone of positive semidefinite matrices, and show that none contains the other. So we can minimize in polynomial time some non-convex and some (including all separable) convex quadrics. We conclude by extending our results to efficient integer minimization of multivariate polynomial functions of arbitrary degree lying in suitable cones.
Configuration of singular optical cones in gyrotropic crystals with dichroism
Energy Technology Data Exchange (ETDEWEB)
Merkulov, V. S., E-mail: merkul@physics.by [National Academy of Sciences of Belarus, Material Science Applied Research Center (Belarus)
2015-02-15
Optical conic singularities in crystals with linear dichroism and natural optical activity at the point of intersection of dispersion curves for the main refractive indices are considered. The possible existence of singularities like a nodal point, tangency point, triple point, and cusps of the first and second order is demonstrated. Forty-nine different types of irreducible fourth-order optical cones obtained by sequential bifurcations of eight main singular cones are established. The classification is based on the concept of roughness of systems depending on parameters.
Directory of Open Access Journals (Sweden)
Borbon Martin de
2017-02-01
Full Text Available The goal of this article is to provide a construction and classification, in the case of two complex dimensions, of the possible tangent cones at points of limit spaces of non-collapsed sequences of Kähler-Einstein metrics with cone singularities. The proofs and constructions are completely elementary, nevertheless they have an intrinsic beauty. In a few words; tangent cones correspond to spherical metrics with cone singularities in the projective line by means of the Kähler quotient construction with respect to the S1-action generated by the Reeb vector field, except in the irregular case ℂβ₁×ℂβ₂ with β₂/ β₁ ∉ Q.
Space-time singularities and the Kaehler cone
Energy Technology Data Exchange (ETDEWEB)
Jaerv, L.; Mayer, C.; Mohaupt, T.; Saueressig, F. [Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universitaet Jena, Max-Wien-Platz 1, 07743 Jena (Germany)
2004-06-01
We review recent results on the interplay between the five-dimensional space-time and the internal manifold in Calabi-Yau compactifications of M-theory. Black string, black hole and domain wall solutions as well as Kasner type cosmologies cannot develop a naked singularity as long as the moduli take values inside the Kaehler cone. (Abstract Copyright [2004], Wiley Periodicals, Inc.)
Presolving and regularization in mixed-integer second-order cone optimization
DEFF Research Database (Denmark)
Friberg, Henrik Alsing
Mixed-integer second-order cone optimization is a powerful mathematical framework capable of representing both logical conditions and nonlinear relationships in mathematical models of industrial optimization problems. What is more, solution methods are already part of many major commercial solvers...... both continuous and mixed-integer conic optimization in general, is discovered and treated. This part of the thesis continues the studies of facial reduction preceding the work of Borwein and Wolkowicz [17] in 1981, when the first algorithmic cure for these kinds of reliability issues were formulated....... An important distinction to make between continuous and mixed-integer optimization, however, is that the reliability issues occurring in mixed-integer optimization cannot be blamed on the practitioner’s formulation of the problem. Specifically, as shown, the causes for these issues may well lie within...
Singularities, boundary conditions and gauge link in the light cone gauge
Gao, Jian-Hua
2013-01-01
In this work, we first review the issues on the singularities and the boundary conditions in light cone gauge and how to regularize them properly. Then we will further review how these singularities and the boundary conditions can result in the gauge link at the infinity in the light cone direction in the Drell-Yan process. Except for reviewing, we also have verified that the gauge link at the light cone infinity has no dependence on the path not only for the Abelian field but also for non-Abelian gauge field.
Light-Cone Singularities and Transverse-Momentum-Dependent Factorization at Twist-3
Chen, A P
2016-01-01
We study transverse-momentum-dependent factorization at twist-3 for Drell-Yan processes. The factorization can be derived straightforwardly at leading order of $\\alpha_s$. But at this order we find that light-cone singularities already exist and effects of soft gluons are not correctly factorized. We regularize the singularities with gauge links off the light-cone and introduce a soft factor to factorize the effects of soft gluons. Interestingly, the soft factor must be included in the definition of subtracted TMD parton distributions to correctly factorize the effects of soft gluons. We derive the Collins-Soper equation for one of twist-3 TMD parton distributions. The equation can be useful for resummation of large logarithms terms appearing in the corresponding structure function in collinear factorization. However, the derived equation is nonhomogeneous. This will make the resummation complicated.
Energy Technology Data Exchange (ETDEWEB)
Doolittle, R. [ONR, Arlington, VA (United States)
1994-11-15
The title integer anatomy is intended to convey the idea of a systematic method for displaying the prime decomposition of the integers. Just as the biological study of anatomy does not teach us all things about behavior of species neither would we expect to learn everything about the number theory from a study of its anatomy. But, some number-theoretic theorems are illustrated by inspection of integer anatomy, which tend to validate the underlying structure and the form as developed and displayed in this treatise. The first statement to be made in this development is: the way structure of the natural numbers is displayed depends upon the allowed operations.
Conforti, Michele; Zambelli, Giacomo
2014-01-01
This book is an elegant and rigorous presentation of integer programming, exposing the subject’s mathematical depth and broad applicability. Special attention is given to the theory behind the algorithms used in state-of-the-art solvers. An abundance of concrete examples and exercises of both theoretical and real-world interest explore the wide range of applications and ramifications of the theory. Each chapter is accompanied by an expertly informed guide to the literature and special topics, rounding out the reader’s understanding and serving as a gateway to deeper study. Key topics include: formulations polyhedral theory cutting planes decomposition enumeration semidefinite relaxations Written by renowned experts in integer programming and combinatorial optimization, Integer Programming is destined to become an essential text in the field.
Bounds for the smallest singular value of a class of integer matrices%一类整数矩阵的最小奇异值的界
Institute of Scientific and Technical Information of China (English)
程开敏; 陆婧雅
2012-01-01
令正整数集S={x1,x2,…,xn}(n≥1,xi∈Z+)为因子封闭集,即对任意的xi∈S,它的所有正因子都包含在S中,S上的幂GCD矩阵及倒数幂GCD矩阵分别定义为(Se):=((xi,xj)e)及(1/Se):=(1/(xi,xj)e).本文给出矩阵(Se)及(1/Se)的最小奇异值的上下界.%In this note, we give lower and upper bounds for the smallest singular value of power GCD matrices (Se):=((xi,xj)e) and reciprocal power GCD matrices (1/Se):=(1/(xi,xj)e) defined on factor closed set S={x1,x2,…,xn}.
Dirks, Michael K.
1984-01-01
The abacus method for instruction on addition, subtraction, and multiplication with integers is explained. How to represent the integers for each operation is detailed with words and illustrations. (MNS)
Pong, Wai Yan
2007-01-01
We begin by answering the question, "Which natural numbers are sums of consecutive integers?" We then go on to explore the set of lengths (numbers of summands) in the decompositions of an integer as such sums.
Landman, Bruce
2014-01-01
""Integers"" is a refereed online journal devoted to research in the area of combinatorial number theory. It publishes original research articles in combinatorics and number theory. This work presents all papers of the 2013 volume in book form.
Directory of Open Access Journals (Sweden)
Hans Schonemann
1996-12-01
Full Text Available Some algorithms for singularity theory and algebraic geometry The use of Grobner basis computations for treating systems of polynomial equations has become an important tool in many areas. This paper introduces of the concept of standard bases (a generalization of Grobner bases and the application to some problems from algebraic geometry. The examples are presented as SINGULAR commands. A general introduction to Grobner bases can be found in the textbook [CLO], an introduction to syzygies in [E] and [St1]. SINGULAR is a computer algebra system for computing information about singularities, for use in algebraic geometry. The basic algorithms in SINGULAR are several variants of a general standard basis algorithm for general monomial orderings (see [GG]. This includes wellorderings (Buchberger algorithm ([B1], [B2] and tangent cone orderings (Mora algorithm ([M1], [MPT] as special cases: It is able to work with non-homogeneous and homogeneous input and also to compute in the localization of the polynomial ring in 0. Recent versions include algorithms to factorize polynomials and a factorizing Grobner basis algorithm. For a complete description of SINGULAR see [Si].
Integer and combinatorial optimization
Nemhauser, George L
1999-01-01
Rave reviews for INTEGER AND COMBINATORIAL OPTIMIZATION ""This book provides an excellent introduction and survey of traditional fields of combinatorial optimization . . . It is indeed one of the best and most complete texts on combinatorial optimization . . . available. [And] with more than 700 entries, [it] has quite an exhaustive reference list.""-Optima ""A unifying approach to optimization problems is to formulate them like linear programming problems, while restricting some or all of the variables to the integers. This book is an encyclopedic resource for such f
Okulov, A Yu
2009-01-01
The interaction of the two counter-propagating ultrashort laser pulses of a picosecond duration with a singular wavefronts in the thin slice of the underdense plasma is considered. It is shown that ion-acoustic wave excited via Brillouin three-wave resonance by corkscrew interference pattern acts as a rotating solenoid generating kilogauss quasi-static magnetic fields. The orbital angular momentum carried by light is imprinted into an ion-acoustic liquid. The exact analytical configurations for an ion-acoustic wave current and magnetic field are given for a general class of a paraxial singular beams with an integer topological charges. The range of experimentally accessible parameters is evaluated.
Energy Technology Data Exchange (ETDEWEB)
Meyers, C A; Schulz, A S
2009-01-07
The integer equal flow problem is an NP-hard network flow problem, in which all arcs in given sets R{sub 1}, ..., R{sub {ell}} must carry equal flow. We show this problem is effectively inapproximable, even if the cardinality of each set R{sub k} is two. When {ell} is fixed, it is solvable in polynomial time.
Veugen, P.J.M.
2010-01-01
When processing signals in the encrypted domain, homomorphic encryption can be used to enable linear operations on encrypted data. Integer division of encrypted data however requires an additional protocol with the server and will be relatively expensive. We present new solutions for dividing encryp
Extended gcd of quadratic integers
Miled, Abdelwaheb
2010-01-01
Computation of the extended gcd of two quadratic integers. The ring of integers considered is principal but could be euclidean or not euclidean ring. This method rely on principal ideal ring and reduction of binary quadratic forms.
CBLIB 2014: a benchmark library for conic mixed-integer and continuous optimization
DEFF Research Database (Denmark)
Friberg, Henrik Alsing
2016-01-01
The Conic Benchmark Library is an ongoing community-driven project aiming to challenge commercial and open source solvers on mainstream cone support. In this paper, 121 mixed-integer and continuous second-order cone problem instances have been selected from 11 categories as representative...
Singularity analysis: theory and further developments
Cheng, Qiuming
2015-04-01
Since the concept of singularity and local singularity analysis method (LSA) were originally proposed by the author for characterizing the nonlinear property of hydrothermal mineralization processes, the local singularity analysis technique has been successfully applied for identification of geochemical and geophysical anomalies related to various types of mineral deposits. It has also been shown that the singularity is the generic property of singular geo-processes which result in anomalous amounts of energy release or material accumulation within a narrow spatial-temporal interval. In the current paper we introduce several new developments about singularity analysis. First is a new concept of 'fractal density' which describes the singularity of complex phenomena of fractal nature. While the ordinary density possesses a unit of ratio of mass and volume (e.g. g/cm3, kg/m3) or ratio of energy over volume or time (e.g. J/cm3, w/L3, w/s), the fractal density has a unit of ratio of mass over fractal set or energy over fractal set (e.g. g/cmα, kg/mα, J/ mα, w/Lα, where α can be a non-integer). For the matter with fractal density (a non-integer α), the ordinary density of the phenomena (mass or energy) no longer exists and depicts singularity. We demonstrate that most of extreme geo-processes occurred in the earth crust originated from cascade earth dynamics (mental convection, plate tectonics, orogeny and weathering etc) may cause fractal density of mass accumulation or energy release. The examples to be used to demonstrate the concepts of fractal density and singularity are earthquakes, floods, volcanos, hurricanes, heat flow over oceanic ridge, hydrothermal mineralization in orogenic belt, and anomalies in regolith over mine caused by ore and toxic elements vertical migration. Other developments of singularity theory and methodologies including singular Kriging and singularity weights of evidence model for information integration will also be introduced.
Investigating Students’ Development of Learning Integer Concept and Integer Addition
Directory of Open Access Journals (Sweden)
Nenden Octavarulia Shanty
2016-09-01
Full Text Available This research aimed at investigating students’ development of learning integer concept and integer addition. The investigation was based on analyzing students’ works in solving the given mathematical problems in each instructional activity designed based on Realistic Mathematics Education (RME levels. Design research was chosen to achieve and to contribute in developing a local instruction theory for teaching and learning of integer concept and integer addition. In design research, the Hypothetical Learning Trajectory (HLT plays important role as a design and research instrument. It was designed in the phase of preliminary design and tested to three students of grade six OASIS International School, Ankara – Turkey. The result of the experiments showed that temperature in the thermometer context could stimulate students’ informal knowledge of integer concept. Furthermore, strategies and tools used by the students in comparing and relating two temperatures were gradually be developed into a more formal mathematics. The representation of line inside thermometer which then called the number line could bring the students to the last activity levels, namely rules for adding integer, and became the model for more formal reasoning. Based on these findings, it can be concluded that students’ learning integer concept and integer addition developed through RME levels.Keywords: integer concept, integer addition, Realistic Mathematics Education DOI: http://dx.doi.org/10.22342/jme.7.2.3538.57-72
Non-singular circulant graphs and digraphs
Lal, A K
2011-01-01
We give necessary and sufficient conditions for a few classes of circulant graphs/digraphs to be singular. We also give two generalizations of the above graphs/digraphs, namely $(r,s,t)$-digraphs for non-negative integers $r,s$ and $t$, and the digraph $C_n^{i,j,k,l}$ with certain restrictions. A necessary and sufficient condition for the digraphs $C_n^{i,j,k,l}$ to be singular is obtained. Some necessary conditions are given under which the $(r,s,t)$-digraphs are singular.
Elitzur, Shmuel; Rabinovici, Eliezer; Elitzur, Shmuel; Giveon, Amit; Rabinovici, Eliezer
2003-01-01
Big bang/crunch curvature singularities in exact CFT string backgrounds can be removed by turning on gauge fields. This is described within a family of {SL(2)xSU(2)xU(1)_x}/{U(1)xU(1)} quotient CFTs. Uncharged incoming wavefunctions from the ``whiskers'' of the extended universe can be fully reflected if and only if a big bang/crunch curvature singularity, from which they are scattered, exists. Extended BTZ-like singularities remain as long as U(1)_x is compact.
Belinski, V
2009-01-01
The talk at international conference in honor of Ya. B. Zeldovich 95th Anniversary, Minsk, Belarus, April 2009. The talk represents a review of the old results and contemporary development on the problem of cosmological singularity.
Integer-valued trawl processes
DEFF Research Database (Denmark)
Barndorff-Nielsen, Ole E.; Lunde, Asger; Shephard, Neil;
2014-01-01
This paper introduces a new continuous-time framework for modelling serially correlated count and integer-valued data. The key component in our new model is the class of integer-valued trawl processes, which are serially correlated, stationary, infinitely divisible processes. We analyse the proba......This paper introduces a new continuous-time framework for modelling serially correlated count and integer-valued data. The key component in our new model is the class of integer-valued trawl processes, which are serially correlated, stationary, infinitely divisible processes. We analyse...
Integer roots of quadratic and cubic polynomials with integer coefficients
Zelator, Konstantine
2011-01-01
The subject matter of this work is quadratic and cubic polynomial functions with integer coefficients;and all of whose roots are integers. The material of this work is directed primarily at educators,students,and teachers of mathematics,grades K12 to K20.The results of this work are expressed in Theorems3,4,and5. Of these theorems, Theorem3, is the one that most likely, the general reader of this article will have some familiarity with.In Theorem3, precise coefficient conditions are given;in order that a quadratic trinomial(with integer) have two integer roots or zeros.On the other hand, Theorems4 and5 are largely unfamiliar territory. In Theorem4, precise coefficient conditions are stated; for a monic cubic polynomial to have a double(i.e.of multiplicity 2) integer root, and a single integer root(i.e.of multiplicity 1).The entire family of such cubics can be described in terms of four groups or subfamilies; each such group being a two-integer parameter subfamily. In Theorem5, a one-integer parameter family o...
Integer and Half-Integer Quantization Conditions in Quantum Mechanics
Institute of Scientific and Technical Information of China (English)
DUAN Yi-Shi; JIA Duo-Jie
2001-01-01
The integer and half-integer quantization conditions are found in quantum mechanics based on the topological structure of symmetry group of the singlet and spinor wavefunction. The internal symmetry of the physical system is shown to be sufficient to determine the topological structure in quantum mechanics without taking int account the dynamical details about the interaction.
Geodesics in the space of K\\"ahler cone metrics
Calama, Simone
2012-01-01
In this paper, we prove the existence and uniqueness of the weak cone geodesics in the space of K\\"ahler cone metrics by solving the singular, homogeneous complex Monge-Amp\\`{e}re equation. As an application, we prove the metric space structure of the appropriate subspace of the space of K\\"ahler cone metrics.
Integer Quadratic Quasi-polyhedra
Letchford, Adam N.
This paper introduces two fundamental families of 'quasi-polyhedra' - polyhedra with a countably infinite number of facets - that arise in the context of integer quadratic programming. It is shown that any integer quadratic program can be reduced to the minimisation of a linear function over a quasi-polyhedron in the first family. Some fundamental properties of the quasi-polyhedra are derived, along with connections to some other well-studied convex sets. Several classes of facet-inducing inequalities are also derived. Finally, extensions to the mixed-integer case are briefly examined.
Frahm, K M; Shepelyansky, D L
2012-01-01
We build up a directed network tracing links from a given integer to its divisors and analyze the properties of the Google matrix of this network. The PageRank vector of this matrix is computed numerically and it is shown that its probability is inversely proportional to the PageRank index thus being similar to the Zipf law and the dependence established for the World Wide Web. The spectrum of the Google matrix of integers is characterized by a large gap and a relatively small number of nonzero eigenvalues. A simple semi-analytical expression for the PageRank of integers is derived that allows to find this vector for matrices of billion size. This network provides a new PageRank order of integers.
Image Watermarking Method Using Integer-to-Integer Wavelet Transforms
Institute of Scientific and Technical Information of China (English)
陈韬; 王京春
2002-01-01
Digital watermarking is an efficient method for copyright protection for text, image, audio, and video data. This paper presents a new image watermarking method based on integer-to-integer wavelet transforms. The watermark is embedded in the significant wavelet coefficients by a simple exclusive OR operation. The method avoids complicated computations and high computer memory requirements that are the main drawbacks of common frequency domain based watermarking algorithms. Simulation results show that the embedded watermark is perceptually invisible and robust to various operations, such as low quality joint picture expert group (JPEG) compression, random and Gaussian noises, and smoothing (mean filtering).
Recent Existence Results for Second-Order Singular Periodic Differential Equations
Directory of Open Access Journals (Sweden)
Nieto JuanJ
2009-01-01
Full Text Available We present some recent existence results for second-order singular periodic differential equations. A nonlinear alternative principle of Leray-Schauder type, a well-known fixed point theorem in cones, and Schauder's fixed point theorem are used in the proof. The results shed some light on the differences between a strong singularity and a weak singularity.
Nonlinear singular vectors and nonlinear singular values
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
A novel concept of nonlinear singular vector and nonlinear singular value is introduced, which is a natural generalization of the classical linear singular vector and linear singular value to the nonlinear category. The optimization problem related to the determination of nonlinear singular vectors and singular values is formulated. The general idea of this approach is demonstrated by a simple two-dimensional quasigeostrophic model in the atmospheric and oceanic sciences. The advantage and its applications of the new method to the predictability, ensemble forecast and finite-time nonlinear instability are discussed. This paper makes a necessary preparation for further theoretical and numerical investigations.
Singular (Lipschitz) homology and homology of integral currents
Riedweg, Christian; Schäppi, Daniel
2009-01-01
We compare the homology groups $H_n ^{IC}(X)$ of the chain complex of integral currents with compact support of a metric space $X$ with the singular Lipschitz homology $H^L_n (X)$ and with ordinary singular homology. If $X$ satisfies certain cone inequalities all these homology theories coincide. On the other hand, for the Hawaiian Earring the homology of integral currents differs from the singular Lipschitz homology and it differs also from the classical singular homology $H_n(X)$.
Note on Integer Factoring Methods IV
Carella, N. A.
2008-01-01
This note continues the theoretical development of deterministic integer factorization algorithms based on systems of polynomials equations. The main result establishes a new deterministic time complexity bench mark in integer factorization.
A Euclidean algorithm for integer matrices
DEFF Research Database (Denmark)
Lauritzen, Niels; Thomsen, Jesper Funch
2015-01-01
We present a Euclidean algorithm for computing a greatest common right divisor of two integer matrices. The algorithm is derived from elementary properties of finitely generated modules over the ring of integers.......We present a Euclidean algorithm for computing a greatest common right divisor of two integer matrices. The algorithm is derived from elementary properties of finitely generated modules over the ring of integers....
On minimal integer representations of weighted games
Freixas, Josep
2011-01-01
We study minimum integer representations for the weights of weighted games, which is linked with some solution concepts in game theory. Closing some gaps in the existing literature we prove that each weighted game with two types of voters admits a unique minimum integer presentation and give examples for more than two types of voters without a minimum integer representation. We characterize the possible weights in minimum integer representations and give examples for at least four types of voters without minimum integer representations preserving types.
Integer programming theory, applications, and computations
Taha, Hamdy A
1975-01-01
Integer Programming: Theory, Applications, and Computations provides information pertinent to the theory, applications, and computations of integer programming. This book presents the computational advantages of the various techniques of integer programming.Organized into eight chapters, this book begins with an overview of the general categorization of integer applications and explains the three fundamental techniques of integer programming. This text then explores the concept of implicit enumeration, which is general in a sense that it is applicable to any well-defined binary program. Other
Fast resolution of integer Vandermonde systems
Directory of Open Access Journals (Sweden)
Rosa di Salvo
2014-10-01
Full Text Available The resolution of polynomial interpolation problems with integer coefficients directly involves the open issue of the integer inversion of a general Vandermonde matrix defined over the field Z/pZ, for p prime number. The purpose of this paper is to demonstrate the possibility to invert a Vandermonde matrix with integer mod p coefficients and exactly compute the integer inverse matrix in the ring Mat(Z/pZ of square matrices over Z/pZ through the new fast algorithm InVanderMOD. The explicit formula derived for the integer inversion of Vandermonde matrices entirely develops inside the field of the integers mod p, with due consideration to the operation of integer division. The inversion procedure InVanderMOD is valid for any prime number p and competitive in terms of computational effort, since its computational cost is less than O(n^3.
Stringy Resolutions of Null Singularities
Energy Technology Data Exchange (ETDEWEB)
Fabinger, Michal
2003-02-06
We study string theory in supersymmetric time-dependent backgrounds. In the framework of general relativity, supersymmetry for spacetimes without flux implies the existence of a covariantly constant null vector, and a relatively simple form of the metric. As a result, the local nature of any such spacetime can be easily understood. We show that we can view any such geometry as a sequence of solutions to lower-dimensional Euclidean gravity. If we choose the lower-dimensional solutions to degenerate at some light-cone time, we obtain null singularities, which may be thought of as generalizations of the parabolic orbifold singularity. We find that in string theory, many such null singularities get repaired by {alpha}{prime}-corrections--in particular, by worldsheet instantons. As a consequence, the resulting string theory solutions do not suffer from any instability. Even though the CFT description of these solutions is not always valid, they can still be well understood after taking the effects of light D-branes into account; the breakdown of the worldsheet conformal field theory is purely gauge-theoretic, not involving strong gravitational effects.
Lowest Landau level on a cone and zeta determinants
Klevtsov, Semyon
2017-06-01
We consider the integer QH state on Riemann surfaces with conical singularities, with the main objective of detecting the effect of the gravitational anomaly directly from the form of the wave function on a singular geometry. We suggest the formula expressing the normalisation factor of the holomorphic state in terms of the regularized zeta determinant on conical surfaces and check this relation for some model geometries. We also comment on possible extensions of this result to the fractional QH states.
Lowest Landau level on a cone and zeta determinants
Klevtsov, Semyon
2016-01-01
We consider the integer QH state on Riemann surfaces with conical singularities, with the main objective of detecting the effect of the gravitational anomaly directly from the form of the wave function on a singular geometry. We suggest the formula expressing the normalisation factor of the holomorphic state in terms of the regularized zeta determinant on conical surfaces and check this relation for some model geometries. We also comment on possible extensions of this result to the fractional QH states.
Cho Decomposition of One-Half Integer Monopoles Solutions
Teh, Rosy; Ng, Ban-Loong; Wong, Khai-Ming
2013-11-01
We performed the Cho decomposition of the SU(2) Yang-Mills-Higgs gauge potentials of the finite energy (1) one-half monopole solution and (2) the one and a half monopoles solution into Abelian and non-Abelian components. We found that the semi-infinite string singularity in the gauge potentials is a contribution from the Higgs field of the one-half monopole in both of the solutions. The non-Abelian components of the gauge potentials are able to remove the point singularity of the Abelian components of the 't Hooft-Polyakov monopole but not the string singularity of the one-half monopole which is topological in nature. Hence the total energy of a one monopole is infinite in the Maxwell electromagnetic theory but the total energy of a one-half monopole is finite. By analyzing the magnetic fields and the gauge covariant derivatives of the Higgs field, we are able to conclude that both the one-half integer monopoles solutions are indeed non-BPS even in the limit of vanishing Higgs self-coupling constant.
Mariwalla, K H
2002-01-01
Basis and limitations of singularity theorems for Gravity are examined. As singularity is a critical situation in course of time, study of time paths, in full generality of Equivalence principle, provides two mechanisms to prevent singularity. Resolution of singular Time translation generators into space of its orbits, and essential higher dimensions for Relativistic particle interactions has facets to resolve any real singularity problem. Conceptually, these varied viewpoints have a common denominator: arbitrariness in the definition of `energy' intrinsic to the space of operation in each case, so as to render absence of singularity a tautology for self-consistency of the systems.
Resolution of quantum singularities
Konkowski, Deborah; Helliwell, Thomas
2017-01-01
A review of quantum singularities in static and conformally static spacetimes is given. A spacetime is said to be quantum mechanically non-singular if a quantum wave packet does not feel, in some sense, the presence of a singularity; mathematically, this means that the wave operator is essentially self-adjoint on the space of square integrable functions. Spacetimes with classical mild singularities (quasiregular ones) to spacetimes with classical strong curvature singularities have been tested. Here we discuss the similarities and differences between classical singularities that are healed quantum mechanically and those that are not. Possible extensions of the mathematical technique to more physically realistic spacetimes are discussed.
MULTIPLE POSITIVE SOLUTIONS TO FOURTH-ORDER SINGULAR BOUNDARY VALUE PROBLEMS
Institute of Scientific and Technical Information of China (English)
无
2011-01-01
In this paper,using the Krasnaselskii's fixed point theory in cones and localization method,under more general conditions,the existence of n positive solutions to a class of fourth-order singular boundary value problems is considered.
Singular solutions of a singular differential equation
Directory of Open Access Journals (Sweden)
Naito Manabu
2000-01-01
Full Text Available An attempt is made to study the problem of existence of singular solutions to singular differential equations of the type which have never been touched in the literature. Here and are positive constants and is a positive continuous function on . A solution with initial conditions given at is called singular if it ceases to exist at some finite point . Remarkably enough, it is observed that the equation may admit, in addition to a usual blowing-up singular solution, a completely new type of singular solution with the property that Such a solution is named a black hole solution in view of its specific behavior at . It is shown in particular that there does exist a situation in which all solutions of are black hole solutions.
On exceptional quotient singularities
Cheltsov, Ivan; Shramov, Constantin
2011-01-01
We study exceptional quotient singularities. In particular, we prove an exceptionality criterion in terms of the $\\alpha$-invariant of Tian, and utilize it to classify four-dimensional and five-dimensional exceptional quotient singularities.
Applied Integer Programming Modeling and Solution
Chen, Der-San; Dang, Yu
2011-01-01
An accessible treatment of the modeling and solution of integer programming problems, featuring modern applications and software In order to fully comprehend the algorithms associated with integer programming, it is important to understand not only how algorithms work, but also why they work. Applied Integer Programming features a unique emphasis on this point, focusing on problem modeling and solution using commercial software. Taking an application-oriented approach, this book addresses the art and science of mathematical modeling related to the mixed integer programming (MIP) framework and
... squamous cells - cone biopsy; Pap smear - cone biopsy; HPV - cone biopsy; Human papilloma virus - cone biopsy; Cervix - ... exam. The health care provider will place an instrument (speculum) into your vagina to better see the ...
Singular solutions of fully nonlinear elliptic equations and applications
Armstrong, Scott N; Smart, Charles K
2011-01-01
We study the properties of solutions of fully nonlinear, positively homogeneous elliptic equations near boundary points of Lipschitz domains at which the solution may be singular. We show that these equations have two positive solutions in each cone of $\\mathbb{R}^n$, and the solutions are unique in an appropriate sense. We introduce a new method for analyzing the behavior of solutions near certain Lipschitz boundary points, which permits us to classify isolated boundary singularities of solutions which are bounded from either above or below. We also obtain a sharp Phragm\\'en-Lindel\\"of result as well as a principle of positive singularities in certain Lipschitz domains.
Rotationally Invariant Singular Solutions to the Kapustin-Witten Equations
He, Siqi
2015-01-01
In the present paper, we find a system of non-linear ODEs that gives rotationally invariant solutions to the Kapustin-Witten equations in 4-dimensional Euclidean space. We explicitly solve these ODEs in some special cases and find decaying rational solutions, which provide solutions to the Kapustin-Witten equations. The imaginary parts of the solutions are singular. By rescaling, we can prove the existence of the Uhlenbeck bubbling phenomenon for these solutions. In addition, for any integer $k$, we can construct a 5$|k|$ dimensional family of $C^1$ solutions to the Kapustin-Witten equations on Euclidean space, again with singular imaginary parts.
Stochastic Programming with Simple Integer Recourse
Louveaux, François V.; van der Vlerk, Maarten H.
1993-01-01
Stochastic integer programs are notoriously difficult. Very few properties are known and solution algorithms are very scarce. In this paper, we introduce the class of stochastic programs with simple integer recourse, a natural extension of the simple recourse case extensively studied in stochastic c
Integer Programming Models for Computational Biology Problems
Institute of Scientific and Technical Information of China (English)
Giuseppe Lancia
2004-01-01
The recent years have seen an impressive increase in the use of Integer Programming models for the solution of optimization problems originating in Molecular Biology. In this survey, some of the most successful Integer Programming approaches are described, while a broad overview of application areas being is given in modern Computational Molecular Biology.
Fractional quantum Hall states of bosons on cones
Wu, Ying-Hai; Sreejith, G J
2016-01-01
Motivated by a recent experiment which synthesizes Landau levels for photons on cones (Schine {\\em et al.}, arXiv: 1511.07381), and more generally the interest in understanding gravitational responses of quantum Hall systems, we study fractional quantum Hall states of bosons on cones. We construct several trial wave functions and compare them with exact diagonalization results. The tip of a cone is a localized geometrical defect with singular curvature around which excessive charges accumulate. We study the density profiles of some states on cones and show that the excessive charges agree with analytical predictions.
Effective integer-to-integer transforms for JPEG2000 coder
Przelaskowski, Artur
2001-12-01
This paper considers reversible transforms which are used in wavelet compression according to nowadays JPEG2000 standard. Original data decomposition in a form of integer wavelet transformation realized in subband decomposition scheme is optimized by design and selection of the most effective transforms. Lifting scheme is used to construct new biorthogonal symmetric wavelets. Number and distribution of vanishing moments, subband coding gain, associated filter length, computational complexity and number of lifting steps were mainly analyzed in the optimization of designed transforms. Coming from many tests of compression efficiency evaluation in JPEG2000 standardization process, the best selected transforms have been compared to designed ones to conclude the most efficient for compression wavelet bases and their important features. Certain new transforms overcome all other in both phases of lossy-to-lossless compression (e.g. up to 0.5 dB of PSNR for 0.5 bpp in comparison to the state-of-art transforms of JPEG2000 compression, and up to 3dB over 5/3 standard reversible transform). Moreover, the lossy compression efficiency of proposed reversible wavelets is comparable to reference irreversible wavelets potential in several cases. The highest improvement over that reference PSNR values is close to 1.2 dB.
Boundary constraints for singular value decomposition of spectral data
Gruninger, John; Dothe, Hoang
2013-10-01
Singular value decomposition (SVD) and principal component analysis enjoy a broad range of applications, including, rank estimation, noise reduction, classification and compression. The resulting singular vectors form orthogonal basis sets for subspace projection techniques. The procedures are applicable to general data matrices. Spectral matrices belong to a special class known as non-negative matrices. A key property of non-negative matrices is that their columns/rows form non-negative cones, with any non-negative linear combination of the columns/rows belonging to the cone. This special property has been implicitly used in popular rank estimation techniques know as virtual dimension (VD) and hyperspectral signal identification by minimum error (HySime). Data sets of spectra reside in non-negative orthants. The subspace spanned by a SVD of a set of spectra includes all orthants. However SVD projections can be constrained to the non-negative orthants. In this paper two types of singular vector projection constraints are identified, one that confines the projection to lie within the cone formed by the spectral data set, and a second that only restricts projections to the non-negative orthant. The former is referred to here as the inner constraint set, the latter the outer constraint set. The outer constraint set forms a broader cone since it includes projections outside the cone formed by the data array. The two cones form boundaries for the cones formed by non-negative matrix factorizations (NNF). Ambiguities in the NNF lead to a variety of possible sets of left and right non-negative vectors and their cones. The paper presents the constraint set approach and illustrates it with applications to spectral classification.
Parallel Integer Relation Detection: Techniques and Applications
Bailey, David H.; Broadhurst, David J.
1999-01-01
Let $\\{x_1, x_2, ..., x_n\\}$ be a vector of real numbers. An integer relation algorithm is a computational scheme to find the $n$ integers $a_k$, if they exist, such that $a_1 x_1 + a_2 x_2 + ... + a_n x_n= 0$. In the past few years, integer relation algorithms have been utilized to discover new results in mathematics and physics. Existing programs for this purpose require very large amounts of computer time, due in part to the requirement for multiprecision arithmetic, yet are poorly suited ...
Halyo, Edi
2009-01-01
We describe solitons that live on the world--volumes of D5 branes wrapped on deformed $A_2$ singularities fibered over $C(x)$. We show that monopoles are D3 branes wrapped on a node of the deformed singularity and stretched along $C(x)$. F and D--term strings are D3 branes wrapped on a node of a singularity that is deformed and resolved respectively. Domain walls require deformed $A_3$ singularities and correspond to D5 branes wrapped on a node and stretched along $C(x)$.
Singular stochastic differential equations
Cherny, Alexander S
2005-01-01
The authors introduce, in this research monograph on stochastic differential equations, a class of points termed isolated singular points. Stochastic differential equations possessing such points (called singular stochastic differential equations here) arise often in theory and in applications. However, known conditions for the existence and uniqueness of a solution typically fail for such equations. The book concentrates on the study of the existence, the uniqueness, and, what is most important, on the qualitative behaviour of solutions of singular stochastic differential equations. This is done by providing a qualitative classification of isolated singular points, into 48 possible types.
Energy Technology Data Exchange (ETDEWEB)
2016-04-12
Singularity is a container solution designed to facilitate mobility of compute across systems and HPC infrastructures. It does this by creating minimal containers that are defined by a specfile and files from the host system are used to build the container. The resulting container can then be launched by any Linux computer with Singularity installed regardless if the programs inside the container are present on the target system, or if they are a different version, or even incompatible versions. Singularity achieves extreme portability without sacrificing usability thus solving the need of mobility of compute. Singularity containers can be executed within a normal/standard command line process flow.
Vaz, C; Vaz, Cenalo; Witten, Louis
1995-01-01
A naked singularity is formed by the collapse of a Sine-Gordon soliton in 1+1 dimensional dilaton gravity with a negative cosmological constant. We examine the quantum stress tensor resulting from the formation of the singularity. Consistent boundary conditions require that the incoming soliton is accompanied by a flux of incoming radiation across past null infinity, but neglecting the back reaction of the spacetime leads to the absurd conclusion that the total energy entering the system by the time the observer is able to receive information from the singularity is infinite. We conclude that the back reaction must prevent the formation of the naked singularity.
On singular and sincerely singular compact patterns
Rosenau, Philip; Zilburg, Alon
2016-08-01
A third order dispersive equation ut +(um)x +1/b[ua∇2ub]x = 0 is used to explore two very different classes of compact patterns. In the first, the prevailing singularity at the edge induces traveling compactons, solitary waves with a compact support. In the second, the singularity induced at the perimeter of the initial excitation, entraps the dynamics within the domain's interior (nonetheless, certain very singular excitations may escape it). Here, overlapping compactons undergo interaction which may result in an interchange of their positions, or form other structures, all confined within their initial support. We conjecture, and affirm it empirically, that whenever the system admits more than one type of compactons, only the least singular compactons may be evolutionary. The entrapment due to singularities is also unfolded and confirmed numerically in a class of diffusive equations ut =uk∇2un with k > 1 and n > 0 with excitations entrapped within their initial support observed to converge toward a space-time separable structure. A similar effect is also found in a class of nonlinear Klein-Gordon Equations.
A Cone Pseudo-differential Calculus
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
@@ The calculus of pseudo-differential operators on singular spaces and theconcept of ellipti-city in operator algebras on manifolds with singularitieshave become an enormous challenge for analysists. The so-called cone algebras(with discrete and continuous asymptotics) are investigated by manymathematicians, especially by B. W. Schulze, who developed and enrichedcone and edge pseudo-differential calculus, see Schulze［4-7］, Rempel and Schulze ［2, 3］. In this note,we construct a cone pseudo-differentialcalculus for operators which respect conormal asymptotics of a prescribedasymptotic type.
Garbageless reversible implementation of integer linear transformations
DEFF Research Database (Denmark)
Burignat, Stéphane; Vermeirsch, Kenneth; De Vos, Alexis;
2013-01-01
Discrete linear transformations are important tools in information processing. Many such transforms are injective and therefore prime candidates for a physically reversible implementation into hardware. We present here reversible digital implementations of different integer transformations on fou...
On a correlational clustering of integers
Aszalós László; Hajdu Lajos (1968-) (matematikus); Pethő Attila (1950-) (matematikus, informatikus)
2016-01-01
Correlation clustering is a concept of machine learning. The ultimate goal of such a clustering is to find a partition with minimal conflicts. In this paper we investigate a correlation clustering of integers, based upon the greatest common divisor.
Solving Parity Games on Integer Vectors
Abdulla, Parosh Aziz; Mayr, Richard; Sangnier, Arnaud; Sproston, Jeremy
2013-01-01
We consider parity games on infinite graphs where configurations are represented by control-states and integer vectors. This framework subsumes two classic game problems: parity games on vector addition systems with states (vass) and multidimensional energy parity games. We show that the multidimensional energy parity game problem is inter-reducible with a subclass of single-sided parity games on vass where just one player can modify the integer counters and the opponent can only change contr...
Fernández-Jambrina, L
2015-01-01
In this talk we would like to analyse the appearance of singularities in FLRW cosmological models which evolve close to w=-1, where w is the barotropic index of the universe. We relate small terms in cosmological time around w=-1 with the correspondent scale factor of the universe and check for the formation of singularities.
Halyo, Edi
2009-01-01
We describe domain walls that live on $A_2$ and $A_3$ singularities. The walls are BPS if the singularity is resolved and non--BPS if it is deformed and fibered. We show that these domain walls may interpolate between vacua that support monopoles and/or vortices.
Ishii, Shihoko
2014-01-01
This book is an introduction to singularities for graduate students and researchers. It is said that algebraic geometry originated in the seventeenth century with the famous work Discours de la méthode pour bien conduire sa raison, et chercher la vérité dans les sciences by Descartes. In that book he introduced coordinates to the study of geometry. After its publication, research on algebraic varieties developed steadily. Many beautiful results emerged in mathematicians’ works. Most of them were about non-singular varieties. Singularities were considered “bad” objects that interfered with knowledge of the structure of an algebraic variety. In the past three decades, however, it has become clear that singularities are necessary for us to have a good description of the framework of varieties. For example, it is impossible to formulate minimal model theory for higher-dimensional cases without singularities. Another example is that the moduli spaces of varieties have natural compactification, the boundar...
Singular Continuous Spectrum for Singular Potentials
Jitomirskaya, Svetlana; Yang, Fan
2017-05-01
We prove that Schrödinger operators with meromorphic potentials {(H_{α,θ}u)_n=u_{n+1}+u_{n-1}+ g(θ+nα)/f(θ+nα) u_n} have purely singular continuous spectrum on the set {{E: L(E) operator. Preprint, 2015) for the almost Mathieu operator to the general family of meromorphic potentials.
Exact Asymptotic Expansion of Singular Solutions for the (2+1-D Protter Problem
Directory of Open Access Journals (Sweden)
Lubomir Dechevski
2012-01-01
Full Text Available We study three-dimensional boundary value problems for the nonhomogeneous wave equation, which are analogues of the Darboux problems in ℝ2. In contrast to the planar Darboux problem the three-dimensional version is not well posed, since its homogeneous adjoint problem has an infinite number of classical solutions. On the other hand, it is known that for smooth right-hand side functions there is a uniquely determined generalized solution that may have a strong power-type singularity at one boundary point. This singularity is isolated at the vertex of the characteristic light cone and does not propagate along the cone. The present paper describes asymptotic expansion of the generalized solutions in negative powers of the distance to this singular point. We derive necessary and sufficient conditions for existence of solutions with a fixed order of singularity and give a priori estimates for the singular solutions.
Sharp Lower Bounds on Density of Area-Minimizing Cones
Ilmanen, Tom
2010-01-01
We prove that the density of a topologically nontrivial, area-minimizing hypercone with an isolated singularity must be greater than the square root of 2. The Simons' cones show that this is the best possible constant. If one of the components of the complement of the cone has nontrivial kth homotopy group, we prove a better bound in terms of k; that bound is also best possible. The proofs use mean curvature flow.
Null surfaces of null curves on 3-null cone
Sun, Jianguo; Pei, Donghe
2014-03-01
The null surfaces of null curves on 3-null cone have the applications in the studying of horizon types. Via the pseudo-scalar product and Frenet equations, the differential geometry of null curves on 3-null cone is obtained. In the local sense, the curvature describes the contact of submanifolds with pseudo-spheres. We introduce the geometric properties of the curvatures and show the singularities of null surfaces, which are constructed over the null curves.
Singularities and Closed String Tachyons
Silverstein, E
2006-01-01
A basic problem in gravitational physics is the resolution of spacetime singularities where general relativity breaks down. The simplest such singularities are conical singularities arising from orbifold identifications of flat space, and the most challenging are spacelike singularities inside black holes (and in cosmology). Topology changing processes also require evolution through classically singular spacetimes. I briefly review how a phase of closed string tachyon condensate replaces, and helps to resolve, basic singularities of each of these types. Finally I discuss some interesting features of singularities arising in the small volume limit of compact negatively curved spaces and the emerging zoology of spacelike singularities.
Vertman, Boris
2010-01-01
We identify the metric anomaly of the analytic torsion for an odd-dimensional bounded generalized cone coming from the non-product structure at the regular boundary, hereby filtering out the actual contribution of the conical singularity. This allows us to identify the analytic torsion of a cone purely in terms of cohomology, up to a naturally arising torsion-like spectral invariant of the cross section. The arguments are based on the computation of the analytic torsion of the bounded generalized cone, truncated at the conical singularity.
Vertman, Boris
2010-01-01
We identify the metric anomaly of the analytic torsion for an even-dimensional bounded generalized cone coming from the non-product structure at the regular boundary, hereby filtering out the actual contribution of the conical singularity. This allows us to identify the analytic torsion of a cone purely in terms of cohomology, up to a naturally arising topological invariant - the analytic torsion of the cross section. The arguments are based on the computation of the analytic torsion of the bounded generalized cone, truncated at the conical singularity.
Slip and Slide Method of Factoring Trinomials with Integer Coefficients over the Integers
Donnell, William A.
2012-01-01
In intermediate and college algebra courses there are a number of methods for factoring quadratic trinomials with integer coefficients over the integers. Some of these methods have been given names, such as trial and error, reversing FOIL, AC method, middle term splitting method and slip and slide method. The purpose of this article is to discuss…
Elementary Theory of Factoring Trinomials with Integer Coefficients over the Integers
Donnell, William A.
2010-01-01
An important component of intermediate and college algebra courses involves teaching students methods to factor a trinomial with integer coefficients over the integers. The aim of this article is to present a theoretical justification of that which is often taught, but really never explained as to why it works. The theory is presented, and a…
Directory of Open Access Journals (Sweden)
Gabriel Martínez-Niconoff
2012-01-01
Full Text Available With the purpose to compare the physical features of the electromagnetic field, we describe the synthesis of optical singularities propagating in the free space and on a metal surface. In both cases the electromagnetic field has a slit-shaped curve as a boundary condition, and the singularities correspond to a shock wave that is a consequence of the curvature of the slit curve. As prototypes, we generate singularities that correspond to fold and cusped regions. We show that singularities in free space may generate bifurcation effects while plasmon fields do not generate these kinds of effects. Experimental results for free-space propagation are presented and for surface plasmon fields, computer simulations are shown.
Ling, Eric
The big bang theory is a model of the universe which makes the striking prediction that the universe began a finite amount of time in the past at the so called "Big Bang singularity." We explore the physical and mathematical justification of this surprising result. After laying down the framework of the universe as a spacetime manifold, we combine physical observations with global symmetrical assumptions to deduce the FRW cosmological models which predict a big bang singularity. Next we prove a couple theorems due to Stephen Hawking which show that the big bang singularity exists even if one removes the global symmetrical assumptions. Lastly, we investigate the conditions one needs to impose on a spacetime if one wishes to avoid a singularity. The ideas and concepts used here to study spacetimes are similar to those used to study Riemannian manifolds, therefore we compare and contrast the two geometries throughout.
Singularities in Speckled Speckle
Freund, Isaac
2007-01-01
Speckle patterns produced by random optical fields with two (or more) widely different correlation lengths exhibit speckle spots that are themselves highly speckled. Using computer simulations and analytic theory we present results for the point singularities of speckled speckle fields: optical vortices in scalar (one polarization component) fields; C points in vector (two polarization component) fields. In single correlation length fields both types of singularities tend to be more{}-or{}-less uniformly distributed. In contrast, the singularity structure of speckled speckle is anomalous: for some sets of source parameters vortices and C points tend to form widely separated giant clusters, for other parameter sets these singularities tend to form chains that surround large empty regions. The critical point statistics of speckled speckle is also anomalous. In scalar (vector) single correlation length fields phase (azimuthal) extrema are always outnumbered by vortices (C points). In contrast, in speckled speckl...
Complex singularities and PDEs
Caflisch, R E; Sammartino, M; Sciacca, V
2015-01-01
In this paper we give a review on the computational methods used to characterize the complex singularities developed by some relevant PDEs. We begin by reviewing the singularity tracking method based on the analysis of the Fourier spectrum. We then introduce other methods generally used to detect the hidden singularities. In particular we show some applications of the Pad\\'e approximation, of the Kida method, and of Borel-Polya method. We apply these techniques to the study of the singularity formation of some nonlinear dispersive and dissipative one dimensional PDE of the 2D Prandtl equation, of the 2D KP equation, and to Navier-Stokes equation for high Reynolds number incompressible flows in the case of interaction with rigid boundaries.
Singularity methods for magnetohydrodynamics
Directory of Open Access Journals (Sweden)
A. D. Alawneh
1986-01-01
Full Text Available Singular solutions for linearized MHD equations based on Oseen approximations have been obtained such as Oseenslet. Oseenrotlet, mass source, etc. By suitably distributing these singular solutions along the axes of symmetry of an axially symmetric bodies, we derive the approximate values for the velocity fields, the force and the momentum for the case of translational and rotational motions of such bodies in a steady flow of an incompressible viscous and magnetized fluid.
Generic singularity studies revisited
Barrow, John D.; Tipler, Frank J.
1981-04-01
We comment on a reply by Belinskii, Khalatnikov and Lifshitz to our analysis of their conclusions regarding the general structure of space-time singularities. We support our contention that it is impossible to provide a reliable analysis of the evolution of a general (or stable) solution with local techniques in a synchronous coordinate system having a simultaneous physical singularity. Work supported in part by the National Science Foundation under grant number PHY 78-26592.
Stevens, Jan
2003-01-01
These notes deal with deformation theory of complex analytic singularities and related objects. The first part treats general theory. The central notion is that of versal deformation in several variants. The theory is developed both in an abstract way and in a concrete way suitable for computations. The second part deals with more specific problems, specially on curves and surfaces. Smoothings of singularities are the main concern. Examples are spread throughout the text.
Linear and integer programming made easy
Hu, T C
2016-01-01
Linear and integer programming are fundamental toolkits for data and information science and technology, particularly in the context of today’s megatrends toward statistical optimization, machine learning, and big data analytics. Drawn from over 30 years of classroom teaching and applied research experience, this textbook provides a crisp and practical introduction to the basics of linear and integer programming. The authors’ approach is accessible to students from all fields of engineering, including operations research, statistics, machine learning, control system design, scheduling, formal verification, and computer vision. Readers will learn to cast hard combinatorial problems as mathematical programming optimizations, understand how to achieve formulations where the objective and constraints are linear, choose appropriate solution methods, and interpret results appropriately. •Provides a concise introduction to linear and integer programming, appropriate for undergraduates, graduates, a short cours...
Integer Discontinuity of Density Functional Theory
Mosquera, Martin A
2014-01-01
Density functional approximations to the exchange-correlation energy of Kohn-Sham theory, such as the local density approximation and generalized gradient approximations, lack the well-known integer discontinuity, a feature that is critical to describe molecular dissociation correctly. Moreover, standard approximations to the exchange-correlation energy also fail to yield the correct linear dependence of the ground-state energy on the number of electrons when this is a non-integer number obtained from the grand canonical ensemble statistics. We present a formal framework to restore the integer discontinuity of any density functional approximation. Our formalism derives from a formula for the exact energy functional and a new constrained search functional that recovers the linear dependence of the energy on the number of electrons.
Institute of Scientific and Technical Information of China (English)
Xing-qiu Zhang; Jing-xian Sun
2009-01-01
By constructing a special cone and using cone compression and expansion fixed point theorem,this paper presents some existence results of positive solutions of singular boundary value problem on unbounded domains for a class of first order differential equation.As applications of the main results,two examples are given at the end of this paper.
Hermitian K-theory of the integers
Berrick, A. J.; Karoubi, M.
2005-01-01
The 2-primary torsion of the higher algebraic K-theory of the integers has been computed by Rognes and Weibel. In this paper we prove analogous results for the Hermitian K-theory of the integers with 2 inverted (denoted by Z'). We also prove in this case the analog of the Lichtenbaum conjecture for the hermitian K-theory of Z' : the homotopy fixed point set of a suitable Z/2 action on the classifying space of the algebraic K-theory of Z' is the hermitian K-theory of Z' after 2-adic completion.
NEW ALGORITHM FOR FAST INTEGER AMBIGUITY RESOLUTION
Institute of Scientific and Technical Information of China (English)
HEXiao-feng; HUXiao-ping
2005-01-01
Fast integer ambiguity resolution is referred as a key part in precision relative positioning of the GPS carrier phase. A new algorithm for fast integer ambiguity resolution based on LAMBDA and FASF methods is proposed. This algorithm integrates the LAMBDA method and the FASF method, thus improving the efficiency of the ambiguity resolution. Firstly, the ambiguity search space transformation in the LAMBDA method is used,and then the FASF method is used to search ambiguities. Experiments in the relative positioning of about 1 km static baseline demonstrate that the error is less than 1 cm.
A Binomial Integer-Valued ARCH Model.
Ristić, Miroslav M; Weiß, Christian H; Janjić, Ana D
2016-11-01
We present an integer-valued ARCH model which can be used for modeling time series of counts with under-, equi-, or overdispersion. The introduced model has a conditional binomial distribution, and it is shown to be strictly stationary and ergodic. The unknown parameters are estimated by three methods: conditional maximum likelihood, conditional least squares and maximum likelihood type penalty function estimation. The asymptotic distributions of the estimators are derived. A real application of the novel model to epidemic surveillance is briefly discussed. Finally, a generalization of the introduced model is considered by introducing an integer-valued GARCH model.
Domínguez, Luis F.
2010-12-01
This work introduces two algorithms for the solution of pure integer and mixed-integer bilevel programming problems by multiparametric programming techniques. The first algorithm addresses the integer case of the bilevel programming problem where integer variables of the outer optimization problem appear in linear or polynomial form in the inner problem. The algorithm employs global optimization techniques to convexify nonlinear terms generated by a reformulation linearization technique (RLT). A continuous multiparametric programming algorithm is then used to solve the reformulated convex inner problem. The second algorithm addresses the mixed-integer case of the bilevel programming problem where integer and continuous variables of the outer problem appear in linear or polynomial forms in the inner problem. The algorithm relies on the use of global multiparametric mixed-integer programming techniques at the inner optimization level. In both algorithms, the multiparametric solutions obtained are embedded in the outer problem to form a set of single-level (M)(I)(N)LP problems - which are then solved to global optimality using standard fixed-point (global) optimization methods. Numerical examples drawn from the open literature are presented to illustrate the proposed algorithms. © 2010 Elsevier Ltd.
CONDITIONAL FACTORIZATION BASED ON LATTICE THEORY FOR -INTEGERS
Institute of Scientific and Technical Information of China (English)
Zheng Yonghui; Zhu Yuefei
2008-01-01
In this paper, the integer N = pkq is called a -integer, if p and q are odd primes with almost the same size and k is a positive integer. Such integers were previously proposed for various cryptographic applications. The conditional factorization based on lattice theory for n-bit -integers is considered, and there is an algorithm in time polynomial in n to factor these integers if the least significant |(2k-1)n/(3k-1)(k-1)| bits of p are given.
Singular Continuous Spectrum for Singular Potentials
Jitomirskaya, Svetlana; Yang, Fan
2017-01-01
We prove that Schrödinger operators with meromorphic potentials {(H_{α,θ}u)_n=u_{n+1}+u_{n-1}+ g(θ+nα)/f(θ+nα) u_n} have purely singular continuous spectrum on the set {{E: L(E) Lyapunov exponent. This extends results of Jitomirskaya and Liu (Arithmetic spectral transitions for the Maryland model. CPAM, to appear) for the Maryland model and of Avila,You and Zhou (Sharp Phase transitions for the almost Mathieu operator. Preprint, 2015) for the almost Mathieu operator to the general family of meromorphic potentials.
Quadratic forms representing all odd positive integers
Rouse, Jeremy
2011-01-01
We consider the problem of classifying all positive-definite integer-valued quadratic forms that represent all positive odd integers. Kaplansky considered this problem for ternary forms, giving a list of 23 candidates, and proving that 19 of those represent all positive odds. (Jagy later dealt with a 20th candidate.) Assuming that the remaining three forms represent all positive odds, we prove that an arbitrary, positive-definite quadratic form represents all positive odds if and only if it represents the odd numbers from 1 up to 451. This result is analogous to Bhargava and Hanke's celebrated 290-theorem. In addition, we prove that these three remaining ternaries represent all positive odd integers, assuming the generalized Riemann hypothesis. This result is made possible by a new analytic method for bounding the cusp constants of integer-valued quaternary quadratic forms $Q$ with fundamental discriminant. This method is based on the analytic properties of Rankin-Selberg $L$-functions, and we use it to prove...
Linear and integer programming theory and practice
Sierksma, Gerard
2001-01-01
Linear optimisation; basic concepts; Dantzig's simplex method; duality and optimality; sensitivity analysis; karmarkar's interior path method; integer linear optimisation; linear network models; computational complexity issues; model building, case studies, and advanced techniques; solutions to selected exercises. Appendices: linear algebra; convexity; graph theory; optimisation theory; computer package INTPM.
Sums of Integer Squares: A New Look.
Sastry, K. R. S.; Pranesachar, C. R.; Venkatachala, B. J.
1998-01-01
Focuses on the study of the sum of two integer squares, neither of which is zero square. Develops some new interesting and nonstandard ideas that can be put to use in number theory class, mathematics club meetings, or popular lectures. (ASK)
Predecessor queries in dynamic integer sets
DEFF Research Database (Denmark)
Brodal, Gerth Stølting
1997-01-01
We consider the problem of maintaining a set of n integers in the range 0.2w–1 under the operations of insertion, deletion, predecessor queries, minimum queries and maximum queries on a unit cost RAM with word size w bits. Let f (n) be an arbitrary nondecreasing smooth function satisfying n...
Integer programming techniques for educational timetabling
DEFF Research Database (Denmark)
Fonseca, George H.G.; Santos, Haroldo G.; Carrano, Eduardo G.
2017-01-01
in recent studies in the field. This work presents new cuts and reformulations for the existing integer programming model for XHSTT. The proposed cuts improved hugely the linear relaxation of the formulation, leading to an average gap reduction of 32%. Applied to XHSTT-2014 instance set, the alternative...
Mixed integer evolution strategies for parameter optimization.
Li, Rui; Emmerich, Michael T M; Eggermont, Jeroen; Bäck, Thomas; Schütz, M; Dijkstra, J; Reiber, J H C
2013-01-01
Evolution strategies (ESs) are powerful probabilistic search and optimization algorithms gleaned from biological evolution theory. They have been successfully applied to a wide range of real world applications. The modern ESs are mainly designed for solving continuous parameter optimization problems. Their ability to adapt the parameters of the multivariate normal distribution used for mutation during the optimization run makes them well suited for this domain. In this article we describe and study mixed integer evolution strategies (MIES), which are natural extensions of ES for mixed integer optimization problems. MIES can deal with parameter vectors consisting not only of continuous variables but also with nominal discrete and integer variables. Following the design principles of the canonical evolution strategies, they use specialized mutation operators tailored for the aforementioned mixed parameter classes. For each type of variable, the choice of mutation operators is governed by a natural metric for this variable type, maximal entropy, and symmetry considerations. All distributions used for mutation can be controlled in their shape by means of scaling parameters, allowing self-adaptation to be implemented. After introducing and motivating the conceptual design of the MIES, we study the optimality of the self-adaptation of step sizes and mutation rates on a generalized (weighted) sphere model. Moreover, we prove global convergence of the MIES on a very general class of problems. The remainder of the article is devoted to performance studies on artificial landscapes (barrier functions and mixed integer NK landscapes), and a case study in the optimization of medical image analysis systems. In addition, we show that with proper constraint handling techniques, MIES can also be applied to classical mixed integer nonlinear programming problems.
CHARACTERIZATION OF SOLID CONES
Institute of Scientific and Technical Information of China (English)
Qiu Jinghui
2008-01-01
The author gives a dual characterization of solid cones in locally convex spaces.From this the author obtains some criteria for judging convex cones to be solid in various inds of locally convex spaces. Using a general expression of the interior of a solid cone,the author obtains a number of necessary and sufficient conditions for convex cones to be solid in the framework of Banach spaces. In particular, the author gives a dual relationship between solid cones and generalized sharp cones. The related known results are improved and extended.
Abelian Vortices with Singularities
Baptista, J M
2012-01-01
Let L --> X be a complex line bundle over a compact connected Riemann surface. We consider the abelian vortex equations on L when the metric on the surface has finitely many point degeneracies or conical singularities and the line bundle has parabolic structure. These conditions appear naturally in the study of vortex configurations with constraints, or configurations invariant under the action of a finite group. We first show that the moduli space of singular vortex solutions is the same as in the regular case. Then we compute the total volume and total scalar curvature of the moduli space singular vortex solutions. These numbers differ from the case of regular vortices by a very natural term. Finally we exhibit explicit non-trivial vortex solutions over the thrice punctured hyperbolic sphere.
Gil, José J; José, Ignacio San
2015-01-01
Singular Mueller matrices play an important role in polarization algebra and have peculiar properties that stem from the fact that either the medium exhibits maximum diattenuation and/or polarizance, or because its associated canonical depolarizer has the property of fully randomizing, the circular component (at least) of the states of polarization of light incident on it. The formal reasons for which the Mueller matrix M of a given medium is singular are systematically investigated, analyzed and interpreted in the framework of the serial decompositions and the characteristic ellipsoids of M. The analysis allows for a general classification and geometric representation of singular Mueller matrices, of potential usefulness to experimentalists dealing with such media.
Constrained spacecraft reorientation using mixed integer convex programming
Tam, Margaret; Glenn Lightsey, E.
2016-10-01
A constrained attitude guidance (CAG) system is developed using convex optimization to autonomously achieve spacecraft pointing objectives while meeting the constraints imposed by on-board hardware. These constraints include bounds on the control input and slew rate, as well as pointing constraints imposed by the sensors. The pointing constraints consist of inclusion and exclusion cones that dictate permissible orientations of the spacecraft in order to keep objects in or out of the field of view of the sensors. The optimization scheme drives a body vector towards a target inertial vector along a trajectory that consists solely of permissible orientations in order to achieve the desired attitude for a given mission mode. The non-convex rotational kinematics are handled by discretization, which also ensures that the quaternion stays unity norm. In order to guarantee an admissible path, the pointing constraints are relaxed. Depending on how strict the pointing constraints are, the degree of relaxation is tuneable. The use of binary variables permits the inclusion of logical expressions in the pointing constraints in the case that a set of sensors has redundancies. The resulting mixed integer convex programming (MICP) formulation generates a steering law that can be easily integrated into an attitude determination and control (ADC) system. A sample simulation of the system is performed for the Bevo-2 satellite, including disturbance torques and actuator dynamics which are not modeled by the controller. Simulation results demonstrate the robustness of the system to disturbances while meeting the mission requirements with desirable performance characteristics.
Singularities of invariant connections
Energy Technology Data Exchange (ETDEWEB)
Amores, A.M. (Universidad Complutense, Madrid (Spain)); Gutierrez, M. (Universidad Politecnica, Madrid (Spain))
1992-12-01
A reductive homogeneous space M = P/G is considered, endowed with an invariant connection, i.e., such that all left translations of M induced by members of P preserve it. The authors study the set of singularities of such connections giving sufficient conditions for it to be empty, or, in other cases, familities of b-incomplete curves converging to singularities. A full description of the b-completion of a connection with M = R[sup m] (or a quotient of it) is given with information on its topology. 5 refs.
Maslov indices, Poisson brackets, and singular differential forms
Esterlis, I.; Haggard, H. M.; Hedeman, A.; Littlejohn, R. G.
2014-06-01
Maslov indices are integers that appear in semiclassical wave functions and quantization conditions. They are often notoriously difficult to compute. We present methods of computing the Maslov index that rely only on typically elementary Poisson brackets and simple linear algebra. We also present a singular differential form, whose integral along a curve gives the Maslov index of that curve. The form is closed but not exact, and transforms by an exact differential under canonical transformations. We illustrate the method with the 6j-symbol, which is important in angular-momentum theory and in quantum gravity.
MULTIPLE POSITIVE SOLUTIONS TO A SINGULAR THIRD-ORDER THREE-POINT BOUNDARY VALUE PROBLEM
Institute of Scientific and Technical Information of China (English)
无
2011-01-01
In this paper,we study a singular third-order three-point boundary value problem. By a fixed point theorem of cone expansion-compression type due to Krasnosel'skii,we obtain various new results on the existence of two positive solutions to the problem,whose coefficient is allowed to have suitable singularities. Finally,we give an example to verify our results.
Integer least-squares theory for the GNSS compass
Teunissen, P.J.G.
2010-01-01
Global navigation satellite system (GNSS) carrier phase integer ambiguity resolution is the key to highprecision positioning and attitude determination. In this contribution, we develop new integer least-squares (ILS) theory for the GNSS compass model, together with efficient integer search strategi
On the Delone property of (−β-integers
Directory of Open Access Journals (Sweden)
Wolfgang Steiner
2011-08-01
Full Text Available The (−β-integers are natural generalisations of the β-integers, and thus of the integers, for negative real bases. They can be described by infinite words which are fixed points of anti-morphisms. We show that they are not necessarily uniformly discrete and relatively dense in the real numbers.
Integer least-squares theory for the GNSS compass
Teunissen, P.J.G.
2010-01-01
Global navigation satellite system (GNSS) carrier phase integer ambiguity resolution is the key to highprecision positioning and attitude determination. In this contribution, we develop new integer least-squares (ILS) theory for the GNSS compass model, together with efficient integer search
Supersymmetry in singular spaces
Bergshoeff, E; Kallosh, R; Van Proeyen, A
2000-01-01
We develop the concept of supersymmetry in singular spaces, apply it in an example for 3-branes in D = 5 and comment on 8-branes in D = 10. The new construction has an interpretation that the brane is a sink for the flux and requires adding to the standard supergravity a (D - 1)-form field and a sup
Supersymmetry in singular spaces
Bergshoeff, E; Kallosh, R; Van Proeyen, A
2000-01-01
We develop the concept of supersymmetry in singular spaces, apply it in an example for 3-branes in D = 5 and comment on 8-branes in D = 10. The new construction has an interpretation that the brane is a sink for the flux and requires adding to the standard supergravity a (D - 1)-form field and a
Supersymmetry in Singular Spaces
Bergshoeff, E. A.; Kallosh, R.; Proeyen, A. van
2000-01-01
Published in: J. High Energy Phys. 10 (2000) 033 citations recorded in [Science Citation Index] Abstract: We develop the concept of supersymmetry in singular spaces, apply it in an example for 3-branes in D=5 and comment on 8-branes in D=10. The new construction has an interpretation that the brane
Pseudospherical surfaces with singularities
DEFF Research Database (Denmark)
Brander, David
2016-01-01
We study a generalization of constant Gauss curvature −1 surfaces in Euclidean 3-space, based on Lorentzian harmonic maps, that we call pseudospherical frontals. We analyse the singularities of these surfaces, dividing them into those of characteristic and non-characteristic type. We give methods...
Szydlowski, Marek; Borowiec, Andrzej; Wojnar, Aneta
2015-01-01
We investigate modified gravity cosmological model $f(R)=R+\\gamma R^2$ in Palatini formalism. We consider the universe filled with the Chaplygin gas and baryonic matter. The dynamics is reduced to the 2D sewn dynamical system of a Newtonian type. For this aim we use dynamical system theory. We classify all evolutional paths in the model as well as trajectories in the phase space. We demonstrate that the presence of a degenerate freeze singularity (glued freeze type singularities) is a generic feature of early evolution of the universe. We point out that a degenerate type III of singularity can be considered as an endogenous model of inflation between the matter dominating epoch and the dark energy phase. We also investigate cosmological models with negative $\\gamma$. It is demonstrated that $\\gamma$ equal zero is a bifurcation parameter and dynamics qualitatively changes in comparison to positive $\\gamma$. Instead of the big bang the sudden singularity appears and there is a generic class of bouncing solution...
Quantum effects near future singularities
Barrow, John D; Dito, Giuseppe; Fabris, Julio C; Houndjo, Mahouton J S
2012-01-01
General relativity allows a variety of future singularities to occur in the evolution of the universe. At these future singularities, the universe will end in a singular state after a finite proper time and geometrical invariants of the space time will diverge. One question that naturally arises with respect to these cosmological scenarios is the following: can quantum effects lead to the avoidance of these future singularities? We analyze this problem considering massless and conformally coupled scalar fields in an isotropic and homogeneous background leading to future singularities. It is shown that near strong, big rip-type singularities, with violation of the energy conditions, the quantum effects are very important, while near some milder classes of singularity like the sudden singularity, which preserve the energy conditions, quantum effects are irrelevant.
Logic integer programming models for signaling networks.
Haus, Utz-Uwe; Niermann, Kathrin; Truemper, Klaus; Weismantel, Robert
2009-05-01
We propose a static and a dynamic approach to model biological signaling networks, and show how each can be used to answer relevant biological questions. For this, we use the two different mathematical tools of Propositional Logic and Integer Programming. The power of discrete mathematics for handling qualitative as well as quantitative data has so far not been exploited in molecular biology, which is mostly driven by experimental research, relying on first-order or statistical models. The arising logic statements and integer programs are analyzed and can be solved with standard software. For a restricted class of problems the logic models reduce to a polynomial-time solvable satisfiability algorithm. Additionally, a more dynamic model enables enumeration of possible time resolutions in poly-logarithmic time. Computational experiments are included.
PSLQ: An Algorithm to Discover Integer Relations
Energy Technology Data Exchange (ETDEWEB)
Bailey, David H.; Borwein, J. M.
2009-04-03
Let x = (x{sub 1}, x{sub 2} {hor_ellipsis}, x{sub n}) be a vector of real or complex numbers. x is said to possess an integer relation if there exist integers a{sub i}, not all zero, such that a{sub 1}x{sub 1} + a{sub 2}x{sub 2} + {hor_ellipsis} + a{sub n}x{sub n} = 0. By an integer relation algorithm, we mean a practical computational scheme that can recover the vector of integers ai, if it exists, or can produce bounds within which no integer relation exists. As we will see in the examples below, an integer relation algorithm can be used to recognize a computed constant in terms of a formula involving known constants, or to discover an underlying relation between quantities that can be computed to high precision. At the present time, the most effective algorithm for integer relation detection is the 'PSLQ' algorithm of mathematician-sculptor Helaman Ferguson [10, 4]. Some efficient 'multi-level' implementations of PSLQ, as well as a variant of PSLQ that is well-suited for highly parallel computer systems, are given in [4]. PSLQ constructs a sequence of integer-valued matrices B{sub n} that reduces the vector y = xB{sub n}, until either the relation is found (as one of the columns of B{sub n}), or else precision is exhausted. At the same time, PSLQ generates a steadily growing bound on the size of any possible relation. When a relation is found, the size of smallest entry of the vector y abruptly drops to roughly 'epsilon' (i.e. 10{sup -p}, where p is the number of digits of precision). The size of this drop can be viewed as a 'confidence level' that the relation is real and not merely a numerical artifact - a drop of 20 or more orders of magnitude almost always indicates a real relation. Very high precision arithmetic must be used in PSLQ. If one wishes to recover a relation of length n, with coefficients of maximum size d digits, then the input vector x must be specified to at least nd digits, and one must employ nd
Integer sparse distributed memory: analysis and results.
Snaider, Javier; Franklin, Stan; Strain, Steve; George, E Olusegun
2013-10-01
Sparse distributed memory is an auto-associative memory system that stores high dimensional Boolean vectors. Here we present an extension of the original SDM, the Integer SDM that uses modular arithmetic integer vectors rather than binary vectors. This extension preserves many of the desirable properties of the original SDM: auto-associativity, content addressability, distributed storage, and robustness over noisy inputs. In addition, it improves the representation capabilities of the memory and is more robust over normalization. It can also be extended to support forgetting and reliable sequence storage. We performed several simulations that test the noise robustness property and capacity of the memory. Theoretical analyses of the memory's fidelity and capacity are also presented.
D. Veestraeten
2015-01-01
Sums of the parabolic cylinder function for, in absolute value, growing half-integer and integer orders emerge in numerous fields such as time-series analysis, quantum optics and transmission in wireless channels. This paper derives recursion formulas for the parabolic cylinder function with integer
Solving Integer Programming by Evolutionary Soft Agent
Institute of Scientific and Technical Information of China (English)
Yin Jian
2003-01-01
Many practical problems in commerce and industry involve finding the best way to allocate scarce resources a mong competing activities. This paper focuses on the problem of integer programming, and describes an evolutionary soft agent model to solve it. In proposed model, agent is composed of three components: goal, environment and behavior. Experirnental shows thne model has the characters of parallel computing and goal driving.
Approximation by Multivariate Singular Integrals
Anastassiou, George A
2011-01-01
Approximation by Multivariate Singular Integrals is the first monograph to illustrate the approximation of multivariate singular integrals to the identity-unit operator. The basic approximation properties of the general multivariate singular integral operators is presented quantitatively, particularly special cases such as the multivariate Picard, Gauss-Weierstrass, Poisson-Cauchy and trigonometric singular integral operators are examined thoroughly. This book studies the rate of convergence of these operators to the unit operator as well as the related simultaneous approximation. The last cha
String theory and cosmological singularities
Indian Academy of Sciences (India)
Sumit R Das
2007-07-01
In general relativity space-like or null singularities are common: they imply that `time' can have a beginning or end. Well-known examples are singularities inside black holes and initial or final singularities in expanding or contracting universes. In recent times, string theory is providing new perspectives of such singularities which may lead to an understanding of these in the standard framework of time evolution in quantum mechanics. In this article, we describe some of these approaches.
Can we see naked singularities?
Deshingkar, Shrirang S.
2007-01-01
We study singularities which can form in a spherically symmetric gravitational collapse of a general matter field obeying weak energy condition. We show that no energy can reach an outside observer from a null naked singularity. That means they will not be a serious threat to the Cosmic Censorship Conjecture (CCC). For the timelike naked singularities, where only the central shell gets singular, the redshift is always finite and they can in principle, carry energy to a faraway observer. Hence...
Holographic complexity and spacetime singularities
Energy Technology Data Exchange (ETDEWEB)
Barbón, José L.F. [Instituto de Física Teórica IFT UAM/CSIC,C/ Nicolás Cabrera 13, Campus Universidad Autónoma de Madrid,Madrid 28049 (Spain); Rabinovici, Eliezer [Racah Institute of Physics, The Hebrew University,Jerusalem 91904 (Israel); Laboratoire de Physique Théorique et Hautes Energies, Université Pierre et Marie Curie, 4 Place Jussieu, 75252 Paris Cedex 05 (France)
2016-01-15
We study the evolution of holographic complexity in various AdS/CFT models containing cosmological crunch singularities. We find that a notion of complexity measured by extremal bulk volumes tends to decrease as the singularity is approached in CFT time, suggesting that the corresponding quantum states have simpler entanglement structure at the singularity.
A New Generalized FB Complementarity Function for Symmetric Cone Complementarity Problems
Institute of Scientific and Technical Information of China (English)
Zhang Yun-sheng; Gao Lei-fu∗
2016-01-01
We establish that the generalized Fischer-Burmeister(FB) function and penalized Generalized Fischer-Burmeister (FB) function defined on symmetric cones are complementarity functions (C-functions), in terms of Euclidean Jordan algebras, and the Generalized Fischer-Burmeister complementarity function for the symmetric cone complementarity problem (SCCP). It provides an aﬃrmative answer to the open question by Kum and Lim (Kum S H, Lim Y. Penalized complementarity functions on symmetric cones. J. Glob. Optim.. 2010, 46: 475–485) for any positive integer.
Chiral Condensate and Short-Time Evolution of QCD(1+1) on the Light-Cone
Burkardt, M; Thies, M; Burkardt, Matthias; Lenz, Frieder; Thies, Michael
2002-01-01
Chiral condensates in the trivial light-cone vacuum emerge if defined as short-time limits of fermion propagators. In gauge theories, the necessary inclusion of a gauge string in combination with the characteristic light-cone infrared singularities contain the relevant non-perturbative ingredients responsible for formation of the condensate, as demonstrated for the 't Hooft model.
Tunable multiple layered Dirac cones in optical lattices.
Lan, Z; Celi, A; Lu, W; Öhberg, P; Lewenstein, M
2011-12-16
We show that multiple layered Dirac cones can emerge in the band structure of properly addressed multicomponent cold fermionic gases in optical lattices. The layered Dirac cones contain multiple copies of massless spin-1/2 Dirac fermions at the same location in momentum space, whose different Fermi velocity can be tuned at will. On-site microwave Raman transitions can further be used to mix the different Dirac species, resulting in either splitting of or preserving the Dirac point (depending on the symmetry of the on-site term). The tunability of the multiple layered Dirac cones allows us to simulate a number of fundamental phenomena in modern physics, such as neutrino oscillations and exotic particle dispersions with E~p(N) for arbitrary integer N.
Singularities in loop quantum cosmology.
Cailleteau, Thomas; Cardoso, Antonio; Vandersloot, Kevin; Wands, David
2008-12-19
We show that simple scalar field models can give rise to curvature singularities in the effective Friedmann dynamics of loop quantum cosmology (LQC). We find singular solutions for spatially flat Friedmann-Robertson-Walker cosmologies with a canonical scalar field and a negative exponential potential, or with a phantom scalar field and a positive potential. While LQC avoids big bang or big rip type singularities, we find sudden singularities where the Hubble rate is bounded, but the Ricci curvature scalar diverges. We conclude that the effective equations of LQC are not in themselves sufficient to avoid the occurrence of curvature singularities.
Fractional quantum Hall states of bosons on cones
Wu, Ying-Hai; Tu, Hong-Hao; Sreejith, G. J.
2017-09-01
Motivated by a recent experiment, which synthesizes Landau levels for photons on cones [Schine et al., Nature (London) 534, 671 (2016), 10.1038/nature17943], and more generally the interest in understanding gravitational responses of quantum Hall states, we study fractional quantum Hall states of bosons on cones. A variety of trial wave functions for conical systems are constructed and compared with exact diagonalization results. The tip of a cone is a localized geometrical defect with singular curvature, which can modify the density profiles of quantum Hall states. The density profiles on cones can be used to extract some universal information about quantum Hall states. The values of certain quantities are computed numerically using the density profiles of some quantum Hall states and they agree with analytical predictions.
Holographic entanglement entropy for hollow cones and banana shaped regions
Dorn, Harald
2016-01-01
We consider banana shaped regions as examples of compact regions, whose boundary has two conical singularities. Their regularised holographic entropy is calculated with all divergent as well as finite terms. The coefficient of the squared logarithmic divergence, also in such a case with internally curved boundary, agrees with that calculated in the literature for infinite circular cones with their internally flat boundary. For the otherwise conformally invariant coefficient of the ordinary logarithmic divergence an anomaly under exceptional conformal transformations is observed. The construction of minimal submanifolds, needed for the entanglement entropy of cones, requires fine-tuning of Cauchy data. Perturbations of such fine-tuning leads to solutions relevant for hollow cones. The divergent parts for the entanglement entropy of hollow cones are calculated. Increasing the difference between the opening angles of their outer and inner boundary, one finds a transition between connected solutions for small dif...
Infinitesimal Structure of Singularities
Directory of Open Access Journals (Sweden)
Michael Heller
2017-02-01
Full Text Available Some important problems of general relativity, such as the quantisation of gravity or classical singularity problems, crucially depend on geometry on very small scales. The so-called synthetic differential geometry—a categorical counterpart of the standard differential geometry—provides a tool to penetrate infinitesimally small portions of space-time. We use this tool to show that on any “infinitesimal neighbourhood” the components of the curvature tensor are themselves infinitesimal, and construct a simplified model in which the curvature singularity disappears, owing to this effect. However, one pays a price for this result. Using topoi as a generalisation of spaces requires a weakening of arithmetic (the existence of infinitesimals and of logic (to the intuitionistic logic. Is this too high a price to pay for acquiring a new method of solving unsolved problems in physics? Without trying, we shall never know the answer.
DEFF Research Database (Denmark)
Somchaipeng, Kerawit; Sporring, Jon; Johansen, Peter
2007-01-01
We propose MultiScale Singularity Trees (MSSTs) as a structure to represent images, and we propose an algorithm for image comparison based on comparing MSSTs. The algorithm is tested on 3 public image databases and compared to 2 state-of-theart methods. We conclude that the computational complexity...... of our algorithm only allows for the comparison of small trees, and that the results of our method are comparable with state-of-the-art using much fewer parameters for image representation....
Can, T.; Chiu, Y. H.; Laskin, M.; Wiegmann, P.
2016-12-01
We study quantum Hall states on surfaces with conical singularities. We show that the electronic fluid at the cone tip possesses an intrinsic angular momentum, which is due solely to the gravitational anomaly. We also show that quantum Hall states behave as conformal primaries near singular points, with a conformal dimension equal to the angular momentum. Finally, we argue that the gravitational anomaly and conformal dimension determine the fine structure of the electronic density at the conical point. The singularities emerge as quasiparticles with spin and exchange statistics arising from adiabatically braiding conical singularities. Thus, the gravitational anomaly, which appears as a finite size correction on smooth surfaces, dominates geometric transport on singular surfaces.
Neural Excitability and Singular Bifurcations.
De Maesschalck, Peter; Wechselberger, Martin
2015-12-01
We discuss the notion of excitability in 2D slow/fast neural models from a geometric singular perturbation theory point of view. We focus on the inherent singular nature of slow/fast neural models and define excitability via singular bifurcations. In particular, we show that type I excitability is associated with a novel singular Bogdanov-Takens/SNIC bifurcation while type II excitability is associated with a singular Andronov-Hopf bifurcation. In both cases, canards play an important role in the understanding of the unfolding of these singular bifurcation structures. We also explain the transition between the two excitability types and highlight all bifurcations involved, thus providing a complete analysis of excitability based on geometric singular perturbation theory.
Photonic Landau levels on cones
Schine, Nathan; Ryou, Albert; Gromov, Andrey; Sommer, Ariel; Simon, Jonathan
2016-05-01
We present the first experimental realization of a bulk magnetic field for optical photons. By using a non-planar ring resonator, we induce an image rotation on each round trip through the resonator. This results in a Coriolis/Lorentz force and a centrifugal anticonfining force, the latter of which is cancelled by mirror curvature. Using a digital micromirror device to control both amplitude and phase, we inject arbitrary optical modes into our resonator. Spatial- and energy- resolved spectroscopy tracks photonic eigenstates as residual trapping is reduced, and we observe photonic Landau levels as the eigenstates become degenerate. We show that there is a conical geometry of the resulting manifold for photon dynamics and present a measurement of the local density of states that is consistent with Landau levels on a cone. While our work already demonstrates an integer quantum Hall material composed of photons, we have ensured compatibility with strong photon-photon interactions, which will allow quantum optical studies of entanglement and correlation in manybody systems including fractional quantum Hall fluids.
Decimal Integer Multiplication based on Molecular Beacons
Directory of Open Access Journals (Sweden)
Jing Wang
2013-12-01
Full Text Available Due to the enhancement of circuit integration level, and the accelerating of working frequency of traditional computer, it requires components dimension must be constantly decreased. So encapsulation, etching and other problems of chip are becoming more and more difficult to solve, which causes its performance also become unstable. In order to overcome this problem, DNA computing as a new kind of molecular computing mode, with its high parallelism, huge amounts of storage capacity, low energy consumption advantages has received extensive attention. Being the same with traditional electronic computer, DNA computer is composed by arithmetic operations such as addition, subtraction, multiplication and dividing and basic logic units such as AND, OR, NON gate. This paper puts forward a new method to realize decimal integer multiplication based on molecular beacons. The algorithm firstly converts decimal integer to binary number, and then resolves the multiplication process into multiplication of current bit and addition of intermediate result after shifting two steps. Molecular beacon is used as multiplying unit, coding sequence is used as multiplier in this method. Based on the working principle of molecular beacon, multiplication operation of two one-bit binary is simulated. And by recording fluorescence status of molecular beacon to observe intermediate result and carry-bit situation, the final result can be obtained through addition after shifting. Examples prove that this method can realize decimal integer multiplication rapidly and accurately. This method is similar to multiplication system in traditional electronic computer, and it provides a simple, easier operation method for DNA computer to realize arithmetic operation.
Integer Set Compression and Statistical Modeling
DEFF Research Database (Denmark)
Larsson, N. Jesper
2014-01-01
Compression of integer sets and sequences has been extensively studied for settings where elements follow a uniform probability distribution. In addition, methods exist that exploit clustering of elements in order to achieve higher compression performance. In this work, we address the case where...... enumeration of elements may be arbitrary or random, but where statistics is kept in order to estimate probabilities of elements. We present a recursive subset-size encoding method that is able to benefit from statistics, explore the effects of permuting the enumeration order based on element probabilities...
Division Unit for Binary Integer Decimals
DEFF Research Database (Denmark)
Lang, Tomas; Nannarelli, Alberto
2009-01-01
-recurrence algorithm to BID representation and implement the division unit in standard cell technology. The implementation of the proposed BID division unit is compared to that of a BCD based unit implementing the same algorithm. The comparison shows that for normalized operands the BID unit has the same latency......In this work, we present a radix-10 division unit that is based on the digit-recurrence algorithm and implements binary encodings (binary integer decimal or BID) for significands. Recent decimal division designs are all based on the binary coded decimal (BCD) encoding. We adapt the radix-10 digit...
Indian Academy of Sciences (India)
Oscar Valero
2006-05-01
Given a normed cone (, ) and a subcone , we construct and study the quotient normed cone $(X/Y,\\tilde{p})$ generated by . In particular we characterize the bicompleteness of $(X/Y,\\tilde{p})$ in terms of the bicompleteness of (, ), and prove that the dual quotient cone $((X/Y)^∗,\\|\\cdot\\|_{\\tilde{p},u})$ can be identified as a distinguished subcone of the dual cone $(X^∗,\\|\\cdot\\|_{\\tilde{p},u})$. Furthermore, some parts of the theory are presented in the general setting of the space $CL(X,Y)$ of all continuous linear mappings from a normed cone (, ) to a normed cone (, ), extending several well-known results related to open continuous linear mappings between normed linear spaces.
Positive Solutions for Nonlinear Singular Differential Systems Involving Parameter on the Half-Line
Directory of Open Access Journals (Sweden)
Lishan Liu
2012-01-01
Full Text Available By using the upper-lower solutions method and the fixed-point theorem on cone in a special space, we study the singular boundary value problem for systems of nonlinear second-order differential equations involving two parameters on the half-line. Some results for the existence, nonexistence and multiplicity of positive solutions for the problem are obtained.
Quantum Singularity of Quasiregular Spacetimes
Konkowski, Deborah A.; Helliwell, Thomas M.
2001-04-01
A quasiregular spacetime is a spacetime with a classical quasiregular singularity, the mildest form of true singularity [G.F.R. Ellis and B.G. Schmidt, Gen. Rel. Grav. 8, 915 (1977)]. The definition of G.T. Horowitz and D. Marolf [Phys. Rev. D52, 5670 (1995)] for a quantum-mechanically singular spacetime is one in which the spatial-derivative operator in the Klein-Gordon equation for a massive scalar field is not essentially self-adjoint. In such a quantum-mechanically singular spacetime, the time evolution of a quantum test particle is not uniquely determined. Horowitz and Marolf showed that a two-dimensional spacetime with a classical conical singularity (i.e., a two-dimensional quasiregular singularity) is also quantum-mechanically singular. Here we show that a class of static quasiregular spacetimes possessing disclinations and dislocations [R.A.Puntigam and H.H. Soleng , Class. Quantum Grav. 14, 1129 (1997)] is quantum-mechanically singular, since the scalar wave operator is not essentially self-adjoint. These spacetimes include an idealized cosmic string spacetime, i.e., a four-dimensional spacetime with conical singularity, and a Galtsov/Letelier/Tod spacetime featuring a screw dislocation [K.P. Tod, Class. Quantum Grav. 11, 1331 (1994); D.V. Galtsov and P.S. Letelier, Phys. Rev. D47, 4273 (1993)]. In addition, we show that the definition of quantum-mechanically singular spacetimes can be extended to include Maxwell and Dirac fields.
Bornological Locally Convex Cones
Directory of Open Access Journals (Sweden)
Davood Ayaseh
2014-10-01
Full Text Available In this paper we define bornological and b-bornological cones and investigate their properties. We give some characterization for these cones. In the special case of locally convex topological vector space both these concepts reduce to the known concept of bornological spaces. We introduce and investigate the convex quasiuniform structures U_{tau}, U_{sigma}(P,P* and \\U_{beta}(P,P* on locally convex cone (P,U.
Energy Technology Data Exchange (ETDEWEB)
Lask, Kathleen [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Gadgil, Ashok [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
2016-10-24
A lighting cone is a simple metal cone placed on the fuel bed of a stove during ignition to act as a chimney, increasing the draft through the fuel bed. Many stoves tend to be difficult to light due to poor draft through the fuel bed, so lighting cones are used in various parts of the world as an inexpensive accessory to help with ignition.
Horizontal visibility graphs from integer sequences
Lacasa, Lucas
2016-09-01
The horizontal visibility graph (HVG) is a graph-theoretical representation of a time series and builds a bridge between dynamical systems and graph theory. In recent years this representation has been used to describe and theoretically compare different types of dynamics and has been applied to characterize empirical signals, by extracting topological features from the associated HVGs which have shown to be informative on the class of dynamics. Among some other measures, it has been shown that the degree distribution of these graphs is a very informative feature that encapsulates nontrivial information of the series's generative dynamics. In particular, the HVG associated to a bi-infinite real-valued series of independent and identically distributed random variables is a universal exponential law P(k)=(1/3){(2/3)}k-2, independent of the series marginal distribution. Most of the current applications have however only addressed real-valued time series, as no exact results are known for the topological properties of HVGs associated to integer-valued series. In this paper we explore this latter situation and address univariate time series where each variable can only take a finite number n of consecutive integer values. We are able to construct an explicit formula for the parametric degree distribution {P}n(k), which we prove to converge to the continuous case for large n and deviates otherwise. A few applications are then considered.
Network interdiction and stochastic integer programming
2003-01-01
On March 15, 2002 we held a workshop on network interdiction and the more general problem of stochastic mixed integer programming at the University of California, Davis. Jesús De Loera and I co-chaired the event, which included presentations of on-going research and discussion. At the workshop, we decided to produce a volume of timely work on the topics. This volume is the result. Each chapter represents state-of-the-art research and all of them were refereed by leading investigators in the respective fields. Problems - sociated with protecting and attacking computer, transportation, and social networks gain importance as the world becomes more dep- dent on interconnected systems. Optimization models that address the stochastic nature of these problems are an important part of the research agenda. This work relies on recent efforts to provide methods for - dressing stochastic mixed integer programs. The book is organized with interdiction papers first and the stochastic programming papers in the second part....
An experiment on Lowest Unique Integer Games
Yamada, Takashi; Hanaki, Nobuyuki
2016-12-01
We experimentally study Lowest Unique Integer Games (LUIGs) to determine if and how subjects self-organize into different behavioral classes. In a LUIG, N(≥ 3) players submit a positive integer up to M and the player choosing the smallest number not chosen by anyone else wins. LUIGs are simplified versions of real systems such as Lowest/Highest Unique Bid Auctions that have been attracting attention from scholars, yet experimental studies are scarce. Furthermore, LUIGs offer insights into choice patterns that can shed light on the alleviation of congestion problems. Here, we consider four LUIGs with N = { 3 , 4 } and M = { 3 , 4 } . We find that (a) choices made by more than 1/3 of subjects were not significantly different from what a symmetric mixed-strategy Nash equilibrium (MSE) predicts; however, (b) subjects who behaved significantly differently from what the MSE predicts won the game more frequently. What distinguishes subjects was their tendencies to change their choices following losses.
Prime labeling of families of trees with Gaussian integers
Directory of Open Access Journals (Sweden)
Steven Klee
2016-08-01
Full Text Available A graph on n vertices is said to admit a prime labeling if we can label its vertices with the first n natural numbers such that any two adjacent vertices have relatively prime labels. Here we extend the idea of prime labeling to the Gaussian integers, which are the complex numbers whose real and imaginary parts are both integers. We begin by defining an order on the Gaussian integers that lie in the first quadrant. Using this ordering, we show that several families of trees admit a prime labeling with the Gaussian integers.
Dilatonic effects near naked singularities
Morris, J R
2011-01-01
Static spherically symmetric solutions of 4d Brans-Dicke theory include a set of naked singularity solutions. Dilatonic effects near the naked singularities result in either a shielding or an antishielding effect from intruding massive test particles. One result is that for a portion of the solution parameter space, no communication between the singularity and a distant observer is possible via massive particle exchanges. Kaluza-Klein gravity is considered as a special case.
How Does Naked Singularity Look?
Nakao, Ken-ichi; Kobayashi, Naoki; Ishihara, Hideki
2002-01-01
There are non-radial null geodesics emanating from the shell focusing singularity formed at the symmetric center in a spherically symmetric dust collapse. In this article, assuming the self-similarity in the region filled with the dust fluid, we study these singular null geodesics in detail. We see the time evolution of the angular diameter of the central naked singularity and show that it might be bounded above by the value corresponding to the circular null geodesic in the Schwarzschild spa...
On the use of Kontorovich-Lebedev transform in electromagnetic diffraction by an impedance cone
Salem, Mohamed
2012-08-01
We consider the boundary-value problem for the Helmholtz equation connected with an infinite circular cone with an impedance boundary on its face. The scheme of solution includes applying the Kontorovich-Lebedev (KL) transform to reduce the problem to that of a KL spectral amplitude function satisfying a singular integral equation of the non-convolution type with a variable coefficient. The singularities of the spectral function are deduced and representations for the field at the tip of the cone and in the near and far field regions are given together with the conditions of validity of these representations. © 2012 IEEE.
Smithson, Hannah E
2014-03-01
We review the features of the S-cone system that appeal to the psychophysicist and summarize the celebrated characteristics of S-cone mediated vision. Two factors are emphasized: First, the fine stimulus control that is required to isolate putative visual mechanisms and second, the relationship between physiological data and psychophysical approaches. We review convergent findings from physiology and psychophysics with respect to asymmetries in the retinal wiring of S-ON and S-OFF visual pathways, and the associated treatment of increments and decrements in the S-cone system. Beyond the retina, we consider the lack of S-cone projections to superior colliculus and the use of S-cone stimuli in experimental psychology, for example to address questions about the mechanisms of visually driven attention. Careful selection of stimulus parameters enables psychophysicists to produce entirely reversible, temporary, "lesions," and to assess behavior in the absence of specific neural subsystems.
Holographic entanglement entropy for hollow cones and banana shaped regions
Dorn, Harald
2016-06-01
We consider banana shaped regions as examples of compact regions, whose boundary has two conical singularities. Their regularised holographic entropy is calculated with all divergent as well as finite terms. The coefficient of the squared logarithmic divergence, also in such a case with internally curved boundary, agrees with that calculated in the literature for infinite circular cones with their internally flat boundary. For the otherwise conformally invariant coefficient of the ordinary logarithmic divergence an anomaly under exceptional conformal transformations is observed.
On Secure Two-Party Integer Division
DEFF Research Database (Denmark)
Dahl, Morten; Ning, Chao; Toft, Tomas
2012-01-01
We consider the problem of secure integer division: given two Paillier encryptions of ℓ-bit values n and d, determine an encryption of $\\lfloor \\frac{n}{d}\\rfloor$ without leaking any information about n or d. We propose two new protocols solving this problem. The first requires $\\ensuremath......{\\mathcal{O}}(\\ell)$ arithmetic operations on encrypted values (secure addition and multiplication) in $\\ensuremath{\\mathcal{O}}(1)$ rounds. This is the most efficient constant-rounds solution to date. The second protocol requires only $\\ensuremath{\\mathcal{O}} \\left( (\\log^2 \\ell)(\\kappa + \\operatorname{loglog} \\ell) \\right......)$ arithmetic operations in $\\ensuremath{\\mathcal{O}}(\\log^2 \\ell)$ rounds, where κ is a correctness parameter. Theoretically, this is the most efficient solution to date as all previous solutions have required Ω(ℓ) operations. Indeed, the fact that an o(ℓ) solution is possible at all is highly surprising....
Bivium as a Mixed Integer Programming Problem
DEFF Research Database (Denmark)
Borghoff, Julia; Knudsen, Lars Ramkilde; Stolpe, Mathias
2009-01-01
Trivium is a stream cipher proposed for the eSTREAM project. Raddum introduced some reduced versions of Trivium, named Bivium A and Bivium B. In this article we present a numerical attack on the Biviums. The main idea is to transform the problem of solving a sparse system of quadratic equations...... over $GF(2)$ into a combinatorial optimization problem. We convert the Boolean equation system into an equation system over $\\mathbb{R}$ and formulate the problem of finding a $0$-$1$-valued solution for the system as a mixed-integer programming problem. This enables us to make use of several...... algorithms in the field of combinatorial optimization in order to find a solution for the problem and recover the initial state of Bivium. In particular this gives us an attack on Bivium B in estimated time complexity of $2^{63.7}$ seconds. But this kind of attack is also applicable to other cryptographic...
Statistical Mechanical Models of Integer Factorization Problem
Nakajima, Chihiro H.; Ohzeki, Masayuki
2017-01-01
We formulate the integer factorization problem via a formulation of the searching problem for the ground state of a statistical mechanical Hamiltonian. The first passage time required to find a correct divisor of a composite number signifies the exponential computational hardness. The analysis of the density of states of two macroscopic quantities, i.e., the energy and the Hamming distance from the correct solutions, leads to the conclusion that the ground state (correct solution) is completely isolated from the other low-energy states, with the distance being proportional to the system size. In addition, the profile of the microcanonical entropy of the model has two peculiar features that are each related to two marked changes in the energy region sampled via Monte Carlo simulation or simulated annealing. Hence, we find a peculiar first-order phase transition in our model.
Ensemble segmentation using efficient integer linear programming.
Alush, Amir; Goldberger, Jacob
2012-10-01
We present a method for combining several segmentations of an image into a single one that in some sense is the average segmentation in order to achieve a more reliable and accurate segmentation result. The goal is to find a point in the "space of segmentations" which is close to all the individual segmentations. We present an algorithm for segmentation averaging. The image is first oversegmented into superpixels. Next, each segmentation is projected onto the superpixel map. An instance of the EM algorithm combined with integer linear programming is applied on the set of binary merging decisions of neighboring superpixels to obtain the average segmentation. Apart from segmentation averaging, the algorithm also reports the reliability of each segmentation. The performance of the proposed algorithm is demonstrated on manually annotated images from the Berkeley segmentation data set and on the results of automatic segmentation algorithms.
Superposition of two optical vortices with opposite integer or non-integer orbital angular momentum
Directory of Open Access Journals (Sweden)
Carlos Fernando Díaz Meza
2016-04-01
Full Text Available This work develops a brief proposal to achieve the superposition of two opposite vortex beams, both with integer or non-integer mean value of the orbital angular momentum. The first part is about the generation of this kind of spatial light distributions through a modified Brown and Lohmann’s hologram. The inclusion of a simple mathematical expression into the pixelated grid’s transmittance function, based in Fourier domain properties, shifts the diffraction orders counterclockwise and clockwise to the same point and allows the addition of different modes. The strategy is theoretically and experimentally validated for the case of two opposite rotation helical wavefronts.
Garbage-free reversible constant multipliers for arbitrary integers
DEFF Research Database (Denmark)
Mogensen, Torben Ægidius
2013-01-01
We present a method for constructing reversible circuitry for multiplying integers by arbitrary integer constants. The method is based on Mealy machines and gives circuits whose size are (in the worst case) linear in the size of the constant. This makes the method unsuitable for large constants......, but gives quite compact circuits for small constants. The circuits use no garbage or ancillary lines....
On the Relationship between Integer Lifting and Rounding Transform
Directory of Open Access Journals (Sweden)
R. Vargic
2007-12-01
Full Text Available In this paper we analyze the relationship between integer Lifting scheme and Rounding transform as means to compute the wavelet transform in signal processing area. We bring some new results which better describe relationship, reversibility and equivalence of integer lifting scheme and rounding transform concept.
A Paper-and-Pencil gcd Algorithm for Gaussian Integers
Szabo, Sandor
2005-01-01
As with natural numbers, a greatest common divisor of two Gaussian (complex) integers "a" and "b" is a Gaussian integer "d" that is a common divisor of both "a" and "b". This article explores an algorithm for such gcds that is easy to do by hand.
Pseudo-differential operators on manifolds with singularities
Schulze, B-W
1991-01-01
The analysis of differential equations in domains and on manifolds with singularities belongs to the main streams of recent developments in applied and pure mathematics. The applications and concrete models from engineering and physics are often classical but the modern structure calculus was only possible since the achievements of pseudo-differential operators. This led to deep connections with index theory, topology and mathematical physics. The present book is devoted to elliptic partial differential equations in the framework of pseudo-differential operators. The first chapter contains the Mellin pseudo-differential calculus on R+ and the functional analysis of weighted Sobolev spaces with discrete and continuous asymptotics. Chapter 2 is devoted to the analogous theory on manifolds with conical singularities, Chapter 3 to manifolds with edges. Employed are pseudo-differential operators along edges with cone-operator-valued symbols.
Bunge, Marta
2006-01-01
The self-contained theory of certain singular coverings of toposes called complete spreads, that is presented in this volume, is a field of interest to topologists working in knot theory, as well as to various categorists. It extends the complete spreads in topology due to R. H. Fox (1957) but, unlike the classical theory, it emphasizes an unexpected connection with topos distributions in the sense of F. W. Lawvere (1983). The constructions, though often motivated by classical theories, are sometimes quite different from them. Special classes of distributions and of complete spreads, inspired respectively by functional analysis and topology, are studied. Among the former are the probability distributions; the branched coverings are singled out amongst the latter. This volume may also be used as a textbook for an advanced one-year graduate course introducing topos theory with an emphasis on geometric applications. Throughout the authors emphasize open problems. Several routine proofs are left as exercises, but...
A SINGULARLY UNFEMININE PROFESSION
2016-01-01
Mary K Gaillard back to CERN to present her book and talk diversity - In 1981 Mary K Gaillard became the first woman on the physics faculty at the University of California at Berkeley. Her career as a theoretical physicist spanned the period from the inception — in the late 1960s and early 1970s — of what is now known as the Standard Model of particle physics and its experimental confirmation, culminating with the discovery of the Higgs particle in 2012. Her book A Singularly Unfeminine Profession recounts Gaillard's experiences as a woman in a very male-dominated field, while tracing the development of the Standard Model as she witnessed it and participated in it.
Entanglement Entropy for Singular Surfaces
Myers, Robert C
2012-01-01
We study entanglement entropy for regions with a singular boundary in higher dimensions using the AdS/CFT correspondence and find that various singularities make new universal contributions. When the boundary CFT has an even spacetime dimension, we find that the entanglement entropy of a conical surface contains a term quadratic in the logarithm of the UV cut-off. In four dimensions, the coefficient of this contribution is proportional to the central charge 'c'. A conical singularity in an odd number of spacetime dimensions contributes a term proportional to the logarithm of the UV cut-off. We also study the entanglement entropy for various boundary surfaces with extended singularities. In these cases, similar universal terms may appear depending on the dimension and curvature of the singular locus.
The super-Virasoro singular vectors and Jack superpolynomials relationship revisited
Blondeau-Fournier, O.; Mathieu, P.; Ridout, D.; Wood, S.
2016-12-01
A recent novel derivation of the representation of Virasoro singular vectors in terms of Jack polynomials is extended to the supersymmetric case. The resulting expression of a generic super-Virasoro singular vector is given in terms of a simple differential operator (whose form is characteristic of the sector, Neveu-Schwarz or Ramond) acting on a Jack superpolynomial. The latter is indexed by a superpartition depending upon the two integers r , s that specify the reducible module under consideration. The corresponding singular vector (at grade rs / 2), when expanded as a linear combination of Jack superpolynomials, results in an expression that (in addition to being proved) turns out to be more compact than those that have been previously conjectured. As an aside, in relation with the differential operator alluded to above, a remarkable property of the Jack superpolynomials at α = - 3 is pointed out.
Central charge from adiabatic transport of cusp singularities in the quantum Hall effect
Can, Tankut
2017-04-01
We study quantum Hall (QH) states on a punctured Riemann sphere. We compute the Berry curvature under adiabatic motion in the moduli space in the large N limit. The Berry curvature is shown to be finite in the large N limit and controlled by the conformal dimension of the cusp singularity, a local property of the mean density. Utilizing exact sum rules obtained from a Ward identity, we show that for the Laughlin wave function, the dimension of a cusp singularity is given by the central charge, a robust geometric response coefficient in the QHE. Thus, adiabatic transport of curvature singularities can be used to determine the central charge of QH states. We also consider the effects of threaded fluxes and spin-deformed wave functions. Finally, we give a closed expression for all moments of the mean density in the integer QH state on a punctured disk.
Central charge from adiabatic transport of cusp singularities in the quantum Hall effect
Can, Tankut
2016-01-01
We study quantum Hall (QH) states on a punctured Riemann sphere. We compute the Berry curvature under adiabatic motion in the moduli space in the large N limit. The Berry curvature is shown to be finite in the large N limit and controlled by the conformal dimension of the cusp singularity, a local property of the mean density. Utilizing exact sum rules obtained from a Ward identity, we show that for the Laughlin wave function, the dimension of a cusp singularity is given by the central charge, a robust geometric response coefficient in the QHE. Thus, adiabatic transport of curvature singularities can be used to determine the central charge of QH states. We also consider the effects of threaded fluxes and spin-deformed wave functions. Finally, we give a closed expression for all moments of the mean density in the integer QH state on a punctured disk.
Discrete Dirac equation on a finite half-integer lattice
Smalley, L. L.
1986-01-01
The formulation of the Dirac equation on a discrete lattice with half-integer spacing and periodic boundary conditions is investigated analytically. The importance of lattice formulations for problems in field theory and quantum mechanics is explained; the concept of half-integer Fourier representation is introduced; the discrete Dirac equation for the two-dimensional case is derived; dispersion relations for the four-dimensional case are developed; and the spinor formulation for the Dirac fields on the half-integer lattice and the discrete time variable for the four-dimensional time-dependent Dirac equation are obtained. It is argued that the half-integer lattice, because it takes the Dirac Lagrangian into account, is more than a mere relabeling of the integer lattice and may have fundamental physical meaning (e.g., for the statistics of fermions). It is noted that the present formulation does not lead to species doubling, except in the continuum limit.
Cook, Geoffrey M W; Jareonsettasin, Prem; Keynes, Roger J
2014-01-01
The growth cone collapse assay has proved invaluable in detecting and purifying axonal repellents. Glycoproteins/proteins present in detergent extracts of biological tissues are incorporated into liposomes, added to growth cones in culture and changes in morphology are then assessed. Alternatively purified or recombinant molecules in aqueous solution may be added directly to the cultures. In both cases after a defined period of time (up to 1 h), the cultures are fixed and then assessed by inverted phase contrast microscopy for the percentage of growth cones showing a collapsed profile with loss of flattened morphology, filopodia, and lamellipodia.
Naked singularities are not singular in distorted gravity
Energy Technology Data Exchange (ETDEWEB)
Garattini, Remo, E-mail: Remo.Garattini@unibg.it [Università degli Studi di Bergamo, Facoltà di Ingegneria, Viale Marconi 5, 24044 Dalmine (Bergamo) (Italy); I.N.F.N. – sezione di Milano, Milan (Italy); Majumder, Barun, E-mail: barunbasanta@iitgn.ac.in [Indian Institute of Technology Gandhinagar, Ahmedabad, Gujarat 382424 (India)
2014-07-15
We compute the Zero Point Energy (ZPE) induced by a naked singularity with the help of a reformulation of the Wheeler–DeWitt equation. A variational approach is used for the calculation with Gaussian Trial Wave Functionals. The one loop contribution of the graviton to the ZPE is extracted keeping under control the UltraViolet divergences by means of a distorted gravitational field. Two examples of distortion are taken under consideration: Gravity's Rainbow and Noncommutative Geometry. Surprisingly, we find that the ZPE is no more singular when we approach the singularity.
McGetchin, T R; Head, J W
1973-04-01
Data on terrestrial eruptions of pyroclastic material and ballistic considerations suggest that in the lunar environment (vacuum and reduced gravity) low-rimmed pyroclastic rings are formed rather than the high-rimmed cinder cones so abundant on the earth. Dark blanketing deposits in the Taurus-Littrow region (Apollo 17 landing area) are interpreted as being at least partly composed of lunar counterparts of terrestrial cinder cones.
The theory of singular perturbations
De Jager, E M
1996-01-01
The subject of this textbook is the mathematical theory of singular perturbations, which despite its respectable history is still in a state of vigorous development. Singular perturbations of cumulative and of boundary layer type are presented. Attention has been given to composite expansions of solutions of initial and boundary value problems for ordinary and partial differential equations, linear as well as quasilinear; also turning points are discussed. The main emphasis lies on several methods of approximation for solutions of singularly perturbed differential equations and on the mathemat
BOUNDEDNESS OF MAXIMAL SINGULAR INTEGRALS
Institute of Scientific and Technical Information of China (English)
CHEN JIECHENG; ZHU XIANGRONG
2005-01-01
The authors study the singular integrals under the Hormander condition and the measure not satisfying the doubling condition. At first, if the corresponding singular integral is bounded from L2 to itseff, it is proved that the maximal singu lar integral is bounded from L∞ to RBMO except that it is infinite μ-a.e. on Rd. A sufficient condition and a necessary condition such that the maximal singular integral is bounded from L2 to itself are also obtained. There is a small gap between the two conditions.
Singular solutions to Protter's problem for the 3-D wave equation involving lower order terms
Directory of Open Access Journals (Sweden)
Myron K. Grammatikopoulos
2003-01-01
Full Text Available In 1952, at a conference in New York, Protter formulated some boundary value problems for the wave equation, which are three-dimensional analogues of the Darboux problems (or Cauchy-Goursat problems on the plane. Protter studied these problems in a 3-D domain $Omega_0$, bounded by two characteristic cones $Sigma_1$ and $Sigma_{2,0}$, and by a plane region $Sigma_0$. It is well known that, for an infinite number of smooth functions in the right-hand side, these problems do not have classical solutions. Popivanov and Schneider (1995 discovered the reason of this fact for the case of Dirichlet's and Neumann's conditions on $Sigma_0$: the strong power-type singularity appears in the generalized solution on the characteristic cone $Sigma_{2,0}$. In the present paper we consider the case of third boundary-value problem on $Sigma_0$ and obtain the existence of many singular solutions for the wave equation involving lower order terms. Especifica ally, for Protter's problems in $mathbb{R}^{3}$ it is shown here that for any $nin N$ there exists a $C^{n}({Omega}_0$-function, for which the corresponding unique generalized solution belongs to $C^{n}({Omega}_0slash O$ and has a strong power type singularity at the point $O$. This singularity is isolated at the vertex $O$ of the characteristic cone $Sigma_{2,0}$ and does not propagate along the cone. For the wave equation without lower order terms, we presented the exact behavior of the singular solutions at the point $O$.
Contrast structure for singular singularly perturbed boundary value problem
Institute of Scientific and Technical Information of China (English)
王爱峰; 倪明康
2014-01-01
The step-type contrast structure for a singular singularly perturbed problem is shown. By use of the method of boundary function, the formal asymptotic expansion is constructed. At the same time, based on sewing orbit smooth, the existence of the step-type solution and the uniform validity of the asymptotic expansion are proved. Finally, an example is given to demonstrate the effectiveness of the present results.
Integer lattice dynamics for Vlasov-Poisson
Mocz, Philip; Succi, Sauro
2017-03-01
We revisit the integer lattice (IL) method to numerically solve the Vlasov-Poisson equations, and show that a slight variant of the method is a very easy, viable, and efficient numerical approach to study the dynamics of self-gravitating, collisionless systems. The distribution function lives in a discretized lattice phase-space, and each time-step in the simulation corresponds to a simple permutation of the lattice sites. Hence, the method is Lagrangian, conservative, and fully time-reversible. IL complements other existing methods, such as N-body/particle mesh (computationally efficient, but affected by Monte Carlo sampling noise and two-body relaxation) and finite volume (FV) direct integration schemes (expensive, accurate but diffusive). We also present improvements to the FV scheme, using a moving-mesh approach inspired by IL, to reduce numerical diffusion and the time-step criterion. Being a direct integration scheme like FV, IL is memory limited (memory requirement for a full 3D problem scales as N6, where N is the resolution per linear phase-space dimension). However, we describe a new technique for achieving N4 scaling. The method offers promise for investigating the full 6D phase-space of collisionless systems of stars and dark matter.
Integer Lattice Dynamics for Vlasov-Poisson
Mocz, Philip
2016-01-01
We revisit the integer lattice (IL) method to numerically solve the Vlasov-Poisson equations, and show that a slight variant of the method is a very easy, viable, and efficient numerical approach to study the dynamics of self-gravitating, collisionless systems. The distribution function lives in a discretized lattice phase-space, and each time-step in the simulation corresponds to a simple permutation of the lattice sites. Hence, the method is Lagrangian, conservative, and fully time-reversible. IL complements other existing methods, such as N-body/particle mesh (computationally efficient, but affected by Monte-Carlo sampling noise and two-body relaxation) and finite volume (FV) direct integration schemes (expensive, accurate but diffusive). We also present improvements to the FV scheme, using a moving mesh approach inspired by IL, to reduce numerical diffusion and the time-step criterion. Being a direct integration scheme like FV, IL is memory limited (memory requirement for a full 3D problem scales as N^6, ...
The integer quantum hall effect revisited
Energy Technology Data Exchange (ETDEWEB)
Michalakis, Spyridon [Los Alamos National Laboratory; Hastings, Matthew [Q STATION, CALIFORNIA
2009-01-01
For T - L x L a finite subset of Z{sup 2}, let H{sub o} denote a Hamiltonian on T with periodic boundary conditions and finite range, finite strength intetactions and a unique ground state with a nonvanishing spectral gap. For S {element_of} T, let q{sub s} denote the charge at site s and assume that the total charge Q = {Sigma}{sub s {element_of} T} q{sub s} is conserved. Using the local charge operators q{sub s}, we introduce a boundary magnetic flux in the horizontal and vertical direction and allow the ground state to evolve quasiadiabatically around a square of size one magnetic flux, in flux space. At the end of the evolution we obtain a trivial Berry phase, which we compare, via a method reminiscent of Stokes Theorem. to the Berry phase obtained from an evolution around an exponentially small loop near the origin. As a result, we show, without any averaging assumption, that the Hall conductance is quantized in integer multiples of e{sup 2}/h up to exponentially small corrections of order e{sup -L/{zeta}}, where {zeta}, is a correlation length that depends only on the gap and the range and strength of the interactions.
Diversity and non-integer differentiation for system dynamics
Oustaloup, Alain
2014-01-01
Based on a structured approach to diversity, notably inspired by various forms of diversity of natural origins, Diversity and Non-integer Derivation Applied to System Dynamics provides a study framework to the introduction of the non-integer derivative as a modeling tool. Modeling tools that highlight unsuspected dynamical performances (notably damping performances) in an ""integer"" approach of mechanics and automation are also included. Written to enable a two-tier reading, this is an essential resource for scientists, researchers, and industrial engineers interested in this subject area. Ta
Generalization of a few results in Integer Partitions
Dastidar, Manosij Ghosh
2011-01-01
In this paper, we generalize a few important results in Integer Partitions; namely the results known as Stanley's theorem and Elder's theorem, and the congruence results proposed by Ramanujan for the partition function. We generalize the results of Stanley and Elder from a fixed integer to an array of subsequent integers, and propose an analogue of Ramanujan's congruence relations for the `number of parts' function instead of the partition function. We also deduce the generating function for the `number of parts', and relate the technical results with their graphical interpretations through a novel use of the Ferrer's diagrams.
Gravitational collapse and naked singularities
Indian Academy of Sciences (India)
Tomohiro Harada
2004-10-01
Gravitational collapse is one of the most striking phenomena in gravitational physics. The cosmic censorship conjecture has provided strong motivation for research in this field. In the absence of a general proof for censorship, many examples have been proposed, in which naked singularity is the outcome of gravitational collapse. Recent developments have revealed that there are examples of naked singularity formation in the collapse of physically reasonable matter fields, although the stability of these examples is still uncertain. We propose the concept of `effective naked singularities', which will be quite helpful because general relativity has limitation in its application at the high-energy end. The appearance of naked singularities is not detestable but can open a window for the new physics of strongly curved space-times.
Holographic signatures of cosmological singularities.
Engelhardt, Netta; Hertog, Thomas; Horowitz, Gary T
2014-09-19
To gain insight into the quantum nature of cosmological singularities, we study anisotropic Kasner solutions in gauge-gravity duality. The dual description of the bulk evolution towards the singularity involves N=4 super Yang-Mills theory on the expanding branch of deformed de Sitter space and is well defined. We compute two-point correlators of Yang-Mills operators of large dimensions using spacelike geodesics anchored on the boundary. The correlators show a strong signature of the singularity around horizon scales and decay at large boundary separation at different rates in different directions. More generally, the boundary evolution exhibits a process of particle creation similar to that in inflation. This leads us to conjecture that information on the quantum nature of cosmological singularities is encoded in long-wavelength features of the boundary wave function.
Penrose Limits and Spacetime Singularities
Blau, Matthias; O'Loughlin, M; Papadopoulos, G; Blau, Matthias; Borunda, Monica; Loughlin, Martin O'; Papadopoulos, George
2003-01-01
We give a covariant characterisation of the Penrose plane wave limit: the plane wave profile matrix $A(u)$ is the restriction of the null geodesic deviation matrix (curvature tensor) of the original spacetime metric to the null geodesic, evaluated in a comoving frame. We also consider the Penrose limits of spacetime singularities and show that for a large class of black hole, cosmological and null singularities (of Szekeres-Iyers ``power-law type''), including those of the FRW and Schwarzschild metrics, the result is a singular homogeneous plane wave with profile $A(u)\\sim u^{-2}$, the scale invariance of the latter reflecting the power-law behaviour of the singularities.
Dual geometries and spacetime singularities
Quirós, I
2000-01-01
The concept of geometrical duality is disscused in the context of Brans-Dicke theory and extended to general relativity. It is shown, in some generic cases, that spacetime singularities that arise in usual Riemannian general relativity, may be avoided in its dual representation: Weyl-like general relativity, thus providing a singularity-free picture of the World that is physicaly equivalent to the canonical general relativistic one.
Polarization singularity anisotropy: determining monstardom
Dennis, Mark R
2008-01-01
C points, that is isolated points of circular polarization in transverse fields of varying polarization, are classified morphologically into three distinct types, known as lemons, stars and monstars. These morphologies are interpreted here according to two natural parameters associated with the singularity, namely the anisotropy of the C point, and the polarization azimuth on the anisotropy axis. In addition to providing insight into singularity morphology, this observation applies to the densities of the various morphologies in isotropic random polarization speckle fields.
Singular traces theory and applications
Sukochev, Fedor; Zanin, Dmitriy
2012-01-01
This text is the first complete study and monograph dedicated to singular traces. For mathematical readers the text offers, due to Nigel Kalton's contribution, a complete theory of traces on symmetrically normed ideals of compact operators. For mathematical physicists and other users of Connes' noncommutative geometry the text offers a complete reference to Dixmier traces and the deeper mathematical features of singular traces. An application section explores the consequences of these features, which previously were not discussed in general texts on noncommutative geometry.
Dynkin graphs and quadrilateral singularities
Urabe, Tohsuke
1993-01-01
The study of hypersurface quadrilateral singularities can be reduced to the study of elliptic K3 surfaces with a singular fiber of type I * 0 (superscript *, subscript 0), and therefore these notes consider, besides the topics of the title, such K3 surfaces too. The combinations of rational double points that can occur on fibers in the semi-universal deformations of quadrilateral singularities are examined, to show that the possible combinations can be described by a certain law from the viewpoint of Dynkin graphs. This is equivalent to saying that the possible combinations of singular fibers in elliptic K3 surfaces with a singular fiber of type I * 0 (superscript *, subscript 0) can be described by a certain law using classical Dynkin graphs appearing in the theory of semi-simple Lie groups. Further, a similar description for thecombination of singularities on plane sextic curves is given. Standard knowledge of algebraic geometry at the level of graduate students is expected. A new method based on graphs wil...
Multiple Positive Solutions to Third-Order Three-Point Singular Semipositone Boundary Value Problem
Indian Academy of Sciences (India)
Huimin Yu; L Haiyan; Yansheng Liu
2004-11-01
By using a specially constructed cone and the fixed point index theory, this paper investigates the existence of multiple positive solutions for the third-order three-point singular semipositone BVP: \\begin{equation*}\\begin{cases}x'"(t)- f(t,x)=0, & t\\in(0, 1);\\\\ x(0)=x'()=x"(1)=0,\\end{cases}\\end{equation*} where $\\frac{1}{2} < < 1$, the non-linear term $f(t,x): (0,1)×(0,=∞)→(-∞ +∞)$ is continuous and may be singular at = 0, = 1, and = 0, also may be negative for some values of and , is a positive parameter.
SINGULAR INTEGRALS ALONG SURFACES ON PRODUCT DOMAINS
Institute of Scientific and Technical Information of China (English)
Hussain Al-Qassem
2004-01-01
In this paper, we study the mapping properties of singular integral operator along surfaces of revolution. We prove Lp bounds (1 ＜ p ＜∞) for such singular integral operators as well as for their corresponding maximal truncated singular integrals if the singular kernels are allowed to be in certain block spaces.
A New Type of Singularity Theorem
Senovilla, José M M
2007-01-01
A new type of singularity theorem, based on spatial averages of physical quantities, is presented and discussed. Alternatively, the results inform us of when a spacetime can be singularity-free. This theorem provides a decisive observational difference between singular and non-singular, globally hyperbolic, open cosmological models.
Compiler for Fast, Accurate Mathematical Computing on Integer Processors Project
National Aeronautics and Space Administration — The proposers will develop a computer language compiler to enable inexpensive, low-power, integer-only processors to carry our mathematically-intensive comptutations...
Directory of Open Access Journals (Sweden)
Baoqiang Yan
2006-07-01
Full Text Available In this paper, Krasnoselskii's theorem and the fixed point theorem of cone expansion and compression are improved. Using the results obtained, we establish the existence of multiple positive solutions for the singular second-order boundary-value problems with derivative dependance on finite and infinite intervals.
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
By constructing an explicit Green function and using the fixed point index theory on a cone, we present some existence results of positive solutions to a class of second-order singular semipositive Neumann boundary value problem, where the nonlinear term is allowed to be nonnegative and unbounded.
Institute of Scientific and Technical Information of China (English)
无
2011-01-01
This paper deals with the existence of denumberable positive solutions to boundary value problems of delay differential equations with denumberable singularities on infinite intervals. By the fixed-point index theory and a new fixed-point theorem in cones, the existence of denumberable positive solutions is obtained under some suitable growth conditions imposed on the nonlinear term.
Mixed-integer vertex covers on bipartite graphs
Gerards, A.M.H.; Conforti, M.; Zambelli, G.; Fischetti, M.; Williamson, D.P.
2007-01-01
Let $A$ be the edge-node incidence matrix of a bipartite graph $G = (U, V ; E)$, $I$ be a subset of the nodes of $G$, and $b$ be a vector such that $2b$ is integral. We consider the following mixed-integer set: $X(G, b, I) = {x : Ax ≥ b, x ≥ 0, x_i$ integer for all $i ∈ I}$
Short Rational Generating Functions For Multiobjective Linear Integer Programming
Blanco, Victor
2007-01-01
This paper presents an algorithm for solving multiobjective integer programming problems. The algorithm uses Barvinok's rational functions of the polytope that defines the feasible region and provides as output the entire set of nondominated solutions for the problem. Theoretical complexity results on the algorithm are provided in the paper and an implementation of the algorithm shows that it is useful for solving multiobjective integer linear programs.
AN ALGORITHM FOR FINDING GLOBAL MINIMUM OF NONLINEAR INTEGER PROGRAMMING
Institute of Scientific and Technical Information of China (English)
Wei-wenTian; Lian-shengZhang
2004-01-01
A filled function is proposed by R.Ge[2] for finding a global minimizer of a function of several continuous variables. In [4], an approach for finding a global integer minimizer of nonlinear flmction using the above filled function is given. Meanwhile a major obstacle is met: if ρ > 0 is small, and ‖xI- xI* is large, where xI - an integer point, xI* - a current local integer minimizer, then the value of the filled function almost equals zero. Thus it is difficult to recognize the size of the value of the filled flmction and can not to find the global integer minimizer of nonlinear function. In this paper, two new filled functions are proposed for finding global integer minimizer of nonlinear flmction, the new filled function improves some properties of the filled function proposed by R. Ge [2]. Some numerical results are given, which indicate the new filled function (4.1) to find global integer minimizer of nonlinear function is efficient.
Negative Point Mass Singularities in General Relativity
Robbins, Nicholas
2010-01-01
First we review the definition of a negative point mass singularity. Then we examine the gravitational lensing effects of these singularities in isolation and with shear and convergence from continuous matter. We review the Inverse Mean Curvature Flow and use this flow to prove some new results about the mass of a singularity, the ADM mass of the manifold, and the capacity of the singularity. We describe some particular examples of these singularities that exhibit additional symmetries.
On the Milnor fibers of sandwiched singularities
Nemethi, Andras; Popescu-Pampu, Patrick
2009-01-01
The sandwiched surface singularities are those rational surface singularities which dominate birationally smooth surface singularities. de Jong and van Straten showed that one can reduce the study of the deformations of a sandwiched surface singularity to the study of deformations of a 1-dimensional object, a so-called decorated plane curve singularity. In particular, the Milnor fibers corresponding to their various smoothing components may be reconstructed up to diffeomorphisms from those de...
On the genericity of spacetime singularities
Indian Academy of Sciences (India)
Pankaj S Joshi
2007-07-01
We consider here the genericity aspects of spacetime singularities that occur in cosmology and in gravitational collapse. The singularity theorems (that predict the occurrence of singularities in general relativity) allow the singularities of gravitational collapse to be either visible to external observers or covered by an event horizon of gravity. It is shown that the visible singularities that develop as final states of spherical collapse are generic. Some consequences of this fact are discussed.
Electromagnetic scattering of a vector Bessel beam in the presence of an impedance cone
Salem, Mohamed
2013-07-01
The electromagnetic field scattering of a vector Bessel beam in the presence of an infinite circular cone with an impedance boundary on its surface is considered. The impinging field is normal to the tip of the cone and is expanded in terms of vector spherical wave functions; a Kontorovich-Lebedev (KL) transform is employed to expand the scattered fields. The problem is reduced to a singular integral equation with a variable coefficient of the non-convolution type. The singularities of the spectral function are deduced and representations for the field at the tip of the cone as well as other regions are given together with the conditions of validity of these representations. © 2013 IEEE.
Flow Lines Under Perturbation within Section Cones
DEFF Research Database (Denmark)
Wisniewski, Rafal
that a point is greater than or equal to a point if there exists a flow line from to corresponding to some vector field in . The partial order that - under a certain condition - arises from the transitive closure of that relation -- gives rise to (the concept of) a di-path (directed path). That is a continuous......We want to examine a closed smooth manifold together with a certain partial order: In the set of vector fields on , , we define a section cone - a convex subset of characterized by the property that if is a singular point for some vector field in then this is the case for all members of . We say...
The cone dysfunction syndromes
Aboshiha, Jonathan; Dubis, Adam M; Hardcastle, Alison J; Michaelides, Michel
2016-01-01
The cone dysfunction syndromes are a heterogeneous group of inherited, predominantly stationary retinal disorders characterised by reduced central vision and varying degrees of colour vision abnormalities, nystagmus and photophobia. This review details the following conditions: complete and incomplete achromatopsia, blue-cone monochromatism, oligocone trichromacy, bradyopsia and Bornholm eye disease. We describe the clinical, psychophysical, electrophysiological and imaging findings that are characteristic to each condition in order to aid their accurate diagnosis, as well as highlight some classically held notions about these diseases that have come to be challenged over the recent years. The latest data regarding the genetic aetiology and pathological changes observed in the cone dysfunction syndromes are discussed, and, where relevant, translational avenues of research, including completed and anticipated interventional clinical trials, for some of the diseases described herein will be presented. Finally, we briefly review the current management of these disorders. PMID:25770143
On the logarithmic divergent part of entanglement entropy, smooth versus singular regions
Dorn, Harald
2016-01-01
The entanglement entropy for smooth regions $\\cal A$ has a logarithmic divergent contribution with a shape dependent coefficient and that for regions with conical singularities an additional $\\log ^2$ term. Comparing the coefficient of this extra term, obtained by direct holographic calculation for an infinite cone, with the corresponding limiting case for the shape dependent coefficient for a regularised cone, a mismatch by a factor two has been observed in the literature. We discuss several aspects of this issue. In particular a regularisation of $\\cal A$, intrinsically delivered by the holographic picture, is proposed and applied to an example of a compact region with two conical singularities. Finally, the mismatch is removed in all studied regularisations of $\\cal A$, if equal scale ratios are chosen for the limiting procedure.
Spacetime Singularities in Quantum Gravity
Minassian, Eric A.
2000-04-01
Recent advances in 2+1 dimensional quantum gravity have provided tools to study the effects of quantization of spacetime on black hole and big bang/big crunch type singularities. I investigate effects of quantization of spacetime on singularities of the 2+1 dimensional BTZ black hole and the 2+1 dimensional torus universe. Hosoya has considered the BTZ black hole, and using a "quantum generalized affine parameter" (QGAP), has shown that, for some specific paths, quantum effects "smear" the singularities. Using gaussian wave functions as generic wave functions, I found that, for both BTZ black hole and the torus universe, there are families of paths that still reach the singularities with a finite QGAP, suggesting that singularities persist in quantum gravity. More realistic calculations, using modular invariant wave functions of Carlip and Nelson for the torus universe, offer further support for this conclusion. Currently work is in progress to study more realistic quantum gravity effects for BTZ black holes and other spacetime models.
Singular solutions of doubly singular parabolic equations with absorption
Directory of Open Access Journals (Sweden)
Yuanwei Qi
2000-11-01
Full Text Available In this paper we study a doubly singular parabolic equation with absorption, $$ u_t = hbox{ m div} ( |abla u^m|^{p-2}abla u^m -u^q $$ with $m>0$, $p>1$, $m(p-11$. We give a complete classification of solutions, which we call singular, that are non-negative, non-trivial, continuous in ${mathbb R}^n imes [0, inftybackslash{(0,0} $, and satisfy $u(x,0=0$ for all $xeq 0$. Applications of similar but simpler equations show that these solutions are very important in the study of intermediate asymptotic behavior of general solutions.
On the singularities of solutions to singular perturbation problems
Energy Technology Data Exchange (ETDEWEB)
Fruchard, A [Laboratoire de Mathematiques, Informatique et Applications, Faculte des Sciences et Techniques, Universite de Haute Alsace, 4 rue des Freres Lumiere, 68093 Mulhouse cedex (France); Schaefke, R [Departement de Mathematiques, Universite Louis Pasteur, 7 rue Rene-Descartes, 67084 Strasbourg cedex (France)
2005-01-01
We consider a singularly perturbed complex first order ODE {epsilon}u ' {phi}(x, u, a, {epsilon}), x, u element of C, {epsilon} > 0 is a small complex parameter and a element of C is a control parameter. It is proven that the singularities of some solutions are regularly spaced and that they move from one to the next as a runs about a loop of index one around a value of overstability. This gives a positive answer to a question of J. L. Callot.
Shatter Cones: (Mis)understood?
Osinski, G. R.; Ferrière, L.
2016-08-01
In this study we provide new observations of shatter cones from several complex impact craters in various target rocks and in different preservation states. We show that shatter cones are present in several stratigraphic settings.
Steinbacher, D
2005-01-01
The summation of all rainbow diagrams in QED in a strong magnetic field leads to a dynamical electron mass on the light-cone. Further contributions to this summation however can cause problems with light-cone singularities. It is shown that these problems are generally avoided by applying the point-splitting regularization to every diagram. The possibility of implementing this procedure into the Lagrangian of the theory is discussed.
Brane-like singularities with no brane
Energy Technology Data Exchange (ETDEWEB)
Yurov, A.V., E-mail: artyom_yurov@mail.r [I. Kant Russian State University, Theoretical Physics Department, Al. Nevsky St. 14, Kaliningrad 236041 (Russian Federation)
2010-05-17
We use a method of linearization to study the emergence of the future cosmological singularity characterized by finite value of the cosmological radius. We uncover such singularities that keep Hubble parameter finite while making all higher derivatives of the scale factor (starting out from the a) diverge as the cosmological singularity is approached. Since such singularities has been obtained before in the brane world model we name them the 'brane-like' singularities. These singularities can occur during the expanding phase in usual Friedmann universe filled with both a self-acting, minimally coupled scalar field and a homogeneous tachyon field. We discover a new type of finite-time, future singularity which is different from type I-IV cosmological singularities in that it has the scale factor, pressure and density finite and nonzero. The generalization of w-singularity is obtained as well.
Self-similar singular solution of doubly singular parabolic equation with gradient absorption term
Directory of Open Access Journals (Sweden)
Shi Peihu
2006-01-01
Full Text Available We deal with the self-similar singular solution of doubly singular parabolic equation with a gradient absorption term for , and in . By shooting and phase plane methods, we prove that when there exists self-similar singular solution, while there is no any self-similar singular solution. In case of existence, the self-similar singular solution is the self-similar very singular solutions which have compact support. Moreover, the interface relation is obtained.
Minimizing the Integer Ambiguity Search Space for RTK
Institute of Scientific and Technical Information of China (English)
Yang Yun-chun; R. R. Hatch; R. T. Sharpe
2003-01-01
Differential GPS carrier phase measurements have much lower noise and multipath error than that of pseudorange measurements.The result is centimeter accuracy for Real-Time Kinematic (RTK).However, the measurement of the carrier phase has a constant unknown integer ambiguity. Several technical issues are related to solving the integer ambiguity correctly. They are: proper stochastic model, search space definition and initialization, search space reduction, state and standard deviation calculation, validation and rejection criteria for the unique and correct candidate. Search space reduction is critically important. It not only affects the ambiguity resolution speed, but also defines the ambiguity resolution success rate. The smaller the search space, the easier it is to find the unique and correct candidate set. The paper analyzes the integer ambiguity search space in its residual domain.The search space is minimized by: Analyzing the maximum independent integer ambiguity measurement set theoretically; Selecting the best initial measurement set that minimizes the search range of each satellite in the set and reduces the error effects from noise that may cause the wrong integer ambiguity solution for the remaining satellites not contained in the initial measurement set.Since the Residual Sensitive Matrix (S-Matrix) relates the integer ambiguity candidate set directly to post-fix residuals, it is not necessary to compute a fix for each candidate set thus making the integ erambiguity search process much more efficient. Also, minimizing the search space in the residual domain improves the search efficiency significantly and at the same time improves its reliability. Performance issues, such as recursive and weighted search techniques as well as methods for improving reliability, are also discussed in the article.
Naked singularities as particle accelerators
Patil, Mandar; 10.1103/PhysRevD.82.104049
2010-01-01
We investigate here the particle acceleration by naked singularities to arbitrarily high center of mass energies. Recently it has been suggested that black holes could be used as particle accelerators to probe the Planck scale physics. We show that the naked singularities serve the same purpose and probably would do better than their black hole counterparts. We focus on the scenario of a self-similar gravitational collapse starting from a regular initial data, leading to the formation of a globally naked singularity. It is seen that when particles moving along timelike geodesics interact and collide near the Cauchy horizon, the energy of collision in the center of mass frame will be arbitrarily high, thus offering a window to Planck scale physics.
El singular como diferencia divina
Directory of Open Access Journals (Sweden)
Maria Jose Binetti
2012-01-01
Full Text Available Mucho se ha hablado sobre la posición de la diferencia como motor dialéctico de la existencia singular kierkegaardiana. El pecado, el otro o el Otro fisuran la subjetividad humana y la obligan a una identidad que guardará siempre la herida. El sujeto de la escisión es, en este sentido, el existente mismo, y tal debe ser el caso si la perspectiva se concentra en la individualidad. No obstante, y desde el punto de vista especulativo, creemos que los mismos principios utilizados por Kierkegaard para explicar el dinamismo de la existencia singular nos llevan más lejos, a saber, nos conducen al absoluto mismo como sujeto último de toda alteridad, respecto del cual el singular hace la diferencia.
Infrared singularities in QCD amplitudes
Gardi, Einan
2009-01-01
We review recent progress in determining the infrared singularity structure of on-shell scattering amplitudes in massless gauge theories. We present a simple ansatz where soft singularities of any scattering amplitude of massless partons, to any loop order, are written as a sum over colour dipoles, governed by the cusp anomalous dimension. We explain how this formula was obtained, as the simplest solution to a newly-derived set of equations constraining the singularity structure to all orders. We emphasize the physical ideas underlying this derivation: the factorization of soft and collinear modes, the special properties of soft gluon interactions, and the notion of the cusp anomaly. Finally, we briefly discuss potential multi-loop contributions going beyond the sum-over-dipoles formula, which cannot be excluded at present.
Singular Integrals with Bilinear Phases
Institute of Scientific and Technical Information of China (English)
Elena PRESTINI
2006-01-01
We prove the boundedness from Lp(T2) to itself, 1 ＜ p ＜∞, of highly oscillatory singular integrals Sf(x, y) presenting singularities of the kind of the double Hilbert transform on a non-rectangular domain of integration, roughly speaking, defined by |y′| ＞ | x′|, and presenting phases λ(Ax + By) with 0 ≤ A, B ≤ 1 and λ≥ 0. The norms of these oscillatory singular integrals are proved to be independent of all parameters A, B and λ involved. Our method extends to a more general family of phases. These results are relevant to problems of almost everywhere convergence of double Fourier and Walsh series.
Ambient cosmology and spacetime singularities
Antoniadis, Ignatios
2015-01-01
We present a new approach to the issues of spacetime singularities and cosmic censorship in general relativity. This is based on the idea that standard 4-dimensional spacetime is the conformal infinity of an ambient metric for the 5-dimensional Einstein equations with fluid sources. We then find that the existence of spacetime singularities in four dimensions is constrained by asymptotic properties of the ambient 5-metric, while the non-degeneracy of the latter crucially depends on cosmic censorship holding on the boundary.
Ambient cosmology and spacetime singularities
Energy Technology Data Exchange (ETDEWEB)
Antoniadis, Ignatios [Bern University, Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, Bern (Switzerland); Ecole Polytechnique, Palaiseau (France); Cotsakis, Spiros [CERN, Theory Division, Department of Physics, Geneva 23 (Switzerland); National Technical University, School of Applied Mathematics and Physical Sciences, Athens (Greece)
2015-01-01
We present a new approach to the issues of spacetime singularities and cosmic censorship in general relativity. This is based on the idea that standard 4-dimensional spacetime is the conformal infinity of an ambient metric for the 5-dimensional Einstein equations with fluid sources. We then find that the existence of spacetime singularities in four dimensions is constrained by asymptotic properties of the ambient 5-metric, while the non-degeneracy of the latter crucially depends on cosmic censorship holding on the boundary. (orig.)
Singularity Theory and its Applications
Stewart, Ian; Mond, David; Montaldi, James
1991-01-01
A workshop on Singularities, Bifuraction and Dynamics was held at Warwick in July 1989, as part of a year-long symposium on Singularity Theory and its applications. The proceedings fall into two halves: Volume I mainly on connections with algebraic geometry and volume II on connections with dynamical systems theory, bifurcation theory and applications in the sciences. The papers are original research, stimulated by the symposium and workshop: All have been refereed and none will appear elsewhere. The main topic of volume II is new methods for the study of bifurcations in nonlinear dynamical systems, and applications of these.
The Non-Singularity and Regularity of GP-V'-Rings
Institute of Scientific and Technical Information of China (English)
Xiao Bin YIN; Rui WANG; Xiao Long LI
2011-01-01
In this paper,we introduce a non-trivial generalization of ZI-rings-quasi ZI-rings.A ring R is called a quasi ZI-ring,if for any non-zero elements a,b ∈ R,ab =0 implies that there exists a positive integer n such that an ≠ 0 and anRbn =0.The non-singularity and regularity of quasi ZI,GP-V’-rings are studied.Some new characterizations of strong regular rings are obtained.These effectively extend some known results.
Fractal electrodynamics via non-integer dimensional space approach
Energy Technology Data Exchange (ETDEWEB)
Tarasov, Vasily E., E-mail: tarasov@theory.sinp.msu.ru
2015-09-25
Using the recently suggested vector calculus for non-integer dimensional space, we consider electrodynamics problems in isotropic case. This calculus allows us to describe fractal media in the framework of continuum models with non-integer dimensional space. We consider electric and magnetic fields of fractal media with charges and currents in the framework of continuum models with non-integer dimensional spaces. An application of the fractal Gauss's law, the fractal Ampere's circuital law, the fractal Poisson equation for electric potential, and equation for fractal stream of charges are suggested. Lorentz invariance and speed of light in fractal electrodynamics are discussed. An expression for effective refractive index of non-integer dimensional space is suggested. - Highlights: • Electrodynamics of fractal media is described by non-integer dimensional spaces. • Applications of the fractal Gauss's and Ampere's laws are suggested. • Fractal Poisson equation, equation for fractal stream of charges are considered.
Non-integer expansion embedding techniques for reversible image watermarking
Xiang, Shijun; Wang, Yi
2015-12-01
This work aims at reducing the embedding distortion of prediction-error expansion (PE)-based reversible watermarking. In the classical PE embedding method proposed by Thodi and Rodriguez, the predicted value is rounded to integer number for integer prediction-error expansion (IPE) embedding. The rounding operation makes a constraint on a predictor's performance. In this paper, we propose a non-integer PE (NIPE) embedding approach, which can proceed non-integer prediction errors for embedding data into an audio or image file by only expanding integer element of a prediction error while keeping its fractional element unchanged. The advantage of the NIPE embedding technique is that the NIPE technique can really bring a predictor into full play by estimating a sample/pixel in a noncausal way in a single pass since there is no rounding operation. A new noncausal image prediction method to estimate a pixel with four immediate pixels in a single pass is included in the proposed scheme. The proposed noncausal image predictor can provide better performance than Sachnev et al.'s noncausal double-set prediction method (where data prediction in two passes brings a distortion problem due to the fact that half of the pixels were predicted with the watermarked pixels). In comparison with existing several state-of-the-art works, experimental results have shown that the NIPE technique with the new noncausal prediction strategy can reduce the embedding distortion for the same embedding payload.
Exact behavior of singular solutions to Protter's problem with lower order terms
Directory of Open Access Journals (Sweden)
Aleksey Nikolov
2012-08-01
Full Text Available For the (2+1-D wave equation Protter formulated (1952 some boundary value problems which are three-dimensional analogues of the Darboux problems on the plane. Protter studied these problems in a 3-D domain, bounded by two characteristic cones and by a planar region. Now it is well known that, for an infinite number of smooth functions in the right-hand side, these problems do not have classical solutions, because of the strong power-type singularity which appears in the generalized solution. In the present paper we consider the wave equation involving lower order terms and obtain new a priori estimates describing the exact behavior of singular solutions of the third boundary value problem. According to the new estimates their singularity is of the same order as in case of the wave equation without lower order terms.
Witzel, Christoph; Cinotti, François; O'Regan, J Kevin
2015-01-01
The relationship between the sensory signal of the photoreceptors on one hand and color appearance and language on the other hand is completely unclear. A recent finding established a surprisingly accurate correlation between focal colors, unique hues, and so-called singularities in the laws governing how sensory signals for different surfaces change across illuminations. This article examines how this correlation with singularities depends on reflectances, illuminants, and cone sensitivities. Results show that this correlation holds for a large range of illuminants and for a large range of sensors, including sensors that are fundamentally different from human photoreceptors. In contrast, the spectral characteristics of the reflectance spectra turned out to be the key factor that determines the correlation between focal colors, unique hues, and sensory singularities. These findings suggest that the origins of color appearance and color language may be found in particular characteristics of the reflectance spectra that correspond to focal colors and unique hues.
On the singularities of 3-D Protter's problem for the wave equation
Directory of Open Access Journals (Sweden)
Myron K. Grammatikopoulos
2001-01-01
Full Text Available In this paper we study boundary-value problems for the wave equation, which are three-dimensional analogue of Darboux-problems (or of Cauchy-Goursat problems on the plane. It is shown that for $n$ in $mathbb{N}$ there exists a right hand side smooth function from $C^n(ar{Omega}_{0}$, for which the corresponding unique generalized solution belongs to $C^n(ar{Omega}_{0}ackslash O$, and it has a strong power-type singularity at the point $O$. This singularity is isolated at the vertex $O$ of the characteristic cone and does not propagate along the cone. In this paper we investigate the behavior of the singular solutions at the point $O$. Also, we study more general boundary-value problems and find that there exist an infinite number of smooth right-hand side functions for which the corresponding unique generalized solutions are singular. Some a priori estimates are also stated.
Ejecta evolution during cone impact
Marston, Jeremy
2014-07-07
We present findings from an experimental investigation into the impact of solid cone-shaped bodies onto liquid pools. Using a variety of cone angles and liquid physical properties, we show that the ejecta formed during the impact exhibits self-similarity for all impact speeds for very low surface tension liquids, whilst for high-surface tension liquids similarity is only achieved at high impact speeds. We find that the ejecta tip can detach from the cone and that this phenomenon can be attributed to the air entrainment phenomenon. We analyse of a range of cone angles, including some ogive cones, and impact speeds in terms of the spatiotemporal evolution of the ejecta tip. Using superhydrophobic cones, we also examine the entry of cones which entrain an air layer.
Singularity: Raychaudhuri equation once again
Indian Academy of Sciences (India)
Naresh Dadhich
2007-07-01
I first recount Raychaudhuri's deep involvement with the singularity problem in general relativity. I then argue that precisely the same situation has arisen today in loop quantum cosmology as obtained when Raychaudhuri discovered his celebrated equation. We thus need a new analogue of the Raychaudhuri equation in quantum gravity.
Singularity: zijn wij technologisch upgradable
drs. Frans van den Reep
2013-01-01
1e alinea column: Ik wil een paar dingen kwijt over singularity en de hele horde van buitengewoon slimme mensen die daar vorm aan geven. Aanleiding hiervoor is de speech van Peter Diamandis, cofounder en chairman of the Singularty University, Nasa Research Park, Silicon Valley, die hij vorige week
Lightlike singularities in compactified supergravity
Baal, P. van; Bais, F.A.
1983-01-01
We discuss the (causal) structure of a recently found black hole solution of compatified d = 11 supergravity. It is shown that the singularity is in fact lightlike and coincides with the horizon. Consequences are that the Hawking temperature is undetermined and that there is no other universe connec
Singularity: zijn wij technologisch upgradable
drs. Frans van den Reep
2013-01-01
1e alinea column: Ik wil een paar dingen kwijt over singularity en de hele horde van buitengewoon slimme mensen die daar vorm aan geven. Aanleiding hiervoor is de speech van Peter Diamandis, cofounder en chairman of the Singularty University, Nasa Research Park, Silicon Valley, die hij vorige week i
Lightlike singularities in compactified supergravity
Baal, P. van; Bais, F.A.
1983-01-01
We discuss the (causal) structure of a recently found black hole solution of compatified d = 11 supergravity. It is shown that the singularity is in fact lightlike and coincides with the horizon. Consequences are that the Hawking temperature is undetermined and that there is no other universe connec
Singularities in Speckled Speckle: Screening
Kessler, David A
2008-01-01
We study screening of optical singularities in random optical fields with two widely different length scales. We call the speckle patterns generated by such fields speckled speckle, because the major speckle spots in the pattern are themselves highly speckled. We study combinations of fields whose components exhibit short- and long-range correlations, and find unusual forms of screening.
Singularity: zijn wij technologisch upgradable
Reep, Frans van der
2013-01-01
1e alinea column: Ik wil een paar dingen kwijt over singularity en de hele horde van buitengewoon slimme mensen die daar vorm aan geven. Aanleiding hiervoor is de speech van Peter Diamandis, cofounder en chairman of the Singularty University, Nasa Research Park, Silicon Valley, die hij vorige week i
Multiplicity of Summands in the Random Partitions of an Integer
Indian Academy of Sciences (India)
Ghurumuruhan Ganesan
2013-02-01
In this paper, we prove a conjecture of Yakubovich regarding limit shapes of `slices’ of two-dimensional (2D) integer partitions and compositions of when the number of summands $m\\sim An^$ for some >0 and $ < \\frac{1}{2}$. We prove that the probability that there is a summand of multiplicity in any randomly chosen partition or composition of an integer goes to zero asymptotically with provided is larger than a critical value. As a corollary, we strengthen a result due to Erdös and Lehner (Duke Math. J. 8(1941) 335–345) that concerns the relation between the number of integer partitions and compositions when $=\\frac{1}{3}$.
Integer Programming and m-irreducibility of numerical semigroups
Blanco, Víctor
2011-01-01
This paper addresses the problem of decomposing a numerical semigroup into m-irreducible numerical semigroups. The problem originally stated in algebraic terms is translated, introducing the so called Kunz-coordinates, to resolve a series of several discrete optimization problems. First, we prove that finding a minimal m-irreducible decomposition is equivalent to solve a multiobjective linear integer problem. Then, we restate that problem as the problem of finding all the optimal solutions of a finite number of single objective integer linear problems plus a set covering problem. Finally, we prove that there is a suitable transformation that reduces the original problem to find an optimal solution of a compact integer linear problem. This result ensures a polynomial time algorithm for each given multiplicity m. We have implemented the different algorithms and have performed some computational experiments to show the efficiency of our methodology.
The lattice of integer flows of a regular matroid
Su, Yi
2009-01-01
For a finite multigraph G, let \\Lambda(G) denote the lattice of integer flows of G -- this is a finitely generated free abelian group with an integer-valued positive definite bilinear form. Bacher, de la Harpe, and Nagnibeda show that if G and H are 2-isomorphic graphs then \\Lambda(G) and \\Lambda(H) are isometric, and remark that they were unable to find a pair of nonisomorphic 3-connected graphs for which the corresponding lattices are isometric. We explain this by examining the lattice \\Lambda(M) of integer flows of any regular matroid M. Let M_\\bullet be the minor of M obtained by contracting all co-loops. We show that \\Lambda(M) and \\Lambda(N) are isometric if and only if M_\\bullet and N_\\bullet are isomorphic.
Cone Algorithm of Spinning Vehicles under Dynamic Coning Environment
Directory of Open Access Journals (Sweden)
Shuang-biao Zhang
2015-01-01
Full Text Available Due to the fact that attitude error of vehicles has an intense trend of divergence when vehicles undergo worsening coning environment, in this paper, the model of dynamic coning environment is derived firstly. Then, through investigation of the effect on Euler attitude algorithm for the equivalency of traditional attitude algorithm, it is found that attitude error is actually the roll angle error including drifting error and oscillating error, which is induced directly by dynamic coning environment and further affects the pitch angle and yaw angle through transferring. Based on definition of the cone frame and cone attitude, a cone algorithm is proposed by rotation relationship to calculate cone attitude, and the relationship between cone attitude and Euler attitude of spinning vehicle is established. Through numerical simulations with different conditions of dynamic coning environment, it is shown that the induced error of Euler attitude fluctuates by the variation of precession and nutation, especially by that of nutation, and the oscillating frequency of roll angle error is twice that of pitch angle error and yaw angle error. In addition, the rotation angle is more competent to describe the spinning process of vehicles under coning environment than Euler angle gamma, and the real pitch angle and yaw angle are calculated finally.
Cones and craters on Mount Pavagadh, Deccan Traps: Rootless cones?
Indian Academy of Sciences (India)
Hetu C Sheth; George Mathew; Kanchan Pande; Soumen Mallick; Balaram Jena
2004-12-01
Rootless cones, also (erroneously) called pseudocraters, form due to explosions that ensue when a lava ﬂow enters a surface water body, ice, or wet ground. They do not represent primary vents connected by vertical conduits to a subsurface magma source. Rootless cones in Iceland are well studied. Cones on Mars, morphologically very similar to Icelandic rootless cones, have also been suggested to be rootless cones formed by explosive interaction between surface lava ﬂows and ground ice. We report here a group of gentle cones containing nearly circular craters from Mount Pavagadh, Deccan volcanic province, and suggest that they are rootless cones. They are very similar morphologically to the rootless cones of the type locality of Mý vatn in northeastern Iceland. A group of three phreatomagmatic craters was reported in 1998 from near Jabalpur in the northeastern Deccan, and these were suggested to be eroded cinder cones. A recent geophysical study of the Jabalpur craters does not support the possibility that they are located over volcanic vents. They could also be rootless cones. Many more probably exist in the Deccan, and volcanological studies of the Deccan are clearly of value in understanding planetary basaltic volcanism.
On the concept of spectral singularities
Indian Academy of Sciences (India)
Gusein Sh Guseinov
2009-09-01
In this paper, we discuss the concept of spectral singularities for non-Hermitian Hamiltonians. We exihibit spectral singularities of some well-known concrete Hamiltonians with complex-valued coefficients.
FPGA Implementation of Optimal 3D-Integer DCT Structure for Video Compression.
Jacob, J Augustin; Kumar, N Senthil
2015-01-01
A novel optimal structure for implementing 3D-integer discrete cosine transform (DCT) is presented by analyzing various integer approximation methods. The integer set with reduced mean squared error (MSE) and high coding efficiency are considered for implementation in FPGA. The proposed method proves that the least resources are utilized for the integer set that has shorter bit values. Optimal 3D-integer DCT structure is determined by analyzing the MSE, power dissipation, coding efficiency, and hardware complexity of different integer sets. The experimental results reveal that direct method of computing the 3D-integer DCT using the integer set [10, 9, 6, 2, 3, 1, 1] performs better when compared to other integer sets in terms of resource utilization and power dissipation.
Disclinations, e-cones, and their interactions in extensible sheets.
Chopin, Julien; Kudrolli, Arshad
2016-05-11
We investigate the nucleation, growth, and spatial organization of topological defects with a ribbon shaped elastic sheet which is stretched and twisted. Singularities are found to spontaneously arrange in a triangular lattice in the form of vertices connected by stretched ridges that result in a self-rigidified structure. The vertices are shown to be negative disclinations or e-cones which occur in sheets with negative Gaussian curvature, in contrast with d-cones in sheets with zero-Gaussian curvature. We find the growth of the wrinkled width of the ribbon to be consistent with a far-from-threshold approach assuming a compression-free base state. The system is found to show a transition from a regime where the wavelength is given by the ribbon geometry, to where it is given by its elasticity as a function of the ratio of the applied tension to the elastic modulus and cross-sectional area of the ribbon.
Instantons, Integrability and Discrete Light-Cone Quantisation
Dorey, Nick
2014-01-01
We study supersymmetric quantum mechanics on the moduli space of Yang-Mills instantons on R^2 x T^2 and its application to the discrete light-cone quantisation (DLCQ) of N=4 SUSY Yang-Mills. In the presence of a target space magnetic field, the model has a discrete spectrum with the wavefunctions of generic energy eigenstates supported away from the singular points of the moduli space. The corresponding Hamiltonian is part of an osp(1,1|4) superalgebra which enlarges to su(1,1|4) superconformal invariance in the sector corresponding to the N=4 theory. The Hamiltonian is isospectral to the light-cone dilatation operator of the N=4 theory in this sector. The model also has an interesting scaling limit where it becomes integrable. We determine the semiclassical spectrum in this limit. We discuss a possible approach to constructing the dilatation operator of N=4 supersymmetric Yang-Mills theory in DLCQ.
Exploiting Symmetry in Integer Convex Optimization using Core Points
Herr, Katrin; Schürmann, Achill
2012-01-01
We consider convex programming problems with integrality constraints that are invariant under a linear symmetry group. We define a core point of such a symmetry group as an integral point for which the convex hull of its orbit does not contain integral points other than the orbit points themselves. These core points allow us to decompose symmetric integer convex programming problems. Especially for symmetric integer linear programs we describe two algorithms based on this decomposition. Using a characterization of core points for direct products of symmetric groups, we show that prototype implementations can compete with state-of-the art commercial solvers and solve an open MIPLIB problem.
Integer Programming Model for Maximum Clique in Graph
Institute of Scientific and Technical Information of China (English)
YUAN Xi-bo; YANG You; ZENG Xin-hai
2005-01-01
The maximum clique or maximum independent set of graph is a classical problem in graph theory. Combined with Boolean algebra and integer programming, two integer programming models for maximum clique problem,which improve the old results were designed in this paper. Then, the programming model for maximum independent set is a corollary of the main results. These two models can be easily applied to computer algorithm and software, and suitable for graphs of any scale. Finally the models are presented as Lingo algorithms, verified and compared by several examples.
A new heuristic algorithm for general integer linear programming problems
Institute of Scientific and Technical Information of China (English)
GAO Pei-wang; CAI Ying
2006-01-01
A new heuristic algorithm is proposed for solving general integer linear programming problems.In the algorithm,the objective function hyperplane is used as a cutting plane,and then by introducing a special set of assistant sets,an efficient heuristic search for the solution to the integer linear program is carried out in the sets on the objective function hyperplane.A simple numerical example shows that the algorithm is efficient for some problems,and therefore,of practical interest.
Arithmetic progressions in Salem-type subsets of the integers
Potgieter, Paul
2010-01-01
Given a subset of the integers of zero density, we define the weaker notion of fractional density of such a set. It is shown how this notion corresponds to that of the Hausdorff dimension of a compact subset of the reals. We then show that a version of a theorem of {\\L}aba and Pramanik on 3-term arithmetic progressions in subsets of the unit interval also holds for subsets of the integers with fractional density and satisfying certain Fourier-decay conditions.
Singular Soliton Operators and Indefinite Metrics
Grinevich, P. G.; Novikov, S. P.
2011-01-01
The singular real second order 1D Schrodinger operators are considered here with such potentials that all local solutions near singularities to the eigenvalue problem are meromorphic for all values of the spectral parameter. All algebro-geometrical or "singular finite-gap" potentials satisfy to this condition. A Spectral Theory is constructed here for the periodic and rapidly decreasing cases in the special classes of functions with singularities and indefinite inner product. It has a finite ...
Free string evolution across plane wave singularities
Craps, Ben; Evnin, Oleg
2009-01-01
In these proceedings, we summarize our studies of free string propagation in (near-)singular scale-invariant plane wave geometries. We analyze the singular limit of the evolution for the center-of-mass motion and all excited string modes. The requirement that the entire excitation energy of the string should be finite excludes consistent propagation across the singularity, in case no dimensionful scales are introduced at the singular locus (in an otherwise scale-invariant space-time).
Singular integral on bounded strictly pseudoconvex domain
Institute of Scientific and Technical Information of China (English)
GONG Ding-dong
2008-01-01
Kytmanov and Myslivets gave a special Cauchy principal value of the singular integral on the bounded strictly pseudoconvex domain with smooth boundary. By means of this Cauchy integral principal value, the corresponding singular integral and a composition formula are obtained. This composition formula is quite different from usual ones in form. As an application, the corresponding singular integral equation and the system of singular integral equations are discussed as well.
Energy Technology Data Exchange (ETDEWEB)
Hastings, Matthew B [Los Alamos National Laboratory
2009-01-01
We show how to combine the light-cone and matrix product algorithms to simulate quantum systems far from equilibrium for long times. For the case of the XXZ spin chain at {Delta} = 0.5, we simulate to a time of {approx} 22.5. While part of the long simulation time is due to the use of the light-cone method, we also describe a modification of the infinite time-evolving bond decimation algorithm with improved numerical stability, and we describe how to incorporate symmetry into this algorithm. While statistical sampling error means that we are not yet able to make a definite statement, the behavior of the simulation at long times indicates the appearance of either 'revivals' in the order parameter as predicted by Hastings and Levitov (e-print arXiv:0806.4283) or of a distinct shoulder in the decay of the order parameter.
Singularities from colliding plane gravitational waves
Tipler, Frank J.
1980-12-01
A simple geometrical argument is given which shows that a collision between two plane gravitational waves must result in singularities. The argument suggests that these singularities are a peculiar feature of plane waves, because singularities are also a consequence of a collision between self-gravitating plane waves of other fields with arbitrarily small energy density.
Singularities from colliding plane gravitational waves
Energy Technology Data Exchange (ETDEWEB)
Tipler, F.J.
1980-12-15
A simple geometrical argument is given which shows that a collision between two plane gravitational waves must result in singularities. The argument suggests that these singularities are a peculiar feature of plane waves, because singularities are also a consequence of a collision between self-gravitating plane waves of other fields with arbitrarily small energy density.
Singularity development and supersymmetry in holography
Buchel, Alex
2017-08-01
We study the effects of supersymmetry on singularity development scenario in holography presented in [1] (BBL). We argue that the singularity persists in a supersymmetric extension of the BBL model. The challenge remains to find a string theory embedding of the singularity mechanism.
Numerical Quadrature of Periodic Singular Integral Equations
DEFF Research Database (Denmark)
Krenk, Steen
1978-01-01
This paper presents quadrature formulae for the numerical integration of a singular integral equation with Hilbert kernel. The formulae are based on trigonometric interpolation. By integration a quadrature formula for an integral with a logarithmic singularity is obtained. Finally...... it is demonstrated how a singular integral equation with infinite support can be solved by use of the preceding formulae....
OPTIMIZED STRAPDOWN CONING CORRECTION ALGORITHM
Institute of Scientific and Technical Information of China (English)
黄磊; 刘建业; 曾庆化
2013-01-01
Traditional coning algorithms are based on the first-order coning correction reference model .Usually they reduce the algorithm error of coning axis (z) by increasing the sample numbers in one iteration interval .But the increase of sample numbers requires the faster output rates of sensors .Therefore ,the algorithms are often lim-ited in practical use .Moreover ,the noncommutivity error of rotation usually exists on all three axes and the in-crease of sample numbers has little positive effect on reducing the algorithm errors of orthogonal axes (x ,y) . Considering the errors of orthogonal axes cannot be neglected in the high-precision applications ,a coning algorithm with an additional second-order coning correction term is developed to further improve the performance of coning algorithm .Compared with the traditional algorithms ,the new second-order coning algorithm can effectively reduce the algorithm error without increasing the sample numbers .Theoretical analyses validate that in a coning environ-ment with low frequency ,the new algorithm has the better performance than the traditional time-series and fre-quency-series coning algorithms ,while in a maneuver environment the new algorithm has the same order accuracy as the traditional time-series and frequency-series algorithms .Finally ,the practical feasibility of the new coning al-gorithm is demonstrated by digital simulations and practical turntable tests .
Shatter cones: Diagnostic impact signatures
Mchone, J. F.; Dietz, R. S.
1988-01-01
Uniquely fractured target rocks known as shatter cones are associated with more than one half the world's 120 or so presently known impact structures. Shatter cones are a form of tensile rock failure in which a positive conical plug separates from a negative outer cup or mold and delicate ornaments radiating from an apex are preserved on surfaces of both portions. Although distinct, shatter cones are sometimes confused with other striated geologic features such as ventifacts, stylolites, cone-in-cone, slickensides, and artificial blast plumes. Complete cones or solitary cones are rare, occurrences are usually as swarms in thoroughly fractured rock. Shatter cones may form in a zone where an expanding shock wave propagating through a target decays to form an elastic wave. Near this transition zone, the expanding primary wave may strike a pebble or other inhomogeneity whose contrasting transmission properties produce a scattered secondary wave. Interference between primary and secondary scattered waves produce conical stress fields with axes perpendicular to the plane of an advancing shock front. This model supports mechanism capable of producing such shatter cone properties as orientation, apical clasts, lithic dependence, and shock pressure zonation. Although formational mechanics are still poorly understood, shatter cones have become the simplest geologic field criterion for recognizing astroblemes (ancient terrestrial impact structures).
Directory of Open Access Journals (Sweden)
Hamel Christian P
2007-02-01
Full Text Available Abstract Cone rod dystrophies (CRDs (prevalence 1/40,000 are inherited retinal dystrophies that belong to the group of pigmentary retinopathies. CRDs are characterized by retinal pigment deposits visible on fundus examination, predominantly localized to the macular region. In contrast to typical retinitis pigmentosa (RP, also called the rod cone dystrophies (RCDs resulting from the primary loss in rod photoreceptors and later followed by the secondary loss in cone photoreceptors, CRDs reflect the opposite sequence of events. CRD is characterized by primary cone involvement, or, sometimes, by concomitant loss of both cones and rods that explains the predominant symptoms of CRDs: decreased visual acuity, color vision defects, photoaversion and decreased sensitivity in the central visual field, later followed by progressive loss in peripheral vision and night blindness. The clinical course of CRDs is generally more severe and rapid than that of RCDs, leading to earlier legal blindness and disability. At end stage, however, CRDs do not differ from RCDs. CRDs are most frequently non syndromic, but they may also be part of several syndromes, such as Bardet Biedl syndrome and Spinocerebellar Ataxia Type 7 (SCA7. Non syndromic CRDs are genetically heterogeneous (ten cloned genes and three loci have been identified so far. The four major causative genes involved in the pathogenesis of CRDs are ABCA4 (which causes Stargardt disease and also 30 to 60% of autosomal recessive CRDs, CRX and GUCY2D (which are responsible for many reported cases of autosomal dominant CRDs, and RPGR (which causes about 2/3 of X-linked RP and also an undetermined percentage of X-linked CRDs. It is likely that highly deleterious mutations in genes that otherwise cause RP or macular dystrophy may also lead to CRDs. The diagnosis of CRDs is based on clinical history, fundus examination and electroretinogram. Molecular diagnosis can be made for some genes, genetic counseling is
Multidimensional singular integrals and integral equations
Mikhlin, Solomon Grigorievich; Stark, M; Ulam, S
1965-01-01
Multidimensional Singular Integrals and Integral Equations presents the results of the theory of multidimensional singular integrals and of equations containing such integrals. Emphasis is on singular integrals taken over Euclidean space or in the closed manifold of Liapounov and equations containing such integrals. This volume is comprised of eight chapters and begins with an overview of some theorems on linear equations in Banach spaces, followed by a discussion on the simplest properties of multidimensional singular integrals. Subsequent chapters deal with compounding of singular integrals
Universality of Tip Singularity Formation in Freezing Water Drops
Marin, Alvaro G; Brunet, Philipe; Colinet, Pierre; Snoeijer, Jacco H
2014-01-01
A drop of water deposited on a cold plate freezes into an ice drop with a pointy tip. While this phenomenon clearly finds its origin in the expansion of water upon freezing, a quantitative description of the tip singularity has remained elusive. Here we demonstrate how the geometry of the freezing front, determined by heat transfer considerations, is crucial for the tip formation. We perform systematic measurements of the angles of the conical tip, and reveal the dynamics of the solidification front in a Hele-Shaw geometry. It is found that the cone angle is independent of substrate temperature and wetting angle, suggesting a universal, self-similar mechanism that does not depend on the rate of solidification. We propose a model for the freezing front and derive resulting tip angles analytically, in good agreement with observations.
Quantum recurrence and integer ratios in neutron resonances
Energy Technology Data Exchange (ETDEWEB)
Ohkubo, Makio
1998-03-01
Quantum recurrence of the compound nucleus in neutron resonance reactions are described for normal modes which are excited on the compound nucleus simultaneously. In the structure of the recurrence time, integer relations among dominant level spacings are derived. The `base modes` are assumed as stable combinations of the normal modes, preferably excited in many nuclei. (author)
Designing fractional factorial split-plot experiments using integer programming
DEFF Research Database (Denmark)
Capehart, Shay R.; Keha, Ahmet; Kulahci, Murat
2011-01-01
factorial (FF) design, with the restricted randomisation structure to account for the whole plots and subplots. We discuss the formulation of FFSP designs using integer programming (IP) to achieve various design criteria. We specifically look at the maximum number of clear two-factor interactions...
Method for solving a convex integer programming problem
Stefanov, Stefan M.
2003-01-01
We consider a convex integer program which is a nonlinear version of the assignment problem. This problem is reformulated as an equivalent problem. An algorithm for solving the original problem is suggested which is based on solving the simple assignment problem via some of known algorithms.
Solving linear integer programming problems by a novel neural model.
Cavalieri, S
1999-02-01
The paper deals with integer linear programming problems. As is well known, these are extremely complex problems, even when the number of integer variables is quite low. Literature provides examples of various methods to solve such problems, some of which are of a heuristic nature. This paper proposes an alternative strategy based on the Hopfield neural network. The advantage of the strategy essentially lies in the fact that hardware implementation of the neural model allows for the time required to obtain a solution so as not depend on the size of the problem to be solved. The paper presents a particular class of integer linear programming problems, including well-known problems such as the Travelling Salesman Problem and the Set Covering Problem. After a brief description of this class of problems, it is demonstrated that the original Hopfield model is incapable of supplying valid solutions. This is attributed to the presence of constant bias currents in the dynamic of the neural model. A demonstration of this is given and then a novel neural model is presented which continues to be based on the same architecture as the Hopfield model, but introduces modifications thanks to which the integer linear programming problems presented can be solved. Some numerical examples and concluding remarks highlight the solving capacity of the novel neural model.
Unique Factorization in Cyclotomic Integers of Degree Seven
Duckworth, W. Ethan
2008-01-01
This article provides a survey of some basic results in algebraic number theory and applies this material to prove that the cyclotomic integers generated by a seventh root of unity are a unique factorization domain. Part of the proof uses the computer algebra system Maple to find and verify factorizations. The proofs use a combination of historic…
Leveraging Structure: Logical Necessity in the Context of Integer Arithmetic
Bishop, Jessica Pierson; Lamb, Lisa L.; Philipp, Randolph A.; Whitacre, Ian; Schappelle, Bonnie P.
2016-01-01
Looking for, recognizing, and using underlying mathematical structure is an important aspect of mathematical reasoning. We explore the use of mathematical structure in children's integer strategies by developing and exemplifying the construct of logical necessity. Students in our study used logical necessity to approach and use numbers in a…
Limit theorems for bifurcating integer-valued autoregressive processes
Blandin, Vassili
2012-01-01
We study the asymptotic behavior of the weighted least squares estimators of the unknown parameters of bifurcating integer-valued autoregressive processes. Under suitable assumptions on the immigration, we establish the almost sure convergence of our estimators, together with the quadratic strong law and central limit theorems. All our investigation relies on asymptotic results for vector-valued martingales.
Designing fractional factorial split-plot experiments using integer programming
DEFF Research Database (Denmark)
Capehart, Shay R.; Keha, Ahmet; Kulahci, Murat
2011-01-01
factorial (FF) design, with the restricted randomisation structure to account for the whole plots and subplots. We discuss the formulation of FFSP designs using integer programming (IP) to achieve various design criteria. We specifically look at the maximum number of clear two-factor interactions...
Happy and Sad Thoughts: An Exploration of Children's Integer Reasoning
Whitacre, Ian; Bishop, Jessica Pierson; Lamb, Lisa L. C.; Philipp, Randolph A.; Schappelle, Bonnie P.; Lewis, Melinda L.
2012-01-01
The purpose of this study was to investigate elementary children's conceptions that might serve as foundations for integer reasoning. Working from an abstract algebraic perspective and using an opposite-magnitudes context that is relevant to children, we analyzed the reasoning of 33 children in grades K-5. We focus our report on three prominent…
Automorphisms of semigroups of invertible matrices with nonnegative integer elements
Energy Technology Data Exchange (ETDEWEB)
Semenov, Pavel P [M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow (Russian Federation)
2012-09-30
Let G{sub n}(Z) be the subsemigroup of GL{sub n}(Z) consisting of the matrices with nonnegative integer coefficients. In the paper, the automorphisms of this semigroup are described for n{>=}2. Bibliography: 5 titles.
A fast DFT algorithm using complex integer transforms
Reed, I. S.; Truong, T. K.
1978-01-01
Winograd's algorithm for computing the discrete Fourier transform is extended considerably for certain large transform lengths. This is accomplished by performing the cyclic convolution, required by Winograd's method, by a fast transform over certain complex integer fields. This algorithm requires fewer multiplications than either the standard fast Fourier transform or Winograd's more conventional algorithms.
Triangular Numbers, Gaussian Integers, and KenKen
Watkins, John J.
2012-01-01
Latin squares form the basis for the recreational puzzles sudoku and KenKen. In this article we show how useful several ideas from number theory are in solving a KenKen puzzle. For example, the simple notion of triangular number is surprisingly effective. We also introduce a variation of KenKen that uses the Gaussian integers in order to…
Algorithms and Data Structures for Strings, Points and Integers
DEFF Research Database (Denmark)
Vind, Søren Juhl
This dissertation presents our research in the broad area of algorithms and data structures. More specifically, we show solutions for the following problems related to strings, points and integers. Results hold on the Word RAM and we measure space in w-bit words. Compressed Fingerprints. The Karp...
Negative Integer Understanding: Characterizing First Graders' Mental Models
Bofferding, Laura
2014-01-01
This article presents results of a research study. Sixty-one first graders' responses to interview questions about negative integer values and order and directed magnitudes were examined to characterize the students' mental models. The models reveal that initially, students overrelied on various combinations of whole-number principles as…
Happy and Sad Thoughts: An Exploration of Children's Integer Reasoning
Whitacre, Ian; Bishop, Jessica Pierson; Lamb, Lisa L. C.; Philipp, Randolph A.; Schappelle, Bonnie P.; Lewis, Melinda L.
2012-01-01
The purpose of this study was to investigate elementary children's conceptions that might serve as foundations for integer reasoning. Working from an abstract algebraic perspective and using an opposite-magnitudes context that is relevant to children, we analyzed the reasoning of 33 children in grades K-5. We focus our report on three prominent…
Currency Arbitrage Detection Using a Binary Integer Programming Model
Soon, Wanmei; Ye, Heng-Qing
2011-01-01
In this article, we examine the use of a new binary integer programming (BIP) model to detect arbitrage opportunities in currency exchanges. This model showcases an excellent application of mathematics to the real world. The concepts involved are easily accessible to undergraduate students with basic knowledge in Operations Research. Through this…
Stochastic level-value approximation for quadratic integer convex programming
Institute of Scientific and Technical Information of China (English)
PENG Zheng; WU Dong-hua
2008-01-01
We propose a stochastic level value approximation method for a quadratic integer convex minimizing problem in this paper. This method applies an importance sampling technique, and make use of the cross-entropy method to update the sample density functions. We also prove the asymptotic convergence of this algorithm, and re-port some numerical results to illuminate its effectiveness.
Solving the Water Jugs Problem by an Integer Sequence Approach
Man, Yiu-Kwong
2012-01-01
In this article, we present an integer sequence approach to solve the classic water jugs problem. The solution steps can be obtained easily by additions and subtractions only, which is suitable for manual calculation or programming by computer. This approach can be introduced to secondary and undergraduate students, and also to teachers and…
Simple integer recourse models : convexity and convex approximations
Klein Haneveld, W.K.; Stougie, L.; van der Vlerk, M.H.
We consider the objective function of a simple recourse problem with fixed technology matrix and integer second-stage variables. Separability due to the simple recourse structure allows to study a one-dimensional version instead. Based on an explicit formula for the objective function, we derive a
Simple Integer Recourse Models : Convexity and Convex Approximations
Klein Haneveld, Willem K.; Stougie, L; van der Vlerk, Maarten H.
2004-01-01
We consider the objective function of a simple recourse problem with fixed technology matrix and integer second-stage variables. Separability due to the simple recourse structure allows to study a one-dimensional version instead. Based on an explicit formula for the objective function, we derive a
Singularities formation, structure, and propagation
Eggers, J
2015-01-01
Many key phenomena in physics and engineering are described as singularities in the solutions to the differential equations describing them. Examples covered thoroughly in this book include the formation of drops and bubbles, the propagation of a crack and the formation of a shock in a gas. Aimed at a broad audience, this book provides the mathematical tools for understanding singularities and explains the many common features in their mathematical structure. Part I introduces the main concepts and techniques, using the most elementary mathematics possible so that it can be followed by readers with only a general background in differential equations. Parts II and III require more specialised methods of partial differential equations, complex analysis and asymptotic techniques. The book may be used for advanced fluid mechanics courses and as a complement to a general course on applied partial differential equations.
Energy conditions and spacetime singularities
Energy Technology Data Exchange (ETDEWEB)
Tipler, F.J.
1978-05-15
In this paper, a number of theorems are proven which collectively show that singularities will occur in spacetime under weaker energy conditions than the strong energy condition. In particular, the Penrose theorem, which uses only the weak energy condition but which applies only to open universes, is extended to all closed universes which have a Cauchy surface whose universal covering manifold is not a three-sphere. Furthermore, it is shown that the strong energy condition in the Hawking-Penrose theorem can be replaced by the weak energy condition and the assumption that the strong energy condition holds only on the average. In addition, it is demonstrated that if the Universe is closed, then the existence of singularities follows from the averaged strong energy condition alone. It is argued that any globally hyperbolic spacetime which satisfies the weak energy condition and which contains a black hole must be null geodesically incomplete.
Singularities in fully developed turbulence
Energy Technology Data Exchange (ETDEWEB)
Shivamoggi, Bhimsen K., E-mail: bhimsen.shivamoggi@ucf.edu
2015-09-18
Phenomenological arguments are used to explore finite-time singularity (FTS) development in different physical fully-developed turbulence (FDT) situations. Effects of spatial intermittency and fluid compressibility in three-dimensional (3D) FDT and the role of the divorticity amplification mechanism in two-dimensional (2D) FDT and quasi-geostrophic FDT and the advection–diffusion mechanism in magnetohydrodynamic turbulence are considered to provide physical insights into the FTS development in variant cascade physics situations. The quasi-geostrophic FDT results connect with the 2D FDT results in the barotropic limit while they connect with 3D FDT results in the baroclinic limit and hence apparently provide a bridge between 2D and 3D. - Highlights: • Finite-time singularity development in turbulence situations is phenomenologically explored. • Spatial intermittency and compressibility effects are investigated. • Quasi-geostrophic turbulence is shown to provide a bridge between two-dimensional and three-dimensional cases.
Ortiz, Néstor; Sarbach, Olivier; Zannias, Thomas
2015-08-01
We analyze the redshift suffered by photons originating from an external source, traversing a collapsing dust cloud, and finally being received by an asymptotic observer. In addition, we study the shadow that the collapsing cloud casts on the sky of the asymptotic observer. We find that the resulting redshift and properties of the shadow depend crucially on whether the final outcome of the complete gravitational collapse is a black hole or a naked singularity. In the black hole case, the shadow is due to the high redshift acquired by the photons as they approach the event horizon, implying that their energy is gradually redshifted toward zero within a few crossing times associated with the event horizon radius. In contrast to this, a naked singularity not only absorbs photons originating from the source, but it also emits infinitely redshifted photons with and without angular momenta. This emission introduces an abrupt cutoff in the frequency shift of the photons detected in directions close to the radial one, and it is responsible for the shadow masking the source in the naked singularity case. Furthermore, even though the shadow forms and begins to grow immediately after the observer crosses the Cauchy horizon, it takes many more crossing times than in the black hole case for the source to be occulted from the observer's eyes. We discuss possible implications of our results for testing the weak cosmic censorship hypothesis. Even though at late times the image of the source perceived by the observer looks the same in both cases, the dynamical formation of the shadow and the redshift images has distinct features and time scales in the black hole versus the naked singularity case. For stellar collapse, these time scales seem to be too short to be resolved with existing technology. However, our results may be relevant for the collapse of seeds leading to supermassive black holes.
Singularities in Speckled Speckle: Statistics
Freund, Isaac
2008-01-01
Random optical fields with two widely different correlation lengths generate far field speckle spots that are themselves highly speckled. We call such patterns speckled speckle, and study their critical points (singularities and stationary points) using analytical theory and computer simulations. We find anomalous spatial arrangements of the critical points and orders of magnitude anomalies in their relative number densities, and in the densities of the associated zero crossings.
Geometric phases in graphitic cones
Energy Technology Data Exchange (ETDEWEB)
Furtado, Claudio [Departamento de Fisica, CCEN, Universidade Federal da Paraiba, Cidade Universitaria, 58051-970 Joao Pessoa, PB (Brazil)], E-mail: furtado@fisica.ufpb.br; Moraes, Fernando [Departamento de Fisica, CCEN, Universidade Federal da Paraiba, Cidade Universitaria, 58051-970 Joao Pessoa, PB (Brazil); Carvalho, A.M. de M [Departamento de Fisica, Universidade Estadual de Feira de Santana, BR116-Norte, Km 3, 44031-460 Feira de Santana, BA (Brazil)
2008-08-04
In this Letter we use a geometric approach to study geometric phases in graphitic cones. The spinor that describes the low energy states near the Fermi energy acquires a phase when transported around the apex of the cone, as found by a holonomy transformation. This topological result can be viewed as an analogue of the Aharonov-Bohm effect. The topological analysis is extended to a system with n cones, whose resulting configuration is described by an effective defect00.
Singularity Problem in Teleparallel Dark Energy Models
Geng, Chao-Qiang; Lee, Chung-Chi
2013-01-01
We study the singularity problem in teleparallel dark energy models. A future singularity may occur due to the non-minimal coupling of the dark energy scalar field to teleparallel gravity that effectively changes the gravitational coupling strength and can even make it diverge. This singularity may be avoided by a binding-type self-potential that keeps the scalar field away from the singularity point. For demonstration we analyze the model with a quadratic potential and show how the (non)occurrence of the singularity depends on the initial conditions and the steepness of the potential, both of which affect the competition between the self-interaction and the non-minimal coupling. To examine the capability of the binding-type potential to fit observational data and meanwhile to avoid the singularity, we perform the data fitting for this model and show that the observationally viable region up to the $3\\sigma$ confidence level is free of the future singularity.
On the Milnor fibers of sandwiched singularities
Nemethi, Andras
2009-01-01
The sandwiched surface singularities are those rational surface singularities which dominate birationally smooth surface singularities. de Jong and van Straten showed that one can reduce the study of the deformations of a sandwiched surface singularity to the study of deformations of a 1-dimensional object, a so-called decorated plane curve singularity. In particular, the Milnor fibers corresponding to their various smoothing components may be reconstructed up to diffeomorphisms from those deformations of associated decorated curves which have only ordinary singularities. Part of the topology of such a deformation is encoded in the incidence matrix between the irreducible components of the deformed curve and the points which decorate it, well-defined up to permutations of columns. Extending a previous theorem ofours, which treated the case of cyclic quotient singularities, we show that the Milnor fibers which correspond to deformations whose incidence matrices are different up to permutations of columns are n...
Non-singular dislocation fields
Energy Technology Data Exchange (ETDEWEB)
Aifantis, Elias C, E-mail: mom@mom.gen.auth.gr [Laboratory of Mechanics and Materials, Faculty of Engineering, Aristotle University of Thessaloniki, GR-54124, Thessaloniki (Greece); Center for Mechanics of Materials, Michigan Technological University, Houghton MI 49931 (United States)
2009-07-15
Non-singular solutions for dislocation and disclination fields have recently been obtained by the author and his co-workers by using a robust model of gradient elasticity theory. These solutions, whose form is simple and easy to implement, are obtained by reducing the gradient elasticity problem to a corresponding linear elasticity boundary value problem through the solutions of an inhomogeneous Helmholtz equation where the source term is the classical singular solution. The Laplacian in the Helmholtz equation, involving the extra gradient coefficient, produces a new term in the gradient solution which asymptotically approaches the negative of the classical elasticity solution on the dislocation line. Thus, the singularity is eliminated and an arbitrary estimate of the dislocation core size introduced in classical theory, is not required. These predictions are tested against atomistic calculations and their implications to various dislocation related configurations are discussed. Due to the simple and elegant form of these solutions, it is hoped that they will be useful in discrete dislocation dynamics simulations.
A Light-Cone QCD Inspired Meson Model with a Relativistic Confining Potential in Momentum Space
Institute of Scientific and Technical Information of China (English)
LI Lei; WANG Shun-Jin; ZHOU Shan-Gui; ZHANG Guang-Biao
2007-01-01
For describing the radial excited states a relativistic confining potential in momentum space is included in the meson effective light-cone Hamiltonian. The meson eigen equations are transformed from the front form to the instant form and formulated in total angular representation. Details about numerically solving these equations are discussed, mainly focusing on treating singularities arising from one-gluon exchange interactions and confinement. The results of pseudo-scalar mesons indicate that the improved meson effective light-cone Hamiltonian can describe the ground states and radial excited states well. Some radial excited states are also predicted and waiting for experimental test.
Infinite Families of Singular K-tight Integers%奇异k-紧整数无限族
Institute of Scientific and Technical Information of China (English)
陈协彬
2006-01-01
设n,s1,s2是3个正整数,使得s1＜s2＜n,gcd(n,s1,s2)=1.双环网G(n;s1,s2)是个有向图,其结点集为V={0,1,2,…,n-1},其弧集为A={i→i+s1(mod n),i→i+s2(mod n)|i∈V},S1和S2称为步长.设d(n;S1,S2)为双环网G(n;s1,s2)的直径.令d(n)=min{d(n;s1,s2)|s1＜s2＜n},d1(n)=min{d(n;1,s)|1＜s＜n}.已知d1(n)≥d(n)≥|√3n |-2=lb(n).若d(n;s1,s2)=d(n)=lb(n)+k(k≥0),则称G(n;s1,s2)是个k-紧优的双环网.虽然等式d1(n)=d(n)对于无限多个整数n成立,但也存在无限多个整数n使得d1(n)＞ d(n),这样的n称为奇异整数.若d1(n)＞d(n)=lb(n)+k,k≥0,则这样的n称为奇异k-紧整数.本文给出构造奇异k-紧整数无限族的方法,并对于k:1,2,…,20,构造出这样的无限族.
Directory of Open Access Journals (Sweden)
Baoqiang Yan
2008-10-01
Full Text Available Using the fixed point theorem in cones, this paper shows the existence of multiple positive solutions for the singular $m$-point boundary-value problem $$displaylines{ x''(t+a(tf(t,x(t,x'(t=0,quad 0
Directory of Open Access Journals (Sweden)
Gai Gongqi
2011-01-01
Full Text Available Abstract This article studies the boundary value problems for the third-order nonlinear singular difference equations Δ 3 u ( i - 2 + λ a ( i f ( i , u ( i = 0 , i ∈ [ 2 , T + 2 ] , satisfying five kinds of different boundary value conditions. This article shows the existence of positive solutions for positone and semi-positone type. The nonlinear term may be singular. Two examples are also given to illustrate the main results. The arguments are based upon fixed point theorems in a cone. MSC [2008]: 34B15; 39A10.
Fritzsch, Harald
2003-01-01
This talk follows by a few months a talk by the same authors on nearly the same subject at the Coral Gables Conference. The ideas presented here are basically the same, but with some amplification, some change of viewpoint, and a number of new questions for the future. For our own convenience, we have transcribed the Coral Gables paper, but with an added ninth section, entitled "Problems of light cone current algebra", dealing with our present views and emphasizing research topics that require study.
Mathematical models with singularities a zoo of singular creatures
Torres, Pedro J
2015-01-01
The book aims to provide an unifying view of a variety (a 'zoo') of mathematical models with some kind of singular nonlinearity, in the sense that it becomes infinite when the state variable approaches a certain point. Up to 11 different concrete models are analyzed in separate chapters. Each chapter starts with a discussion of the basic model and its physical significance. Then the main results and typical proofs are outlined, followed by open problems. Each chapter is closed by a suitable list of references. The book may serve as a guide for researchers interested in the modelling of real world processes.
Efficient Algorithms for gcd and Cubic Residuosity in the Ring of Eisenstein Integers
DEFF Research Database (Denmark)
Damgård, Ivan Bjerre; Frandsen, Gudmund Skovbjerg
2003-01-01
We present simple and efficient algorithms for computing gcd and cubic residuosity in the ring of Eisenstein integers, bf Z[ ]i.e. the integers extended with , a complex primitive third root of unity. The algorithms are similar and may be seen as generalisations of the binary integer gcd and deri...... primality tests and the implementation of cryptographic protocols....
GNSS integer ambiguity estimation and evaluation: LAMBDA and Ps-LAMBDA
Li, B.; Verhagen, A.A.; Teunissen, P.J.G.
2013-01-01
Successful integer carrier-phase ambiguity resolution is crucial for high precision GNSS applications. It includes both integer estimation and evaluation. For integer estimation, the LAMBDA method has been applied in a wide variety of GNSS applications. The method’s popularity stems from its numeric
Asymptotics of bivariate generating functions with algebraic singularities
Greenwood, Torin
Flajolet and Odlyzko (1990) derived asymptotic formulae the coefficients of a class of uni- variate generating functions with algebraic singularities. Gao and Richmond (1992) and Hwang (1996, 1998) extended these results to classes of multivariate generating functions, in both cases by reducing to the univariate case. Pemantle and Wilson (2013) outlined new multivariate ana- lytic techniques and used them to analyze the coefficients of rational generating functions. After overviewing these methods, we use them to find asymptotic formulae for the coefficients of a broad class of bivariate generating functions with algebraic singularities. Beginning with the Cauchy integral formula, we explicity deform the contour of integration so that it hugs a set of critical points. The asymptotic contribution to the integral comes from analyzing the integrand near these points, leading to explicit asymptotic formulae. Next, we use this formula to analyze an example from current research. In the following chapter, we apply multivariate analytic techniques to quan- tum walks. Bressler and Pemantle (2007) found a (d + 1)-dimensional rational generating function whose coefficients described the amplitude of a particle at a position in the integer lattice after n steps. Here, the minimal critical points form a curve on the (d + 1)-dimensional unit torus. We find asymptotic formulae for the amplitude of a particle in a given position, normalized by the number of steps n, as n approaches infinity. Each critical point contributes to the asymptotics for a specific normalized position. Using Groebner bases in Maple again, we compute the explicit locations of peak amplitudes. In a scaling window of size the square root of n near the peaks, each amplitude is asymptotic to an Airy function.
DEFF Research Database (Denmark)
Simonsen, Bo Cerup
1997-01-01
The present paper is concerned with steady-state plate tearing by a cone. This is a scenario where a cone is forced through a ductile metal plate with a constant lateral tip penetration in a motion in the plane of the plate. The considered process could be an idealisaton of the damage, which...
DEFF Research Database (Denmark)
Simonsen, Bo Cerup
1998-01-01
The present paper is concerned with steady-state plate tearing by a cone. This is a scenario where a cone is forced through a ductile metal plate with a constant lateral tip penetration in a motion in the plane of the plate. The considered process could be an idealisation of the damage, which...
Making An Impact: Shatter Cones
Blank, Lisa M.; Plautz, Michael R.; Crews, Jeffrey W.
2004-01-01
In 1990, a group of geologists discovered a large number of shatter cones in southwestern Montana. Shatter cones are a type of metamorphosed rock often found in impact structures (the remains of a crater after a meteor impact and years of Earth activity). Scientists have discovered only 168 impact craters around the world. If rocks could talk,…
The Indispensability of Ghost Fields in the Light-Cone Gauge Quantization of Gauge Fields
Nakawaki, Yuji; McCartor, Gary
1999-01-01
We continue McCartor and Robertson's recent demonstration of the indispensability of ghost fields in the light-cone gauge quantization of gauge fields. It is shown that the ghost fields are indispensable in deriving well-defined antiderivatives and in regularizing the most singular component of gauge field propagator. To this end it is sufficient to confine ourselves to noninteracting abelian fields. Furthermore to circumvent dealing with constrained systems, we construct the temporal gauge c...
Boundary effects on the supersymmetric sine-Gordon model through light-cone lattice approach
Matsui, Chihiro
2014-01-01
We discussed subspaces of the N=1 supersymmetric sine-Gordon model with Dirichlet boundaries through light-cone lattice regularization. In this paper, we showed, unlike the periodic boundary case, both of Neveu-Schwarz (NS) and Ramond (R) sectors of a superconformal field theory were obtained. Using a method of nonlinear integral equations for auxiliary functions defined by eigenvalues of transfer matrices, we found that an excitation state with an odd number of particles is allowed for a certain value of a boundary parameter even on a system consisting of an even number of sites. In a small-volume limit where conformal invariance shows up in the theory, we derived conformal dimensions of states constructed through the lattice-regularized theory. The result shows existence of the R sector, which cannot be obtained from the periodic system, while a winding number is restricted to an integer or a half-integer depending on boundary parameters.
Dimensional Mutation and Spacelike Singularities
Silverstein, E
2006-01-01
I argue that critical string theory on a Riemann surface of genus $h >> 1$ crosses over, when the surface approaches the string scale in size, to a background of supercritical string theory with effective central charge as large as $2h$. Concrete evidence for this proposal is provided by the high energy density of states (realized on the Riemann surface side by strings wrapping nontrivial elements of the fundamental group) and by a linear sigma model which at large $h$ approximates the time evolution through the initial transition. This suggests that cosmological singularities arising in negatively curved FRW backgrounds may be replaced by a phase of supercritical string theory.
Multichannel framework for singular quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Camblong, Horacio E., E-mail: camblong@usfca.edu [Department of Physics and Astronomy, University of San Francisco, San Francisco, CA 94117-1080 (United States); Epele, Luis N., E-mail: epele@fisica.unlp.edu.ar [Laboratorio de Física Teórica, Departamento de Física, IFLP, CONICET, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, C.C. 67–1900 La Plata (Argentina); Fanchiotti, Huner, E-mail: huner@fisica.unlp.edu.ar [Laboratorio de Física Teórica, Departamento de Física, IFLP, CONICET, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, C.C. 67–1900 La Plata (Argentina); García Canal, Carlos A., E-mail: garcia@fisica.unlp.edu.ar [Laboratorio de Física Teórica, Departamento de Física, IFLP, CONICET, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, C.C. 67–1900 La Plata (Argentina); Ordóñez, Carlos R., E-mail: ordonez@uh.edu [Department of Physics, University of Houston, Houston, TX 77204-5506 (United States)
2014-01-15
A multichannel S-matrix framework for singular quantum mechanics (SQM) subsumes the renormalization and self-adjoint extension methods and resolves its boundary-condition ambiguities. In addition to the standard channel accessible to a distant (“asymptotic”) observer, one supplementary channel opens up at each coordinate singularity, where local outgoing and ingoing singularity waves coexist. The channels are linked by a fully unitary S-matrix, which governs all possible scenarios, including cases with an apparent nonunitary behavior as viewed from asymptotic distances. -- Highlights: •A multichannel framework is proposed for singular quantum mechanics and analogues. •The framework unifies several established approaches for singular potentials. •Singular points are treated as new scattering channels. •Nonunitary asymptotic behavior is subsumed in a unitary multichannel S-matrix. •Conformal quantum mechanics and the inverse quartic potential are highlighted.
Weyl Anomaly and Initial Singularity Crossing
Awad, Adel
2015-01-01
We consider the role of quantum effects, mainly, Weyl anomaly in modifying FLRW model singular behavior at early times. Weyl anomaly corrections to FLRW models have been considered in the past, here we reconsider this model and show the following: The singularity of this model is weak according to Tipler and Krolak, therefore, the spacetime might admit a geodesic extension. Weyl anomaly corrections changes the nature of the initial singularity from a big bang singularity to a sudden singularity. The two branches of solutions consistent with the semiclassical treatment form a disconnected manifold. Joining these two parts at the singularity provides us with a $C^1$ extension to nonspacelike geodesics and leaves the spacetime geodesically complete. Using Gauss-Codazzi equations one can derive generalized junction conditions for this higher-derivative gravity. The extended spacetime obeys Friedmann and Raychaudhuri equations and the junction conditions. The junction does not generate Dirac delta functions in mat...
Homogeneous spacelike singularities inside spherical black holes
Burko, L M
1997-01-01
Recent numerical simulations have found that the Cauchy horizon inside spherical charged black holes, when perturbed nonlinearly by a self-gravitating, minimally-coupled, massless, spherically-symmetric scalar field, turns into a null weak singularity which focuses monotonically to $r=0$ at late times, where the singularity becomes spacelike. Our main objective is to study this spacelike singularity. We study analytically the spherically-symmetric Einstein-Maxwell-scalar equations asymptotically near the singularity. We obtain a series-expansion solution for the metric functions and for the scalar field near $r=0$ under the simplifying assumption of homogeneity. Namely, we neglect spatial derivatives and keep only temporal derivatives. We find that there indeed exists a generic spacelike singularity solution for these equations (in the sense that the solution depends on enough free parameters), with similar properties to those found in the numerical simulations. This singularity is strong in the Tipler sense,...
Conformal anomaly around the sudden singularity
Houndjo, S J M
2010-01-01
Quantum effects due to particle creation on a classical sudden singularity have been investigated in a previous work. The conclusion was that quantum effects do not lead to the avoidance nor the modification of the sudden future singularity. In this paper, we investigate quantum corrections coming from conformal anomaly near the sudden future singularity. We conclude that when the equation of state is chosen to be $p=-\\rho-A\\rho^\\alpha$, the conformal anomaly can transform the sudden singularity in the singularity of type III for any $\\alpha> 1/2$ and in the singularity of the type I (the big rip) or the big crunch for $1/2<\\alpha<3/2$.
Conformal anomaly around the sudden singularity
Houndjo, S. J. M.
2010-10-01
Quantum effects due to particle creation on a classical sudden singularity have been investigated in a previous work. The conclusion was that quantum effects do not lead to the avoidance nor the modification of the sudden future singularity. In this paper, we investigate quantum corrections coming from conformal anomaly near the sudden future singularity. We conclude that when the equation of state is chosen to be p=-ρ-Aρα, the conformal anomaly can transform the sudden singularity into the singularity of type III for any α>1/2 and into the singularity of the type I (the big rip) or the big crunch for 1/2<α<3/2.
The geometry of warped product singularities
Stoica, Ovidiu Cristinel
In this article, the degenerate warped products of singular semi-Riemannian manifolds are studied. They were used recently by the author to handle singularities occurring in General Relativity, in black holes and at the big-bang. One main result presented here is that a degenerate warped product of semi-regular semi-Riemannian manifolds with the warping function satisfying a certain condition is a semi-regular semi-Riemannian manifold. The connection and the Riemann curvature of the warped product are expressed in terms of those of the factor manifolds. Examples of singular semi-Riemannian manifolds which are semi-regular are constructed as warped products. Applications include cosmological models and black holes solutions with semi-regular singularities. Such singularities are compatible with a certain reformulation of the Einstein equation, which in addition holds at semi-regular singularities too.
Topological resolution of gauge theory singularities
Energy Technology Data Exchange (ETDEWEB)
Saracco, Fabio; Tomasiello, Alessandro; Torroba, Gonzalo
2013-08-21
Some gauge theories with Coulomb branches exhibit singularities in perturbation theory, which are usually resolved by nonperturbative physics. In string theory this corresponds to the resolution of timelike singularities near the core of orientifold planes by effects from F or M theory. We propose a new mechanism for resolving Coulomb branch singularities in three-dimensional gauge theories, based on Chern-Simons interactions. This is illustrated in a supersymmetric S U ( 2 ) Yang-Mills-Chern-Simons theory. We calculate the one-loop corrections to the Coulomb branch of this theory and find a result that interpolates smoothly between the high-energy metric (that would exhibit the singularity) and a regular singularity-free low-energy result. We suggest possible applications to singularity resolution in string theory and speculate a relationship to a similar phenomenon for the orientifold six-plane in massive IIA supergravity.
Singularity Analysis of Geometric Constraint Systems
Institute of Scientific and Technical Information of China (English)
彭小波; 陈立平; 周凡利; 周济
2002-01-01
Singularity analysis is an important subject of the geometric constraint sat-isfaction problem. In this paper, three kinds of singularities are described and corresponding identification methods are presented for both under-constrained systems and over-constrained systems. Another special but common singularity for under-constrained geometric systems, pseudo-singularity, is analyzed. Pseudo-singularity is caused by a variety of constraint match ing of under-constrained systems and can be removed by improving constraint distribution. To avoid pseudo-singularity and decide redundant constraints adaptively, a differentiation algo rithm is proposed in the paper. Its correctness and efficiency have been validated through its practical applications in a 2D/3D geometric constraint solver CBA.
Topological resolution of gauge theory singularities
Saracco, Fabio; Torroba, Gonzalo
2013-01-01
Some gauge theories with Coulomb branches exhibit singularities in perturbation theory, which are usually resolved by nonperturbative physics. In string theory this corresponds to the resolution of timelike singularities near the core of orientifold planes by effects from F or M theory. We propose a new mechanism for resolving Coulomb branch singularities in three dimensional gauge theories, based on Chern-Simons interactions. This is illustrated in a supersymmetric SU(2) Yang-Mills-Chern-Simons theory. We calculate the one loop corrections to the Coulomb branch of this theory and find a result that interpolates smoothly between the high energy metric (that would exhibit the singularity) and a regular singularity-free low energy result. We suggest possible applications to singularity resolution in string theory and speculate a relationship to a similar phenomenon for the orientifold six-plane in massive IIA supergravity.
String spectra near some null cosmological singularities
Madhu, Kallingalthodi
2009-01-01
We construct cosmological spacetimes with null Kasner-like singularities as purely gravitational solutions with no other background fields turned on. These can be recast as anisotropic plane-wave spacetimes by coordinate transformations. We analyse string quantization to find the spectrum of string modes in these backgrounds. The classical string modes can be solved for exactly in these time-dependent backgrounds, which enables a detailed study of the near singularity string spectrum, (time-dependent) oscillator masses and wavefunctions. We find that for low lying string modes(finite oscillation number), the classical near-singularity string mode functions are non-divergent for various families of singularities. Furthermore, for any infinitesimal regularization of the vicinity of the singularity, we find a tower of string modes of ultra-high oscillation number which propagate essentially freely in the background. The resulting picture suggests that string interactions are non-negligible near the singularity.
Singularities of Type-Q ABS Equations
Directory of Open Access Journals (Sweden)
James Atkinson
2011-07-01
Full Text Available The type-Q equations lie on the top level of the hierarchy introduced by Adler, Bobenko and Suris (ABS in their classification of discrete counterparts of KdV-type integrable partial differential equations. We ask what singularities are possible in the solutions of these equations, and examine the relationship between the singularities and the principal integrability feature of multidimensional consistency. These questions are considered in the global setting and therefore extend previous considerations of singularities which have been local. What emerges are some simple geometric criteria that determine the allowed singularities, and the interesting discovery that generically the presence of singularities leads to a breakdown in the global consistency of such systems despite their local consistency property. This failure to be globally consistent is quantified by introducing a natural notion of monodromy for isolated singularities.
A Secret Image Sharing Method Using Integer Wavelet Transform
Directory of Open Access Journals (Sweden)
Li Ching-Chung
2007-01-01
Full Text Available A new image sharing method, based on the reversible integer-to-integer (ITI wavelet transform and Shamir's threshold scheme is presented, that provides highly compact shadows for real-time progressive transmission. This method, working in the wavelet domain, processes the transform coefficients in each subband, divides each of the resulting combination coefficients into shadows, and allows recovery of the complete secret image by using any or more shadows . We take advantages of properties of the wavelet transform multiresolution representation, such as coefficient magnitude decay and excellent energy compaction, to design combination procedures for the transform coefficients and processing sequences in wavelet subbands such that small shadows for real-time progressive transmission are obtained. Experimental results demonstrate that the proposed method yields small shadow images and has the capabilities of real-time progressive transmission and perfect reconstruction of secret images.
Extracting vascular networks under physiological constraints via integer programming.
Rempfler, Markus; Schneider, Matthias; Ielacqua, Giovanna D; Xiao, Xianghui; Stock, Stuart R; Klohs, Jan; Székely, Gábor; Andres, Bjoern; Menze, Bjoern H
2014-01-01
We introduce an integer programming-based approach to vessel network extraction that enforces global physiological constraints on the vessel structure and learn this prior from a high-resolution reference network. The method accounts for both image evidence and geometric relationships between vessels by formulating and solving an integer programming problem. Starting from an over-connected network, it is pruning vessel stumps and spurious connections by evaluating bifurcation angle and connectivity of the graph. We utilize a high-resolution micro computed tomography (μCT) dataset of a cerebrovascular corrosion cast to obtain a reference network, perform experiments on micro magnetic resonance angiography (μMRA) images of mouse brains and discuss properties of the networks obtained under different tracking and pruning approaches.
A fuzzy mixed integer programming for marketing planning
Directory of Open Access Journals (Sweden)
Abolfazl Danaei
2014-03-01
Full Text Available One of the primary concerns to market a product is to find appropriate channel to target customers. The recent advances on information technology have created new products with tremendous opportunities. This paper presents a mixed integer programming technique based on McCarthy's 4PS to locate suitable billboards for marketing newly introduced IPHONE product. The paper considers two types of information including age and income and tries to find the best places such that potential consumers aged 25-35 with high income visit the billboards and the cost of advertisement is minimized. The model is formulated in terms of mixed integer programming and it has been applied for potential customers who live in city of Tabriz, Iran. Using a typical software package, the model detects appropriate places in various parts of the city.
Two dimensional convolute integers for machine vision and image recognition
Edwards, Thomas R.
1988-01-01
Machine vision and image recognition require sophisticated image processing prior to the application of Artificial Intelligence. Two Dimensional Convolute Integer Technology is an innovative mathematical approach for addressing machine vision and image recognition. This new technology generates a family of digital operators for addressing optical images and related two dimensional data sets. The operators are regression generated, integer valued, zero phase shifting, convoluting, frequency sensitive, two dimensional low pass, high pass and band pass filters that are mathematically equivalent to surface fitted partial derivatives. These operators are applied non-recursively either as classical convolutions (replacement point values), interstitial point generators (bandwidth broadening or resolution enhancement), or as missing value calculators (compensation for dead array element values). These operators show frequency sensitive feature selection scale invariant properties. Such tasks as boundary/edge enhancement and noise or small size pixel disturbance removal can readily be accomplished. For feature selection tight band pass operators are essential. Results from test cases are given.
Integer-ambiguity resolution in astronomy and geodesy
Lannes, André
2013-01-01
Recent theoretical developments in astronomical aperture synthesis have revealed the existence of integer-ambiguity problems. Those problems, which appear in the self-calibration procedures of radio imaging, have been shown to be similar to the nearest-lattice point (NLP) problems encountered in high-precision geodetic positioning, and in global navigation satellite systems. In this paper, we analyse the theoretical aspects of the matter and propose new methods for solving those NLP problems. The related optimization aspects concern both the preconditioning stage, and the discrete-search stage in which the integer ambiguities are finally fixed. Our algorithms, which are described in an explicit manner, can easily be implemented. They lead to substantial gains in the processing time of both stages. Their efficiency was shown via intensive numerical tests.
Optimization of integer wavelet transforms based on difference correlation structures.
Li, Hongliang; Liu, Guizhong; Zhang, Zhongwei
2005-11-01
In this paper, a novel lifting integer wavelet transform based on difference correlation structure (DCCS-LIWT) is proposed. First, we establish a relationship between the performance of a linear predictor and the difference correlations of an image. The obtained results provide a theoretical foundation for the following construction of the optimal lifting filters. Then, the optimal prediction lifting coefficients in the sense of least-square prediction error are derived. DCCS-LIWT puts heavy emphasis on image inherent dependence. A distinct feature of this method is the use of the variance-normalized autocorrelation function of the difference image to construct a linear predictor and adapt the predictor to varying image sources. The proposed scheme also allows respective calculations of the lifting filters for the horizontal and vertical orientations. Experimental evaluation shows that the proposed method produces better results than the other well-known integer transforms for the lossless image compression.
A NOVEL INTEGER FREQUENCY OFFSET ESTIMATOR FOR OFDM
Institute of Scientific and Technical Information of China (English)
Cai Xuelian; Li Jiandong; Li Changle; Chen Chen
2005-01-01
One of the principal disadvantages of Orthogonal Frequency Division Multiplexing (OFDM) is very sensitive to carrier frequency offset. The integer frequency offset has no effect on the orthogonality among the subcarriers, but it causes a circular shift and phase rotation of the received data symbols sequence, resulting in a Bit Error Rate(BER) of 0.5. In this paper,a novel integer frequency offset estimator for OFDM is derived based on maximum likelihood estimation technique and exploration of the differential relation between two consecutive OFDM data symbol sequences in frequency domain. Its performance is compared with the conventional method by computer simulations for the additive white Gaussian noise channel and a multipath fading channel. Simulation results show that the performance of the proposed estimator is better than the conventional estimator.
Linear Independence of -Logarithms over the Eisenstein Integers
Directory of Open Access Journals (Sweden)
Peter Bundschuh
2010-01-01
Full Text Available For fixed complex with ||>1, the -logarithm is the meromorphic continuation of the series ∑>0/(−1,||1,≠,2,3,…. In 2004, Tachiya showed that this is true in the Subcase =ℚ, ∈ℤ, =−1, and the present authors extended this result to arbitrary integer from an imaginary quadratic number field , and provided a quantitative version. In this paper, the earlier method, in particular its arithmetical part, is further developed to answer the above question in the affirmative if is the Eisenstein number field √ℚ(−3, an integer from , and a primitive third root of unity. Under these conditions, the linear independence holds also for 1,(,(−1, and both results are quantitative.
Some new thin sets of integers in Harmonic Analysis
Li, Daniel; Rodriguez-Piazza, Luis
2009-01-01
We randomly construct various subsets $\\Lambda$ of the integers which have both smallness and largeness properties. They are small since they are very close, in various meanings, to Sidon sets: the continuous functions with spectrum in $\\Lambda$ have uniformly convergent series, and their Fourier coefficients are in $\\ell_p$ for all $p>1$; moreover, all the Lebesgue spaces $L^q_\\Lambda$ are equal for $q<+\\infty$. On the other hand, they are large in the sense that they are dense in the Bohr group and that the space of the bounded functions with spectrum in $\\Lambda$ is non separable. So these sets are very different from the thin sets of integers previously known.
Low Complexity Integer Transform and Adaptive Quantization Optimization
Institute of Scientific and Technical Information of China (English)
Si-Wei Ma; Wen Gao
2006-01-01
In this paper, a new low complexity integer transform is proposed, which has been adopted by AVS1-PT. The proposed transform can enable AVS1-P7 to share the same quantization/dequantization table with AVS1-P2. As the bases of the proposed transform coefficients are very close, the transform normalization can be implemented only on the encoder side and the dequantization table size can be reduced compared with the transform used in H.264/MPEG-4 AVC. Along with the feature of the proposed transform, adaptive dead-zone quantization optimization for the proposed transform is studied.Experimental results show that the proposed integer transform has similar coding performance compared with the transform used in H.264/MPEG-4 AVC, and would gain near 0.1dB with the adaptive dead-zone quantization optimization.
Relaxation and decomposition methods for mixed integer nonlinear programming
Nowak, Ivo; Bank, RE
2005-01-01
This book presents a comprehensive description of efficient methods for solving nonconvex mixed integer nonlinear programs, including several numerical and theoretical results, which are presented here for the first time. It contains many illustrations and an up-to-date bibliography. Because on the emphasis on practical methods, as well as the introduction into the basic theory, the book is accessible to a wide audience. It can be used both as a research and as a graduate text.
Consequences of the Continuity of the Monic Integer Transfinite Diameter
Hilmar, Jan
2007-01-01
We consider the problem of determining the monic integer transfinite diameter t_M(I)&=&\\lim_{n\\to\\infty}\\inf_{p_n\\in{\\mathcal M_n}}\\supnorm{p_n}{I}^{1/n} for real intervals of length less than 4. We show the $t_M([0,x])$, as a function in $x>0$, is continuous, therefore disproving two conjectures due to Hare and Smyth. Consequently, for $n>2\\in\
Computing Integer Powers in Floating-Point Arithmetic
Kornerup, Peter; Muller, Jean-Michel
2007-01-01
We introduce two algorithms for accurately evaluating powers to a positive integer in floating-point arithmetic, assuming a fused multiply-add (fma) instruction is available. We show that our log-time algorithm always produce faithfully-rounded results, discuss the possibility of getting correctly rounded results, and show that results correctly rounded in double precision can be obtained if extended-precision is available with the possibility to round into double precision (with a single rounding).
Computing Integer Powers in Floating-Point Arithmetic
Kornerup, Peter; Lefèvre, Vincent; Muller, Jean-Michel
2007-01-01
We introduce two algorithms for accurately evaluating powers to a positive integer in floating-point arithmetic, assuming a fused multiply-add (fma) instruction is available. We show that our log-time algorithm always produce faithfully-rounded results, discuss the possibility of getting correctly rounded results, and show that results correctly rounded in double precision can be obtained if extended-precision is available with the possibility to round into double precision (with a single rou...
THE ALGORITHMS OF AN INTEGER PARTITIONING WITH ITS APPLICATIONS
Institute of Scientific and Technical Information of China (English)
曹立明; 周强
1994-01-01
In the light of the ideals of Artificial Intelligence(AI) , three algorithms of an integer partitioning have been given in this paper:generate and test algorithm ,and two heuristic algorithms about forward partition and backward partition. PROLOG has been used to describe algorithms, it is reasonable, direct and simple. In the sight of describing algorithms ,it is a new and valid try. At last, some intresting applications of the algorithms mentioned in the paper have been presented.
Optimal source codes for geometrically distributed integer alphabets
Gallager, R. G.; Van Voorhis, D. C.
1975-01-01
An approach is shown for using the Huffman algorithm indirectly to prove the optimality of a code for an infinite alphabet if an estimate concerning the nature of the code can be made. Attention is given to nonnegative integers with a geometric probability assignment. The particular distribution considered arises in run-length coding and in encoding protocol information in data networks. Questions of redundancy of the optimal code are also investigated.
Optimizing Marine Corps Personnel Assignments Using an Integer Programming Model
2012-12-01
would assist the Monitors in the assignment process. Though these studies contain very thorough analyses, they differ from the approach taken in this...thesis in that they do not look into using a low cost, yet very efficient, decision modeling approach of integer programming as a method of...2012 BAH Rates-with Dependents. Defense Travel Mangement Office. (2011, December). 2012 BAH Rates-without Dependents. M ileage C ost 1 Per D iem
On Integers, Primes and UniqueFactorization in Quadratic Fields
Hedenlund, Alice
2013-01-01
Abstract. This thesis will deal with quadratic elds. The prob- lem is to study such elds and their properties including, but not limited to, determining integers, nding primes and deciding which quadratic elds have unique factorization. The goal is to get famil- iar with these concepts and to provide a starting point for students with an interest in algebra to explore eld extensions and inte- gral closures in relation to elementary number theory. The reader will be assumed to have a basic kn...
Application of Integer and Fractional Models in Electrochemical Systems
Directory of Open Access Journals (Sweden)
Isabel S. Jesus
2012-01-01
Full Text Available This paper describes the use of integer and fractional electrical elements, for modelling two electrochemical systems. A first type of system consists of botanical elements and a second type is implemented by electrolyte processes with fractal electrodes. Experimental results are analyzed in the frequency domain, and the pros and cons of adopting fractional-order electrical components for modelling these systems are compared.
Integers without Large Prime Factors in Short Intervals: Conditional Results
Indian Academy of Sciences (India)
Goutam Pal; Satadal Ganguly
2010-11-01
Under the Riemann hypothesis and the conjecture that the order of growth of the argument of $(1/2+it)$ is bounded by $(\\log t)^{\\frac{1}{2}+o(1)}$, we show that for any given > 0 the interval $(X, X+\\sqrt{X}(\\log X)^{1/2+o(1)}]$ contains an integer having no prime factor exceeding $X^$ for all sufficiently large.
Precursory singularities in spherical gravitational collapse
Lake, Kayll
1992-05-01
General conditions are developed for the formation of naked precursory ('shell-focusing') singularities in spherical gravitational collapse. These singularities owe their nakedness to the fact that the gravitational potential fails to be single valued prior to the onset of a true gravitational singularity. It is argued that they do not violate the spirit of cosmic censorship. Rather, they may well be an essentially generic feature of relativistic gravitational collapse.
Quantum dress for a naked singularity
Casals, Marc; Fabbri, Alessandro; Martínez, Cristián; Zanelli, Jorge
2016-09-01
We investigate semiclassical backreaction on a conical naked singularity space-time with a negative cosmological constant in (2 + 1)-dimensions. In particular, we calculate the renormalized quantum stress-energy tensor for a conformally coupled scalar field on such naked singularity space-time. We then obtain the backreacted metric via the semiclassical Einstein equations. We show that, in the regime where the semiclassical approximation can be trusted, backreaction dresses the naked singularity with an event horizon, thus enforcing (weak) cosmic censorship.
Connections Between Singular Control and Optimal Switching
Guo, Xin; Tomecek, Pascal
2007-01-01
This paper builds a new theoretical connection between singular control of finite variation and optimal switching problems. This correspondence provides a novel method for solving high-dimensional singular control problems, and enables us to extend the theory of reversible investment: sufficient conditions are derived for the existence of optimal controls and for the regularity of value functions. Consequently, our regularity result links singular controls and Dynkin games through sequential ...
Discrete equations and the singular manifold method
Estévez, P G
1999-01-01
The Painleve expansion for the second Painleve equation (PII) and fourth Painleve equation (PIV) have two branches. The singular manifold method therefore requires two singular manifolds. The double singular manifold method is used to derive Miura transformations from PII and PIV to modified Painleve type equations for which auto-Backlund transformations are obtained. These auto-Backlund transformations can be used to obtain discrete equations.
Quantum dress for a naked singularity
Casals, Marc; Martínez, Cristián; Zanelli, Jorge
2016-01-01
We investigate semiclassical backreaction on a conical naked singularity space-time with a negative cosmological constant in (2+1)-dimensions. In particular, we calculate the renormalized quantum stress-energy tensor for a conformally coupled scalar field on such naked singularity space-time. We then obtain the backreacted metric via the semiclassical Einstein equations. We show that, in the regime where the semiclassical approximation can be trusted, backreaction dresses the naked singularity with an event horizon, thus enforcing cosmic censorship.
Integer Sequences of the Form $\\alpha^n \\pm \\beta^n$
Abdulaziz, Abdulrahman Ali
2010-01-01
In this paper, we find all integer sequences of the form a^n + b^n, where a and b are complex numbers and n is a nonnegative integer. We prove that if p and q are integers, then there is a correspondence between the roots of the quadratic equation z^2 - pz - q = 0 and integer sequences of the form a^n + b^n. In addition, we will show that there are no integer sequences of the form a^n - b^n. Finally, we use special values of a and b to obtain a range of formulas involving Lucas and Fibonacci numbers.
Partial Gr\\"obner bases for multiobjective integer programming
Blanco, Victor
2007-01-01
In this paper we present two new methodologies for solving multiobjective integer programming using tools from algebraic geometry. We introduce the concept of partial Gr\\"obner basis for a family of multiobjective programs where the right-hand side varies. This new structure extends the notion of usual Gr\\"obner basis for the single objective case, to the case of multiple objectives, i.e., a partial ordering instead of a total ordering over the feasible vectors. The main property of these bases is that partial reduction of the integer elements in the kernel of the constraint matrix by the different blocks of the basis is zero. It allows us to prove that this new construction is a test family for a family of multiobjective programs. An algorithm '\\`a la Buchberger' is developed to compute partial Gr\\"obner basis. Specifically, with this tool we compute the entire set of efficient solutions of any multiobjective integer linear problem (MOILP). Some examples illustrate the application of the algorithms and compu...
Efficient Big Integer Multiplication and Squaring Algorithms for Cryptographic Applications
Directory of Open Access Journals (Sweden)
Shahram Jahani
2014-01-01
Full Text Available Public-key cryptosystems are broadly employed to provide security for digital information. Improving the efficiency of public-key cryptosystem through speeding up calculation and using fewer resources are among the main goals of cryptography research. In this paper, we introduce new symbols extracted from binary representation of integers called Big-ones. We present a modified version of the classical multiplication and squaring algorithms based on the Big-ones to improve the efficiency of big integer multiplication and squaring in number theory based cryptosystems. Compared to the adopted classical and Karatsuba multiplication algorithms for squaring, the proposed squaring algorithm is 2 to 3.7 and 7.9 to 2.5 times faster for squaring 32-bit and 8-Kbit numbers, respectively. The proposed multiplication algorithm is also 2.3 to 3.9 and 7 to 2.4 times faster for multiplying 32-bit and 8-Kbit numbers, respectively. The number theory based cryptosystems, which are operating in the range of 1-Kbit to 4-Kbit integers, are directly benefited from the proposed method since multiplication and squaring are the main operations in most of these systems.
A singularity theorem based on spatial averages
Indian Academy of Sciences (India)
J M M Senovilla
2007-07-01
Inspired by Raychaudhuri's work, and using the equation named after him as a basic ingredient, a new singularity theorem is proved. Open non-rotating Universes, expanding everywhere with a non-vanishing spatial average of the matter variables, show severe geodesic incompletness in the past. Another way of stating the result is that, under the same conditions, any singularity-free model must have a vanishing spatial average of the energy density (and other physical variables). This is very satisfactory and provides a clear decisive difference between singular and non-singular cosmologies.
On curves on sandwiched surface singularities
Fernandez-Sanchez, Jesus
2007-01-01
Fixed a point O on a non-singular surface S and a complete mO-primary ideal I in its local ring, the curves on the surface X obtained by blowing-up I are studied in terms of the base points of I. Criteria for the principality of these curves are obtained. New formulas for their multiplicity, intersection numbers and order of singularity at the singularities of X are given. The semigroup of branches going through a sandwiched singularity is effectively determined, too.
Three-qutrit entanglement and simple singularities
Holweck, Frédéric; Jaffali, Hamza
2016-11-01
In this paper, we use singularity theory to study the entanglement nature of pure three-qutrit systems. We first consider the algebraic variety X of separable three-qutrit states within the projective Hilbert space {{P}}({ H })={{{P}}}26. Given a quantum pure state | \\varphi > \\in {{P}}({ H }) we define the X φ -hypersuface by cutting X with a hyperplane H φ defined by the linear form ranges over the stochastic local operation and classical communication entanglement classes, the ‘worst’ possible singular X φ -hypersuface with isolated singularities, has a unique singular point of type D 4.
Generalised hyperbolicity in spacetimes with singular submanifolds
Sanchez, Yafet Sanchez
2015-01-01
The idea of defining a gravitational singularity as an obstruction to the dynamical evolution of a test field (described by a PDE) rather than the dynamical evolution of a particle (described by a geodesics) is explored. In this paper we obtain general conditions under which the wave equation is well-posed in spacetimes with weak singularities in which the singularity is concentrated in a submanifold. In particular, the results can be applied to spacetimes with shell-crossing singularities, surface layers and generalised cosmic strings.
On Type I Singularities in Ricci flow
Enders, Joerg; Topping, Peter M
2010-01-01
We define several notions of singular set for Type I Ricci flows and show that they all coincide. In order to do this, we prove that blow-ups around singular points converge to nontrivial gradient shrinking solitons, thus extending work of Naber. As a by-product we conclude that the volume of a finite-volume singular set vanishes at the singular time. We also define a notion of density for Type I Ricci flows and use it to prove a regularity theorem reminiscent of White's partial regularity result for mean curvature flow.
Ordered cones and approximation
Keimel, Klaus
1992-01-01
This book presents a unified approach to Korovkin-type approximation theorems. It includes classical material on the approximation of real-valuedfunctions as well as recent and new results on set-valued functions and stochastic processes, and on weighted approximation. The results are notonly of qualitative nature, but include quantitative bounds on the order of approximation. The book is addressed to researchers in functional analysis and approximation theory as well as to those that want to applythese methods in other fields. It is largely self- contained, but the readershould have a solid background in abstract functional analysis. The unified approach is based on a new notion of locally convex ordered cones that are not embeddable in vector spaces but allow Hahn-Banach type separation and extension theorems. This concept seems to be of independent interest.
Singularities of slice regular functions
Stoppato, Caterina
2010-01-01
Beginning in 2006, G. Gentili and D.C. Struppa developed a theory of regular quaternionic functions with properties that recall classical results in complex analysis. For instance, in each Euclidean ball centered at 0 the set of regular functions coincides with that of quaternionic power series converging in the same ball. In 2009 the author proposed a classification of singularities of regular functions as removable, essential or as poles and studied poles by constructing the ring of quotients. In that article, not only the statements, but also the proving techniques were confined to the special case of balls centered at 0. In a subsequent paper, F. Colombo, G. Gentili, I. Sabadini and D.C. Struppa (2009) identified a larger class of domains, on which the theory of regular functions is natural and not limited to quaternionic power series. The present article studies singularities in this new context, beginning with the construction of the ring of quotients and of Laurent-type expansions at points other than ...
Institute of Scientific and Technical Information of China (English)
Smail Djebali; Ouiza Saifi; Yan Baoqiang
2012-01-01
In this work,we are concerned with the existence and multiplicity of positive solutions for singular boundary value problems on the half-line.Two problems from epidemiology and combustion theory set on the positive half-line are investigated.We use upper and lower solution techniques combined with fixed point index on cones in appropriate Banach spaces.The results complement recent ones in the literature.
Institute of Scientific and Technical Information of China (English)
Jing Bao YANG; Zhong Li WEI
2011-01-01
By employing the fixed point theorem of cone expansion and compression of norm type,we investigate the existence of positive solutions of generalized Sturm-Liouville boundary value problems for a nonlinear singular differential equation with a parameter.Some sufficient conditions for the existence of positive solutions are established.In the last section,an example is presented to illustrate the applications of our main results.
Ejecta evolution during cone impact
Marston, Jeremy; Vakarelski, Ivan; Thoroddsen, Sigurdur
2013-11-01
We present results from an experimental study of the impact of conical shaped bodies into a pool of liquid. By varying the cone angle, impact speed and liquid physical properties, we examine a broad parameter space and seek to find conditions when self-similarity can be observed during this phenomena. We use high-speed imaging to capture the early-time motion of the liquid ejecta which emanates from the tip of the cone and travels up along the cone surface. Surprisingly, we find that the detachment of the ejecta can be simply described by air entrainment relationships derived from coating experiments.
Sasakian quiver gauge theories and instantons on cones over lens 5-spaces
Directory of Open Access Journals (Sweden)
Olaf Lechtenfeld
2015-10-01
Full Text Available We consider SU(3-equivariant dimensional reduction of Yang–Mills theory over certain cyclic orbifolds of the 5-sphere which are Sasaki–Einstein manifolds. We obtain new quiver gauge theories extending those induced via reduction over the leaf spaces of the characteristic foliation of the Sasaki–Einstein structure, which are projective planes. We describe the Higgs branches of these quiver gauge theories as moduli spaces of spherically symmetric instantons which are SU(3-equivariant solutions to the Hermitian Yang–Mills equations on the associated Calabi–Yau cones, and further compare them to moduli spaces of translationally-invariant instantons on the cones. We provide an explicit unified construction of these moduli spaces as Kähler quotients and show that they have the same cyclic orbifold singularities as the cones over the lens 5-spaces.
Sasakian quiver gauge theories and instantons on cones over lens 5-spaces
Lechtenfeld, Olaf; Sperling, Marcus; Szabo, Richard J
2015-01-01
We consider SU(3)-equivariant dimensional reduction of Yang-Mills theory over certain cyclic orbifolds of the 5-sphere which are Sasaki-Einstein manifolds. We obtain new quiver gauge theories extending those induced via reduction over the leaf spaces of the characteristic foliation of the Sasaki-Einstein structure, which are projective planes. We describe the Higgs branches of these quiver gauge theories as moduli spaces of spherically symmetric instantons which are SU(3)-equivariant solutions to the Hermitian Yang-Mills equations on the associated Calabi-Yau cones, and further compare them to moduli spaces of translationally-invariant instantons on the cones. We provide an explicit unified construction of these moduli spaces as K\\"ahler quotients and show that they have the same cyclic orbifold singularities as that of the cones.
Causes and consequences of inherited cone disorders
Roosing, S.; Thiadens, A.A.H.J.; Hoyng, C.B.; Klaver, C.C.; Hollander, A.I. den; Cremers, F.P.M.
2014-01-01
Hereditary cone disorders (CDs) are characterized by defects of the cone photoreceptors or retinal pigment epithelium underlying the macula, and include achromatopsia (ACHM), cone dystrophy (COD), cone-rod dystrophy (CRD), color vision impairment, Stargardt disease (STGD) and other maculopathies. Fo
Directory of Open Access Journals (Sweden)
Nedyu Popivanov
2014-01-01
Full Text Available For the four-dimensional nonhomogeneous wave equation boundary value problems that are multidimensional analogues of Darboux problems in the plane are studied. It is known that for smooth right-hand side functions the unique generalized solution may have a strong power-type singularity at only one point. This singularity is isolated at the vertex O of the boundary light characteristic cone and does not propagate along the bicharacteristics. The present paper describes asymptotic expansions of the generalized solutions in negative powers of the distance to O. Some necessary and sufficient conditions for existence of bounded solutions are proven and additionally a priori estimates for the singular solutions are obtained.
New singular solutions of Protter's problem for the 3D wave equation
Directory of Open Access Journals (Sweden)
T. P. Popov
2004-04-01
Full Text Available In 1952, for the wave equation,Protter formulated some boundary value problems (BVPs, which are multidimensional analogues of Darboux problems on the plane. He studied these problems in a 3D domain ÃŽÂ©0, bounded by two characteristic cones ÃŽÂ£1 and ÃŽÂ£2,0 and a plane region ÃŽÂ£0. What is the situation around these BVPs now after 50 years? It is well known that, for the infinite number of smooth functions in the right-hand side of the equation, these problems do not have classical solutions. Popivanov and Schneider (1995 discovered the reason of this fact for the cases of Dirichlet's or Neumann's conditions on ÃŽÂ£0. In the present paper, we consider the case of third BVP on ÃŽÂ£0 and obtain the existence of many singular solutions for the wave equation. Especially, for Protter's problems in Ã¢Â„Â3, it is shown here that for any nÃ¢ÂˆÂˆÃ¢Â„Â• there exists a Cn(ÃŽÂ©Ã‚Â¯0 - right-hand side function, for which the corresponding unique generalized solution belongs to Cn(ÃŽÂ©Ã‚Â¯0O, but has a strong power-type singularity of order n at the point O. This singularity is isolated only at the vertex O of the characteristic cone ÃŽÂ£2,0 and does not propagate along the cone.
Timelike Constant Mean Curvature Surfaces with Singularities
DEFF Research Database (Denmark)
Brander, David; Svensson, Martin
2014-01-01
We use integrable systems techniques to study the singularities of timelike non-minimal constant mean curvature (CMC) surfaces in the Lorentz–Minkowski 3-space. The singularities arise at the boundary of the Birkhoff big cell of the loop group involved. We examine the behavior of the surfaces at ...
Timelike Constant Mean Curvature Surfaces with Singularities
DEFF Research Database (Denmark)
Brander, David; Svensson, Martin
2014-01-01
We use integrable systems techniques to study the singularities of timelike non-minimal constant mean curvature (CMC) surfaces in the Lorentz–Minkowski 3-space. The singularities arise at the boundary of the Birkhoff big cell of the loop group involved. We examine the behavior of the surfaces...
Discrete variable representation for singular Hamiltonians
DEFF Research Database (Denmark)
Schneider, B. I.; Nygaard, Nicolai
2004-01-01
We discuss the application of the discrete variable representation (DVR) to Schrodinger problems which involve singular Hamiltonians. Unlike recent authors who invoke transformations to rid the eigenvalue equation of singularities at the cost of added complexity, we show that an approach based...
On non-singular inhomogeneous cosmological models
Fernández-Jambrina, L
2009-01-01
In this talk we would like to review recent results on non-singular cosmological models. It has been recently shown that among stiff perfect fluid inhomogeneous spacetimes the absence of singularities is more common than it was expected in the literature. We would like to generalize these results and apply them to other matter sources.
Singularities inside non-Abelian black holes
Gal'tsov, D. V.; Donets, E. E.; Zotov, M. Yu.
1997-01-01
Singularities inside static spherically symmetric black holes in the SU(2) Einstein-Yang-Mills and Einstein-Yang-Mills-dilaton theories are investigated. Analytical formulas are presented describing oscillatory and power law metric behavior near spacelike singularities in generic solutions.
Twisting singular solutions of Bethe's equations
Nepomechie, Rafael I
2014-01-01
The Bethe equations for the periodic XXX and XXZ spin chains admit singular solutions, for which the corresponding eigenvalues and eigenvectors are ill-defined. We use a twist regularization to derive conditions for such singular solutions to be physical, in which case they correspond to genuine eigenvalues and eigenvectors of the Hamiltonian.
The Geometry of Black Hole Singularities
Directory of Open Access Journals (Sweden)
Ovidiu Cristinel Stoica
2014-01-01
Full Text Available Recent results show that important singularities in General Relativity can be naturally described in terms of finite and invariant canonical geometric objects. Consequently, one can write field equations which are equivalent to Einstein's at nonsingular points but, in addition remain well-defined and smooth at singularities. The black hole singularities appear to be less undesirable than it was thought, especially after we remove the part of the singularity due to the coordinate system. Black hole singularities are then compatible with global hyperbolicity and do not make the evolution equations break down, when these are expressed in terms of the appropriate variables. The charged black holes turn out to have smooth potential and electromagnetic fields in the new atlas. Classical charged particles can be modeled, in General Relativity, as charged black hole solutions. Since black hole singularities are accompanied by dimensional reduction, this should affect Feynman's path integrals. Therefore, it is expected that singularities induce dimensional reduction effects in Quantum Gravity. These dimensional reduction effects are very similar to those postulated in some approaches to make Quantum Gravity perturbatively renormalizable. This may provide a way to test indirectly the effects of singularities, otherwise inaccessible.
Quantum fields and "Big Rip" expansion singularities
Calderon, H; Calderon, Hector; Hiscock, William A.
2005-01-01
The effects of quantized conformally invariant massless fields on the evolution of cosmological models containing a ``Big Rip'' future expansion singularity are examined. Quantized scalar, spinor, and vector fields are found to strengthen the accelerating expansion of such models as they approach the expansion singularity.
Reasons for singularity in robot teleoperation
DEFF Research Database (Denmark)
Marhenke, Ilka; Fischer, Kerstin; Savarimuthu, Thiusius Rajeeth
2014-01-01
In this paper, the causes for singularity of a robot arm in teleoperation for robot learning from demonstration are analyzed. Singularity is the alignment of robot joints, which prevents the configuration of the inverse kinematics. Inspired by users' own hypotheses, we investigated speed and delay...
An extension theorem for conformal gauge singularities
Tod, Paul
2007-01-01
We analyse conformal gauge, or isotropic, singularities in cosmological models in general relativity. Using the calculus of tractors, we find conditions in terms of tractor curvature for a local extension of the conformal structure through a cosmological singularity and prove a local extension theorem.
Correlation singularities in partially coherent electromagnetic beams
Raghunathan, S.B.; Schouten, H.F.; Visser, T.D.
2012-01-01
We demonstrate that coherence vortices, singularities of the correlation function, generally occur in partially coherent electromagnetic beams. In successive cross sections of Gaussian Schell-model beams, their locus is found to be a closed string. These coherence singularities have implications for
Resolving curvature singularities in holomorphic gravity
Mantz, C.L.M.; Prokopec, T.
2011-01-01
We formulate a holomorphic theory of gravity and study how the holomorphy symmetry alters the two most important singular solutions of general relativity: black holes and cosmology. We show that typical observers (freely) falling into a holomorphic black hole do not encounter a curvature singularity
Valley Singularities and Baryon Number Violation
Provero, P
1994-01-01
We consider the valley--method computation of the inclusive cross section of baryon number violating processes in the Standard Model. We show that any physically correct model of the valley action should present a singularity in the saddle point valley parameters as functions of the energy of the process. This singularity prevents the saddle point configuration from collapsing into the perturbative vacuum.
Institute of Scientific and Technical Information of China (English)
李仁贵; 刘立山
2001-01-01
New existence results are presented for the singular second-order nonlinear boundary value problems u" + g(t)f(u) = 0, 0 ＜ t ＜ 1, au(0) - βu′(0) = 0,γu(1) +δu'(l) = 0 under the conditions 0 ≤ fn+ ＜ M1, m1 ＜ f∞-≤∞ or 0 ≤ f∞+＜M1, m1 ＜ f 0-≤ ∞, where f +0＝ limu→of(u)/u, f∞-＝ limu-→∞(u)/u, f0-＝limu-→of(u)/u, f+∞＝ limu→=f(u)/u, g may be singular att ＝ 0 and/ort ＝ 1 . Theproof uses a fixed point theorem in cone theory.
Directory of Open Access Journals (Sweden)
Jingfu Jin
2012-04-01
Full Text Available This article shows the existence of a positive solution for the singular fractional differential equation with integral boundary condition $$displaylines{ {}^C!D^p u(t=lambda h(tf(t, u(t, quad tin(0, 1, cr u(0-au(1=int^1_0g_0(su(s,ds, cr u'(0-b,{}^C!D^qu(1=int^1_0g_1(su(s,ds, cr u''(0=u'''(0=dots =u^{(n-1}(0=0, }$$ where $lambda $ is a parameter and the nonlinear term is allowed to be singular at $t=0, 1$ and $u=0$. We obtain an explicit interval for $lambda$ such that for any $lambda$ in this interval, existence of at least one positive solution is guaranteed. Our approach is by a fixed point theory in cones combined with linear operator theory.
Pindza, Edson; Maré, Eben
2017-03-01
A modified discrete singular convolution method is proposed. The method is based on the single (SE) and double (DE) exponential transformation to speed up the convergence of the existing methods. Numerical computations are performed on a wide variety of singular boundary value and singular perturbed problems in one and two dimensions. The obtained results from discrete singular convolution methods based on single and double exponential transformations are compared with each other, and with the existing methods too. Numerical results confirm that these methods are considerably efficient and accurate in solving singular and regular problems. Moreover, the method can be applied to a wide class of nonlinear partial differential equations.
DEFF Research Database (Denmark)
Cappellin, Cecilia; Breinbjerg, Olav; Frandsen, Aksel
2008-01-01
An effective technique for extracting the singularity of plane wave spectra in the computation of antenna aperture fields is proposed. The singular spectrum is first factorized into a product of a finite function and a singular function. The finite function is inverse Fourier transformed...... numerically using the Inverse Fast Fourier Transform, while the singular function is inverse Fourier transformed analytically, using the Weyl-identity, and the two resulting spatial functions are then convolved to produce the antenna aperture field. This article formulates the theory of the singularity...
Generalized Strong Curvature Singularities and Cosmic Censorship
Rudnicki, W; Kondracki, W
2002-01-01
A new definition of a strong curvature singularity is proposed. This definition is motivated by the definitions given by Tipler and Krolak, but is significantly different and more general. All causal geodesics terminating at these new singularities, which we call generalized strong curvature singularities, are classified into three possible types; the classification is based on certain relations between the curvature strength of the singularities and the causal structure in their neighborhood. A cosmic censorship theorem is formulated and proved which shows that only one class of generalized strong curvature singularities, corresponding to a single type of geodesics according to our classification, can be naked. Implications of this result for the cosmic censorship hypothesis are indicated.
Singularities in gravitational collapse with radial pressure
Gonçalves, S M C V; Goncalves, Sergio M. C. V.; Jhingan, Sanjay
2001-01-01
We analyze spherical dust collapse with non-vanishing radial pressure, $\\Pi$, and vanishing tangential stresses. Considering a barotropic equation of state, $\\Pi=\\gamma\\rho$, we obtain an analytical solution in closed form---which is exact for $\\gamma=-1,0$, and approximate otherwise---near the center of symmetry (where the curvature singularity forms). We study the formation, visibility, and curvature strength of singularities in the resulting spacetime. We find that visible, Tipler strong singularities can develop from generic initial data. Radial pressure alters the spectrum of possible endstates for collapse, increasing the parameter space region that contains no visible singularities, but cannot by itself prevent the formation of visible singularities for sufficiently low values of the energy density. Known results from pressureless dust are recovered in the $\\gamma=0$ limit.
Are loop quantum cosmos never singular?
Singh, Parampreet
2009-01-01
A unified treatment of all known types of singularities for flat, isotropic and homogeneous spacetimes in the framework of loop quantum cosmology (LQC) is presented. These include bangs, crunches and all future singularities. Using effective spacetime description we perform a model independent general analysis of the properties of curvature, behavior of geodesics and strength of singularities. For illustration purposes a phenomenological model based analysis is also performed. We show that all values of the scale factor at which a strong singularity may occur are excluded from the effective loop quantum spacetime. Further, if the evolution leads to either a vanishing or divergent scale factor then the loop quantum universe is asymptotically deSitter in that regime. We also show that there exist a class of sudden extremal events, which includes a recently discussed possibility, for which the curvature or its derivatives will always diverge. Such events however turn out to be harmless weak curvature singulariti...
On non-singular GRADELA crack fields
Directory of Open Access Journals (Sweden)
Elias C. Aifantis
2014-01-01
Full Text Available A brief account is provided on crack-tip solutions that have recently been published in the literature by employing the so-called GRADELA model and its variants. The GRADELA model is a simple gradient elasticity theory involving one internal length in addition to the two Lame' constants, in an effort to eliminate elastic singularities and discontinuities and to interpret elastic size effects. The non-singular strains and non-singular (but sometimes singular or even hypersingular stresses derived this way under different boundary conditions differ from each other and their physical meaning in not clear. This is discussed which focus on the form and physical meaning of non-singular solutions for crack-tip stresses and strains that are possible to obtain within the GRADELA model and its extensions.
Biclustering via Sparse Singular Value Decomposition
Lee, Mihee
2010-02-16
Sparse singular value decomposition (SSVD) is proposed as a new exploratory analysis tool for biclustering or identifying interpretable row-column associations within high-dimensional data matrices. SSVD seeks a low-rank, checkerboard structured matrix approximation to data matrices. The desired checkerboard structure is achieved by forcing both the left- and right-singular vectors to be sparse, that is, having many zero entries. By interpreting singular vectors as regression coefficient vectors for certain linear regressions, sparsity-inducing regularization penalties are imposed to the least squares regression to produce sparse singular vectors. An efficient iterative algorithm is proposed for computing the sparse singular vectors, along with some discussion of penalty parameter selection. A lung cancer microarray dataset and a food nutrition dataset are used to illustrate SSVD as a biclustering method. SSVD is also compared with some existing biclustering methods using simulated datasets. © 2010, The International Biometric Society.
New Isotropic and Anisotropic Sudden Singularities
Barrow, J D; Barrow, John D.; Tsagas, Christos G.
2004-01-01
We show the existence of an infinite family of finite-time singularities in isotropically expanding universes which obey the weak, strong, and dominant energy conditions. We show what new type of energy condition is needed to exclude them ab initio. We also determine the conditions under which finite-time future singularities can arise in a wide class of anisotropic cosmological models. New types of finite-time singularity are possible which are characterised by divergences in the time-rate of change of the anisotropic-pressure tensor. We investigate the conditions for the formation of finite-time singularities in a Bianchi type $VII_{0}$ universe with anisotropic pressures and construct specific examples of anisotropic sudden singularities in these universes.
Singularities in minimax optimization of networks
DEFF Research Database (Denmark)
Madsen, Kaj; Schjær-Jacobsen, Hans
1976-01-01
A theoretical treatment of singularities in nonlinear minimax optimization problems, which allows for a classification in regular and singular problems, is presented. A theorem for determining a singularity that is present in a given problem is formulated. A group of problems often used...... in the literature to test nonlinear minimax algorithms, i.e., minimax design of multisection quarter-wave transformers, is shown to exhibit singularities and the reason for this is pointed out. Based on the theoretical results presented an algorithm for nonlinear minimax optimization is developed. The new algorithm...... maintains the quadratic convergence property of a recent algorithm by Madsen et al. when applied to regular problems and it is demonstrated to significantly improve the final convergence on singular problems....
$f(R,T)$ and future singularities
Mirza, Behrouz
2014-01-01
We investigate equations of motion and future singularities of $f(R,T)$ gravity where $R$ is the Ricci scalar and $T$ is the trace of stress-energy tensor. Future singularities for two kinds of equation of state (barotropic perfect fluid and generalized form of equation of state) are studied. While no future singularity is found for the first case, some kind of singularity is found to be possible for the second. Using the method of fixed points and certain assumptions, a large number of singularities can be removed. Finally, the effect of the Noether symmetry on $f(R,T)$ is studied and the consistent form of $f(R,T)$ function is found using the symmetry and the conserved charge.
Energy Technology Data Exchange (ETDEWEB)
Choquet-Bruhat, Yvonne [Academie des Sciences, Paris (France); Chrusciel, Piotr T [Federation Denis Poisson, LMPT, Tours (France); MartIn-GarcIa, Jose M [Laboratoire Univers et Theories, CNRS, Meudon, and Universite Paris Diderot (France)
2009-07-07
We prove that the area of cross-sections of light cones, in spacetimes satisfying suitable energy conditions, is smaller than or equal to that of the corresponding cross-sections in Minkowski, or de Sitter, or anti-de Sitter spacetime. The equality holds if and only if the metric coincides with the corresponding model in the domain of dependence of the light cone.
Choquet-Bruhat, Yvonne; Martin-Garcia, Jose M
2009-01-01
We prove that the area of cross-sections of light-cones, in space-times satisfying suitable energy conditions, is smaller than or equal to that of the corresponding cross-sections in Minkowski, or de Sitter, or anti-de Sitter space-time. The equality holds if and only if the metric coincides with the corresponding model in the domain of dependence of the light-cone.
Delay-Dependent H∞ Filtering for Singular Time-Delay Systems
Directory of Open Access Journals (Sweden)
Zhenbo Li
2011-01-01
Full Text Available This paper deals with the problem of delay-dependent H∞ filtering for singular time-delay systems. First, a new delay-dependent condition which guarantees that the filter error system has a prescribed H∞ performance γ is given in terms of linear matrix inequalities (LMIs. Then, the sufficient condition is obtained for the existence of the H∞ filter, and the explicit expression for the desired H∞ filter is presented by using LMIs and the cone complementarity linearization iterative algorithm. A numerical example is provided to illustrate the effectiveness of the proposed method.
Singular solution of the Liouville equation under perturbation
Kalyakin, L A
1999-01-01
Small perturbation of the Liouville equation under singular initial data is considered. An asymptotics of the singular solution is constructed by the method which is similar to Bogolubov -- Krylov one. The main object is an asymptotics of the singular lines.
The SL(V)-ample Cone of Product of Flag Varieties
Institute of Scientific and Technical Information of China (English)
Ming Shuo ZHOU
2015-01-01
Let k be an algebraically closed field, and V be a vector space of dimension n over k. For a set ω = (−→d (1), . . . ,−→d (m)) of sequences of positive integers, denote by Lω the ample line bundle corresponding to the polarization on the product X=? mi=1 Flag(V,−→n (i)) of flag varieties of type−→n (i) determined byω. We study the SL(V )-linearization of the diagonal action of SL(V ) on X with respect to Lω . We give a suﬃ cient and necessary condition on ω such that Xss (Lω ) ?=∅ (resp., Xs (Lω ) ?=∅). As a consequence, we characterize the SL(V )-ample cone (for the diagonal action of SL(V ) on X), which turns out to be a polyhedral convex cone.
Initial Singularity of the Little Bang
Fukushima, K; McLerran, L; Fukushima, Kenji; Gelis, Francois; Lerran, Larry Mc
2006-01-01
The Color Glass Condensate (CGC) predicts the form of the nuclear wavefunction in QCD at very small $x$. Using this, we compute the wavefunction for the collision of two nuclei, infinitesimally in the forward light cone. We show that the Wigner transformation of this wavefunction generates rapidity dependent fluctuations around the boost invariant classical solution which describe the Glasma in the forward light cone.
Definition and classification of singularities in GR: classical and quantum
Konkowski, D A
2004-01-01
We will briefly review the definition and classification of classical and quantum singularities in general relativity. Examples of classically singular spacetimes that do not have quantum singularities will be given. We will present results on quantum singularities in quasiregular spacetimes. We will also show that a strong repulsive "potential" near the classical singularity can turn a classically singular spacetime into a quantum mechanically nonsingular spacetime.
Bleimann, Butzer, and Hahn Operators Based on the -Integers
Directory of Open Access Journals (Sweden)
Doğru Ogün
2007-01-01
Full Text Available We give a new generalization of Bleimann, Butzer, and Hahn operators, which includes -integers. We investigate uniform approximation of these new operators on some subspace of bounded and continuous functions. In Section, we show that the rates of convergence of the new operators in uniform norm are better than the classical ones. We also obtain a pointwise estimation in a general Lipschitz-type maximal function space. Finally, we define a generalization of these new operators and study the uniform convergence of them.
Gaps and the exponent of convergence of an integer sequence
Grekos, Georges; Sleziak, Martin
2012-01-01
Professor Tibor \\v{S}al\\'at, at one of his seminars at Comenius University, Bratislava, asked to study the influence of gaps of an integer sequence A={a_1
Efficient Reversible Watermarking Using Differential Expansible Integer Wavelet Transform
Directory of Open Access Journals (Sweden)
Sanjay Patel
2016-07-01
Full Text Available Digital watermarking has been utilized widely to claim the ownership and to protect images from alternation. Reversible watermarking is having great importance as it provided original image and the embedded logo without any loss. This paper proposed reversible watermarking algorithm using integer wavelet transform to satisfy the reversibility requirement. Further difference expansion based lifting scheme is used to make algorithm fast. To show the robustness of algorithm, various attacks like noise, rotating/scaling an image and filtering to the watermarked image is employed. The extraction of original image against such attacks is quantified in terms of peak signal to noise ratio (PSNR
Integer Valued Autoregressive Models for Tipping Bucket Rainfall Measurements
DEFF Research Database (Denmark)
Thyregod, Peter; Carstensen, Niels Jacob; Madsen, Henrik
1999-01-01
A new method for modelling the dynamics of rain sampled by a tipping bucket rain gauge is proposed. The considered models belong to the class of integer valued autoregressive processes. The models take the autocorelation and discrete nature of the data into account. A first order, a second order...... and a threshold model are presented together with methods to estimate the parameters of each model. The models are demonstrated to provide a good description of dt from actual rain events requiring only two to four parameters....
Integer programming for the generalized high school timetabling problem
DEFF Research Database (Denmark)
Kristiansen, Simon; Sørensen, Matias; Stidsen, Thomas Riis
2015-01-01
Recently, the XHSTT format for high school timetabling was introduced. It provides a uniform way of modeling problem instances and corresponding solutions. The format supports a wide variety of constraints, and currently 38 real-life instances from 11 different countries are available. Thereby......, the XHSTT format serves as a common ground for researchers within this area. This paper describes the first exact method capable of handling an arbitrary instance of the XHSTT format. The method is based on a mixed-integer linear programming (MIP) model, which is solved in two steps with a commercial...
Integer least-squares theory for the GNSS compass
Teunissen, P. J. G.
2010-07-01
Global navigation satellite system (GNSS) carrier phase integer ambiguity resolution is the key to high-precision positioning and attitude determination. In this contribution, we develop new integer least-squares (ILS) theory for the GNSS compass model, together with efficient integer search strategies. It extends current unconstrained ILS theory to the nonlinearly constrained case, an extension that is particularly suited for precise attitude determination. As opposed to current practice, our method does proper justice to the a priori given information. The nonlinear baseline constraint is fully integrated into the ambiguity objective function, thereby receiving a proper weighting in its minimization and providing guidance for the integer search. Different search strategies are developed to compute exact and approximate solutions of the nonlinear constrained ILS problem. Their applicability depends on the strength of the GNSS model and on the length of the baseline. Two of the presented search strategies, a global and a local one, are based on the use of an ellipsoidal search space. This has the advantage that standard methods can be applied. The global ellipsoidal search strategy is applicable to GNSS models of sufficient strength, while the local ellipsoidal search strategy is applicable to models for which the baseline lengths are not too small. We also develop search strategies for the most challenging case, namely when the curvature of the non-ellipsoidal ambiguity search space needs to be taken into account. Two such strategies are presented, an approximate one and a rigorous, somewhat more complex, one. The approximate one is applicable when the fixed baseline variance matrix is close to diagonal. Both methods make use of a search and shrink strategy. The rigorous solution is efficiently obtained by means of a search and shrink strategy that uses non-quadratic, but easy-to-evaluate, bounding functions of the ambiguity objective function. The theory
Bayesian integer frequency offset estimator for MIMO-OFDM systems
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
Carrier frequency offset (CFO) in MIMO-OFDM systems can be decoupled into two parts: fraction frequency offset (FFO) and integer frequency offset (IFO). The problem of IFO estimation is addressed and a new IFO estimator based on the Bayesian philosophy is proposed. Also, it is shown that the Bayesian IFO estimator is optimal among all the IFO estimators. Furthermore, the Bayesian estimator can take advantage of oversampling so that better performance can be obtained. Finally, numerical results show the optimality of the Bayesian estimator and validate the theoretical analysis.
Using Set Model for Learning Addition of Integers
Directory of Open Access Journals (Sweden)
Umi Puji Lestari
2015-07-01
Full Text Available This study aims to investigate how set model can help students' understanding of addition of integers in fourth grade. The study has been carried out to 23 students and a teacher of IVC SD Iba Palembang in January 2015. This study is a design research that also promotes PMRI as the underlying design context and activity. Results showed that the use of set models that is packaged in activity of recording of financial transactions in two color chips and card game can help students to understand the concept of zero pair, addition with the same colored chips, and cancellation strategy.
Gaussian free fields at the integer quantum Hall plateau transition
Energy Technology Data Exchange (ETDEWEB)
Bondesan, R., E-mail: roberto.bondesan@phys.ox.ac.uk [Rudolf Peierls Centre for Theoretical Physics, 1 Keble Road, Oxford OX1 3NP (United Kingdom); Wieczorek, D.; Zirnbauer, M.R. [Institut für Theoretische Physik, Universität zu Köln, Zülpicher Straße 77, 50937 Köln (Germany)
2017-05-15
In this work we put forward an effective Gaussian free field description of critical wavefunctions at the transition between plateaus of the integer quantum Hall effect. To this end, we expound our earlier proposal that powers of critical wave intensities prepared via point contacts behave as pure scaling fields obeying an Abelian operator product expansion. Our arguments employ the framework of conformal field theory and, in particular, lead to a multifractality spectrum which is parabolic. We also derive a number of old and new identities that hold exactly at the lattice level and hinge on the correspondence between the Chalker–Coddington network model and a supersymmetric vertex model.
$W_{\\infty}$ algebra in the integer quantum Hall effects
Azuma, Hiroo
1994-01-01
We investigate the $W_{\\infty}$ algebra in the integer quantum Hall effects. Defining the simplest vacuum, the Dirac sea, we evaluate the central extension for this algebra. A new algebra which contains the central extension is called the $W_{1+\\infty}$ algebra. We show that this $W_{1+\\infty}$ algebra is an origin of the Kac-Moody algebra which determines the behavior of edge states of the system. We discuss the relation between the $W_{1+\\infty}$ algebra and the incompressibility of the int...
Sidi, A.; Israeli, M.
1986-01-01
High accuracy numerical quadrature methods for integrals of singular periodic functions are proposed. These methods are based on the appropriate Euler-Maclaurin expansions of trapezoidal rule approximations and their extrapolations. They are used to obtain accurate quadrature methods for the solution of singular and weakly singular Fredholm integral equations. Such periodic equations are used in the solution of planar elliptic boundary value problems, elasticity, potential theory, conformal mapping, boundary element methods, free surface flows, etc. The use of the quadrature methods is demonstrated with numerical examples.
The structure of the classical cosmological singularity
Tipler, Frank J.
The existence of an all-encompassing initial classical cosmological singularity is established: it is shown that if: (1) global hyperbolicity, (2) the timelike convergence condition, and (3) all past-directed nonspacelike geodesics start to reconverge within a compact region in the causal past of the present-day earth, then all timelike curves in the past have a finite proper time length less than a universal constant L. It is argued that an analogue of this predicted cosmological singularity should exist even when quantum effects are taken into account. In particular, in a closed Friedmann radiation-filled universe quantized via the ADM method, the R = 0 singularity still exists and influences wave packet evolution at all times. Furthermore, quantum effects can in most cases eliminate curvature singularities only by introducing singularities in the universal action; most classical closed universes have finite action if and only if they begin and end in curvature singularities. Finally, the two basic ways of studying the structure of cosmological singularities are reviewed: completion methods (e.g., the c-boundary construction), and approach methods (e.g., analyzing metric behavior in a synchronous coordinate system).
Spin Singularities: Clifford Kaleidoscopes and Particle Masses
Cohen, Marcus S
2009-01-01
Are particles singularities- vortex lines, tubes, or sheets in some global ocean of dark energy? We visit the zoo of Lagrangian singularities, or caustics in a spin(4,C) phase flow over compactifed Minkowsky space, and find that their varieties and energies parallel the families and masses of the elementary particles. Singularities are classified by tensor products of J Coxeter groups s generated by reflections. The multiplicity, s, is the number reflections needed to close a cycle of null zigzags: nonlinear resonances of J chiral pairs of lightlike matter spinors with (4-J) Clifford mirrors: dyads in the remaining unperturbed vacuum pairs. Using singular perturbations to "peel" phase-space singularities by orders in the vacuum intensity, we find that singular varieties with quantized mass, charge, and spin parallel the families of leptons (J=1), mesons (J=2), and hadrons (J=3). Taking the symplectic 4 form - the volume element in the 8- spinor phase space- as a natural Lagrangian, these singularities turn ou...
An Integer Programming-based Local Search for Large-scale Maximal Covering Problems
Directory of Open Access Journals (Sweden)
Junha Hwang
2011-02-01
Full Text Available Maximal covering problem (MCP is classified as a linear integer optimization problem which can be effectively solved by integer programming technique. However, as the problem size grows, integerprogramming requires excessive time to get an optimal solution. This paper suggests a method for applying integer programming-based local search (IPbLS to solve large-scale maximal covering problems. IPbLS, which is a hybrid technique combining integer programming and local search, is a kind of local search using integer programming for neighbor generation. IPbLS itself is very effective for MCP. In addition, we improve the performance of IPbLS for MCP through problem reduction based on the current solution. Experimental results show that the proposed method considerably outperforms any other local search techniques and integer programming.
Bebel, Joseph
2011-01-01
There's something really strange about quantum mechanics. It's not just that cats can be dead and alive at the same time, and that entanglement seems to violate the principle of locality; quantum mechanics seems to be what Aaronson calls "an island in theoryspace", because even slight perturbations to the theory of quantum mechanics seem to generate absurdities. In [Aar 04] and [Aar 05], he explores these perturbations and the corresponding absurdities in the context of computation. In particular, he shows that a quantum theory where the measurement probabilities are computed using p-norm instead of the standard 2-norm has the effect of blowing up the class BQP (the class of problems that can be efficiently solved on a quantum computer) to at least PP (the class of problems that can be solved in probabilistic polynomial time). He showed that PP \\subseteq BQP_p \\subseteq PSPACE for all constants p != 2, and that BQP_p = PP for even integers p > 2. Here, we show that this equality holds for all integers p > 2.
Using Integer Programming for Airport Service Planning in Staff Scheduling
Directory of Open Access Journals (Sweden)
W.H. Ip
2010-09-01
Full Text Available Reliability and safety in flight is extremely necessary and that depend on the adoption of proper maintenance system. Therefore, it is essential for aircraft maintenance companies to perform the manpower scheduling efficiently. One of the objectives of this paper is to provide an Integer Programming approach to determine the optimal solutions to aircraft maintenance planning and scheduling and hence the planning and scheduling processes can become more efficient and effective. Another objective is to develop a set of computational schedules for maintenance manpower to cover all scheduled flights. In this paper, a sequential methodology consisting of 3 stages is proposed. They are initial maintenance demand schedule, the maintenance pairing and the maintenance group(s assignment. Since scheduling would split up into different stages, different mathematical techniques have been adopted to cater for their own problem characteristics. Microsoft Excel would be used. Results from the first stage and second stage would be inputted into integer programming model using Microsoft Excel Solver to find the optimal solution. Also, Microsoft Excel VBA is used for devising a scheduling system in order to reduce the manual process and provide a user friendly interface. For the results, all can be obtained optimal solution and the computation time is reasonable and acceptable. Besides, the comparison of the peak time and non-peak time is discussed.
Integer Representations towards Efficient Counting in the Bit Probe Model
DEFF Research Database (Denmark)
Brodal, Gerth Stølting; Greve, Mark; Pandey, Vineet
2011-01-01
Abstract We consider the problem of representing numbers in close to optimal space and supporting increment, decrement, addition and subtraction operations efficiently. We study the problem in the bit probe model and analyse the number of bits read and written to perform the operations, both...... in the worst-case and in the average-case. A counter is space-optimal if it represents any number in the range [0,...,2 n − 1] using exactly n bits. We provide a space-optimal counter which supports increment and decrement operations by reading at most n − 1 bits and writing at most 3 bits in the worst...... of the counter as the ratio between L + 1 and 2 n . We present various representations that achieve different trade-offs between the read and write complexities and the efficiency. We also give another representation of integers that uses n + O(logn ) bits to represent integers in the range [0,...,2 n − 1...
Optimal power system management via mixed integer dynamic programming
Energy Technology Data Exchange (ETDEWEB)
Kwatny, H.G.; Mensah, E. [Drexel Univ., Philadelphia, PA (United States). Dept. of Mechanical Engineering and Mechanics; Niebur, D. [Drexel Univ., Philadelphia, PA (United States). Dept. of Electrical and Computer Engineering; Teolis, C. [Techno-Sciences Inc., Lanham, MD (United States)
2006-07-01
Power systems are comprised of continuous and discrete acting components and subsystems. This paper discussed a logical specification that was used to define the transition dynamics of the discrete subsystem. It also presented a computational tool that reduced the logical specification to a set of inequalities as well as the use of the transformed model in a dynamic programming approach to the design of the optimal feedback controls. An example of optimal load shedding within a power system with an aggregate induction motor and constant admittance loads was presented. Specifically, the paper outlined the problem and discussed the modeling of hybrid systems and the control problem. A solution to the optimal control problem was presented. The essential feature of the model was the characterization of the discrete subsystem in terms of a set of mixed-integer formulas. The case example showed how logical constraints involving system real variables, such as case excitation voltage, could be incorporated in the problem via transformation to mixed-integer formulas. 10 refs., 4 figs.
A virtual network mapping algorithm based on integer programming
Institute of Scientific and Technical Information of China (English)
Bo LU; Jian-ya CHEN; Hong-yan CUI; Tao HUANG; Yun-jie LIU
2013-01-01
The virtual network (VN) embedding/mapping problem is recognized as an essential question of network virtualiza-tion. The VN embedding problem is a major challenge in this field. Its target is to efficiently map the virtual nodes and virtual links onto the substrate network resources. Previous research focused on designing heuristic-based algorithms or attempting two-stage solutions by solving node mapping in the first stage and link mapping in the second stage. In this study, we propose a new VN embedding algorithm based on integer programming. We build a model of an augmented substrate graph, and formulate the VN embedding problem as an integer program with an objective function and some constraints. A factor of topology-awareness is added to the objective function. The VN embedding problem is solved in one stage. Simulation results show that our algorithm greatly enhances the acceptance ratio, and increases the revenue/cost (R/C) ratio and the revenue while decreasing the cost of the VN embedding problem.
Direct comparison of fractional and integer quantized Hall resistance
Ahlers, Franz J.; Götz, Martin; Pierz, Klaus
2017-08-01
We present precision measurements of the fractional quantized Hall effect, where the quantized resistance {{R}≤ft[ 1/3 \\right]} in the fractional quantum Hall state at filling factor 1/3 was compared with a quantized resistance {{R}[2]} , represented by an integer quantum Hall state at filling factor 2. A cryogenic current comparator bridge capable of currents down to the nanoampere range was used to directly compare two resistance values of two GaAs-based devices located in two cryostats. A value of 1-(5.3 ± 6.3) 10-8 (95% confidence level) was obtained for the ratio ({{R}≤ft[ 1/3 \\right]}/6{{R}[2]} ). This constitutes the most precise comparison of integer resistance quantization (in terms of h/e 2) in single-particle systems and of fractional quantization in fractionally charged quasi-particle systems. While not relevant for practical metrology, such a test of the validity of the underlying physics is of significance in the context of the upcoming revision of the SI.
Split diversity in constrained conservation prioritization using integer linear programming.
Chernomor, Olga; Minh, Bui Quang; Forest, Félix; Klaere, Steffen; Ingram, Travis; Henzinger, Monika; von Haeseler, Arndt
2015-01-01
Phylogenetic diversity (PD) is a measure of biodiversity based on the evolutionary history of species. Here, we discuss several optimization problems related to the use of PD, and the more general measure split diversity (SD), in conservation prioritization.Depending on the conservation goal and the information available about species, one can construct optimization routines that incorporate various conservation constraints. We demonstrate how this information can be used to select sets of species for conservation action. Specifically, we discuss the use of species' geographic distributions, the choice of candidates under economic pressure, and the use of predator-prey interactions between the species in a community to define viability constraints.Despite such optimization problems falling into the area of NP hard problems, it is possible to solve them in a reasonable amount of time using integer programming. We apply integer linear programming to a variety of models for conservation prioritization that incorporate the SD measure.We exemplarily show the results for two data sets: the Cape region of South Africa and a Caribbean coral reef community. Finally, we provide user-friendly software at http://www.cibiv.at/software/pda.
An Approach to Integer Wavelet Transform for Medical Image Compression in PACS
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
We study an approach to integer wavelet transform for lossless compression of medical image in medical picture archiving and communication system (PACS). By lifting scheme a reversible integer wavelet transform is generated, which has the similar features with the corresponding biorthogonal wavelet transform. Experimental results of the method based on integer wavelet transform are given to show better performance and great applicable potentiality in medical image compression.
Potential singularity mechanism for the Euler equations
Brenner, Michael P.; Hormoz, Sahand; Pumir, Alain
2016-12-01
Singular solutions to the Euler equations could provide essential insight into the formation of very small scales in highly turbulent flows. Previous attempts to find singular flow structures have proven inconclusive. We reconsider the problem of interacting vortex tubes, for which it has long been observed that the flattening of the vortices inhibits sustained self-amplification of velocity gradients. Here we consider an iterative mechanism, based on the transformation of vortex filaments into sheets and their subsequent instability back into filaments. Elementary fluid mechanical arguments are provided to support the formation of a singular structure via this iterated mechanism, which we analyze based on a simplified model of filament interactions.
Isotropic cosmological singularities other matter models
Tod, K P
2003-01-01
Isotropic cosmological singularities are singularities which can be removed by rescaling the metric. In some cases already studied (gr-qc/9903008, gr-qc/9903009, gr-qc/9903018) existence and uniqueness of cosmological models with data at the singularity has been established. These were cosmologies with, as source, either perfect fluids with linear equations of state or massless, collisionless particles. In this article we consider how to extend these results to a variety of other matter models. These are scalar fields, massive collisionless matter, the Yang-Mills plasma of Choquet-Bruhat, or matter satisfying the Einstein-Boltzmann equation.
Quantum dress for a naked singularity
Directory of Open Access Journals (Sweden)
Marc Casals
2016-09-01
Full Text Available We investigate semiclassical backreaction on a conical naked singularity space–time with a negative cosmological constant in (2+1-dimensions. In particular, we calculate the renormalized quantum stress–energy tensor for a conformally coupled scalar field on such naked singularity space–time. We then obtain the backreacted metric via the semiclassical Einstein equations. We show that, in the regime where the semiclassical approximation can be trusted, backreaction dresses the naked singularity with an event horizon, thus enforcing (weak cosmic censorship.
Singular Value Decomposition for Unitary Symmetric Matrix
Institute of Scientific and Technical Information of China (English)
ZOUHongxing; WANGDianjun; DAIQionghai; LIYanda
2003-01-01
A special architecture called unitary sym-metric matrix which embodies orthogonal, Givens, House-holder, permutation, and row (or column) symmetric ma-trices as its special cases, is proposed, and a precise corre-spondence of singular values and singular vectors between the unitary symmetric matrix and its mother matrix is de-rived. As an illustration of potential, it is shown that, for a class of unitary symmetric matrices, the singular value decomposition (SVD) using the mother matrix rather than the unitary symmetric matrix per se can save dramatically the CPU time and memory without loss of any numerical precision.
Generalizations of the Abstract Boundary singularity theorem
Whale, Ben E; Scott, Susan M
2015-01-01
The Abstract Boundary singularity theorem was first proven by Ashley and Scott. It links the existence of incomplete causal geodesics in strongly causal, maximally extended spacetimes to the existence of Abstract Boundary essential singularities, i.e., non-removable singular boundary points. We give two generalizations of this theorem: the first to continuous causal curves and the distinguishing condition, the second to locally Lipschitz curves in manifolds such that no inextendible locally Lipschitz curve is totally imprisoned. To do this we extend generalized affine parameters from $C^1$ curves to locally Lipschitz curves.
ON THE SINGULAR VARIATIONAL PROBLEMS
Institute of Scientific and Technical Information of China (English)
谭经刚; 杨健夫
2004-01-01
The authors deal with the singular variational problem S(a,b,λ0):=infu∈E,u(≡／)0 ∫RN(||X|-a(△)u|m+∫|x|-(a+1)m|u|m)dx/(∫RN||X|-bU|P dx)m/p as well as (S)=(S)(a,b,λ1,λ2):=u,ν,E∈,u(u,ν)(≡／)(1,1) ∫RN J(u,ν)dx/(∫RN|x|-bp|u|α|ν|βdx)m/p, whereJ(u, v) = ||x|- au|m + λ1|x|- (a+1)m|u|m + ||x|- av|m + λ2|x|- (a+1)m|v|m,N ≥ m+ 1 ＞ 2, 0 ≤ a ＜ N-m/m, a ≤ b ＜ a+ 1 and p = p(a,b) = α+β =Nm/N-m+m(b-a), α, β≥ 1, E = D1,mα(RN). The aim of this paper is to show the existence of minimizer for S(a, b, A0) and S(a, b, λ1, λ2).
Conformal window and Landau singularities
Grunberg, G
2001-01-01
A physical characterization of Landau singularities is emphasized, which should trace the lower boundary N_f^* of the conformal window in QCD and supersymmetric QCD. A natural way to disentangle ``perturbative'' from ``non-perturbative'' contributions below N_f^* is suggested. Assuming an infrared fixed point is present in the perturbative part of the QCD coupling even in some range below N_f^* leads to the condition gamma(N_f^*)=1, where gamma is the critical exponent. Using the Banks-Zaks expansion, one gets 4
Causal viscous cosmology without singularities
Laciana, Carlos E
2016-01-01
An isotropic and homogeneous cosmological model with a source of dark energy is studied. That source is simulated with a viscous relativistic fluid with minimal causal correction. In this model the restrictions on the parameters coming from the following conditions are analized: a) energy density without singularities along time, b) scale factor increasing with time, c) universe accelerated at present time, d) state equation for dark energy with "w" bounded and close to -1. It is found that those conditions are satified for the following two cases. i) When the transport coefficient ({\\tau}_{{\\Pi}}), associated to the causal correction, is negative, with the aditional restriction {\\zeta}|{\\tau}_{{\\Pi}}|>2/3, where {\\zeta} is the relativistic bulk viscosity coefficient. The state equation is in the "phantom" energy sector. ii) For {\\tau}_{{\\Pi}} positive, in the "k-essence" sector. It is performed an exact calculation for the case where the equation of state is constant, finding that option (ii) is favored in r...
An alternative approach to calculate the posterior probability of GNSS integer ambiguity resolution
Yu, Xianwen; Wang, Jinling; Gao, Wang
2017-03-01
When precise positioning is carried out via GNSS carrier phases, it is important to make use of the property that every ambiguity should be an integer. With the known float solution, any integer vector, which has the same degree of freedom as the ambiguity vector, is the ambiguity vector in probability. For both integer aperture estimation and integer equivariant estimation, it is of great significance to know the posterior probabilities. However, to calculate the posterior probability, we have to face the thorny problem that the equation involves an infinite number of integer vectors. In this paper, using the float solution of ambiguity and its variance matrix, a new approach to rapidly and accurately calculate the posterior probability is proposed. The proposed approach consists of four steps. First, the ambiguity vector is transformed via decorrelation. Second, the range of the adopted integer of every component is directly obtained via formulas, and a finite number of integer vectors are obtained via combination. Third, using the integer vectors, the principal value of posterior probability and the correction factor are worked out. Finally, the posterior probability of every integer vector and its error upper bound can be obtained. In the paper, the detailed process to calculate the posterior probability and the derivations of the formulas are presented. The theory and numerical examples indicate that the proposed approach has the advantages of small amount of computations, high calculation accuracy and strong adaptability.
An alternative approach to calculate the posterior probability of GNSS integer ambiguity resolution
Yu, Xianwen; Wang, Jinling; Gao, Wang
2016-10-01
When precise positioning is carried out via GNSS carrier phases, it is important to make use of the property that every ambiguity should be an integer. With the known float solution, any integer vector, which has the same degree of freedom as the ambiguity vector, is the ambiguity vector in probability. For both integer aperture estimation and integer equivariant estimation, it is of great significance to know the posterior probabilities. However, to calculate the posterior probability, we have to face the thorny problem that the equation involves an infinite number of integer vectors. In this paper, using the float solution of ambiguity and its variance matrix, a new approach to rapidly and accurately calculate the posterior probability is proposed. The proposed approach consists of four steps. First, the ambiguity vector is transformed via decorrelation. Second, the range of the adopted integer of every component is directly obtained via formulas, and a finite number of integer vectors are obtained via combination. Third, using the integer vectors, the principal value of posterior probability and the correction factor are worked out. Finally, the posterior probability of every integer vector and its error upper bound can be obtained. In the paper, the detailed process to calculate the posterior probability and the derivations of the formulas are presented. The theory and numerical examples indicate that the proposed approach has the advantages of small amount of computations, high calculation accuracy and strong adaptability.
Exact Discrete Analogs of Derivatives of Integer Orders: Differences as Infinite Series
Directory of Open Access Journals (Sweden)
Vasily E. Tarasov
2015-01-01
Full Text Available New differences of integer orders, which are connected with derivatives of integer orders not approximately, are proposed. These differences are represented by infinite series. A characteristic property of the suggested differences is that its Fourier series transforms have a power-law form. We demonstrate that the proposed differences of integer orders n are directly connected with the derivatives ∂n/∂xn. In contrast to the usual finite differences of integer orders, the suggested differences give the usual derivatives without approximation.
A Characterization of Generalized Monotone Normed Cones
Institute of Scientific and Technical Information of China (English)
S.ROMAGUERA; E.A.S(A)NCHEZ-P(E)REZ; O.VALERO
2007-01-01
Let C be a cone and consider a quasi-norm p defined on it. We study the structure of the couple (C, p) as a topological space in the case where the function p is also monotone. We characterize when the topology of a quasi-normed cone can be defined by means of a monotone norm. We also define and study the dual cone of a monotone normed cone and the monotone quotient of a general cone.We provide a decomposition theorem which allows us to write a cone as a direct sum of a monotone subcone that is isomorphic to the monotone quotient and other particular subcone.
Shatter cones at sierra madera, Texas.
Howard, K A; Offield, T W
1968-10-11
Shatter cones abound in the central uplift of Sierra Madera and they occur as far as 6.5 kilometers from the center. Apical angles average near 90 degrees. Whole cones and full cones represented by diversely oriented cone segments in any structural block show relatively uniform orientations of axes and a dominant direction of point. The cones predate faulting and folding in the central uplift, and, when beds are restored to horizontal, most cones point inward and upward, a pattern that supports the hypothesis of an impact origin.
Self-similar singular solution of doubly singular parabolic equation with gradient absorption term
Directory of Open Access Journals (Sweden)
2006-01-01
Full Text Available We deal with the self-similar singular solution of doubly singular parabolic equation with a gradient absorption term u t = div ( | ∇ u m | p − 2 ∇ u m − | ∇ u | q for 1$"> p > 1 , 1$"> m ( p − 1 > 1 and 1$"> q > 1 in ℝ n × ( 0 , ∞ . By shooting and phase plane methods, we prove that when {1+n}/({1+mn}q+{mn}/({mn+1}$"> p > 1 + n / ( 1 + m n q + m n / ( m n + 1 there exists self-similar singular solution, while p ≤ n + 1 / ( 1 + m n q + m n / ( m n + 1 there is no any self-similar singular solution. In case of existence, the self-similar singular solution is the self-similar very singular solutions which have compact support. Moreover, the interface relation is obtained.
Curvature singularities and abstract boundary singularity theorems for space-time
Ashley, M J S L; Ashley, Michael J. S. L.; Scott, Susan M.
2003-01-01
The abstract boundary construction of Scott and Szekeres is a general and flexible way to define singularities in General Relativity. The abstract boundary construction also proves of great utility when applied to questions about more general boundary features of space-time. Within this construction an essential singularity is a non-regular boundary point which is accessible by a curve of interest (e.g. a geodesic) within finite (affine) parameter distance and is not removable. Ashley and Scott proved the first theorem linking abstract boundary essential singularities with the notion of causal geodesic incompleteness for strongly causal, maximally extended space-times. The relationship between this result and the classical singularity theorems of Penrose and Hawking has enabled us to obtain abstract boundary singularity theorems. This paper describes essential singularity results for maximally extended space-times and presents our recent efforts to establish a relationship between the strong curvature singula...
Interaction Dynamics of Singular Wave Fronts
Holm, Darryl D
2013-01-01
Some of the most impressive singular wave fronts seen in Nature are the transbasin oceanic internal waves, which may be observed from the Space Shuttle as they propagate and interact with each other, for example, in the South China Sea. The characteristic feature of these strongly nonlinear wavefronts is that they reconnect when two of them collide transversely. We derive the EPDiff equation, and use it to model this phenomenon as elastic collisions between singular wave fronts (solitons) whose momentum is distributed along curves moving in the plane. Numerical methods for EPDiff based on compatible differencing algorithms (CDAs) are used for simulating these collisions among curves. The numerical results show the same nonlinear behavior of wavefront reconnections as that observed for internal waves in the South China Sea. We generalize the singular solutions of EPDiff for other applications, in computational anatomy and in imaging science, where the singular wavefronts are evolving image outlines, whose mome...
Topological Signals of Singularities in Ricci Flow
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Paul M. Alsing
2017-08-01
Full Text Available We implement methods from computational homology to obtain a topological signal of singularity formation in a selection of geometries evolved numerically by Ricci flow. Our approach, based on persistent homology, produces precise, quantitative measures describing the behavior of an entire collection of data across a discrete sample of times. We analyze the topological signals of geometric criticality obtained numerically from the application of persistent homology to models manifesting singularities under Ricci flow. The results we obtain for these numerical models suggest that the topological signals distinguish global singularity formation (collapse to a round point from local singularity formation (neckpinch. Finally, we discuss the interpretation and implication of these results and future applications.
Dark matter annihilation near a naked singularity
Patil, Mandar
2011-01-01
We investigate here the dark matter annihilation near a Kerr naked singularity. We show that when dark matter particles collide and annihilate in vicinity of the singularity, the escape fraction to infinity of particles produced is much larger, at least 10^2 - 10^3 times the corresponding black hole values. As high energy collisions are generically possible near a naked singularity, this provides an excellent environment for efficient conversion of dark matter into ordinary standard model particles. If the center of galaxy harbored such a naked singularity, it follows that the observed emergent flux of particles with energy comparable to mass of the dark matter particles is much larger compared to the blackhole case, thus providing an intriguing observational test on the nature of the galactic center
Resonance Van Hove Singularities in Wave Kinetics
Shi, Yi-Kang
2015-01-01
Wave kinetic theory has been developed to describe the statistical dynamics of weakly nonlinear, dispersive waves. However, we show that systems which are generally dispersive can have resonant sets of wave modes with identical group velocities, leading to a local breakdown of dispersivity. This shows up as a geometric singularity of the resonant manifold and possibly as an infinite phase measure in the collision integral. Such singularities occur widely for classical wave systems, including acoustical waves, Rossby waves, helical waves in rotating fluids, light waves in nonlinear optics and also in quantum transport, e.g. kinetics of electron-hole excitations (matter waves) in graphene. These singularities are the exact analogue of the critical points found by Van Hove in 1953 for phonon dispersion relations in crystals. The importance of these singularities in wave kinetics depends on the dimension of phase space $D=(N-2)d$ ($d$ physical space dimension, $N$ the number of waves in resonance) and the degree ...
NEW RESULTS ON ESTIMATES FOR SINGULAR VALUES
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
New results are provided to estimate matrix singular values in terms of partial absolute deleted row sums and column sums. Illustrative examples are presented to show comparisons with results in literature.
Classically stable non-singular cosmological bounces
Ijjas, Anna
2016-01-01
One of the fundamental questions of theoretical cosmology is whether the universe can undergo a non-singular bounce, i.e., smoothly transit from a period of contraction to a period of expansion through violation of the null energy condition (NEC) at energies well below the Planck scale and at finite values of the scale factor such that the entire evolution remains classical. A common claim has been that a non-singular bounce either leads to ghost or gradient instabilities or a cosmological singularity. In this letter, we examine cubic Galileon theories and present a procedure for explicitly constructing examples of a non-singular cosmological bounce without encountering any pathologies and maintaining a sub-luminal sound speed for co-moving curvature modes throughout the NEC violating phase. We also discuss the relation between our procedure and earlier work.
A reinterpretation of the Taub singularity
Jensen, Bjorn; Kučera, Jaromír
1994-01-01
We reinterpret the well known Taub-singularity in terms of a cylinder symmetric geometry. It is shown that a cylindrical analog to the Einstein-Rosen bridge as well as a cosmic string will be present in the geometry.
Hybrid singular systems of differential equations
Institute of Scientific and Technical Information of China (English)
殷刚; 张纪峰
2002-01-01
This work develops hybrid models for large-scale singular differential system and analyzestheir asymptotic properties. To take into consideration the discrete shifts in regime across whichthe behavior of the corresponding dynamic systems is markedly different, our goals are to develophybrid systems in which continuous dynamics are intertwined with discrete events under random-jumpdisturbances and to reduce complexity of large-scale singular systems via singularly perturbed Markovchains. To reduce the complexity of large-scale hybrid singular systems, two-time scale is used in theformulation. Under general assumptions, limit behavior of the underlying system is examined. Usingweak convergence methods, it is shown that the systems can be approximated by limit systems inwhich the coefficients are averaged out with respect to the quasi-stationary distributions. Since thelimit systems have fewer states, the complexity is much reduced.
Algunas aclaraciones acerca del conocimiento del singular.
Directory of Open Access Journals (Sweden)
Carlos Llano Cifuentes
2013-11-01
Full Text Available Llano tries to explain the main purpose of El Conocimiento del Singular, showing how the individuals about which the book is concerned are basically human individuals: people as decision makers.
Tidal Forces in Naked Singularity Backgrounds
Goel, Akash; Roy, Pratim; Sarkar, Tapobrata
2015-01-01
The end stage of a gravitational collapse process can generically result in a black hole or a naked singularity. Here we undertake a comparative analysis of the nature of tidal forces in these backgrounds. The effect of such forces is generically exemplified by the Roche limit, which predicts the distance within which a celestial object disintegrates due to the tidal effects of a second more massive object. In this paper, using Fermi normal coordinates, we numerically compute the Roche limit for a class of non-rotating naked singularity backgrounds, and compare them with known results for Schwarzschild black holes. Our analysis indicates that there might be substantially large deviations in the magnitudes of tidal forces in naked singularity backgrounds, compared to the black hole cases. If observationally established, these can prove to be an effective indicator of the nature of the singularity at a galactic centre.
Stable computation of generalized singular values
Energy Technology Data Exchange (ETDEWEB)
Drmac, Z.; Jessup, E.R. [Univ. of Colorado, Boulder, CO (United States)
1996-12-31
We study floating-point computation of the generalized singular value decomposition (GSVD) of a general matrix pair (A, B), where A and B are real matrices with the same numbers of columns. The GSVD is a powerful analytical and computational tool. For instance, the GSVD is an implicit way to solve the generalized symmetric eigenvalue problem Kx = {lambda}Mx, where K = A{sup {tau}}A and M = B{sup {tau}}B. Our goal is to develop stable numerical algorithms for the GSVD that are capable of computing the singular value approximations with the high relative accuracy that the perturbation theory says is possible. We assume that the singular values are well-determined by the data, i.e., that small relative perturbations {delta}A and {delta}B (pointwise rounding errors, for example) cause in each singular value {sigma} of (A, B) only a small relative perturbation {vert_bar}{delta}{sigma}{vert_bar}/{sigma}.
Constraints on Singular Evolution from Gravitational Baryogenesis
Oikonomou, V K
2015-01-01
We investigate how the gravitational baryogenesis mechanism can potentially constrain the form of a Type IV singularity. Specifically, we study two different models with interesting phenomenology, that realize two distinct Type IV singularities, one occurring at the end of inflation and one during the radiation domination era or during the matter domination era. As we demonstrate, the Type IV singularities occurring at the matter domination era or during the radiation domination era, are constrained by the gravitational baryogenesis, in such a way so that these do not render the baryon to entropy ratio singular. Both the cosmological models we study cannot be realized in the context of ordinary Einstein-Hilbert gravity, and hence our work can only be realized in the context of $F(R)$ gravity and more generally in the context of modified gravity only.
SINGULAR INTEGRAL EQUATIONS ALONG AN OPEN ARC WITH SOLUTIONS HAVING SINGULARITIES OF HIGHER ORDER
Institute of Scientific and Technical Information of China (English)
Zhong Shouguo
2005-01-01
In this paper, the difficulties on calculation in solving singular integral equations are overcome when the restriction of curve of integration to be a closed contour is cancelled. When the curve is an open arc and the solutions for singular integral equations possess singularities of higher order, the solution and the solvable condition for characteristic equations as well as the generalized Noether theorem for complete equations are given.
Directory of Open Access Journals (Sweden)
Li Yuanlu
2015-06-01
Full Text Available Non–integer order differentiation is changing application of traditional differentiation because it can achieve a continuous interpolation of the integer order differentiation. However, implementation of the non–integer order differentiation is much more complex than that of integer order differentiation. For this purpose, a Haar wavelet-based implementation method of non–integer order differentiation is proposed. The basic idea of the proposed method is to use the operational matrix to compute the non–integer order differentiation of a signal through expanding the signal by the Haar wavelets and constructing Haar wavelet operational matrix of the non–integer order differentiation. The effectiveness of the proposed method was verified by comparison of theoretical results and those obtained by another non–integer order differential filtering method. Finally, non–integer order differentiation was applied to enhance signal.
Singularities in universes with negative cosmological constant
Energy Technology Data Exchange (ETDEWEB)
Tipler, F.J.
1976-10-01
It is well known that many universes with negative cosmological constant contain singularities. We shall generalize this result by proving that all closed universes with negative cosmological constant are both future and past timelike geodesically incomplete if the strong energy condition holds. No global causality conditions or restrictions on the initial data are used in the proof. Furthermore, we shall show that all open universes with a Cauchy surface and a negative cosmological constant are singular if the strong energy condition holds. (AIP)
Noncommutative Black Holes and the Singularity Problem
Energy Technology Data Exchange (ETDEWEB)
Bastos, C; Bertolami, O [Instituto de Plasmas e Fusao Nuclear, Instituto Superior Tecnico, Avenida Rovisco Pais 1, 1049-001 Lisboa (Portugal); Dias, N C; Prata, J N, E-mail: cbastos@fisica.ist.utl.pt, E-mail: orfeu.bertolami@fc.up.pt, E-mail: ncdias@mail.telepac.pt, E-mail: joao.prata@mail.telepac.pt [Departamento de Matematica, Universidade Lusofona de Humanidades e Tecnologias, Avenida Campo Grande, 376, 1749-024 Lisboa (Portugal)
2011-09-22
A phase-space noncommutativity in the context of a Kantowski-Sachs cosmological model is considered to study the interior of a Schwarzschild black hole. Due to the divergence of the probability of finding the black hole at the singularity from a canonical noncommutativity, one considers a non-canonical noncommutativity. It is shown that this more involved type of noncommutativity removes the problem of the singularity in a Schwarzschild black hole.
Asymptotic expansions of the error for hyper-singular integrals with an interval variable
Directory of Open Access Journals (Sweden)
Chong Chen
2016-01-01
Full Text Available Abstract In this paper, we present high accuracy quadrature formulas for hyper-singular integrals ∫ a b g ( x q α ( x , t d x $\\int_{a}^{b}g(xq^{\\alpha}(x,t\\, dx$ , where q ( x , t = | x − t | $q(x,t=|x-t|$ (or x − t $x-t$ , t ∈ ( a , b $t\\in(a,b$ , and α ≤ − 1 $\\alpha\\leq-1$ (or α < − 1 $\\alpha<-1$ . If g ( x $g(x$ is 2 m + 1 $2m+1$ times differentiable on [ a , b ] $[a,b]$ , the asymptotic expansions of the error show that the convergence order is O ( h 2 μ + 1 + α $O(h^{2\\mu+1+\\alpha}$ with q ( x , t = | x − t | $q(x,t=|x-t|$ (or x − t $x-t$ for α ≤ − 1 $\\alpha\\leq-1$ (or α < − 1 $\\alpha<-1$ and α being non-integer, and the error power is O ( h η $O(h^{\\eta}$ with q ( x , t = x − t $q(x,t=x-t$ for α being integers less than −1, where η = min ( 2 μ , 2 μ + 2 + α $\\eta =\\min(2\\mu,2\\mu+2+\\alpha$ and μ = 1 , … , m $\\mu=1,\\ldots,m$ . Since the derivatives of the density function g ( x $g(x$ in the quadrature formulas can be eliminated by means of the extrapolation method, the formulas can easily be applied to solving corresponding hyper-singular boundary integral equations. The reliability and efficiency of the proposed formulas in this paper are demonstrated by some numerical examples.
Quantum Field-Theory in Non-Integer Dimensions.
Eyink, Gregory Lawrence
In a 1973 paper entitled "Quantum Field-Theory Models in Less Than 4 Dimensions," Kenneth G. Wilson studied field-theories for spacetime dimension d between 2 and 4. With unconventional renormalizations, these models were found to have non-Gaussian ultraviolet renormalization group fixed points. Wilson's method was perturbative "dimensional regularization": the Feynman-graph integrals were analytically continued to non-integer d. His work left open the question of the nonperturbative existence of the models. Since that landmark paper, Yuval Gefen, Amnon Aharony and Benoit B. Mandelbrot have shown that Ising spin models on fractal lattices have critical properties like those predicted for non-integer dimensions by the analytic continuation, or "varepsilon-expansion," method. Our work shows that fractal lattices and continua provide also a nonperturbative definition of field-theories in non-integer dimensions. The fractal point-sets employed are the Sierpinski carpets and their higher-dimensional generalizations. This class of point-sets has a tunable dimension which allows the approach to four from below. Furthermore, the carpets have discrete groups of scale or dilation invariances and infinite order of ramification. A class of scalar field models are defined on these sets which should reduce to the standard models when dnearrow4. The propagator for these models is given by a proper-time or heat-kernel representation. For this propagator, reflection -positivity is established, a general scaling law is conjectured (and established in a special case), and the perturbative renormalizability shown to be governed by the spectral dimensionality. Scalar models with another choice of propagator, the hierarchical propagator, are studied by rigorous renormalization -group methods. Both massless and massive solutions with non-Gaussian ultraviolet fixed points are mathematically constructed. The definition of higher-spin fields, gauge and fermion fields, on fractal spacetimes
Dynamic Singularity Spectrum Distribution of Sea Clutter
Xiong, Gang; Yu, Wenxian; Zhang, Shuning
2015-12-01
The fractal and multifractal theory have provided new approaches for radar signal processing and target-detecting under the background of ocean. However, the related research mainly focuses on fractal dimension or multifractal spectrum (MFS) of sea clutter. In this paper, a new dynamic singularity analysis method of sea clutter using MFS distribution is developed, based on moving detrending analysis (DMA-MFSD). Theoretically, we introduce the time information by using cyclic auto-correlation of sea clutter. For transient correlation series, the instantaneous singularity spectrum based on multifractal detrending moving analysis (MF-DMA) algorithm is calculated, and the dynamic singularity spectrum distribution of sea clutter is acquired. In addition, we analyze the time-varying singularity exponent ranges and maximum position function in DMA-MFSD of sea clutter. For the real sea clutter data, we analyze the dynamic singularity spectrum distribution of real sea clutter in level III sea state, and conclude that the radar sea clutter has the non-stationary and time-varying scale characteristic and represents the time-varying singularity spectrum distribution based on the proposed DMA-MFSD method. The DMA-MFSD will also provide reference for nonlinear dynamics and multifractal signal processing.
Observational constraints on cosmological future singularities
Energy Technology Data Exchange (ETDEWEB)
Beltran Jimenez, Jose [Aix Marseille Univ, Universite de Toulon CNRS, CPT, Marseille (France); Lazkoz, Ruth [Euskal Herriko Unibertsitatea, Fisika Teorikoaren eta Zientziaren Historia Saila, Zientzia eta Teknologia Fakultatea, Bilbao (Spain); Saez-Gomez, Diego [Faculdade de Ciencias da Universidade de Lisboa, Departamento de Fisica, Instituto de Astrofisica e Ciencias do Espaco, Lisbon (Portugal); Salzano, Vincenzo [University of Szczecin, Institute of Physics, Szczecin (Poland)
2016-11-15
In this work we consider a family of cosmological models featuring future singularities. This type of cosmological evolution is typical of dark energy models with an equation of state violating some of the standard energy conditions (e.g. the null energy condition). Such a kind of behavior, widely studied in the literature, may arise in cosmologies with phantom fields, theories of modified gravity or models with interacting dark matter/dark energy. We briefly review the physical consequences of these cosmological evolution regarding geodesic completeness and the divergence of tidal forces in order to emphasize under which circumstances the singularities in some cosmological quantities correspond to actual singular spacetimes. We then introduce several phenomenological parameterizations of the Hubble expansion rate to model different singularities existing in the literature and use SN Ia, BAO and H(z) data to constrain how far in the future the singularity needs to be (under some reasonable assumptions on the behavior of the Hubble factor). We show that, for our family of parameterizations, the lower bound for the singularity time cannot be smaller than about 1.2 times the age of the universe, what roughly speaking means ∝2.8 Gyrs from the present time. (orig.)
Hitchin Equation, Irregular Singularity, and $N=2$ Asymptotical Free Theories
Nanopoulos, Dimitri
2010-01-01
In this paper, we study irregular singular solution to Hitchin's equation and use it to describe four dimensional $N=2$ asymptotically free gauge theories. For $SU(2)$ $A$ type quiver, two kinds of irregular singularities besides one regular singularity are needed for the solution of Hitchin's equation; We then classify irregular singularities needed for the general $SU(N)$ $A$ type quiver.
Minimal solution of singular LR fuzzy linear systems.
Nikuie, M; Ahmad, M Z
2014-01-01
In this paper, the singular LR fuzzy linear system is introduced. Such systems are divided into two parts: singular consistent LR fuzzy linear systems and singular inconsistent LR fuzzy linear systems. The capability of the generalized inverses such as Drazin inverse, pseudoinverse, and {1}-inverse in finding minimal solution of singular consistent LR fuzzy linear systems is investigated.
Design of switched controllers for discrete singular bilinear systems
Institute of Scientific and Technical Information of China (English)
Xiuhua ZHANG; Qingling ZHANG
2007-01-01
In this paper, switched controllers are designed for a class of nonlinear discrete singular systems and a class of discrete singular bilinear systems. An invariant principle is presented for such switched nonlinear singular systems.The invariant principle and the switched controllers are used to globally stabilize a class of singular bilinear systems that are not open-loop stable.
What is a Singularity in Geometrized Newtonian Gravitation?
Weatherall, James Owen
2013-01-01
I discuss singular spacetimes in the context of the geometrized formulation of Newtonian gravitation. I argue first that geodesic incompleteness is a natural criterion for when a model of geometrized Newtonian gravitation is singular, and then I show that singularities in this sense arise naturally in classical physics by stating and proving a classical version of the Raychaudhuri-Komar singularity theorem.
Ivkovic, Stefan
2015-01-01
In this thesis we will consider Markov operators on cones . More precisely, we let X equipped with certain norm be a real Banach space, K in X be a closed, normal cone with nonempty interior, e in Int (K) be an order unit. A bounded, linear operator T from X into X is a Markov operator w.r.t. K and e if K is invariant under T and e is fixed by T. We consider then the adjoint of T, T* and homogeneous, discrete time Markov system given by u_k+1 = T*(u_k), k = 0,1,2 where u_0(x) is nonnegative f...
New Integer Programming Formulations of the Generalized Travelling Salesman Problem
Directory of Open Access Journals (Sweden)
P. C. Pop
2007-01-01
Full Text Available The Generalized Travelling Salesman Problem, denoted by GTSP, is a variant of the classical travelling salesman problem (TSP, in which the nodes of an undirected graph are partitioned into node sets (clusters and the salesman has to visit exactly one node from every cluster. In this paper we described six distinct formulations of the GTSP as an integer programming. Apart from the standard formulations all the new formulations that we describe are 'compact' in the sense that the number of constraints and variables is a polynomial function of the number of nodes in the problem. In order to provide compact formulations for the GTSP we used two approaches using auxiliary flow variables beyond the natural binary edge and node variables and the second one by distinguishing between global and local variables. Comparisons of the polytopes corresponding to their linear relaxations are established.
Non-chiral 2d CFT with integer energy levels
Ashrafi, M.; Loran, F.
2016-09-01
The partition function of 2d conformal field theory is a modular invariant function. It is known that the partition function of a holomorphic CFT whose central charge is a multiple of 24 is a polynomial in the Klein function. In this paper, by using the medium temperature expansion we show that every modular invariant partition function can be mapped to a holomorphic partition function whose structure can be determined similarly. We use this map to study partition function of CFTs with half-integer left and right conformal weights. We show that the corresponding left and right central charges are necessarily multiples of 4. Furthermore, the degree of degeneracy of high-energy levels can be uniquely determined in terms of the degeneracy in the low energy states.
Non-chiral 2d CFT with integer energy levels
Ashrafi, M
2016-01-01
The partition function of 2d conformal field theory is a modular invariant function. It is known that the partition function of a holomorphic CFT whose central charge is a multiple of 24 is a polynomial in the Klein function. In this paper, by using the medium temperature expansion we show that every modular invariant partition function can be mapped to a holomorphic partition function whose structure can be determined similarly. We use this map to study partition function of CFTs with half-integer left and right conformal weights. We show that the corresponding left and right central charges are necessarily multiples of 4. Furthermore, the degree of degeneracy of high-energy levels can be uniquely determined in terms of the degeneracy in the low energy states.
Analytical estimation of the correlation dimension of integer lattices
Energy Technology Data Exchange (ETDEWEB)
Lacasa, Lucas, E-mail: l.lacasa@qmul.ac.uk [School of Mathematical Sciences, Queen Mary University of London, Mile End Road, E14NS London (United Kingdom); Gómez-Gardeñes, Jesús, E-mail: gardenes@gmail.com [Institute for Biocomputation and Physics of Complex System (BIFI), Universidad de Zaragoza, Zaragoza (Spain); Departamento de Fisica de la Materia Condensada, Universidad de Zaragoza, Zaragoza (Spain)
2014-12-01
Recently [L. Lacasa and J. Gómez-Gardeñes, Phys. Rev. Lett. 110, 168703 (2013)], a fractal dimension has been proposed to characterize the geometric structure of networks. This measure is an extension to graphs of the so called correlation dimension, originally proposed by Grassberger and Procaccia to describe the geometry of strange attractors in dissipative chaotic systems. The calculation of the correlation dimension of a graph is based on the local information retrieved from a random walker navigating the network. In this contribution, we study such quantity for some limiting synthetic spatial networks and obtain analytical results on agreement with the previously reported numerics. In particular, we show that up to first order, the correlation dimension β of integer lattices ℤ{sup d} coincides with the Haussdorf dimension of their coarsely equivalent Euclidean spaces, β = d.
Integer programming model for optimizing bus timetable using genetic algorithm
Wihartiko, F. D.; Buono, A.; Silalahi, B. P.
2017-01-01
Bus timetable gave an information for passengers to ensure the availability of bus services. Timetable optimal condition happened when bus trips frequency could adapt and suit with passenger demand. In the peak time, the number of bus trips would be larger than the off-peak time. If the number of bus trips were more frequent than the optimal condition, it would make a high operating cost for bus operator. Conversely, if the number of trip was less than optimal condition, it would make a bad quality service for passengers. In this paper, the bus timetabling problem would be solved by integer programming model with modified genetic algorithm. Modification was placed in the chromosomes design, initial population recovery technique, chromosomes reconstruction and chromosomes extermination on specific generation. The result of this model gave the optimal solution with accuracy 99.1%.
Parallel Matrix Implementation of an Integer Division Algorithm Using FPGA
Directory of Open Access Journals (Sweden)
Eshwararao. Boddepalli
2011-12-01
Full Text Available This paper presents a method for fast, parallel matrix implementation of an integer division algorithm inside FPGA that can be used for real-time control systems. An essential improvement over the known matrix structure was made, with all the matrix lines having the same width which leads to equal and reduced propagation time. The alignment was also improved by reducing one algorithm step and eliminating one matrix line. Both fully combinational and pipelined versions of the algorithm were designed and tested until a functional physical implementation was obtained, including a user interface. The paper also presents new way to implement hardware structures inside programmable circuits, using portable schematic design from “Altium Designer” software environment instead textual description with HDL languages
Three-Dimensional Image Compression With Integer Wavelet Transforms
Bilgin, Ali; Zweig, George; Marcellin, Michael W.
2000-04-01
A three-dimensional (3-D) image-compression algorithm based on integer wavelet transforms and zerotree coding is presented. The embedded coding of zerotrees of wavelet coefficients (EZW) algorithm is extended to three dimensions, and context-based adaptive arithmetic coding is used to improve its performance. The resultant algorithm, 3-D CB-EZW, efficiently encodes 3-D image data by the exploitation of the dependencies in all dimensions, while enabling lossy and lossless decompression from the same bit stream. Compared with the best available two-dimensional lossless compression techniques, the 3-D CB-EZW algorithm produced averages of 22%, 25%, and 20% decreases in compressed file sizes for computed tomography, magnetic resonance, and Airborne Visible Infrared Imaging Spectrometer images, respectively. The progressive performance of the algorithm is also compared with other lossy progressive-coding algorithms.
An Optimal Decision Procedure for MPNL over the Integers
Directory of Open Access Journals (Sweden)
Davide Bresolin
2011-06-01
Full Text Available Interval temporal logics provide a natural framework for qualitative and quantitative temporal reason- ing over interval structures, where the truth of formulae is defined over intervals rather than points. In this paper, we study the complexity of the satisfiability problem for Metric Propositional Neigh- borhood Logic (MPNL. MPNL features two modalities to access intervals "to the left" and "to the right" of the current one, respectively, plus an infinite set of length constraints. MPNL, interpreted over the naturals, has been recently shown to be decidable by a doubly exponential procedure. We improve such a result by proving that MPNL is actually EXPSPACE-complete (even when length constraints are encoded in binary, when interpreted over finite structures, the naturals, and the in- tegers, by developing an EXPSPACE decision procedure for MPNL over the integers, which can be easily tailored to finite linear orders and the naturals (EXPSPACE-hardness was already known.
Some locally self-interacting walks on the integers
Erschler, Anna; Werner, Wendelin
2010-01-01
We study certain self-interacting walks on the set of integers, that choose to jump to the right or to the left randomly but influenced by the number of times they have previously jumped along the edges in the finite neighbourhood of their current position (in the present paper, typically, we will discuss the case where one considers the neighbouring edges and the next-to-neighbouring edges). We survey a variety of possible behaviours, including some where the walk is eventually confined to an interval of large length. We also focus on certain "asymmetric" drifts, where we prove that with positive probability, the walks behave deterministically on large scale and move like a constant times the square root of time, or like a constant times the logarithm of time.
$\\sigma$-Set Theory and the Integer Space
Araus, Ivan Gatica
2009-01-01
In this article we develop an alternative theory to the ZF Set Theory called $\\sigma$-Set Theory. The goal of this theory is to build the Integer Space $3^{X}$, that will be the algebraic completion of the Power Set $2^{X}$, i.e., $3^{X}$ contains the inverse element for the union, that in this case we call fusion. We first give an introduction where we explain in a more detailed way the motivations and the objectives of this new theory. Later we present the language of the theory that will be the same as that of the Set Theory. Finally, we present the axioms of the $\\sigma$-Set Theory and their individual analysis.
Developing optimal nurses work schedule using integer programming
Shahidin, Ainon Mardhiyah; Said, Mohd Syazwan Md; Said, Noor Hizwan Mohamad; Sazali, Noor Izatie Amaliena
2017-08-01
Time management is the art of arranging, organizing and scheduling one's time for the purpose of generating more effective work and productivity. Scheduling is the process of deciding how to commit resources between varieties of possible tasks. Thus, it is crucial for every organization to have a good work schedule for their staffs. The job of Ward nurses at hospitals runs for 24 hours every day. Therefore, nurses will be working using shift scheduling. This study is aimed to solve the nurse scheduling problem at an emergency ward of a private hospital. A 7-day work schedule for 7 consecutive weeks satisfying all the constraints set by the hospital will be developed using Integer Programming. The work schedule for the nurses obtained gives an optimal solution where all the constraints are being satisfied successfully.
Designing Networks: A Mixed-Integer Linear Optimization Approach
Gounaris, Chrysanthos E; Kevrekidis, Ioannis G; Floudas, Christodoulos A
2015-01-01
Designing networks with specified collective properties is useful in a variety of application areas, enabling the study of how given properties affect the behavior of network models, the downscaling of empirical networks to workable sizes, and the analysis of network evolution. Despite the importance of the task, there currently exists a gap in our ability to systematically generate networks that adhere to theoretical guarantees for the given property specifications. In this paper, we propose the use of Mixed-Integer Linear Optimization modeling and solution methodologies to address this Network Generation Problem. We present a number of useful modeling techniques and apply them to mathematically express and constrain network properties in the context of an optimization formulation. We then develop complete formulations for the generation of networks that attain specified levels of connectivity, spread, assortativity and robustness, and we illustrate these via a number of computational case studies.
Self-Avoiding Random Dynamics on Integer Complex Systems
Hamze, Firas; de Freitas, Nando
2011-01-01
This paper introduces a new specialized algorithm for equilibrium Monte Carlo sampling of binary-valued systems, which allows for large moves in the state space. This is achieved by constructing self-avoiding walks (SAWs) in the state space. As a consequence, many bits are flipped in a single MCMC step. We name the algorithm SARDONICS, an acronym for Self-Avoiding Random Dynamics on Integer Complex Systems. The algorithm has several free parameters, but we show that Bayesian optimization can be used to automatically tune them. SARDONICS performs remarkably well in a broad number of sampling tasks: toroidal ferromagnetic and frustrated Ising models, 3D Ising models, restricted Boltzmann machines and chimera graphs arising in the design of quantum computers.
An Integer Programming Approach to Solving Tantrix on Fixed Boards
Directory of Open Access Journals (Sweden)
Yushi Uno
2012-03-01
Full Text Available Tantrix (Tantrix R ⃝ is a registered trademark of Colour of Strategy Ltd. in New Zealand, and of TANTRIX JAPAN in Japan, respectively, under the license of M. McManaway, the inventor. is a puzzle to make a loop by connecting lines drawn on hexagonal tiles, and the objective of this research is to solve it by a computer. For this purpose, we first give a problem setting of solving Tantrix as making a loop on a given fixed board. We then formulate it as an integer program by describing the rules of Tantrix as its constraints, and solve it by a mathematical programming solver to have a solution. As a result, we establish a formulation that can solve Tantrix of moderate size, and even when the solutions are invalid only by elementary constraints, we achieved it by introducing additional constraints and re-solve it. By this approach we succeeded to solve Tantrix of size up to 60.
Steganography Based on Integer Wavelet Transform and Bicubic Interpolation
Directory of Open Access Journals (Sweden)
N. Ajeeshvali
2012-11-01
Full Text Available Steganography is the art and science of hiding information in unremarkable cover media so as not to observe any suspicion. It is an application under information security field, being classified under information security, Steganography will be characterized by having set of measures that rely on strengths and counter attacks that are caused by weaknesses and vulnerabilities. The aim of this paper is to propose a modified high capacity image steganography technique that depends on integer wavelet transform with acceptable levels of imperceptibility and distortion in the cover image as a medium file and high levels of security. Bicubic interpolation causes overshoot, which increases acutance (apparent sharpness. The Bicubic algorithm is frequently used for scaling images and video for display. The algorithm preserves fine details of the image better than the common bilinear algorithm.
An integer linear programming for a comprehensive reverse supply chain
Directory of Open Access Journals (Sweden)
Hoda Mahmoudi
2014-12-01
Full Text Available Reverse supply chain is a cycle of recovery for the products and materials used by the customers but can be returned to the chain performing some operations. Due to significance of reverse supply chain in the content of environmental and economical aspects, we formulate a mathematical model of reverse multi-layer multi-product supply chain for minimizing the total costs including returning, disassembly, processing, recycling, remanufacturing, and distribution centers. The presented model is an integer linear programming model being solved using Lingo 9 software. Numerical experiments are conducted to gain insight into the proposed model. The solutions provide a decision aid stream strengthening the concept of reverse supply network design and analysis for profit-making organization.
The transport mechanism of the integer quantum Hall effect
LiMing, W
2016-01-01
The integer quantum Hall effect is analysed using a transport mechanism with a semi-classic wave packages of electrons in this paper. A strong magnetic field perpendicular to a slab separates the electron current into two branches with opposite wave vectors $({\\it k})$ and locating at the two edges of the slab, respectively, along the current. In this case back scattering of electrons ($k\\rightarrow -k$) is prohibited by the separation of electron currents. Thus the slab exhibits zero longitudinal resistance and plateaus of Hall resistance. When the Fermi level is scanning over a Landau level when the magnetic field increases, however, the electron waves locate around the central axis of the slab and overlap each other thus back scattering of electrons takes place frequently. Then longitudinal resistance appears and the Hall resistance goes up from one plateau to a new plateau.
Two Shatter-Coned NWA Meteorites
McHone, J. F.; Shoemaker, C.; Killgore, M.; Killgore, K.
2012-03-01
Shatter cones are found in target rocks at more than 70 terrestrial impact sites and are regarded as reliable field criteria for meteoroid impact events. Shatter cones are now seen in chondritic meteorites and indicate early collision events.
Distributing Earthquakes Among California's Faults: A Binary Integer Programming Approach
Geist, E. L.; Parsons, T.
2016-12-01
Statement of the problem is simple: given regional seismicity specified by a Gutenber-Richter (G-R) relation, how are earthquakes distributed to match observed fault-slip rates? The objective is to determine the magnitude-frequency relation on individual faults. The California statewide G-R b-value and a-value are estimated from historical seismicity, with the a-value accounting for off-fault seismicity. UCERF3 consensus slip rates are used, based on geologic and geodetic data and include estimates of coupling coefficients. The binary integer programming (BIP) problem is set up such that each earthquake from a synthetic catalog spanning millennia can occur at any location along any fault. The decision vector, therefore, consists of binary variables, with values equal to one indicating the location of each earthquake that results in an optimal match of slip rates, in an L1-norm sense. Rupture area and slip associated with each earthquake are determined from a magnitude-area scaling relation. Uncertainty bounds on the UCERF3 slip rates provide explicit minimum and maximum constraints to the BIP model, with the former more important to feasibility of the problem. There is a maximum magnitude limit associated with each fault, based on fault length, providing an implicit constraint. Solution of integer programming problems with a large number of variables (>105 in this study) has been possible only since the late 1990s. In addition to the classic branch-and-bound technique used for these problems, several other algorithms have been recently developed, including pre-solving, sifting, cutting planes, heuristics, and parallelization. An optimal solution is obtained using a state-of-the-art BIP solver for M≥6 earthquakes and California's faults with slip-rates > 1 mm/yr. Preliminary results indicate a surprising diversity of on-fault magnitude-frequency relations throughout the state.
Mixed Integer Programming and Heuristic Scheduling for Space Communication
Lee, Charles H.; Cheung, Kar-Ming
2013-01-01
Optimal planning and scheduling for a communication network was created where the nodes within the network are communicating at the highest possible rates while meeting the mission requirements and operational constraints. The planning and scheduling problem was formulated in the framework of Mixed Integer Programming (MIP) to introduce a special penalty function to convert the MIP problem into a continuous optimization problem, and to solve the constrained optimization problem using heuristic optimization. The communication network consists of space and ground assets with the link dynamics between any two assets varying with respect to time, distance, and telecom configurations. One asset could be communicating with another at very high data rates at one time, and at other times, communication is impossible, as the asset could be inaccessible from the network due to planetary occultation. Based on the network's geometric dynamics and link capabilities, the start time, end time, and link configuration of each view period are selected to maximize the communication efficiency within the network. Mathematical formulations for the constrained mixed integer optimization problem were derived, and efficient analytical and numerical techniques were developed to find the optimal solution. By setting up the problem using MIP, the search space for the optimization problem is reduced significantly, thereby speeding up the solution process. The ratio of the dimension of the traditional method over the proposed formulation is approximately an order N (single) to 2*N (arraying), where N is the number of receiving antennas of a node. By introducing a special penalty function, the MIP problem with non-differentiable cost function and nonlinear constraints can be converted into a continuous variable problem, whose solution is possible.
Han, Kyung T.; Rudner, Lawrence M.
2014-01-01
This study uses mixed integer quadratic programming (MIQP) to construct multiple highly equivalent item pools simultaneously, and compares the results from mixed integer programming (MIP). Three different MIP/MIQP models were implemented and evaluated using real CAT item pool data with 23 different content areas and a goal of equal information…
Sabrewing: a lightweight architecture for combined floating-point and integer arithmetic
Bruintjes, Tom M.; Walters, Karel H.G.; Gerez, Sabih H.; Molenkamp, Bert; Smit, Gerard J.M.
2012-01-01
In spite of the fact that floating-point arithmetic is costly in terms of silicon area, the joint design of hardware for floating-point and integer arithmetic is seldom considered. While components like multipliers and adders can potentially be shared, floating-point and integer units in contemporar
Optimized Waterspace Management and Scheduling Using Mixed-Integer Linear Programming
2016-01-01
TECHNICAL REPORT NSWC PCD TR 2015-003 OPTIMIZED WATERSPACE MANAGEMENT AND SCHEDULING USING MIXED-INTEGER LINEAR PROGRAMMING...constraints required for the mathematical formulation of the MCM scheduling problem pertaining to the survey constraints and logistics management . The...Floudas, Nonlinear and Mixed-Integer Optimization: Fundamentals and Applications, Oxford University Press, 1995. [10] M. J. Bays, A. Shende, D. J
On the series of the reciprocals lcm's of sequences of positive integers: A curious interpretation
Farhi, Bakir
2009-01-01
In this paper, we prove the following result: {quote} Let $\\A$ be an infinite set of positive integers. For all positive integer $n$, let $\\tau_n$ denote the smallest element of $\\A$ which does not divide $n$. Then we have
Institute of Scientific and Technical Information of China (English)
Jia Li-Xin; Dai Hao; Hui Meng
2010-01-01
This paper focuses on the synchronisation between fractional-order and integer-order chaotic systems.Based on Lyapunov stability theory and numerical differentiation，a nonlinear feedback controller is obtained to achieve the synchronisation between fractional-order and integer-order chaotic systems.Numerical simulation results are presented to illustrate the effectiveness of this method.
Sabrewing: A lightweight architecture for combined floating-point and integer arithmetic
Bruintjes, Tom; Walters, K.H.G.; Gerez, Sabih H.; Molenkamp, Egbert; Smit, Gerardus Johannes Maria
In spite of the fact that floating-point arithmetic is costly in terms of silicon area, the joint design of hardware for floating-point and integer arithmetic is seldom considered. While components like multipliers and adders can potentially be shared, floating-point and integer units in
Mixed integer (0-1) fractional programming for decision support in paper production industry
Claassen, G.D.H.
2014-01-01
This paper presents an effective and efficient method for solving a special class of mixed integer fractional programming (FP) problems. We take a classical reformulation approach for continuous FP as a starting point and extend it for solving a more general class of mixed integer (0–1) fractional p
Integral-valued polynomials over sets of algebraic integers of bounded degree.
Peruginelli, Giulio
2014-04-01
Let K be a number field of degree n with ring of integers [Formula: see text]. By means of a criterion of Gilmer for polynomially dense subsets of the ring of integers of a number field, we show that, if [Formula: see text] maps every element of [Formula: see text] of degree n to an algebraic integer, then [Formula: see text] is integral-valued over [Formula: see text], that is, [Formula: see text]. A similar property holds if we consider the set of all algebraic integers of degree n and a polynomial [Formula: see text]: if [Formula: see text] is integral over [Formula: see text] for every algebraic integer α of degree n, then [Formula: see text] is integral over [Formula: see text] for every algebraic integer β of degree smaller than n. This second result is established by proving that the integral closure of the ring of polynomials in [Formula: see text] which are integer-valued over the set of matrices [Formula: see text] is equal to the ring of integral-valued polynomials over the set of algebraic integers of degree equal to n.
Cone positioning device for oral radiation therapy.
Mahanna, G K; Ivanhoe, J R; Attanasio, R A
1994-06-01
This article describes the fabrication and modification of a peroral cone-positioning device. The modification provides added cone stability and prevents tongue intrusion into the radiation field. This device provides a repeatable accurate cone/lesion relationship and the fabrication technique is simplified, accurate, and minimizes patient discomfort.
Small Molecules in the Cone Snail Arsenal.
Neves, Jorge L B; Lin, Zhenjian; Imperial, Julita S; Antunes, Agostinho; Vasconcelos, Vitor; Olivera, Baldomero M; Schmidt, Eric W
2015-10-16
Cone snails are renowned for producing peptide-based venom, containing conopeptides and conotoxins, to capture their prey. A novel small-molecule guanine derivative with unprecedented features, genuanine, was isolated from the venom of two cone snail species. Genuanine causes paralysis in mice, indicating that small molecules and not just polypeptides may contribute to the activity of cone snail venom.
Cone selectivity derived from the responses of the retinal cone mosaic to natural scenes.
Wachtler, Thomas; Doi, Eizaburo; Lee, Te- Won; Sejnowski, Terrence J
2007-06-18
To achieve color vision, the brain has to process signals of the cones in the retinal photoreceptor mosaic in a cone-type-specific way. We investigated the possibility that cone-type-specific wiring is an adaptation to the statistics of the cone signals. We analyzed estimates of cone responses to natural scenes and found that there is sufficient information in the higher order statistics of L- and M-cone responses to distinguish between cones of different types, enabling unsupervised learning of cone-type specificity. This was not the case for a fourth cone type with spectral sensitivity between L and M cones, suggesting an explanation for the lack of strong tetrachromacy in heterozygous carriers of color deficiencies.
Resonance Van Hove singularities in wave kinetics
Shi, Yi-Kang; Eyink, Gregory L.
2016-10-01
Wave kinetic theory has been developed to describe the statistical dynamics of weakly nonlinear, dispersive waves. However, we show that systems which are generally dispersive can have resonant sets of wave modes with identical group velocities, leading to a local breakdown of dispersivity. This shows up as a geometric singularity of the resonant manifold and possibly as an infinite phase measure in the collision integral. Such singularities occur widely for classical wave systems, including acoustical waves, Rossby waves, helical waves in rotating fluids, light waves in nonlinear optics and also in quantum transport, e.g. kinetics of electron-hole excitations (matter waves) in graphene. These singularities are the exact analogue of the critical points found by Van Hove in 1953 for phonon dispersion relations in crystals. The importance of these singularities in wave kinetics depends on the dimension of phase space D =(N - 2) d (d physical space dimension, N the number of waves in resonance) and the degree of degeneracy δ of the critical points. Following Van Hove, we show that non-degenerate singularities lead to finite phase measures for D > 2 but produce divergences when D ≤ 2 and possible breakdown of wave kinetics if the collision integral itself becomes too large (or even infinite). Similar divergences and possible breakdown can occur for degenerate singularities, when D - δ ≤ 2, as we find for several physical examples, including electron-hole kinetics in graphene. When the standard kinetic equation breaks down, then one must develop a new singular wave kinetics. We discuss approaches from pioneering 1971 work of Newell & Aucoin on multi-scale perturbation theory for acoustic waves and field-theoretic methods based on exact Schwinger-Dyson integral equations for the wave dynamics.
Kwapiński, Tomasz
2017-03-01
The electron transport properties of a linear atomic chain are studied theoretically within the tight-binding Hamiltonian and the Green’s function method. Variations of the local density of states (DOS) along the chain are investigated. They are crucial in scanning tunnelling experiments and give important insight into the electron transport mechanism and charge distribution inside chains. It is found that depending on the chain parity the local DOS at the Fermi level can form cone-like structures (DOS cones) along the chain. The general condition for the local DOS oscillations is obtained and the linear behaviour of the local density function is confirmed analytically. DOS cones are characterized by a linear decay towards the chain which is in contrast to the propagation properties of charge density waves, end states and Friedel oscillations in one-dimensional systems. We find that DOS cones can appear due to non-resonant electron transport, the spin–orbit scattering or for chains fabricated on a substrate with localized electrons. It is also shown that for imperfect chains (e.g. with a reduced coupling strength between two neighboring sites) a diamond-like structure of the local DOS along the chain appears.
Singular Integral Equations with Cosecant Kernel in Solutions with Singularities of High Order
Institute of Scientific and Technical Information of China (English)
HAN Hui-li; DU Jin-yuan
2005-01-01
We have discussed and solved the boundary value problem with period 2aπ and the singular integral equation with kernel csc t-t0/a in solution having singularities of high order, where the smooth contour of integration is in the strip 0＜Rez＜aπ.
Institute of Scientific and Technical Information of China (English)
Chen Hua; Zhang Zhixiong
2005-01-01
In this paper the authors consider the summability of formal solutions for some first order singular PDEs with irregular singularity. They prove that in this case the formal solutions will be divergent, but except a enumerable directions, the formal solutions are Borel summable.
Hanford waste tank cone penetrometer
Energy Technology Data Exchange (ETDEWEB)
Seda, R.Y.
1995-12-01
A new tool is being developed to characterize tank waste at the Hanford Reservation. This tool, known as the cone penetrometer, is capable of obtaining chemical and physical properties in situ. For the past 50 years, this tool has been used extensively in soil applications and now has been modified for usage in Hanford Underground Storage tanks. These modifications include development of new ``waste`` data models as well as hardware design changes to accommodate the hazardous and radioactive environment of the tanks. The modified cone penetrometer is scheduled to be deployed at Hanford by Fall 1996. At Hanford, the cone penetrometer will be used as an instrumented pipe which measures chemical and physical properties as it pushes through tank waste. Physical data, such as tank waste stratification and mechanical properties, is obtained through three sensors measuring tip pressure, sleeve friction and pore pressure. Chemical data, such as chemical speciation, is measured using a Raman spectroscopy sensor. The sensor package contains other instrumentation as well, including a tip and side temperature sensor, tank bottom detection and an inclinometer. Once the cone penetrometer has reached the bottom of the tank, a moisture probe will be inserted into the pipe. This probe is used to measure waste moisture content, water level, waste surface moisture and tank temperature. This paper discusses the development of this new measurement system. Data from the cone penetrometer will aid in the selection of sampling tools, waste tank retrieval process, and addressing various tank safety issues. This paper will explore various waste models as well as the challenges associated with tank environment.
Singular Value Decomposition of Pinhole SPECT Systems.
Palit, Robin; Kupinski, Matthew A; Barrett, Harrison H; Clarkson, Eric W; Aarsvold, John N; Volokh, Lana; Grobshtein, Yariv
2009-03-12
A single photon emission computed tomography (SPECT) imaging system can be modeled by a linear operator H that maps from object space to detector pixels in image space. The singular vectors and singular-value spectra of H provide useful tools for assessing system performance. The number of voxels used to discretize object space and the number of collection angles and pixels used to measure image space make the matrix dimensions H large. As a result, H must be stored sparsely which renders several conventional singular value decomposition (SVD) methods impractical. We used an iterative power methods SVD algorithm (Lanczos) designed to operate on very large sparsely stored matrices to calculate the singular vectors and singular-value spectra for two small animal pinhole SPECT imaging systems: FastSPECT II and M(3)R. The FastSPECT II system consisted of two rings of eight scintillation cameras each. The resulting dimensions of H were 68921 voxels by 97344 detector pixels. The M(3)R system is a four camera system that was reconfigured to measure image space using a single scintillation camera. The resulting dimensions of H were 50864 voxels by 6241 detector pixels. In this paper we present results of the SVD of each system and discuss calculation of the measurement and null space for each system.
Quantum cosmology and late-time singularities
Kamenshchik, A Yu
2013-01-01
The development of dark energy models has stimulated interest to cosmological singularities, which differ from the traditional Big Bang and Big Crunch singularities. We review a broad class of phenomena connected with soft cosmological singularities in classical and quantum cosmology. We discuss the classification of singularities from the geometrical point of view and from the point of view of the behaviour of finite size objects, crossing such singularities. We discuss in some detail quantum and classical cosmology of models based on perfect fluids (anti-Chaplygin gas and anti-Chaplygin gas plus dust), of models based on the Born-Infeld-type fields and of the model of a scalar field with a potential inversely proportional to the field itself. We dwell also on the phenomenon of the phantom divide line crossing in the scalar field models with cusped potentials. Then we discuss the Friedmann equations modified by quantum corrections to the effective action of the models under considerations and the influence o...
Action spectra of zebrafish cone photoreceptors.
Directory of Open Access Journals (Sweden)
Duco Endeman
Full Text Available Zebrafish is becoming an increasingly popular model in the field of visual neuroscience. Although the absorption spectra of its cone photopigments have been described, the cone action spectra were still unknown. In this study we report the action spectra of the four types of zebrafish cone photoreceptors, determined by measuring voltage responses upon light stimulation using whole cell patch clamp recordings. A generic template of photopigment absorption spectra was fit to the resulting action spectra in order to establish the maximum absorption wavelength, the A2-based photopigment contribution and the size of the β-wave of each cone-type. Although in general there is close correspondence between zebrafish cone action- and absorbance spectra, our data suggest that in the case of MWS- and LWS-cones there is appreciable contribution of A2-based photopigments and that the β-wave for these cones is smaller than expected based on the absorption spectra.
Singularity hypotheses a scientific and philosophical assessment
Moor, James; Søraker, Johnny; Steinhart, Eric
2012-01-01
Singularity Hypotheses: A Scientific and Philosophical Assessment offers authoritative, jargon-free essays and critical commentaries on accelerating technological progress and the notion of technological singularity. It focuses on conjectures about the intelligence explosion, transhumanism, and whole brain emulation. Recent years have seen a plethora of forecasts about the profound, disruptive impact that is likely to result from further progress in these areas. Many commentators however doubt the scientific rigor of these forecasts, rejecting them as speculative and unfounded. We therefore invited prominent computer scientists, physicists, philosophers, biologists, economists and other thinkers to assess the singularity hypotheses. Their contributions go beyond speculation, providing deep insights into the main issues and a balanced picture of the debate.
Naked Singularities as Particle Accelerators II
Patil, Mandar; Malafarina, Daniele
2011-01-01
We generalize here our earlier results on particle acceleration by naked singularities. We showed recently[1] that the naked singularities that form due to gravitational collapse of massive stars provide a suitable environment where particles could get accelerated and collide at arbitrarily high center of mass energies. However, we focussed there only on the spherically symmetric gravitational collapse models, which were also assumed to be self-similar. In this paper, we broaden and generalize the result to all gravitational collapse models leading to the formation of a naked singularity as final state of collapse, evolving from a regular initial data, without making any prior restrictive assumptions about the spacetime symmetries such as above. We show that when the particles interact and collide near the Cauchy horizon, the energy of collision in the center of mass frame will be arbitrarily high, thus offering a window to the Planck scale physics. We also consider the issue of various possible physical mech...
A stringy cloak for a classical singularity
Energy Technology Data Exchange (ETDEWEB)
Dabholkar, Atish [Department of Theoretical Physics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005 (India); Kallosh, Renata [Institute for Theoretical Physics, Department of Physics, Stanford University, Stanford, CA 94305 (United States); Maloney, Alexander [Institute for Theoretical Physics, Department of Physics, Stanford University, Stanford, CA 94305 (United States) and Theory Group, Stanford Linear Accelerator Center, 2575 Sand Hill Rd, Menlo Park, CA 94025 (United States)]. E-mail: maloney@slac.stanford.edu
2004-12-01
We consider a class of 4D supersymmetric black hole solutions, arising from string theory compactifications, which classically have vanishing horizon area and singular space-time geometry. String theory motivates the inclusion of higher derivative terms, which convert these singular classical solutions into regular black holes with finite horizon area. In particular, the supersymmetric attractor equations imply that the central charge, which determines the radius of the AdS{sub 2} x S{sup 2} near horizon geometry, acquires a non-vanishing value due to quantum effects. In this case quantum corrections to the Bekenstein-Hawking relation between entropy and area are large. This is the first explicit example where stringy quantum gravity effects replace a classical null singularity by a black hole with finite horizon area. (author)
EDITORIAL: The plurality of optical singularities
Berry, Michael; Dennis, Mark; Soskin, Marat
2004-05-01
This collection of papers arose from an Advanced Research Workshop on Singular Optics, held at the Bogolyubov Institute in Kiev, Ukraine, during 24-28 June 2003. The workshop was generously financed by NATO, with welcome additional support from Institute of Physics Publishing and the National Academy of Sciences of Ukraine. There had been two previous international meetings devoted to singular optics, in Crimea in 1997 and 2000, reflecting the strong involvement of former Soviet Union countries in this research. Awareness of singular optics is growing within the wider optics community, indicated by symposia on the subject at several general optics meetings. As the papers demonstrate, the field of singular optics has reached maturity. Although the subject originated in an observation on ultrasound, it has been largely theory-driven until recently. Now, however, there is close contact between theory and experiment, and we speculate that this is one reason for its accelerated development. To single out particular papers for mention here would be invidious, and since the papers speak for themselves it is not necessary to describe them all. Instead, we will confine ourselves to a brief description of the main areas included in singular optics, to illustrate the broad scope of the subject. Optical vortices are lines of phase singularity: nodal lines where the intensity of the light, represented by a complex scalar field, vanishes. The subject has emerged from flatland, where the vortices are points characterized by topological charges, into the much richer world of vortex lines in three dimensions. By combining Laguerre-Gauss or Bessel beams, or reflecting light from plates with spiral steps, intricate arrangements can be generated, with vortices that are curved, looped, knotted, linked or braided. With light whose state of polarization varies with position, different singularities occur, associated with the vector nature of light. These are also lines, on which the
Weights on cohomology and invariants of singularities
Arapura, Donu; Włodarczyk, Jarosław
2011-01-01
In this paper, we extract natural invariants of a singularity by using the Deligne weight filtration on the cohomology of an exceptional fibre of a resolution, and also on the intersection cohomology of the link. Our primary goal is to study and give natural bounds on the weights in terms of direct images of differential forms. These bounds can be made explicit for various standard classes such as rational, isolated normal Cohen-Macaulay and toroidal singularities, and lead to strong restrictions on the topology of these singularities. A secondary goal of this paper is to make the weight filtration, and related constructions, more widely accessible. So we have tried to make the presentation somewhat self contained. This is supersedes our earlier preprint arXiv:0902.4234.
Automorphic forms with singularities on Grassmannians
Borcherds, R E
1996-01-01
We construct some families of automorphic forms on Grassmannians which have singularities along smaller sub Grassmannians, using a version of the theta correspondence extended to modular forms with poles at cusps. Some of the applications are as follows. We construct families of holomorphic automorphic forms which can be written as infinite products, which give many new examples of generalized Kac-Moody superalgebras. We extend the Shimura and Maass-Gritsenko correspondences to modular forms with singularities. We prove some congruences satisfied by the theta functions of positive definite lattices, and find a sufficient condition for a Lorentzian lattice to have a reflection group with a finite volume fundamental domain. We give some examples suggesting that these automorphic forms with singularities are related to Donaldson polynomials and to mirror symmetry for K3 surfaces.
Equations of States in Singular Statistical Estimation
Watanabe, Sumio
2007-01-01
Learning machines which have hierarchical structures or hidden variables are singular statistical models because they are nonidentifiable and their Fisher information matrices are singular. In singular statistical models, neither the Bayes a posteriori distribution converges to the normal distribution nor the maximum likelihood estimator satisfies asymptotic normality. This is the main reason why it has been difficult to predict their generalization performances from trained states. In this paper, we study four errors, (1) Bayes generalization error, (2) Bayes training error, (3) Gibbs generalization error, and (4) Gibbs training error, and prove that there are mathematical relations among these errors. The formulas proved in this paper are equations of states in statistical estimation because they hold for any true distribution, any parametric model, and any a priori distribution. Also we show that Bayes and Gibbs generalization errors are estimated by Bayes and Gibbs training errors, and propose widely appl...